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-LyX's detailed Math manual\r
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-by the LyX Team\r
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-\r
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-If you have comments or error corrections, please send them to the LyX Documenta\r
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-author: Uwe Stöhr\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
-\begin_layout Standard\r
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-status collapsed\r
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-\begin_layout Plain Layout\r
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-\backslash\r
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-\r
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-\r
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-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
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-\backslash\r
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-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
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-\r
-\begin_layout Subsection*\r
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-\r
-\begin_layout Standard\r
-Most of the LaTeX-commands for math constructs have the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-commandname[optional\r
-\series default\r
- \r
-\series bold\r
-argument]{required\r
-\series default\r
- \r
-\series bold\r
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-\end_layout\r
-\r
-\begin_layout Standard\r
-A command always starts with a backslash \r
-\begin_inset Quotes gld\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-\r
-\series default\r
-\r
-\begin_inset Quotes grd\r
-\end_inset\r
-\r
-.\r
- To omit optional arguments, also omit the associated brackets.\r
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-\begin_inset Index idx\r
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-\r
-\begin_layout Plain Layout\r
-T@TeX-braces\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- If you add in a formula a left brace to a command name, LyX automatically\r
- creates a TeX-brace.\r
- In all other cases TeX-braces are created in formulas with the command\r
- \r
-\series bold\r
-\r
-\backslash\r
-{\r
-\series default\r
-.\r
- TeX-braces appear red in LyX, in contrary to normal braces which appear\r
- blue.\r
- In TeX-mode no command is needed to get TeX-braces.\r
- TeX-braces don't appear in the output.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When commands without arguments, like commands for symbols are entered in\r
- TeX-mode, a space character must \r
-\emph on\r
-always\r
-\emph default\r
- be behind the command to end it.\r
- This space doesn't appear in the output.\r
- When the space should appear in the output, the space must be followed\r
- by a protected space in normal text.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A protected space is inserted with \r
-\begin_inset Info\r
-type "shortcuts"\r
-arg "command-alternatives space-insert protected ; math-space"\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection*\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-Syntax Explanation\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-The symbol\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-This visible space character can be created with the command \r
-\series bold\r
-\r
-\backslash\r
-textvisiblespace\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! T ! \r
-\backslash\r
-textvisiblespace\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, inserted in TeX-mode.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-denotes a space character to be input.\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-An arrow like \r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
- denotes the usage of the corresponding arrow key on the keyboard.\r
- The \r
-\family sans\r
-Tab\r
-\family default\r
- key can often be used instead of \r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
- and \r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-, and \r
-\family sans\r
-Shift+Tab\r
-\family default\r
- instead of \r
-\begin_inset Formula $\leftarrow$\r
-\end_inset\r
-\r
- and \r
-\begin_inset Formula $\uparrow$\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection*\r
-Available units\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Float table\r
-placement H\r
-wide false\r
-sideways false\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\align center\r
-\begin_inset Caption Standard\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "tab:Available-units"\r
-\r
-\end_inset\r
-\r
-Available units\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Plain Layout\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="13" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Unit\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Name / Description\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-mm\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Millimeter\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-cm\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Centimeter\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-in\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Inch (1\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-in = 2,54\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-cm)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-pt\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Point (72.27\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt = 1\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-in)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-pc\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Pica (1\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pc = 12\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-sp\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-scaled point (65536\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-sp = 1\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-bp\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-big point (72\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-bp = 1\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-in)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-dd\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Didot (1\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-dd \r
-\begin_inset Formula $\approx$\r
-\end_inset\r
-\r
- 0.376\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-cc\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Cicero (1\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-cc = 12\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-dd)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-ex\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Height of letter \r
-\emph on\r
-\r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-x\r
-\emph default\r
-\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- in the current font\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-em\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-width of letter \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-\r
-\emph on\r
-M\r
-\emph default\r
-\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- in the current font\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-mu\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-math unit (1\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mu = \r
-\begin_inset Formula $\nicefrac{1}{18}$\r
-\end_inset\r
-\r
-\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-em)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Basic Functions\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Exponents\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Exponents\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and Indices\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Indices\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Superscripts|see\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Exponents\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Subscripts|see\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Indices\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Indices are created with an underscore \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-_\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- or via the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math-subscript.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-, exponents with a caret \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-^\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- or via the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math-superscript.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-B_V\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $B_{V}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-B^V\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}B^{V}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-B^\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}B^{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-As the caret is in some languages an accent, vowels will be accentuated\r
- in this case and not set as exponents\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Depending on the used keyboard settings this can also happen for characters\r
- other than vowels.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- To get exponents in this case, press \r
-\family sans\r
-Space\r
-\family default\r
- after the caret as in the last example.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Fractions\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Fractions"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Fractions\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Fractions are generated with the command \r
-\series bold\r
-\r
-\backslash\r
-frac\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! F ! \r
-\backslash\r
-frac\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- or via the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/frac.png\r
- scale 50\r
-\r
-\end_inset\r
-\r
-.\r
- The font size is adjusted automatically, depending on whether the fraction\r
- is in an inline or display style formula.\r
- With the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/frac-square.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- you can select different fraction types.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With the command \r
-\series bold\r
-\r
-\backslash\r
-dfrac\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! D ! \r
-\backslash\r
-dfrac\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- a fraction can be created that always has the size of a display style formula.\r
- With \r
-\series bold\r
-\r
-\backslash\r
-tfrac\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! T ! \r
-\backslash\r
-tfrac\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- the fraction appears always with the size of an inline formula.\r
- An example:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A line with the fraction \r
-\begin_inset Formula $\frac{1}{2}$\r
-\end_inset\r
-\r
- that was created with the command \r
-\series bold\r
-\r
-\backslash\r
-frac\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A line with the fraction \r
-\begin_inset Formula $\dfrac{1}{2}$\r
-\end_inset\r
-\r
- that was created with the command \r
-\series bold\r
-\r
-\backslash\r
-dfrac\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-frac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dfrac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dfrac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-e^\r
-\backslash\r
-frac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-1\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-2\r
-\begin_inset Formula $\downarrow\downarrow$\r
-\end_inset\r
-\r
-3\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-For nested fractions the command \r
-\series bold\r
-\r
-\backslash\r
-cfrac\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! C ! \r
-\backslash\r
-cfrac\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- can be used.\r
- Here is an example:\r
-\begin_inset VSpace -3mm\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \r
-\begin{align*}\r
-\textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\\r
-\frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\r
-\end{align*}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command for the example above is:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-cfrac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-B+\r
-\backslash\r
-cfrac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-C+\r
-\backslash\r
-cfrac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-E\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-F\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-D\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-cfrac\r
-\series default\r
- sets the fraction always in the size of a displayed formula, also when\r
- it is part of another fraction.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-It is possible to specify the alignment of the numerator.\r
- The command \r
-\series bold\r
-\r
-\backslash\r
-cfracleft\r
-\series default\r
- is used to left align it, the command \r
-\series bold\r
-\r
-\backslash\r
-cfracright\r
-\series default\r
- to right-align it.\r
- \r
-\series bold\r
-\r
-\backslash\r
-cfrac\r
-\series default\r
- centers the numerator.\r
- These fractions demonstrate the different alignments:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\begin_inset Formula \r
-\[\r
-\cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-Note:\r
-\series default\r
- \r
-\series bold\r
-\r
-\backslash\r
-cfracleft\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-cfracright\r
-\series default\r
- are no real LaTeX commands but represent the command \r
-\series bold\r
-\r
-\backslash\r
-cfrac[alignment]{numerator}{denominator}\r
-\series default\r
- .\r
- Therefore you cannot use them in TeX code.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-It is often advantageous to combine \r
-\series bold\r
-\r
-\backslash\r
-cfrac\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-frac\r
-\series default\r
-:\r
-\begin_inset Formula \r
-\[\r
-\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For inline fractions with a sloped fraction stroke you can use the command\r
- \r
-\series bold\r
-\r
-\backslash\r
-nicefrac\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! N ! \r
-\backslash\r
-nicefrac\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-: \r
-\begin_inset Formula $\nicefrac{5}{31}$\r
-\end_inset\r
-\r
- or \r
-\series bold\r
-\r
-\backslash\r
-unitfrac\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! U ! \r
-\backslash\r
-unitfrac\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-: \r
-\begin_inset Formula $\unitfrac{5}{31}$\r
-\end_inset\r
-\r
- There is furthermore the command \r
-\series bold\r
-\r
-\backslash\r
-unitfracthree\r
-\series default\r
- that offers to write a fraction in combination with a number: \r
-\begin_inset Formula $\unitfrac[2]{1}{3}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-Note:\r
-\series default\r
- \r
-\series bold\r
-\r
-\backslash\r
-unitfracthree\r
-\series default\r
- is not a real LaTeX command but the command\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-unitfrac[number]{numerator}{denominator}\r
-\series default\r
- .\r
- Therefore you cannot use it in TeX code.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-How to define own fractions where the fraction stroke can be changed, is\r
- explained in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Self-defined-Fractions"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Roots\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Roots\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Square roots are created with \r
-\series bold\r
-\r
-\backslash\r
-sqrt\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! S ! \r
-\backslash\r
-sqrt\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- or the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/sqrt.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-, all other roots with the command \r
-\series bold\r
-\r
-\backslash\r
-root\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! R ! \r
-\backslash\r
-root\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- or with the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/root.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="3" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sqrt\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-root\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-3\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-A-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A square root can also be created with \r
-\series bold\r
-\r
-\backslash\r
-root\r
-\series default\r
- when the root index field is left empty.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With certain indices the distance to the root is too small, like in this\r
- formula: \r
-\begin_inset Formula $\sqrt[\beta]{B}$\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-The \r
-\begin_inset Formula $\beta$\r
-\end_inset\r
-\r
- touches the root.\r
- To avoid this, the commands \r
-\series bold\r
-\r
-\backslash\r
-leftroot\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! L ! \r
-\backslash\r
-leftroot\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-uproot\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! U ! \r
-\backslash\r
-uproot\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- are used with the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-leftroot{distance}\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-uproot{distance}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Distance is the number of Big Points (unit bp; \r
-\begin_inset Formula $\mathrm{72\, bp=1\, inch}$\r
-\end_inset\r
-\r
-), that the index should be moved to the left or top, resp..\r
- The commands are written to the index.\r
- This way the command\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-root\r
-\backslash\r
-leftroot{-1\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-uproot{2\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-beta\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-B\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series default\r
-produces a correct typeset formula: \r
-\begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Binomial Coefficients\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Binomial coefficients\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Binomial coefficients are inserted with the command \r
-\series bold\r
-\r
-\backslash\r
-binom\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! B ! \r
-\backslash\r
-binom\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- or with the submenu of the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/frac-square.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
- As with fractions (\r
-\series bold\r
-\r
-\backslash\r
-frac\r
-\series default\r
-) in addition to \r
-\series bold\r
-\r
-\backslash\r
-binom\r
-\series default\r
- there are the commands \r
-\series bold\r
-\r
-\backslash\r
-dbinom\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! D ! \r
-\backslash\r
-dbinom\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-tbinom\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! T ! \r
-\backslash\r
-tbinom\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- For other brackets around binomial coeficients there are the commands \r
-\series bold\r
-\r
-\backslash\r
-brace\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! B ! \r
-\backslash\r
-brace\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-brack\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! B ! \r
-\backslash\r
-brack\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="6" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-binom\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dbinom\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-tbinom\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-brack\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-brace\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Case Differentiations\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Case differentiations \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="3" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-cases\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-B>0\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! C ! \r
-\backslash\r
-cases\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\begin{cases}\r
-A & B>0\end{cases}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-cases\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Info\r
-type "shortcut"\r
-arg "newline-insert newline"\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\begin{cases}\r
-A & \textrm{for }x>0\\\r
-B & \textrm{for }x=0\r
-\end{cases}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-After inserting \r
-\series bold\r
-\r
-\backslash\r
-cases\r
-\series default\r
- or pressing the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/cases.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- you can create new lines with the shortcut \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "newline-insert newline"\r
-\end_inset\r
-\r
- or the table toolbar button \r
-\begin_inset Graphics\r
- filename ../images/tabular-feature_append-row.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command \r
-\series bold\r
-\r
-\backslash\r
-cases\r
-\series default\r
- is also available via the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Cases-Environment\r
-\family default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Negations\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Negations\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-By inserting \r
-\series bold\r
-\r
-\backslash\r
-not\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! N ! \r
-\backslash\r
-not\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- every character can be displayed canceled.\r
- The characters are quasi accentuated by a slash.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-not=\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\not=$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-not \r
-\backslash\r
-le\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\not\le$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-not \r
-\backslash\r
-parallel\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\not\parallel$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The last example shows that not all negations look good.\r
- Therefore there are special commands for some negations (see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Mathematical-Symbols"\r
-\r
-\end_inset\r
-\r
- and \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Relations"\r
-\r
-\end_inset\r
-\r
-).\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Placeholders\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Placeholders"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Placeholders\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Chemical characters ! Isotopes\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Isotopes|see\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Chemical characters\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When displaying e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-isotopes\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Typesetting isotopes and chemical symbols is described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Chemical-Symbols-and"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- the following problem occurs:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="2" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Indices created with sub- and superscripts:\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-correct indices:\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The shorter index is by default placed below or above the first character\r
- of the longer index.\r
- To avoid this there is the command \r
-\series bold\r
-\r
-\backslash\r
-phantom\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! P ! \r
-\backslash\r
-phantom\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- or the math toolbar button\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-can be found in the submenu of the toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/space.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- \r
-\begin_inset Graphics\r
- filename ../images/math/phantom.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- that creates one or more phantom characters.\r
- When inserting \r
-\series bold\r
-\r
-\backslash\r
-phantom\r
-\series default\r
- a small blue box appears that is superposed with two red arrows.\r
- The arrows indicate that the complete width and height of the box content\r
- will be created as placeholder.\r
- Phantom characters are accordingly placeholders with the size of the characters.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-^19\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-_\r
-\backslash\r
-phantom\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-1\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-9\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-F\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-^235\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-_\r
-\backslash\r
-phantom\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-23\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-9\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-F\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Lambda^\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-phantom\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-ii\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-t\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-_MMt\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Furthermore there are the commands \r
-\series bold\r
-\r
-\backslash\r
-vphantom\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! V ! \r
-\backslash\r
-vphantom\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- (toolbar button \r
-\begin_inset space ~\r
-\end_inset\r
-\r
-\r
-\begin_inset Graphics\r
- filename ../images/math/vphantom.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-) and \r
-\series bold\r
-\r
-\backslash\r
-hphantom\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! H ! \r
-\backslash\r
-hphantom\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- (toolbar button \r
-\begin_inset space ~\r
-\end_inset\r
-\r
-\r
-\begin_inset Graphics\r
- filename ../images/math/hphantom.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-).\r
- \r
-\series bold\r
-\r
-\backslash\r
-hphantom\r
-\series default\r
- creates only space for the maximal height of the characters in the box\r
- but not for its width.\r
- \r
-\series bold\r
-\r
-\backslash\r
-vphantom\r
-\series default\r
- creates only space for the width of the box content.\r
- Therefore the boxes of both commands have only one red arrow.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For example the command \r
-\series bold\r
-\r
-\backslash\r
-vphantom\r
-\series default\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series bold\r
-a\r
-\backslash\r
-int\r
-\series default\r
- creates space for the height of the integral sign,\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-The command \r
-\series bold\r
-\r
-\backslash\r
-int\r
-\series default\r
- creates an integral sign, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Big-Operators"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- because this is the larger character.\r
- An example application is in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Multiline-Brackets"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Placeholders can also be used for text when they are inserted via the menu\r
- \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Formatting\SpecialChar \menuseparator\r
-Phantom\r
-\family default\r
-:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This is a sentence.\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom Phantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-This\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is a sentence.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Lines\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Lines\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! underlined\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-overline\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A+B\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! O ! \r
-\backslash\r
-overline\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-underline\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A+B\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! U ! \r
-\backslash\r
-underline\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-overline\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-underline\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A+B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In the last example it doesn't matter if first \r
-\series bold\r
-\r
-\backslash\r
-overline\r
-\series default\r
- or \r
-\series bold\r
-\r
-\backslash\r
-underline\r
-\series default\r
- is inserted.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To double underline use \r
-\series bold\r
-\r
-\backslash\r
-underline\r
-\series default\r
- twice.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-It is possible to place up to 6 lines above or below characters.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-Custom lines can be created using the command \r
-\series bold\r
-\r
-\backslash\r
-rule\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! R ! \r
-\backslash\r
-rule\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- which has the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-rule[vertical offset]{length}{thickness}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The optional vertical offset shifts the line upwards (or downwards, when\r
- the value is negative).\r
- The units listed in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "tab:Available-units"\r
-\r
-\end_inset\r
-\r
- can be used for the values.\r
- Here are two example lines created with the commands\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-rule[-2ex]{3cm}{2pt}\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-rule{2cm}{1pt}\r
-\series default\r
-:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This is a sentence \r
-\begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$\r
-\end_inset\r
-\r
- with two lines.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-rule\r
-\series default\r
- can also be used for text when a line is inserted via the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Formatting\SpecialChar \menuseparator\r
-Horizontal\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Line\r
-\family default\r
-:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This is a sentence \r
-\begin_inset CommandInset line\r
-LatexCommand rule\r
-offset "0.5ex"\r
-width "3cm"\r
-height "1pt"\r
-\r
-\end_inset\r
-\r
- with one line.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Ellipses\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Ellipses"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Ellipses\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-There are different types of ellipses available.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-In the math toolbar in the submenu of the button \r
-\begin_inset Graphics\r
- filename ../images/math/ldots.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- For listings dots at the baseline are used (\r
-\series bold\r
-\r
-\backslash\r
-ldots\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! L ! \r
-\backslash\r
-ldots\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-), while for operations dots are needed that are on the same height as the\r
- operators (\r
-\series bold\r
-\r
-\backslash\r
-cdots\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! C ! \r
-\backslash\r
-cdots\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-).\r
- When using the command \r
-\series bold\r
-\r
-\backslash\r
-dots\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! D ! \r
-\backslash\r
-dots\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, LaTeX decides on the basis of the next character what type is used.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="9" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A_1\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-,\r
-\backslash\r
-dots\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-,A_n\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A_{1},\dots,A_{n}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A_1\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-+\r
-\backslash\r
-dots\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-+A_n\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A_{1}+\dots+A_{n}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A_1\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-,\r
-\backslash\r
-ldots\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-,A_n\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A_{1},\ldots,A_{n}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A_1\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-+\r
-\backslash\r
-cdots\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-+A_n\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A_{1}+\cdots+A_{n}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-vdots\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\vdots$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ddots\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\ddots$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-iddots\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\iddots$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-3×3\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-matrix with the different dots\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\begin{array}{ccc}\r
-A_{11} & \cdots & A_{1m}\\\r
-\vdots & \ddots & \vdots\\\r
-A_{n1} & \cdots & A_{nm}\r
-\end{array}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The ellipses available in menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Special\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Character\r
-\family default\r
- are \r
-\series bold\r
-\r
-\backslash\r
-ldots\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-To use \r
-\series bold\r
-\r
-\backslash\r
-iddots\r
-\series default\r
-, one of the options \r
-\family sans\r
-Use mathdots package (automatically)\r
-\family default\r
- must be set in the document settings under \r
-\family sans\r
-Math\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Options\r
-\family default\r
-.\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-Using the option \r
-\family sans\r
-Use mathdots package\r
-\family default\r
- will improve the appearance of all dots in the documents if their font\r
- style or size is not the default.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-Specially for matrices there are ellipses that span over several columns.\r
- They are created with the command \r
-\series bold\r
-\r
-\backslash\r
-hdotsfor\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! H ! \r
-\backslash\r
-hdotsfor\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, that has the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-hdotsfor[distance]{number of columns}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The number of columns specifies how many columns should be spanned.\r
- Distance is a factor for the distance between the dots.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In the following matrix the command \r
-\series bold\r
-\r
-\backslash\r
-hdotsfor[2]{4}\r
-\series default\r
- was inserted in the first box of the second line, to get an ellipsis with\r
- a dot distance twice as long as with the command \r
-\series bold\r
-\r
-\backslash\r
-dots\r
-\series default\r
-:\r
-\begin_inset Formula \r
-\[\r
-\left(\begin{array}{cccc}\r
-A & B & C & D\\\r
-\hdotsfor[2]{4}\\\r
-q & w & e & r\r
-\end{array}\right)\r
-\]\r
-\r
-\end_inset\r
-\r
-Note that the matrix fields that should be spanned must be empty, otherwise\r
- you get LaTeX-errors.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-Furthermore you can fill with the command \r
-\series bold\r
-\r
-\backslash\r
-dotfill\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! D ! \r
-\backslash\r
-dotfill\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- the rest of a line with dots.\r
- The effect of these commands is the same as with \r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\series default\r
-, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Variable-Space"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For example the command \r
-\series bold\r
-A\r
-\backslash\r
-dotfill\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-B\r
-\series default\r
- produces\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula $A\dotfill B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Similar to\r
-\series bold\r
- \r
-\backslash\r
-dotfill\r
-\series default\r
- there is for a line the command \r
-\series bold\r
-\r
-\backslash\r
-hrulefill\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! H ! \r
-\backslash\r
-hrulefill\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula $A\hrulefill B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To use the commands for text, they have to be inserted in TeX-mode.\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Matrices\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sec:Matrices"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Matrices\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Matrices can be inserted via the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/dialog-show_mathmatrix.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- or the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Matrix\r
-\family default\r
-.\r
- In the matrix dialog you can specify the number of columns and rows, the\r
- alignment and the decoration.\r
- The vertical alignment is only of importance for matrices in inline formulas:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The first matrix is top \r
-\begin_inset Formula $\begin{array}[t]{cccc}\r
-A & D & G & J\\\r
-B & E & H & K\\\r
-C & F & I & L\r
-\end{array}$\r
-\end_inset\r
-\r
-, the second middle \r
-\begin_inset Formula $\begin{array}{cccc}\r
-A & D & G & J\\\r
-B & E & H & K\\\r
-C & F & I & L\r
-\end{array}$\r
-\end_inset\r
-\r
- and the third bottom \r
-\begin_inset Formula $\begin{array}[b]{cccc}\r
-A & D & G & J\\\r
-B & E & H & K\\\r
-C & F & I & L\r
-\end{array}$\r
-\end_inset\r
-\r
- aligned.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The horizontal alignment specifies how the column entries should be aligned.\r
- It is set by entering a letter for every column.\r
- \r
-\emph on\r
-l\r
-\emph default\r
- denotes left aligned, \r
-\emph on\r
-c\r
-\emph default\r
- centered and \r
-\emph on\r
-r\r
-\emph default\r
- right aligned.\r
- To create for example a 4\r
-\series bold\r
-×\r
-\series default\r
-4\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-matrix where the first column is left aligned, the second and third are\r
- centered and the last one is right aligned, one enters for the horizontal\r
- alignment \r
-\series bold\r
-lccr\r
-\series default\r
-.\r
- Normally in a matrix all columns are centered, therefore the default for\r
- every column is a \r
-\series bold\r
-c\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Horizontal alignment:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-lll\r
-\series default\r
- : \r
-\begin_inset Formula $\begin{array}{lll}\r
-10000 & D & G\\\r
-B & 10000 & H\\\r
-C & F & 10000\r
-\end{array}$\r
-\end_inset\r
-\r
- , \r
-\series bold\r
-ccc\r
-\series default\r
- : \r
-\begin_inset Formula $\begin{array}{ccc}\r
-10000 & D & G\\\r
-B & 10000 & H\\\r
-C & F & 10000\r
-\end{array}$\r
-\end_inset\r
-\r
- , \r
-\series bold\r
-rrr\r
-\series default\r
- : \r
-\begin_inset Formula $\begin{array}{rrr}\r
-10000 & D & G\\\r
-B & 10000 & H\\\r
-C & F & 10000\r
-\end{array}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To add or delete rows and columns subsequently, the math toolbar buttons\r
- \r
-\begin_inset Graphics\r
- filename ../images/tabular-feature_append-row.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-, \r
-\begin_inset Graphics\r
- filename ../images/tabular-feature_delete-row.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-, etc.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-, or the menu \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Rows & Columns\r
-\family default\r
- can be used.\r
- New rows can also be created with \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "newline-insert newline"\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-The \r
-\family sans\r
-Decoration\r
-\family default\r
- adds parentheses in the selected style around the matrix.\r
- Alternatively, parentheses can can either be created with the commands\r
- \r
-\series bold\r
-\r
-\backslash\r
-left\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! L ! \r
-\backslash\r
-left\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-right\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! R ! \r
-\backslash\r
-right\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- (shortcut \r
-\family sans\r
-Alt+M\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Parenthesis\r
-\family default\r
-), see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Automatic-Bracket-Size"\r
-\r
-\end_inset\r
-\r
-, or by using the following commands:\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bmatrix\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-2\r
-\series bold\r
-×\r
-\series default\r
-2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-matrix\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}\r
-0 & \textrm{-}\mathrm{i}\\\r
-\mathrm{i} & 0\r
-\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Bmatrix\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-2\r
-\series bold\r
-×\r
-\series default\r
-2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-matrix\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}\r
-0 & \textrm{-}\mathrm{i}\\\r
-\mathrm{i} & 0\r
-\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-pmatrix\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-2\r
-\series bold\r
-×\r
-\series default\r
-2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-matrix\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}\r
-0 & \textrm{-}\mathrm{i}\\\r
-\mathrm{i} & 0\r
-\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-vmatrix\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-2\r
-\series bold\r
-×\r
-\series default\r
-2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-matrix\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}\r
-0 & \textrm{-}\mathrm{i}\\\r
-\mathrm{i} & 0\r
-\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Vmatrix\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-2\r
-\series bold\r
-×\r
-\series default\r
-2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-matrix\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}\r
-0 & \textrm{-}\mathrm{i}\\\r
-\mathrm{i} & 0\r
-\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-matrix\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-2\r
-\series bold\r
-×\r
-\series default\r
-2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-matrix\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}\r
-0 & \textrm{-}\mathrm{i}\\\r
-\mathrm{i} & 0\r
-\end{array}\end{matrix}\raisebox{-5.3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-When e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-vmatrix\r
-\series default\r
- is inserted, a blue box appears between two vertical lines where the matrix\r
- is inserted.\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-Note that decorated matrices ignore the vertical alignment.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-As all multiline formulas are matrices, the length \r
-\series bold\r
-\r
-\backslash\r
-arraycolsep\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! A ! \r
-\backslash\r
-arraycolsep\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- that is described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Column-Separation"\r
-\r
-\end_inset\r
-\r
- can also be used to change the column separation of matrices.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To change the row separation, the command \r
-\series bold\r
-\r
-\backslash\r
-arraystretch\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! A ! \r
-\backslash\r
-arraystretch\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is used.\r
- It is used as follows:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-arraystretch}{stretch factor}\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! R ! \r
-\backslash\r
-renewcommand\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command \r
-\series bold\r
-\r
-\backslash\r
-renewcommand\r
-\series default\r
- assigns the stretch factor to the predefined command \r
-\series bold\r
-\r
-\backslash\r
-arraystretch\r
-\series default\r
-.\r
- To double e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-the row separation, use the factor 2.\r
- This is then used for all following matrices.\r
- To go back to the original separation, assign the factor 1 to \r
-\series bold\r
-\r
-\backslash\r
-arraystretch\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To set matrices into a text line, the command \r
-\series bold\r
-\r
-\backslash\r
-smallmatrix\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! S ! \r
-\backslash\r
-smallmatrix\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is used.\r
- When it is inserted a blue box with two dashed lines appears.\r
- In this box the matrix is inserted.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This is a matrix \r
-\begin_inset Formula $\left(\begin{smallmatrix}A & B\\\r
-C & D\r
-\end{smallmatrix}\right)$\r
-\end_inset\r
-\r
- in a text line.\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Brackets and Delimiters\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Brackets\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Delimiters\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Vertical Brackets and Delimiters\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Brackets ! vertical\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="9" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-(\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $($\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-{\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\{$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-[\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $[$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-langle\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\langle$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-lceil\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\lceil$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-lfloor\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\lfloor$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-/\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $/$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-|\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $|$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="9" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $)$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-]\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $]$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-rangle\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\rangle$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-rceil\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\rceil$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-rfloor\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\rfloor$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-\r
-\backslash\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\backslash$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-|\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\|$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series medium\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-Note:\r
-\series default\r
- In TeX-mode the command \r
-\series bold\r
-\r
-\backslash\r
-textbackslash\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! T ! \r
-\backslash\r
-textbackslash\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- must be used for the backslash, because the command \r
-\series bold\r
-\r
-\backslash\r
-\r
-\backslash\r
-\r
-\series default\r
- produces a line break there.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For all characters listed above the size can be adjusted with the commands\r
- described in the following two subsections.\r
- When using these commands, the characters < and > can directly be used\r
- instead of the commands \r
-\series bold\r
-\r
-\backslash\r
-langle\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-rangle\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Manual Bracket Size\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Manual-Bracket-Size"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Bracket size ! manual\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The bracket size can be specified manually by the LaTeX-commands \r
-\series bold\r
-\r
-\backslash\r
-big\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! B ! \r
-\backslash\r
-big\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, \r
-\series bold\r
-\r
-\backslash\r
-Big\r
-\series default\r
-, \r
-\series bold\r
-\r
-\backslash\r
-bigg\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-Bigg\r
-\series default\r
-.\r
- \r
-\series bold\r
-\r
-\backslash\r
-big\r
-\series default\r
- denotes the smallest and \r
-\series bold\r
-\r
-\backslash\r
-Bigg\r
-\series default\r
- the largest bracket size.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-These commands are used to emphasize levels of brackets:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="2" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-all brackets in the same size:\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-this looks better:\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For the second formula the command \r
-\series bold\r
-\r
-\backslash\r
-Big((A+B)(A-B)\r
-\backslash\r
-Big)^\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-C\r
-\series default\r
- has been used.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Here is an overview about all bracket sizes:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\r
-\backslash\r
-Bigg(\r
-\backslash\r
-exp\r
-\backslash\r
-bigg<\r
-\backslash\r
-Big[\r
-\backslash\r
-big{\r
-\backslash\r
-ln(3x)\r
-\backslash\r
-big}^2\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-sin(x)\r
-\backslash\r
-Big]^\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-bigg>\r
-\backslash\r
-Bigg)^0,5\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Besides the \r
-\series bold\r
-\r
-\backslash\r
-big\r
-\series default\r
--commands there is the variant \r
-\series bold\r
-\r
-\backslash\r
-bigm\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! B ! \r
-\backslash\r
-bigm\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- that adds a bit more space between the bracket and its content, and the\r
- variant \r
-\series bold\r
-\r
-\backslash\r
-bigl\r
-\series default\r
--\r
-\series bold\r
-\r
-\backslash\r
-bigr\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! B ! \r
-\backslash\r
-bigl - \r
-\backslash\r
-bigr\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, that don't add additional space.\r
- The \r
-\emph on\r
-l\r
-\emph default\r
- at the end of the command \r
-\series bold\r
-\r
-\backslash\r
-bigl\r
-\series default\r
- is for a left bracket; for a right bracket this will be replaced by an\r
- \r
-\emph on\r
-r\r
-\emph default\r
-.\r
- A left or right bracket can each be an opening or closing bracket.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In the following table is a comparison of the variants:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="5" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="middle">\r
-<column alignment="center" valignment="middle">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Bigm(\r
-\backslash\r
-bigm(\r
-\backslash\r
-ln(3x)\r
-\backslash\r
-bigm)^2\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-\r
-\backslash\r
-Bigm)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Big(\r
-\backslash\r
-big(\r
-\backslash\r
-ln(3x)\r
-\backslash\r
-big)^2\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-\r
-\backslash\r
-Big)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Bigl(\r
-\backslash\r
-bigl(\r
-\backslash\r
-ln(3x)\r
-\backslash\r
-bigr)^2\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-\r
-\backslash\r
-Bigr)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bigl)\r
-\backslash\r
-ln(3x)\r
-\backslash\r
-bigr(\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Automatic Bracket Size\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Automatic-Bracket-Size"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Bracket size ! automatic\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Brackets with variable size can be inserted with the commands \r
-\series bold\r
-\r
-\backslash\r
-left\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! L ! \r
-\backslash\r
-left\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-right\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! R ! \r
-\backslash\r
-right\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- or via the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/dialog-show_mathdelimiter.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
- Directly behind \r
-\series bold\r
-\r
-\backslash\r
-left\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-right\r
-\series default\r
- the wanted bracket must be inserted.\r
- The bracket size will then automatically be calculated for the output.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-normal bracket: The command \r
-\series bold\r
-\r
-\backslash\r
-ln(\r
-\backslash\r
-frac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-C\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-)\r
-\series default\r
- creates\r
-\begin_inset Formula \r
-\[\r
-\ln(\frac{A}{C})\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-multiline bracket: The command \r
-\series bold\r
-\r
-\backslash\r
-ln\r
-\backslash\r
-left(\r
-\backslash\r
-frac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-C\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-right)\r
-\series default\r
- creates\r
-\begin_inset Formula \r
-\[\r
-\ln\left(\frac{A}{C}\right)\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Instead of \r
-\series bold\r
-\r
-\backslash\r
-left\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-right\r
-\series default\r
- the shortcut \r
-\family sans\r
-Alt+M\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Bracket\r
-\family default\r
- can be used.\r
- This has the advantage that you can see in LyX immediately the real bracket\r
- size and that the matching right bracket will be created too.\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-The command for the last example would then be: \r
-\series bold\r
-\r
-\backslash\r
-ln Alt+M\r
-\series default\r
- \r
-\series bold\r
-(\r
-\backslash\r
-frac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-C\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To omit a left or right bracket, a dot is inserted for the omitted bracket.\r
- For example the command \r
-\series bold\r
-\r
-\backslash\r
-left.\r
-\backslash\r
-frac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-B\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-right}\r
-\series default\r
- creates:\r
-\series bold\r
-\r
-\begin_inset Formula \r
-\[\r
-\left.\frac{A}{B}\right\} \r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-The commands \r
-\series bold\r
-\r
-\backslash\r
-left\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-right\r
-\series default\r
- will be converted by LyX to brackets in the right size when the document\r
- is reloaded and an omitted bracket will appear as dashed line.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,\r
- the command \r
-\series bold\r
-\r
-\backslash\r
-middle\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! M ! \r
-\backslash\r
-middle\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is additionally available for all brackets and limits.\r
- With this command the height of the following character is adapted to the\r
- one of the surrounding brackets, what is e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-needed for physical vectors:\r
-\begin_inset Formula \r
-\[\r
-\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \r
-\]\r
-\r
-\end_inset\r
-\r
-For physical vectors there is a special LaTeX-package, described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Physical-Vectors"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Horizontal Brackets\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Brackets ! horizontal\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-raisebox{2.3mm}{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-overbrace\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A+B\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-^\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-3\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! O ! \r
-\backslash\r
-overbrace\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\overbrace{A+B}^{3}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-raisebox{-2.2mm}{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-underbrace\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A+B\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-_5\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! U ! \r
-\backslash\r
-underbrace\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\underbrace{A+B}_{5}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-overbrace\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-underbrace\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A+B_w\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-_7\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-^\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-C\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In the last example it doesn't matter if \r
-\series bold\r
-\r
-\backslash\r
-overbrace\r
-\series default\r
- or \r
-\series bold\r
-\r
-\backslash\r
-underbrace\r
-\series default\r
- is inserted at first.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-When brackets are needed that overlap each other, multiline formulas, as\r
- described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Multiline-Formulas"\r
-\r
-\end_inset\r
-\r
-, must be used:\r
-\begin_inset Formula \r
-\begin{eqnarray*}\r
-A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\\r
- & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\r
-\end{eqnarray*}\r
-\r
-\end_inset\r
-\r
-In the first row the formula is inserted together with the first brace.\r
- It is hereby important that the space command\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Space commands are explained in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Predefined-Space"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- \r
-\series bold\r
-\r
-\backslash\r
-:\r
-\series default\r
- is inserted before the first \r
-\begin_inset Formula $d$\r
-\end_inset\r
-\r
-, because the brace that ends behind the \r
-\begin_inset Formula $q$\r
-\end_inset\r
-\r
- prevents that the following \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-+\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- is surrounded by space.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-because a bracket is not handled as a character, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Binary-Operators"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- In the second row the second brace is inserted.\r
- As it should begin before the \r
-\begin_inset Formula $b$\r
-\end_inset\r
-\r
-, first the command \r
-\series bold\r
-\r
-\backslash\r
-hphantom{gggg+\r
-\backslash\r
-:}\r
-\series default\r
- is inserted.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-more about \r
-\series bold\r
-\r
-\backslash\r
-hphantom\r
-\series default\r
- see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Placeholders"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- This space is needed because the \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-+\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- is also surrounded by space in the formula.\r
- The brace is placed under the command \r
-\series bold\r
-\r
-\backslash\r
-hphantom{bbqq+dddd}\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-It gets more complicated when brackets overlap each other, like in the following\r
- example:\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-jot}{-6pt}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{eqnarray*}\r
- & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\\r
-A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\r
-\end{eqnarray*}\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-jot}{3pt}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-The first formula row is the same as the second row of the previous example,\r
- with the difference that the brace is above.\r
- The second row contains the formula together with the second brace.\r
- To avoid that there is space between the upper brace in the first row and\r
- the formula, the row spacing needs to be reduced.\r
- This is not easily possible due to a bug in LyX\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset CommandInset href\r
-LatexCommand href\r
-name "LyX-bug #1505"\r
-target "http://www.lyx.org/trac/ticket/1505"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- As a solution for the problem, the global formula row separation \r
-\series bold\r
-\r
-\backslash\r
-jot\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! J ! \r
-\backslash\r
-jot\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- must be changed to -6\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt before the formula with the command \r
-\series bold\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-jot}{-6pt}\r
-\series default\r
- in TeX-mode.\r
- \r
-\series bold\r
-\r
-\backslash\r
-jot\r
-\series default\r
- is set back after the formula to the standard value of 3\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt using the same command.\r
- More about the row separation in formulas is explained in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Line-Separation"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Arrows\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Arrows\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Arrows can be inserted via the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/leftarrow.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- or the commands listed in the following subsections.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Horizontal Arrows\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Arrows ! horizontal\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="8" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-gets\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\gets$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Leftarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Leftarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-longleftarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\longleftarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Longleftarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Longleftarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-leftharpoonup\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\leftharpoonup$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-leftharpoondown\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\leftharpoondown$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-hookleftarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\hookleftarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="8" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-to\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Rightarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Rightarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-longrightarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\longrightarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Longrightarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Longrightarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-rightharpoonup\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\rightharpoonup$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-rightharpoondown\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\rightharpoondown$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-hookrightarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\hookrightarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="6" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-leftrightarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\leftrightarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Leftrightarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Leftrightarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-longleftrightarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\longleftrightarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Longleftrightarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Longleftrightarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-rightleftharpoons\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\rightleftharpoons$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hspace{}\r
-\length 25pt\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="5" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mapsto\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mapsto$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-longmapsto\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\longmapsto$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-leadsto\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\leadsto$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dasharrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\dasharrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-Arrows used as accents like e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-vector arrows are listed in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Accents"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-Furthermore there are the labeled arrows\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Arrows ! labeled\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- \r
-\series bold\r
-\r
-\backslash\r
-xleftarrow\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! X ! \r
-\backslash\r
-xleftarrow\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-xrightarrow\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! X ! \r
-\backslash\r
-xrightarrow\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-vspace{4mm}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- When inserting one of these commands in a formula, an arrow with two blue\r
- boxes appear where the label can be inserted.\r
- The length of the arrow adapts to the label width.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="3" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-F(a)\r
-\backslash\r
-xleftarrow\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-x=a\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-x>0\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-F(x)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-F(x)\r
-\backslash\r
-xrightarrow\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-x=a\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-x>0\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-F(a)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Vertical and diagonal Arrows\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Arrows ! diagonal\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Arrows ! vertical\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="7" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-uparrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\uparrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Uparrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Uparrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-updownarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\updownarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Updownarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Updownarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Downarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Downarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-downarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="5" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-nearrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\nearrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-searrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\searrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-swarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\swarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-nwarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\nwarrow$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-Vertical arrows can be used also as delimiters together with the commands\r
- described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Manual-Bracket-Size"\r
-\r
-\end_inset\r
-\r
- and \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Automatic-Bracket-Size"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Accents\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sec:Accents"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Accents\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Accents can be inserted via the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/hat.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- or the commands listed in the following subsections.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Accents for one Character\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-texorpdfstring{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-accents in text see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Accents-in-Text"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}{}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-texorpdfstring\r
-\series default\r
- is used to avoid that the footnote appears in the PDF-bookmark.\r
-\end_layout\r
-\r
-\begin_layout Plain Layout\r
-More about \r
-\series bold\r
-\r
-\backslash\r
-texorpdfstring\r
-\series default\r
- is in section \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Formulas-in-Section"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Accents-for-one"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Accents ! for one character\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="8" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dot\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\dot{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ddot\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dddot\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ddddot\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-vec\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Vectors\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\vec{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bar\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\bar{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mathring\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="7" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-tilde\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-hat\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\hat{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-check\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\check{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-acute\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\acute{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-grave\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\grave{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-breve\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\breve{A}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-You can directly insert accents like é to formulas.\r
- LyX will transform them to the corresponding accent command.\r
- For umlauts\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Umlauts\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- it is better to insert a quotation mark before the vowel.\r
- These two characters are then treated by LaTeX as \r
-\emph on\r
-one\r
-\emph default\r
- character when the formula part with the umlaut is marked as German.\r
- In contrary to \r
-\series bold\r
-\r
-\backslash\r
-ddot\r
-\series default\r
-, with this method \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-real\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- umlauts are created as demonstrated in the following example:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace -2mm\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="3" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- and the 0\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt space are only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\lang ngerman\r
-\begin_inset Quotes grd\r
-\end_inset\r
-\r
-i\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset space \hspace{}\r
-\length 0pt\r
-\end_inset\r
-\r
-\r
-\lang ngerman\r
-\r
-\begin_inset Formula $"i$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ddot\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-i\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\ddot{i}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Another advantage to \r
-\series bold\r
-\r
-\backslash\r
-ddot\r
-\series default\r
- is that umlauts can directly be converted to mathematical text because\r
- the accent commands above are \r
-\emph on\r
-not allowed\r
-\emph default\r
- \r
-\emph on\r
-in mathematical text\r
-\emph default\r
-.\r
- To convert an accented character to mathematical text, only the character\r
- under the accent may be converted.\r
- This applies also for all other conversions, e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-to italic or bold.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In mathematical text, umlauts and other accented characters can directly\r
- be inserted.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Accents for several Characters\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Accents ! for several characters\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="5" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-overleftarrow\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-underleftarrow\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-overleftrightarrow\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-underleftrightarrow\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="5" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-overrightarrow\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-underrightarrow\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-widetilde\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-widehat\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-With these commands as many characters as you like can be accented.\r
- But the accents \r
-\series bold\r
-\r
-\backslash\r
-widetilde\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-widehat\r
-\series default\r
- will only be set in the output with a length of three characters, as shown\r
- in the following example:\r
-\begin_inset Formula \r
-\[\r
-\widetilde{A+B=C-D}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With the commands \r
-\series bold\r
-\r
-\backslash\r
-overset\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! O ! \r
-\backslash\r
-overset\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-underset\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! U ! \r
-\backslash\r
-underset\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- described in the previous subsection it is also possible to accent several\r
- characters.\r
- The command \r
-\series bold\r
-\r
-\backslash\r
-underset\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-***\r
-\series default\r
- creates:\r
-\begin_inset Formula \r
-\[\r
-\underset{***}{A=B}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Space\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Space"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Space ! horizontal\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Predefined Space\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Predefined-Space"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Space ! horizontal ! predefined\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Sometimes it is necessary to insert horizontal space into a formula.\r
- This is done by inserting a protected space (shortcut \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "command-alternatives space-insert protected ; math-space"\r
-\end_inset\r
-\r
-).\r
- A \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-\r
-\color blue\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\color inherit\r
-\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- appears and by pressing \r
-\family sans\r
-Space\r
-\family default\r
- several times one can select one of eight different space sizes.\r
- The spaces can also be inserted using the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/space.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- or special commands.\r
- Independent from the inserted command, one can select the size again by\r
- pressing \r
-\family sans\r
-Space\r
-\family default\r
- afterwards.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\noindent\r
-\align center\r
-\begin_inset VSpace -5mm\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="3" columns="7">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="middle" width="6.8cm">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-,\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-:\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-;\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-quad\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-qquad\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-!\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Number of \r
-\family sans\r
-Space\r
-\family default\r
- keystrokes after inserting the protected space\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-0\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-1\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-2\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-3\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-4\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-5\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\, B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\: B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\; B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\quad B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\qquad B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\! B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The last size seem to produce no space.\r
- It is displayed red in LyX contrary to the other sizes, because it is a\r
- negative space.\r
- There are two more negative spaces:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="3" columns="3">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="middle" width="6.8cm">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-negmedspace\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-negthickspace\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Number of \r
-\family sans\r
-Space\r
-\family default\r
- keystrokes after inserting the protected space\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-6\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-7\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\negmedspace B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\negthickspace B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Negative spaces can lead to characters overlapping each other.\r
- Thus they can be used to enforce ligatures, which are e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-useful for summation operators:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="3" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sum\r
-\backslash\r
-sum\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-f_kl\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sum\r
-\backslash\r
-negmedspace\r
-\backslash\r
-sum\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-f_kl\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Relations like for example equal signs, are always surrounded by space.\r
- To suppress this, the equal sign is placed into a TeX-brace.\r
- The following example demonstrates this:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="2" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-normal equation\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A=B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\raisebox{5mm}{}$\r
-\end_inset\r
-\r
-equation without space\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell multicolumn="1" alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A{=}B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\noindent\r
-The command for the last formula is: \r
-\series bold\r
-A\r
-\backslash\r
-{=\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-Spaces are needed for physical units, because the space between the value\r
- and the unit is the smallest one and not a normal space.\r
- For units in text, the smallest space is inserted via the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Formatting\SpecialChar \menuseparator\r
-Thin\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Space\r
-\family default\r
- (shortcut \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "space-insert thin"\r
-\end_inset\r
-\r
-).\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-An example to visualize the difference:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="2" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="left" valignment="top">\r
-<column alignment="left" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-24 kW\r
-\begin_inset Formula $\cdot$\r
-\end_inset\r
-\r
-h\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-space between value and unit\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-24\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-kW\r
-\begin_inset Formula $\cdot$\r
-\end_inset\r
-\r
-h\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-smallest space between value and unit\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Variable Space\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-texorpdfstring{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-for vertical space in formulas see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Line-Separation"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}{}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.\r
-\end_layout\r
-\r
-\begin_layout Plain Layout\r
-More about \r
-\backslash\r
-texorpdfstring is in section \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Formulas-in-Section"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Variable-Space"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Space ! horizontal ! variable\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Space with a defined length can be inserted with the command \r
-\series bold\r
-\r
-\backslash\r
-hspace\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! H ! \r
-\backslash\r
-hspace\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- Then a long \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-\r
-\color blue\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\color inherit\r
-\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- appears.\r
- The length can be specified by left-clicking on the \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-\r
-\color blue\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\color inherit\r
-\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
-.\r
- The length may also be negative.\r
- To insert as much space as is available, the command \r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! H ! \r
-\backslash\r
-hfill\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is used.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace -1mm\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command (\r
-\backslash\r
-hspace length)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A=B\r
-\backslash\r
-hspace\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-A\r
-\backslash\r
-not=C (3\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-cm)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A=B\hspace{3cm}A\not=C$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A\r
-\backslash\r
-hspace\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-A\r
-\backslash\r
-not=A (-1\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\hspace{-1mm}A\not=A$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A=A\r
-\backslash\r
-hfill\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-B=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A=A\hfill B=B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In the last example the available space is given by the longest column entry\r
- of the table.\r
- In an inline formula the space depends on the length of the line in which\r
- \r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\series default\r
- is inserted.\r
- Thus, when the line uses the full width, no space will be created.\r
- \r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\series default\r
- only has an effect on displayed formulas when the formula style \r
-\series bold\r
-Indented\r
-\series default\r
- is used.\r
- (Formula styles are explained in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Formula-Styles"\r
-\r
-\end_inset\r
-\r
-.)\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Besides \r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\series default\r
-, there are the commands \r
-\series bold\r
-\r
-\backslash\r
-dotfill\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-hrulefill\r
-\series default\r
- that fill the space with a pattern, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Ellipses"\r
-\r
-\end_inset\r
-\r
- for an example.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For text, variable space can be inserted via the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Formatting\SpecialChar \menuseparator\r
-Horizontal\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Space\r
-\family default\r
-:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This is a line with\r
-\begin_inset space \hspace{}\r
-\length 2cm\r
-\end_inset\r
-\r
-2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-cm space.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This is a line with\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-maximum space.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Space besides inline Formulas\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Space ! besides inline formulas\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The space that surrounds inline formulas can be adjusted with the length\r
- \r
-\series bold\r
-\r
-\backslash\r
-mathsurround\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! M ! \r
-\backslash\r
-mathsurround\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- The value of a length is set with the command \r
-\series bold\r
-\r
-\backslash\r
-setlength\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! S ! \r
-\backslash\r
-setlength\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- which has the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-setlength{length name}{value}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To set \r
-\series bold\r
-\r
-\backslash\r
-mathsurround\r
-\series default\r
- to the value 5\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm, the command\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-mathsurround}{5mm}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-is inserted in TeX-mode.\r
- 5\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm space will now be set around all inline formulas:\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-mathsurround}{5mm}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This is a line with an inline formula \r
-\begin_inset Formula $A=B$\r
-\end_inset\r
-\r
- with 5\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm surrounding space.\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-mathsurround}{0pt}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To return to the predefined value, \r
-\series bold\r
-\r
-\backslash\r
-mathsurround\r
-\series default\r
- is set to the value 0\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt.\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Boxes and Frames\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Boxes\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Frames | see\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Boxes\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Boxes for text are described in chapter \r
-\family typewriter\r
-Boxes\r
-\family default\r
- in the \r
-\family typewriter\r
-Embedded\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Objects\r
-\family default\r
- manual.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Boxes with Frame\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Boxes-with-Frame"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Boxes ! with frame\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-It is possible to frame a formula or part of one with the commands \r
-\series bold\r
-\r
-\backslash\r
-fbox\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! F ! \r
-\backslash\r
-fbox\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-boxed\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! B ! \r
-\backslash\r
-boxed\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When one of these commands is inserted in a formula, a blue box appears\r
- within a frame to enter formula parts.\r
- For \r
-\series bold\r
-\r
-\backslash\r
-fbox\r
-\series default\r
- an additional formula has to be created by \r
-\family sans\r
-Ctrl+M\r
-\family default\r
- within this box, because the box content will otherwise be treated as mathemati\r
-cal text.\r
- When \r
-\series bold\r
-\r
-\backslash\r
-boxed\r
-\series default\r
- is used, a new formula is automatically created inside the frame.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command \r
-\series bold\r
-\r
-\backslash\r
-fbox\r
-\series default\r
- is not suitable to frame displayed formulas because the formula will always\r
- be set in the size of the text.\r
- \r
-\series bold\r
-\r
-\backslash\r
-boxed\r
-\series default\r
- is in contrary not suitable to frame inline formulas, because the formula\r
- will always be set in the size of a displayed formula.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-An extension to \r
-\series bold\r
-\r
-\backslash\r
-fbox\r
-\series default\r
- is the command \r
-\series bold\r
-\r
-\backslash\r
-framebox\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! F ! \r
-\backslash\r
-framebox\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- where additionally the frame width and the alignment can be specified.\r
- \r
-\series bold\r
-\r
-\backslash\r
-framebox\r
-\series default\r
- is used in the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-framebox[frame width][position]{box content}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The position can either be \r
-\emph on\r
-l\r
-\emph default\r
- or \r
-\emph on\r
-r\r
-\emph default\r
-.\r
- \r
-\emph on\r
-l\r
-\emph default\r
- left aligns, \r
-\emph on\r
-r\r
-\emph default\r
- right aligns the formula in the box.\r
- When no position is given, the formula will be centered.\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-If no width is given, also no position can be given.\r
- In this case the frame width is adjusted to the box content like for \r
-\series bold\r
-\r
-\backslash\r
-fbox\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When the command \r
-\series bold\r
-\r
-\backslash\r
-framebox\r
-\series default\r
- is inserted, a box appears containing three blue boxes.\r
- The first two boxes are surrounded by brackets and denote the two optional\r
- arguments.\r
- The third box is for formula parts like for \r
-\series bold\r
-\r
-\backslash\r
-fbox\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="5" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-fbox\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\family sans\r
-Ctrl+M\r
-\family default\r
- \r
-\backslash\r
-int\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-boxed\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-int\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A+\r
-\backslash\r
-fbox\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-framebox\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-20mm\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\family sans\r
-Ctrl+M\r
-\family default\r
- \r
-\backslash\r
-frac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}$\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The frame thickness can also be adjusted.\r
- To do this the following commands have to be inserted in TeX-mode before\r
- the formula\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-fboxrule\r
-\series default\r
- \r
-\series bold\r
-\r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-thickness\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
-\r
-\series default\r
- \r
-\series bold\r
-\r
-\backslash\r
-fboxsep\r
-\series default\r
- \r
-\series bold\r
-\r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-distance\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-distance\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- specifies the minimal distance between the frame and the first character\r
- in the box.\r
- An example for this is the following framed formula:\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-fboxrule 2mm \r
-\backslash\r
-fboxsep 3mm\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\[\r
-\boxed{A+B=C}\r
-\]\r
-\r
-\end_inset\r
-\r
-Before this formula the commands\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-fboxrule\r
-\series default\r
- \r
-\series bold\r
-2mm\r
-\series default\r
- \r
-\series bold\r
-\r
-\backslash\r
-fboxsep\r
-\series default\r
- \r
-\series bold\r
-3mm\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-were inserted in TeX-mode.\r
- The given values are used for all following boxes.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To return to the standard frame size, the command\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-fboxrule\r
-\series default\r
- \r
-\series bold\r
-0.4pt\r
-\series default\r
- \r
-\series bold\r
-\r
-\backslash\r
-fboxsep\r
-\series default\r
- \r
-\series bold\r
-3pt\r
-\series default\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-fboxrule 0.4pt \r
-\backslash\r
-fboxsep 3pt\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-is inserted in TeX-mode before the next formula.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Boxes without Frame\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Boxes-without-Frame"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Boxes ! without frame\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For boxes without a frame there are the following box commands: \r
-\series bold\r
-\r
-\backslash\r
-mbox\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! M ! \r
-\backslash\r
-mbox\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, \r
-\series bold\r
-\r
-\backslash\r
-makebox\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! M ! \r
-\backslash\r
-makebox\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! R ! \r
-\backslash\r
-raisebox\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With \r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- a box can be super- or subscripted.\r
- But in contrary to normal super- and subscripting, the characters in the\r
- box keep their font size.\r
- \r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is used in the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox{height}{box content}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When the box should contain a formula, an extra formula is needed like for\r
- \r
-\series bold\r
-\r
-\backslash\r
-fbox\r
-\series default\r
-.\r
- \r
-\series medium\r
-\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-Note:\r
-\series default\r
- For \r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- this extra formula is created by pressing \r
-\family sans\r
-Ctrl+M\r
-\family default\r
- twice instead of once because LyX doesn't yet support \r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- directly.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-H\r
-\backslash\r
-raisebox{2mm\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{al\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
- lo\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $H\raisebox{2mm}{al}lo$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-H\r
-\backslash\r
-raisebox{-2mm\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{al\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-lo\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $H\raisebox{-2mm}{al}lo$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A=\r
-\backslash\r
-raisebox{-2mm\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{\r
-\family sans\r
-Ctrl+M\r
-\family default\r
- \r
-\family sans\r
-Ctrl+M\r
-\family default\r
- \r
-\backslash\r
-sqrt\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-B \r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command \r
-\series bold\r
-\r
-\backslash\r
-mbox\r
-\series default\r
- is equivalent to \r
-\series bold\r
-\r
-\backslash\r
-fbox\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-makebox\r
-\series default\r
- is equivalent to \r
-\series bold\r
-\r
-\backslash\r
-framebox\r
-\series default\r
-, with the difference that there is no frame.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Colored Boxes\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Colored-Boxes"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Boxes ! colored\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To be able to use all commands explained in this section, the LaTeX-package\r
- \r
-\series bold\r
-color\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-The LaTeX-package \r
-\series bold\r
-color\r
-\series default\r
- is part of every LaTeX standard installation.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! color\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- has to be loaded in the LaTeX-preamble with the line\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-When text is colored somewhere in the document with a predefined color,\r
- LyX loads the LaTeX-package \r
-\series bold\r
-color\r
-\series default\r
- automatically.\r
- Thus it is possible that the package is loaded twice, but this does not\r
- cause problems.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre\r
-amble.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage{color}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-To color boxes, the command \r
-\series bold\r
-\r
-\backslash\r
-colorbox\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! C ! \r
-\backslash\r
-colorbox\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is used in the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-colorbox{color}{box content}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The box content can also be a box and a \r
-\series bold\r
-\r
-\backslash\r
-colorbox\r
-\series default\r
- can also be part of another box (see the 2nd and 3rd example).\r
- When the box should contain a formula, an extra formula has to be created,\r
- the same way as for \r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
-.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-This also applies for the command \r
-\series bold\r
-\r
-\backslash\r
-fcolorbox\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-One of the following predefined colors can be chosen:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-black\r
-\series default\r
-, \r
-\series bold\r
-blue\r
-\series default\r
-, \r
-\series bold\r
-cyan\r
-\series default\r
-, \r
-\series bold\r
-green\r
-\series default\r
-, \r
-\series bold\r
-magenta\r
-\series default\r
-, \r
-\series bold\r
-red\r
-\series default\r
-, \r
-\series bold\r
-white\r
-\series default\r
- and \r
-\series bold\r
-yellow\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-colorbox{yellow\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-colorbox{green\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{\r
-\backslash\r
-fbox\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-fbox\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-colorbox{green\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{\r
-\family sans\r
-Ctrl+M\r
-\family default\r
- \r
-\family sans\r
-Ctrl+M\r
-\family default\r
- \r
-\backslash\r
-int\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-C=D\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-colorbox\r
-\series default\r
- only colors the box but not the characters in the box.\r
- To color all characters, the whole formula is highlighted and the desired\r
- color is chosen in the \r
-\family sans\r
-Text\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Style\r
-\family default\r
- dialog.\r
- The dialog can be called with the toolbar button \r
-\begin_inset Graphics\r
- filename ../images/dialog-show_character.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- or the menu \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Text\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Style\SpecialChar \menuseparator\r
-Customized\r
-\family default\r
-.\r
- The formula number then has the same color as the formula.\r
- When the formula number should get another color than the formula characters,\r
- the color must be changed within the formula.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-An example:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\color red\r
-\begin_inset Formula \r
-\begin{equation}\r
-\int A=B\label{eq:red}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\color green\r
-\r
-\begin_inset Formula \r
-\begin{equation}\r
-\textcolor{red}{\int A=B}\label{eq:redgreen}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Formula \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:red"\r
-\r
-\end_inset\r
-\r
- is completely colored red.\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-Formula \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:redgreen"\r
-\r
-\end_inset\r
-\r
- was first completely colored green to set the color for the formula number.\r
- Subsequently the formula characters were colored red.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-To color the frame different than the rest of the box, the command \r
-\series bold\r
-\r
-\backslash\r
-fcolorbox\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! F ! \r
-\backslash\r
-fcolorbox\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is used in the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-fcolorbox{frame color}{color}{box content}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-So \r
-\series bold\r
-\r
-\backslash\r
-fcolorbox\r
-\series default\r
- is an extension of the command \r
-\series bold\r
-\r
-\backslash\r
-colorbox\r
-\series default\r
-.\r
- The frame width is set, like for \r
-\series bold\r
-\r
-\backslash\r
-framebox\r
-\series default\r
-, with \r
-\series bold\r
-\r
-\backslash\r
-fboxrule\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-fboxsep\r
-\series default\r
-.\r
- An example:\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-fboxrule 1mm \r
-\backslash\r
-fboxsep 1mm\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\[\r
-\fcolorbox{cyan}{magenta}{A=B}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-fboxrule 0.4pt \r
-\backslash\r
-fboxsep 3pt\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This formula was created with the command\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-fcolorbox{cyan\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{magenta\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{A=B\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-To use other colors than the predefined ones, they have to be defined first.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-One can for example define the color \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-\r
-\series bold\r
-darkgreen\r
-\series default\r
-\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- with the LaTeX-preamble line:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-definecolor{darkgreen}{cmyk}{0.5,\r
-\series default\r
- \r
-\series bold\r
-0,\r
-\series default\r
- \r
-\series bold\r
-1,\r
-\series default\r
- \r
-\series bold\r
-0.5}\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! D ! \r
-\backslash\r
-definecolor\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-cmyk\r
-\series default\r
- is the color space that denotes the colors \r
-\series bold\r
-cyan\r
-\series default\r
-, \r
-\series bold\r
-magenta\r
-\series default\r
-, \r
-\series bold\r
-yellow\r
-\series default\r
- and \r
-\series bold\r
-black\r
-\series default\r
-.\r
- The four comma separated numbers are the portion factor for the corresponding\r
- colors of the color space.\r
- The factors can be in the range of 0\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
--\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-1.\r
- Instead of \r
-\series bold\r
-cmyk\r
-\series default\r
- also the color space \r
-\series bold\r
-rgb\r
-\series default\r
- can be used for definitions.\r
- \r
-\series bold\r
-rgb\r
-\series default\r
- denotes \r
-\series bold\r
-red\r
-\series default\r
-, \r
-\series bold\r
-green\r
-\series default\r
- and \r
-\series bold\r
-blue\r
-\series default\r
-, so that there are in this case three portion factors for the corresponding\r
- colors.\r
- Furthermore there is the color space \r
-\series bold\r
-gray\r
-\series default\r
- with one portion factor for the gray value.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-As example a framed box with the new defined color \r
-\series bold\r
-darkgreen\r
-\series default\r
- where the characters have been colored \r
-\series bold\r
-yellow\r
-\series default\r
-:\r
-\begin_inset Formula \r
-\begin{equation}\r
-\colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Self-defined colors can also be used for text with the help of the command\r
- \r
-\series bold\r
-\r
-\backslash\r
-textcolor\r
-\series default\r
-:\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Text ! colored\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-textcolor{darkgreen}{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-This sentence is \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-darkgreen\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
-.\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-textcolor\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! T ! \r
-\backslash\r
-textcolor\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is used in the scheme \r
-\series bold\r
-\r
-\backslash\r
-textcolor{color}{characters to color}\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Paragraph Boxes\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Paragraph-Boxes"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Boxes ! as paragraph\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A box that can contain several lines and paragraphs, a so-called paragraph\r
- box (parbox), can be created with the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Box\r
-\family default\r
- or the toolbar button \r
-\begin_inset Graphics\r
- filename ../images/box-insert.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The following example shows a framed parbox in a line:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-This is a line \r
-\begin_inset Box Boxed\r
-position "c"\r
-hor_pos "c"\r
-has_inner_box 1\r
-inner_pos "t"\r
-use_parbox 1\r
-use_makebox 0\r
-width "5cm"\r
-special "none"\r
-height "1in"\r
-height_special "totalheight"\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-This is a paragraph box.\r
- It is exactly 5\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-cm long and can also contain formulas: \r
-\begin_inset Formula $\int A\,\mathrm{d}s=C$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- with a parbox.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Such a box is created by right-clicking on the gray box inset.\r
- A dialog pops up showing the box properties.\r
- In our case set: \r
-\emph on\r
-Decoration\r
-\emph default\r
-: Rectangular box, \r
-\emph on\r
-Inner Box\r
-\emph default\r
-: Parbox, \r
-\emph on\r
-Width\r
-\emph default\r
-: 5\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-cm, \r
-\emph on\r
-Vertical Box Alignment\r
-\emph default\r
-: Middle\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-In LaTeX a parbox is created with the command \r
-\series bold\r
-\r
-\backslash\r
-parbox\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! P ! \r
-\backslash\r
-parbox\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- which has the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-parbox[position]{width}{box content}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The positions \r
-\emph on\r
-b\r
-\emph default\r
- and \r
-\emph on\r
-t\r
-\emph default\r
- are possible.\r
- \r
-\emph on\r
-b\r
-\emph default\r
- for \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-bottom\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- means that the box is aligned within the surrounding text with its last\r
- line.\r
- With \r
-\emph on\r
-t\r
-\emph default\r
- for \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-top\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- this is done with the first line.\r
- When no position is given, the box will be vertically centered, see section\r
- \r
-\emph on\r
-Boxes\r
-\emph default\r
- of the \r
-\emph on\r
-Embedded\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Objects\r
-\emph default\r
- manual for examples.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-To frame formulas completely, including the formula number, the formula\r
- must be set into a parbox.\r
- To do this, the command \r
-\series bold\r
-\r
-\backslash\r
-fbox{\r
-\backslash\r
-parbox{\r
-\backslash\r
-linewidth-2\r
-\backslash\r
-fboxsep-2\r
-\backslash\r
-fboxrule}{\r
-\series default\r
- is inserted in TeX-mode before the formula.\r
- \r
-\series bold\r
-\r
-\backslash\r
-linewidth\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! L ! \r
-\backslash\r
-linewidth\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is hereby the line width set for the document.\r
- Because the frame is outside the parbox, 2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-times the frame separation and the frame thickness must be subtracted from\r
- the line width.\r
- As this is not automatically done by LyX due to a bug\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset CommandInset href\r
-LatexCommand href\r
-name "LyX-bug #4483"\r
-target "http://www.lyx.org/trac/ticket/4483"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, TeX-mode has to be used.\r
- To be able to multiply and subtract in arguments, the LaTeX-package \r
-\series bold\r
-calc\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-calc\r
-\series default\r
- is part of every LaTeX standard installation.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! calc\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- must be loaded in the LaTeX-preamble with the line\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage{calc}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Behind the formula both boxes are closed by entering \r
-\series bold\r
-}}\r
-\series default\r
- in TeX-mode.\r
- Here is an example:\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-fboxsep 5mm \r
-\backslash\r
-fboxrule 5mm\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-fbox{\r
-\backslash\r
-parbox{\r
-\backslash\r
-linewidth-2\r
-\backslash\r
-fboxsep-2\r
-\backslash\r
-fboxrule}{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{equation}\r
-\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-fboxrule 0.4pt \r
-\backslash\r
-fboxsep 3pt\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-As a parbox is used as the argument of \r
-\series bold\r
-\r
-\backslash\r
-fbox\r
-\series default\r
-, there is in this case no difference between \r
-\series bold\r
-\r
-\backslash\r
-fbox\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-boxed\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-Paragraph boxes are very useful to comment formulas directly.\r
- To do this, \r
-\series bold\r
-\r
-\backslash\r
-parbox\r
-\series default\r
- is used in combination with the command \r
-\series bold\r
-\r
-\backslash\r
-tag\r
-\series default\r
-.\r
- (more about \r
-\series bold\r
-\r
-\backslash\r
-tag\r
-\series default\r
- see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:User-defined-Numbering"\r
-\r
-\end_inset\r
-\r
-)\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-An example of a formula commented with \r
-\series bold\r
-\r
-\backslash\r
-parbox\r
-\series default\r
-:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-[5x-7b=3b\r
-\backslash\r
-tag*{\r
-\backslash\r
-parbox{5cm}{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-This is a description.\r
- It is distinctly separated from the formula and multiline.\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}}\r
-\backslash\r
-]\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Such a formula must be inserted completely in TeX-mode because LyX does\r
- not yet support the command \r
-\series bold\r
-\r
-\backslash\r
-parbox\r
-\series default\r
- in formulas.\r
- The formula is created with the following command sequence:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command \r
-\series bold\r
-\r
-\backslash\r
-[5x-7b=3b\r
-\backslash\r
-tag*\r
-\backslash\r
-{\r
-\backslash\r
-parbox{5cm}{\r
-\series default\r
- is inserted in TeX-mode.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-When the formula style \r
-\series bold\r
-Indented\r
-\series default\r
- is used, \r
-\series bold\r
-\r
-\backslash\r
-tag*\r
-\backslash\r
-{\r
-\series default\r
- can also be replaced by \r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\series default\r
-.\r
- (formula styles see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Formula-Styles"\r
-\r
-\end_inset\r
-\r
-)\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- Then the description follows as normal text and finally \r
-\series bold\r
-}}\r
-\backslash\r
-]\r
-\series default\r
- is inserted in TeX-mode.\r
- The commands \r
-\series bold\r
-\r
-\backslash\r
-[\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-]\r
-\series default\r
- hereby create a displayed formula.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The advantages of \r
-\series bold\r
-\r
-\backslash\r
-parbox\r
-\series default\r
- can be seen in this example that was \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-commented\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- using the mathematical textmode:\r
-\begin_inset Formula \r
-\[\r
-5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Operators\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Operators\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Big Operators\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Big-Operators"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Operators ! big\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Sums\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Integrals\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To be able to use all integral operators listed here, the option \r
-\family sans\r
-Use esint package automatically\r
-\family default\r
- must be set in the document settings under \r
-\family sans\r
-Math\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Options\r
-\family default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="11" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-int\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! I ! \r
-\backslash\r
-int\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\int$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-oint\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\oint$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ointctrclockwise\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\ointctrclockwise$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ointclockwise\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\ointclockwise$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sqint\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\sqint$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-fint\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
- \r
-\begin_inset Formula $\fint$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-landupint\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
- \r
-\begin_inset Formula $\landupint$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-landdownint\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
- \r
-\begin_inset Formula $\landdownint$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bigcap\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bigcap$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bigcup\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bigcup$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="11" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sum\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! S ! \r
-\backslash\r
-sum\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\sum$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-prod\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! P ! \r
-\backslash\r
-prod\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-vspace{4mm}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\prod$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-coprod\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\coprod$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bigodot\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bigodot$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bigotimes\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bigotimes$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bigoplus\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bigoplus$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bigwedge\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bigwedge$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bigvee\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bigvee$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bigsqcup\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bigsqcup$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-biguplus\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\biguplus$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-All big operators can also be inserted via the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/intop.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The operators are called big because they are bigger than the sometimes\r
- equal looking binary operators.\r
- All big operators can have limits as described in the next subsection.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For all integral operators there is a second version available, ending in\r
- \r
-\series bold\r
-op\r
-\series default\r
-: \r
-\series bold\r
-\r
-\backslash\r
-intop\r
-\series default\r
-, \r
-\series bold\r
-\r
-\backslash\r
-ointop\r
-\series default\r
- etc..\r
- These operators are different from \r
-\series bold\r
-\r
-\backslash\r
-int\r
-\series default\r
- etc.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-in the style the operator limits are displayed, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Operator-Limits"\r
-\r
-\end_inset\r
-\r
-.\r
- \r
-\end_layout\r
-\r
-\begin_layout Subsubsection*\r
-Advice for Integrals\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The letter \r
-\emph on\r
-d\r
-\emph default\r
- in an integral is an operator, that therefore has to be set upright.\r
- This is done by highlighting the \r
-\emph on\r
-d\r
-\emph default\r
- and using the keyboard shortcut \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "font-roman"\r
-\end_inset\r
-\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Font styles\r
-\series bold\r
- \r
-\series default\r
-see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Font-Styles"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- Finally the smallest space is inserted before the \r
-\emph on\r
-d\r
-\emph default\r
-, as this is usual for operators.\r
- An example:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-incorrect: \r
-\begin_inset Formula $\int A(x)dx$\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom HPhantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-in\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-correct: \r
-\begin_inset Formula $\int A(x)\,\mathrm{d}x$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For multiple integrals there are the following commands:\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-iint\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-oiint\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sqiint\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-iiint\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-iiiint\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dotsint\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Operator Limits\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Operator-Limits"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Operators ! Limits\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Limits are created by super- and subscripts:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="2" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-prod^\r
-\backslash\r
-infty\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-_0\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-A(x)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Limits of inline formulas are set right beside the operator.\r
- Limits in displayed formulas are set above or below the operator, except\r
- for integral limits.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To force that the limits are set beside the operator, the cursor is set\r
- directly behind the operator and the limits type is changed with the menu\r
- \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Change Limits Type\r
-\family default\r
- to \r
-\family sans\r
-\series bold\r
-Inline\r
-\family default\r
-\series default\r
- (shortcut \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "math-limits"\r
-\end_inset\r
-\r
-).\r
- An example:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The default limits type is this:\r
-\begin_inset Formula \r
-\[\r
-\sum_{x=0}^{\infty}\frac{1}{x^{2}}\r
-\]\r
-\r
-\end_inset\r
-\r
-This is how it looks when the limits type was changed to \r
-\family sans\r
-\series bold\r
-Inline\r
-\family default\r
-\series default\r
-:\r
-\begin_inset Formula \r
-\[\r
-\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\r
-\]\r
-\r
-\end_inset\r
-\r
-For integrals, except those ending with \r
-\series bold\r
-op\r
-\series default\r
- like \r
-\series bold\r
-\r
-\backslash\r
-intop\r
-\series default\r
-, \r
-\series bold\r
-\r
-\backslash\r
-ointop\r
-\series default\r
- etc., the limits are by default set beside the operator.\r
- But for multiple integrals the limits are often set below the operator.\r
- In the following example the limits type was therefore set to \r
-\series bold\r
-Display\r
-\series default\r
- and so set below the integrals:\r
-\begin_inset Formula \r
-\begin{equation}\r
-\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-To specify conditions for limits, the commands \r
-\series bold\r
-\r
-\backslash\r
-subarray\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! S ! \r
-\backslash\r
-subarray\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-substack\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! S ! \r
-\backslash\r
-substack\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- are used.\r
- To create for example this expression \r
-\begin_inset Formula \r
-\begin{equation}\r
-\sum_{\begin{subarray}{c}\r
-0<k<1000\\\r
-\\\r
-k\,\in\,\mathbb{N}\r
-\end{subarray}}^{n}k^{-2}\label{eq:substack}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-the following has to be done:\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-First the command \r
-\series bold\r
-\r
-\backslash\r
-sum\r
-\series default\r
-^\r
-\series bold\r
-n\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-_\r
-\series default\r
- is typed in.\r
- One is now in a blue box under the summation operator and insert there\r
- the command \r
-\series bold\r
-\r
-\backslash\r
-subarray\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-.\r
- The blue box is now within a purple box and now several lines can be written\r
- among each other.\r
- A new line is created by inserting a line break (\r
-\begin_inset Info\r
-type "shortcut"\r
-arg "newline-insert newline"\r
-\end_inset\r
-\r
-).\r
- When now\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-0<k<1000 Ctrl+Return\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series default\r
-is typed in, a new box appears below for the new line.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The alignment of the lines can be changed to left aligned with the \r
-\family sans\r
-table\r
-\family default\r
- \r
-\family sans\r
-toolbar\r
-\family default\r
- or the menu \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Rows &Columns\r
-\family default\r
-.\r
- To get right alignment, \r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
- is inserted at the beginning of the line.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command \r
-\series bold\r
-\r
-\backslash\r
-substack\r
-\series default\r
- is equivalent to \r
-\series bold\r
-\r
-\backslash\r
-subarray\r
-\series default\r
- with the difference that the lines are always centered.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-Like in formula \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:substack"\r
-\r
-\end_inset\r
-\r
- there can be too much space beside an operator, because the characters\r
- following the operator are set beside the limits.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To avoid this, the following macro can be used in the LaTeX-preamble:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-def\r
-\backslash\r
-clap#1{\r
-\backslash\r
-hbox to 0pt{\r
-\backslash\r
-hss #1\r
-\backslash\r
-hss}}\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\backslash\r
-def\r
-\backslash\r
-mathclap {\r
-\backslash\r
-mathpalette \r
-\backslash\r
-mathclapinternal}\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\backslash\r
-def\r
-\backslash\r
-mathclapinternal #1#2{\r
-\backslash\r
-clap{$\r
-\backslash\r
-mathsurround =0pt #1{#2}$}}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This defines the command \r
-\series bold\r
-\r
-\backslash\r
-mathclap\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! M ! \r
-\backslash\r
-mathclap\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- that sets the width of the limit to 0\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt.\r
- The command scheme is\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-mathclap{limit}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-where the limit can consist of several conditions.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Applied on formula \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:substack"\r
-\r
-\end_inset\r
-\r
-, one uses the command\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-sum_\r
-\backslash\r
-mathclap{\r
-\backslash\r
-substack\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-0<k<1000 Ctrl+Return\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-to create the lower limit.\r
- The summand is now directly behind the summation operator:\r
-\begin_inset Formula \r
-\[\r
-\sum_{\mathclap{\substack{0<k<1000\\\r
-\\\r
-k\,\in\,\mathbb{N}\r
-}\r
-}}^{n}k^{-2}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-How to use one limit for several operators is described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Self-defined-Operators"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Decoration for Operators\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Operators ! Decoration\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With the commands \r
-\series bold\r
-\r
-\backslash\r
-overset\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! O ! \r
-\backslash\r
-overset\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-underset\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! U ! \r
-\backslash\r
-underset\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- characters can be placed above or below an operator, respectively.\r
- With the command \r
-\series bold\r
-\r
-\backslash\r
-sideset\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! S ! \r
-\backslash\r
-sideset\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- characters can be set before and behind a big operator.\r
- The command scheme is:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-sideset{character\r
-\series default\r
- \r
-\series bold\r
-before}{character\r
-\series default\r
- \r
-\series bold\r
-behind}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-sideset\r
-\series default\r
- must always be before the operator.\r
- You can decorate with several characters and even with other operators\r
- and symbols.\r
- To place for example only characters behind a big operator, write nothing\r
- between the first braces but don't omit the braces.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For example the command \r
-\series bold\r
-\r
-\backslash\r
-sideset{\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{\r
-\series default\r
-'\r
-\series bold\r
-\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-sum_k=1\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-^\r
-\series bold\r
-n\r
-\series default\r
- produces:\r
-\begin_inset Formula \r
-\[\r
-\sideset{}{'}\sum_{k=1}^{n}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-Note: \r
-\backslash\r
-sideset\r
-\series default\r
- can only be used to decorate big operators, binary operators are not allowed.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-overset\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-underset\r
-\series default\r
- can also be used to decorate symbols and characters.\r
- For example, the command \r
-\series bold\r
-\r
-\backslash\r
-overset\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-maltese\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-\r
-\begin_inset Formula $\uparrow$\r
-\end_inset\r
-\r
-\r
-\series bold\r
-a\r
-\series default\r
- produces:\r
-\begin_inset Formula \r
-\[\r
-\overset{a}{\maltese}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Binary Operators\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Binary-Operators"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Operators ! binary\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Binary operators are surrounded by space when there is a character before\r
- and after them.\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="13" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-+\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $+$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
--\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-*\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\r
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-\begin_inset Text\r
-\r
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-\r
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-\r
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-\r
-\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
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-\r
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-\r
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-\r
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-\r
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-\begin_inset Text\r
-\r
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-\r
-\backslash\r
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-\r
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-\r
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-\r
-\r
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-\r
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-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
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-\r
-\r
-\begin_inset Tabular\r
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-\begin_inset Text\r
-\r
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-Command\r
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-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
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-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-nabla\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\nabla$\r
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-\r
-\r
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-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
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-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bigtriangledown$\r
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-\r
-\r
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-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
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-\r
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-\begin_inset Text\r
-\r
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-\begin_inset Formula $\bigtriangleup$\r
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-\r
-\r
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-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Box\r
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-\r
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Box$\r
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-\r
-\r
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-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-cap \r
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-\r
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\cap$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
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-\r
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\cup$\r
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-\r
-\r
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-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dagger\r
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-\r
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\dagger$\r
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-\r
-\r
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-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ddagger\r
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-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\ddagger$\r
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-\r
-\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-wr\r
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-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\wr$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bigcirc\r
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-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bigcirc$\r
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-\r
-\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-wedge\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\wedge$\r
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-\r
-\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-vee\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
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-\begin_inset Formula $\vee$\r
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-\r
-\r
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-\r
-\end_inset\r
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-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
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-\r
-\r
-\begin_inset Tabular\r
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-\begin_inset Text\r
-\r
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-Command\r
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-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
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-\r
-\end_inset\r
-</cell>\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-oplus\r
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-\r
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-\begin_inset Text\r
-\r
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-\begin_inset Formula $\oplus$\r
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-\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ominus\r
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-\r
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-\r
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-\r
-\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
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-\r
-\backslash\r
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-\r
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-\r
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-\r
-\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
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-\r
-\backslash\r
-oslash\r
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-\r
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-\begin_inset Text\r
-\r
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-\begin_inset Formula $\oslash$\r
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-\r
-\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
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-\r
-\backslash\r
-odot\r
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-\r
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-\begin_inset Text\r
-\r
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-\begin_inset Formula $\odot$\r
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-\r
-\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-amalg\r
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-\r
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-\r
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-\begin_inset Formula $\amalg$\r
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-\r
-\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
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-\r
-\backslash\r
-uplus\r
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-\r
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
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-\begin_inset Formula $\uplus$\r
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-\r
-\r
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-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
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-\r
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
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-\begin_inset Formula $\setminus$\r
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-\r
-\r
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-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sqcap\r
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-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\sqcap$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sqcup\r
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-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\sqcup$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-triangleleft\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\triangleleft$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-triangleright\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\triangleright$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-All binary operators can also be inserted via the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/pm.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To typeset the Laplace operator also \r
-\series bold\r
-\r
-\backslash\r
-Delta\r
-\series default\r
- or \r
-\series bold\r
-\r
-\backslash\r
-nabla\r
-\series default\r
-^\r
-\series bold\r
-2\r
-\series default\r
- (\r
-\begin_inset Formula $\nabla^{2}$\r
-\end_inset\r
-\r
-) can be used instead of \r
-\series bold\r
-\r
-\backslash\r
-bigtriangleup\r
-\series default\r
- .\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The character \r
-\family sans\r
-Menu Separator\r
-\family default\r
- from the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Special Character\r
-\family default\r
- is the operator \r
-\series bold\r
-\r
-\backslash\r
-triangleright\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Self-defined Operators\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Self-defined-Operators"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Operators ! self-defined\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With the help of the command \r
-\series bold\r
-\r
-\backslash\r
-DeclareMathOperator\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! D ! \r
-\backslash\r
-dbinom@\r
-\backslash\r
-DeclareMathOperator\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- custom operators can be defined in the LaTeX-preamble.\r
- Its command scheme is:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-DeclareMathOperator{new command}{display}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Display can be characters or symbols that define how the operator looks\r
- in the output.\r
- To define a big operator a * is set behind the command.\r
- All self-defined big operators can have limits as described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Operator-Limits"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For example the LaTeX-preamble line\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-DeclareMathOperator*{\r
-\backslash\r
-Lozenge}{\r
-\backslash\r
-blacklozenge}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-defines the command \r
-\series bold\r
-\r
-\backslash\r
-Lozenge\r
-\series default\r
-, that inserts a big operator consisting of the lozenge symbol from \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Miscellaneous-Symbols"\r
-\r
-\end_inset\r
-\r
-:\r
-\begin_inset Formula \r
-\[\r
-\Lozenge_{n=1}^{\infty}\r
-\]\r
-\r
-\end_inset\r
-\r
-The command for this formula is: \r
-\series bold\r
-\r
-\backslash\r
-Lozenge\r
-\series default\r
-^\r
-\series bold\r
-\r
-\backslash\r
-infty\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-_n=1\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-When self-defined operators are not used several times in the document,\r
- they can also be defined with the commands \r
-\series bold\r
-\r
-\backslash\r
-mathop\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! M ! \r
-\backslash\r
-mathop\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-mathbin\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! M ! \r
-\backslash\r
-mathbin\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, which have the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-mathop{display}\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-mathbin{display}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-mathop\r
-\series default\r
- defines big operators, \r
-\series bold\r
-\r
-\backslash\r
-mathbin\r
-\series default\r
- binary operators.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-mathop\r
-\series default\r
- can e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-be used to use one limit for several operators:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \r
-\[\r
-\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command for the formula above is:\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-mathop{\r
-\backslash\r
-sum\r
-\backslash\r
-negmedspace\r
-\backslash\r
-sum\r
-\series default\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-^N\r
-\series default\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series bold\r
-_i,j=1\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Fonts\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Fonts\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Font Styles\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Font-Styles"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Font ! style\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Latin letters in formulas can be set in one of the following font styles:\r
-\begin_inset VSpace -2mm\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="7" columns="3">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-shortcut\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mathbb\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-ABC\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mathbb{ABC}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Info\r
-type "shortcuts"\r
-arg "font-noun"\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mathbf\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-AbC\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mathbf{AbC}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Info\r
-type "shortcuts"\r
-arg "font-bold"\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-boldsymbol\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-AbC\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\boldsymbol{AbC}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Info\r
-type "shortcuts"\r
-arg "font-boldsymbol"\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mathcal\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-ABC\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mathcal{ABC}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Info\r
-type "shortcuts"\r
-arg "font-emph"\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mathfrak\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-AbC\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mathfrak{AbC}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
--\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mathscr\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-AbC\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mathscr{AbC}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
--\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="5" columns="3">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-shortcut\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mathit\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-AbC\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mathit{AbC}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
--\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mathrm\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-AbC\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mathrm{AbC}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Info\r
-type "shortcuts"\r
-arg "font-roman"\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mathsf\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-AbC\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mathsf{AbC}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Info\r
-type "shortcuts"\r
-arg "font-sans"\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mathtt\r
-\series bold\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-AbC\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mathtt{AbC}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Info\r
-type "shortcuts"\r
-arg "font-typewriter"\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-Note:\r
-\series default\r
- The styles \r
-\series bold\r
-\r
-\backslash\r
-mathbb\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-mathcal\r
-\series default\r
- can only be used for big letters.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Predefined is the style \r
-\series bold\r
-\r
-\backslash\r
-mathnormal\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The style commands work also for letters in mathematical constructs:\r
-\begin_inset Formula \r
-\[\r
-\mathfrak{A=\frac{b}{C}}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Characters in mathematical text don't appear in a math font style but in\r
- the text font style \r
-\series bold\r
-\r
-\backslash\r
-textrm\r
-\series default\r
-.\r
- That their style can't be set correctly via the text style dialog is a\r
- bug in LyX.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset CommandInset href\r
-LatexCommand href\r
-name "LyX-bug #4629"\r
-target "http://www.lyx.org/trac/ticket/4629"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Instead of the style commands the dialog \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Text Style\r
-\family default\r
- or the toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/font.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- can be used.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Bold Formulas\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Bold-Formulas"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! bold\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To make a complete formula bold, the command \r
-\series bold\r
-\r
-\backslash\r
-mathbf\r
-\series default\r
- from the previous subsection cannot be used, because it doesn't work for\r
- small Greek letters.\r
- Furthermore it prints Latin letters always upright, like in the following\r
- equation:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \r
-\[\r
-\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To display the formula correctly, the command \r
-\series bold\r
-\r
-\backslash\r
-boldsymbol\r
-\series default\r
- is used:\r
-\begin_inset Formula \r
-\[\r
-\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\r
-\]\r
-\r
-\end_inset\r
-\r
-It is also possible to set the formula in a \r
-\series bold\r
-boldmath environment\r
-\series default\r
-.\r
- This environment is created by inserting the command \r
-\series bold\r
-\r
-\backslash\r
-boldmath\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! B ! \r
-\backslash\r
-boldmath\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- in TeX-mode.\r
- To end the environment, the command \r
-\series bold\r
-\r
-\backslash\r
-unboldmath\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! U ! \r
-\backslash\r
-unboldmath\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is inserted in TeX-mode.\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-boldmath \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\[\r
-\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-unboldmath \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Colored Formulas\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! colored\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Formulas can be colored like normal text: Highlight a formula or a formula\r
- part and use the \r
-\family sans\r
-Text Style\r
-\family default\r
- dialog.\r
- Here is a formula in magenta:\r
-\begin_inset Formula \r
-\[\r
-{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-You can also define your own colors as described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Colored-Boxes"\r
-\r
-\end_inset\r
-\r
-.\r
- They can be used with the TeX code command \r
-\series bold\r
-\r
-\backslash\r
-textcolor\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! T ! \r
-\backslash\r
-textcolor\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- in the scheme\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-textcolor{color}{characters or formula}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The following example was colored completely dark green and partly red:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-textcolor{darkgreen}{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\[\r
-\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Due to a bug in LyX only complete formulas can be colored with self-defined\r
- colors.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset CommandInset href\r
-LatexCommand href\r
-name "LyX-bug #5269"\r
-target "http://www.lyx.org/trac/ticket/5269"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Font Sizes\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Font-Sizes"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Font ! size\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For characters in formulas there are, analog to characters in text, the\r
- following size commands:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-Huge\r
-\series default\r
-, \r
-\series bold\r
-\r
-\backslash\r
-huge\r
-\series default\r
-, \r
-\series bold\r
-\r
-\backslash\r
-LARGE\r
-\series default\r
-, \r
-\series bold\r
-\r
-\backslash\r
-Large\r
-\series default\r
-, \r
-\series bold\r
-\r
-\backslash\r
-large\r
-\series default\r
-, \r
-\series bold\r
-\r
-\backslash\r
-normalsize\r
-\series default\r
-, \r
-\series bold\r
-\r
-\backslash\r
-small\r
-\series default\r
-,\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-footnotesize\r
-\series default\r
-, \r
-\series bold\r
-\r
-\backslash\r
-scriptsize\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-tiny\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The size produced by the commands depends on the document font size, which\r
- corresponds to the command \r
-\series bold\r
-\r
-\backslash\r
-normalsize\r
-\series default\r
-.\r
- The other commands produce smaller or larger sizes than \r
-\series bold\r
-\r
-\backslash\r
-normalsize\r
-\series default\r
-.\r
- The font size can however not exceed a certain value.\r
- Is for example the document font size 12\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt, the command \r
-\series bold\r
-\r
-\backslash\r
-Huge\r
-\series default\r
- switches to the same size as \r
-\series bold\r
-\r
-\backslash\r
-huge\r
-\series default\r
-.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A size command is inserted in TeX-mode before the formula and sets the size\r
- for all following formula and text characters.\r
- To switch back to the initial size, the command \r
-\series bold\r
-\r
-\backslash\r
-normalsize\r
-\series default\r
- is inserted behind the formula in TeX-mode.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Within a formula the size can be changed using the following size commands:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\noindent\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="5" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-displaystyle\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! D ! \r
-\backslash\r
-displaystyle\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-textstyle\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-scriptstyle\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-scriptscriptstyle\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-After entering these commands, a blue box appears in which the formula parts\r
- are inserted.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-There is a further method to change the font size, that though only works\r
- for symbols or letters in mathematical text.\r
- To use it, one of the above text size commands is inserted in mathematical\r
- text.\r
- All following characters until the end of the mathematical text or until\r
- another size command will have the selected size.\r
- Two examples:\r
-\begin_inset VSpace -2mm\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-huge \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\[\r
-A=\frac{B}{c}\cdot\maltese\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\[\r
-\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-normalsize \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-Before both formulas the command \r
-\series bold\r
-\r
-\backslash\r
-huge\r
-\series default\r
- was inserted.\r
- The command for the second formula is:\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-maltese\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A Alt+M M \r
-\backslash\r
-Large\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-maltese\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-textit\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hspace*{}\r
-\length 1cm\r
-\end_inset\r
-\r
-Alt+M\r
-\series default\r
- \r
-\series bold\r
-M \r
-\backslash\r
-tiny\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-maltese\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-textit\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-If a symbol cannot be displayed in different sizes, it will always be displayed\r
- in the default size.\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Greek Letters\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Greek letters\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Greek letters can also be inserted via the toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/alpha.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
- All international typesetting norms purport that Greek letters in math\r
- have to be typeset italic/slanted.\r
- In some languages, like French or Russian, they are nevertheless sometimes\r
- typeset upright.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Small Letters\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Greek letters ! small\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="11" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-alpha\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\alpha$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-beta\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\beta$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-gamma\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\gamma$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-delta\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\delta$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-epsilon\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\epsilon$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-varepsilon\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\varepsilon$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-zeta\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\zeta$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-eta\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\eta$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-theta\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\theta$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-vartheta\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\vartheta$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="12" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-iota\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\iota$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-kappa\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\kappa$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-varkappa\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\varkappa$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-lambda\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\lambda$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mu\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mu$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-nu\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\nu$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-xi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\xi$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-o\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $o$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-pi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\pi$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-varpi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\varpi$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-rho\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\rho$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="11" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-varrho\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\varrho$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sigma\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\sigma$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-varsigma\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\varsigma$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-tau\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\tau$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-upsilon\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\upsilon$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-phi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\phi$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-varphi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\varphi$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-chi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\chi$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-psi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\psi$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-omega\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\omega$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-How to create special upright Greek letters is explained in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Upright-small-Greek"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Big Letters\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Greek letters ! big\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="7" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Gamma\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Gamma$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Delta\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Delta$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Theta\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Theta$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Lambda\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Lambda$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Xi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Xi$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Pi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Pi$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="6" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Sigma\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Sigma$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Upsilon\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Upsilon$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Phi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Phi$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Psi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Psi$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Omega\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Omega$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-That the big Greek letters appear upright is caused by a design bug when\r
- TeX was developed.\r
- To get correct italic big letters, begin every command with \r
-\series bold\r
-var\r
-\series default\r
-.\r
- For example the command \r
-\series bold\r
-\r
-\backslash\r
-varGamma\r
-\series default\r
- produces \r
-\begin_inset Formula $\varGamma$\r
-\end_inset\r
-\r
-.\r
- Another way is to load the package \r
-\series bold\r
-fixmath\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-fixmath\r
-\series default\r
- is part of the LaTeX-package \r
-\series bold\r
-was\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! was\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-vspace{4mm}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! fixmath\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- with the LaTeX-preamble line\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage{fixmath}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Then all big Greek letters in a document will automatically be typeset italic.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Bold Letters\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Greek letters ! bold\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Greek letters cannot be set with different font styles like Latin letters.\r
- They can only be made bold with the command \r
-\series bold\r
-\r
-\backslash\r
-boldsymbol\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! B ! \r
-\backslash\r
-boldsymbol\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="3" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Upsilon\r
-\backslash\r
-boldsymbol\r
-\backslash\r
-Upsilon\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-theta\r
-\backslash\r
-boldsymbol\r
-\backslash\r
-theta\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\theta\boldsymbol{\theta}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Symbols\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-texorpdfstring{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-A list with all symbols of most of the LaTeX-packages can be found in \r
-\begin_inset CommandInset citation\r
-LatexCommand cite\r
-key "Symbols"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}{}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.\r
-\end_layout\r
-\r
-\begin_layout Plain Layout\r
-More about \r
-\backslash\r
-texorpdfstring is in section \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Formulas-in-Section"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Symbols\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Many of the symbols listed in this section can also be inserted via the\r
- toolbar buttons \r
-\begin_inset Graphics\r
- filename ../images/math/nabla.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- and \r
-\begin_inset Graphics\r
- filename ../images/math/digamma.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Mathematical Symbols\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Mathematical-Symbols"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Symbols ! mathematical\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="10" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-neg\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\neg$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Im\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Im$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Re\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Re$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-aleph\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\aleph$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-partial\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\partial$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-infty\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\infty$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-wp\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\wp$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-imath\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\imath$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-jmath\r
-\end_layout\r
-\r
-\end_inset\r
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-\r
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-\r
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-\r
-\end_inset\r
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-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="10" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
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-\begin_inset Text\r
-\r
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-\r
-\end_inset\r
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-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-forall\r
-\end_layout\r
-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
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-\r
-\r
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-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-exists\r
-\end_layout\r
-\r
-\end_inset\r
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
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-\r
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-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
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-\end_layout\r
-\r
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-\r
-\begin_layout Plain Layout\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
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-\r
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\emptyset$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
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-\end_layout\r
-\r
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\varnothing$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dag\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\dag$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ddag\r
-\end_layout\r
-\r
-\end_inset\r
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-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\ddag$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
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-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-complement\r
-\end_layout\r
-\r
-\end_inset\r
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-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-raisebox{-0.8mm}{\r
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-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\complement$\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
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-\begin_layout Plain Layout\r
-\r
-}\r
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-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Bbbk\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Bbbk$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="10" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-prime\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\prime$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-backprime\r
-\end_layout\r
-\r
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\backprime$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
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-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-mho\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mho$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-triangle\r
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-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\triangle$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-angle\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\angle$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-measuredangle\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\measuredangle$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sphericalangle\r
-\end_layout\r
-\r
-\end_inset\r
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-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\sphericalangle$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-top\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\top$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bot\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bot$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Miscellaneous Symbols\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Miscellaneous-Symbols"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Symbols ! miscellaneous\r
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-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\noindent\r
-\align center\r
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-<lyxtabular version="3" rows="10" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
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-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-flat\r
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-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\flat$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-natural\r
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-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\natural$\r
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-\r
-\r
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-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sharp\r
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-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\sharp$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
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-\r
-\end_inset\r
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-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\surd$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
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-\r
-\end_inset\r
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-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\checkmark$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-yen\r
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-\r
-\end_inset\r
-</cell>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\yen$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-pounds\r
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-\r
-\end_inset\r
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-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\pounds$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-<row>\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-$\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\$$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
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-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-§\r
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-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $§$\r
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-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
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-\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="10" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-hbar\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\hbar$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-hslash\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\hslash$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-clubsuit\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\clubsuit$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-spadesuit\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\spadesuit$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bigstar\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bigstar$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-blacklozenge\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\blacklozenge$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-blacktriangle\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\blacktriangle$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-blacktiangledown\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\blacktriangledown$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bullet\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\bullet$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="10" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-diamondsuit\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\diamondsuit$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Diamond\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Diamond$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-heartsuit\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\heartsuit$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-P\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\P$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-copyright\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\copyright$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-circledR\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\circledR$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-maltese\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\maltese$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-diagup\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\diagup$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-diagdown\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\diagdown$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-More symbols are listed in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Miscellaneous-special-Characters"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Some symbols can be displayed in different sizes, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Font-Sizes"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-The Euro-Symbol €\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Symbols ! Euro-symbol\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-@\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-officialeuro\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To use the Euro symbol in formulas, the LaTeX-package \r
-\series bold\r
-eurosym\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! eurosym\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- must be installed and loaded with the LaTeX-preamble line\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage[gennarrow]{eurosym}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The Euro symbol can now be inserted with the command \r
-\series bold\r
-\r
-\backslash\r
-euro\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! E ! \r
-\backslash\r
-euro\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The Euro symbol can directly be inserted with the € key in mathematical\r
- text, without having \r
-\series bold\r
-eurosym\r
-\series default\r
- installed.\r
- When \r
-\series bold\r
-eurosym\r
-\series default\r
- is installed, \r
-\series bold\r
-\r
-\backslash\r
-euro\r
-\series default\r
- can also be inserted in TeX-mode.\r
- The official currency symbol can then be inserted with the command \r
-\series bold\r
-\r
-\backslash\r
-officialeuro\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! O ! \r
-\backslash\r
-officialeuro\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, that is only available in TeX-mode.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-ifeurosym \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-The following table will only be displayed when the LaTeX-package \r
-\series bold\r
-eurosym\r
-\series default\r
- is installed.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-An overview about the different Euro symbols:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="3">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command \r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-formula\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-euro\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\euro$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-mathematical text\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-€\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mbox{€}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-TeX-mode\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-officialeuro\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-officialeuro\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-else \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-The following will be displayed when the LaTeX-package \r
-\series bold\r
-eurosym\r
-\series default\r
- is not installed:\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-You need to install the LaTeX-package \r
-\series bold\r
-eurosym\r
-\series default\r
- to see the rest of this subsection in the output.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-fi \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Relations\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sec:Relations"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Relations\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Comparisons|see\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Relations\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-All relations can also be inserted via the toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/leq.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="17" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
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-\r
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-\r
-\r
-\begin_inset space \hfill{}\r
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-\r
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-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
->\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $>$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ge\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\ge$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-gg\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\gg$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-succ\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\succ$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-succeq\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\succeq$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-supset\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\supset$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-supseteq\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\supseteq$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sqsupseteq\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\sqsupseteq$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ni\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\ni$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dashv\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\dashv$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-frown\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\frown$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-rhd\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\rhd$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-unrhd\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\unrhd$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-lessgtr\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\lessgtr$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-parallel\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\parallel$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-nparallel\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\nparallel$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-The characters \r
-\series bold\r
-\r
-\backslash\r
-lhd\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-rhd\r
-\series default\r
- are bigger than the equal looking operators \r
-\series bold\r
-\r
-\backslash\r
-triangleleft\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-triangleright\r
-\series default\r
-, respectively.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Relations are, in contrary to symbols, always surrounded by space.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Relations with labels can be created with the command \r
-\series bold\r
-\r
-\backslash\r
-stackrel\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! S ! \r
-\backslash\r
-stackrel\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="2" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A(r)\r
-\backslash\r
-stackrel\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-r\r
-\backslash\r
-to\r
-\backslash\r
-infty\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-approx\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Functions\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Predefined Functions\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Predefined-Functions"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Functions ! predefined\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In general, variables are set \r
-\emph on\r
-italic\r
-\emph default\r
- in mathematical expressions, but not function names, because \r
-\begin_inset Formula $sin$\r
-\end_inset\r
-\r
- could be misunderstood as \r
-\begin_inset Formula $s\cdot i\cdot n$\r
-\end_inset\r
-\r
-.\r
- Therefore there are predefined functionswhich are additionally a bit separated\r
- from prefactors.\r
- They are inserted as commands starting with a backslash before their name.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="2" columns="4">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Asin(x)+B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $Asin(x)+B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A\r
-\backslash\r
-sin(x)+B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\sin(x)+B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The following functions are predefined:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace -2mm\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="9" columns="4">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sin\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sinh\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-arcsin\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sup\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-cos\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-cosh\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-arccos\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-inf\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-tan\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-tanh\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-arctan\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-lim\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-cot\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-coth\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-arg\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-liminf\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-sec\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-min\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-deg\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-limsup\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-csc\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-max\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-det\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Pr\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ln\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-exp\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dim\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-hom\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-lg\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-log\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ker\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-gcd\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-They can also be inserted with the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/functions.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Self-defined Functions\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Functions ! self-defined\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To use a function that is not predefined, like for example the sign function\r
- sgn(x), there are two possibilities:\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-Define the function by inserting the following line to the LaTeX-preamble\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-For more about \r
-\series bold\r
-\r
-\backslash\r
-DeclareMathOperator\r
-\series default\r
- see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Self-defined-Operators"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset VSpace -3mm\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-DeclareMathOperator{\r
-\backslash\r
-sgn}{sgn}\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! D ! \r
-\backslash\r
-dbinom@\r
-\backslash\r
-DeclareMathOperator\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset VSpace -2mm\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-Now the new defined function can be called with the command \r
-\series bold\r
-\r
-\backslash\r
-sgn\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-Write the formula as usual, mark the formula name, in our example the letters\r
- \r
-\emph on\r
-sgn\r
-\emph default\r
-, and change it to mathematical text.\r
- Finally, a space is inserted between prefactor and function.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The result is the same with both methods as with a predefined function\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-In LyX self-defined functions are displayed red, predefined ones black.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="3" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A\r
-\backslash\r
-sgn(x)+B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\sgn(x)+B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A\r
-\backslash\r
-,\r
-\begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$\r
-\end_inset\r
-\r
-(x)+B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\,\textrm{sgn}(x)+B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The first method is more suitable when the self-defined function should\r
- be used several times.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Limits\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Limits\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For limits, in addition to the commands \r
-\series bold\r
-\r
-\backslash\r
-lim\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! L ! \r
-\backslash\r
-lim\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, \r
-\series bold\r
-\r
-\backslash\r
-liminf\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-limsup\r
-\series default\r
- the following functions are defined:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="5" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-varliminf\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\varliminf$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-varlimsup\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\varlimsup$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-varprojlim\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\varprojlim$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-varinjlim\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\varinjlim$\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-The limit is created by inserting a subscript.\r
- It is set right beside the function in an inline formula:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="2" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset space \hspace{}\r
-\length 1cm\r
-\end_inset\r
-\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-The space and\r
-\series bold\r
- \r
-\backslash\r
-raisebox\r
-\series default\r
- are used here as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-lim_x\r
-\backslash\r
-to\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-x=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In a displayed formula the limit is set below the formula, as usual:\r
-\begin_inset Formula \r
-\[\r
-\lim_{x\to A}x=B\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Modulo-Functions\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Functions ! modulo-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The modulo-function is special, because it exists in four variants.\r
- The variants in a displayed formula are:\r
-\begin_inset Formula \r
-\begin{align*}\r
-\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\\r
-\mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\\r
-\mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\\r
-\mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\\r
-\mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\r
-\end{align*}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In an inline formula less space is set before the function names for all\r
- variants.\r
- By default the modulo-functions take only the first following character\r
- into account.\r
- To use more than one character, one has to put them into TeX-braces:\r
-\begin_inset Formula \r
-\begin{align*}\r
-\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\\r
-\mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\\r
-\mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d\r
-\end{align*}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Special Characters\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Special characters\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Special Characters in Mathematical Text\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The following commands can only be used in mathematical text or in TeX-mode:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="8" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="block" valignment="top">\r
-<column alignment="block" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-oe\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{œ}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-OE\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{Œ}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ae\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{æ}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-AE\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{Æ}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-aa\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{\aa}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-AA\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-@\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-textrm{\r
-\backslash\r
-AA}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{Å}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-i\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{ı}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="8" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="block" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-command\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-The space of 0\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm is used for separation, because otherwise the output will be ¡ and ¿\r
- respectively.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-o\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{ø}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-O\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{Ø}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-l\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{ł}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-L\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{Ł}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-!\r
-\begin_inset space \hspace{}\r
-\length 0mm\r
-\end_inset\r
-\r
-`\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{!`}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-?\r
-\begin_inset space \hspace{}\r
-\length 0mm\r
-\end_inset\r
-\r
-`\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{?`}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-j\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\textrm{ȷ}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The characters \r
-\begin_inset Formula $\textrm{\textrm{Å}}$\r
-\end_inset\r
-\r
- and \r
-\begin_inset Formula $\textrm{\textrm{Ø}}$\r
-\end_inset\r
-\r
- can also be inserted via the math toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math/digamma.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-An exception are the commands \r
-\series bold\r
-!\r
-\begin_inset space \hspace{}\r
-\length 0mm\r
-\end_inset\r
-\r
-`\r
-\series default\r
- and \r
-\series bold\r
-?\r
-\begin_inset space \hspace{}\r
-\length 0mm\r
-\end_inset\r
-\r
-`\r
-\series default\r
-, because they can be inserted in LyX directly to text.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Accents in Text\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Accents-in-Text"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Accents ! in text\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With the following commands all letters can be accented.\r
- The commands must be inserted in TeX-mode.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="8" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="block" valignment="top">\r
-<column alignment="block" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-\r
-\begin_inset Quotes grd\r
-\end_inset\r
-\r
-e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-"e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-`e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-`e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-^\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-^e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-=e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-=e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-u\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-u e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-b\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-b e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-t\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-ee\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-t ee\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="8" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="block" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-H\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-H e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-'e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-'e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-~e\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Tilde\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-~e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-.e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-.e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-v\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-v e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-d\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-d e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-c\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-e\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-c e\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-With the command \r
-\series bold\r
-\r
-\backslash\r
-t\r
-\series default\r
- also two different characters can be accented.\r
- The command \r
-\series bold\r
-\r
-\backslash\r
-t\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-sz\r
-\series default\r
- creates: \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-t sz\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The accents \r
-\series bold\r
-`\r
-\series default\r
- , \r
-\series bold\r
-'\r
-\series default\r
- and \r
-\series bold\r
-^\r
-\series default\r
- can in combination with vowels directly be inserted with the keyboard without\r
- using TeX-mode.\r
- The same applies for the tilde\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-This only applies for keyboards where the tilde is defined as accent.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- \r
-\series bold\r
-~\r
-\series default\r
- in combination with \r
-\emph on\r
-a\r
-\emph default\r
- , \r
-\emph on\r
-n\r
-\emph default\r
- , or \r
-\emph on\r
-o\r
-\emph default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The commands \r
-\series bold\r
-\r
-\backslash\r
-b\r
-\series default\r
- , \r
-\series bold\r
-\r
-\backslash\r
-c\r
-\series default\r
- , \r
-\series bold\r
-\r
-\backslash\r
-d\r
-\series default\r
- , \r
-\series bold\r
-\r
-\backslash\r
-H\r
-\series default\r
- , \r
-\series bold\r
-\r
-\backslash\r
-t\r
-\series default\r
- , \r
-\series bold\r
-\r
-\backslash\r
-u\r
-\series default\r
- , \r
-\series bold\r
-\r
-\backslash\r
-v\r
-\series default\r
- and accents that are inserted directly with the keyboard are also available\r
- in mathematical text.\r
- For the other accents there are special math commands to be used in formulas,\r
- see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Accents-for-one"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-Furthermore, with the command \r
-\series bold\r
-\r
-\backslash\r
-textcircled\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! T ! \r
-\backslash\r
-textcircled\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- all numbers and letters can be set into a circle, quasi accented with a\r
- circle, similar to the copyright symbol.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="3" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-textcircled{w}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-textcircled{w}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Large \r
-\backslash\r
-textcircled{\r
-\backslash\r
-normalsize\r
-\backslash\r
-protect\r
-\backslash\r
-raisebox{-1.5pt}{W}}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Large \r
-\backslash\r
-textcircled{\r
-\backslash\r
-normalsize\r
-\backslash\r
-protect\r
-\backslash\r
-raisebox{-1.5pt}W}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-One has to take care that the character fits in the circle.\r
- \r
-\series bold\r
-\r
-\backslash\r
-Large\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Font-Sizes"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- specifies thereby the size of the circle.\r
- With the help of \r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Boxes-without-Frame"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- the character can be centered.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Old-style Figures\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Old-style Figures\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Old-style figures (also known as old-style numerals) are created with the\r
- command \r
-\series bold\r
-\r
-\backslash\r
-oldstylenums\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! O ! \r
-\backslash\r
-oldstylenums\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- The command can be used in formulas and in TeX-mode.\r
- The command scheme is:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-oldstylenums{number}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command \r
-\series bold\r
-\r
-\backslash\r
-oldstylenums{0123456789\r
-\series default\r
- produces: \r
-\begin_inset Formula $\oldstylenums{0123456789}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Miscellaneous special Characters\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Miscellaneous-special-Characters"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Special characters ! miscellaneous\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The following characters can only be inserted to formulas by using commands:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-^\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\mathcircumflex$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-_\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\_$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-^\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-circ\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-@°\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $^{\circ}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble\r
- contains the following line\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-More about this is described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Text-Characters-in"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-DeclareInputtext{176}{\r
-\backslash\r
-ifmmode^\r
-\backslash\r
-circ\r
-\backslash\r
-else\r
-\backslash\r
-textdegree\r
-\backslash\r
-fi}\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Formula Styles\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sec:Formula-Styles"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! styles\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-There are two different alignment styles:\r
-\end_layout\r
-\r
-\begin_deeper\r
-\begin_layout Description\r
-Centered is the predefined standard\r
-\end_layout\r
-\r
-\begin_layout Description\r
-Indented for this the option \r
-\series bold\r
-fleqn\r
-\series default\r
- must be inserted in the menu \r
-\family sans\r
-Document\SpecialChar \menuseparator\r
-Settings\r
-\family default\r
- under \r
-\family sans\r
-Document\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Class\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When \r
-\series bold\r
-Indented\r
-\series default\r
- is used, the indentation can be adjusted with the length \r
-\series bold\r
-\r
-\backslash\r
-mathindent\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! M ! \r
-\backslash\r
-mathindent\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- Should the distance be 15\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm, the following command line is inserted in the LaTeX-preamble\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-mathindent}{15mm}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When no length is specified, the predefined value of 30\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt will be used.\r
-\end_layout\r
-\r
-\end_deeper\r
-\begin_layout Itemize\r
-And two different numbering styles:\r
-\end_layout\r
-\r
-\begin_deeper\r
-\begin_layout Description\r
-Right is the predefined standard\r
-\end_layout\r
-\r
-\begin_layout Description\r
-Left for this the option \r
-\series bold\r
-leqno\r
-\series default\r
- must be inserted in the menu \r
-\family sans\r
-Document\SpecialChar \menuseparator\r
-Settings\r
-\family default\r
- under \r
-\family sans\r
-Document\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Class\r
-\end_layout\r
-\r
-\end_deeper\r
-\begin_layout Standard\r
-\r
-\series bold\r
-fleqn\r
-\series default\r
- and \r
-\series bold\r
-leqno\r
-\series default\r
- can also be used together.\r
- In this case both options are inserted, separated by a comma.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The chosen styles are used for all displayed formulas of the document.\r
- When both, centered and indented formulas should be created in a document,\r
- the style \r
-\series bold\r
-Centered\r
-\series default\r
- is used.\r
- The indented formulas are then set in a flalign environment, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Flalign-Environment"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Multiline Formulas\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sec:Multiline-Formulas"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! multiline\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-General\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In LyX multiline formulas are created by pressing \r
-\series bold\r
-\r
-\begin_inset Info\r
-type "shortcut"\r
-arg "newline-insert newline"\r
-\end_inset\r
-\r
-\r
-\series default\r
- inside a formula.\r
- This creates either an \r
-\series bold\r
-eqnarray environment\r
-\series default\r
- that is described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Eqnarray-Environment"\r
-\r
-\end_inset\r
-\r
- or, when the option \r
-\family sans\r
-Use AMS math package\r
-\family default\r
- in the document settings is selected, an \r
-\series bold\r
-align environment\r
-\series default\r
- that is described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Standard-align-Environment"\r
-\r
-\end_inset\r
-\r
-.\r
- The align environment is recommended because it provides in any case a\r
- typographically correct output.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-There are other multiline formula environments that can be created via the\r
- menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Math\r
-\family default\r
-.\r
- These environments are described in the following sections.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In all multiline formula environments a new line is created by pressing\r
- \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "newline-insert newline"\r
-\end_inset\r
-\r
-.\r
- To add or delete lines, the math toolbar buttons \r
-\begin_inset Graphics\r
- filename ../images/tabular-feature_append-row.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- or \r
-\begin_inset Graphics\r
- filename ../images/tabular-feature_delete-row.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-, respectively, or the menu \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Rows & Columns\r
-\family default\r
- can be used.\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Line Separation\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Line-Separation"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! multiline ! Line separation\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-There is sometimes not enough space in multiline formulas between the lines:\r
-\begin_inset Formula \r
-\begin{eqnarray*}\r
-B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\\r
-4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0\r
-\end{eqnarray*}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In LaTeX additional line space is specified as optional argument of the\r
- new line command.\r
- This is not yet possible in LyX\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-see \r
-\begin_inset CommandInset href\r
-LatexCommand href\r
-name "LyX-bug #1505"\r
-target "http://www.lyx.org/trac/ticket/1505"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, therefore the whole formula must be inserted in TeX-mode.\r
- To add in our example space, the command \r
-\series bold\r
-\r
-\backslash\r
-\r
-\backslash\r
-[3mm]\r
-\series default\r
- is inserted at the end of the first line.\r
- One gets: \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-begin{eqnarray*}\r
-\end_layout\r
-\r
-\begin_layout Plain Layout\r
-\r
-B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &\r
- = & \r
-\backslash\r
-textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\r
-\backslash\r
-\r
-\backslash\r
-[3mm]\r
-\end_layout\r
-\r
-\begin_layout Plain Layout\r
-\r
-4x^{2}\r
-\backslash\r
-left(B^{2}+x_{0}^{2}\r
-\backslash\r
-right)+4x_{0}x\r
-\backslash\r
-left(D-B^{2}\r
-\backslash\r
-right)+B^{2}\r
-\backslash\r
-left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\r
-\backslash\r
-right) & = & 0\r
-\end_layout\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-end{eqnarray*}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-To set the line separation for all lines in a formula, the length \r
-\series bold\r
-\r
-\backslash\r
-jot\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! J ! \r
-\backslash\r
-jot\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is changed.\r
- The definition is: \r
-\begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$\r
-\end_inset\r
-\r
-.\r
- Predefined for \r
-\series bold\r
-\r
-\backslash\r
-jot\r
-\series default\r
- is the value 3\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt.\r
- To create 3\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm additional line separation as in the previous example, the command\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-jot}{3mm+3pt}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-is inserted in TeX-mode before the formula.\r
- This requires that the LaTeX-package \r
-\series bold\r
-calc\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-calc\r
-\series default\r
- is part of every LaTeX standard installation.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! calc\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- was loaded in LaTeX-preamble with the line\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage{calc}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-One gets: \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-jot}{3mm+3pt}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{eqnarray*}\r
-B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\\r
-4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0\r
-\end{eqnarray*}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-jot}{3pt}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- To get back to the predefined distance, \r
-\series bold\r
-\r
-\backslash\r
-jot\r
-\series default\r
- is set to the value 3\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt.\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Column Separation\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Column-Separation"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! multiline ! Column separation\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Multiline formulas form a matrix.\r
- A formula in the eqnarray environment is for example a matrix with three\r
- columns.\r
- By changing the column separation in this environment, the space beside\r
- the relation sign can be changed.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The column separation is specified with the length \r
-\series bold\r
-\r
-\backslash\r
-arraycolsep\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! A ! \r
-\backslash\r
-arraycolsep\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- according to:\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-column separation = 2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-arraycolsep\r
-\series default\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-Thus, the command\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-arraycolsep}{1cm}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-inserted in TeX-mode, sets for all following formulas a column separation\r
- of 2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-cm.\r
- To get back to the predefined distance, \r
-\series bold\r
-\r
-\backslash\r
-arraycolsep\r
-\series default\r
- is set to 5\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A formula with 2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-cm column separation:\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-arraycolsep}{1cm}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{eqnarray*}\r
-A & = & B\\\r
-C & \ne & A\r
-\end{eqnarray*}\r
-\r
-\end_inset\r
-\r
-A formula with the predefined column separation for matrices of 10\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt:\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-arraycolsep}{5pt}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{eqnarray*}\r
-A & = & B\\\r
-C & \ne & A\r
-\end{eqnarray*}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Long Formulas\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! long\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Long formulas can be typeset using these methods:\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-When one side of the equation is much shorter than the line width, this\r
- one is chosen for the left side and the right side is typeset over two\r
- lines:\r
-\begin_inset Formula \r
-\begin{eqnarray}\r
-H & = & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\nonumber \\\r
- & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:shortlong}\r
-\end{eqnarray}\r
-\r
-\end_inset\r
-\r
-The minus sign at the beginning of the second line does normally not appear\r
- as an operator because it is the first character of the line.\r
- Thus it would not be surrounded by space and could not be distinguished\r
- from the fraction bar.\r
- To avoid this, 3\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt space was inserted behind the minus sign with the command \r
-\series bold\r
-\r
-\backslash\r
-hspace\r
-\series default\r
-.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-for more about \r
-\series bold\r
-\r
-\backslash\r
-hspace\r
-\series default\r
- see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Variable-Space"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! H ! \r
-\backslash\r
-hspace\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-When both sides of the equation are too long, the command \r
-\series bold\r
-\r
-\backslash\r
-lefteqn\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! L ! \r
-\backslash\r
-lefteqn\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is used.\r
- It is inserted in the first column of the first line and causes all further\r
- insertions to overwrite the following columns:\r
-\begin_inset Formula \r
-\begin{eqnarray}\r
-\lefteqn{4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}}\nonumber \\\r
- & & -\hspace{3pt}B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\nonumber \\\r
- & & =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\label{eq:lefteqn}\r
-\end{eqnarray}\r
-\r
-\end_inset\r
-\r
-After the insertion of \r
-\series bold\r
-\r
-\backslash\r
-lefteqn\r
-\series default\r
-, the cursor is in a purple box that is a bit shifted to the left from the\r
- blue one.\r
- In this the formula is inserted.\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-The content of the further lines is inserted to the second or another formula\r
- column.\r
- The greater the column number where it was inserted, the larger the indentation.\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-Note the following when using \r
-\series bold\r
-\r
-\backslash\r
-lefteqn\r
-\series default\r
-:\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-The formula doesn't use the full page width.\r
- When e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-the term \r
-\begin_inset Formula $-B^{2}$\r
-\end_inset\r
-\r
- is added to the first line in the above example, it would have been outside\r
- the page margin.\r
- To better use the width, negative space can be inserted at the beginning\r
- of the first line.\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-Due to a bug in LyX the cursor cannot be set with the mouse into the first\r
- line.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset CommandInset href\r
-LatexCommand href\r
-name "LyX-bug #1429"\r
-target "http://www.lyx.org/trac/ticket/1429"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- One can only set the cursor at the beginning of the line and move it with\r
- the arrow keys.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-Other methods to set long formulas are offered by the environments described\r
- in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Multline-Environment"\r
-\r
-\end_inset\r
-\r
- and \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Multiline-Formula-Parts"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Multiline Brackets\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Multiline-Brackets"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Brackets ! for multiline expressions\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For brackets spanning multiple lines the following problem occurs:\r
-\begin_inset Formula \r
-\begin{eqnarray*}\r
-A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\\r
- & & \left.\cdots+B-D\right]\r
-\end{eqnarray*}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The closing bracket is smaller than the opening bracket because brackets\r
- with variable size may not span multiple lines.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To set the bracket size for the second line correctly, the first line is\r
- ended with \r
-\series bold\r
-\r
-\backslash\r
-right.\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! R ! \r
-\backslash\r
-right\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and the second line with \r
-\series bold\r
-\r
-\backslash\r
-left.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-for more about \r
-\series bold\r
-\r
-\backslash\r
-left\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-right\r
-\series default\r
- see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Automatic-Bracket-Size"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! L ! \r
-\backslash\r
-left\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- After \r
-\series bold\r
-\r
-\backslash\r
-left.\r
-\r
-\series default\r
- the command \r
-\series bold\r
-\r
-\backslash\r
-vphantom\r
-\series default\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-prod\r
-\series default\r
-^\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-infty\r
-\series default\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-_R=1}\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! V ! \r
-\backslash\r
-vphantom\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is inserted, because the multiplication operator with its limits is the\r
- largest symbol in the first line and this should be the size for the bracket\r
- in the second line.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The result is this:\r
-\begin_inset Formula \r
-\begin{eqnarray*}\r
-A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\\r
- & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\r
-\end{eqnarray*}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Align Environments\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Align environments can be used for every kind of multiline formulas.\r
- They are especially useful to set several formulas side by side.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Align environments consist of columns.\r
- The odd columns are right aligned, the even ones left aligned.\r
- Every line in an Align environment can be numbered.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Align environments are created via the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Math\r
-\family default\r
-.\r
- With the menu \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Change Formula Type\r
-\family default\r
- already existing formulas can be converted to Align environments.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To add or delete columns, the math toolbar buttons \r
-\begin_inset Graphics\r
- filename ../images/tabular-feature_append-column.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
- or \r
-\begin_inset Graphics\r
- filename ../images/tabular-feature_delete-column.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-, respectively, or the menu \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Rows & Columns\r
-\family default\r
- can be used.\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Standard align Environment\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Standard-align-Environment"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! multiline ! align environment\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This Align environment is created by pressing \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "newline-insert newline"\r
-\end_inset\r
-\r
- in a formula or by the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-AMS align Environment\r
-\family default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-An example for two formulas set side by side, that are created with a four\r
- column align environment:\r
-\begin_inset Formula \r
-\begin{align*}\r
-A & =\sin(B) & C & =D\\\r
-C & \ne A & B & \ne D\r
-\end{align*}\r
-\r
-\end_inset\r
-\r
-As it can be seen, the formulas in this environment are placed so as if\r
- there would be a \r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-more about \r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\series default\r
- see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Variable-Space"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
- before the first and after every even column.\r
- When the formula style \r
-\series bold\r
-Indented\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-formula styles see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Formula-Styles"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
- is used, the formula is set without the \r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\series default\r
- before the first column.\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Alignat Environment\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! multiline ! alignat environment\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The alignat environment has no predefined column separation.\r
- It can be inserted manually with the spaces that are described \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Space"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The above example in the alignat environment where 1\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-cm space was inserted at the beginning of the second formula:\r
-\begin_inset Formula \r
-\begin{alignat*}{2}\r
-A & =\sin(B) & \hspace{1cm}C & =D\\\r
-C & \ne A & B & \ne D\r
-\end{alignat*}\r
-\r
-\end_inset\r
-\r
-Because the column separation can be set separately for every column, this\r
- environment is especially suitable to set three and more formulas side\r
- by side.\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Flalign Environment\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Flalign-Environment"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! multiline ! flalign environment\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In this environment the first two columns are always set as much as possible\r
- to the left and the last two ones to the right.\r
- An example:\r
-\begin_inset Formula \r
-\begin{flalign*}\r
-A & =1 & B & =2 & C & =3\\\r
-X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\r
-\end{flalign*}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-By creating a flalign environment with an odd number of columns where an\r
- empty TeX-brace is inserted to the last column, several formulas in a document\r
- can be set to the left, although the formula style \r
-\series bold\r
-Centered\r
-\series default\r
- is used.\r
- As example the indented formula \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:VolInt"\r
-\r
-\end_inset\r
-\r
-:\r
-\begin_inset Formula \r
-\begin{flalign}\r
-\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\r
-\end{flalign}\r
-\r
-\end_inset\r
-\r
-The first two columns contain the formula.\r
- To indent it as with the formula style \r
-\series bold\r
-Indented\r
-\series default\r
-, 30\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt space was inserted at the beginning of the first column.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Eqnarray Environment\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Eqnarray-Environment"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! multiline ! eqnarray environment\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When this environment has been created, three blue boxes appear.\r
- The content of the first box is right aligned, the content of the last\r
- one left aligned.\r
- The content of the middle box appears centered and a bit smaller, because\r
- it is designed to insert there only relation characters.\r
-\begin_inset Formula \r
-\begin{eqnarray*}\r
-\frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\\r
-AB & AB & AB\\\r
-A & = & A\r
-\end{eqnarray*}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Gather Environment\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! multiline ! gather environment\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This environment consists of only one centered column.\r
- Every line can be numbered.\r
-\begin_inset Formula \r
-\begin{gather}\r
-A=1\\\r
-X=\textrm{-}1\r
-\end{gather}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Multline Environment\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Multline-Environment"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! multiline ! multline environment\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The multline environment consists, like the gather environment, of only\r
- one column.\r
- But the first line is left aligned, the last one right aligned.\r
- All other lines are centered.\r
- Therefore this environment is suitable for long formulas.\r
- As example formula \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:lefteqn"\r
-\r
-\end_inset\r
-\r
- in the multline environment:\r
-\begin_inset Formula \r
-\begin{multline}\r
-4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\\r
--B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\\\r
-=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\r
-\end{multline}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In the output only the last (first) line of a multline environment appears\r
- numbered when the document numbering is right (left).\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-numbering styles see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Formula-Styles"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With the commands \r
-\series bold\r
-\r
-\backslash\r
-shoveright\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! S ! \r
-\backslash\r
-shoveright\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- and \r
-\series bold\r
-\r
-\backslash\r
-shoveleft\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! S ! \r
-\backslash\r
-shoveleft\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- a centered line can be right or left aligned, respectively.\r
- The commands are used as follows:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-shoveright{line content}\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-shoveleft{line content}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-The length \r
-\series bold\r
-\r
-\backslash\r
-multlinegap\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! M ! \r
-\backslash\r
-multlinegap\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- specifies the distance of the first line from the left page margin.\r
- Predefined is the length 0\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-As example the above formula where the command\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-multlinegap}{2cm}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-was inserted in TeX-mode before:\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-multlinegap}{2cm}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{multline}\r
-4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\\r
-\shoveleft{-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}\\\r
-=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\r
-\end{multline}\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-setlength{\r
-\backslash\r
-multlinegap}{0pt}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-The second line was left aligned using \r
-\series bold\r
-\r
-\backslash\r
-shoveleft\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Multiline Formula Parts\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Multiline-Formula-Parts"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! multiline ! formula parts\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To display only parts of a formula with multiple lines, one of the following\r
- environments is used: \r
-\series bold\r
-aligned\r
-\series default\r
-, \r
-\series bold\r
-alignedat\r
-\series default\r
-, \r
-\series bold\r
-gathered\r
-\series default\r
- or \r
-\series bold\r
-split\r
-\series default\r
-.\r
- They can be inserted via the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Math\r
-\family default\r
- or by using the commands described in this section.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The first three have the same properties as the corresponding multiline\r
- formula environments, but it is possible to set further formula parts beside\r
- them.\r
- An example:\r
-\begin_inset Formula \r
-\[\r
-\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\\r
-\Delta E\Delta t & \ge\frac{\hbar}{2}\r
-\end{aligned}\r
-\right\} \textrm{Uncertainty relations}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To get this formula, a displayed formula is created where the command \r
-\series bold\r
-\r
-\backslash\r
-aligned\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! A ! \r
-\backslash\r
-aligned\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is inserted.\r
- A purple box appears around the blue formula box where now columns and\r
- lines can be added.\r
- Outside the multiline environment other formula parts can be set, like\r
- the brace.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The aligned environment is also suitable for long formulas whose lines are\r
- horizontally aligned.\r
- Using aligned in a displayed formula has the advantage that the formula\r
- number is vertically centered behind the lines.\r
- As example formula \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:shortlong"\r
-\r
-\end_inset\r
-\r
- in the aligned environment:\r
-\begin_inset Formula \r
-\begin{equation}\r
-\begin{aligned}H=\; & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\\\r
- & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\r
-\end{aligned}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To use the environments \r
-\series bold\r
-alignedat\r
-\series default\r
-, \r
-\series bold\r
-gathered\r
-\series default\r
-, or \r
-\series bold\r
-split\r
-\series default\r
-, the command \r
-\series bold\r
-\r
-\backslash\r
-alignedat\r
-\series default\r
-,\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! A ! \r
-\backslash\r
-alignedat\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- \r
-\series bold\r
-\r
-\backslash\r
-gathered\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! G ! \r
-\backslash\r
-gathered\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, or \r
-\series bold\r
-\r
-\backslash\r
-split\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! S ! \r
-\backslash\r
-split\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- are inserted, respectively.\r
- The split environment has the same properties as the aligned environment\r
- but it can only have two columns.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Text in multiline Formulas\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Text-in-multiline"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Text ! in formulas\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! multiline ! text\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In the Align environments, and the multline and gather environment, text\r
- can be inserted that will appear in a separate line and doesn't affect\r
- the column alignment.\r
- To do this, the command \r
-\series bold\r
-\r
-\backslash\r
-intertext\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! I ! \r
-\backslash\r
-intertext\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is used in the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-intertext{text}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The text should not be longer than a line because it cannot be hyphenated.\r
- As LyX doesn't yet support \r
-\series bold\r
-\r
-\backslash\r
-intertext\r
-\series default\r
- directly, the text is written as mathematical text.\r
- \r
-\series bold\r
-\r
-\backslash\r
-intertext\r
-\series default\r
- must hereby be at the beginning of a line and appears in the output above\r
- this line.\r
- An example where the text was inserted at the beginning of the second line:\r
-\begin_inset Formula \r
-\begin{align}\r
-I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\\r
-\intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\r
-\end{align}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Formula Numbering\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula numbering\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! numbering|see\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Formula numbering\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-General\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Numbered formulas can be created with the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Numbered\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Formula\r
-\family default\r
- (shortcut \r
-\family sans\r
-Ctrl+Alt\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-N\r
-\family default\r
-).\r
- Existing formulas can be numbered with the menu \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Toggle\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Numbering\r
-\family default\r
- (shortcut \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "math-number-toggle"\r
-\end_inset\r
-\r
-).\r
- The formula number is displayed in LyX behind the formula as a number sign\r
- in parentheses.\r
- The number sign is replaced in the output by the formula number.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When numbering is turned on in multiline formulas, all lines will be numbered.\r
- But the numbering can be controlled with the menu \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Toggle\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Numbering\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-of\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Line\r
-\family default\r
- (shortcut \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "math-number-line-toggle"\r
-\end_inset\r
-\r
-) for every line.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Except for inline formulas, all formulas can be numbered with two different\r
- styles, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Formula-Styles"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Cross-References\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Cross-references ! to formulas\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-All labeled formulas can be cross-referenced.\r
- A label is added by the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Label\r
-\family default\r
- or the toolbar button \r
-\begin_inset Graphics\r
- filename ../images/label-insert.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
- The cursor must hereby be inside a displayed formula.\r
- Alternatively you can right-click on the formula and choose \r
-\family sans\r
-Equation Label\r
-\family default\r
-.\r
- A dialog pops up displaying the prefix \r
-\series bold\r
-eq:\r
-\series default\r
- in a text field.\r
- The label is inserted there behind the prefix.\r
- The predefined prefix means \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-equation\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- and makes it easier to find labels in large documents because it marks\r
- it as formula label to divide it from e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-section labels.\r
- To change a label, the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Label\r
-\family default\r
- is used again or you right-click on a formula and then on \r
-\family sans\r
-Equation Label\r
-\family default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The name of the label is displayed in LyX within two parentheses behind\r
- formula.\r
- A formula with a label is always numbered.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Cross-references are inserted via the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Cross-Reference\r
-\family default\r
- or with the toolbar button \r
-\begin_inset Graphics\r
- filename ../images/dialog-show-new-inset_ref.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
- A formula cross-reference appears in the output as formula number.\r
- When in the cross-reference dialog window the format \r
-\series bold\r
-(<reference>)\r
-\series default\r
- is chosen, the cross-reference appears in the output as formula number\r
- in parentheses.\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-By right-clicking on a cross-reference in LyX, one jumps to the formula\r
- that is referenced.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Here are as examples cross-references to formulas of the following subsections:\r
-\begin_inset Note Note\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-Note the different cross-reference types.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The equations \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:tag"\r
-\r
-\end_inset\r
-\r
- and \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:c"\r
-\r
-\end_inset\r
-\r
- are equivalent.\r
- In (\r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "eq:Lat"\r
-\r
-\end_inset\r
-\r
-) big Latin letters are used for the numbering in contrary to (\r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "eq:Rom"\r
-\r
-\end_inset\r
-\r
-).\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-When the argument of \r
-\series bold\r
-\r
-\backslash\r
-tag\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-tag\r
-\series default\r
- is described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:User-defined-Numbering"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
- contains a box like in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Paragraph-Boxes"\r
-\r
-\end_inset\r
-\r
-, the formula cannot be referenced.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Subnumbering\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula numbering ! subnumbering\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With the help of the commands \r
-\series bold\r
-\r
-\backslash\r
-begin{subequations}\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-end{subequations}\r
-\series default\r
- formulas can be subnumbered.\r
- Both commands are inserted in TeX-mode.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-An example:\r
-\begin_inset Formula \r
-\begin{equation}\r
-A=C-B\label{eq:a}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-addtocounter{equation}{-1}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-begin{subequations}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset VSpace -5mm\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{equation}\r
-B=C-A\label{eq:b}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{equation}\r
-C=A+B\label{eq:c}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-end{subequations}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To create the example, the following is done:\r
-\end_layout\r
-\r
-\begin_layout Enumerate\r
-first formula is inserted\r
-\end_layout\r
-\r
-\begin_layout Enumerate\r
-\r
-\series bold\r
-\r
-\backslash\r
-addtocounter{equation}{-1} \r
-\backslash\r
-begin{subequations}\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! A ! \r
-\backslash\r
-addtocounter\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series default\r
-is inserted after the first formula\r
-\end_layout\r
-\r
-\begin_layout Enumerate\r
-second formula is inserted\r
-\end_layout\r
-\r
-\begin_layout Enumerate\r
-third formula is inserted\r
-\end_layout\r
-\r
-\begin_layout Enumerate\r
-\r
-\series bold\r
-\r
-\backslash\r
-end{subequations}\r
-\series default\r
- is inserted after the third formula\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Every formula between the commands \r
-\series bold\r
-\r
-\backslash\r
-begin\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-end\r
-\series default\r
- is subnumbered as a, b, \r
-\begin_inset Newline linebreak\r
-\end_inset\r
-\r
-c, \SpecialChar \ldots{}\r
- For multiline formulas every line will be subnumbered.\r
- All subnumbered formulas are treated as \r
-\emph on\r
-one\r
-\emph default\r
- numbered formula.\r
- But as every numbered formula increases the counter \r
-\series bold\r
-equation\r
-\series default\r
- by one, the command \r
-\series bold\r
-\r
-\backslash\r
-addtocounter\r
-\series default\r
- is needed to decrease it.\r
- Otherwise the formulas \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:a"\r
-\r
-\end_inset\r
-\r
-, \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:b"\r
-\r
-\end_inset\r
-\r
-, \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:c"\r
-\r
-\end_inset\r
-\r
- would be numbered as \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:a"\r
-\r
-\end_inset\r
-\r
-, \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:d"\r
-\r
-\end_inset\r
-\r
-, \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:f"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-By inserting the commands in TeX-mode, a space is created between the first\r
- two formulas.\r
- To revert this -5\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm vertical space is inserted after the command \r
-\series bold\r
-\r
-\backslash\r
-begin{subequations}\r
-\series default\r
-.\r
- When the formula style \r
-\series bold\r
-Indented\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-formula styles see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Formula-Styles"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
- is used, -7\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm space is inserted instead.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Here is an example for a multiline formula where the numbering was turned\r
- off for the second line:\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-begin{subequations}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{eqnarray}\r
-A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\\r
- & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\\r
- & = & B^{2}-2BZ+Z^{2}\label{eq:f}\r
-\end{eqnarray}\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-end{subequations}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-User-defined Numbering\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:User-defined-Numbering"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula numbering ! user-defined\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula numbering ! self-defined delimiters\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-With the standard numbering parentheses are set around the formula number.\r
- To replace the parentheses for example by vertical bars, the following\r
- line is added to the LaTeX-preamble:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-def\r
-\backslash\r
-tagform@#1{\r
-\backslash\r
-maketag@@@{|#1|}}\r
-\series default\r
-\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-This macro is already declared in the LaTeX-preamble for testing.\r
- To activate it, remove the percent sign at the beginning.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To use other characters, the vertical bars besides the \r
-\series bold\r
-#1\r
-\series default\r
- are replaced by one ore more characters.\r
- To get only the formula number the vertical bars are omitted.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-When there should be an expression of your choice instead of the consecutive\r
- formula number in parentheses behind the formula, the command \r
-\series bold\r
-\r
-\backslash\r
-tag\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! T ! \r
-\backslash\r
-tag\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is used:\r
-\begin_inset Formula \r
-\begin{equation}\r
-A+B=C\tag{something}\label{eq:tag}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-In this example the command \r
-\series bold\r
-\r
-\backslash\r
-tag\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-something\r
-\series default\r
- was inserted in the formula.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When the command \r
-\series bold\r
-\r
-\backslash\r
-tag*\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-something\r
-\series default\r
- is inserted instead, the star prevents the parentheses around the expression:\r
-\begin_inset Formula \r
-\[\r
-A+B=C\tag*{something}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-To restart the formula numbering with new document parts or sections, the\r
- following command is used:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-@addtoreset{equation}{part}\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-"\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-@\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-"\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- ! \r
-\backslash\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-"\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-@\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-"\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-addtoreset\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-resp.\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-@addtoreset{equation}{section}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To be able to use these commands in TeX-mode, the \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-@\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- character has to be made \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-active\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- for LaTeX using the command \r
-\series bold\r
-\r
-\backslash\r
-makeatletter.\r
-\r
-\series default\r
- The command \r
-\series bold\r
-\r
-\backslash\r
-makeatother\r
-\series default\r
- reverts this.\r
- So the command sequence in TeX-mode is:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-makeatletter\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\backslash\r
-@addtoreset{equation}{section}\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\backslash\r
-makeatother\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In the LaTeX-preamble \r
-\series bold\r
-\r
-\backslash\r
-makeatletter\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-makeatother\r
-\series default\r
- can be omitted as they are automatically internally inserted by LyX.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To revert \r
-\series bold\r
-\r
-\backslash\r
-@addtoreset\r
-\series default\r
-, the file \r
-\series bold\r
-remreset.sty\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-remreset\r
-\series default\r
- is part of the LaTeX-package \r
-\series bold\r
-carlisle\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! carlisle\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- that is part of every LaTeX standard installation.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! remreset\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- has to be loaded in the LaTeX-preamble with the line\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage{remreset}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Then the command \r
-\series bold\r
-\r
-\backslash\r
-@removefromreset\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-"\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-@\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-"\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- ! \r
-\backslash\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-"\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-@\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-"\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-removefromreset\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- can be used with the same scheme as \r
-\series bold\r
-\r
-\backslash\r
-@addtoreset\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-Sometimes formulas should be numbered in the following form:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\family typewriter\r
-(section number.formula number)\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The formula number should start with every section with \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-1\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For this case there is the command \r
-\series bold\r
-\r
-\backslash\r
-numberwithin\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! N ! \r
-\backslash\r
-numberwithin\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, which is used with the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-numberwithin{counter}{sectioning}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Counter denotes what kind of numbering is affected, sectioning denotes what\r
- number is before the dot.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Thus in our case the following LaTeX-preamble or TeX code line is used:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-numberwithin{equation}{section}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This is the result:\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-numberwithin{equation}{section}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{equation}\r
-A+B=C\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To number e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-tables so that the number of the part is the sectioning,\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-numberwithin{table}{part}\r
-\series default\r
- is used.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To go back to the standard numbering or to prevent this kind of numbering\r
- when it is defined by the document class, the following command is inserted\r
- as TeX code or to the LaTeX-preamble:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-theequation}{\r
-\backslash\r
-arabic{equation}}\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! A ! \r
-\backslash\r
-arabic\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-theequation}{\r
-\backslash\r
-arabic{equation}}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series default\r
-or\r
-\series bold\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-thetable}{\r
-\backslash\r
-arabic{table}}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-numberwithin\r
-\series default\r
- uses internally the command \r
-\series bold\r
-\r
-\backslash\r
-@addtoreset\r
-\series default\r
-, described above, that also needs to be reverted.\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-makeatletter\r
-\end_layout\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-@removefromreset{equation}{section}\r
-\end_layout\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-makeatother\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Numbering with Roman Numbers and Letters\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula numbering ! with letters\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula numbering ! with Roman numbers\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Formulas can also be numbered with Roman numbers and Latin letters.\r
- To number for example with small Roman numbers, the command\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-theequation}{\r
-\backslash\r
-roman{equation}}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-is inserted before the formula in TeX-mode.\r
- \r
-\series bold\r
-\r
-\backslash\r
-renewcommand\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! R ! \r
-\backslash\r
-renewcommand\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- redefines the predefined command \r
-\series bold\r
-\r
-\backslash\r
-theequation\r
-\series default\r
- to the command \r
-\series bold\r
-\r
-\backslash\r
-roman{equation}\r
-\series default\r
-.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-The command \r
-\series bold\r
-\r
-\backslash\r
-renewcommand\r
-\series default\r
- has the same scheme like the command \r
-\series bold\r
-\r
-\backslash\r
-newcommand\r
-\series default\r
- that is described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:The-Command-newcommand"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- \r
-\series bold\r
-equation\r
-\series default\r
- is the formula counter.\r
- When the command \r
-\series bold\r
-\r
-\backslash\r
-the\r
-\series default\r
- is used as prefix for a counter, the value of the counter is output as\r
- Arabic number.\r
- When a formula is numbered, LaTeX sets internally the command \r
-\series bold\r
-\r
-\backslash\r
-theequation\r
-\series default\r
- behind the formula.\r
- \r
-\series bold\r
-\r
-\backslash\r
-roman{equation}\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! R ! \r
-\backslash\r
-roman\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
- outputs the counter as small Roman number.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-All formulas behind the command \r
-\series bold\r
-\r
-\backslash\r
-renew\r
-\series default\r
-c\r
-\series bold\r
-ommand\r
-\series default\r
- are now numbered Roman.\r
- To switch to numbering with big Roman numbers, the command is inserted\r
- again, but \r
-\series bold\r
-\r
-\backslash\r
-roman\r
-\series default\r
- is replaced by \r
-\series bold\r
-\r
-\backslash\r
-Roman\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! R ! \r
-\backslash\r
-roman@\r
-\backslash\r
-Roman\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
- To \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-number\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- with small Latin letters there is the command \r
-\series bold\r
-\r
-\backslash\r
-alph\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! A ! \r
-\backslash\r
-alph\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, for big ones there is the command \r
-\series bold\r
-\r
-\backslash\r
-Alph\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! A ! \r
-\backslash\r
-alph@\r
-\backslash\r
-Alph\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\color none\r
-Note:\r
-\series default\r
- Only maximal 26\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-formulas can be numbered with Latin letters in one document.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-theequation}{\r
-\backslash\r
-roman{equation}}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \r
-\begin{equation}\r
-A=\textrm{small roman}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-theequation}{\r
-\backslash\r
-Roman{equation}}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{equation}\r
-B=\textrm{big Roman}\label{eq:Rom}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-theequation}{\r
-\backslash\r
-alph{equation}}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{equation}\r
-C=\textrm{small Latin}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-theequation}{\r
-\backslash\r
-Alph{equation}}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{equation}\r
-D=\textrm{big Latin}\label{eq:Lat}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To switch back to the default numbering, insert the command:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-theequation}{\r
-\backslash\r
-arabic{equation}}\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! A ! \r
-\backslash\r
-arabic\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-theequation}{\r
-\backslash\r
-arabic{equation}}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{equation}\r
-E=\textrm{Arabic}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-As you see, formulas are numbered serially independent from the numbering\r
- style.\r
- When then numbering should start with \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-1\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- when the style is changed, new equation counters have to be defined.\r
- A description about this can be found in the file \r
-\begin_inset CommandInset href\r
-LatexCommand href\r
-name "Formula-numbering.lyx"\r
-target "run:Formula-numbering.lyx"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Chemical Symbols and Equations\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Chemical-Symbols-and"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Chemical characters ! Symbols\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Chemical equations\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Symbols ! chemical\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-An example text from chemistry:\r
-\end_layout\r
-\r
-\begin_layout Quote\r
-The \r
-\begin_inset Formula $\mathrm{SO_{4}^{2-}}$\r
-\end_inset\r
-\r
--ion reacts with two \r
-\begin_inset Formula $\mathrm{Na^{+}}$\r
-\end_inset\r
-\r
--ions to sodium sulfate \r
-\begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$\r
-\end_inset\r
-\r
-.\r
- The chemical equation for this is:\r
-\begin_inset Formula \r
-\begin{equation}\r
-\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This chemical equation can directly be created as formula.\r
- To avoid that the symbols appear italic, everything is highlighted and\r
- changed by the shortcut \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "font-roman"\r
-\end_inset\r
-\r
- to the upright font style.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-font styles\r
-\series bold\r
- \r
-\series default\r
-see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Font-Styles"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A more convenient way to typeset chemical formulas is to use the command\r
- \r
-\series bold\r
-\r
-\backslash\r
-ce\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! C ! \r
-\backslash\r
-ce\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- that is available when the LaTeX-package \r
-\series bold\r
-mhchem\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! mhchem\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is installed.\r
- After inserting \r
-\series bold\r
-\r
-\backslash\r
-ce\r
-\series default\r
- to a formula a new blue box appears where chemical formulas can be inserted\r
- in an intuitive way.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="9" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ce\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-H2CO3\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ce\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-SO4^2-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ce\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-(NH4)2S\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ce\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-KCr(SO4)2.12H2O\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ce\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A-B\r
-\backslash\r
-dbond\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-C\r
-\backslash\r
-tbond\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-D\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ce\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-^227\r
-\begin_inset Formula $\downarrow$\r
-\end_inset\r
-\r
-_90\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-Th+\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ce\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-CO2\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-+\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-C\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-<=>\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-2CO\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ce\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-CO2\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-+\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-C\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-->[\r
-\backslash\r
-alpha][\r
-\backslash\r
-beta]\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-2CO}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\color none\r
-Note:\r
-\series default\r
- Inserting a formula to a \r
-\series bold\r
-\r
-\backslash\r
-ce\r
-\series default\r
- box will lead to LaTeX errors due to a LyX bug.\r
-\color inherit\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset CommandInset href\r
-LatexCommand href\r
-name "LyX-bug #8566"\r
-target "http://www.lyx.org/trac/ticket/8566"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\color none\r
- In this case TeX code has to be used like for \r
-\series bold\r
-\r
-\backslash\r
-ce{$\r
-\backslash\r
-mu\r
-\backslash\r
-hyphen$Cl}\r
-\series default\r
-: \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-ce{$\r
-\backslash\r
-mu\r
-\backslash\r
-hyphen$Cl}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\color none\r
-Note:\r
-\series default\r
- It is not possible in LyX to use the character ^ to get an up-arrow as\r
- described in the \r
-\series bold\r
-mhchem\r
-\series default\r
- manual.\r
- One instead uses a negative thin space followed by the command \r
-\series bold\r
-\r
-\backslash\r
-uparrow\r
-\series default\r
-: \r
-\begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Using \r
-\series bold\r
-\r
-\backslash\r
-ce\r
-\series default\r
- the command for equation\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-\r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:chem-reaction"\r
-\r
-\end_inset\r
-\r
- is:\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
- \r
-\backslash\r
-ce\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-2Na+\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-+\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-SO4^2-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-->\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Na2SO4\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To create multiline chemical equations first a multiline formula is created\r
- as described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Multiline-Formulas"\r
-\r
-\end_inset\r
-\r
-.\r
- Afterwards the command \r
-\series bold\r
-\r
-\backslash\r
-ce\r
-\series default\r
- is used in every small blue box of the formula.\r
- \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:TEOS-reaction-1"\r
-\r
-\end_inset\r
-\r
- and \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:TEOS-reaction-2"\r
-\r
-\end_inset\r
-\r
- are an example of a multi-stage chemical reaction where every equation\r
- has its own number.\r
-\begin_inset Formula \r
-\begin{eqnarray}\r
-\ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\\r
-\ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}\r
-\end{eqnarray}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Besides \r
-\series bold\r
-\r
-\backslash\r
-ce\r
-\series default\r
- the \r
-\series bold\r
-mhchem\r
-\series default\r
- package provides the command \r
-\series bold\r
-\r
-\backslash\r
-cf\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! C ! \r
-\backslash\r
-cf\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- that has to be used for special cases.\r
- For more information about \r
-\series bold\r
-\r
-\backslash\r
-cf\r
-\series default\r
- and more examples have a look at the documentation of \r
-\series bold\r
-mhchem\r
-\series default\r
-, \r
-\begin_inset CommandInset citation\r
-LatexCommand cite\r
-key "mhchem"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Diagrams\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-LyX supports two types of commutative diagrams: \r
-\series bold\r
-amscd\r
-\series default\r
- and \r
-\series bold\r
-xymatrix\r
-\series default\r
- that are explained in the following.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Amscd Diagrams\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Diagrams ! amscd\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Diagrams of this type visualize relations by vertical and horizontal lines\r
- or arrows:\r
-\begin_inset Formula \r
-\[\r
-\begin{CD}A@>>>B@>>>C\\\r
-@AAA@.@VVV\\\r
-F@<<<E@<<<D\r
-\end{CD}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To get them, the command \r
-\series bold\r
-\r
-\backslash\r
-CD\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! C ! \r
-\backslash\r
-CD\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
- is inserted to a formula.\r
- A blue box appears with two dashed lines where further commands can be\r
- inserted.\r
- With \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "newline-insert newline"\r
-\end_inset\r
-\r
- a new line is created.\r
- Horizontal relations are inserted in odd, vertical in even formula lines.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To create the relations there are the following commands:\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-\r
-\series bold\r
-@<<<\r
-\series default\r
- creates a left arrow, \r
-\series bold\r
-@>>>\r
-\series default\r
- a right arrow and \r
-\series bold\r
-@=\r
-\series default\r
- a long equal sign\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-\r
-\series bold\r
-@AAA\r
-\series default\r
- creates an up arrow, \r
-\series bold\r
-@VVV\r
-\series default\r
- a down arrow and \r
-\series bold\r
-@|\r
-\series default\r
- a vertical equal sign\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-\r
-\series bold\r
-@.\r
-\r
-\series default\r
- is a placeholder for non-existent relations\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-All arrows can be labeled as follows:\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-If text inserted between the first and second < or >, resp., it is placed\r
- above the arrow.\r
- When it is inserted between the second and third one, it appears under\r
- the arrow.\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-When text for vertical arrows is inserted between the first and second A\r
- or V, resp., it is placed left beside the arrow.\r
- When it is inserted between the second and third one, it appears right\r
- beside the arrow.\r
- If the text contains an A or V, these letters must be set into a TeX-brace.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-As example a diagram with all possible relations:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \r
-\[\r
-\begin{CD}A@>j>>B@>>k>C@=F\\\r
-@AmAA@.@VV{V}V@|\\\r
-D@<<j<E@>k>>F@=C\r
-\end{CD}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command for this is:\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-CD\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A@>j>>B@>>k>C@=F Ctrl+Return\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom HPhantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-CD\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-@AmAA@.@VV\r
-\backslash\r
-{V\r
-\series default\r
-\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\series bold\r
-V@| Ctrl+Return\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom HPhantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-CD\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-D@<<j<E@>k>>F@=C\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Xymatrix Diagrams\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Diagrams ! xymatrix\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To be able to use xymatrices, the LaTeX-package \r
-\series bold\r
-xypic\r
-\series default\r
- must be installed.\r
- A xymatrix is created by inserting the command \r
-\series bold\r
-\r
-\backslash\r
-xymatrix\r
-\series default\r
- in a formula.\r
- Then you are able to add new matrix columns and rows like for normal matrices,\r
- see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Matrices"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,\r
- and much more.\r
- All possibilities to create commutative diagrams and decorations are explained\r
- in detail in the \r
-\emph on\r
-XY-pic manual\r
-\emph default\r
- that you find in the menu \r
-\family sans\r
-Help\SpecialChar \menuseparator\r
-Specific\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Manuals\r
-\family default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-\r
-\noun on\r
-Feynman\r
-\noun default\r
- Diagrams\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Diagrams ! Feynman\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To be able to use \r
-\noun on\r
-Feynman\r
-\noun default\r
--diagrams, the LaTeX-package \r
-\series bold\r
-feyn\r
-\series default\r
- must be installed.\r
- A \r
-\noun on\r
-Feynman\r
-\noun default\r
--diagram is created by inserting the command \r
-\series bold\r
-\r
-\backslash\r
-Diagram\r
-\series default\r
- in a formula.\r
- Then you are able to add new matrix columns and rows like for normal matrices,\r
- see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Matrices"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Examples how to create \r
-\noun on\r
-Feynman-\r
-\noun default\r
-diagrams in LyX is given in the \r
-\emph on\r
-Feynman-diagram manual\r
-\emph default\r
- that you find in the menu \r
-\family sans\r
-Help\SpecialChar \menuseparator\r
-Specific\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Manuals\r
-\family default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-User-defined Commands\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-User-defined commands\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-Note:\r
-\series default\r
- The names of user-defined commands and macros may only consist of Latin\r
- letters.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-The Command \r
-\backslash\r
-newcommand\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:The-Command-newcommand"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-User-defined commands ! \r
-\backslash\r
-newcommand\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! N ! \r
-\backslash\r
-newcommand\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Many LaTeX-commands are too long to be used frequently.\r
- But it is possible to define with the command \r
-\series bold\r
-\r
-\backslash\r
-newcommand\r
-\series default\r
- new shorter commands.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command scheme of \r
-\series bold\r
-\r
-\backslash\r
-newcommand\r
-\series default\r
- is:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-newcommand{new command name}[number of arguments][optional\r
-\series default\r
- \r
-\series bold\r
-value]\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom HPhantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-newcommand\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-{command definition}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-Note:\r
-\series default\r
- Assure that the name of the new command is not already used in your document\r
- or by LaTeX-packages that you use.\r
- When you for example define the command \r
-\series bold\r
-\r
-\backslash\r
-le\r
-\series default\r
- for \r
-\series bold\r
-\r
-\backslash\r
-Leftarrow\r
-\series default\r
-, you get an error message because \r
-\series bold\r
-\r
-\backslash\r
-le\r
-\series default\r
- is already defined as command for \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $\le$\r
-\end_inset\r
-\r
-\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The number of arguments is an integer in the range 0\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
--\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-9 and specifies how many arguments the new command should have.\r
- With the optional value a value for an optional argument can be predefined.\r
- When this is done, the \r
-\emph on\r
-first\r
-\emph default\r
- \r
-\emph on\r
-a\r
-\emph default\r
-rgument of the new command is automatically an optional one.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Here are some examples:\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-To define the command \r
-\series bold\r
-\r
-\backslash\r
-gr\r
-\series default\r
- for \r
-\series bold\r
-\r
-\backslash\r
-Longrightarrow\r
-\series default\r
-, the LaTeX-preamble line is:\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-newcommand{\r
-\backslash\r
-gr}{\r
-\backslash\r
-Longrightarrow}\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-To define the command \r
-\series bold\r
-\r
-\backslash\r
-us\r
-\series default\r
- for \r
-\series bold\r
-\r
-\backslash\r
-underline\r
-\series default\r
-, the argument (that should be underlined) must be taken into account.\r
- For this the preamble line is:\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-newcommand{\r
-\backslash\r
-us}[1]{\r
-\backslash\r
-underline{#1}}\r
-\series default\r
-\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-The character \r
-\series bold\r
-#\r
-\series default\r
- acts as argument placeholder, the \r
-\series bold\r
-1\r
-\series default\r
- behind it denotes that it is the placeholder for the first argument.\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-For \r
-\series bold\r
-\r
-\backslash\r
-framebox\r
-\series default\r
- one can e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-define the command \r
-\series bold\r
-\r
-\backslash\r
-fb\r
-\series default\r
-:\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-newcommand{\r
-\backslash\r
-fb}[3]{\r
-\backslash\r
-framebox#1#2{$#3$}}\r
-\series default\r
-\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-The two Dollar signs creates the extra formula needed for \r
-\series bold\r
-\r
-\backslash\r
-framebox\r
-\series default\r
-, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Boxes-with-Frame"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-To create a new command for \r
-\series bold\r
-\r
-\backslash\r
-fcolorbox\r
-\series default\r
- where the color for the box need not be specified, the argument for the\r
- color is defined optional:\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-newcommand{\r
-\backslash\r
-cb}[3][white]{\r
-\backslash\r
-fcolorbox{#2}{#1}{$#3$}}\r
-\series default\r
-\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-When the color is not specified when using \r
-\series bold\r
-\r
-\backslash\r
-cb\r
-\series default\r
-, the predefined color \r
-\series bold\r
-white\r
-\series default\r
- will be used.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A test of the new defined commands:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="6" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-A\r
-\backslash\r
-gr\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $A\gr B$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-us{ABcd\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-fb{[2cm]\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{\r
-\backslash\r
-int\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-cb{red\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{\r
-\backslash\r
-int\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-cb[green]\r
-\backslash\r
-{red\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{\r
-\backslash\r
-int\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Math Macros\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-User-defined commands! Math macros\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Macros\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-User-defined commands are especially convenient for complex expressions.\r
- When you are for example dealing with a document that has quadratic equations,\r
- the same solution type occurs several times.\r
- The general form of a quadratic equation is\r
-\begin_inset Formula \r
-\[\r
-0=\lambda^{2}+p\lambda+q\r
-\]\r
-\r
-\end_inset\r
-\r
-The general form of the solution is\r
-\begin_inset Formula \r
-\[\r
-\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To define a command for the solution formula where only the three parameters\r
- \r
-\begin_inset Formula $\lambda$\r
-\end_inset\r
-\r
-, \r
-\begin_inset Formula $p$\r
-\end_inset\r
-\r
- and \r
-\begin_inset Formula $q$\r
-\end_inset\r
-\r
- need to be specified and the index of \r
-\begin_inset Formula $\lambda$\r
-\end_inset\r
-\r
- can be given optionally, the LaTeX-preamble line is\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-newcommand{\r
-\backslash\r
-qG}[4][1,\r
-\backslash\r
-,2]{#2_{#1}=-\r
-\backslash\r
-frac{#3}{2}\r
-\backslash\r
-pm\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom HPhantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-newcommand\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\backslash\r
-sqrt{\r
-\backslash\r
-frac{#3^{2}}{4}-#4}}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To create with this the solution formula, the command\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-qG{\r
-\backslash\r
-lambda\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{p\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{q\r
-\series default\r
- is inserted to a formula\r
-\series bold\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The definition of the new command is unintuitive because one has to know\r
- the schemes of all used LaTeX commands, e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-that a fraction is inserted in LaTeX as \r
-\series bold\r
-\r
-\backslash\r
-frac{numerator}{denominator}\r
-\series default\r
-.\r
- Furthermore one can easily forget a brace in the definition and cannot\r
- see in LyX what the new command is doing.\r
- To avoid these problems LyX offers the possibility to use math macros instead\r
- of the command \r
-\series bold\r
-\r
-\backslash\r
-newcommand\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A math macro is created by using the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\family default\r
- or the toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math-macro_newmacroname_newcommand.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
- The math macro toolbar appears together with the following box where the\r
- macro is defined:\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hspace*{\fill}\r
-\end_inset\r
-\r
-\r
-\begin_inset Graphics\r
- filename clipart/macrobox.png\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hspace*{\fill}\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset FormulaMacro\r
-\newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}\r
-\end_inset\r
-\r
-\r
-\backslash\r
-newmacroname is the default name of the macro that should be changed to\r
- something sensible.\r
- The wanted formula is inserted in the first blue box.\r
- An argument placeholder is inserted with the command \r
-\series bold\r
-\r
-\backslash\r
-#argumentnumber\r
-\series default\r
-, e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-\r
-\series bold\r
-\r
-\backslash\r
-#1\r
-\series default\r
- or by using the macro toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math-macro-add-param.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
- Argument placeholders are displayed red.\r
- A maximum of 9\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-arguments are possible.\r
- Optional arguments are created with the toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math-macro-add-optional-param.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
- The first non-optional argument can be transformed to an optional one with\r
- the toolbar button \r
-\begin_inset Graphics\r
- filename ../images/math-macro-make-optional.png\r
- scale 85\r
-\r
-\end_inset\r
-\r
-.\r
- In the second blue box the appearance of the macro in LyX can be defined.\r
- Normally you want to see it as it is defined, so the box is kept empty.\r
- But when you have created a macro that needs lot of space on the screen,\r
- you can insert in the box for example\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series bold\r
-qG: \r
-\backslash\r
-#1\r
-\series default\r
- \r
-\series bold\r
-,\r
-\series default\r
- \r
-\series bold\r
-\r
-\backslash\r
-#2\r
-\series default\r
- \r
-\series bold\r
-,\r
-\series default\r
- \r
-\series bold\r
-\r
-\backslash\r
-#3, \r
-\backslash\r
-#4\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series default\r
-For the macro only the arguments with the macro name in front of them will\r
- then be displayed in LyX, leading to a better overview.\r
- The formula appears in the output as defined in the first box.\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-The appearance of macros in formulas can furthermore be changed for single\r
- macros by setting the cursor in the macro and using the menu \r
-\family sans\r
-View\SpecialChar \menuseparator\r
-(Un)fold\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Math\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Macro\r
-\family default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To use a macro, the macro name is inserted as command to a formula, in our\r
- case \r
-\series bold\r
-\r
-\backslash\r
-qG\r
-\series default\r
-.\r
- Our macro looks in LyX like this:\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hspace*{\fill}\r
-\end_inset\r
-\r
-\r
-\begin_inset Graphics\r
- filename clipart/macrouse.png\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hspace*{\fill}\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-Here is our macro example with the arguments \r
-\begin_inset Formula $x$\r
-\end_inset\r
-\r
-, \r
-\begin_inset Formula $\ln(x)$\r
-\end_inset\r
-\r
- and \r
-\begin_inset Formula $B$\r
-\end_inset\r
-\r
-:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \r
-\[\r
-\qG x{\ln(x)}B\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-LyX offers in the menu \r
-\family sans\r
-Tools\SpecialChar \menuseparator\r
-Preferences\SpecialChar \menuseparator\r
-Editing\SpecialChar \menuseparator\r
-Control\r
-\family default\r
- different styles to edit macros.\r
- To find the style that suits you the most, choose a style and set the cursor\r
- in a macro formula to see the difference.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A math macro is transformed internally to a \r
-\series bold\r
-\r
-\backslash\r
-newcommand\r
-\series default\r
- command when exporting the document.\r
- The created \r
-\series bold\r
-\r
-\backslash\r
-newcommand\r
-\series default\r
- command is not placed in the LaTeX-preamble, therefore macros can only\r
- be used in formulas that are in the document below the macro definition\r
- box.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Math macros can also be directly created from a \r
-\series bold\r
-\r
-\backslash\r
-newcommand\r
-\series default\r
- command.\r
- When writing for example the command\r
-\series bold\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\backslash\r
-newcommand{\r
-\backslash\r
-larrow}[2]{\r
-\backslash\r
-xleftarrow[#2]{#1}}\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\series default\r
-in LyX as normal text, highlighting it completely and using then the shortcut\r
- \r
-\family sans\r
-Ctrl+M\r
-\family default\r
-, the command will be transformed to a math macro.\r
- Using this method you need to be careful that the \r
-\series bold\r
-\r
-\backslash\r
-newcommand\r
-\series default\r
- command is typed correctly, otherwise you get a faulty macro leading to\r
- LaTeX errors.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Math macros currently have the problem that further formulas in macro definition\r
-s are handled wrongly.\r
- Therefore the example \r
-\series bold\r
-\r
-\backslash\r
-fb\r
-\series default\r
- from \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:The-Command-newcommand"\r
-\r
-\end_inset\r
-\r
- cannot be created as macro.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When the cursor is in a macro definition box, you will see the macro toolbar\r
- in LyX:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace defskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Graphics\r
- filename clipart/MacroToolbar.png\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Macros ! Toolbar\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace defskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The macro toolbar contains from left to right the following buttons:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace defskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="9" columns="2">\r
-<features rotate="0" islongtable="true" longtabularalignment="center">\r
-<column alignment="left" valignment="top">\r
-<column alignment="left" valignment="top" width="85col%">\r
-<row interlinespace="2.5mm">\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Graphics\r
- filename ../images/math-macro-remove-param.png\r
- rotateOrigin center\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-Remove Last Argument\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row interlinespace="2.5mm">\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Graphics\r
- filename ../images/math-macro-add-param.png\r
- rotateOrigin center\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-Append Argument\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row interlinespace="2.5mm">\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Graphics\r
- filename ../images/math-macro-make-optional.png\r
- rotateOrigin center\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-Make First Non-Optional into\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom HPhantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Optional Argument\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row interlinespace="2.5mm">\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Graphics\r
- filename ../images/math-macro-make-nonoptional.png\r
- rotateOrigin center\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-Make Last Optional into\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom HPhantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Non-Optional Argument\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row interlinespace="2.5mm">\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Graphics\r
- filename ../images/math-macro-remove-optional-param.png\r
- rotateOrigin center\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-Remove Optional Argument\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row interlinespace="2.5mm">\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Graphics\r
- filename ../images/math-macro-add-optional-param.png\r
- rotateOrigin center\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-Insert Optional Argument\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row interlinespace="2.5mm">\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Graphics\r
- filename ../images/math-macro-remove-greedy-param.png\r
- rotateOrigin center\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-Remove Last Argument\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom HPhantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Spitting Out To The Right\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row interlinespace="2.5mm">\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Graphics\r
- filename ../images/math-macro-append-greedy-param.png\r
- rotateOrigin center\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-Append Argument\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom HPhantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Eating From The Right\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row interlinespace="2.5mm">\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Graphics\r
- filename ../images/math-macro-add-greedy-optional-param.png\r
- rotateOrigin center\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-Append Optional Argument\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom HPhantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Macro\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Definition\SpecialChar \menuseparator\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Eating From The Right\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Computer Algebra Systems\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-LyX offers the exchange between mathematical expressions written in LyX's\r
- math editor and external applications or user defined scripts.\r
- Currently supported applications are \r
-\family sans\r
-Maple\r
-\family default\r
-, \r
-\family sans\r
-Mathematica\r
-\family default\r
-, \r
-\family sans\r
-Maxima\r
-\family default\r
- and \r
-\family sans\r
-Octave\r
-\family default\r
-.\r
- Note that the set of supported mathematical constructs is limited only\r
- to very simple cases.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Usage\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Write some expression in a formula, go to the \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Use Computer Algebra System\r
-\family default\r
- menu and choose the application you have installed on the computer.\r
- After that the result of computation should show on the right side of the\r
- expression together with the \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-=\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- operator.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Here are few simple examples (with results from \r
-\family typewriter\r
-Maxima\r
-\family default\r
-) to show what kind of computations can be performed:\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-\begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-\begin_inset Formula $\frac{37.0}{3}=12.33333333333333$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-\begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-\begin_inset Formula $\det\left[\begin{array}{ccc}\r
-1 & 6 & 7\\\r
-2 & 5 & 8\\\r
-3 & 4 & 17\r
-\end{array}\right]=-56$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-\begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Keyboard shortcut\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Currently there is no keyboard shortcut for calling the algebra applications.\r
- One can easily bind a shortcut to the \r
-\family sans\r
-math-extern\r
-\family default\r
- LyX function (see the \r
-\family sans\r
-\emph on\r
-LyX Functions\r
-\family default\r
-\emph default\r
- manual).\r
- One could e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-bind the \r
-\family sans\r
-Return\r
-\family default\r
- key inside the math editor.\r
- To bind it to \r
-\family typewriter\r
-Maxima\r
-\family default\r
- one would use this shortcut definition command:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-command-alternatives break-paragraph;math-extern maxima\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Miscellaneous\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Miscellaneous\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Negative Numbers\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Numbers ! negative\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Negative numbers often look ugly in formulas because the minus sign before\r
- the number is set with the same length as the minus operator sign.\r
- When writing the negative number in normal text, the minus sign appears\r
- correctly.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Thus, the problem disappears when converting the minus sign to mathematical\r
- text.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-An example to visualize the problem:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="3" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="right" valignment="top">\r
-<column alignment="left" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-normal text:\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-x = -2\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-formula:\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $x=-2$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-solution:\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $x=\textrm{-}2$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Comma as decimal Separator\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Comma\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In LaTeX a comma inside a formula is used, according to the English convention,\r
- as number group separator.\r
- So there will be space added behind all commas in formulas.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To avoid this, the comma is highlighted and changed to mathematical text\r
- (shortcut \r
-\begin_inset Info\r
-type "shortcut"\r
-arg "math-mode"\r
-\end_inset\r
-\r
-).\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To use all formula commas in the document as decimal separator, the file\r
- \r
-\series bold\r
-icomma.sty\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-icomma\r
-\series default\r
- is part of the LaTeX-package \r
-\series bold\r
-was\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! was\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-vspace{4mm}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! icomma\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is loaded with the LaTeX-preamble line\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage{icomma}\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Physical Vectors\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Physical-Vectors"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Vectors ! physical\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Predefined vectors are offered by the LaTeX-package \r
-\series bold\r
-braket\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! braket\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- that is loaded with the LaTeX-preamble line\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage{braket}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-ifbraket \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-The following table will only be displayed when the LaTeX-package \r
-\series bold\r
-braket\r
-\series default\r
- is installed.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The following commands are defined:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="4" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Bra{\r
-\backslash\r
-psi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Bra{\psi}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Ket{\r
-\backslash\r
-psi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Ket{\psi}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Braket{\r
-\backslash\r
-psi|\r
-\backslash\r
-phi\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\Braket{\psi|\phi}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The command \r
-\series bold\r
-\r
-\backslash\r
-Braket\r
-\series default\r
- assures that all vertical bars are set in the size of the surrounding brackets:\r
-\begin_inset Formula \r
-\[\r
-\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-else \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-The following will be displayed when the LaTeX-package \r
-\series bold\r
-braket\r
-\series default\r
- is not installed:\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-You need to install the LaTeX-package \r
-\series bold\r
-braket\r
-\series default\r
- to see the rest of this subsection in the output.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-fi \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The effect of \r
-\series bold\r
-\r
-\backslash\r
-Braket\r
-\series default\r
- can also be achieved using the command \r
-\series bold\r
-\r
-\backslash\r
-middle\r
-\series default\r
-, that is described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Automatic-Bracket-Size"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Self-defined Fractions\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Self-defined-Fractions"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Fractions ! self-defined\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To define custom commands for fractions, the command \r
-\series bold\r
-\r
-\backslash\r
-genfrac\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! G ! \r
-\backslash\r
-genfrac\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-vspace{4mm}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is used in the following scheme:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-genfrac{left\r
-\series default\r
- \r
-\series bold\r
-bracket}{right\r
-\series default\r
- \r
-\series bold\r
-bracket}{fraction bar thickness}{style}\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\begin_inset Phantom HPhantom\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-genfrac\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-{numerator}{denominator}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The style is a number in the range of 0\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
--\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-3.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="5" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Number\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Style (Size)\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-0\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-display style formula\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-1\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-inline formula\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-2\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-small\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-3\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-tiny\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When no style is given, the size is adjusted to the surrounding environment\r
- like for the command \r
-\series bold\r
-\r
-\backslash\r
-frac\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When no fraction bar thickness is given, the predefined value of 0.4\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-pt will be used.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-For example, the commands \r
-\series bold\r
-\r
-\backslash\r
-dfrac\r
-\series default\r
- and \r
-\series bold\r
-\r
-\backslash\r
-tbinom\r
-\series default\r
- from \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Fractions"\r
-\r
-\end_inset\r
-\r
- are defined with the commands\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-newcommand{\r
-\backslash\r
-dfrac}[2]{\r
-\backslash\r
-genfrac{}{}{}{0}{#1}{#2}}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-and\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-newcommand{\r
-\backslash\r
-tbinom}[2]{\r
-\backslash\r
-genfrac{(}{)}{0pt}{1}{#1}{#2}}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-To define a fraction where the fraction bar thickness can be given as optional\r
- argument, the following line is inserted to the LaTeX-preamble:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-newcommand{\r
-\backslash\r
-fracS}[3][]{\r
-\backslash\r
-genfrac{}{}{#1}{}{#2}{#3}}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A test:\r
-\begin_inset Formula \r
-\begin{align*}\r
-\text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\\r
-\text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\r
-\end{align*}\r
-\r
-\end_inset\r
-\r
-As one can see, the distance of the numerator and the denominator to the\r
- fraction bar is round about three times the bar thickness.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Canceled Formulas\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! canceled\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To cancel formulas or formula parts, the LaTeX-package \r
-\series bold\r
-cancel\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! cancel\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- has to be loaded with the LaTeX-preamble line\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage{cancel}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-ifcancel \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-The following table will only be displayed when the LaTeX-package \r
-\series bold\r
-cancel\r
-\series default\r
- is installed.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-There are four ways to cancel formulas:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\align center\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="5" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top">\r
-<column alignment="center" valignment="top">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-The space and\r
-\series bold\r
- \r
-\backslash\r
-raisebox\r
-\series default\r
- are used here as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-cancel{\r
-\backslash\r
-int\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-bcancel{\r
-\backslash\r
-int\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-xcancel{\r
-\backslash\r
-int\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-cancelto{1\r
-\begin_inset Formula $\to$\r
-\end_inset\r
-\r
-\r
-\backslash\r
-{\r
-\backslash\r
-int\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-A=B\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-cancelto\r
-\series default\r
- is especially suitable to visualize the reduction of fractions within formulas:\r
-\begin_inset Formula \r
-\[\r
-\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To change the size of \r
-\series bold\r
-\r
-\backslash\r
-cancelto\r
-\series default\r
-'s \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-subscript\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- value one can load the package \r
-\series bold\r
-cancel\r
-\series default\r
- with either the option \r
-\series bold\r
-samesize\r
-\series default\r
- which leads to the same size as for the canceled value or with the option\r
- \r
-\series bold\r
-Smaller\r
-\series default\r
- which makes is it a bit smaller than the size one gets without using a\r
- package option.\r
- In this document \r
-\series bold\r
-cancel\r
-\series default\r
- was loaded with this line:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage[samesize]{cancel}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To color the cancellation bar one adds this command as TeX code:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-CancelColor}{\r
-\backslash\r
-color{red}}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-red\r
-\series default\r
- can be replaced by a color of your choice.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-CancelColor}{\r
-\backslash\r
-color{red}}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \r
-\[\r
-\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-renewcommand{\r
-\backslash\r
-CancelColor}{\r
-\backslash\r
-color{black}}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-reset the color\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For further customizations, see the documentation of the package \r
-\series bold\r
-cancel\r
-\series default\r
-, \r
-\begin_inset CommandInset citation\r
-LatexCommand cite\r
-key "cancel"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-else \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-The following will be displayed when the LaTeX-package \r
-\series bold\r
-cancel\r
-\series default\r
- is not installed:\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-You need to install the LaTeX-package \r
-\series bold\r
-cancel\r
-\series default\r
- to see the rest of this subsection in the output.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-fi \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Formulas in Section Headings\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Formulas-in-Section"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! in section headings\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When formulas are used in section headings, the following has to be taken\r
- into account:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-When \r
-\series bold\r
-hyperref\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! hyperref\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- support is enabled in the document settings dialog under \r
-\family sans\r
-PDF\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Properties\r
-\family default\r
-, PDF-bookmarks are created for every section heading in the table of contents.\r
- If a section heading contains formulas, they are incorrectly displayed\r
- in the bookmark text, because formulas in bookmarks infringe the PDF convention\r
-s.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Both problems can be solved by inserting at the end of the section heading\r
- a short title with the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Short\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Title\r
-\family default\r
-.\r
- Short titles are used as alternative for multiline section headings to\r
- keep the table of contents clearly arranged.\r
- Only the short title appears in the table of contents and therefore also\r
- in the PDF-bookmark.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When formulas should be used in the table of contents but \r
-\series bold\r
-hyperref\r
-\series default\r
- is used, one can use the following command in TeX-mode:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-texorpdfstring{part}{alternative}\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Commands ! T ! \r
-\backslash\r
-texorpdfstring\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Part is the part of the heading that shouldn't appear in the PDF-bookmark.\r
- This can be characters, formulas, footnotes, but also cross-references.\r
- The alternative is used instead of the part for the bookmark.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Here are two example headings:\r
-\begin_inset VSpace -3mm\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-boldmath \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Heading without formula in table of contents \r
-\begin_inset Formula $\sqrt{-1}=\mathrm{i}$\r
-\end_inset\r
-\r
-\r
-\begin_inset Argument 1\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Heading without formula in table of contents\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Heading with formula in table of contents\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-texorpdfstring{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- \r
-\begin_inset Formula $\sqrt{-1}=\mathrm{i}$\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}{}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-unboldmath \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-In the first heading a short title was used, in the second one \r
-\series bold\r
-\r
-\backslash\r
-texorpdfstring\r
-\series default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To get the same formatting as for the other headings, the complete heading\r
- was set into a \r
-\series bold\r
-boldmath\r
-\series default\r
- environment\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Bold-Formulas"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Formulas in multi-column Text\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! in multi-column text\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Formulas in multi-column text are often too wide to fit into a column and\r
- thus need to be set over the whole page width.\r
- This is done by using the LaTeX-package \r
-\series bold\r
-multicol\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-multicol\r
-\series default\r
- is part of every LaTeX standard installation.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! multicol\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, that is loaded with the LaTeX-preamble line\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage{multicol}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Note Greyedout\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-Note that in this case the setting \r
-\family sans\r
-Two-column\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-document\r
-\family default\r
- in the menu \r
-\family sans\r
-Document\SpecialChar \menuseparator\r
-Settings\r
-\family default\r
- under \r
-\family sans\r
-Text\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Layout\r
-\family default\r
-\emph on\r
- \r
-\emph default\r
-must \r
-\emph on\r
-not\r
-\emph default\r
- be selected.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Before the multi-column text the command\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-begin{multicols}{column number}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-is written in TeX-mode.\r
- The column number is a number in the range of 2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
--\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-10.\r
- Before the formula the multi-column text is ended by inserting the command\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-end{multicols}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-in TeX-mode.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Due to the command some space is automatically added before the formula.\r
- To revert this, -6\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm vertical space is inserted before the formula.\r
- When the formula style \r
-\series bold\r
-Indented\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-formula styles see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Formula-Styles"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
- is used, -9\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-mm space is inserted instead.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-As example a multi-column text with a displayed formula:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\lang german\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-begin{multicols}{2}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-Das Spektrum wird fouriertransformiert.\r
- Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk\r
-, Lösungsmittel) zu trennen.\r
- Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns\r
- nun das Aussehen des Ausgangssignals.\r
- Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man\r
- über alle Phasen integrieren muss.\r
- Sei nun \r
-\begin_inset Formula $S$\r
-\end_inset\r
-\r
- unser normiertes Ausgangssignal und \r
-\begin_inset Formula $P$\r
-\end_inset\r
-\r
- die Phasenverteilungsfunktion, so ergibt sich die Beziehung\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-end{multicols}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset VSpace -6mm\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \r
-\begin{equation}\r
-S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\r
-\end{equation}\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-begin{multicols}{2}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-wobei \r
-\begin_inset Formula $S_{0}$\r
-\end_inset\r
-\r
- das Signal ohne Gradient ist und die Normierungsbedingung \r
-\begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$\r
-\end_inset\r
-\r
- gilt.\r
- Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.\r
- Direkt nach dem \r
-\begin_inset Formula $\nicefrac{\pi}{2}$\r
-\end_inset\r
-\r
-\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
--rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich\r
- das Signal zusätzlich abschwächt.\r
- Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten\r
- \r
-\begin_inset Formula $T_{2}$\r
-\end_inset\r
-\r
--Zeit.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\lang german\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-end{multicols}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Formulas with Description of Variables\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Formula ! with description of variables\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-To describe variables within a formula, like in formula \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:within"\r
-\r
-\end_inset\r
-\r
-, a 2\r
-\series bold\r
-×\r
-\series default\r
-\r
-\begin_inset Formula $n$\r
-\end_inset\r
-\r
-\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-matrix is used with left aligned columns for the \r
-\begin_inset Formula $n$\r
-\end_inset\r
-\r
- used variables.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-matrices see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Matrices"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- To set the description in a smaller size, before the matrix e.\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-g.\r
-\begin_inset space \space{}\r
-\end_inset\r
-\r
-the command \r
-\series bold\r
-\r
-\backslash\r
-footnotesize\r
-\series default\r
- is inserted.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-font sizes see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Font-Sizes"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When the formula style \r
-\series bold\r
-Indented\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-formula styles see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sec:Formula-Styles"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\series default\r
- is used, a \r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-hfill\r
-\series default\r
- only works in formulas with the style \r
-\series bold\r
-Indented\r
-\series default\r
-, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Variable-Space"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- is inserted before and after the matrix to have the same separation of\r
- the matrix from the equation and the side margin.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When the formula style \r
-\series bold\r
-Centered\r
-\series default\r
- is used, the method described in \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Flalign-Environment"\r
-\r
-\end_inset\r
-\r
- is used to indent formulas.\r
- Formula \r
-\begin_inset CommandInset ref\r
-LatexCommand eqref\r
-reference "eq:within"\r
-\r
-\end_inset\r
-\r
- consists of five columns where in the first two columns contain the equation,\r
- the third the matrix and the last one an empty TeX-brace.\r
-\begin_inset Formula \r
-\begin{flalign}\r
-\hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}\r
-\rho & \textrm{density}\\\r
-V & \textrm{volume}\\\r
-g & \textrm{gravitational acceleration}\r
-\end{array} & & {}\label{eq:within}\r
-\end{flalign}\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Upright small Greek Letters\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Upright-small-Greek"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Greek letters ! upright\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Most of the math fonts only provide italic small Greek letters.\r
- But for symbols of elementary particles like pions and neutrinos, upright\r
- Greek letters are needed.\r
- The file \r
-\series bold\r
-upgreek.sty\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-upgreek\r
-\series default\r
- is part of the LaTeX-package \r
-\series bold\r
-was\r
-\series default\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! was\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-vspace{4mm}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Packages ! upgreek\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- that is loaded with the LaTeX-preamble line\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-usepackage{upgreek}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-provides them.\r
- \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-ifupgreek \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-The following table will only be displayed when the LaTeX-package \r
-\series bold\r
-upgreek\r
-\series default\r
- is installed:\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- They are created when the command for a small Greek letter is started with\r
- \r
-\series bold\r
-up\r
-\series default\r
-.\r
- For example the command \r
-\series bold\r
-\r
-\backslash\r
-uptau\r
-\series default\r
- creates this: \r
-\begin_inset Formula $\uptau$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With these commands reactions of elementary particles can be typeset:\r
-\begin_inset Formula \r
-\[\r
-\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The upright letters are more bold and wider than the italic ones.\r
- They should therefore not be used for units like \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-µm\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-else \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Note Note\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-The following will be displayed when the LaTeX-package \r
-\series bold\r
-upgreek\r
-\series default\r
- is not installed:\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-You need to install the LaTeX-package \r
-\series bold\r
-upgreek\r
-\series default\r
- to see the rest of this subsection in the output.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-fi \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Text Characters in Formulas\r
-\begin_inset CommandInset label\r
-LatexCommand label\r
-name "sub:Text-Characters-in"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Text ! in formulas\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In some cases you might want to insert text characters directly into formulas.\r
- When for example the centered dot · is often used in formulas like \r
-\begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$\r
-\end_inset\r
-\r
-, one would have to insert the command \r
-\series bold\r
-\r
-\backslash\r
-cdot\r
-\series default\r
-\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Binary-Operators"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- all the time, because this character is defined in all encodings as text\r
- character.\r
- But the encoding can be changed by this LaTeX-preamble line:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-Declare Inputtext{183}{\r
-\backslash\r
-ifmmode\r
-\backslash\r
-cdot\r
-\backslash\r
-else\r
-\backslash\r
-textperiodcentered\r
-\backslash\r
-f\SpecialChar \textcompwordmark{}\r
-i}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The character encoding (menu \r
-\family sans\r
-Document\SpecialChar \menuseparator\r
-Settings\SpecialChar \menuseparator\r
-Language\r
-\family default\r
-) specifies what character appears when a keyboard key is pressed.\r
- When the key for the character '·' is pressed, internally the command \r
-\series bold\r
-\r
-\backslash\r
-textperiodcentered\r
-\series default\r
- is used.\r
- But this command is not available in a formula so that you would get LaTeX-erro\r
-rs.\r
- With the changed encoding the right command is chosen automatically, depending\r
- on if the character was inserted into a formula or not.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The encoding of several characters is saved in definition files.\r
- For example the encoding \r
-\series bold\r
-latin9\r
-\series default\r
- is defined in the file \r
-\series bold\r
-latin9.def\r
-\series default\r
- which is in the installation folder of LaTeX.\r
- Encodings should only be changed via the LaTeX-preamble and not in the\r
- definition files.\r
- Otherwise documents could not be edited by other LyX users working on other\r
- computers.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace medskip\r
-\end_inset\r
-\r
-Besides the centered dot, in this document the degree sign ° is defined\r
- with the following LaTeX-preamble line so that it can be directly inserted\r
- into a formula:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\series bold\r
-\r
-\backslash\r
-DeclareInputtext{176}{\r
-\backslash\r
-ifmmode^\r
-\backslash\r
-circ\r
-\backslash\r
-else\r
-\backslash\r
-textdegree\r
-\backslash\r
-f\SpecialChar \textcompwordmark{}\r
-i}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-\start_of_appendix\r
-Typographic Advice\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Typographic advice\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This section is a summary of the most important typographic rules, listed\r
- in ISO norms.\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-This collection was partly taken from the German semi-official dictionary\r
- called \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-Duden\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- \r
-\begin_inset CommandInset citation\r
-LatexCommand cite\r
-key "Duden"\r
-\r
-\end_inset\r
-\r
- that lists some of the ISO rules.\r
- More rules are listed in \r
-\begin_inset CommandInset citation\r
-LatexCommand cite\r
-key "Checklist"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-Physical units are \r
-\emph on\r
-always\r
-\emph default\r
- set upright\r
-\begin_inset Foot\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-done with font styles, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Font-Styles"\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-, no matter if they appear in italic text: 30\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-km/h\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-Between the value and the unit is the smallest space, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Predefined-Space"\r
-\r
-\end_inset\r
-\r
-.\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-This convention is automatically fulfilled when the command \r
-\series bold\r
-\r
-\backslash\r
-unittwo\r
-\series default\r
- is used.\r
- When it is entered to a formula, two boxes appear.\r
- In the first one the value is inserted, in the second one the unit, and\r
- one gets as above: \r
-\begin_inset Formula $\unit[30]{km/h}$\r
-\end_inset\r
-\r
-\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-.\r
- Note that \r
-\series bold\r
-\r
-\backslash\r
-unittwo\r
-\series default\r
- is not a real LaTeX command but the command \r
-\series bold\r
-\r
-\backslash\r
-unit[value]{unit}\r
-\series default\r
-, therefore you cannot use it in TeX code.\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-Percent and perthousand signs are set like physical units:\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-1.2\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-‰ alcohol in blood\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-The degree sign follows directly on the value: 15°, but not when it is used\r
- in units: 15\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-°C\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-In numbers with more than four digits the smallest space is inserted before\r
- every third digit to group them: \r
-\family roman\r
-\series medium\r
-\shape up\r
-\size normal\r
-\emph off\r
-\bar no\r
-\noun off\r
-\color none\r
-18\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-473\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-588\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-For dimensions like 120×90×40\r
-\begin_inset space \thinspace{}\r
-\end_inset\r
-\r
-cm the multiplication sign \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-×\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- is used.\r
- It is available either via the command \r
-\series bold\r
-\r
-\backslash\r
-times\r
-\series default\r
- or via the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Special Character\SpecialChar \menuseparator\r
-Symbols\r
-\family default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-Functions with names consisting of several letters are set upright to avoid\r
- confusions, see \r
-\begin_inset CommandInset ref\r
-LatexCommand ref\r
-reference "sub:Predefined-Functions"\r
-\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-Indices consisting of several letters, are set upright: \r
-\begin_inset Formula $E_{\mathrm{kin}}$\r
-\end_inset\r
-\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-Components of matrices are set italic: \r
-\begin_inset Formula $\hat{H}_{kl}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-The differentiation/integration operator 'd', the Euler's number 'e' and\r
- the imaginary unit 'i' should be set upright, to avoid mixing them up with\r
- other variables.\r
-\end_layout\r
-\r
-\begin_layout Itemize\r
-The character that denotes a \r
-\noun on\r
-Fourier\r
-\noun default\r
- transformation is inserted either by the command \r
-\series bold\r
-\r
-\backslash\r
-mathscr\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-spce \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-F\r
-\series default\r
- or via the menu \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Special Character\SpecialChar \menuseparator\r
-Symbols\SpecialChar \menuseparator\r
-Letterlike\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-Symbols\r
-\family default\r
-: \r
-\begin_inset Formula $\mathscr{F}$\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Synonyms\r
-\begin_inset Index idx\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-Synonyms\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Some characters and symbols can be created with several commands.\r
- Here is a list of the synonym commands:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace bigskip\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="12" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-equivalent to\r
-\begin_inset Note Note\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\series bold\r
-\r
-\backslash\r
-raisebox\r
-\series default\r
- is only used as spacer.\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ast\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-raisebox{-1.2mm}{\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-*\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-choose\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-binom\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-geq\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ge\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-lbrace\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-{\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-lbracket\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-[\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-leftarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-gets\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-leq\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-le\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-lor\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-vee\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-neq\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-not=\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-slash\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-/\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-vert\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-|\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="12" columns="2">\r
-<features rotate="0" tabularvalignment="middle">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<column alignment="center" valignment="top" width="0pt">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Command\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-equivalent to\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-backslash\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-\r
-\backslash\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dasharrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-dashrightarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-land\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-wedge\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-rbrace\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-rbracket\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-]\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-rightarrow\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-to\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-lnot\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-neg\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ne\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-not=\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-owns\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-ni\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-square\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Box\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-Vert\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\backslash\r
-|\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space \hfill{}\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Newpage newpage\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Bibliography\r
-\begin_inset CommandInset bibitem\r
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-\r
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-\end_document\r
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+\textclass scrartcl
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+% DO NOT ALTER THIS PREAMBLE!!!
+%
+% This preamble is designed to ensure that the file prints
+% out as advertised. If you mess with this preamble,
+% parts of this document may not print out as expected. If you
+% have problems LaTeXing this file, please contact
+% the documentation team
+% email: lyx-docs@lists.lyx.org
+
+% solves the following problem:
+% If the dection number consits of too many numerals the section heading
+% will be printed in the TOC without a space between it and the section number.
+% As solution more space between the number and the heading is inserted:
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+% makes caption labels bold
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+% check for package undertilde
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+% check for package eurosym
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+ {\setboolean{eurosym}{false}}
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+% check for package braket
+% used for physical vectors
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+% check for package cancel
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+% check for package upgreek
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+\pdf_title "LyX's Math Manual"
+\pdf_author "LyX Team, Uwe Stöhr"
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+\pdf_keywords "LyX, Mathed"
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+\index Index
+\shortcut idx
+\color #008000
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+\tocdepth 3
+\paragraph_separation skip
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+
+\begin_layout Title
+\SpecialChar LyX
+'s Detailed Math Manual
+\end_layout
+
+\begin_layout Author
+by the \SpecialChar LyX
+ Team
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+\noindent
+If you have comments or error corrections,
+ please send them to the \SpecialChar LyX
+ Documentation mailing list:
+
+\family typewriter
+
+\begin_inset CommandInset href
+LatexCommand href
+name "lyx-docs@lists.lyx.org"
+target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
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+
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+LatexCommand tableofcontents
+
+\end_inset
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+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
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+\begin_layout Plain Layout
+To export this document to PDF,
+ PS or DVI the \SpecialChar LaTeX
+-packages
+\series bold
+braket,
+ cancel,
+ eurosym,
+ mathdots,
+ mathtools,
+ mhchem,
+ undertilde
+\series default
+ and
+\series bold
+was
+\series default
+ should be installed.
+ If they are not installed the document can be exported anyway but the sections where the packages are required will not appear in the output.
+ An exception is
+\series bold
+mhchem
+\series default
+;
+ if it is not installed,
+ this file cannot be exported.
+\end_layout
+
+\begin_layout Plain Layout
+The latest PDF-version of this document can be found here:
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+https://wiki.lyx.org/LyX/Manuals#Math
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Introduction
+\end_layout
+
+\begin_layout Standard
+This document details \SpecialChar LyX
+'s math features and the \SpecialChar LaTeX
+-commands used for mathematical characters and constructs.
+ It is oriented toward the use of commands.
+ The user should read the
+\family typewriter
+Mathematical
+\begin_inset space ~
+\end_inset
+
+Formulas
+\family default
+ section of the User's Guide before proceeding.
+\end_layout
+
+\begin_layout Standard
+Most of the characters and many constructs explained in this manual are also accessible via the menu
+\family sans
+Insert
+\series bold
+\SpecialChar menuseparator
+
+\series default
+Math
+\family default
+ or the
+\family sans
+math
+\family default
+\series bold
+
+\family sans
+\series default
+toolbar
+\family default
+.
+ But everybody who has to write lots of formulas will notice that it is much faster to use commands instead of the math toolbar.
+ Therefore this manual is focused on commands but also mentions the corresponding toolbar buttons when available.
+\end_layout
+
+\begin_layout Standard
+Unless specially mentioned,
+ math commands are only available within formulas.
+ To be able to use all of the commands explained in this document,
+ the option
+\family sans
+Use AMS math package
+\family default
+ must be checked in the document settings (menu
+\family sans
+Document\SpecialChar menuseparator
+Settings\SpecialChar menuseparator
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+).
+\begin_inset Foot
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+
+\begin_layout Plain Layout
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+Use AMS math package automatically
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+ only uses
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+
+\begin_layout Plain Layout
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+
+\backslash
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+
+\end_inset
+
+-math when math constructs are found that are supported by \SpecialChar LyX
+.
+\end_layout
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+\end_inset
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+
+\end_layout
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+This document doesn't list all
+\begin_inset ERT
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+
+\begin_layout Plain Layout
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+
+\backslash
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+\end_layout
+
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+
+-math commands
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+
+
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+
+\end_inset
+
+-math commands is in the file
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+\begin_inset CommandInset href
+LatexCommand href
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+target "https://www.ctan.org/tex-archive/macros/amstex/doc/amsguide.pdf"
+literal "false"
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+
+\family default
+,
+ which is part of every \SpecialChar LaTeX
+ standard installation.
+\end_layout
+
+\end_inset
+
+ for lucidity reasons.
+\end_layout
+
+\begin_layout Section
+General Instructions
+\end_layout
+
+\begin_layout Standard
+To create an inline formula
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+inline
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ that is embedded in a text line,
+ use one of the shortcuts
+\begin_inset Info
+type "shortcuts"
+arg "math-mode"
+\end_inset
+
+ or the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-mode"
+\end_inset
+
+.
+\begin_inset Newline newline
+\end_inset
+
+To create a display style formula
+\begin_inset Index idx
+range none
+pageformat default
+status open
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+display style
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ which will appear bigger,
+ has a different format,
+ and will be in a separate paragraph,
+ use one of these shortcuts:
+
+\begin_inset Info
+type "shortcuts"
+arg "math-display"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+To change a display style formula to an inline formula,
+ place the cursor inside the formula and use the shortcut
+\begin_inset Info
+type "shortcuts"
+arg "math-mutate simple"
+\end_inset
+
+ or the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Change formula type
+\family default
+.
+ Similarly you can use the shortcut
+\begin_inset Info
+type "shortcuts"
+arg "math-mutate equation"
+\end_inset
+
+ to change from an inline to a display style formula.
+
+\end_layout
+
+\begin_layout Standard
+To display parts of an inline formula in the size of a display style formula,
+ enter the command
+\series bold
+
+\backslash
+displaystyle
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+D
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+displaystyle
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ in a formula.
+ A new blue box will appear in which the desired formula part is inserted.
+\end_layout
+
+\begin_layout Standard
+Only inline formulas are allowed inside tables.
+\end_layout
+
+\begin_layout Standard
+
+\family sans
+Math toolbar
+\family default
+ visibility is controlled in the menu
+\family sans
+View\SpecialChar menuseparator
+Toolbars\SpecialChar menuseparator
+Math
+\family default
+.
+ Three options will be presented,
+ On,
+ Off,
+ and Automatic.
+ Selecting On will cause the toolbar to be shown permanently at the bottom of the screen.
+ Selecting Off will disable the toolbar.
+ Selecting Automatic will cause the toolbar to automatically appear when the cursor is located within a formula.
+ The active state of the toolbar is indicated by a checkmark next to the current menu selection.
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The menu functionality appears to have changed,
+ I rewrote the paragraph for the current functionality
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\SpecialChar TeX
+ mode
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset IndexMacro sortkey
+status open
+
+\begin_layout Plain Layout
+T
+\end_layout
+
+\end_inset
+
+\SpecialChar TeX
+-mode
+\end_layout
+
+\end_inset
+
+ is invoked by pressing the toolbar button
+\begin_inset Info
+type "icon"
+arg "ert-insert"
+\end_inset
+
+ or by using the menu
+\family sans
+Insert\SpecialChar menuseparator
+TeX Code
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "ert-insert"
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+To change the \SpecialChar LaTeX
+-preamble
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset IndexMacro sortkey
+status open
+
+\begin_layout Plain Layout
+L
+\end_layout
+
+\end_inset
+
+\SpecialChar LaTeX
+-preamble
+\end_layout
+
+\end_inset
+
+,
+ use the menu
+\family sans
+Document\SpecialChar menuseparator
+Settings\SpecialChar menuseparator
+LaTeX
+\family default
+
+\family sans
+Preamble
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+To edit matrices,
+ case differentiations and multiline formulas,
+ use the menus
+\family sans
+Edit\SpecialChar menuseparator
+Math
+\family default
+ and
+\family sans
+Edit\SpecialChar menuseparator
+Rows
+\begin_inset space \thinspace{}
+\end_inset
+
+&
+\begin_inset space \thinspace{}
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+Columns,
+
+\family default
+ or the
+\family sans
+table toolbar
+\family default
+.
+ When lines and columns are swapped via the menu,
+ the column or line where the cursor is in is exchanged with the column to the right or the line below,
+ respectively.
+ If the cursor is in the last column or row,
+ the exchange is done with the column to the left or the line above.
+\end_layout
+
+\begin_layout Standard
+To write text in formulas
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For multiline formulas the command
+\series bold
+
+\backslash
+intertext
+\series default
+ is used,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Text-in-multiline"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\emph on
+mathematical text
+\emph default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Text
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+in formulas
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Mathematical text
+\end_layout
+
+\end_inset
+
+ is used.
+ This mode is invoked with the shortcut
+\begin_inset Info
+type "shortcut"
+arg "font-default"
+\end_inset
+
+ or by the insertion of the command
+\series bold
+
+\backslash
+text
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+T
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+text
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ The text appears black in \SpecialChar LyX
+ and can therefore be distinguished from the other formula parts which appear blue.
+ In the output,
+ mathematical text is set upright contrary to other formula parts.
+\end_layout
+
+\begin_layout Subsection*
+Command Scheme
+\end_layout
+
+\begin_layout Standard
+Most \SpecialChar LaTeX
+-commands for math constructs have the following syntax:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+commandname[optional
+\series default
+
+\series bold
+argument]{required
+\series default
+
+\series bold
+argument}
+\end_layout
+
+\begin_layout Standard
+A command always starts with a backslash
+\begin_inset Quotes gld
+\end_inset
+
+
+\series bold
+
+\backslash
+
+\series default
+
+\begin_inset Quotes grd
+\end_inset
+
+.
+ To omit the
+\series bold
+optional
+\series default
+
+\series bold
+argument
+\series default
+s,
+ also omit the associated brackets.
+ The braces around the
+\series bold
+required
+\series default
+
+\series bold
+arguments
+\series default
+ are referred to in this document as \SpecialChar TeX
+ braces
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset IndexMacro sortkey
+status open
+
+\begin_layout Plain Layout
+T
+\end_layout
+
+\end_inset
+
+\SpecialChar TeX
+-braces
+\end_layout
+
+\end_inset
+
+.
+ If you append a left brace to a command name inside a formula,
+ \SpecialChar LyX
+ automatically creates a right \SpecialChar TeX
+ brace.
+ In all other cases standalone \SpecialChar TeX
+ braces are created in formulas with the command
+\series bold
+
+\backslash
+{
+\series default
+.
+ Normal braces are created by typing
+\series bold
+{
+\series default
+.
+ \SpecialChar TeX
+ braces appear red in \SpecialChar LyX
+,
+ normal braces appear blue.
+ In \SpecialChar TeX
+ mode a command is not needed to get \SpecialChar TeX
+ braces.
+ \SpecialChar TeX
+ braces don't appear in the output while normal braces do.
+\end_layout
+
+\begin_layout Standard
+When commands without arguments,
+ like commands for symbols,
+ are entered in \SpecialChar TeX
+ mode,
+ a space character must
+\emph on
+always
+\emph default
+ be behind the command to end it.
+ This space doesn't appear in the output.
+ When the space should appear in the output,
+ the space must be followed by a non-breaking space in normal text.
+\end_layout
+
+\begin_layout Standard
+A non-breaking space is inserted with
+\begin_inset Info
+type "shortcuts"
+arg "command-alternatives math-space ; space-insert protected"
+\end_inset
+
+or with the menu selection
+\family sans
+ Insert\SpecialChar menuseparator
+Formatting\SpecialChar menuseparator
+Non-Breaking Normal Space
+\family default
+ or
+\family sans
+Ctrl+Space
+\family default
+.
+\end_layout
+
+\begin_layout Subsection*
+\begin_inset Newpage newpage
+\end_inset
+
+Explanation of Syntax Used in this Manual
+\end_layout
+
+\begin_layout Itemize
+The symbol
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+ denotes a space character to be input by the user.
+\end_layout
+
+\begin_layout Itemize
+An arrow like
+\begin_inset Formula $\to$
+\end_inset
+
+ denotes the usage of the corresponding arrow key on the keyboard.
+ The
+\family sans
+Tab
+\family default
+ key can often be used instead of
+\begin_inset Formula $\to$
+\end_inset
+
+ and
+\begin_inset Formula $\downarrow$
+\end_inset
+
+,
+ and
+\family sans
+Shift+Tab
+\family default
+ instead of
+\begin_inset Formula $\leftarrow$
+\end_inset
+
+ and
+\begin_inset Formula $\uparrow$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection*
+Available Units
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Float table
+placement H
+alignment document
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "tab:Available-units"
+
+\end_inset
+
+Available units
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Unit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Name / Description
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+mm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Millimeter
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+cm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Centimeter
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+in
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Inch (1
+\begin_inset space \thinspace{}
+\end_inset
+
+in = 2.54
+\begin_inset space \thinspace{}
+\end_inset
+
+cm)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+pt
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Point (72.27
+\begin_inset space \thinspace{}
+\end_inset
+
+pt = 1
+\begin_inset space \thinspace{}
+\end_inset
+
+in)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+pc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Pica (1
+\begin_inset space \thinspace{}
+\end_inset
+
+pc = 12
+\begin_inset space \thinspace{}
+\end_inset
+
+pt)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+sp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+scaled point (65536
+\begin_inset space \thinspace{}
+\end_inset
+
+sp = 1
+\begin_inset space \thinspace{}
+\end_inset
+
+pt)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+bp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+big point (72
+\begin_inset space \thinspace{}
+\end_inset
+
+bp = 1
+\begin_inset space \thinspace{}
+\end_inset
+
+in)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+dd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Didot (1
+\begin_inset space \thinspace{}
+\end_inset
+
+dd
+\begin_inset Formula $\approx$
+\end_inset
+
+ 0.376
+\begin_inset space \thinspace{}
+\end_inset
+
+mm)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+cc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Cicero (1
+\begin_inset space \thinspace{}
+\end_inset
+
+cc = 12
+\begin_inset space \thinspace{}
+\end_inset
+
+dd)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+ex
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Height of letter
+\emph on
+
+\begin_inset Quotes eld
+\end_inset
+
+x
+\emph default
+
+\begin_inset Quotes erd
+\end_inset
+
+ in the current font
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+em
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+width of letter
+\begin_inset Quotes eld
+\end_inset
+
+
+\emph on
+M
+\emph default
+
+\begin_inset Quotes erd
+\end_inset
+
+ in the current font
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+mu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+math unit (1
+\begin_inset space \thinspace{}
+\end_inset
+
+mu =
+\begin_inset Formula $\nicefrac{1}{18}$
+\end_inset
+
+
+\begin_inset space \thinspace{}
+\end_inset
+
+em)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Basic Functions
+\end_layout
+
+\begin_layout Subsection
+Exponents
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Exponents
+\end_layout
+
+\end_inset
+
+ and Indices
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Indices
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Superscripts
+\begin_inset IndexMacro see
+status open
+
+\begin_layout Plain Layout
+Exponents
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Subscripts
+\begin_inset IndexMacro see
+status open
+
+\begin_layout Plain Layout
+Indices
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Indices are created with an underscore
+\begin_inset Quotes eld
+\end_inset
+
+_
+\begin_inset Quotes erd
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-subscript"
+\end_inset
+
+,
+ exponents with a caret
+\begin_inset Quotes eld
+\end_inset
+
+^
+\begin_inset Quotes erd
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-superscript"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+B_V
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $B_{V}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+B^V
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $B^{V}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+B^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $B^{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+As the caret is in some languages an accent,
+ vowels will be accentuated in this case and not set as exponents
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+Depending on the keyboard settings used this can also happen for characters other than vowels.
+\end_layout
+
+\end_inset
+
+.
+ To get exponents in this case,
+ press
+\family sans
+Space
+\family default
+ after the caret as in the last example.
+\end_layout
+
+\begin_layout Subsection
+Fractions
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Fractions"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Fractions
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Fractions are generated with the command
+\series bold
+
+\backslash
+frac
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+F
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+frac
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\frac"
+\end_inset
+
+.
+ The font size is adjusted automatically,
+ depending on whether the fraction is in an inline or display style formula.
+ With the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\frac-square"
+\end_inset
+
+ you can select different fraction types.
+\end_layout
+
+\begin_layout Standard
+With the command
+\series bold
+
+\backslash
+dfrac
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+D
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+dfrac
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ a fraction can be created that always has the size of a display style formula.
+ With
+\series bold
+
+\backslash
+tfrac
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+T
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+tfrac
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ the fraction appears always with the size of an inline formula.
+ An example:
+\end_layout
+
+\begin_layout Standard
+A line with the fraction
+\begin_inset Formula $\frac{1}{2}$
+\end_inset
+
+ that was created with the command
+\series bold
+
+\backslash
+frac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+A line with the fraction
+\begin_inset Formula $\dfrac{1}{2}$
+\end_inset
+
+ that was created with the command
+\series bold
+
+\backslash
+dfrac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\frac{A}{B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dfrac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dfrac{A}{B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm" bottomspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dfrac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e^
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+1
+\begin_inset Formula $\downarrow$
+\end_inset
+
+2
+\begin_inset Formula $\downarrow\downarrow$
+\end_inset
+
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\begin_inset Newpage newpage
+\end_inset
+
+For nested fractions the command
+\series bold
+
+\backslash
+cfrac
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+C
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+cfrac
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ can be used.
+ Here is an example:
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\begin{align*}
+\textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
+\frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
+\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command for the example above is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cfrac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B+
+\backslash
+cfrac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C+
+\backslash
+cfrac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+E
+\begin_inset Formula $\downarrow$
+\end_inset
+
+F
+\begin_inset Formula $\downarrow$
+\end_inset
+
+D
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cfrac
+\series default
+ always sets the fraction size to that of a displayed formula,
+ even when it is part of another fraction.
+\end_layout
+
+\begin_layout Standard
+It is possible to specify the alignment of the numerator.
+ The command
+\series bold
+
+\backslash
+cfracleft
+\series default
+ is used to left align it,
+ the command
+\series bold
+
+\backslash
+cfracright
+\series default
+ to right-align it.
+
+\series bold
+
+\backslash
+cfrac
+\series default
+ centers the numerator.
+ These fractions demonstrate the different alignments:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+\begin_inset Formula
+\[
+\cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\series default
+
+\series bold
+
+\backslash
+cfracleft
+\series default
+ and
+\series bold
+
+\backslash
+cfracright
+\series default
+ are not real \SpecialChar LaTeX
+ commands but represent the command
+\series bold
+
+\backslash
+cfrac[alignment]{numerator}{denominator}
+\series default
+ .
+ Therefore you cannot use them in \SpecialChar TeX
+ code.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+It is often advantageous to combine
+\series bold
+
+\backslash
+cfrac
+\series default
+ and
+\series bold
+
+\backslash
+frac
+\series default
+:
+\begin_inset Formula
+\[
+\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For inline fractions with a sloped fraction stroke you can use the command
+\series bold
+
+\backslash
+nicefrac
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+N
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+nicefrac
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+:
+
+\begin_inset Formula $\nicefrac{5}{31}$
+\end_inset
+
+ or
+\series bold
+
+\backslash
+unitfrac
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+unitfrac
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+:
+
+\begin_inset Formula $\unitfrac{5}{31}$
+\end_inset
+
+ There is also the command
+\series bold
+
+\backslash
+unitfracthree
+\series default
+ which allows you to write a fraction in combination with a number:
+
+\begin_inset Formula $\unitfrac[2]{1}{3}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\series default
+
+\series bold
+
+\backslash
+unitfracthree
+\series default
+ is not a real \SpecialChar LaTeX
+ command but the command
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+unitfrac[number]{numerator}{denominator}
+\series default
+ .
+ Therefore you cannot use it in \SpecialChar TeX
+ code.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+How to define your own fractions where the fraction stroke can be changed is explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Self-defined-Fractions"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Multiline fractions are explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Multiline-Fractions"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Roots
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Roots
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Square roots are created with
+\series bold
+
+\backslash
+sqrt
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+sqrt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ or the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\sqrt"
+\end_inset
+
+,
+ all other roots with the command
+\series bold
+
+\backslash
+root
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+root
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ or with the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\root"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqrt
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A-B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqrt{A-B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+root
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+3
+\begin_inset Formula $\downarrow$
+\end_inset
+
+A-B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqrt[3]{A-B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A square root can also be created with
+\series bold
+
+\backslash
+root
+\series default
+ when the root index field is left empty.
+\end_layout
+
+\begin_layout Standard
+With certain indices the distance to the root is too small,
+ like in this formula:
+
+\begin_inset Formula $\sqrt[\beta]{B}$
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+The
+\begin_inset Formula $\beta$
+\end_inset
+
+ touches the root.
+ To avoid this,
+ the commands
+\series bold
+
+\backslash
+leftroot
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+L
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+leftroot
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+uproot
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+uproot
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ are used with the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+leftroot{distance}
+\series default
+ and
+\series bold
+
+\backslash
+uproot{distance}
+\end_layout
+
+\begin_layout Standard
+Distance is the number of Big Points (unit bp;
+
+\begin_inset Formula $\mathrm{72\,bp=1\,inch}$
+\end_inset
+
+),
+ that the index should be moved to the left or up,
+ resp..
+ The commands are written to the index.
+ This way the command
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+root
+\backslash
+leftroot{-1
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+uproot{2
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+beta
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+B
+\begin_inset Newline newline
+\end_inset
+
+
+\series default
+produces a correct typeset formula:
+
+\begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Binomial Coefficients
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Binomial coefficients
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Binomial coefficients are inserted with the command
+\series bold
+
+\backslash
+binom
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+B
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+binom
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ or with the submenu of the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\frac-square"
+\end_inset
+
+.
+ As with fractions (
+\series bold
+
+\backslash
+frac
+\series default
+) in addition to
+\series bold
+
+\backslash
+binom
+\series default
+ there are the commands
+\series bold
+
+\backslash
+dbinom
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+D
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+dbinom
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+tbinom
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+T
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+tbinom
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ For other brackets around binomial coefficients there are the commands
+\series bold
+
+\backslash
+brace
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+B
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+brace
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+brack
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+B
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+brack
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+binom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\binom{A}{B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dbinom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dbinom{A}{B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm" bottomspace="0.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+tbinom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\tbinom{A}{B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1mm">
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+brack
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula ${A \brack B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm" bottomspace="0.5mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+brace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula ${A \brace B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Case Differentiations
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Case differentiations
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cases
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\to$
+\end_inset
+
+B>0
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+C
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+cases
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\begin{cases}
+A & B>0\end{cases}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cases
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\begin{cases}
+A & \textrm{for }x>0\\
+B & \textrm{for }x=0
+\end{cases}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+After inserting
+\series bold
+
+\backslash
+cases
+\series default
+ or pressing the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\cases"
+\end_inset
+
+ you can create new lines with the shortcut
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+ or the table toolbar button
+\begin_inset Info
+type "icon"
+arg "tabular-feature append-row"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+cases
+\series default
+ is also available via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Cases-Environment
+\family default
+.
+\end_layout
+
+\begin_layout Subsection
+Negations
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Negations
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+By inserting
+\series bold
+
+\backslash
+not
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+N
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+not
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ every character can be displayed canceled.
+ The characters are quasi accentuated by a slash.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\not=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+not
+\backslash
+le
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\not\le$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+not
+\backslash
+parallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\not\parallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The last example shows that not all negations look good.
+ Therefore there are special commands for some negations (see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Mathematical-Symbols"
+nolink "false"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Relations"
+nolink "false"
+
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Subsection
+Placeholders
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Placeholders"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Placeholders
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Chemical characters
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+Isotopes
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status open
+
+\begin_layout Plain Layout
+Isotopes
+\begin_inset IndexMacro see
+status open
+
+\begin_layout Plain Layout
+Chemical characters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When displaying e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+isotopes
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+Typesetting isotopes and chemical symbols is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Chemical-Symbols-and"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ the following problem occurs:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Indices created with sub- and superscripts:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $_{9}^{19}\mathrm{F}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Correct indices:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The shorter index is placed by default below or above the first character of the longer index.
+ This is corrected using the command
+\series bold
+
+\backslash
+phantom
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+P
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+phantom
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ or the math toolbar button
+\begin_inset space \thinspace{}
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+Found in the submenu of the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\space"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Info
+type "icon"
+arg "math/phantom"
+\end_inset
+
+ to create one or more phantom characters.
+ When inserting phantom characters a small blue box appears that is superposed with two red arrows.
+ The arrows indicate the width and height of the box to be created as a placeholder.
+ Phantom characters are placeholders with the same character size.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+^19
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_
+\backslash
+phantom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+1
+\begin_inset Formula $\to$
+\end_inset
+
+9
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+mathrm
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+F
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm" bottomspace="0.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+^235
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_
+\backslash
+phantom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+23
+\begin_inset Formula $\to$
+\end_inset
+
+9
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+mathrm
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+F
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm" bottomspace="0.5mm">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Lambda
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^
+\backslash
+phantom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+ii
+\begin_inset Formula $\to$
+\end_inset
+
+t
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_MMt
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Furthermore there are the commands
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+V
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+vphantom
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ (toolbar button
+\begin_inset Info
+type "icon"
+arg "math/vphantom"
+\end_inset
+
+) and
+\series bold
+
+\backslash
+hphantom
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+H
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+hphantom
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ (toolbar button
+\begin_inset Info
+type "icon"
+arg "math/hphantom"
+\end_inset
+
+).
+
+\series bold
+
+\backslash
+hphantom
+\series default
+ creates only space for the maximal height of the characters in the box but not for its width.
+
+\series bold
+
+\backslash
+vphantom
+\series default
+ creates only space for the width of the box content.
+ Therefore the boxes of both commands have only one red arrow.
+\end_layout
+
+\begin_layout Standard
+For example the command
+\series bold
+
+\backslash
+vphantom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+a
+\backslash
+int
+\series default
+ creates space for the height of the integral sign,
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+The command
+\series bold
+
+\backslash
+int
+\series default
+ creates an integral sign,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Big-Operators"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ because this is the larger character.
+ An example application is in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Multiline-Brackets"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Placeholders can also be used for text when they are inserted via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Formatting\SpecialChar menuseparator
+Phantom
+\family default
+:
+\end_layout
+
+\begin_layout Standard
+This is a sentence.
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom Phantom
+status open
+
+\begin_layout Plain Layout
+This
+\end_layout
+
+\end_inset
+
+ is a sentence.
+\end_layout
+
+\begin_layout Subsection
+Lines
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Lines
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+underlined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overline
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A+B
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+O
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+overline
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overline{A+B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+underline
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A+B
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+underline
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\underline{A+B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm" bottomspace="1mm">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overline
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+underline
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overline{\underline{A+B}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the last example it doesn't matter if
+\series bold
+
+\backslash
+overline
+\series default
+ or
+\series bold
+
+\backslash
+underline
+\series default
+ is inserted first.
+\end_layout
+
+\begin_layout Standard
+To double underline use
+\series bold
+
+\backslash
+underline
+\series default
+ twice (or as many times you want).
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Custom lines can be created using the command
+\series bold
+
+\backslash
+rule
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+rule
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ which has the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+rule[vertical offset]{length}{thickness}
+\end_layout
+
+\begin_layout Standard
+The optional vertical offset shifts the line upwards (or downwards,
+ when the value is negative).
+ The units listed in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "tab:Available-units"
+nolink "false"
+
+\end_inset
+
+ can be used for the values.
+ Here are two example lines created with the commands
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+rule[-2ex]{3cm}{2pt}
+\series default
+ and
+\series bold
+
+\backslash
+rule{2cm}{1pt}
+\series default
+:
+\end_layout
+
+\begin_layout Standard
+This is a sentence
+\begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
+\end_inset
+
+ with two lines.
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+rule
+\series default
+ can also be used for text when a line is inserted via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Formatting\SpecialChar menuseparator
+Horizontal
+\begin_inset space ~
+\end_inset
+
+Line
+\family default
+:
+\end_layout
+
+\begin_layout Standard
+This is a sentence
+\begin_inset CommandInset line
+LatexCommand rule
+offset "0.5ex"
+width "3cm"
+height "1pt"
+
+\end_inset
+
+ with one line.
+\end_layout
+
+\begin_layout Subsection
+Ellipses
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Ellipses"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Ellipses
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+There are different types of ellipses available.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+In the math toolbar in the submenu of the button
+\begin_inset Info
+type "icon"
+arg "math-insert \\ldots"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ For listings,
+ dots at the baseline are used (
+\series bold
+
+\backslash
+ldots
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+L
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+ldots
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+),
+ while for operations,
+ dots are needed that are on the same height as the operators (
+\series bold
+
+\backslash
+cdots
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+C
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+cdots
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+).
+ When using the command
+\series bold
+
+\backslash
+dots
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+D
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+dots
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ \SpecialChar LaTeX
+ decides on the basis of the next character what type is used.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A_1
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+,
+\backslash
+dots
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+,A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A_{1},\dots,A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A_1
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++
+\backslash
+dots
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A_{1}+\dots+A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A_1
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+,
+\backslash
+ldots
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+,A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A_{1},\ldots,A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A_1
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++
+\backslash
+cdots
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A_{1}+\cdots+A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vdots
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\vdots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddots
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ddots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iddots
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\iddots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+3×3
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix with the different dots
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\begin{array}{ccc}
+A_{11} & \cdots & A_{1m}\\
+\vdots & \ddots & \vdots\\
+A_{n1} & \cdots & A_{nm}
+\end{array}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The ellipses available in menu
+\family sans
+Insert\SpecialChar menuseparator
+Special
+\begin_inset space ~
+\end_inset
+
+Character
+\family default
+ are
+\series bold
+
+\backslash
+ldots
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+To use
+\series bold
+
+\backslash
+iddots
+\series default
+,
+ the option
+\family sans
+Use mathdots package (automatically)
+\family default
+ must be set in the document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+.
+\begin_inset Newline newline
+\end_inset
+
+Using the option
+\family sans
+Use mathdots package
+\family default
+ will improve the appearance of all dots in the documents if their font style or size is not the default.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Specially for matrices there are ellipses that span over several columns.
+ They are created with the command
+\series bold
+
+\backslash
+hdotsfor
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+H
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+hdotsfor
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and have the following scheme (
+\family sans
+mathtools
+\family default
+ must be loaded
+\family sans
+always
+\family default
+ under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ for this to work):
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hdotsfor[distance]{number of columns}
+\end_layout
+
+\begin_layout Standard
+The number of columns specifies how many columns should be spanned.
+ Distance is a factor for the distance between the dots.
+\end_layout
+
+\begin_layout Standard
+In the following matrix the command
+\series bold
+
+\backslash
+hdotsfor[2]{4}
+\series default
+ was inserted in the first box of the second line to get an ellipsis with a dot distance twice as long as with the command
+\series bold
+
+\backslash
+dots
+\series default
+:
+\begin_inset Formula
+\[
+\left(\begin{array}{cccc}
+A & B & C & D\\
+\hdotsfor[2]{4}\\
+q & w & e & r
+\end{array}\right)
+\]
+
+\end_inset
+
+Note that the matrix fields that should be spanned must be empty,
+ otherwise you get \SpecialChar LaTeX
+-errors.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Furthermore you can fill with the command
+\series bold
+
+\backslash
+dotfill
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status open
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+D
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+dotfill
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ the rest of a line with dots.
+ The effect of these commands is the same as with
+\series bold
+
+\backslash
+hfill
+\series default
+,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Variable-Space"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+For example the command
+\series bold
+A
+\backslash
+dotfill
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B
+\series default
+ produces
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\dotfill B$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Similar to
+\series bold
+
+\backslash
+dotfill
+\series default
+ there is for a line the command
+\series bold
+
+\backslash
+hrulefill
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+H
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+hrulefill
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\hrulefill B$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use the commands for text,
+ they have to be inserted in \SpecialChar TeX
+ mode.
+\end_layout
+
+\begin_layout Section
+Matrices
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Matrices"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Matrices
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Matrices can be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "dialog-show mathmatrix"
+\end_inset
+
+ or the menu
+\family sans
+Insert\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Matrix
+\family default
+.
+ In the matrix dialog you can specify the number of columns and rows,
+ the alignment and the decoration.
+ The vertical alignment is only of importance for matrices in inline formulas:
+\end_layout
+
+\begin_layout Standard
+The first matrix is top
+\begin_inset Formula $\begin{array}[t]{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L
+\end{array}$
+\end_inset
+
+,
+ the second middle
+\begin_inset Formula $\begin{array}{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L
+\end{array}$
+\end_inset
+
+ and the third bottom
+\begin_inset Formula $\begin{array}[b]{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L
+\end{array}$
+\end_inset
+
+ aligned.
+\end_layout
+
+\begin_layout Standard
+The horizontal alignment specifies how the column entries should be aligned.
+ It is set by entering a letter for every column.
+
+\emph on
+l
+\emph default
+ denotes left aligned,
+
+\emph on
+c
+\emph default
+ centered and
+\emph on
+r
+\emph default
+ right aligned.
+ To create for example a 4
+\series bold
+×
+\series default
+4
+\begin_inset space ~
+\end_inset
+
+matrix where the first column is left aligned,
+ the second and third are centered and the last one is right aligned,
+ one enters for the horizontal alignment
+\series bold
+lccr
+\series default
+.
+ Normally in a matrix all columns are centered,
+ therefore the default for every column is a
+\series bold
+c
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Horizontal alignment:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+lll
+\series default
+ :
+
+\begin_inset Formula $\begin{array}{lll}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000
+\end{array}$
+\end_inset
+
+ ,
+
+\series bold
+ccc
+\series default
+ :
+
+\begin_inset Formula $\begin{array}{ccc}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000
+\end{array}$
+\end_inset
+
+ ,
+
+\series bold
+rrr
+\series default
+ :
+
+\begin_inset Formula $\begin{array}{rrr}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000
+\end{array}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To subsequently add or delete rows and columns,
+ the math toolbar buttons
+\begin_inset Info
+type "icon"
+arg "tabular-feature append-row"
+\end_inset
+
+,
+
+\begin_inset Info
+type "icon"
+arg "tabular-feature delete-row"
+\end_inset
+
+,
+ etc.
+\begin_inset space \thinspace{}
+\end_inset
+
+,
+ or the menu
+\family sans
+Edit\SpecialChar menuseparator
+Rows & Columns
+\family default
+ can be used.
+ New rows can also be created with
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\family sans
+Appearance
+\family default
+ can be used to add parentheses in the selected style around the matrix or to select the
+\family sans
+small
+\family default
+ style,
+ suitable for an inline matrix like this one
+\begin_inset Formula $\bigl(\begin{smallmatrix}0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0
+\end{smallmatrix}\bigr)$
+\end_inset
+
+.
+ Here the parentheses have been added manually using commands
+\series bold
+
+\backslash
+bigl(
+\series default
+ and
+\series bold
+
+\backslash
+bigr).
+\end_layout
+
+\begin_layout Standard
+Alternatively,
+ parentheses can be created with the commands
+\series bold
+
+\backslash
+left
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+L
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+left
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+right
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+right
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ (shortcut
+\family sans
+Alt+M
+\begin_inset space ~
+\end_inset
+
+Parenthesis
+\family default
+),
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Automatic-Bracket-Size"
+nolink "false"
+
+\end_inset
+
+,
+ or by using the following commands:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bmatrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+×
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0
+\end{array}\end{bmatrix}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm" bottomspace="0.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Bmatrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+×
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0
+\end{array}\end{Bmatrix}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+pmatrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+×
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0
+\end{array}\end{pmatrix}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vmatrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+×
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0
+\end{array}\end{vmatrix}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm" bottomspace="0.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Vmatrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+×
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0
+\end{array}\end{Vmatrix}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+matrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+×
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\begin{matrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0
+\end{array}\end{matrix}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+When e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+
+\series bold
+
+\backslash
+vmatrix
+\series default
+ is inserted,
+ a blue box appears between two vertical lines where the matrix is inserted.
+\begin_inset Newline newline
+\end_inset
+
+Note that decorated matrices ignore the vertical alignment.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+As all multiline formulas are matrices,
+ the length
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+A
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+arraycolsep
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ that is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Column-Separation"
+nolink "false"
+
+\end_inset
+
+ can also be used to change the column separation of matrices.
+\end_layout
+
+\begin_layout Standard
+To change the row separation,
+ the command
+\series bold
+
+\backslash
+arraystretch
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+A
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+arraystretch
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is used as follows:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+arraystretch}{stretch factor}
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+renewcommand
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+renewcommand
+\series default
+ assigns the stretch factor to the predefined command
+\series bold
+
+\backslash
+arraystretch
+\series default
+.
+ For example to double the row separation,
+ use a stretch factor of 2.
+ This is then used for all following matrices.
+ To restore the original separation,
+ assign a stretch factor of 1 to
+\series bold
+
+\backslash
+arraystretch
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Small inline matrices can also be obtained using the command
+\series bold
+
+\backslash
+smallmatrix
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+smallmatrix
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ When it is inserted in a line a blue box with two dashed lines appears.
+ Adjust the matrix rows and columns as desired.
+\end_layout
+
+\begin_layout Standard
+This is a matrix
+\begin_inset Formula $\left(\begin{smallmatrix}A & B\\
+C & D
+\end{smallmatrix}\right)$
+\end_inset
+
+ in a text line with automatic delimiters around it.
+\end_layout
+
+\begin_layout Section
+Brackets and Delimiters
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Brackets
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Delimiters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vertical Brackets and Delimiters
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Brackets
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+vertical
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+(
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $($
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+{
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\{$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+[
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $[$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+langle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\langle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lceil
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\lceil$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lfloor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\lfloor$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+/
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $/$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+|
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $|$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+}
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $]$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rceil
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rceil$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rfloor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rfloor$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\backslash
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\backslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+|
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\|$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series medium
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\series default
+ In \SpecialChar TeX
+ mode the command
+\series bold
+
+\backslash
+textbackslash
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+T
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+textbackslash
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ must be used for the backslash,
+ because the command
+\series bold
+
+\backslash
+
+\backslash
+
+\series default
+ produces a line break there.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For all characters listed above the size can be adjusted with the commands described in the following two subsections.
+ When using these commands,
+ the characters < and > can directly be used instead of the commands
+\series bold
+
+\backslash
+langle
+\series default
+ and
+\series bold
+
+\backslash
+rangle
+\series default
+.
+\end_layout
+
+\begin_layout Subsubsection
+Manual Bracket Size
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Manual-Bracket-Size"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Bracket size
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+manual
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The bracket size can be specified manually by the \SpecialChar LaTeX
+-commands
+\series bold
+
+\backslash
+big
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+B
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+big
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+
+\series bold
+
+\backslash
+Big
+\series default
+,
+
+\series bold
+
+\backslash
+bigg
+\series default
+ and
+\series bold
+
+\backslash
+Bigg
+\series default
+.
+
+\series bold
+
+\backslash
+big
+\series default
+ denotes the smallest and
+\series bold
+
+\backslash
+Bigg
+\series default
+ the largest bracket size.
+\end_layout
+
+\begin_layout Standard
+These commands are used to emphasize levels of brackets:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+All brackets in the same size:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $((A+B)(A-B))^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+This looks better:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For the second formula the command
+\series bold
+
+\backslash
+Big((A+B)(A-B)
+\backslash
+Big)^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\series default
+ has been used.
+\end_layout
+
+\begin_layout Standard
+Here is an example containing all bracket sizes:
+\end_layout
+
+\begin_layout Standard
+\align center
+
+\backslash
+Bigg(
+\backslash
+exp
+\backslash
+bigg<
+\backslash
+Big[
+\backslash
+big{
+\backslash
+ln(3x)
+\backslash
+big}^2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+sin(x)
+\backslash
+Big]^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+bigg>
+\backslash
+Bigg)^0,5
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In addition to the
+\series bold
+
+\backslash
+big
+\series default
+-commands there is a variant,
+
+\series bold
+
+\backslash
+bigm
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+B
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+bigm
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ that adds a bit more space between the bracket and its content.
+ Other variants
+\series bold
+
+\backslash
+bigl
+\series default
+and
+\series bold
+
+\backslash
+bigr
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+B
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+bigl –
+\backslash
+bigr
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ don't add additional space.
+ The
+\emph on
+l
+\emph default
+ at the end of the command
+\series bold
+
+\backslash
+bigl
+\series default
+ is for a left bracket;
+ for a right bracket this is replaced by an
+\emph on
+r
+\emph default
+.
+ A left or right bracket can each be an opening or closing bracket.
+\end_layout
+
+\begin_layout Standard
+The following table contains comparisons of the variants:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="middle">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Bigm(
+\backslash
+bigm(
+\backslash
+ln(3x)
+\backslash
+bigm)^2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+Bigm)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Big(
+\backslash
+big(
+\backslash
+ln(3x)
+\backslash
+big)^2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+Big)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm" bottomspace="0.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Bigl(
+\backslash
+bigl(
+\backslash
+ln(3x)
+\backslash
+bigr)^2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+Bigr)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm" bottomspace="0.5mm">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigl)
+\backslash
+ln(3x)
+\backslash
+bigr(
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigl)\ln(3x)\bigr($
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Automatic Bracket Size
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Automatic-Bracket-Size"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Bracket size
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+automatic
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Variably sized brackets can be inserted with the commands
+\series bold
+
+\backslash
+left
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+L
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+left
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+right
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+right
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "dialog-show mathdelimiter"
+\end_inset
+
+.
+ The desired bracket must be inserted directly behind the
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ commands.
+ The bracket size will then automatically be calculated for the output.
+\end_layout
+
+\begin_layout Standard
+\align center
+normal bracket:
+ The command
+\series bold
+
+\backslash
+ln(
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+)
+\series default
+ creates
+\begin_inset Formula
+\[
+\ln(\frac{A}{C})
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+multiline bracket:
+ The command
+\series bold
+
+\backslash
+ln
+\backslash
+left(
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+right)
+\series default
+ creates
+\begin_inset Formula
+\[
+\ln\left(\frac{A}{C}\right)
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Instead of
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ the shortcut
+\family sans
+Alt+M
+\begin_inset space ~
+\end_inset
+
+Bracket
+\family default
+ can be used.
+ This has the advantage that you can see in \SpecialChar LyX
+ immediately the real bracket size and that the matching right bracket will be created too.
+\begin_inset Newline newline
+\end_inset
+
+The command for the last example would then be:
+
+\series bold
+
+\backslash
+ln Alt+M
+\series default
+
+\series bold
+(
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\end_layout
+
+\begin_layout Standard
+To omit a left or right bracket,
+ a dot is inserted for the omitted bracket.
+ For example the command
+\series bold
+
+\backslash
+left.
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+right}
+\series default
+ creates:
+\series bold
+
+\begin_inset Formula
+\[
+\left.\frac{A}{B}\right\}
+\]
+
+\end_inset
+
+
+\series default
+The commands
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ will be converted by \SpecialChar LyX
+ to brackets with the correct size when the document is reloaded and an omitted bracket will appear as dashed line.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Because all popular \SpecialChar LaTeX
+ distributions use e\SpecialChar TeX
+,
+ an extension to \SpecialChar LaTeX
+,
+ the command
+\series bold
+
+\backslash
+middle
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+M
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+middle
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is available for all brackets and limits.
+ With this command the height of the following character is adapted to the one of the surrounding brackets,
+ for example in the case of physical vectors:
+\begin_inset Formula
+\[
+\left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
+\]
+
+\end_inset
+
+For physical vectors there is a special \SpecialChar LaTeX
+-package,
+ described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Physical-Vectors"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Horizontal Brackets
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Brackets
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+horizontal
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overbrace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^3
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+O
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+overbrace
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbrace{A+B}^{3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+underbrace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_5
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+underbrace
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\underbrace{A+B}_{5}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overbrace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+underbrace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A+B_w
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_7
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the last example it doesn't matter if
+\series bold
+
+\backslash
+overbrace
+\series default
+ or
+\series bold
+
+\backslash
+underbrace
+\series default
+ is inserted first.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+If in document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ the option for the package
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+mathtools
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is set to
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+,
+ you will also have access to square brackets:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+overbracket
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+{A+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^3
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+O
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+overbracket
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbracket{A+B}^{3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+under
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+bracket
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+{A+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_5
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+under
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+bracket
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\underbracket{A+B}_{5}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overbracket{
+\backslash
+underbracket{A+B_w
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_7
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^C
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For
+\series bold
+
+\backslash
+overbracket
+\series default
+ and
+\series bold
+
+\backslash
+underbracket
+\series default
+ you can change the thickness of the bracket's stroke by specifying the desired thickness in square brackets behind the command:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+overbracket
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+[3pt]
+\backslash
+{A+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+under
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+bracket
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+[1pt]
+\backslash
+{A+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_5
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+When brackets overlap each other,
+ multiline formulas as described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Multiline-Formulas"
+nolink "false"
+
+\end_inset
+
+ must be used:
+\begin_inset Formula
+\begin{eqnarray*}
+A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
+ & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
+\end{eqnarray*}
+
+\end_inset
+
+In the first row,
+ the formula is inserted together with the first brace.
+ It is important that the space command
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+Space commands are explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Predefined-Space"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+:
+
+\series default
+ is inserted before the first
+\begin_inset Formula $d$
+\end_inset
+
+ because the brace that ends behind the
+\begin_inset Formula $q$
+\end_inset
+
+ prevents the following
+\begin_inset Quotes eld
+\end_inset
+
++
+\begin_inset Quotes erd
+\end_inset
+
+ from being surrounded by spaces.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+Because a bracket is not handled as a character,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Binary-Operators"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ The second brace is inserted in the second row.
+ As it should begin before the
+\begin_inset Formula $b$
+\end_inset
+
+,
+ first the command
+\series bold
+
+\backslash
+hphantom{gggg+
+\backslash
+:}
+\series default
+ is inserted.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+More about
+\series bold
+
+\backslash
+hphantom
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Placeholders"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ This space is needed because the
+\begin_inset Quotes eld
+\end_inset
+
++
+\begin_inset Quotes erd
+\end_inset
+
+ is surrounded by spaces in the formula.
+ The brace is placed under the command
+\series bold
+
+\backslash
+hphantom{bbqq+dddd}
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+It gets more complicated when brackets overlap each other above and under the formula as in the following example:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+jot}{-6pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{eqnarray*}
+ & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
+A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
+\end{eqnarray*}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+jot}{3pt}
+\end_layout
+
+\end_inset
+
+The first formula row is the same as the second row of the previous example,
+ with the difference that the brace is above.
+ The second row contains the formula together with the second brace.
+ To avoid the space between the upper brace in the first row and the formula,
+ the row spacing needs to be reduced.
+ This is not easily done due to a bug in \SpecialChar LyX
+.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset CommandInset href
+LatexCommand href
+name "LyX-bug #1505"
+target "https://www.lyx.org/trac/ticket/1505"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ As a solution for the problem,
+ the global formula row separation
+\series bold
+
+\backslash
+jot
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+J
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+jot
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ must be changed to -6
+\begin_inset space \thinspace{}
+\end_inset
+
+pt before the formula with the command
+\series bold
+
+\backslash
+setlength{
+\backslash
+jot}{-6pt}
+\series default
+ in \SpecialChar TeX
+ mode.
+
+\series bold
+
+\backslash
+jot
+\series default
+ is set back after the formula to the standard value of 3
+\begin_inset space \thinspace{}
+\end_inset
+
+pt using the same command.
+ More about the row separation in formulas is explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Line-Separation"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Arrows
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Arrows
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Arrows can be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\leftarrow"
+\end_inset
+
+ or the commands listed in the following subsections.
+\end_layout
+
+\begin_layout Subsection
+Horizontal Arrows
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Arrows
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+horizontal
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+gets
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\gets$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Leftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Leftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+longleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\longleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Longleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Longleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leftharpoonup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\leftharpoonup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leftharpoondown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\leftharpoondown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hookleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\hookleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+to
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\to$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Rightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Rightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+longrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\longrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Longrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Longrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rightharpoonup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rightharpoonup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rightharpoondown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rightharpoondown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hookrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\hookrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\leftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Leftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Leftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+longleftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\longleftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Longleftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Longleftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rightleftharpoons
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rightleftharpoons$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hspace{}
+\length 25pt
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mapsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mapsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+longmapsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\longmapsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leadsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\leadsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dasharrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dasharrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Arrows used as accents such as vector arrows are listed in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Accents"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Labeled arrows
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Arrows
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+labeled
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ are also available using the commands
+\series bold
+
+\backslash
+xleftarrow
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+X
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+xleftarrow
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+xrightarrow
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+X
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+xrightarrow
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ When inserting one of these commands in a formula,
+ an arrow with two blue boxes appears indicating where the labels can be inserted.
+ The length of the arrow adapts to the label width.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+F(a)
+\backslash
+xleftarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+x=a
+\begin_inset Formula $\downarrow$
+\end_inset
+
+x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+F(x)
+\backslash
+xrightarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+x=a
+\begin_inset Formula $\downarrow$
+\end_inset
+
+x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(a)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+If in the document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ for the package
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+mathtools
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ the option
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+ is set,
+ you will have access to the following labeled arrows:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Example
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
+\backslash
+xleftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
+\backslash
+xLeftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xLeftarrow[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xRightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xRightarrow[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xLeftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
+\backslash
+xhookleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
+\backslash
+xhookrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Example
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xleftharpoondown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xleftharpoonup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xrightharpoondown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xrightharpoonup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xleftrightharpoons
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="2mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xrightleftharpoons
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command scheme for all of these arrows is:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="0.5mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+F(a)
+\backslash
+xleftrightarrow[x=a]
+\backslash
+{x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vertical and Diagonal Arrows
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Arrows
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+diagonal
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Arrows
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+vertical
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+uparrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\uparrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Uparrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Uparrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+updownarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\updownarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Updownarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Updownarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Downarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Downarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+downarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\downarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nearrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nearrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+searrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\searrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+swarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\swarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nwarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nwarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Vertical arrows can also be used as delimiters together with the commands described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Manual-Bracket-Size"
+nolink "false"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Automatic-Bracket-Size"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Accents
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Accents"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Accents
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Accents can be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\hat"
+\end_inset
+
+ or the commands listed in the following subsections.
+\end_layout
+
+\begin_layout Subsection
+Accents for One Character
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For accents in text see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Accents-in-Text"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ is used to avoid that the footnote appears in the PDF-bookmark.
+\end_layout
+
+\begin_layout Plain Layout
+More about
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ is in section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Formulas-in-Section"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Accents-for-one"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Accents
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+for one character
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dot
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddot
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dddot
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddddot
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ddddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vec
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Vectors
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\vec{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bar
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bar{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathring
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathring{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+tilde
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\tilde{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hat
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\hat{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+check
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\check{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+acute
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\acute{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+grave
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\grave{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+breve
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\breve{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You can directly insert accents such as é in formulas.
+ \SpecialChar LyX
+ will transform them to the corresponding accent command.
+ For umlauts
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Umlauts
+\end_layout
+
+\end_inset
+
+ however it is better to insert a quotation mark before the vowel.
+ These two characters are then treated by \SpecialChar LaTeX
+ as
+\emph on
+one
+\emph default
+ character when the formula part with the umlaut is marked as German.
+ In contrast to
+\series bold
+
+\backslash
+ddot
+\series default
+,
+ with this method
+\begin_inset Quotes eld
+\end_inset
+
+real
+\begin_inset Quotes erd
+\end_inset
+
+ umlauts are created as demonstrated in the following example:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Quotes grd
+\end_inset
+
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset space \hspace{}
+\length 0pt
+\end_inset
+
+
+\lang ngerman
+
+\begin_inset Formula $"i$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddot
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ddot{i}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+One advantage with
+\series bold
+
+\backslash
+ddot
+\series default
+ is that umlauts can be directly converted to mathematical text because the accent commands above are
+\emph on
+not allowed
+\emph default
+
+\emph on
+in mathematical text
+\emph default
+.
+ To convert an accented character to mathematical text,
+ only the character under the accent may be converted.
+ This applies for all conversions,
+ e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+to italic or bold.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\SpecialChar LyX
+ also supports a tilde under the character if the \SpecialChar LaTeX
+-package
+\series bold
+undertilde
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+undertilde
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is installed on your system:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+ifundertilde
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following table will only be displayed when the \SpecialChar LaTeX
+-package
+\series bold
+undertilde
+\series default
+ is installed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+utilde
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\utilde{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+else
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following will be displayed when the \SpecialChar LaTeX
+-package
+\series bold
+undertilde
+\series default
+ is not installed:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You need to install the \SpecialChar LaTeX
+-package
+\series bold
+undertilde
+\series default
+ to see the rest of this subsection in the output.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+fi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Accents for Several Characters
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Accents
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+for several characters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overleftarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overleftarrow{A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+underleftarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\underleftarrow{A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overleftrightarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overleftrightarrow{A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm" bottomspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+underleftrightarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\underleftrightarrow{A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overrightarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overrightarrow{A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+underrightarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\underrightarrow{A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+widetilde
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\widetilde{A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm" bottomspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+widehat
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\widehat{A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Using these commands you can accent as many characters as you like.
+ But the accents
+\series bold
+
+\backslash
+widetilde
+\series default
+ and
+\series bold
+
+\backslash
+widehat
+\series default
+ will only be set in the output with a length of three characters,
+ as shown in the following example:
+\begin_inset Formula
+\[
+\widetilde{A+B=C-D}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+It is also possible to accent several characters using the commands
+\series bold
+
+\backslash
+overset
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+O
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+overset
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+underset
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+underset
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ described in the previous subsection.
+ The command
+\series bold
+
+\backslash
+underset
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\begin_inset Formula $\downarrow$
+\end_inset
+
+***
+\series default
+ creates:
+\begin_inset Formula
+\[
+\underset{***}{A=B}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Space
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Space"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Space
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+horizontal
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Predefined Space
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Predefined-Space"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Space
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+horizontal
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+predefined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Sometimes it is necessary to insert horizontal space into a formula.
+ This is done by inserting a non-breaking space (shortcut
+\begin_inset Info
+type "shortcut"
+arg "command-alternatives math-space ; space-insert protected"
+\end_inset
+
+).
+ A
+\begin_inset Quotes eld
+\end_inset
+
+
+\color blue
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+ appears and by pressing
+\family sans
+Space
+\family default
+ several times one can select one of eight different space sizes.
+ The spaces can also be inserted using the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\space"
+\end_inset
+
+ or special commands.
+ The size can be adjusted at any time by positioning the cursor on the
+\begin_inset Info
+type "icon"
+arg "math-insert \\space"
+\end_inset
+
+ and pressing
+\family sans
+Space
+\family default
+ until the desired size is achieved.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="3">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top" width="15col%">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Number of
+\family sans
+Space
+\family default
+ keystrokes
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+,
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\,B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\:B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+;
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\;B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+quad
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\quad B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+qquad
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+4
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\qquad B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="3">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top" width="15col%">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Number of
+\family sans
+Space
+\family default
+ keystrokes
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hfill
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+5
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\hfill B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hspace*{1em}
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+6
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\hspace*{1em}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hspace{1em}
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+7
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\hspace{1em}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+8
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\ B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+!
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+9
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\!B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Space's
+\begin_inset space ~
+\end_inset
+
+5
+\begin_inset space \thinspace{}
+\end_inset
+
+–
+\begin_inset space \thinspace{}
+\end_inset
+
+7 are variable spaces which are explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Variable-Space"
+nolink "false"
+
+\end_inset
+
+.
+ Space
+\begin_inset space ~
+\end_inset
+
+9 appears to produce no space.
+ It is displayed red in \SpecialChar LyX
+ contrary to the other sizes,
+ because it is a negative space.
+ There are two more negative spaces:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="3">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="middle" width="6.8cm">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+negmedspace
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+negthickspace
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Number of
+\family sans
+Space
+\family default
+ keystrokes after inserting the non-breaking space
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+10
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+11
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\negmedspace B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\negthickspace B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Negative spaces can lead to characters overlapping each other.
+ Thus they can be used to enforce ligatures,
+ which are useful for things such as summation operators:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sum
+\backslash
+sum
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+f_kl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sum\sum f_{kl}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sum
+\backslash
+negmedspace
+\backslash
+sum
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+f_kl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sum\negmedspace\sum f_{kl}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+Relational operators,
+ for example equal or less than signs,
+ are always surrounded by space.
+ To suppress this,
+ the operator is placed into a \SpecialChar TeX
+ brace.
+ The following example demonstrates this:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Normal equation
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Equation without space
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A{=}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+The command for the last formula is:
+
+\series bold
+A
+\backslash
+{=
+\begin_inset Formula $\to$
+\end_inset
+
+B
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Another example of controlled spaces is physical units.
+ The space between a value and its unit is smaller than a normal space,
+ typically a thin space is used.
+ For units in text,
+ the smaller space is inserted via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Formatting\SpecialChar menuseparator
+Thin
+\begin_inset space ~
+\end_inset
+
+Space
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "space-insert thin"
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+An example to visualize the difference:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features tabularvalignment="middle">
+<column alignment="left" valignment="top">
+<column alignment="left" valignment="top">
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+24 kW
+\begin_inset Formula $\cdot$
+\end_inset
+
+h
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Space between value and unit
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+24
+\begin_inset space \thinspace{}
+\end_inset
+
+kW
+\begin_inset Formula $\cdot$
+\end_inset
+
+h
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Thin space between value and unit
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Variable Space
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For vertical space in formulas see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Line-Separation"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+
+\backslash
+texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
+\end_layout
+
+\begin_layout Plain Layout
+More about
+\backslash
+texorpdfstring is in section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Formulas-in-Section"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Variable-Space"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Space
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+horizontal
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+variable
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Space with a defined length can be inserted with the command
+\series bold
+
+\backslash
+hspace
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+H
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+hspace
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ A long
+\begin_inset Quotes eld
+\end_inset
+
+
+\color blue
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+ will appear,
+ the length of which can be specified by left-clicking on the
+\begin_inset Quotes eld
+\end_inset
+
+
+\color blue
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+.
+ The length may also be negative.
+ If the space is the first character in a line,
+ it will ordinarily be omitted.
+ To force its output use the command
+\series bold
+
+\backslash
+hspace*
+\series default
+ instead of
+\series bold
+
+\backslash
+hspace
+\series default
+ or left-click on the
+\begin_inset Quotes eld
+\end_inset
+
+
+\color blue
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+ and check the option
+\family sans
+Protect
+\family default
+.
+\begin_inset Newline newline
+\end_inset
+
+To insert as much space as is available,
+ the command
+\series bold
+
+\backslash
+hfill
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+H
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+hfill
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is used.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command (
+\backslash
+hspace length)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A=B
+\backslash
+hspace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\backslash
+not=C (3
+\begin_inset space \thinspace{}
+\end_inset
+
+cm)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A=B\hspace{3cm}A\not=C$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A
+\backslash
+hspace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\backslash
+not=A (-1
+\begin_inset space \thinspace{}
+\end_inset
+
+mm)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\hspace{-1mm}A\not=A$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A=A
+\backslash
+hfill
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A=A\hfill B=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the last example the available space is given by the longest column entry of the table.
+ In an inline formula the space depends on the length of the line in which
+\series bold
+
+\backslash
+hfill
+\series default
+ is inserted.
+ Thus,
+ when the line uses the full width,
+ no space will be created.
+
+\series bold
+
+\backslash
+hfill
+\series default
+ only has an effect on displayed formulas when the formula style
+\series bold
+Indented
+\series default
+ is used.
+ (Formula styles are explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+nolink "false"
+
+\end_inset
+
+.)
+\end_layout
+
+\begin_layout Standard
+Besides
+\series bold
+
+\backslash
+hfill
+\series default
+,
+ there are also commands,
+
+\series bold
+
+\backslash
+dotfill
+\series default
+ and
+\series bold
+
+\backslash
+hrulefill,
+
+\series default
+ that fill the space with a pattern.
+ See
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Ellipses"
+nolink "false"
+
+\end_inset
+
+ for an example.
+\end_layout
+
+\begin_layout Standard
+For text,
+ variable space can be inserted via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Formatting\SpecialChar menuseparator
+Horizontal
+\begin_inset space ~
+\end_inset
+
+Space
+\family default
+:
+\end_layout
+
+\begin_layout Standard
+This is a line with
+\begin_inset space \hspace{}
+\length 2cm
+\end_inset
+
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+cm space.
+\end_layout
+
+\begin_layout Standard
+This is a line with
+\begin_inset space \hfill{}
+\end_inset
+
+maximum space.
+\end_layout
+
+\begin_layout Subsection
+Space Besides Inline Formulas
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Space
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+besides inline formulas
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The space that surrounds inline formulas can be adjusted with the length
+\series bold
+
+\backslash
+mathsurround
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+M
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+mathsurround
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ The value of a length is set with the command
+\series bold
+
+\backslash
+setlength
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+setlength
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ which has the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{length name}{value}
+\end_layout
+
+\begin_layout Standard
+To set
+\series bold
+
+\backslash
+mathsurround
+\series default
+ to the value 5
+\begin_inset space \thinspace{}
+\end_inset
+
+mm,
+ the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+mathsurround}{5mm}
+\end_layout
+
+\begin_layout Standard
+is inserted in \SpecialChar TeX
+ mode.
+ 5
+\begin_inset space \thinspace{}
+\end_inset
+
+mm space will now be set around all inline formulas:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+mathsurround}{5mm}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This is a line with an inline formula
+\begin_inset Formula $A=B$
+\end_inset
+
+ with 5
+\begin_inset space \thinspace{}
+\end_inset
+
+mm surrounding space.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+mathsurround}{0pt}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To return to the predefined value,
+
+\series bold
+
+\backslash
+mathsurround
+\series default
+ is set to the value 0
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+\end_layout
+
+\begin_layout Section
+Boxes and Frames
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Boxes
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Frames
+\begin_inset IndexMacro see
+status open
+
+\begin_layout Plain Layout
+Boxes
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Boxes for text are described in chapter
+\family typewriter
+Boxes
+\family default
+ in the
+\family typewriter
+Embedded
+\begin_inset space ~
+\end_inset
+
+Objects
+\family default
+ manual.
+\end_layout
+
+\begin_layout Subsection
+Boxes with Frame
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Boxes-with-Frame"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Boxes
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+with frame
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+It is possible to frame a formula or part of one with the commands
+\series bold
+
+\backslash
+fbox
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+F
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+fbox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+boxed
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+B
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+boxed
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+When one of these commands is inserted in a formula,
+ a blue box appears within a frame to enter formula parts.
+ For
+\series bold
+
+\backslash
+fbox
+\series default
+ an additional formula has to be created by
+\family sans
+Ctrl+M
+\family default
+ within this box,
+ because the box content will otherwise be treated as mathematical text.
+ When
+\series bold
+
+\backslash
+boxed
+\series default
+ is used,
+ a new formula is automatically created inside the frame.
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+fbox
+\series default
+ is not suitable to frame displayed formulas because the formula will always be set in the size of the documents text.
+ Conversly
+\series bold
+
+\backslash
+boxed
+\series default
+ is not suitable to frame inline formulas because the formula will always be set in the size of a displayed formula.
+\end_layout
+
+\begin_layout Standard
+An extension to
+\series bold
+
+\backslash
+fbox
+\series default
+ is the command
+\series bold
+
+\backslash
+framebox
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+F
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+framebox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ with which the frame width and the alignment can be specified.
+
+\series bold
+
+\backslash
+framebox
+\series default
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+framebox[frame width][position]{box content}
+\end_layout
+
+\begin_layout Standard
+The position can either be
+\emph on
+l
+\emph default
+ or
+\emph on
+r
+\emph default
+.
+
+\emph on
+l
+\emph default
+ left aligns and
+\emph on
+r
+\emph default
+ right aligns the formula in the box.
+ If no position is given the formula will be centered.
+\begin_inset Newline newline
+\end_inset
+
+If width is not given then position can not be given.
+ In this case the frame width is adjusted to the box content like for
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+When the command
+\series bold
+
+\backslash
+framebox
+\series default
+ is inserted,
+ a box appears containing three blue boxes.
+ The first two boxes are surrounded by brackets and denote the two optional arguments.
+ The third box is for formula parts like for
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+fbox
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\family sans
+Ctrl+M
+\family default
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+boxed
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\boxed{\int A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A+
+\backslash
+fbox
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A+\fbox{B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm" bottomspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+framebox
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+20mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\family sans
+Ctrl+M
+\family default
+
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To adjust the frame thickness the following commands are inserted in \SpecialChar TeX
+ mode before the formula:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+
+\begin_inset Quotes eld
+\end_inset
+
+thickness
+\begin_inset Quotes erd
+\end_inset
+
+
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+
+\begin_inset Quotes eld
+\end_inset
+
+distance
+\begin_inset Quotes erd
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Quotes eld
+\end_inset
+
+distance
+\begin_inset Quotes erd
+\end_inset
+
+ specifies the minimum distance between the frame and the first character in the box.
+ An example of this is given in the following framed formula:
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+fboxrule 2mm
+\backslash
+fboxsep 3mm
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+\boxed{A+B=C}
+\]
+
+\end_inset
+
+Before this formula the commands
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+2mm
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+3mm
+\end_layout
+
+\begin_layout Standard
+were inserted in \SpecialChar TeX
+ mode.
+ These values are then used for all following boxes.
+\end_layout
+
+\begin_layout Standard
+To return to the standard frame size,
+ the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+0.4pt
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+3pt
+\series default
+
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+is inserted in \SpecialChar TeX
+ mode before the next formula.
+\end_layout
+
+\begin_layout Subsection
+Boxes Without Frame
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Boxes-without-Frame"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Boxes
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+without frame
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For boxes without a frame the following box commands:
+
+\series bold
+
+\backslash
+mbox
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+M
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+mbox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+
+\series bold
+
+\backslash
+makebox
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+M
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+makebox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+raisebox
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+raisebox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ are available.
+\end_layout
+
+\begin_layout Standard
+With
+\series bold
+
+\backslash
+raisebox
+\series default
+ a box can be super- or subscripted.
+ But in contrary to normal super- and subscripting,
+ the characters in the box keep their font size.
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox{height}{box content}
+\end_layout
+
+\begin_layout Standard
+When the box contains a formula,
+ an extra formula is needed like for
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+
+\series medium
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\series default
+ For
+\series bold
+
+\backslash
+raisebox
+\series default
+ this extra formula is created by pressing
+\family sans
+Ctrl+M
+\family default
+ twice instead of once because \SpecialChar LyX
+ doesn't yet support
+\series bold
+
+\backslash
+raisebox
+\series default
+ directly.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+H
+\backslash
+raisebox{2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{al
+\begin_inset Formula $\to$
+\end_inset
+
+ lo
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $H\raisebox{2mm}{al}lo$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+H
+\backslash
+raisebox{-2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{al
+\begin_inset Formula $\to$
+\end_inset
+
+lo
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $H\raisebox{-2mm}{al}lo$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A=
+\backslash
+raisebox{-2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\family sans
+Ctrl+M
+\family default
+
+\family sans
+Ctrl+M
+\family default
+
+\backslash
+sqrt
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+mbox
+\series default
+ is equivalent to
+\series bold
+
+\backslash
+fbox
+\series default
+ and
+\series bold
+
+\backslash
+makebox
+\series default
+ is equivalent to
+\series bold
+
+\backslash
+framebox
+\series default
+,
+ except that there is no frame.
+\end_layout
+
+\begin_layout Subsection
+Colored Boxes
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Colored-Boxes"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Boxes
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+colored
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To be able to use all commands explained in this section,
+ the \SpecialChar LaTeX
+-package
+\series bold
+color
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+The \SpecialChar LaTeX
+-package
+\series bold
+color
+\series default
+ is part of every \SpecialChar LaTeX
+ standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+color
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ must be loaded in the \SpecialChar LaTeX
+-preamble with the line
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+When text is colored somewhere in the document with a predefined color,
+ \SpecialChar LyX
+ loads the \SpecialChar LaTeX
+ package
+\series bold
+color
+\series default
+ automatically.
+ Thus it is possible that the package is loaded twice,
+ but this does not cause problems.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+To avoid that the package is loaded twice,
+ a macro was inserted to the \SpecialChar LaTeX
+-preamble.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{color}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+To create color boxes,
+ the command
+\series bold
+
+\backslash
+colorbox
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+C
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+colorbox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+colorbox{color}{box content}
+\end_layout
+
+\begin_layout Standard
+The box content can also be a box and a
+\series bold
+
+\backslash
+colorbox
+\series default
+ can also be part of another box (see the 2nd and 3rd example).
+ When the box should contain a formula,
+ an extra formula has to be created,
+ the same way as for
+\series bold
+
+\backslash
+raisebox
+\series default
+.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+This also applies for the command
+\series bold
+
+\backslash
+fcolorbox
+\series default
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+One of the following predefined colors can be chosen:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+black
+\series default
+,
+
+\series bold
+blue
+\series default
+,
+
+\series bold
+cyan
+\series default
+,
+
+\series bold
+green
+\series default
+,
+
+\series bold
+magenta
+\series default
+,
+
+\series bold
+red
+\series default
+,
+
+\series bold
+white
+\series default
+ and
+\series bold
+yellow
+\begin_inset VSpace smallskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+colorbox{yellow
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\colorbox{yellow}{A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+colorbox{green
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+fbox
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Formula $\gets\gets$
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm" bottomspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+fbox
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Formula $\gets\gets$
+\end_inset
+
+
+\backslash
+colorbox{green
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\family sans
+Ctrl+M
+\family default
+
+\family sans
+Ctrl+M
+\family default
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C=D
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset VSpace smallskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+colorbox
+\series default
+ only colors the box background,
+ not the characters in the box.
+ To color all characters,
+ the whole formula is highlighted and the desired color is chosen in the
+\family sans
+Text
+\begin_inset space ~
+\end_inset
+
+Style
+\family default
+ dialog.
+ The dialog can be called with the toolbar button
+\begin_inset Info
+type "icon"
+arg "dialog-show character"
+\end_inset
+
+ or the menu
+\family sans
+Edit\SpecialChar menuseparator
+Text
+\begin_inset space ~
+\end_inset
+
+Properties\SpecialChar menuseparator
+Customized
+\family default
+.
+ The formula number will have the same color as the formula.
+ If a different color for the formula number is desired,
+ the color must be changed within the formula.
+\end_layout
+
+\begin_layout Standard
+An example:
+\end_layout
+
+\begin_layout Standard
+
+\color red
+\begin_inset Formula
+\begin{equation}
+\int A=B\label{eq:red}
+\end{equation}
+
+\end_inset
+
+
+\color green
+
+\begin_inset Formula
+\begin{equation}
+\textcolor{red}{\int A=B}\label{eq:redgreen}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:red"
+nolink "false"
+
+\end_inset
+
+ is completely colored red.
+\begin_inset Newline newline
+\end_inset
+
+Formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:redgreen"
+nolink "false"
+
+\end_inset
+
+ was first completely colored green to set the color for the formula number.
+ Subsequently the formula characters were colored red.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To color the frame different than the rest of the box,
+ the command
+\series bold
+
+\backslash
+fcolorbox
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+F
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+fcolorbox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fcolorbox{frame color}{color}{box content}
+\end_layout
+
+\begin_layout Standard
+So
+\series bold
+
+\backslash
+fcolorbox
+\series default
+ is an extension of the command
+\series bold
+
+\backslash
+colorbox
+\series default
+.
+ The frame width is set,
+ like for
+\series bold
+
+\backslash
+framebox
+\series default
+,
+ with
+\series bold
+
+\backslash
+fboxrule
+\series default
+ and
+\series bold
+
+\backslash
+fboxsep
+\series default
+.
+ An example:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+fboxrule 1mm
+\backslash
+fboxsep 1mm
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+\fcolorbox{cyan}{magenta}{A=B}
+\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This formula was created with the command
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+fcolorbox{cyan
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{magenta
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To use colors other than predefined ones,
+ they must be defined first.
+\end_layout
+
+\begin_layout Standard
+One can for example define the color
+\begin_inset Quotes eld
+\end_inset
+
+
+\series bold
+darkgreen
+\series default
+
+\begin_inset Quotes erd
+\end_inset
+
+ with the \SpecialChar LaTeX
+-preamble line:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+definecolor{darkgreen}{cmyk}{0.5,
+
+\series default
+
+\series bold
+0,
+
+\series default
+
+\series bold
+1,
+
+\series default
+
+\series bold
+0.5}
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+D
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+definecolor
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+cmyk
+\series default
+ is the color space denoting the colors
+\series bold
+cyan
+\series default
+,
+
+\series bold
+magenta
+\series default
+,
+
+\series bold
+yellow
+\series default
+ and
+\series bold
+black
+\series default
+.
+ The four comma separated numbers are the portion factors for the corresponding colors of the color space.
+ The factors can be in the range of 0
+\begin_inset space \thinspace{}
+\end_inset
+
+-
+\begin_inset space \thinspace{}
+\end_inset
+
+1.
+ Instead of
+\series bold
+cmyk,
+
+\series default
+ the color space
+\series bold
+rgb
+\series default
+ can also be used for definitions.
+
+\series bold
+rgb
+\series default
+ denotes
+\series bold
+red
+\series default
+,
+
+\series bold
+green
+\series default
+ and
+\series bold
+blue
+\series default
+,
+ so there are three portion factors for the corresponding colors.
+ Furthermore there is the color space
+\series bold
+gray
+\series default
+ with one portion factor for the gray value.
+\end_layout
+
+\begin_layout Standard
+As an example here is a framed box with the newly defined color
+\series bold
+darkgreen
+\series default
+ where the characters have been colored
+\series bold
+yellow
+\series default
+:
+\begin_inset Formula
+\begin{equation}
+\colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Self-defined colors can also be used for text with the help of the command
+\series bold
+
+\backslash
+textcolor
+\series default
+:
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Text
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+colored
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+textcolor{darkgreen}{
+\end_layout
+
+\end_inset
+
+This sentence is
+\begin_inset Quotes eld
+\end_inset
+
+darkgreen
+\begin_inset Quotes erd
+\end_inset
+
+.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+textcolor
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+T
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+textcolor
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is used in the scheme
+\series bold
+
+\backslash
+textcolor{color}{characters to color}
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Paragraph Boxes
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Paragraph-Boxes"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Boxes
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+as paragraph
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A box that can contain several lines and paragraphs,
+ a so-called paragraph box (parbox),
+ can be created with the menu
+\family sans
+Insert\SpecialChar menuseparator
+Box
+\family default
+ or the toolbar button
+\begin_inset Info
+type "icon"
+arg "box-insert"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The following example shows a framed parbox in a line:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+This is a line
+\begin_inset Box Boxed
+position "c"
+hor_pos "c"
+has_inner_box 1
+inner_pos "t"
+use_parbox 1
+use_makebox 0
+width "5cm"
+special "none"
+height "1in"
+height_special "totalheight"
+thickness "0.4pt"
+separation "3pt"
+shadowsize "4pt"
+framecolor "black"
+backgroundcolor "none"
+status open
+
+\begin_layout Plain Layout
+This is a paragraph box.
+ It is exactly 5
+\begin_inset space \thinspace{}
+\end_inset
+
+cm long and can also contain formulas:
+
+\begin_inset Formula $\int A\,\mathrm{d}s=C$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ with a parbox.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Such a box is created by right-clicking on the gray box inset.
+ A dialog pops up showing the box properties.
+ In our case set:
+
+\emph on
+Decoration
+\emph default
+:
+ Rectangular box,
+
+\emph on
+Inner Box
+\emph default
+:
+ Parbox,
+
+\emph on
+Width
+\emph default
+:
+ 5
+\begin_inset space \thinspace{}
+\end_inset
+
+cm,
+
+\emph on
+Vertical Box Alignment
+\emph default
+:
+ Middle
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+In \SpecialChar LaTeX
+ a parbox is created with the command
+\series bold
+
+\backslash
+parbox
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+P
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+parbox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ which has the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+parbox[position]{width}{box content}
+\end_layout
+
+\begin_layout Standard
+The positions
+\emph on
+b
+\emph default
+ and
+\emph on
+t
+\emph default
+ are possible.
+
+\emph on
+b
+\emph default
+ for
+\begin_inset Quotes eld
+\end_inset
+
+bottom
+\begin_inset Quotes erd
+\end_inset
+
+ means that the box is aligned within the surrounding text with its last line.
+ With
+\emph on
+t
+\emph default
+ for
+\begin_inset Quotes eld
+\end_inset
+
+top
+\begin_inset Quotes erd
+\end_inset
+
+ this is done with the first line.
+ When no position is given,
+ the box will be vertically centered,
+ see section
+\emph on
+Boxes
+\emph default
+ of the
+\emph on
+Embedded
+\begin_inset space ~
+\end_inset
+
+Objects
+\emph default
+ manual for examples.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To frame formulas completely,
+ including the formula number,
+ the formula must be set into a parbox.
+ To do this,
+ the command
+\series bold
+
+\backslash
+fbox{
+\backslash
+parbox{
+\backslash
+linewidth-2
+\backslash
+fboxsep-2
+\backslash
+fboxrule}{
+\series default
+ is inserted in \SpecialChar TeX
+ mode before the formula.
+
+\series bold
+
+\backslash
+linewidth
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+L
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+linewidth
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is the line width set for the document.
+ Because the frame is outside the parbox,
+ two times the frame separation and the frame thickness must be subtracted from the line width.
+ To be able to multiply and subtract in arguments,
+ the \SpecialChar LaTeX
+-package
+\series bold
+calc
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+calc
+\series default
+ is part of every \SpecialChar LaTeX
+ standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+calc
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ must be loaded in the \SpecialChar LaTeX
+-preamble with the line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{calc}
+\end_layout
+
+\begin_layout Standard
+Behind the formula both boxes are closed by entering
+\series bold
+}}
+\series default
+ in \SpecialChar TeX
+ mode.
+ Here is an example:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+fboxsep 5mm
+\backslash
+fboxrule 5mm
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+fbox{
+\backslash
+parbox{
+\backslash
+linewidth-2
+\backslash
+fboxsep-2
+\backslash
+fboxrule}{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{equation}
+\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
+\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+As a parbox is used as the argument of
+\series bold
+
+\backslash
+fbox
+\series default
+,
+ there is in this case no difference between
+\series bold
+
+\backslash
+fbox
+\series default
+ and
+\series bold
+
+\backslash
+boxed
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Paragraph boxes are very useful to comment formulas directly.
+ To do this,
+
+\series bold
+
+\backslash
+parbox
+\series default
+ is used in combination with the command
+\series bold
+
+\backslash
+tag
+\series default
+.
+ (more about
+\series bold
+
+\backslash
+tag
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:User-defined-Numbering"
+nolink "false"
+
+\end_inset
+
+)
+\end_layout
+
+\begin_layout Standard
+An example of a formula commented with
+\series bold
+
+\backslash
+parbox
+\series default
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+[5x-7b=3b
+\backslash
+tag*{
+\backslash
+parbox{5cm}{
+\end_layout
+
+\end_inset
+
+This is a description.
+ It is distinctly separated from the formula and multiline.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}}
+\backslash
+]
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Such a formula must be inserted completely in \SpecialChar TeX
+ mode because \SpecialChar LyX
+ does not yet support the command
+\series bold
+
+\backslash
+parbox
+\series default
+ in formulas.
+ The formula is created with the following command sequence:
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+[5x-7b=3b
+\backslash
+tag*
+\backslash
+{
+\backslash
+parbox{5cm}{
+\series default
+ is inserted in \SpecialChar TeX
+ mode.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+When the formula style
+\series bold
+Indented
+\series default
+ is used,
+
+\series bold
+
+\backslash
+tag*
+\backslash
+{
+\series default
+ can also be replaced by
+\series bold
+
+\backslash
+hfill
+\series default
+.
+ (formula styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+nolink "false"
+
+\end_inset
+
+)
+\end_layout
+
+\end_inset
+
+ Then the description follows as normal text and finally
+\series bold
+}}
+\backslash
+]
+\series default
+ is inserted in \SpecialChar TeX
+ mode.
+ The commands
+\series bold
+
+\backslash
+[
+\series default
+ and
+\series bold
+
+\backslash
+]
+\series default
+ create a displayed formula.
+\end_layout
+
+\begin_layout Standard
+The advantages of
+\series bold
+
+\backslash
+parbox
+\series default
+ can be seen in this example that was
+\begin_inset Quotes eld
+\end_inset
+
+commented
+\begin_inset Quotes erd
+\end_inset
+
+ using the mathematical textmode:
+\begin_inset Formula
+\[
+5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Operators
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Operators
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Big Operators
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Big-Operators"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Operators
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+big
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Sums
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Integrals
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To be able to use all of the integral operators listed here,
+ the
+\family sans
+Load automatically
+\family default
+ option for the
+\family sans
+ esint package
+\family default
+ must be set in the document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+int
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+I
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+int
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\int$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+oint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\oint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ointctrclockwise
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ointctrclockwise$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ointclockwise
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ointclockwise$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+fint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\begin_inset Formula $\fint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+landupint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\begin_inset Formula $\landupint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+landdownint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\begin_inset Formula $\landdownint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigcap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigcap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sum
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+sum
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sum$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+prod
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+P
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+prod
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\prod$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+coprod
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\coprod$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigodot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigodot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigotimes
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigotimes$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigoplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigoplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigwedge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigwedge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigvee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigvee$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigsqcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigsqcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+biguplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\biguplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All big operators can also be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\intop"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The operators are called big because they are bigger than the sometimes equal looking binary operators.
+ All big operators can have limits as described in the next subsection.
+\end_layout
+
+\begin_layout Standard
+For all integral operators there is a second version available,
+ ending in
+\series bold
+op
+\series default
+:
+
+\series bold
+
+\backslash
+intop
+\series default
+,
+
+\series bold
+
+\backslash
+ointop
+\series default
+ etc.
+ These operators differ in the style the operator limits are displayed,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Operator-Limits"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsubsection*
+Advice for Integrals
+\end_layout
+
+\begin_layout Standard
+The letter
+\emph on
+d
+\emph default
+ in an integral is an operator that has to be set upright.
+ This is done by highlighting the
+\emph on
+d
+\emph default
+ and using the keyboard shortcut
+\begin_inset Info
+type "shortcut"
+arg "font-roman"
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+Font styles
+\series bold
+
+\series default
+see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Font-Styles"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ Also the smallest space is inserted before the
+\emph on
+d
+\emph default
+,
+ as this is usual for operators.
+ An example:
+\end_layout
+
+\begin_layout Standard
+incorrect:
+
+\begin_inset Formula $\int A(x)dx$
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+in
+\end_layout
+
+\end_inset
+
+correct:
+
+\begin_inset Formula $\int A(x)\,\mathrm{d}x$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The following commands exist for multiple integrals:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\iint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+oiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\oiint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqiint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\iiint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iiiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\iiiint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dotsint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dotsint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Operator Limits
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Operator-Limits"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Operators
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+Limits
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Limits are created by super- and subscripts:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+prod^
+\backslash
+infty
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+_0
+\begin_inset Formula $\to$
+\end_inset
+
+A(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\prod_{0}^{\infty}A(x)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Limits of inline formulas are set on the right side of the operator.
+ Limits in displayed formulas are set above or below the operator,
+ except for integral limits.
+\end_layout
+
+\begin_layout Standard
+To force the limits to be set beside the operator,
+ the cursor is placed directly behind the operator and the limits type is changed with the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Change Limits Type
+\family default
+ to
+\family sans
+\series bold
+Inline
+\family default
+\series default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-limits"
+\end_inset
+
+).
+ An example:
+\end_layout
+
+\begin_layout Standard
+The default displayed formulas limits type is this:
+\begin_inset Formula
+\[
+\sum_{x=0}^{\infty}\frac{1}{x^{2}}
+\]
+
+\end_inset
+
+This is how it looks when the limits type is changed to
+\family sans
+\series bold
+Inline
+\family default
+\series default
+:
+\begin_inset Formula
+\[
+\sum\nolimits_{x=0}^{\infty}\frac{1}{x^{2}}
+\]
+
+\end_inset
+
+For integrals,
+ except those ending with
+\series bold
+op
+\series default
+ like
+\series bold
+
+\backslash
+intop
+\series default
+,
+
+\series bold
+
+\backslash
+ointop
+\series default
+ etc.,
+ the limits by default are set beside the operator.
+ But for multiple integrals the limits are often set below the operator.
+ In the following example the limits type was set to
+\series bold
+Display
+\series default
+ and so set below the integrals:
+\begin_inset Formula
+\begin{equation}
+\iiint\limits_{V}X\,\mathrm{d}V=U\label{eq:VolInt}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+To specify conditions for limits,
+ the commands
+\series bold
+
+\backslash
+subarray
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+subarray
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+substack
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+substack
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ are used.
+ To create this expression
+\begin_inset Formula
+\begin{equation}
+\sum_{\begin{subarray}{c}
+0<k<1000\\
+\\k\,\in\,\mathbb{N}
+\end{subarray}}^{n}k^{-2}\label{eq:substack}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+the following must be done:
+\begin_inset Newline newline
+\end_inset
+
+First the command
+\series bold
+
+\backslash
+sum
+\series default
+^
+\series bold
+n
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_
+\series default
+ is typed in.
+ The cursor is now in a blue box under the summation operator.
+ Insert the command
+\series bold
+
+\backslash
+subarray
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+.
+ The blue box is now within a purple box and now multiple limit lines can be written.
+ A new line is created by inserting a line break (
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+).
+ When
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+0<k<1000 Ctrl+Return
+\begin_inset Newline newline
+\end_inset
+
+
+\series default
+is typed in,
+ a new box appears below for the new limit line.
+\end_layout
+
+\begin_layout Standard
+The alignment of the lines can be changed to left aligned with the
+\family sans
+table
+\family default
+
+\family sans
+toolbar
+\family default
+ or the menu
+\family sans
+Edit\SpecialChar menuseparator
+Rows &Columns
+\family default
+.
+ To get right alignment,
+
+\series bold
+
+\backslash
+hfill
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+ is inserted at the beginning of the line.
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+substack
+\series default
+ is equivalent to
+\series bold
+
+\backslash
+subarray
+\series default
+ with the difference that the lines are always centered.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+As in formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:substack"
+nolink "false"
+
+\end_inset
+
+ there can be too much space beside an operator.
+ This occurs because the characters following the operator are set beside the limits.
+ To avoid this the command
+\series bold
+
+\backslash
+smashoperator
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+smashoperator
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ can be used.
+ To use it,
+ set the package
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+mathtools
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ in the document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ to
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+.
+
+\series bold
+
+\backslash
+smashoperator
+\series default
+ sets the space besides the operator to 0
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+\begin_inset Newline newline
+\end_inset
+
+Applied on formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:substack"
+nolink "false"
+
+\end_inset
+
+,
+ one uses the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+smashoperator{
+\end_layout
+
+\begin_layout Standard
+and inserts the operator with its limits into the braces.
+ Behind the brace one continues the formula:
+\begin_inset Formula
+\[
+\smashoperator{\sum_{\begin{subarray}{c}
+0<k<1000\\
+\\k\,\in\,\mathbb{N}
+\end{subarray}}^{n}}k^{-2}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+It is possible to set the space of only one side of the operator to 0
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+ To do this write either
+\series bold
+[l]
+\series default
+ or
+\series bold
+[r]
+\series default
+ between
+\series bold
+
+\backslash
+smashoperator
+\series default
+ and its brace.
+
+\series bold
+l
+\series default
+ stands for the left and
+\series bold
+r
+\series default
+ for the right side of the operator.
+ Here is an example of the possible
+\series bold
+
+\backslash
+smashoperator
+\series default
+ forms:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+Y\smashoperator{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[l]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[r]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When several consecutive operators have limits the typesetting of the limits looks often imperfect in the output,
+ for example:
+\begin_inset Formula
+\[
+\text{a)}\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\limsup_{n\to\infty}\max_{p\ge n}
+\]
+
+\end_inset
+
+To improve the typesetting,
+ in the document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ for the package
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+mathtools
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ set the option to
+\family sans
+ Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+.
+ Then insert the command
+\series bold
+
+\backslash
+adjustlimits
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+A
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+adjustlimits
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ directly before the first operator.
+ The example will then look like this:
+\begin_inset Formula
+\[
+\text{a)}\adjustlimits\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\adjustlimits\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\adjustlimits\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\adjustlimits\limsup_{n\to\infty}\max_{p\ge n}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+How to use one limit for several operators is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Self-defined-Operators"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Decoration for Operators
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Operators
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+Decoration
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the commands
+\series bold
+
+\backslash
+overset
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+O
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+overset
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+underset
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+underset
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ characters can be placed above or below an operator respectively.
+ With the command
+\series bold
+
+\backslash
+sideset
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+sideset
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ characters can be set before and behind a big operator.
+\end_layout
+
+\begin_layout Standard
+There are 4
+\begin_inset space ~
+\end_inset
+
+variants of
+\series bold
+
+\backslash
+sideset
+\series default
+:
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+
+\backslash
+sideset
+\series default
+ is used to set characters at the corners of the operator
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+
+\backslash
+sidesetn
+\series default
+ is used to set characters before and/or behind the operator (this variant represents \SpecialChar LaTeX
+'s original
+\series bold
+
+\backslash
+sideset
+\series default
+ command)
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+
+\backslash
+sidesetl
+\series default
+ is used to set characters at the left corners and/or behind the operator
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+
+\backslash
+sidesetr
+\series default
+ is used to set characters at the right corners and/or before the operator
+\end_layout
+
+\begin_layout Standard
+For example the command
+\series bold
+
+\backslash
+sidesetn
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+sum
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+'
+\begin_inset Formula $\to$
+\end_inset
+
+_k=1
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+^
+\series bold
+n
+\series default
+ produces:
+\begin_inset Formula
+\[
+\sideset{}{'}\sum_{k=1}^{n}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\backslash
+sideset
+\series default
+ can only be used to decorate big operators,
+ binary operators are not allowed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+overset
+\series default
+ and
+\series bold
+
+\backslash
+underset
+\series default
+ can also be used to decorate symbols and characters.
+ For example,
+ the command
+\series bold
+
+\backslash
+overset
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+
+\begin_inset Formula $\uparrow$
+\end_inset
+
+
+\series bold
+a
+\series default
+ produces:
+\begin_inset Formula
+\[
+\overset{a}{\maltese}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Binary Operators
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Binary-Operators"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Operators
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+binary
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Binary operators are surrounded by space when there is a character before and after them.
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
++
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $+$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+-
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $-$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+pm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\pm$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cdot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cdot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+times
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\times$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+div
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\div$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+raisebox{-1.2mm}{
+\end_layout
+
+\end_inset
+
+*
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $*$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+star
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\star$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+circ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\circ$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+diamond
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\diamond$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bullet
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bullet$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nabla
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nabla$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigtriangledown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigtriangledown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigtriangleup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigtriangleup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Box
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Box$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dagger
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dagger$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddagger
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ddagger$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+wr
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\wr$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigcirc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigcirc$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+wedge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\wedge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\vee$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+oplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\oplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ominus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ominus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+otimes
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\otimes$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+oslash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\oslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+odot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\odot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+amalg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\amalg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+uplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\uplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+setminus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\setminus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqcap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqcap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+triangleleft
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\triangleleft$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+triangleright
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\triangleright$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All binary operators can also be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\pm"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+To typeset the Laplace operator,
+
+\series bold
+
+\backslash
+Delta
+\series default
+ or
+\series bold
+
+\backslash
+nabla
+\series default
+^
+\series bold
+2
+\series default
+ (
+\begin_inset Formula $\nabla^{2}$
+\end_inset
+
+) can also be used instead of
+\series bold
+
+\backslash
+bigtriangleup
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+The character
+\family sans
+Menu Separator
+\family default
+ from the menu
+\family sans
+Insert\SpecialChar menuseparator
+Special Character
+\family default
+ is the operator
+\series bold
+
+\backslash
+triangleright
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Self-defined Operators
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Self-defined-Operators"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Operators
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+self-defined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the help of the command
+\series bold
+
+\backslash
+DeclareMathOperator
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+D
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+\begin_inset IndexMacro sortkey
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+dbinom
+\end_layout
+
+\end_inset
+
+
+\backslash
+DeclareMathOperator
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ custom operators can be defined in the \SpecialChar LaTeX
+-preamble.
+ Its command scheme is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareMathOperator{new command}{display}
+\end_layout
+
+\begin_layout Standard
+Display can be characters or symbols that define how the operator looks in the output.
+ To define a big operator a * is set behind the command.
+ All self-defined big operators can have limits as described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Operator-Limits"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+For example the \SpecialChar LaTeX
+-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareMathOperator*{
+\backslash
+Lozenge}{
+\backslash
+blacklozenge}
+\end_layout
+
+\begin_layout Standard
+defines the command
+\series bold
+
+\backslash
+Lozenge
+\series default
+,
+ that inserts a big operator consisting of the black lozenge symbol from
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Miscellaneous-Symbols"
+nolink "false"
+
+\end_inset
+
+:
+\begin_inset Formula
+\[
+\Lozenge_{n=1}^{\infty}
+\]
+
+\end_inset
+
+The command for this formula is:
+
+\series bold
+
+\backslash
+Lozenge
+\series default
+^
+\series bold
+
+\backslash
+infty
+\begin_inset Formula $\to$
+\end_inset
+
+_n=1
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+When self-defined operators are not used several times in the document,
+ they can also be defined with the commands
+\series bold
+
+\backslash
+mathop
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+M
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+mathop
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+mathbin
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+M
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+mathbin
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ which have the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop{display}
+\series default
+ and
+\series bold
+
+\backslash
+mathbin{display}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop
+\series default
+ defines big operators,
+
+\series bold
+
+\backslash
+mathbin
+\series default
+ binary operators.
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop
+\series default
+ can be used to use one limit for several operators:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command for the formula above is:
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+mathop{
+\backslash
+sum
+\backslash
+negmedspace
+\backslash
+sum
+\series default
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series bold
+
+\begin_inset Formula $\to$
+\end_inset
+
+^N
+\series default
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series bold
+_i,j=1
+\end_layout
+
+\begin_layout Section
+Fonts
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Fonts
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Font Styles
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Font-Styles"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Font
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+style
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Latin letters in formulas can be set in one of the following font styles:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="3">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Shortcut
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathbb
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+ABC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathbb{ABC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathbf
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathbf{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcut"
+arg "font-bold"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+boldsymbol
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\boldsymbol{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcut"
+arg "font-boldsymbol"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathcal
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+ABC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathcal{ABC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathfrak
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathfrak{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="3">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Shortcut
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathit
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathit{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathrm
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathrm{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcut"
+arg "font-roman"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathsf
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathsf{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcut"
+arg "font-sans"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathtt
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathtt{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcut"
+arg "font-typewriter"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathscr
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+ABC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathscr{ABC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\series default
+ The styles
+\series bold
+
+\backslash
+mathbb
+\series default
+,
+
+\series bold
+
+\backslash
+mathcal
+\series default
+ and
+\series bold
+
+\backslash
+mathscr
+\series default
+ can only be used for big letters.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The style
+\series bold
+
+\backslash
+mathnormal
+\series default
+ is predefined.
+\end_layout
+
+\begin_layout Standard
+The style commands also work for letters in mathematical constructs:
+\begin_inset Formula
+\[
+\mathfrak{A=\frac{b}{C}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Characters in mathematical text don't appear in a math font style but in the text font style
+\series bold
+
+\backslash
+textrm
+\series default
+.
+ Note that their style can't be set correctly via the text style dialog.
+ This is a known bug in \SpecialChar LyX
+.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset CommandInset href
+LatexCommand href
+name "LyX-bug #4629"
+target "https://www.lyx.org/trac/ticket/4629"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Instead of the style commands,
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Text Style
+\family default
+ dialog,
+ or the toolbar button,
+
+\begin_inset Info
+type "icon"
+arg "math-insert \\font"
+\end_inset
+
+ can be used.
+\end_layout
+
+\begin_layout Subsection
+Bold Formulas
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Bold-Formulas"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+bold
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To make a complete formula bold,
+ the command
+\series bold
+
+\backslash
+mathbf
+\series default
+ from the previous subsection cannot be used because it doesn't work for small Greek letters.
+ Additionally it always prints Latin letters upright,
+ as in the following equation:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To display the formula correctly,
+ the command
+\series bold
+
+\backslash
+boldsymbol
+\series default
+ is used:
+\begin_inset Formula
+\[
+\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
+\]
+
+\end_inset
+
+It is also possible to set the formula in a
+\series bold
+boldmath environment
+\series default
+.
+ This environment is created by inserting the command
+\series bold
+
+\backslash
+boldmath
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+B
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ in \SpecialChar TeX
+ mode.
+ To end the environment,
+ the command
+\series bold
+
+\backslash
+unboldmath
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+unboldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is inserted in \SpecialChar TeX
+ mode.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
+\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+unboldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Colored Formulas
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+colored
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formulas can be colored like normal text:
+ Highlight a formula or a formula part and use the
+\family sans
+Text Style
+\family default
+ dialog.
+ Here is a formula in magenta:
+\begin_inset Formula
+\[
+{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You can also define your own colors as described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Colored-Boxes"
+nolink "false"
+
+\end_inset
+
+.
+ They can be used with the \SpecialChar TeX
+ code command
+\series bold
+
+\backslash
+textcolor
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+T
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+textcolor
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ in the scheme
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+textcolor{color}{characters or formula}
+\end_layout
+
+\begin_layout Standard
+The following example was colored completely dark green and partly red:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+textcolor{darkgreen}{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
+\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Due to a bug in \SpecialChar LyX
+ only complete formulas can be colored with self-defined colors.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset CommandInset href
+LatexCommand href
+name "LyX-bug #5269"
+target "https://www.lyx.org/trac/ticket/5269"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Font Sizes
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Font-Sizes"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Font
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+size
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+As with characters in text,
+ the following size commands are available for formula characters:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+Huge
+\series default
+,
+
+\series bold
+
+\backslash
+huge
+\series default
+,
+
+\series bold
+
+\backslash
+LARGE
+\series default
+,
+
+\series bold
+
+\backslash
+Large
+\series default
+,
+
+\series bold
+
+\backslash
+large
+\series default
+,
+
+\series bold
+
+\backslash
+normalsize
+\series default
+,
+
+\series bold
+
+\backslash
+small
+\series default
+,
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+footnotesize
+\series default
+,
+
+\series bold
+
+\backslash
+scriptsize
+\series default
+ and
+\series bold
+
+\backslash
+tiny
+\end_layout
+
+\begin_layout Standard
+The font size produced by the commands depends on the document's original font size,
+ which corresponds to the command
+\series bold
+
+\backslash
+normalsize
+\series default
+.
+ The other commands produce character sizes smaller or larger than
+\series bold
+
+\backslash
+normalsize
+\series default
+.
+ There are however limits to how small or large the font size can be changed.
+ If for example the document font size is 12
+\begin_inset space \thinspace{}
+\end_inset
+
+pt,
+ the command
+\series bold
+
+\backslash
+Huge
+\series default
+ switches to the same size as
+\series bold
+
+\backslash
+huge
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+A size command is inserted in \SpecialChar TeX
+ mode before a formula and sets the size for all of the following formulas and text characters.
+ To switch back to the initial size,
+ the command
+\series bold
+
+\backslash
+normalsize
+\series default
+ is inserted behind the formula,
+ again in \SpecialChar TeX
+ mode.
+\end_layout
+
+\begin_layout Standard
+Size can also be changed within a formula using the following size commands or the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\style"
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+displaystyle
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+D
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+displaystyle
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+textstyle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+scriptstyle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+scriptscriptstyle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+After entering these commands,
+ a blue box appears in which the formula parts are inserted.
+\end_layout
+
+\begin_layout Standard
+There is another method for changing the font size,
+ although it only works for symbols or letters in mathematical text.
+ To use it,
+ one of the above text size commands is inserted into mathematical text.
+ All characters until the end of the mathematical text or until another size command will have the selected size.
+ Two examples:
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+huge
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+A=\frac{B}{c}\cdot\maltese
+\]
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+\maltese A\textrm{{\Large \maltese\textit{A}}}\textrm{{\tiny \maltese\textit{A}}}
+\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+normalsize
+\end_layout
+
+\end_inset
+
+
+\begin_inset VSpace medskip
+\end_inset
+
+Before the first formula the command
+\series bold
+
+\backslash
+huge
+\series default
+ was inserted.
+ The command for the second formula is:
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+maltese
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A Alt+M M
+\backslash
+Large
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+textit
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\to$
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset space \hspace*{}
+\length 1cm
+\end_inset
+
+Alt+M
+\series default
+
+\series bold
+M
+\backslash
+tiny
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+textit
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\begin_layout Standard
+If a symbol cannot be displayed in different sizes,
+ it will always be displayed in the default size.
+\end_layout
+
+\begin_layout Section
+Greek Letters
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Greek letters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Greek letters can be inserted via the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\alpha"
+\end_inset
+
+ as well as by command.
+ All international typesetting norms purport that Greek letters in math have to be typeset italic/slanted.
+ In some languages,
+ like French or Russian,
+ they are nevertheless sometimes typeset upright.
+\end_layout
+
+\begin_layout Subsection
+Small Letters
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Greek letters
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+small
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+alpha
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\alpha$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+beta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\beta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+gamma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\gamma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+delta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\delta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+epsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\epsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varepsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varepsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+zeta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\zeta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+eta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\eta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\theta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vartheta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\vartheta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="12" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iota
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\iota$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+kappa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\kappa$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varkappa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varkappa$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lambda
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\lambda$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mu$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nu$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+xi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+o
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $o$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+pi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\pi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varpi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varpi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varrho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varrho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varsigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varsigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+tau
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\tau$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\upsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\phi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varphi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varphi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+chi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\chi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\psi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+omega
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\omega$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Creating upright Greek letters is explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Upright-small-Greek"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Big Letters
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Greek letters
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+big
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Gamma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Gamma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Delta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Delta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Theta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Lambda
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Lambda$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Xi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Xi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Pi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Pi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Sigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Sigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Upsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Phi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Psi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Omega
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Omega$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+The big Greek letters appearing upright is caused by a design bug in \SpecialChar TeX
+.
+ To create correct italic big letters,
+ begin every command with
+\series bold
+var
+\series default
+.
+ For example the command
+\series bold
+
+\backslash
+varGamma
+\series default
+ produces
+\begin_inset Formula $\varGamma$
+\end_inset
+
+.
+ Another way is to load the package
+\series bold
+fixmath
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+fixmath
+\series default
+ is part of the \SpecialChar LaTeX
+-package
+\series bold
+was
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+was
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+fixmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ with the \SpecialChar LaTeX
+-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{fixmath}
+\end_layout
+
+\begin_layout Standard
+Then all big Greek letters in a document will automatically be typeset italic.
+\end_layout
+
+\begin_layout Subsection
+Bold Letters
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Greek letters
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+bold
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Greek letters cannot be set with different font styles like Latin letters.
+ They can only be made bold with the command
+\series bold
+
+\backslash
+boldsymbol
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+B
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+boldsymbol
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Upsilon
+\backslash
+boldsymbol
+\backslash
+Upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+theta
+\backslash
+boldsymbol
+\backslash
+theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\theta\boldsymbol{\theta}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Symbols
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+A list with all symbols of most of the \SpecialChar LaTeX
+-packages can be found in
+\begin_inset CommandInset citation
+LatexCommand cite
+key "Symbols"
+literal "true"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+
+\backslash
+texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
+\end_layout
+
+\begin_layout Plain Layout
+More about
+\backslash
+texorpdfstring is in section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Formulas-in-Section"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Symbols
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Many of the symbols listed in this section can also be inserted via the toolbar buttons
+\begin_inset Info
+type "icon"
+arg "math-insert \\nabla"
+\end_inset
+
+ and
+\begin_inset Info
+type "icon"
+arg "math-insert \\digamma"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Mathematical Symbols
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Mathematical-Symbols"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Symbols
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+mathematical
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Symbol
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+neg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\neg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Im
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Im$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Re
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Re$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+aleph
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\aleph$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+partial
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\partial$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+infty
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+wp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\wp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+imath
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\imath$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+jmath
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\jmath$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Symbol
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+forall
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\forall$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+exists
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\exists$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nexists
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nexists$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+emptyset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\emptyset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varnothing
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varnothing$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dag
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dag$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddag
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ddag$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+complement
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+raisebox{-0.8mm}{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\complement$
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Bbbk
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Bbbk$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Symbol
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+prime
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\prime$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+backprime
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\backprime$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+triangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\triangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+angle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\angle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+measuredangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\measuredangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sphericalangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sphericalangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+top
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\top$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Miscellaneous Symbols
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Miscellaneous-Symbols"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Symbols
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+miscellaneous
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Symbol
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+flat
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\flat$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+natural
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\natural$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sharp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sharp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+surd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\surd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+checkmark
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\checkmark$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+yen
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\yen$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+pounds
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\pounds$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+$
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\$$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+§
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $§$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Symbol
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hbar
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\hbar$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hslash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\hslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+clubsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\clubsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+spadesuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\spadesuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigstar
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigstar$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+blacklozenge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\blacklozenge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+blacktriangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\blacktriangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+blacktiangledown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\blacktriangledown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bullet
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bullet$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Symbol
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+diamondsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\diamondsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Diamond
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Diamond$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+heartsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\heartsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+P
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\P$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+copyright
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\copyright$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+circledR
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\circledR$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+maltese
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\maltese$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+diagup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\diagup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+diagdown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\diagdown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Some symbols can be displayed in different sizes,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Font-Sizes"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+The Euro-Symbol €
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Symbols
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+Euro-symbol
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset IndexMacro sortkey
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+officialeuro
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use the Euro symbol in formulas,
+ the \SpecialChar LaTeX
+-package
+\series bold
+eurosym
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+eurosym
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ must be installed and loaded with the \SpecialChar LaTeX
+-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage[gennarrow]{eurosym}
+\end_layout
+
+\begin_layout Standard
+The Euro symbol can now be inserted with the command
+\series bold
+
+\backslash
+euro
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+E
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+euro
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The Euro symbol can directly be inserted with the € key in mathematical text,
+ without having
+\series bold
+eurosym
+\series default
+ installed.
+ When
+\series bold
+eurosym
+\series default
+ is installed,
+
+\series bold
+
+\backslash
+euro
+\series default
+ can also be inserted in \SpecialChar TeX
+ mode.
+ The official currency symbol can then be inserted with the command
+\series bold
+
+\backslash
+officialeuro
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+O
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+officialeuro
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ which is also only available in \SpecialChar TeX
+ mode.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+ifeurosym
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following table will only be displayed when the \SpecialChar LaTeX
+-package
+\series bold
+eurosym
+\series default
+ is installed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+An overview about the different Euro symbols:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="3">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+cmidrule[0.08em]{2-3}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Symbol
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+formula
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+euro
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\euro$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+mathematical text
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+€
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mbox{€}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\SpecialChar TeX
+ mode
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+officialeuro
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+officialeuro
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+cmidrule
+\series default
+ is used here only for table borders.
+ See sec.
+
+\family sans
+Formal Tables
+\family default
+ of the
+\emph on
+EmbeddedObjects
+\emph default
+ manual for details.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+else
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following will be displayed when the \SpecialChar LaTeX
+-package
+\series bold
+eurosym
+\series default
+ is not installed:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You need to install the \SpecialChar LaTeX
+-package
+\series bold
+eurosym
+\series default
+ to see the rest of this subsection in the output.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+fi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Relations
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Relations"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Relations
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Comparisons
+\begin_inset IndexMacro see
+status open
+
+\begin_layout Plain Layout
+Relations
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All of the following relations can also be inserted via the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\leq"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="17" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Relation
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+<
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $<$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+le
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\le$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ll
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+prec
+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_inset
+
+
+\end_layout
+
+\end_inset
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+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
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+\begin_inset Text
+
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+
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+\end_inset
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+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+\end_layout
+
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
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+
+\end_inset
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+
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
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+
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+
+\end_inset
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+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+\end_layout
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
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+
+\end_inset
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+
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+
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+\end_layout
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
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+
+\end_inset
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+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+\end_layout
+
+\end_inset
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+\begin_inset Text
+
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
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+
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+
+\end_inset
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+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+\end_layout
+
+\end_inset
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+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+
+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nmid
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nmid$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="17" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
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+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Relation
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\not=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+equiv
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\equiv$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sim
+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sim$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+simeq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\simeq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+approx
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\approx$
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+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+cong
+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cong$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+bowtie
+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
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+
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+
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+
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
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+
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+
+\end_inset
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+
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+
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+
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
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+
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+
+\end_layout
+
+\end_inset
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+
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+propto
+\end_layout
+
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+
+\end_layout
+
+\end_inset
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+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
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+asymp
+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
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+
+\end_layout
+
+\end_inset
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+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
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+
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+
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+doteq
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+
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
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+
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+
+\end_inset
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+<row>
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+
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+\end_layout
+
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+
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+
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+
+\end_inset
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+
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+
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+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
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+
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+
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+
+\end_layout
+
+\end_inset
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+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="17" columns="2">
+<features booktabs="true" tabularvalignment="middle">
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+<column alignment="center" valignment="top" width="0pt">
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+
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+Command
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+
+\end_inset
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+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
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+Relation
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+
+\end_inset
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+<row>
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+\begin_inset Text
+
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+
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+
+\end_layout
+
+\end_inset
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+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+supset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\supset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+supseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\supseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqsupseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqsupseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ni
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ni$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dashv
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dashv$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+frown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\frown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+unrhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\unrhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lessgtr
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\lessgtr$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+parallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\parallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nparallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nparallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+The characters
+\series bold
+
+\backslash
+lhd
+\series default
+ and
+\series bold
+
+\backslash
+rhd
+\series default
+ are bigger than the equal looking operators
+\series bold
+
+\backslash
+triangleleft
+\series default
+ and
+\series bold
+
+\backslash
+triangleright
+\series default
+,
+ respectively.
+\end_layout
+
+\begin_layout Standard
+\SpecialChar LyX
+ supports also many special relations.
+ Use the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\leqq"
+\end_inset
+
+ to see a list of these relations.
+\end_layout
+
+\begin_layout Standard
+Contrary to symbols,
+ relations are always surrounded by space.
+\end_layout
+
+\begin_layout Standard
+Relations with labels can be created with the command
+\series bold
+
+\backslash
+stackrel
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+stackrel
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A(r)
+\backslash
+stackrel
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+r
+\backslash
+to
+\backslash
+infty
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Formula $\downarrow$
+\end_inset
+
+
+\backslash
+approx
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Functions
+\end_layout
+
+\begin_layout Subsection
+Predefined Functions
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Predefined-Functions"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Functions
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+predefined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In general,
+ variables are set
+\emph on
+italic
+\emph default
+ in mathematical expressions,
+ but not function names,
+ because
+\begin_inset Formula $sin$
+\end_inset
+
+ could be misunderstood as
+\begin_inset Formula $s\cdot i\cdot n$
+\end_inset
+
+.
+ Also predefined functions are separated a bit from the character in front of them.
+ They are inserted as commands starting with a backslash before their name.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Asin(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $Asin(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \quad{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A
+\backslash
+sin(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\sin(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The following functions are predefined:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="4">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sin
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sinh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+arcsin
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sup
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cos
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cosh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+arccos
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+inf
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+tan
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+tanh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+arctan
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lim
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+coth
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+arg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+liminf
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sec
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+min
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+deg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+limsup
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+csc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+max
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+det
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Pr
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ln
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+exp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hom
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+log
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ker
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+gcd
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+They can also be inserted with the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\functions"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Self-defined Functions
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Functions
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+self-defined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use a function that is not predefined,
+ for instance the sign function sgn(x),
+ there are two possibilities:
+\end_layout
+
+\begin_layout Itemize
+Define the function by inserting the following line in the \SpecialChar LaTeX
+-preamble
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For more about
+\series bold
+
+\backslash
+DeclareMathOperator
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Self-defined-Operators"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+DeclareMathOperator{
+\backslash
+sgn}{sgn}
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+D
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+\begin_inset IndexMacro sortkey
+status collapsed
+
+\begin_layout Plain Layout
+
+\backslash
+dbinom
+\end_layout
+
+\end_inset
+
+
+\backslash
+DeclareMathOperator
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+Now the newly defined function can be called with the command
+\series bold
+
+\backslash
+sgn
+\series default
+.
+\end_layout
+
+\begin_layout Itemize
+Write the formula as usual,
+ mark the formula name,
+ in our example the letters
+\emph on
+sgn
+\emph default
+,
+ and change it to mathematical text.
+ Finally,
+ insert a space between the prefactor and function.
+\end_layout
+
+\begin_layout Standard
+The result is the same with both methods as with a predefined function
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+In \SpecialChar LyX
+ self-defined functions are displayed red,
+ predefined ones black.
+\end_layout
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A
+\backslash
+sgn(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\sgn(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A
+\backslash
+,
+\begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
+\end_inset
+
+(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\,\textrm{sgn}(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The first method is more suitable when the self-defined function will be used several times.
+\end_layout
+
+\begin_layout Subsection
+Limits
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Limits
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For limits,
+ in addition to the commands
+\series bold
+
+\backslash
+lim
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+L
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+lim
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+
+\series bold
+
+\backslash
+liminf
+\series default
+ and
+\series bold
+
+\backslash
+limsup
+\series default
+ the following functions are defined:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varliminf
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varliminf$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varlimsup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varlimsup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varprojlim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varprojlim$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm" bottomspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varinjlim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varinjlim$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+The limit is created by inserting a subscript.
+ It is set right beside the function in an inline formula:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lim_x
+\backslash
+to
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+x=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\lim_{x\to A}x=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In a displayed formula the limit is set below the formula,
+ as usual:
+\begin_inset Formula
+\[
+\lim_{x\to A}x=B
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+How to adjust the typesetting of the limits see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Operator-Limits"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Modulo-Functions
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Functions
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+modulo-
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The modulo-function is special,
+ because it exists in four variants.
+ The variants in an inline formula are:
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="left" valignment="top" width="0pt">
+<column alignment="block" valignment="top">
+<row>
+<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+a
+\backslash
+mod
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+b
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $a\mod b$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+a
+\backslash
+pmod
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+b
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $a\pmod b$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+a
+\backslash
+bmod
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+b
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $a\bmod b$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+a
+\backslash
+pod
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+b
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $a\pod b$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In a display formula,
+ more space is set before the function names for all variants but
+\series bold
+
+\backslash
+mod.
+
+\series default
+ This later version is also the only one that does not take the
+\series bold
+b
+\series default
+ as argument but acts as a binary operator.
+
+\end_layout
+
+\begin_layout Section
+Special Characters
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Special characters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The characters ^ and _ would normally create a superscript and subscript,
+ respectively.
+ To get these characters you have to insert them with a leading
+\backslash
+.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="left" valignment="top" width="0pt">
+<column alignment="block" valignment="top">
+<row>
+<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathcircumflex$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+_
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\_$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Special Characters in Mathematical Text
+\end_layout
+
+\begin_layout Standard
+The following commands can only be used in mathematical text or in \SpecialChar TeX
+ mode:
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="left" valignment="top" width="0pt">
+<column alignment="block" valignment="top">
+<row>
+<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+oe
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{œ}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+OE
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{Œ}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ae
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{æ}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+AE
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{Æ}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+aa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{å}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+AA
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{Å}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{ı}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="left" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+The space of 0
+\begin_inset space \thinspace{}
+\end_inset
+
+mm is used for separation,
+ because otherwise the output will be ¡ and ¿ respectively.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+o
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{ø}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+O
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{Ø}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+l
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{ł}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+L
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{Ł}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+!
+\begin_inset space \hspace{}
+\length 0mm
+\end_inset
+
+`
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{!`}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+?
+\begin_inset space \hspace{}
+\length 0mm
+\end_inset
+
+`
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{?`}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+j
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{ȷ}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The characters
+\begin_inset Formula $\textrm{Å}$
+\end_inset
+
+ and
+\begin_inset Formula $\textrm{Ø}$
+\end_inset
+
+ can also be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\digamma"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The commands
+\series bold
+!
+\begin_inset space \hspace{}
+\length 0mm
+\end_inset
+
+`
+\series default
+ and
+\series bold
+?
+\begin_inset space \hspace{}
+\length 0mm
+\end_inset
+
+`
+\series default
+ are exceptions because they can be inserted in \SpecialChar LyX
+ directly to text.
+\end_layout
+
+\begin_layout Subsection
+Accents in Text
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Accents-in-Text"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Accents
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+in text
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Any letter can be accented with the following commands.
+ The commands must be inserted in \SpecialChar TeX
+ mode.
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="left" valignment="top" width="0pt">
+<column alignment="block" valignment="top">
+<row>
+<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\begin_inset Quotes grd
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+"e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+`e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+`e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+^e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+=e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+=e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+u
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+u e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+b
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+b e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+t
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+ee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+t ee
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="left" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+H
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+H e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+'e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+'e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+~e
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Tilde
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+~e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+.e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+.e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+v
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+v e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+d
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+d e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+c
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+c e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+With the command
+\series bold
+
+\backslash
+t
+\series default
+ also two different characters can be accented.
+ The command
+\series bold
+
+\backslash
+t
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+sz
+\series default
+ creates:
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+t sz
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The accents
+\series bold
+`
+\series default
+ ,
+
+\series bold
+'
+\series default
+ and
+\series bold
+^
+\series default
+ can in combination with vowels be directly inserted with the keyboard without using \SpecialChar TeX
+ mode.
+ The same applies for the tilde
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+This only applies for keyboards where the tilde is defined as accent.
+\end_layout
+
+\end_inset
+
+
+\series bold
+~
+\series default
+ in combination with
+\emph on
+a
+\emph default
+ ,
+
+\emph on
+n
+\emph default
+ ,
+ or
+\emph on
+o
+\emph default
+.
+\end_layout
+
+\begin_layout Standard
+The commands
+\series bold
+
+\backslash
+b
+\series default
+ ,
+
+\series bold
+
+\backslash
+c
+\series default
+ ,
+
+\series bold
+
+\backslash
+d
+\series default
+ ,
+
+\series bold
+
+\backslash
+H
+\series default
+ ,
+
+\series bold
+
+\backslash
+t
+\series default
+ ,
+
+\series bold
+
+\backslash
+u
+\series default
+ ,
+
+\series bold
+
+\backslash
+v
+\series default
+ and accents that are inserted directly with the keyboard are also available in mathematical text.
+ For the other accents there are special math commands used in formulas,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Accents-for-one"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+With the command
+\series bold
+
+\backslash
+textcircled
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+T
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+textcircled
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ any number or letter can be set into a circle,
+ quasi accented with a circle,
+ similar to the copyright symbol.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+textcircled{w}
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+textcircled{w}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Large
+\backslash
+textcircled{
+\backslash
+normalsize
+\backslash
+protect
+\backslash
+raisebox{-1.5pt}{W}}
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+Large
+\backslash
+textcircled{
+\backslash
+normalsize
+\backslash
+protect
+\backslash
+raisebox{-1.5pt}W}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+One has to take care that the character fits into the circle.
+
+\series bold
+
+\backslash
+Large
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+See
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Font-Sizes"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ specifies the size of the circle.
+ With the help of
+\series bold
+
+\backslash
+raisebox
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+See
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Boxes-without-Frame"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ the character can be centered.
+\end_layout
+
+\begin_layout Subsection
+Old-style Figures
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Old-style Figures
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Old-style figures (also known as old-style numerals) are created with the command
+\series bold
+
+\backslash
+oldstylenums
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+O
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+oldstylenums
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ The command can be used in formulas and in \SpecialChar TeX
+ mode.
+ The command scheme is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+oldstylenums{number}
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+oldstylenums{0123456789}
+\series default
+ produces:
+
+\begin_inset Formula $\oldstylenums{0123456789}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Formula Styles
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Formula-Styles"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+styles
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+There are two different alignment styles:
+\end_layout
+
+\begin_deeper
+\begin_layout Description
+Centered is the predefined standard.
+\end_layout
+
+\begin_layout Description
+Indented can be set using the menu
+\family sans
+Document\SpecialChar menuseparator
+Settings
+\family default
+ under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options.
+\end_layout
+
+\begin_layout Standard
+When
+\series bold
+Indented
+\series default
+ is used,
+ the indentation can be adjusted.
+ The default value depends on the document class.
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+Two different numbering styles are available in the menu
+\family sans
+Document\SpecialChar menuseparator
+Settings
+\family default
+ under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+:
+\end_layout
+
+\begin_deeper
+\begin_layout Description
+Right is in most cases the default.
+\end_layout
+
+\begin_layout Description
+Left
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+The chosen styles are used for all displayed formulas of the document.
+ When both,
+ centered and indented formulas should be created in a document,
+ the style
+\series bold
+Centered
+\series default
+ is used.
+ The indented formulas are then set in a flalign environment,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Flalign-Environment"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Multiline Formulas
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Multiline-Formulas"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+General
+\end_layout
+
+\begin_layout Standard
+In \SpecialChar LyX
+,
+ multiline formulas are created by pressing
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+ inside a formula.
+ This creates either an
+\series bold
+align environment
+\series default
+ that is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Standard-align-Environment"
+nolink "false"
+
+\end_inset
+
+ or,
+ when automatically loading of the package
+\family sans
+ AMS math
+\family default
+ is disabled in the document settings,
+ an
+\series bold
+eqnarray environment
+\series default
+ that is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Eqnarray-Environment"
+nolink "false"
+
+\end_inset
+
+.
+ The align environment is recommended as it provides a typographically correct output in all cases.
+\end_layout
+
+\begin_layout Standard
+There are other multiline formula environments that can be created via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Math
+\family default
+.
+ These environments are described in the following sections.
+\end_layout
+
+\begin_layout Standard
+In all multiline formula environments a new line is created by pressing
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+.
+ To add or delete lines,
+ use the math toolbar buttons
+\begin_inset Info
+type "icon"
+arg "tabular-feature append-row"
+\end_inset
+
+ or
+\begin_inset Info
+type "icon"
+arg "tabular-feature delete-row"
+\end_inset
+
+ respectively,
+ or the menu option
+\family sans
+ Edit\SpecialChar menuseparator
+Rows & Columns
+\family default
+.
+\end_layout
+
+\begin_layout Subsubsection
+Line Separation
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Line-Separation"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+Line separation
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Sometimes there is not enough space in multiline formulas between the lines:
+\begin_inset Formula
+\begin{eqnarray*}
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In \SpecialChar LaTeX
+ additional line space is specified as an optional argument of the new line command.
+ This is not yet possible in \SpecialChar LyX
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+see
+\begin_inset CommandInset href
+LatexCommand href
+name "LyX-bug #1505"
+target "https://www.lyx.org/trac/ticket/1505"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ therefore the whole formula must be inserted in \SpecialChar TeX
+ mode.
+ To add in our example space,
+ the command
+\series bold
+
+\backslash
+
+\backslash
+[3mm]
+\series default
+ is inserted at the end of the first line.
+ One gets:
+
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{eqnarray*}
+\end_layout
+
+\begin_layout Plain Layout
+
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = &
+\backslash
+textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
+\backslash
+
+\backslash
+[3mm]
+\end_layout
+
+\begin_layout Plain Layout
+
+4x^{2}
+\backslash
+left(B^{2}+x_{0}^{2}
+\backslash
+right)+4x_{0}x
+\backslash
+left(D-B^{2}
+\backslash
+right)+B^{2}
+\backslash
+left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
+\backslash
+right) & = & 0
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{eqnarray*}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To set the line separation for all lines in a formula,
+ the length of
+\series bold
+
+\backslash
+jot
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+J
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+jot
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is changed.
+ The definition is:
+
+\begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
+\end_inset
+
+.
+
+\series bold
+
+\backslash
+jot
+\series default
+ is predefined as 3
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+ To create 3
+\begin_inset space \thinspace{}
+\end_inset
+
+mm of additional line separation as in the previous example,
+ the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+jot}{3mm+3pt}
+\end_layout
+
+\begin_layout Standard
+is inserted in \SpecialChar TeX
+ mode before the formula.
+ This requires that the \SpecialChar LaTeX
+-package
+\series bold
+calc
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+calc
+\series default
+ is part of every \SpecialChar LaTeX
+ standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+calc
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ was loaded in \SpecialChar LaTeX
+-preamble with the line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{calc}
+\end_layout
+
+\begin_layout Standard
+One gets:
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+jot}{3mm+3pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{eqnarray*}
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+jot}{3pt}
+\end_layout
+
+\end_inset
+
+ To get restore
+\series bold
+
+\backslash
+jot
+\series default
+ to its original value,
+
+\series bold
+
+\backslash
+jot
+\series default
+ is set to the value 3
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+\end_layout
+
+\begin_layout Subsubsection
+Column Separation
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Column-Separation"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+Column separation
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Multiline formulas form a matrix.
+ A formula in the eqnarray environment for example is a matrix with three columns.
+ By changing the column separation in this environment,
+ the space beside the relation sign can be changed.
+\end_layout
+
+\begin_layout Standard
+The column separation is specified with the length
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+A
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+arraycolsep
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ according to the formula:
+ column separation = 2
+\begin_inset space \thinspace{}
+\end_inset
+
+
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset Newline newline
+\end_inset
+
+Thus,
+ the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{1cm}
+\end_layout
+
+\begin_layout Standard
+inserted in \SpecialChar TeX
+ mode,
+ sets all following formula column separations to 2
+\begin_inset space \thinspace{}
+\end_inset
+
+cm.
+ To return to the predefined distance,
+
+\series bold
+
+\backslash
+arraycolsep
+\series default
+ is set to 5
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+\end_layout
+
+\begin_layout Standard
+A formula with 2
+\begin_inset space \thinspace{}
+\end_inset
+
+cm column separation:
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{1cm}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{eqnarray*}
+A & = & B\\
+C & \ne & A
+\end{eqnarray*}
+
+\end_inset
+
+A formula with the predefined column separation for matrices of 10
+\begin_inset space \thinspace{}
+\end_inset
+
+pt:
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{5pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{eqnarray*}
+A & = & B\\
+C & \ne & A
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Long Formulas
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+long
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Long formulas can be typeset using these methods:
+\end_layout
+
+\begin_layout Itemize
+If one side of an equation is much shorter than the line width,
+ this is chosen for the left side and the right side is typeset over two lines:
+\begin_inset Formula
+\begin{eqnarray}
+H & = & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\nonumber \\
+ & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:shortlong}
+\end{eqnarray}
+
+\end_inset
+
+The minus sign at the beginning of the second line does normally not appear as an operator because it is the first character of the line.
+ Thus it would not be surrounded by space and could not be distinguished from the fraction bar.
+ To avoid this,
+ a 3
+\begin_inset space \thinspace{}
+\end_inset
+
+pt space was inserted behind the minus sign with the command
+\series bold
+
+\backslash
+hspace
+\series default
+.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For more about
+\series bold
+
+\backslash
+hspace
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Variable-Space"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+H
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+hspace
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+When both sides of the equation are long,
+ the command
+\series bold
+
+\backslash
+lefteqn
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+L
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+lefteqn
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is used.
+ It is inserted in the first column of the first line and causes all further insertions to overwrite the following columns:
+\begin_inset Formula
+\begin{eqnarray}
+\lefteqn{4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}}\nonumber \\
+ & & -\hspace{3pt}B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\nonumber \\
+ & & =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\label{eq:lefteqn}
+\end{eqnarray}
+
+\end_inset
+
+After the insertion of
+\series bold
+
+\backslash
+lefteqn
+\series default
+,
+ the cursor is in a purple box that is shifted a bit to the left from the blue one.
+ The formula is inserted there.
+\begin_inset Newline newline
+\end_inset
+
+The content of additional lines is inserted in the second or another formula column.
+ The greater the insertion column number ,
+ the larger the indentation.
+\begin_inset VSpace medskip
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+Note the following when using
+\series bold
+
+\backslash
+lefteqn
+\series default
+:
+\end_layout
+
+\begin_layout Itemize
+The formula doesn't use the full page width.
+ When e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+the term
+\begin_inset Formula $-B^{2}$
+\end_inset
+
+ is added to the first line in the above example,
+ it would have been outside the page margin.
+ To better use the width,
+ negative space can be inserted at the beginning of the first line.
+\end_layout
+
+\begin_layout Itemize
+Due to a bug in \SpecialChar LyX
+ the cursor cannot be set with the mouse in the first line.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset CommandInset href
+LatexCommand href
+name "LyX-bug #1429"
+target "https://www.lyx.org/trac/ticket/1429"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ One can only set the cursor at the beginning of the line and move it with the arrow keys.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Other methods to set long formulas are offered by the environments described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Multline-Environment"
+nolink "false"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Multiline-Formula-Parts"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsubsection
+Multiline Fractions
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Multiline-Fractions"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Fractions
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+There are cases where the denominator and/or the numerator of a fraction is so long that the fraction does not fit on one line.
+ It is then necessary to add a line break within the fraction.
+ This can be done using the command
+\series bold
+
+\backslash
+splitfrac
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+splitfrac
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ To activate it,
+ go to the document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ for the package
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+mathtools
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and set its option to
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+.
+
+\series bold
+
+\backslash
+splitfrac
+\series default
+ has the scheme
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+splitfrac{first line}{second line}
+\end_layout
+
+\begin_layout Standard
+and is used for either the denominator or numerator:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+a=\frac{\splitfrac{xy+xy+xy+xy+xy}{+wy+wy+wy+wy}}{z}\ne\frac{\splitdfrac{xy+\frac{xy}{z}+xy+xy+xy}{+xy+xy+xy+xy}}{z}
+\]
+
+\end_inset
+
+The command for the first numerator above is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+splitfrac{xy+xy+xy+xy+xy
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+{+wy+wy+wy+wy
+\end_layout
+
+\begin_layout Subsubsection
+Multiline Brackets
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Multiline-Brackets"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Brackets
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+for multiline expressions
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For brackets spanning multiple lines the following problem occurs:
+\begin_inset Formula
+\begin{eqnarray*}
+A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
+ & & \left.\cdots+B-D\right]
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The closing bracket is smaller than the opening bracket because brackets with variable size may not span multiple lines.
+\end_layout
+
+\begin_layout Standard
+To set the bracket size for the second line correctly,
+ the first line is ended with
+\series bold
+
+\backslash
+right.
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+right
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and the second line with
+\series bold
+
+\backslash
+left.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For more about
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Automatic-Bracket-Size"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+L
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+left
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ After
+\series bold
+
+\backslash
+left.
+
+\series default
+ the command
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series bold
+
+\backslash
+prod
+\series default
+^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series bold
+
+\backslash
+infty
+\series default
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series bold
+
+\begin_inset Formula $\downarrow$
+\end_inset
+
+_R=1}
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+V
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+vphantom
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is inserted,
+ because the multiplication operator with its limits is the largest symbol in the first line and this should be the size for the bracket in the second line.
+\end_layout
+
+\begin_layout Standard
+The result is this:
+\begin_inset Formula
+\begin{eqnarray*}
+A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
+ & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Align Environments
+\end_layout
+
+\begin_layout Standard
+Align environments can be used for every kind of multiline formulas.
+ They are especially useful to set several formulas side by side.
+\end_layout
+
+\begin_layout Standard
+Align environments consist of columns.
+ The odd columns are right aligned,
+ the even ones left aligned.
+ Every line in an Align environment can be numbered.
+\end_layout
+
+\begin_layout Standard
+Align environments are created via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Math
+\family default
+.
+ With the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Change Formula Type
+\family default
+ pre-existing formulas can be converted to Align environments.
+\end_layout
+
+\begin_layout Standard
+To add or delete columns,
+ use the math toolbar buttons
+\begin_inset Info
+type "icon"
+arg "tabular-feature append-column"
+\end_inset
+
+ or
+\begin_inset Info
+type "icon"
+arg "tabular-feature delete-column"
+\end_inset
+
+ respectively,
+ or the menu option
+\family sans
+Edit\SpecialChar menuseparator
+Rows & Columns
+\family default
+ can be used.
+\end_layout
+
+\begin_layout Subsubsection
+Standard Align Environment
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Standard-align-Environment"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+align environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This align environment is created by pressing
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+ in a formula or by the menu
+\family sans
+Insert\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+AMS align Environment
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+An example for two formulas set side by side,
+ that are created with a four column align environment:
+\begin_inset Formula
+\begin{align*}
+A & =\sin(B) & C & =D\\
+C & \ne A & B & \ne D
+\end{align*}
+
+\end_inset
+
+As it can be seen,
+ the formulas in this environment are placed so as if there would be a
+\series bold
+
+\backslash
+hfill
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+For more about
+\series bold
+
+\backslash
+hfill
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Variable-Space"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ before the first and after every even column.
+ When the formula style
+\series bold
+Indented
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+For formula styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used,
+ the formula is set without the
+\series bold
+
+\backslash
+hfill
+\series default
+ before the first column.
+\end_layout
+
+\begin_layout Subsubsection
+Alignat Environment
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+alignat environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The alignat environment has no predefined column separation.
+ It can be inserted manually with the spaces that are described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Space"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The above example is shown in the alignat environment where 1
+\begin_inset space \thinspace{}
+\end_inset
+
+cm space was inserted at the beginning of the second formula:
+\begin_inset Formula
+\begin{alignat*}{2}
+A & =\sin(B) & \hspace{1cm}C & =D\\
+C & \ne A & B & \ne D
+\end{alignat*}
+
+\end_inset
+
+Because the column separation can be set separately for every column,
+ this environment is especially suitable to set three or more formulas side by side.
+\end_layout
+
+\begin_layout Subsubsection
+Flalign Environment
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Flalign-Environment"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+flalign environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In this environment the first column is always set to the left as much as possible and the last one to the right.
+ An example:
+\begin_inset Formula
+\begin{flalign*}
+A & =1 & B & =2 & C & =3\\
+X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
+\end{flalign*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+By creating a flalign environment with an odd number of columns where an empty \SpecialChar TeX
+ brace is inserted in the last column,
+ several formulas in a document can be set to the left,
+ although the formula style
+\series bold
+Centered
+\series default
+ is used.
+ As example the indented formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:VolInt"
+nolink "false"
+
+\end_inset
+
+:
+\begin_inset Formula
+\begin{flalign}
+\hspace{30pt}\iiint_{V}X\,\mathrm{d}V & =U & {}
+\end{flalign}
+
+\end_inset
+
+The first two columns contain the formula.
+ To indent it as with the formula style
+\series bold
+Indented
+\series default
+,
+ a 30
+\begin_inset space \thinspace{}
+\end_inset
+
+pt space was inserted at the beginning of the first column.
+\end_layout
+
+\begin_layout Subsection
+Eqnarray Environment
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Eqnarray-Environment"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+eqnarray environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When this environment is created,
+ three blue boxes appear.
+ The content of the first box is right aligned,
+ the content of the last box left aligned.
+ The content of the middle box appears centered and a bit smaller because it is intended for relational characters only.
+\begin_inset Formula
+\begin{eqnarray*}
+\frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
+AB & AB & AB\\
+A & = & A
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Gather Environment
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+gather environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This environment consists of one centered column.
+ Every line can be numbered.
+\begin_inset Formula
+\begin{gather}
+A=1\\
+X=\textrm{-}1
+\end{gather}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Multline Environment
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Multline-Environment"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multline environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The multline environment consists,
+ like the gather environment,
+ of one column.
+ But the first line is left aligned,
+ the last one right aligned.
+ All other lines are centered.
+ Therefore this environment is suitable for long formulas.
+ Using example formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:lefteqn"
+nolink "false"
+
+\end_inset
+
+ in the multline environment:
+\begin_inset Formula
+\begin{multline}
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
+-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\\
+=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}
+\end{multline}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the output,
+ only the last line of a multline environment appears numbered when the document numbering is on the right .
+ If the document numbering is on the left then only the first line will appear numbered.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For numbering styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the commands
+\series bold
+
+\backslash
+shoveright
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+shoveright
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+shoveleft
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+shoveleft
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ a centered line can be right or left aligned,
+ respectively.
+ The commands are used as follows:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+shoveright{line content}
+\series default
+ and
+\series bold
+
+\backslash
+shoveleft{line content}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+The length
+\series bold
+
+\backslash
+multlinegap
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+M
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+multlinegap
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ specifies the distance of the first line from the left page margin.
+ Predefined is the length 0
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+\end_layout
+
+\begin_layout Standard
+As example the above formula where the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+multlinegap}{2cm}
+\end_layout
+
+\begin_layout Standard
+was inserted in \SpecialChar TeX
+ mode before:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+multlinegap}{2cm}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{multline}
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
+\shoveleft{-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}\\
+=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}
+\end{multline}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+multlinegap}{0pt}
+\end_layout
+
+\end_inset
+
+The second line was left aligned using
+\series bold
+
+\backslash
+shoveleft
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Multiline Formula Parts
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Multiline-Formula-Parts"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+formula parts
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To display only parts of a formula with multiple lines,
+ one of the following environments is used:
+
+\series bold
+aligned
+\series default
+,
+
+\series bold
+alignedat
+\series default
+,
+
+\series bold
+gathered
+\series default
+ or
+\series bold
+split
+\series default
+.
+ They can be inserted via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Math
+\family default
+ or by using the commands described in this section.
+\end_layout
+
+\begin_layout Standard
+The first three have the same properties as the corresponding multiline formula environments,
+ but it is possible to set additional formula parts beside them.
+ An example:
+\begin_inset Formula
+\[
+\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
+\Delta E\Delta t & \ge\frac{\hbar}{2}
+\end{aligned}
+\right\} \textrm{Uncertainty relations}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To get this formula,
+ a displayed formula is created where the command
+\series bold
+
+\backslash
+aligned
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+A
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+aligned
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is inserted.
+ A purple box appears around the blue formula box where now columns and lines can be added.
+ Outside the multiline environment other formula parts can be set,
+ like the brace.
+\end_layout
+
+\begin_layout Standard
+The aligned environment is also suitable for long formulas whose lines are horizontally aligned.
+ Using aligned in a displayed formula has the advantage that the formula number is vertically centered behind the lines.
+ For example here is formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:shortlong"
+nolink "false"
+
+\end_inset
+
+ in the aligned environment:
+\begin_inset Formula
+\begin{equation}
+\begin{aligned}H=\; & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\\
+ & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}
+\end{aligned}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use the environments
+\series bold
+alignedat
+\series default
+,
+
+\series bold
+gathered
+\series default
+,
+ or
+\series bold
+split
+\series default
+,
+ the command
+\series bold
+
+\backslash
+alignedat
+\series default
+,
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+A
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+alignedat
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+gathered
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+G
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+gathered
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ or
+\series bold
+
+\backslash
+split
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+split
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ are inserted,
+ respectively.
+ The split environment has the same properties as the aligned environment but it can only have two columns.
+\end_layout
+
+\begin_layout Subsection
+Text in Multiline Formulas
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Text-in-multiline"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Text
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+in formulas
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multiline
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+text
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the align environments as well as the multline and gather environment,
+ text can be inserted that will appear in a separate line and doesn't affect the column alignment.
+ To do this,
+ the command
+\series bold
+
+\backslash
+intertext
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+I
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+intertext
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+intertext{text}
+\end_layout
+
+\begin_layout Standard
+The text should not be longer than a line because it cannot be hyphenated.
+ As \SpecialChar LyX
+ doesn't yet support
+\series bold
+
+\backslash
+intertext
+\series default
+ directly,
+ the text is written as mathematical text.
+ Therefore
+\series bold
+
+\backslash
+intertext
+\series default
+ must be at the beginning of a line and will appear in the output above this line.
+ An example where the text was inserted at the beginning of the second line:
+\begin_inset Formula
+\begin{align}
+I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
+\intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
+\end{align}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+intertext
+\series default
+ always creates some vertical space between the text and the formula lines.
+ To avoid this space,
+ in the document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ for the package
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+mathtools
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ set the option to
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+.
+ Then you can use the command
+\series bold
+
+\backslash
+shortintertext
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+shortintertext
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ instead of
+\series bold
+
+\backslash
+intertext
+\series default
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\begin{align}
+I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
+\shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
+\end{align}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Formula Numbering
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+numbering
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro see
+status open
+
+\begin_layout Plain Layout
+Formula numbering
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+General
+\end_layout
+
+\begin_layout Standard
+Numbered formulas can be created with the menu
+\family sans
+Insert\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Numbered
+\begin_inset space ~
+\end_inset
+
+Formula
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcuts"
+arg "command-sequence math-display; math-number-toggle;"
+\end_inset
+
+).
+ Existing formulas can be numbered with the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Number
+\begin_inset space ~
+\end_inset
+
+Whole
+\begin_inset space ~
+\end_inset
+
+Formula
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-number-toggle"
+\end_inset
+
+).
+ The formula number is displayed in \SpecialChar LyX
+ behind the formula as a number in parentheses.
+
+\end_layout
+
+\begin_layout Standard
+When numbering is turned on in multiline formulas,
+ all formulas will be numbered.
+ But the numbering can be controlled with the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Number
+\begin_inset space ~
+\end_inset
+
+This
+\begin_inset space ~
+\end_inset
+
+Line
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-number-line-toggle"
+\end_inset
+
+) for every formula.
+\end_layout
+
+\begin_layout Standard
+Except for inline formulas,
+ all formulas can be numbered with two different styles,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Cross-References
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Cross-references
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+to formulas
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All labeled formulas can be cross-referenced.
+ A label is added with the menu
+\family sans
+Insert\SpecialChar menuseparator
+Label
+\family default
+ or the toolbar button
+\begin_inset Info
+type "icon"
+arg "label-insert"
+\end_inset
+
+.
+ The cursor must be inside a displayed formula.
+ Alternatively you can right-click on the formula and choose
+\family sans
+Equation Label
+\family default
+.
+ A dialog pops up displaying the prefix
+\series bold
+eq:
+
+\series default
+ in a text field.
+ The label is inserted behind the prefix.
+ The predefined prefix means
+\begin_inset Quotes eld
+\end_inset
+
+equation
+\begin_inset Quotes erd
+\end_inset
+
+ and makes it easier to find labels in large documents because it marks it as a formula label to distinguish it from e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+section labels.
+ To change a label,
+ the menu
+\family sans
+Insert\SpecialChar menuseparator
+Label
+\family default
+ is used again or you can right-click on a formula and then on
+\family sans
+Equation Label
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+The name of the label is displayed in \SpecialChar LyX
+ within parentheses behind the formula number.
+ A formula with a label is always numbered.
+\end_layout
+
+\begin_layout Standard
+Cross-references are inserted via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Cross-Reference
+\family default
+ or with the toolbar button
+\begin_inset Info
+type "icon"
+arg "dialog-show-new-inset ref"
+\end_inset
+
+.
+ A formula cross-reference appears in the output as formula number.
+ When in the cross-reference dialog window the format
+\series bold
+(<reference>)
+\series default
+ is chosen,
+ the cross-reference appears in the output as formula number in parentheses.
+\begin_inset Newline newline
+\end_inset
+
+By right-clicking on a cross-reference in \SpecialChar LyX
+,
+ one jumps to the formula that is referenced.
+\end_layout
+
+\begin_layout Standard
+Here are as examples cross-references to formulas of the following subsections:
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Note the different cross-reference types.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The equations
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:tag"
+nolink "false"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:c"
+nolink "false"
+
+\end_inset
+
+ are equivalent.
+ In (
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:Lat"
+nolink "false"
+
+\end_inset
+
+) big Latin letters are used for the numbering in contrary to (
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:Rom"
+nolink "false"
+
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+When the argument of
+\series bold
+
+\backslash
+tag
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+tag
+\series default
+ is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:User-defined-Numbering"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series default
+ contains a box like in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Paragraph-Boxes"
+nolink "false"
+
+\end_inset
+
+,
+ the formula cannot be referenced.
+\end_layout
+
+\begin_layout Subsection
+Subnumbering
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+subnumbering
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formulas can be numbered as subequations.
+ To activate this feature,
+ add the module
+\family sans
+Subequations
+\family default
+ to the document in the menu
+\family sans
+Document\SpecialChar menuseparator
+Settings\SpecialChar menuseparator
+Modules
+\family default
+.
+ To insert subequations use the menu
+\family sans
+Insert\SpecialChar menuseparator
+Custom Insets\SpecialChar menuseparator
+Subequations
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+The equations to be subnumbered are put into the
+\family sans
+Subequations
+\family default
+ inset.
+ An example:
+\begin_inset Formula
+\begin{equation}
+A=C-B
+\end{equation}
+
+\end_inset
+
+
+\begin_inset VSpace -5mm
+\end_inset
+
+
+\begin_inset Flex Subequations
+status open
+
+\begin_layout Plain Layout
+\begin_inset Formula
+\begin{equation}
+B=C-A\label{eq:b}
+\end{equation}
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{equation}
+C=A+B\label{eq:c}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Every formula in the
+\family sans
+Subequations
+\family default
+ inset will be subnumbered with a,
+ b,
+ c,
+ \SpecialChar ldots
+ in the output.
+ For multiline formulas every line will be subnumbered.
+\end_layout
+
+\begin_layout Standard
+Referencing subequations works like normal equations:
+
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:b"
+nolink "false"
+
+\end_inset
+
+,
+
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:c"
+nolink "false"
+
+\end_inset
+
+.
+ If you want to reference the subequations collectively,
+ insert a label as first thing in the
+\family sans
+Subequations
+\family default
+ inset.
+ Formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:Here-is-an"
+plural "false"
+caps "false"
+noprefix "false"
+nolink "false"
+
+\end_inset
+
+ is an example.
+\end_layout
+
+\begin_layout Standard
+When inserting subequations,
+ vertical space is added before the equation.
+ To remove this,
+ insert -5
+\begin_inset space \thinspace{}
+\end_inset
+
+mm vertical space right before the
+\family sans
+Subequations
+\family default
+ inset.
+ If the formula style
+\series bold
+Indented
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+For formula styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used,
+ insert -7
+\begin_inset space \thinspace{}
+\end_inset
+
+mm space instead.
+\end_layout
+
+\begin_layout Standard
+To get another subnumber instead of small Latin letters,
+ insert this command as \SpecialChar TeX
+ code before the equations in the
+\family sans
+Subequations
+\family default
+ inset:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+theparentequation -
+\backslash
+roman{equation}}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+theparentequation
+\series default
+ creates the parent number and
+\series bold
+
+\backslash
+roman{equation}
+\series default
+ adds a small Roman number as subnumber.
+ For more information about the customization of the numbering,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Numbering-with-Roman"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Here is an example of a multiline formula where the numbering is customized and turned off for the second line:
+\begin_inset Flex Subequations
+status open
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "eq:Here-is-an"
+
+\end_inset
+
+
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+theparentequation -
+\backslash
+roman{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{eqnarray}
+A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
+ & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
+ & = & B^{2}-2BZ+Z^{2}
+\end{eqnarray}
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Numbering with Roman Numbers and Letters
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Numbering-with-Roman"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+with letters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+with Roman numbers
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formulas can also be numbered with Roman numbers and Latin letters.
+ To number with small Roman numbers,
+ the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+roman{equation}}
+\end_layout
+
+\begin_layout Standard
+is inserted before the formula in \SpecialChar TeX
+ mode.
+
+\series bold
+
+\backslash
+renewcommand
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+renewcommand
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ redefines the predefined command
+\series bold
+
+\backslash
+theequation
+\series default
+ to the command
+\series bold
+
+\backslash
+roman{equation}
+\series default
+.
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+The command
+\series bold
+
+\backslash
+renewcommand
+\series default
+ has the same scheme as the command
+\series bold
+
+\backslash
+newcommand
+\series default
+ described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:The-Command-newcommand"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series bold
+equation
+\series default
+ is the formula counter.
+ When the command
+\series bold
+
+\backslash
+the
+\series default
+ is used as prefix for a counter,
+ the value of the counter is output as Arabic number.
+ When a formula is numbered,
+ \SpecialChar LaTeX
+ sets internally the command
+\series bold
+
+\backslash
+theequation
+\series default
+ behind the formula.
+
+\series bold
+
+\backslash
+roman{equation}
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+roman
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ outputs the counter as small Roman number.
+\end_layout
+
+\begin_layout Standard
+All formulas behind the command
+\series bold
+
+\backslash
+renew
+\series default
+c
+\series bold
+ommand
+\series default
+ are now numbered Roman.
+ To switch to numbering with big Roman numbers,
+ the command is inserted again,
+ but
+\series bold
+
+\backslash
+roman
+\series default
+ is replaced by
+\series bold
+
+\backslash
+Roman
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+\begin_inset IndexMacro sortkey
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+roman
+\end_layout
+
+\end_inset
+
+
+\backslash
+Roman
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ To
+\begin_inset Quotes eld
+\end_inset
+
+number
+\begin_inset Quotes erd
+\end_inset
+
+ with small Latin letters there is the command
+\series bold
+
+\backslash
+alph
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+A
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+alph
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ for big ones there is the command
+\series bold
+
+\backslash
+Alph
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+A
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+\begin_inset IndexMacro sortkey
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+alph
+\end_layout
+
+\end_inset
+
+
+\backslash
+Alph
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\series default
+ Only a maximum of 26
+\begin_inset space ~
+\end_inset
+
+formulas can be numbered with Latin letters in one document.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+roman{equation}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\begin{equation}
+A=\textrm{small roman}
+\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+Roman{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{equation}
+B=\textrm{big Roman}\label{eq:Rom}
+\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+alph{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{equation}
+C=\textrm{small Latin}
+\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+Alph{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{equation}
+D=\textrm{big Latin}\label{eq:Lat}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To switch back to the default numbering,
+ insert the command:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+A
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+arabic
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{equation}
+E=\textrm{Arabic}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+As you see,
+ formulas are numbered serially independent from the numbering style.
+ When then numbering should start with
+\begin_inset Quotes eld
+\end_inset
+
+1
+\begin_inset Quotes erd
+\end_inset
+
+ when the style is changed,
+ new equation counters have to be defined.
+ A description of this can be found in the file
+\begin_inset CommandInset href
+LatexCommand href
+name "Formula-numbering.lyx"
+target "run:Formula-numbering.lyx"
+type "other"
+literal "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+User-defined Numbering
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:User-defined-Numbering"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+user-defined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\series default
+ If the document language is a right-to-left language such as Arabic,
+ you must add this to the to the \SpecialChar LaTeX
+-preamble to be able to use the commands described in this section:
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+AtBeginDocument{
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+\begin_inset space ~
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\backslash
+def
+\backslash
+tagform@#1{
+\backslash
+maketag@@@{(
+\backslash
+ignorespaces#1
+\backslash
+unskip)}} }
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+self-defined delimiters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+With standard numbering,
+ parentheses are set around a formula number.
+ To replace the parentheses for example with vertical bars,
+ the following line is added to the \SpecialChar LaTeX
+-preamble:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+AtBeginDocument{
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+\begin_inset space ~
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\backslash
+def
+\backslash
+tagform@#1{
+\backslash
+maketag@@@{|#1|}} }
+\series default
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+This macro is already declared in the \SpecialChar LaTeX
+-preamble for testing.
+ To activate it,
+ remove the percent signs at the beginning.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use other characters,
+ the vertical bars besides the
+\series bold
+#1
+\series default
+ are replaced by one or more characters.
+ To display only the formula number the vertical bars are omitted.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+When there should be an expression of your choice instead of the consecutive formula number in parentheses behind the formula,
+ the command
+\series bold
+
+\backslash
+tag
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+T
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+tag
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is used:
+\begin_inset Formula
+\begin{equation}
+A+B=C\tag{something}\label{eq:tag}
+\end{equation}
+
+\end_inset
+
+In this example the command
+\series bold
+
+\backslash
+tag
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+something
+\series default
+ was inserted in the formula.
+\end_layout
+
+\begin_layout Standard
+When the command
+\series bold
+
+\backslash
+tag*
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+something
+\series default
+ is inserted instead,
+ the parentheses are removed:
+\begin_inset Formula
+\[
+A+B=C\tag*{something}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To restart the formula numbering with new document parts or sections,
+ the following command is used:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+@addtoreset{equation}{part}
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+"
+\end_layout
+
+\end_inset
+
+@
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+"
+\end_layout
+
+\end_inset
+
+@addtoreset
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+resp.
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+@addtoreset{equation}{section}
+\end_layout
+
+\begin_layout Standard
+To be able to use these commands in \SpecialChar TeX
+ mode,
+ the
+\begin_inset Quotes eld
+\end_inset
+
+@
+\begin_inset Quotes erd
+\end_inset
+
+ character has to be made
+\begin_inset Quotes eld
+\end_inset
+
+active
+\begin_inset Quotes erd
+\end_inset
+
+ for \SpecialChar LaTeX
+ using the command
+\series bold
+
+\backslash
+makeatletter.
+
+\series default
+ The command
+\series bold
+
+\backslash
+makeatother
+\series default
+ disables this.
+ So the command sequence in \SpecialChar TeX
+ mode is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+makeatletter
+\begin_inset Newline newline
+\end_inset
+
+
+\backslash
+@addtoreset{equation}{section}
+\begin_inset Newline newline
+\end_inset
+
+
+\backslash
+makeatother
+\end_layout
+
+\begin_layout Standard
+In the \SpecialChar LaTeX
+-preamble
+\series bold
+
+\backslash
+makeatletter
+\series default
+ and
+\series bold
+
+\backslash
+makeatother
+\series default
+ can be omitted as they are automatically internally inserted by \SpecialChar LyX
+.
+\end_layout
+
+\begin_layout Standard
+To revert
+\series bold
+
+\backslash
+@addtoreset
+\series default
+,
+ the file
+\series bold
+remreset.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+remreset
+\series default
+ is part of the \SpecialChar LaTeX
+-package
+\series bold
+carlisle
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+carlisle
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ that is part of every \SpecialChar LaTeX
+ standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+remreset
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ has to be loaded in the \SpecialChar LaTeX
+-preamble with the line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{remreset}
+\end_layout
+
+\begin_layout Standard
+Then the command
+\series bold
+
+\backslash
+@removefromreset
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+"
+\end_layout
+
+\end_inset
+
+@
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+"
+\end_layout
+
+\end_inset
+
+@removefromreset
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ can be used with the same scheme as
+\series bold
+
+\backslash
+@addtoreset
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Sometimes formulas should be numbered in the following form:
+\end_layout
+
+\begin_layout Standard
+
+\family typewriter
+(section number.formula number)
+\end_layout
+
+\begin_layout Standard
+The formula number should start with every section with
+\begin_inset Quotes eld
+\end_inset
+
+1
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+For this case there is the command
+\series bold
+
+\backslash
+numberwithin
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+N
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+numberwithin
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ which is used with the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin{counter}{sectioning}
+\end_layout
+
+\begin_layout Standard
+Counter denotes what kind of numbering is affected,
+ sectioning denotes what the number before the dot is.
+\end_layout
+
+\begin_layout Standard
+Thus in our case the following \SpecialChar LaTeX
+ preamble or \SpecialChar TeX
+ code line is used:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin{equation}{section}
+\end_layout
+
+\begin_layout Standard
+This is the result:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+numberwithin{equation}{section}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{equation}
+A+B=C
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To number e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+ tables so that the number of the part is the sectioning,
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+numberwithin{table}{part}
+\series default
+ is used.
+\end_layout
+
+\begin_layout Standard
+To go back to the standard numbering or to prevent this kind of numbering when it is defined by the document class,
+ the following command is inserted as \SpecialChar TeX
+ code or to the \SpecialChar LaTeX
+ preamble:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+A
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+arabic
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\begin_inset Newline newline
+\end_inset
+
+
+\series default
+or
+\series bold
+
+\begin_inset Newline newline
+\end_inset
+
+
+\backslash
+renewcommand{
+\backslash
+thetable}{
+\backslash
+arabic{table}}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin
+\series default
+ internally uses the command
+\series bold
+
+\backslash
+@addtoreset
+\series default
+,
+ described above,
+ and would also need to be reverted.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+makeatletter
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+@removefromreset{equation}{section}
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+makeatother
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Chemical Symbols and Equations
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Chemical-Symbols-and"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Chemical characters
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+Symbols
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Chemical equations
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Symbols
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+chemical
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+An example text from chemistry:
+\end_layout
+
+\begin_layout Quote
+The
+\begin_inset Formula $\mathrm{SO_{4}^{2-}}$
+\end_inset
+
+-ion reacts with two
+\begin_inset Formula $\mathrm{Na^{+}}$
+\end_inset
+
+-ions to sodium sulfate
+\begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
+\end_inset
+
+.
+ The chemical equation for this is:
+\begin_inset Formula
+\begin{equation}
+\mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Chemical equations can be created as formulas.
+ To avoid the symbols appearing in italic,
+ everything is highlighted and changed by the shortcut
+\begin_inset Info
+type "shortcut"
+arg "font-roman"
+\end_inset
+
+ to the upright font style.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For font styles
+\series bold
+
+\series default
+see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Font-Styles"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A more convenient way to typeset chemical formulas is to use the command
+\series bold
+
+\backslash
+ce
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+C
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ which is available when the \SpecialChar LaTeX
+-package
+\series bold
+mhchem
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+mhchem
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is installed.
+ After inserting
+\series bold
+
+\backslash
+ce
+\series default
+ in a formula a new blue box appears where chemical formulas can be inserted in an intuitive way.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+H2CO3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ce{H2CO3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+SO4^2-
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ce{SO4^{2-}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+(NH4)2S
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ce{(NH4)2S}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+KCr(SO4)2.12H2O
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A-B
+\backslash
+dbond
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\backslash
+tbond
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+D
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ce{A-B\dbond C\tbond D}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^227
+\begin_inset Formula $\downarrow$
+\end_inset
+
+_90
+\begin_inset Formula $\to$
+\end_inset
+
+Th+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ce{_{90}^{227}Th+}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+mu
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+hyphen
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+Cl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+CO2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+<=>
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2CO
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ce{CO2 + C <=> 2CO}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+CO2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+->[
+\backslash
+alpha][
+\backslash
+beta]
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2CO}
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\series default
+ It is not possible in \SpecialChar LyX
+ to use the character ^ to get an up-arrow as described in the
+\series bold
+mhchem
+\series default
+ manual.
+ One instead uses a negative thin space followed by the command
+\series bold
+
+\backslash
+uparrow
+\series default
+:
+
+\begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Using
+\series bold
+
+\backslash
+ce
+\series default
+ the command for equation
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:chem-reaction"
+nolink "false"
+
+\end_inset
+
+ is:
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2Na+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+SO4^2-
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+->
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+Na2SO4
+\end_layout
+
+\begin_layout Standard
+To create multiline chemical equations first a multiline formula is created as described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Multiline-Formulas"
+nolink "false"
+
+\end_inset
+
+.
+ Afterwards the command
+\series bold
+
+\backslash
+ce
+\series default
+ is used in every small blue box of the formula.
+
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:TEOS-reaction-1"
+nolink "false"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:TEOS-reaction-2"
+nolink "false"
+
+\end_inset
+
+ are an example of a multi-stage chemical reaction where every equation has its own number.
+\begin_inset Formula
+\begin{eqnarray}
+\ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
+\ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
+\end{eqnarray}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Besides
+\series bold
+
+\backslash
+ce
+\series default
+ the
+\series bold
+mhchem
+\series default
+ package provides the command
+\series bold
+
+\backslash
+cf
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+C
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+cf
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ that is used for special cases.
+ For more information about
+\series bold
+
+\backslash
+cf
+\series default
+ and more examples have a look at the documentation of
+\series bold
+mhchem
+\series default
+,
+
+\begin_inset CommandInset citation
+LatexCommand cite
+key "mhchem"
+literal "true"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Diagrams
+\end_layout
+
+\begin_layout Standard
+\SpecialChar LyX
+ supports two types of commutative diagrams:
+
+\series bold
+amscd
+\series default
+ and
+\series bold
+xymatrix
+\series default
+ and are explained below.
+\end_layout
+
+\begin_layout Subsection
+Amscd Diagrams
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Diagrams
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+amscd
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Diagrams of this type visualize relations by vertical and horizontal lines or arrows:
+\begin_inset Formula
+\[
+\begin{CD}A@>>>B@>>>C\\
+@AAA@.@VVV\\
+F@<<<E@<<<D
+\end{CD}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To create them,
+ the command
+\series bold
+
+\backslash
+CD
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+C
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+CD
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is inserted to a formula.
+ A blue box appears with two dashed lines where additional commands can be inserted.
+ With
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+ a new line is created.
+ Horizontal relations are inserted in odd formula lines,
+ vertical in even formula lines.
+\end_layout
+
+\begin_layout Standard
+To create the relations use the following commands:
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@<<<
+\series default
+ creates a left arrow,
+
+\series bold
+@>>>
+\series default
+ a right arrow and
+\series bold
+@=
+\series default
+ a long equal sign
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@AAA
+\series default
+ creates an up arrow,
+
+\series bold
+@VVV
+\series default
+ a down arrow and
+\series bold
+@|
+\series default
+ a vertical equal sign
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@.
+
+\series default
+ is a placeholder for non-existent relations
+\end_layout
+
+\begin_layout Standard
+All arrows can be labeled as follows:
+\end_layout
+
+\begin_layout Itemize
+If text inserted between the first and second < or >,
+ resp.,
+ it is placed above the arrow.
+ When it is inserted between the second and third one,
+ it appears under the arrow.
+\end_layout
+
+\begin_layout Itemize
+When text for vertical arrows is inserted between the first and second A or V,
+ resp.,
+ it is placed left beside the arrow.
+ When it is inserted between the second and third one,
+ it appears right beside the arrow.
+ If the text contains an A or V,
+ these letters must be set into a \SpecialChar TeX
+ brace.
+\end_layout
+
+\begin_layout Standard
+As example a diagram with all possible relations:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+\begin{CD}A@>j>>B@>>k>C@=F\\
+@AmAA@.@VV{V}V@|\\
+D@<<j<E@>k>>F@=C
+\end{CD}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command for this is:
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+CD
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A@>j>>B@>>k>C@=F Ctrl+Return
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+CD
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+@AmAA@.@VV
+\backslash
+{V
+\series default
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\series bold
+V@| Ctrl+Return
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+CD
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+D@<<j<E@>k>>F@=C
+\end_layout
+
+\begin_layout Subsection
+Xymatrix Diagrams
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Diagrams
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+xymatrix
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To be able to use xymatrices,
+ the \SpecialChar LaTeX
+-package
+\series bold
+xypic
+\series default
+ must be installed.
+ A xymatrix is created by inserting the command
+\series bold
+
+\backslash
+xymatrix
+\series default
+ in a formula.
+ Then you are able to add new matrix columns and rows like for normal matrices,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Matrices"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Contrary to amscd diagrams,
+ xymatrices support diagonal and curved arrows,
+ and much more.
+ The commands used to create commutative diagrams and decorations are explained in detail in the
+\emph on
+XY-pic manual
+\emph default
+ found in the menu
+\family sans
+Help\SpecialChar menuseparator
+Specific
+\begin_inset space ~
+\end_inset
+
+Manuals
+\family default
+.
+\end_layout
+
+\begin_layout Subsection
+
+\noun on
+Feynman
+\noun default
+ Diagrams
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Diagrams
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+Feynman
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To be able to use
+\noun on
+Feynman
+\noun default
+-diagrams,
+ the \SpecialChar LaTeX
+-package
+\series bold
+feyn
+\series default
+ must be installed.
+ A
+\noun on
+Feynman
+\noun default
+-diagram is created by inserting the command
+\series bold
+
+\backslash
+Diagram
+\series default
+ in a formula.
+ Then you will be able to add new matrix columns and rows like for normal matrices,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Matrices"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Examples of how to create
+\noun on
+Feynman-
+\noun default
+diagrams in \SpecialChar LyX
+ are given in the
+\emph on
+Feynman-diagram
+\emph default
+ manual that you find in the menu
+\family sans
+Help\SpecialChar menuseparator
+Specific
+\begin_inset space ~
+\end_inset
+
+Manuals
+\family default
+.
+\end_layout
+
+\begin_layout Section
+User-defined Commands
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+User-defined commands
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\series default
+ The names of user-defined commands and macros may only consist of Latin letters.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+The Command
+\backslash
+newcommand
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:The-Command-newcommand"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+User-defined commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+newcommand
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+N
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+newcommand
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Many \SpecialChar LaTeX
+-commands are too long to be used frequently.
+ But it is possible to define with the command
+\series bold
+
+\backslash
+newcommand
+\series default
+ new shorter commands.
+\end_layout
+
+\begin_layout Standard
+The command scheme of
+\series bold
+
+\backslash
+newcommand
+\series default
+ is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{new command name}[number of arguments][optional
+\series default
+
+\series bold
+value]
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+newcommand
+\end_layout
+
+\end_inset
+
+{command definition}
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\series default
+ Verify that the name of the new command is not already used in your document or by the \SpecialChar LaTeX
+-packages that you use.
+ If you for example define the command
+\series bold
+
+\backslash
+le
+\series default
+ for
+\series bold
+
+\backslash
+Leftarrow
+\series default
+,
+ you will get an error message because
+\series bold
+
+\backslash
+le
+\series default
+ is already defined as command for
+\begin_inset Quotes eld
+\end_inset
+
+
+\begin_inset Formula $\le$
+\end_inset
+
+
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The number of arguments is an integer in the range 0
+\begin_inset space \thinspace{}
+\end_inset
+
+-
+\begin_inset space \thinspace{}
+\end_inset
+
+9 and specifies how many arguments the new command should have.
+ With the optional value a value for an optional argument can be predefined.
+ When this is done,
+ the
+\emph on
+first
+\emph default
+
+\emph on
+a
+\emph default
+rgument of the new command is automatically an optional one.
+\end_layout
+
+\begin_layout Standard
+Here are some examples:
+\end_layout
+
+\begin_layout Itemize
+To define the command
+\series bold
+
+\backslash
+gr
+\series default
+ for
+\series bold
+
+\backslash
+Longrightarrow
+\series default
+,
+ the \SpecialChar LaTeX
+-preamble line is:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+gr}{
+\backslash
+Longrightarrow}
+\end_layout
+
+\begin_layout Itemize
+To define the command
+\series bold
+
+\backslash
+us
+\series default
+ for
+\series bold
+
+\backslash
+underline
+\series default
+,
+ the argument (that should be underlined) must be taken into account.
+ For this the preamble line is:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+us}[1]{
+\backslash
+underline{#1}}
+\series default
+
+\begin_inset VSpace medskip
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+The character
+\series bold
+#
+\series default
+ acts as argument placeholder,
+ the
+\series bold
+1
+\series default
+ behind it denotes that it is the placeholder for the first argument.
+\end_layout
+
+\begin_layout Itemize
+For
+\series bold
+
+\backslash
+framebox
+\series default
+ one can e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+define the command
+\series bold
+
+\backslash
+fb
+\series default
+:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+fb}[3]{
+\backslash
+framebox#1#2{$#3$}}
+\series default
+
+\begin_inset VSpace medskip
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+The two Dollar signs creates the extra formula needed for
+\series bold
+
+\backslash
+framebox
+\series default
+,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Boxes-with-Frame"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+To create a new command for
+\series bold
+
+\backslash
+fcolorbox
+\series default
+ where the color for the box need not be specified,
+ the argument for the color is defined optional:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+cb}[3][white]{
+\backslash
+fcolorbox{#2}{#1}{$#3$}}
+\series default
+
+\begin_inset VSpace medskip
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+When the color is not specified when using
+\series bold
+
+\backslash
+cb
+\series default
+,
+ the predefined color
+\series bold
+white
+\series default
+ will be used.
+\end_layout
+
+\begin_layout Standard
+A test of the new defined commands:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+A
+\backslash
+gr
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\gr B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+us{ABcd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\us{ABcd}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+fb{[2cm]
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cb{red
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cb{red}{\int A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm" bottomspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cb[green]
+\backslash
+{red
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cb[green]{red}{\int A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+As is obvious,
+ commands defined in the preamble do not display `nicely' in LyX itself.
+ Most such commands can be defined in LyX using `math macros',
+ however,
+ which we are about to explain,
+ and these do display nicely.
+\end_layout
+
+\begin_layout Subsection
+Math Macros
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+User-defined commands!
+ Math macros
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Macros
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+User-defined commands are especially convenient for complex expressions.
+ For example if you are dealing with a document that has quadratic equations,
+ the same solution type occurs several times.
+ The general form of a quadratic equation is
+\begin_inset Formula
+\[
+0=\lambda^{2}+p\lambda+q
+\]
+
+\end_inset
+
+The general form of the solution is
+\begin_inset Formula
+\[
+\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To define a command for the solution formula where only the three parameters
+\begin_inset Formula $\lambda$
+\end_inset
+
+,
+
+\begin_inset Formula $p$
+\end_inset
+
+ and
+\begin_inset Formula $q$
+\end_inset
+
+ need to be specified and the index of
+\begin_inset Formula $\lambda$
+\end_inset
+
+ can be given optionally,
+ the \SpecialChar LaTeX
+-preamble line is
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+qG}[4][1,
+\backslash
+,2]{#2_{#1}=-
+\backslash
+frac{#3}{2}
+\backslash
+pm
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+newcommand
+\end_layout
+
+\end_inset
+
+
+\backslash
+sqrt{
+\backslash
+frac{#3^{2}}{4}-#4}}
+\end_layout
+
+\begin_layout Standard
+To create with this the solution formula,
+ the command
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+qG{
+\backslash
+lambda
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{p
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{q
+\series default
+ is inserted to a formula
+\series bold
+.
+\end_layout
+
+\begin_layout Standard
+The definition of the new command is unintuitive because one has to know the schemes of all used \SpecialChar LaTeX
+ commands,
+ e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+that a fraction is inserted in \SpecialChar LaTeX
+ as
+\series bold
+
+\backslash
+frac{numerator}{denominator}
+\series default
+.
+ Furthermore one can easily forget a brace in the definition and cannot see in \SpecialChar LyX
+ what the new command is doing.
+ To avoid these problems \SpecialChar LyX
+ offers the possibility to use math macros instead of the command
+\series bold
+
+\backslash
+newcommand
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+A math macro is created by using the menu
+\family sans
+Insert\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\family default
+ or the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-macro newmacroname_newcommand"
+\end_inset
+
+.
+ The math macro toolbar appears together with the following box where the macro is defined:
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Graphics
+ filename clipart/macrobox.png
+ scale 95
+
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
+\end_inset
+
+
+\backslash
+newmacroname is the default name of the macro that should be changed to something sensible.
+ The wanted formula is inserted in the first blue box.
+ An argument placeholder is inserted with the command
+\series bold
+
+\backslash
+#argumentnumber
+\series default
+,
+ e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g
+\begin_inset space \space{}
+\end_inset
+
+
+\series bold
+
+\backslash
+#1
+\series default
+ or by using the macro toolbar button
+\begin_inset Info
+type "icon"
+arg "math-macro-add-param"
+\end_inset
+
+.
+ Argument placeholders are displayed red.
+ A maximum of 9
+\begin_inset space ~
+\end_inset
+
+arguments are possible.
+ Optional arguments are created with the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-macro-add-optional-param"
+\end_inset
+
+.
+ The first non-optional argument can be transformed to an optional one with the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-macro-make-optional"
+\end_inset
+
+.
+ In the second blue box the appearance of the macro in \SpecialChar LyX
+ can be defined.
+ Normally you want to see it as it is defined,
+ so the box is kept empty.
+ But when you have created a macro that needs lot of space on the screen,
+ you can insert in the box for example
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+qG:
+
+\backslash
+#1
+\series default
+
+\series bold
+,
+
+\series default
+
+\series bold
+
+\backslash
+#2
+\series default
+
+\series bold
+,
+
+\series default
+
+\series bold
+
+\backslash
+#3,
+
+\backslash
+#4
+\begin_inset Newline newline
+\end_inset
+
+
+\series default
+For the macro only the arguments with the macro name in front of them will then be displayed in \SpecialChar LyX
+,
+ leading to a better overview.
+ The formula appears in the output as defined in the first box.
+\begin_inset Newline newline
+\end_inset
+
+The appearance of macros in formulas can furthermore be changed for single macros by setting the cursor in the macro and using the menu
+\family sans
+View\SpecialChar menuseparator
+(Un)fold
+\begin_inset space ~
+\end_inset
+
+Math
+\begin_inset space ~
+\end_inset
+
+Macro
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+To use a macro,
+ the macro name is inserted as command to a formula,
+ in our case
+\series bold
+
+\backslash
+qG
+\series default
+.
+ Our macro looks in \SpecialChar LyX
+ like this:
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Graphics
+ filename clipart/macrouse.png
+ scale 95
+
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+Here is our macro example with the arguments
+\begin_inset Formula $x$
+\end_inset
+
+,
+
+\begin_inset Formula $\ln(x)$
+\end_inset
+
+ and
+\begin_inset Formula $B$
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+\qG x{\ln(x)}B
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\SpecialChar LyX
+ offers in the menu
+\family sans
+Tools\SpecialChar menuseparator
+Preferences\SpecialChar menuseparator
+Editing\SpecialChar menuseparator
+Control
+\family default
+ different styles to edit macros.
+ To find the style that suits you best,
+ choose a style and set the cursor in a macro formula to see the difference.
+\end_layout
+
+\begin_layout Standard
+A math macro is transformed internally to a
+\series bold
+
+\backslash
+newcommand
+\series default
+ command when exporting the document.
+ The created
+\series bold
+
+\backslash
+newcommand
+\series default
+ command is not placed in the \SpecialChar LaTeX
+-preamble,
+ therefore macros can only be used in formulas that are in the document below the macro definition box.
+\end_layout
+
+\begin_layout Standard
+Math macros can also be directly created from a
+\series bold
+
+\backslash
+newcommand
+\series default
+ command.
+ When writing for example the command
+\series bold
+
+\begin_inset Newline newline
+\end_inset
+
+
+\backslash
+newcommand{
+\backslash
+larrow}[2]{
+\backslash
+xleftarrow[#2]{#1}}
+\begin_inset Newline newline
+\end_inset
+
+
+\series default
+in \SpecialChar LyX
+ as normal text,
+ highlighting it completely and using the shortcut
+\family sans
+Ctrl+M
+\family default
+,
+ the command will be transformed to a math macro.
+ Using this method you need to be careful that the
+\series bold
+
+\backslash
+newcommand
+\series default
+ command is typed correctly,
+ otherwise you get a faulty macro leading to \SpecialChar LaTeX
+ errors.
+\end_layout
+
+\begin_layout Standard
+Math macros currently have the problem that further formulas in macro definitions are handled wrong.
+ Therefore the example
+\series bold
+
+\backslash
+fb
+\series default
+ from
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:The-Command-newcommand"
+nolink "false"
+
+\end_inset
+
+ cannot be created as macro.
+\end_layout
+
+\begin_layout Standard
+When the cursor is in a macro definition box,
+ you will see the macro toolbar in \SpecialChar LyX
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace defskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename clipart/MacroToolbar.png
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Macros
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+Toolbar
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace defskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The macro toolbar contains from left to right the following buttons:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace defskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="2">
+<features islongtable="true" longtabularalignment="center">
+<column alignment="left" valignment="top">
+<column alignment="left" valignment="top" width="85col%">
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-remove-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+Remove Last Argument
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-add-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+Append Argument
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-make-optional"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+Transform First Non-Optional to
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+
+\end_layout
+
+\end_inset
+
+Optional Argument
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-make-nonoptional"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+Transform Last Optional to
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+
+\end_layout
+
+\end_inset
+
+Non-Optional Argument
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-remove-optional-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+Remove Optional Argument
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-add-optional-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+Insert Optional Argument
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-remove-greedy-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+Remove Last Argument
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+
+\end_layout
+
+\end_inset
+
+Spitting Out To The Right
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-append-greedy-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+Append Argument
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+
+\end_layout
+
+\end_inset
+
+Eating From The Right
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-add-greedy-optional-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+Append Optional Argument
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar menuseparator
+
+\end_layout
+
+\end_inset
+
+Eating From The Right
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Math Macros for External Commands
+\end_layout
+
+\begin_layout Standard
+Sometimes,
+ you may need to use a LaTeX package which defines a math command that is not natively supported in LyX.
+ This is easy enough to do:
+ Just include the package in the preamble and type out the command in math.
+ As with commands defined in the preamble,
+ however,
+ the display in LyX will not be `nice'.
+\end_layout
+
+\begin_layout Standard
+As of LyX 2.4,
+ this problem has been solved.
+ Just define a math macro with empty LaTeX slot!
+ The LyX part will be used for display,
+ but no corresponding LaTeX will be output.
+ For example,
+ the
+\begin_inset Flex Code
+status collapsed
+
+\begin_layout Plain Layout
+godelnum.sty
+\end_layout
+
+\end_inset
+
+ package defines a Godelnum macro that puts a single argument into corner quotes.
+ To get a nice LyX display of this macro,
+ just do:
+\end_layout
+
+\begin_layout Standard
+\begin_inset FormulaMacro
+\newcommand{\Godelnum}[1]{}
+{\ulcorner#1\urcorner}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The same trick,
+ of course,
+ can be used for commands defined in the preamble.
+\end_layout
+
+\begin_layout Section
+Computer Algebra Systems
+\end_layout
+
+\begin_layout Standard
+\SpecialChar LyX
+ offers the exchange between mathematical expressions written in \SpecialChar LyX
+'s math editor and external applications or user defined scripts.
+ Currently supported applications are
+\family sans
+Maple
+\family default
+,
+
+\family sans
+Mathematica
+\family default
+,
+
+\family sans
+Maxima
+\family default
+ and
+\family sans
+Octave
+\family default
+.
+ Note that the set of supported mathematical constructs is limited only to very simple cases.
+\end_layout
+
+\begin_layout Subsection
+Usage
+\end_layout
+
+\begin_layout Standard
+Write some expression in a formula,
+ go to the
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Use Computer Algebra System
+\family default
+ menu and choose the application you have installed on the computer.
+ After that the result of computation should show on the right side of the expression together with the
+\begin_inset Quotes eld
+\end_inset
+
+=
+\begin_inset Quotes erd
+\end_inset
+
+ operator.
+\end_layout
+
+\begin_layout Standard
+Here are few simple examples (with results from
+\family typewriter
+Maxima
+\family default
+) to show what kind of computations can be performed:
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\series default
+ One needs to use proper delimiter insets
+\begin_inset Formula $\left(\right)$
+\end_inset
+
+ instead of simple '(' ')' characters.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\det\left[\begin{array}{ccc}
+1 & 6 & 7\\
+2 & 5 & 8\\
+3 & 4 & 17
+\end{array}\right]=-56$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Keyboard shortcut
+\end_layout
+
+\begin_layout Standard
+Currently there is no keyboard shortcut for calling the algebra applications.
+ One can easily bind a shortcut to the
+\family sans
+math-extern
+\family default
+ \SpecialChar LyX
+ function (see the
+\family sans
+\emph on
+\SpecialChar LyX
+ Functions
+\family default
+\emph default
+ manual).
+ One could e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+bind the
+\family sans
+Return
+\family default
+ key inside the math editor.
+ To bind it to
+\family typewriter
+Maxima
+\family default
+ one would use this shortcut definition command:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+command-alternatives paragraph-break;math-extern maxima
+\end_layout
+
+\begin_layout Section
+Miscellaneous
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Miscellaneous
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Negative Numbers
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Numbers
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+negative
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Negative numbers often look ugly in formulas because the minus sign before the number is set with the same length as the minus operator sign.
+ When writing the negative number in normal text,
+ the minus sign appears correctly.
+\end_layout
+
+\begin_layout Standard
+Thus,
+ the problem disappears when converting the minus sign to mathematical text.
+\end_layout
+
+\begin_layout Standard
+An example to visualize the problem:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="left" valignment="top">
+<row>
+<cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+normal text:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+x = -2
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="right" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+formula:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $x=-2$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+solution:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $x=\textrm{-}2$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Comma as decimal Separator
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Comma
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In \SpecialChar LaTeX
+ a comma inside a formula is used,
+ according to the English convention,
+ as number group separator.
+ So there will be space added behind all commas in formulas.
+\end_layout
+
+\begin_layout Standard
+To avoid this,
+ the comma is highlighted and changed to mathematical text (shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-mode"
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+To use all formula commas in the document as decimal separator,
+ the file
+\series bold
+icomma.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+icomma
+\series default
+ is part of the \SpecialChar LaTeX
+-package
+\series bold
+was
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+was
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+icomma
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is loaded with the \SpecialChar LaTeX
+-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{icomma}
+\end_layout
+
+\begin_layout Subsection
+Physical Vectors
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Physical-Vectors"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Vectors
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+physical
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Predefined vectors are offered by the \SpecialChar LaTeX
+-package
+\series bold
+braket
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+braket
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ that is loaded with the \SpecialChar LaTeX
+-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{braket}
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+ifbraket
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following table will only be displayed when the \SpecialChar LaTeX
+-package
+\series bold
+braket
+\series default
+ is installed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The following commands are defined:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Bra{
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Bra{\psi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Ket{
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Ket{\psi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Braket{
+\backslash
+psi|
+\backslash
+phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Braket{\psi|\phi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+Braket
+\series default
+ assures that all vertical bars are set in the size of the surrounding brackets:
+\begin_inset Formula
+\[
+\Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
+\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+else
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following will be displayed when the \SpecialChar LaTeX
+-package
+\series bold
+braket
+\series default
+ is not installed:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You need to install the \SpecialChar LaTeX
+-package
+\series bold
+braket
+\series default
+ to see the rest of this subsection in the output.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+fi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The effect of
+\series bold
+
+\backslash
+Braket
+\series default
+ can also be achieved using the command
+\series bold
+
+\backslash
+middle
+\series default
+,
+ that is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Automatic-Bracket-Size"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Self-defined Fractions
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Self-defined-Fractions"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Fractions
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+self-defined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To define custom commands for fractions,
+ the command
+\series bold
+
+\backslash
+genfrac
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+G
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+genfrac
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+genfrac{left
+\series default
+
+\series bold
+bracket}{right
+\series default
+
+\series bold
+bracket}{fraction bar thickness}{style}
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+genfrac
+\end_layout
+
+\end_inset
+
+{numerator}{denominator}
+\end_layout
+
+\begin_layout Standard
+The style is a number in the range of 0
+\begin_inset space \thinspace{}
+\end_inset
+
+-
+\begin_inset space \thinspace{}
+\end_inset
+
+3.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Number
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Style (Size)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+display style formula
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+inline formula
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+small
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+tiny
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When no style is given,
+ the size is adjusted to the surrounding environment like for the command
+\series bold
+
+\backslash
+frac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+When no fraction bar thickness is given,
+ the predefined value of 0.4
+\begin_inset space \thinspace{}
+\end_inset
+
+pt will be used.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+For example,
+ the commands
+\series bold
+
+\backslash
+dfrac
+\series default
+ and
+\series bold
+
+\backslash
+tbinom
+\series default
+ from
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Fractions"
+nolink "false"
+
+\end_inset
+
+ are defined with the commands
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+dfrac}[2]{
+\backslash
+genfrac{}{}{}{0}{#1}{#2}}
+\end_layout
+
+\begin_layout Standard
+and
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+tbinom}[2]{
+\backslash
+genfrac{(}{)}{0pt}{1}{#1}{#2}}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+To define a fraction where the fraction bar thickness can be given as optional argument,
+ the following line is inserted to the \SpecialChar LaTeX
+-preamble:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+fracS}[3][]{
+\backslash
+genfrac{}{}{#1}{}{#2}{#3}}
+\end_layout
+
+\begin_layout Standard
+A test:
+\begin_inset Formula
+\begin{align*}
+\text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
+\text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
+\end{align*}
+
+\end_inset
+
+As one can see,
+ the distance of the numerator and the denominator to the fraction bar is round about three times the bar thickness.
+\end_layout
+
+\begin_layout Subsection
+Canceled Formulas
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+canceled
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+There are four ways to cancel formulas or parts of formulas:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+ifcancel
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following table will only be displayed when the \SpecialChar LaTeX
+-package
+\series bold
+cancel
+\series default
+ is installed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cancel
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cancel{\int A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bcancel
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bcancel{\int A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topspace="1.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+xcancel
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xcancel{\int A=B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cancelto
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\begin_inset Formula $\to$
+\end_inset
+
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cancelto
+\series default
+ is especially suitable to visualize the reduction of fractions within formulas:
+\begin_inset Formula
+\[
+\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To change the size of
+\series bold
+
+\backslash
+cancelto
+\series default
+'s
+\begin_inset Quotes eld
+\end_inset
+
+subscript
+\begin_inset Quotes erd
+\end_inset
+
+ value one can add the \SpecialChar LaTeX
+-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+PassOptionsToPackage{option}{cancel}
+\end_layout
+
+\begin_layout Standard
+where
+\series bold
+option
+\series default
+ is either
+\series bold
+samesize
+\series default
+ which leads to the same size as for the canceled value,
+ or
+\series bold
+Smaller
+\series default
+ which makes is it a bit smaller than normal.
+\end_layout
+
+\begin_layout Standard
+To color the cancellation bar one adds this command as \SpecialChar TeX
+ code:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+CancelColor}{
+\backslash
+color{red}}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+red
+\series default
+ can be replaced by a color of your choice.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+renewcommand{
+\backslash
+CancelColor}{
+\backslash
+color{red}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+renewcommand{
+\backslash
+CancelColor}{
+\backslash
+color{black}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+reset the color
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For further customizations,
+ see the documentation of the package
+\series bold
+cancel
+\series default
+,
+
+\begin_inset CommandInset citation
+LatexCommand cite
+key "cancel"
+literal "true"
+
+\end_inset
+
+.
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+cancel
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+else
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following will be displayed when the \SpecialChar LaTeX
+-package
+\series bold
+cancel
+\series default
+ is not installed:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You need to install the \SpecialChar LaTeX
+-package
+\series bold
+cancel
+\series default
+ to see the rest of this subsection in the output.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+fi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Formulas in Section Headings
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Formulas-in-Section"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+in section headings
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When formulas are used in section headings,
+ the following has to be taken into account:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+When
+\series bold
+hyperref
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+hyperref
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ support is enabled in the document settings dialog under
+\family sans
+PDF
+\begin_inset space ~
+\end_inset
+
+Properties
+\family default
+,
+ PDF-bookmarks are created for every section heading in the table of contents.
+ If a section heading contains formulas,
+ they are incorrectly displayed in the bookmark text,
+ because formulas in bookmarks infringe the PDF conventions.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Both problems can be solved by inserting at the end of the section heading a short title with the menu
+\family sans
+Insert\SpecialChar menuseparator
+Short
+\begin_inset space ~
+\end_inset
+
+Title
+\family default
+.
+ Short titles are used as alternative for multiline section headings to keep the table of contents clearly arranged.
+ Only the short title appears in the table of contents and therefore also in the PDF-bookmark.
+\end_layout
+
+\begin_layout Standard
+When formulas should be used in the table of contents but
+\series bold
+hyperref
+\series default
+ is used,
+ one can use the following command in \SpecialChar TeX
+ mode:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+texorpdfstring{part}{alternative}
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+T
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+texorpdfstring
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Part is the part of the heading that shouldn't appear in the PDF-bookmark.
+ This can be characters,
+ formulas,
+ footnotes,
+ but also cross-references.
+ The alternative is used instead of the part for the bookmark.
+\end_layout
+
+\begin_layout Standard
+Here are two example headings:
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Heading without formula in table of contents
+\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
+\end_inset
+
+
+\begin_inset Argument 1
+status collapsed
+
+\begin_layout Plain Layout
+Heading without formula in table of contents
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Heading with formula in table of contents
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+unboldmath
+\end_layout
+
+\end_inset
+
+In the first heading a short title was used,
+ in the second one
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+To get the same formatting as for the other headings,
+ the complete heading was set into a
+\series bold
+boldmath
+\series default
+ environment
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+See
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Bold-Formulas"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Formulas in multi-column Text
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+in multi-column text
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formulas in multi-column text are often too wide to fit into a column and thus need to be set over the whole page width.
+ This is done by using the \SpecialChar LaTeX
+-package
+\series bold
+multicol
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+multicol
+\series default
+ is part of every \SpecialChar LaTeX
+ standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+multicol
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ that is loaded with the \SpecialChar LaTeX
+-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{multicol}
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+Note that in this case the setting
+\family sans
+Two-column
+\begin_inset space ~
+\end_inset
+
+document
+\family default
+ in the menu
+\family sans
+Document\SpecialChar menuseparator
+Settings
+\family default
+ under
+\family sans
+Text
+\begin_inset space ~
+\end_inset
+
+Layout
+\family default
+\emph on
+
+\emph default
+must
+\emph on
+not
+\emph default
+ be selected.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Before the multi-column text the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+begin{multicols}{column number}
+\end_layout
+
+\begin_layout Standard
+is written in \SpecialChar TeX
+ mode.
+ The column number is a number in the range of 2
+\begin_inset space \thinspace{}
+\end_inset
+
+-
+\begin_inset space \thinspace{}
+\end_inset
+
+10.
+ Before the formula the multi-column text is ended by inserting the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+end{multicols}
+\end_layout
+
+\begin_layout Standard
+in \SpecialChar TeX
+ mode.
+\end_layout
+
+\begin_layout Standard
+Due to the command some space is automatically added before the formula.
+ To correct this,
+ -6
+\begin_inset space \thinspace{}
+\end_inset
+
+mm vertical space is inserted before the formula.
+ When the formula style
+\series bold
+Indented
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+For formula styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used,
+ a -9
+\begin_inset space \thinspace{}
+\end_inset
+
+mm space is inserted instead.
+\end_layout
+
+\begin_layout Standard
+As example a multi-column text with a displayed formula:
+\end_layout
+
+\begin_layout Standard
+
+\lang ngerman
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{multicols}{2}
+\end_layout
+
+\end_inset
+
+Das Spektrum wird fouriertransformiert.
+ Die Fouriertransformation wird verwendet,
+ um die überlagerten Signale (Netzwerk,
+ Lösungsmittel) zu trennen.
+ Nachdem wir die Phasenverschiebung bestimmen konnten,
+ interessiert uns nun das Aussehen des Ausgangssignals.
+ Im Experiment haben wir es mit sehr vielen Teilchen zu tun,
+ so dass man über alle Phasen integrieren muss.
+ Sei nun
+\begin_inset Formula $S$
+\end_inset
+
+ unser normiertes Ausgangssignal und
+\begin_inset Formula $P$
+\end_inset
+
+ die Phasenverteilungsfunktion,
+ so ergibt sich die Beziehung
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{multicols}
+\end_layout
+
+\end_inset
+
+
+\begin_inset VSpace -6mm
+\end_inset
+
+
+\begin_inset Formula
+\begin{equation}
+S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
+\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{multicols}{2}
+\end_layout
+
+\end_inset
+
+wobei
+\begin_inset Formula $S_{0}$
+\end_inset
+
+ das Signal ohne Gradient ist und die Normierungsbedingung
+\begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
+\end_inset
+
+ gilt.
+ Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
+ Direkt nach dem
+\begin_inset Formula $\nicefrac{\pi}{2}$
+\end_inset
+
+
+\begin_inset space \thinspace{}
+\end_inset
+
+-rf-Puls beginnt sich die Magnetisierung zu entfokussieren,
+ wodurch sich das Signal zusätzlich abschwächt.
+ Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
+\begin_inset Formula $T_{2}$
+\end_inset
+
+-Zeit.
+\end_layout
+
+\begin_layout Standard
+
+\lang ngerman
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{multicols}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Formulas with Description of Variables
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+with description of variables
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To describe variables within a formula,
+ like in formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:within"
+nolink "false"
+
+\end_inset
+
+,
+ a 2
+\series bold
+×
+\series default
+
+\begin_inset Formula $n$
+\end_inset
+
+
+\begin_inset space ~
+\end_inset
+
+matrix is used with left aligned columns for the
+\begin_inset Formula $n$
+\end_inset
+
+ used variables.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For matrices see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Matrices"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ To set the description in a smaller size,
+ before the matrix e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+the command
+\series bold
+
+\backslash
+footnotesize
+\series default
+ is inserted.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For font sizes see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Font-Sizes"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When the formula style
+\series bold
+Indented
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For formula styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used,
+ a
+\series bold
+
+\backslash
+hfill
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+hfill
+\series default
+ only works in formulas with the style
+\series bold
+Indented
+\series default
+,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Variable-Space"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ is inserted before and after the matrix to have the same separation of the matrix from the equation and the side margin.
+\end_layout
+
+\begin_layout Standard
+When the formula style
+\series bold
+Centered
+\series default
+ is used,
+ the method described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Flalign-Environment"
+nolink "false"
+
+\end_inset
+
+ is used to indent formulas.
+ Formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:within"
+nolink "false"
+
+\end_inset
+
+ consists of five columns where in the first two columns contain the equation,
+ the third the matrix and the last one an empty \SpecialChar TeX
+ brace.
+\begin_inset Formula
+\begin{flalign}
+\hspace{30pt}F_{A} & =\rho·V·g & {\footnotesize \begin{array}{ll}
+\rho & \textrm{density}\\
+V & \textrm{volume}\\
+g & \textrm{gravitational acceleration}
+\end{array}} & & {}\label{eq:within}
+\end{flalign}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Upright small Greek Letters
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Upright-small-Greek"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Greek letters
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+upright
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Most of the math fonts only provide italic small Greek letters.
+ But for symbols of elementary particles like pions and neutrinos,
+ upright Greek letters are needed.
+ The file
+\series bold
+upgreek.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+upgreek
+\series default
+ is part of the \SpecialChar LaTeX
+-package
+\series bold
+was
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+was
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+upgreek
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ that is loaded with the \SpecialChar LaTeX
+-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{upgreek}
+\end_layout
+
+\begin_layout Standard
+provides them.
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+ifupgreek
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following table will only be displayed when the \SpecialChar LaTeX
+-package
+\series bold
+upgreek
+\series default
+ is installed:
+\end_layout
+
+\end_inset
+
+ They are created when the command for a small Greek letter is started with
+\series bold
+up
+\series default
+.
+ For example the command
+\series bold
+
+\backslash
+uptau
+\series default
+ creates this:
+
+\begin_inset Formula $\uptau$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With these commands reactions of elementary particles can be typeset:
+\begin_inset Formula
+\[
+\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The upright letters are more bold and wider than the italic ones.
+ They should therefore not be used for units like
+\begin_inset Quotes eld
+\end_inset
+
+µm
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+else
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following will be displayed when the \SpecialChar LaTeX
+-package
+\series bold
+upgreek
+\series default
+ is not installed:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You need to install the \SpecialChar LaTeX
+-package
+\series bold
+upgreek
+\series default
+ to see the rest of this subsection in the output.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+fi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Text Characters in Formulas
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Text
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+in formulas
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In some cases you might want to insert text characters directly into formulas.
+ For example the centered dot · is often used in formulas like
+\begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
+\end_inset
+
+.
+ One would have to insert the command
+\series bold
+
+\backslash
+cdot
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+See
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Binary-Operators"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ all the time,
+ because this character is defined in all encodings as a text character.
+ But the encoding can be changed by this \SpecialChar LaTeX
+-preamble line:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+Declare Inputtext{183}{
+\backslash
+ifmmode
+\backslash
+cdot
+\backslash
+else
+\backslash
+textperiodcentered
+\backslash
+f\SpecialChar ligaturebreak
+i}
+\end_layout
+
+\begin_layout Standard
+The character encoding (menu
+\family sans
+Document\SpecialChar menuseparator
+Settings\SpecialChar menuseparator
+Language
+\family default
+) specifies what character appears when a keyboard key is pressed.
+ When the key for the character '·' is pressed,
+ internally the command
+\series bold
+
+\backslash
+textperiodcentered
+\series default
+ is used.
+ But this command is not available in a formula so that you would get \SpecialChar LaTeX
+-errors.
+ With the changed encoding the correct command is chosen automatically,
+ depending on if the character was inserted into a formula or not.
+\end_layout
+
+\begin_layout Standard
+The encoding of several characters is saved in definition files.
+ For example the encoding
+\series bold
+latin9
+\series default
+ is defined in the file
+\series bold
+latin9.def
+\series default
+ which is in the installation folder of \SpecialChar LaTeX
+.
+ Encodings should only be changed via the \SpecialChar LaTeX
+-preamble and not in the definition files.
+ Otherwise documents could not be edited by other \SpecialChar LyX
+ users working on other computers.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Besides the centered dot,
+ in this document the degree sign ° is defined with the following \SpecialChar LaTeX
+-preamble line so that it can be directly inserted into a formula:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareInputtext{176}{
+\backslash
+ifmmode^
+\backslash
+circ
+\backslash
+else
+\backslash
+textdegree
+\backslash
+f\SpecialChar ligaturebreak
+i}
+\end_layout
+
+\begin_layout Subsection
+\SpecialChar LaTeX
+-comments in formulas
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+\SpecialChar LaTeX
+-comments
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
+ source code of your file with the menu
+\family sans
+Insert\SpecialChar menuseparator
+Note\SpecialChar menuseparator
+Comment
+\family default
+.
+ This is not possible in a formula but you can insert \SpecialChar LaTeX
+-comments with the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+%
+\end_layout
+
+\begin_layout Standard
+This creates a box in which you can write your comment.
+ Due to a bug in \SpecialChar LyX
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset CommandInset href
+LatexCommand href
+name "LyX-bug #9002"
+target "https://www.lyx.org/trac/ticket/9002"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ you cannot write normal text inside the comment,
+ even when you use mathematical text,
+ you will see its \SpecialChar LaTeX
+-commands in the \SpecialChar LaTeX
+-output.
+\begin_inset Newline newline
+\end_inset
+
+This a formula with a \SpecialChar LaTeX
+-comment:
+\begin_inset Formula
+\[
+A=B%\text{This is the comment}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+\start_of_appendix
+Typographic Advice
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Typographic advice
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This section is a summary of the most important typographic rules,
+ listed in ISO norms.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+This collection was partly taken from the German semi-official dictionary called
+\begin_inset Quotes eld
+\end_inset
+
+Duden
+\begin_inset Quotes erd
+\end_inset
+
+
+\begin_inset CommandInset citation
+LatexCommand cite
+key "Duden"
+literal "true"
+
+\end_inset
+
+ that lists some of the ISO rules.
+ More rules are listed in
+\begin_inset CommandInset citation
+LatexCommand cite
+key "Checklist"
+literal "true"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Physical units are
+\emph on
+always
+\emph default
+ set upright
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+Done with font styles,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Font-Styles"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ no matter if they appear in italic text:
+ 30
+\begin_inset space \thinspace{}
+\end_inset
+
+km/h
+\begin_inset Newline newline
+\end_inset
+
+Between the value and the unit is the smallest space,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Predefined-Space"
+nolink "false"
+
+\end_inset
+
+.
+\begin_inset Newline newline
+\end_inset
+
+This convention is automatically fulfilled when the command
+\series bold
+
+\backslash
+unittwo
+\series default
+ is used.
+ When it is entered in a formula,
+ two boxes appear.
+ In the first one the value is inserted,
+ in the second one the unit,
+ and the result is as above:
+
+\begin_inset Formula $\unit[30]{km/h}$
+\end_inset
+
+
+\begin_inset space \thinspace{}
+\end_inset
+
+.
+ Note that
+\series bold
+
+\backslash
+unittwo
+\series default
+ is not a real \SpecialChar LaTeX
+ command but the command
+\series bold
+
+\backslash
+unit[value]{unit}
+\series default
+,
+ therefore you cannot use it in \SpecialChar TeX
+ code.
+\end_layout
+
+\begin_layout Itemize
+Percent and perthousand signs are set like physical units:
+\begin_inset Newline newline
+\end_inset
+
+1.2
+\begin_inset space \thinspace{}
+\end_inset
+
+‰ alcohol in blood
+\end_layout
+
+\begin_layout Itemize
+The degree sign follows the value directly:
+ 15°,
+ except when it is used in units:
+ 15
+\begin_inset space \thinspace{}
+\end_inset
+
+°C
+\end_layout
+
+\begin_layout Itemize
+In numbers with more than four digits the smallest space is inserted before every third digit to group them:
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+18
+\begin_inset space \thinspace{}
+\end_inset
+
+473
+\begin_inset space \thinspace{}
+\end_inset
+
+588
+\end_layout
+
+\begin_layout Itemize
+For dimensions like 120×90×40
+\begin_inset space \thinspace{}
+\end_inset
+
+cm the multiplication sign
+\begin_inset Quotes eld
+\end_inset
+
+×
+\begin_inset Quotes erd
+\end_inset
+
+ is used.
+ It is available either via the command
+\series bold
+
+\backslash
+times
+\series default
+ or via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Special Character\SpecialChar menuseparator
+Symbols
+\family default
+.
+\end_layout
+
+\begin_layout Itemize
+Functions with names consisting of several letters are set upright to avoid confusions,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Predefined-Functions"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Indices consisting of several letters,
+ are set upright:
+
+\begin_inset Formula $E_{\mathrm{kin}}$
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+Components of matrices are set italic:
+
+\begin_inset Formula $\hat{H}_{kl}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+The differentiation/integration operator 'd',
+ the Euler's number 'e' and the imaginary unit 'i' should be set upright,
+ to avoid mixing them up with other variables.
+\end_layout
+
+\begin_layout Itemize
+The character that denotes a
+\noun on
+Fourier
+\noun default
+ transformation is inserted either by the command
+\series bold
+
+\backslash
+mathscr
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+F
+\series default
+ or via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Special Character\SpecialChar menuseparator
+Symbols\SpecialChar menuseparator
+Letterlike
+\begin_inset space ~
+\end_inset
+
+Symbols
+\family default
+:
+
+\begin_inset Formula $\mathscr{F}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Synonyms
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Synonyms
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Some characters and symbols can be created with several commands.
+ Here is a list of the synonym commands:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="12" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+equivalent to
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ast
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+*
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+choose
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+binom
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+geq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ge
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lbrace
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+{
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lbracket
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+[
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+gets
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+le
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vee
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+neq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+slash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+/
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vert
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+|
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="12" columns="2">
+<features booktabs="true" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+equivalent to
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+backslash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\backslash
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dasharrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dashrightarrow
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+land
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+wedge
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rbrace
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rbracket
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+]
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+to
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lnot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+neg
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ne
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+owns
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ni
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+square
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
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projects / lyx.git / blobdiff