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-% parts of this document may not print out as expected. If you
-% have problems LaTeXing this file, please contact
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-% email: lyx-docs@lists.lyx.org
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-LyX's detailed Math manual
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-
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-by the LyX Team
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-\noindent
-If you have comments or error corrections, please send them to the LyX Documenta
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-
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-\backslash
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-Syntax Explanation
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-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-in
-\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
-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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-pt
-\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
-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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-pc
-\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
-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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-sp
-\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
-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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-bp
-\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
-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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-dd
-\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
-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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-cc
-\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
-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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-ex
-\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
-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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-em
-\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
-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" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-mu
-\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
-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 Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Basic Functions
-\end_layout
-
-\begin_layout Subsection
-Exponents
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Exponents
-\end_layout
-
-\end_inset
-
- and Indices
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Indices
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Superscripts|see
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
-Exponents
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Subscripts|see
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
-Indices
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\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 Graphics
- filename ../images/math-subscript.png
- scale 85
-
-\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 Graphics
- filename ../images/math-superscript.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="4" 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" 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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-B_V
-\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 $B_{V}$
-\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
-B^V
-\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 $\raisebox{5mm}{}B^{V}$
-\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
-B^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\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 $\raisebox{5mm}{}B^{A}$
-\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 collapsed
-
-\begin_layout Plain Layout
-Depending on the used keyboard settings 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 "sub:Fractions"
-
-\end_inset
-
-
-\begin_inset Index idx
-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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! F !
-\backslash
-frac
-\end_layout
-
-\end_inset
-
- or via the math toolbar button
-\begin_inset Graphics
- filename ../images/math/frac.png
- scale 50
-
-\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 Graphics
- filename ../images/math/frac-square.png
- scale 85
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-dfrac
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-tfrac
-\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 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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-frac
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\end_inset
-
-B
-\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 $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
-\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
-dfrac
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\end_inset
-
-B
-\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 $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
-\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
-
-\backslash
-dfrac
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-e^
-\backslash
-frac
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-cfrac
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\end_inset
-
-B+
-\backslash
-cfrac
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-C+
-\backslash
-cfrac
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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
- sets the fraction always in the size of a displayed formula, also 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 no real LaTeX commands but represent the command
-\series bold
-
-\backslash
-cfrac[alignment]{numerator}{denominator}
-\series default
- .
- Therefore you cannot use them in 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! N !
-\backslash
-nicefrac
-\end_layout
-
-\end_inset
-
-:
-\begin_inset Formula $\nicefrac{5}{31}$
-\end_inset
-
- or
-\series bold
-
-\backslash
-unitfrac
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! U !
-\backslash
-unitfrac
-\end_layout
-
-\end_inset
-
-:
-\begin_inset Formula $\unitfrac{5}{31}$
-\end_inset
-
- There is furthermore the command
-\series bold
-
-\backslash
-unitfracthree
-\series default
- that offers 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 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 TeX code.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-How to define own fractions where the fraction stroke can be changed, is
- explained in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Self-defined-Fractions"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Roots
-\begin_inset Index idx
-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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-sqrt
-\end_layout
-
-\end_inset
-
- or the math toolbar button
-\begin_inset Graphics
- filename ../images/math/sqrt.png
- scale 85
-
-\end_inset
-
-, all other roots with the command
-\series bold
-
-\backslash
-root
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-root
-\end_layout
-
-\end_inset
-
- or with the math toolbar button
-\begin_inset Graphics
- filename ../images/math/root.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="3" 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" 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
-\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" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sqrt
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A-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 $\raisebox{4.5mm}{}\sqrt{A-B}$
-\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
-root
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-3
-\begin_inset Formula $\downarrow$
-\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 $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-leftroot
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-uproot
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! U !
-\backslash
-uproot
-\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 top, 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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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
-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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-binom
-\end_layout
-
-\end_inset
-
- or with the submenu of the math toolbar button
-\begin_inset Graphics
- filename ../images/math/frac-square.png
- scale 85
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-dbinom
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-tbinom
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-tbinom
-\end_layout
-
-\end_inset
-
-.
- For other brackets around binomial coeficients there are the commands
-\series bold
-
-\backslash
-brace
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-brace
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-brack
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-brack
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="6" 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" 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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-binom
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\end_inset
-
-B
-\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 $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
-\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
-dbinom
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\end_inset
-
-B
-\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 $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
-\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
-
-\backslash
-tbinom
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\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 $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
-\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
-brack
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\end_inset
-
-B
-\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 $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
-\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
-
-\backslash
-brace
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\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 $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Case Differentiations
-\begin_inset Index idx
-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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-cases
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\to$
-\end_inset
-
-B>0
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-cases
-\end_layout
-
-\end_inset
-
-
-\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 $\begin{cases}
-A & B>0\end{cases}$
-\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
-
-\backslash
-cases
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\begin_inset Info
-type "shortcut"
-arg "newline-insert newline"
-\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
-\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 Graphics
- filename ../images/math/cases.png
- scale 85
-
-\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 Graphics
- filename ../images/tabular-feature_append-row.png
- scale 85
-
-\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
-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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! N !
-\backslash
-not
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-not=
-\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 $\not=$
-\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
-
-\backslash
-not
-\backslash
-le
-\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 $\not\le$
-\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
-
-\backslash
-not
-\backslash
-parallel
-\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 $\not\parallel$
-\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 "sub:Mathematical-Symbols"
-
-\end_inset
-
- and
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Relations"
-
-\end_inset
-
-).
-\end_layout
-
-\begin_layout Subsection
-Placeholders
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Placeholders"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Placeholders
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Chemical characters ! Isotopes
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Isotopes|see
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
-Chemical characters
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\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 "sub:Chemical-Symbols-and"
-
-\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 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 $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<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
-
-
-\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
-
-\begin_layout Standard
-The shorter index is by default placed below or above the first character
- of the longer index.
- To avoid this there is the command
-\series bold
-
-\backslash
-phantom
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! P !
-\backslash
-phantom
-\end_layout
-
-\end_inset
-
- or the math toolbar button
-\begin_inset space \thinspace{}
-\end_inset
-
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-can be found in the submenu of the toolbar button
-\begin_inset Graphics
- filename ../images/math/space.png
- scale 85
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\begin_inset Graphics
- filename ../images/math/phantom.png
- scale 85
-
-\end_inset
-
- that creates one or more phantom characters.
- When inserting
-\series bold
-
-\backslash
-phantom
-\series default
- a small blue box appears that is superposed with two red arrows.
- The arrows indicate that the complete width and height of the box content
- will be created as placeholder.
- Phantom characters are accordingly placeholders with the size of the characters.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="4" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-^19
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-_
-\backslash
-phantom
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-1
-\begin_inset Formula $\to$
-\end_inset
-
-9
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-F
-\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 $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
-\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
-^235
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-_
-\backslash
-phantom
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-23
-\begin_inset Formula $\to$
-\end_inset
-
-9
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-F
-\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 $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
-\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
-
-\backslash
-Lambda^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-phantom
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-ii
-\begin_inset Formula $\to$
-\end_inset
-
-t
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-_MMt
-\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 $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! V !
-\backslash
-vphantom
-\end_layout
-
-\end_inset
-
- (toolbar button
-\begin_inset space ~
-\end_inset
-
-
-\begin_inset Graphics
- filename ../images/math/vphantom.png
- scale 85
-
-\end_inset
-
-) and
-\series bold
-
-\backslash
-hphantom
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! H !
-\backslash
-hphantom
-\end_layout
-
-\end_inset
-
- (toolbar button
-\begin_inset space ~
-\end_inset
-
-
-\begin_inset Graphics
- filename ../images/math/hphantom.png
- scale 85
-
-\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
-\series default
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series bold
-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 "sub:Big-Operators"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
- because this is the larger character.
- An example application is in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Multiline-Brackets"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Lines
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! underlined
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="4" 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" 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
-\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" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-overline
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A+B
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! O !
-\backslash
-overline
-\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
-\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
-\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
-underline
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A+B
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! U !
-\backslash
-underline
-\end_layout
-
-\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 $\underline{A+B}\raisebox{-2.5mm}{}$
-\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
-
-\backslash
-overline
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-underline
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A+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 $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
-\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 first
-\series bold
-
-\backslash
-overline
-\series default
- or
-\series bold
-
-\backslash
-underline
-\series default
- is inserted.
-\end_layout
-
-\begin_layout Standard
-To double underline use
-\series bold
-
-\backslash
-underline
-\series default
- twice.
-\end_layout
-
-\begin_layout Standard
-It is possible to place up to 6 lines above or below characters.
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-rule
-\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"
-
-\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 "sub:Ellipses"
-
-\end_inset
-
-
-\begin_inset Index idx
-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 Graphics
- filename ../images/math/ldots.png
- scale 85
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- For listings dots at the baseline are used (
-\series bold
-
-\backslash
-ldots
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-ldots
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-cdots
-\end_layout
-
-\end_inset
-
-).
- When using the command
-\series bold
-
-\backslash
-dots
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-dots
-\end_layout
-
-\end_inset
-
-, 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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-A_1
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-,
-\backslash
-dots
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-,A_n
-\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 $A_{1},\dots,A_{n}$
-\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
-A_1
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-+
-\backslash
-dots
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-+A_n
-\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 $A_{1}+\dots+A_{n}$
-\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
-A_1
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-,
-\backslash
-ldots
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-,A_n
-\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 $A_{1},\ldots,A_{n}$
-\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_1
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-+
-\backslash
-cdots
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-+A_n
-\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 $A_{1}+\cdots+A_{n}$
-\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
-vdots
-\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 $\vdots$
-\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
-ddots
-\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 $\ddots$
-\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
-
-\backslash
-iddots
-\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 $\iddots$
-\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
-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" leftline="true" rightline="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
-, one of the options
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! H !
-\backslash
-hdotsfor
-\end_layout
-
-\end_inset
-
-, that has the following scheme:
-\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 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-dotfill
-\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 "sub:Variable-Space"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-For example the command
-\series bold
-A
-\backslash
-dotfill
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! H !
-\backslash
-hrulefill
-\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 TeX-mode.
-\end_layout
-
-\begin_layout Section
-Matrices
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Matrices"
-
-\end_inset
-
-
-\begin_inset Index idx
-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 Graphics
- filename ../images/dialog-show_mathmatrix.png
- scale 85
-
-\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 add or delete rows and columns subsequently, the math toolbar buttons
-
-\begin_inset Graphics
- filename ../images/tabular-feature_append-row.png
- scale 85
-
-\end_inset
-
-,
-\begin_inset Graphics
- filename ../images/tabular-feature_delete-row.png
- scale 85
-
-\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
-
-The
-\family sans
-Decoration
-\family default
- adds parentheses in the selected style around the matrix.
- Alternatively, parentheses can can either be created with the commands
-
-\series bold
-
-\backslash
-left
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-left
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-right
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-right
-\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 "sub:Automatic-Bracket-Size"
-
-\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 tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bmatrix
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
-0 & \textrm{-}\mathrm{i}\\
-\mathrm{i} & 0
-\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
-\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
-Bmatrix
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
-0 & \textrm{-}\mathrm{i}\\
-\mathrm{i} & 0
-\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
-\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
-
-\backslash
-pmatrix
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
-0 & \textrm{-}\mathrm{i}\\
-\mathrm{i} & 0
-\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
-\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 tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-vmatrix
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
-0 & \textrm{-}\mathrm{i}\\
-\mathrm{i} & 0
-\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
-\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
-
-\backslash
-Vmatrix
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
-0 & \textrm{-}\mathrm{i}\\
-\mathrm{i} & 0
-\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
-\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
-
-\backslash
-matrix
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
-0 & \textrm{-}\mathrm{i}\\
-\mathrm{i} & 0
-\end{array}\end{matrix}\raisebox{-5.3mm}{}$
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-arraycolsep
-\end_layout
-
-\end_inset
-
- that is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Column-Separation"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-arraystretch
-\end_layout
-
-\end_inset
-
- is used.
- It is used as follows:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-renewcommand{
-\backslash
-arraystretch}{stretch factor}
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-renewcommand
-\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
-.
- To double e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-the row separation, use the factor 2.
- This is then used for all following matrices.
- To go back to the original separation, assign the factor 1 to
-\series bold
-
-\backslash
-arraystretch
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-To set matrices into a text line, the command
-\series bold
-
-\backslash
-smallmatrix
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-smallmatrix
-\end_layout
-
-\end_inset
-
- is used.
- When it is inserted a blue box with two dashed lines appears.
- In this box the matrix is inserted.
-\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.
-\end_layout
-
-\begin_layout Section
-Brackets and Delimiters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Brackets
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Delimiters
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Vertical Brackets and Delimiters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Brackets ! vertical
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-(
-\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 $($
-\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
-{
-\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 $\{$
-\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
-[
-\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 $[$
-\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
-langle
-\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 $\langle$
-\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
-lceil
-\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 $\lceil$
-\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
-lfloor
-\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 $\lfloor$
-\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
-/
-\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 $/$
-\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
-|
-\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 $|$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-)
-\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 $)$
-\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
-}
-\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 $\}$
-\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
-]
-\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 $]$
-\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
-rangle
-\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 $\rangle$
-\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
-rceil
-\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 $\rceil$
-\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
-rfloor
-\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 $\rfloor$
-\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
-
-\backslash
-
-\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 $\backslash$
-\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
-
-\backslash
-|
-\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 $\|$
-\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 TeX-mode the command
-\series bold
-
-\backslash
-textbackslash
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-textbackslash
-\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 "sub:Manual-Bracket-Size"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Bracket size ! manual
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The bracket size can be specified manually by the LaTeX-commands
-\series bold
-
-\backslash
-big
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-big
-\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 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 $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<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
-
-
-\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
-
-\begin_layout Standard
-For the second formula the command
-\series bold
-
-\backslash
-Big((A+B)(A-B)
-\backslash
-Big)^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-C
-\series default
- has been used.
-\end_layout
-
-\begin_layout Standard
-Here is an overview about 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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-sin(x)
-\backslash
-Big]^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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
-Besides the
-\series bold
-
-\backslash
-big
-\series default
--commands there is the variant
-\series bold
-
-\backslash
-bigm
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-bigm
-\end_layout
-
-\end_inset
-
- that adds a bit more space between the bracket and its content, and the
- variant
-\series bold
-
-\backslash
-bigl
-\series default
--
-\series bold
-
-\backslash
-bigr
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-bigl -
-\backslash
-bigr
-\end_layout
-
-\end_inset
-
-, that 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 will be 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
-In the following table is a comparison of the variants:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="5" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="middle" width="0">
-<column alignment="center" valignment="middle" width="0">
-<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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Bigm(
-\backslash
-bigm(
-\backslash
-ln(3x)
-\backslash
-bigm)^2
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-
-\backslash
-Bigm)
-\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 $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
-\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
-Big(
-\backslash
-big(
-\backslash
-ln(3x)
-\backslash
-big)^2
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-
-\backslash
-Big)
-\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 $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
-\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
-
-\backslash
-Bigl(
-\backslash
-bigl(
-\backslash
-ln(3x)
-\backslash
-bigr)^2
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-
-\backslash
-Bigr)
-\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 $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
-\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
-
-\backslash
-bigl)
-\backslash
-ln(3x)
-\backslash
-bigr(
-\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 $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
-\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 "sub:Automatic-Bracket-Size"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Bracket size ! automatic
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Brackets with variable size can be inserted with the commands
-\series bold
-
-\backslash
-left
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-left
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-right
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-right
-\end_layout
-
-\end_inset
-
- or via the math toolbar button
-\begin_inset Graphics
- filename ../images/dialog-show_mathdelimiter.png
- scale 85
-
-\end_inset
-
-.
- Directly behind
-\series bold
-
-\backslash
-left
-\series default
- and
-\series bold
-
-\backslash
-right
-\series default
- the wanted bracket must be inserted.
- 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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\end_inset
-
-C
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\end_inset
-
-C
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\end_inset
-
-B
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 LyX to brackets in the right 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 LaTeX-Distributions use eTeX, an extension to LaTeX,
- the command
-\series bold
-
-\backslash
-middle
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-middle
-\end_layout
-
-\end_inset
-
- is additionally available for all brackets and limits.
- With this command the height of the following character is adapted to the
- one of the surrounding brackets, what is e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-needed for 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 LaTeX-package, described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Physical-Vectors"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Horizontal Brackets
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Brackets ! horizontal
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="4" 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" 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-raisebox{2.3mm}{
-\end_layout
-
-\end_inset
-
-
-\backslash
-overbrace
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A+B
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-3
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! O !
-\backslash
-overbrace
-\end_layout
-
-\end_inset
-
-
-\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 $\overbrace{A+B}^{3}$
-\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
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-raisebox{-2.2mm}{
-\end_layout
-
-\end_inset
-
-
-\backslash
-underbrace
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A+B
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-_5
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! U !
-\backslash
-underbrace
-\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
-\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" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-overbrace
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-underbrace
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A+B_w
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-_7
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-C
-\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 $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
-\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 at first.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-When brackets are needed that overlap each other, multiline formulas, as
- described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Multiline-Formulas"
-
-\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 hereby 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 "sub:Predefined-Space"
-
-\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 that the following
-\begin_inset Quotes eld
-\end_inset
-
-+
-\begin_inset Quotes erd
-\end_inset
-
- is surrounded by space.
-\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 "sub:Binary-Operators"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- In the second row the second brace is inserted.
- 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 "sub:Placeholders"
-
-\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 also surrounded by space 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, like 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 that there is space between the upper brace in the first row and
- the formula, the row spacing needs to be reduced.
- This is not easily possible due to a bug in LyX
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-\begin_inset CommandInset href
-LatexCommand href
-name "LyX-bug #1505"
-target "http://www.lyx.org/trac/ticket/1505"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! J !
-\backslash
-jot
-\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 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 "sub:Line-Separation"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Section
-Arrows
-\begin_inset Index idx
-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 Graphics
- filename ../images/math/leftarrow.png
- scale 85
-
-\end_inset
-
- or the commands listed in the following subsections.
-\end_layout
-
-\begin_layout Subsection
-Horizontal Arrows
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Arrows ! horizontal
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-gets
-\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 $\gets$
-\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
-Leftarrow
-\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 $\Leftarrow$
-\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
-
-\backslash
-longleftarrow
-\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 $\longleftarrow$
-\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
-Longleftarrow
-\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 $\Longleftarrow$
-\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
-leftharpoonup
-\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 $\leftharpoonup$
-\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
-leftharpoondown
-\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 $\leftharpoondown$
-\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
-hookleftarrow
-\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 $\hookleftarrow$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-to
-\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 $\to$
-\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
-Rightarrow
-\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 $\Rightarrow$
-\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
-longrightarrow
-\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 $\longrightarrow$
-\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
-Longrightarrow
-\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 $\Longrightarrow$
-\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
-rightharpoonup
-\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 $\rightharpoonup$
-\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
-
-\backslash
-rightharpoondown
-\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 $\rightharpoondown$
-\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
-hookrightarrow
-\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 $\hookrightarrow$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-leftrightarrow
-\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 $\leftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Leftrightarrow
-\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 $\Leftrightarrow$
-\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
-longleftrightarrow
-\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 $\longleftrightarrow$
-\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
-Longleftrightarrow
-\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 $\Longleftrightarrow$
-\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
-
-\backslash
-rightleftharpoons
-\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 $\rightleftharpoons$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-mapsto
-\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 $\mapsto$
-\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
-longmapsto
-\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 $\longmapsto$
-\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
-leadsto
-\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 $\leadsto$
-\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
-
-\backslash
-dasharrow
-\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 $\dasharrow$
-\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 like e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-vector arrows are listed in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Accents"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-Furthermore there are the labeled arrows
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Arrows ! labeled
-\end_layout
-
-\end_inset
-
-
-\series bold
-
-\backslash
-xleftarrow
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! X !
-\backslash
-xleftarrow
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-xrightarrow
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! X !
-\backslash
-xrightarrow
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-vspace{4mm}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-.
- When inserting one of these commands in a formula, an arrow with two blue
- boxes appear where the label 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 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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-F(a)
-\backslash
-xleftarrow
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
-\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
-F(x)
-\backslash
-xrightarrow
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Vertical and diagonal Arrows
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Arrows ! diagonal
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Arrows ! vertical
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-uparrow
-\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 $\uparrow$
-\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
-Uparrow
-\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 $\Uparrow$
-\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
-updownarrow
-\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 $\updownarrow$
-\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
-Updownarrow
-\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 $\Updownarrow$
-\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
-
-\backslash
-Downarrow
-\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 $\Downarrow$
-\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
-downarrow
-\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 $\downarrow$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-nearrow
-\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 $\nearrow$
-\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
-searrow
-\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 $\searrow$
-\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
-
-\backslash
-swarrow
-\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 $\swarrow$
-\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
-nwarrow
-\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 $\nwarrow$
-\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 be used also as delimiters together with the commands
- described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Manual-Bracket-Size"
-
-\end_inset
-
- and
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Automatic-Bracket-Size"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Section
-Accents
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Accents"
-
-\end_inset
-
-
-\begin_inset Index idx
-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 Graphics
- filename ../images/math/hat.png
- scale 85
-
-\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
-accents in text see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Accents-in-Text"
-
-\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 "sub:Formulas-in-Section"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Accents-for-one"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Accents ! for one character
-\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 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
-\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" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-dot
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\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 $\raisebox{5mm}{}\dot{A}$
-\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
-ddot
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\ddot{A}$
-\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
-dddot
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\dddot{A}$
-\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
-ddddot
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\ddddot{A}$
-\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
-vec
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Vectors
-\end_layout
-
-\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 $\raisebox{5mm}{}\vec{A}$
-\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
-bar
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\bar{A}$
-\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
-mathring
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\mathring{A}$
-\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 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" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-tilde
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\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 $\raisebox{5mm}{}\tilde{A}$
-\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
-hat
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\hat{A}$
-\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
-check
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\check{A}$
-\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
-acute
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\acute{A}$
-\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
-grave
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\grave{A}$
-\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
-breve
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\breve{A}$
-\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 like é to formulas.
- LyX will transform them to the corresponding accent command.
- For umlauts
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Umlauts
-\end_layout
-
-\end_inset
-
- it is better to insert a quotation mark before the vowel.
- These two characters are then treated by LaTeX as
-\emph on
-one
-\emph default
- character when the formula part with the umlaut is marked as German.
- In contrary 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 tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-
-\series bold
-
-\backslash
-raisebox
-\series default
- and the 0
-\begin_inset space \thinspace{}
-\end_inset
-
-pt space are only used as spacer.
-\end_layout
-
-\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
-
-\lang ngerman
-\begin_inset Quotes grd
-\end_inset
-
-i
-\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 space \hspace{}
-\length 0pt
-\end_inset
-
-
-\lang ngerman
-
-\begin_inset Formula $"i$
-\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
-
-\backslash
-ddot
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-i
-\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 $\raisebox{5mm}{}\ddot{i}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Another advantage to
-\series bold
-
-\backslash
-ddot
-\series default
- is that umlauts can directly be 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 also for all other conversions, e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-to italic or bold.
-\end_layout
-
-\begin_layout Standard
-In mathematical text, umlauts and other accented characters can directly
- be inserted.
-\end_layout
-
-\begin_layout Subsection
-Accents for several Characters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Accents ! for several characters
-\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 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
-\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" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-overleftarrow
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=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 $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
-\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
-underleftarrow
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
-\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
-overleftrightarrow
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
-\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
-underleftrightarrow
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
-\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 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" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-overrightarrow
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=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 $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
-\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
-underrightarrow
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
-\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
-widetilde
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
-\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
-widehat
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
-\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 these commands as many characters as you like can be accented.
- 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
-With the commands
-\series bold
-
-\backslash
-overset
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! O !
-\backslash
-overset
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-underset
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! U !
-\backslash
-underset
-\end_layout
-
-\end_inset
-
- described in the previous subsection it is also possible to accent several
- characters.
- The command
-\series bold
-
-\backslash
-underset
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Space
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Space"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Space ! horizontal
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Predefined Space
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Predefined-Space"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Space ! horizontal ! predefined
-\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 protected space (shortcut
-\begin_inset Info
-type "shortcut"
-arg "command-alternatives space-insert protected ; math-space"
-\end_inset
-
-).
- A
-\begin_inset Quotes eld
-\end_inset
-
-
-\color blue
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 Graphics
- filename ../images/math/space.png
- scale 85
-
-\end_inset
-
- or special commands.
- Independent from the inserted command, one can select the size again by
- pressing
-\family sans
-Space
-\family default
- afterwards.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset VSpace -5mm
-\end_inset
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="3" columns="7">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="middle" width="6.8cm">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<row>
-<cell alignment="center" valignment="top" topline="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" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-,
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-:
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-;
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-quad
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-qquad
-\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
-
-\backslash
-!
-\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
-Number of
-\family sans
-Space
-\family default
- keystrokes after inserting the protected space
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-1
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-2
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-3
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-4
-\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
-5
-\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
-Result
-\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
-\begin_inset Formula $A\, B$
-\end_inset
-
-
-\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
-\begin_inset Formula $A\: B$
-\end_inset
-
-
-\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
-\begin_inset Formula $A\; B$
-\end_inset
-
-
-\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
-\begin_inset Formula $A\quad B$
-\end_inset
-
-
-\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
-\begin_inset Formula $A\qquad B$
-\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
-\begin_inset Formula $A\! B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The last size seem to produce no space.
- It is displayed red in 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 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 protected space
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-6
-\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
-7
-\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 e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-useful for summation operators:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="3" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sum
-\backslash
-sum
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-f_kl
-\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 $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
-\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
-
-\backslash
-sum
-\backslash
-negmedspace
-\backslash
-sum
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-f_kl
-\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 $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Relations like for example equal signs, are always surrounded by space.
- To suppress this, the equal sign is placed into a 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
-\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
-
-
-\begin_inset Formula $\raisebox{5mm}{}$
-\end_inset
-
-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
-
-Spaces are needed for physical units, because the space between the value
- and the unit is the smallest one and not a normal space.
- For units in text, the smallest 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" width="0">
-<column alignment="left" valignment="top" width="0">
-<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
-smallest 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 "sub:Line-Separation"
-
-\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 "sub:Formulas-in-Section"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Variable-Space"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Space ! horizontal ! variable
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! H !
-\backslash
-hspace
-\end_layout
-
-\end_inset
-
-.
- Then a long
-\begin_inset Quotes eld
-\end_inset
-
-
-\color blue
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\color inherit
-
-\begin_inset Quotes erd
-\end_inset
-
- appears.
- The length can be specified by left-clicking on the
-\begin_inset Quotes eld
-\end_inset
-
-
-\color blue
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\color inherit
-
-\begin_inset Quotes erd
-\end_inset
-
-.
- The length may also be negative.
- To insert as much space as is available, the command
-\series bold
-
-\backslash
-hfill
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! H !
-\backslash
-hfill
-\end_layout
-
-\end_inset
-
- is used.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace -1mm
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="4" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-A=B
-\backslash
-hspace
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\begin_inset Formula $\to$
-\end_inset
-
-A
-\backslash
-not=C (3
-\begin_inset space \thinspace{}
-\end_inset
-
-cm)
-\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 $A=B\hspace{3cm}A\not=C$
-\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
-hspace
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\begin_inset Formula $\to$
-\end_inset
-
-A
-\backslash
-not=A (-1
-\begin_inset space \thinspace{}
-\end_inset
-
-mm)
-\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 $A\hspace{-1mm}A\not=A$
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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"
-
-\end_inset
-
-.)
-\end_layout
-
-\begin_layout Standard
-Besides
-\series bold
-
-\backslash
-hfill
-\series default
-, there are the 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 "sub:Ellipses"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Space ! besides inline formulas
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-mathsurround
-\end_layout
-
-\end_inset
-
-.
- The value of a length is set with the command
-\series bold
-
-\backslash
-setlength
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-setlength
-\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 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
-status collapsed
-
-\begin_layout Plain Layout
-Boxes
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Frames | see
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
-Boxes
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\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 "sub:Boxes-with-Frame"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Boxes ! with frame
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! F !
-\backslash
-fbox
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-boxed
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-boxed
-\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 mathemati
-cal 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 text.
-
-\series bold
-
-\backslash
-boxed
-\series default
- is in contrary 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! F !
-\backslash
-framebox
-\end_layout
-
-\end_inset
-
- where additionally 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,
-\emph on
-r
-\emph default
- right aligns the formula in the box.
- When no position is given, the formula will be centered.
-\begin_inset Newline newline
-\end_inset
-
-If no width is given, also no position can 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
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="5" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-fbox
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\family sans
-Ctrl+M
-\family default
-
-\backslash
-int
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=B
-\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 $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
-\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
-boxed
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-int
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=B
-\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 $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
-\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
-A+
-\backslash
-fbox
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-B
-\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 $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
-\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
-
-\backslash
-framebox
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset Formula $\downarrow$
-\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 $\raisebox{6mm}{}$
-\end_inset
-
-
-\begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
-\end_inset
-
-
-\begin_inset Formula $\raisebox{-4mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The frame thickness can also be adjusted.
- To do this the following commands have to be inserted in 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 minimal distance between the frame and the first character
- in the box.
- An example for this is the following framed formula:
-\begin_inset ERT
-status collapsed
-
-\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 TeX-mode.
- The given values are 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 collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-fboxrule 0.4pt
-\backslash
-fboxsep 3pt
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-is inserted in TeX-mode before the next formula.
-\end_layout
-
-\begin_layout Subsection
-Boxes without Frame
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Boxes-without-Frame"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Boxes ! without frame
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-For boxes without a frame there are the following box commands:
-\series bold
-
-\backslash
-mbox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-mbox
-\end_layout
-
-\end_inset
-
-,
-\series bold
-
-\backslash
-makebox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-makebox
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-raisebox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-raisebox
-\end_layout
-
-\end_inset
-
-
-\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 should contain a formula, an extra formula is needed like for
-
-\series bold
-
-\backslash
-fbox
-\series default
-.
-
-\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 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 tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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" topline="true" 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" topline="true" 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
-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" topline="true" bottomline="true" 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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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
-, with the difference that there is no frame.
-\end_layout
-
-\begin_layout Subsection
-Colored Boxes
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Colored-Boxes"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Boxes ! colored
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To be able to use all commands explained in this section, the LaTeX-package
-
-\series bold
-color
-\series default
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-The LaTeX-package
-\series bold
-color
-\series default
- is part of every LaTeX standard installation.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! color
-\end_layout
-
-\end_inset
-
- has to be loaded in the 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,
- LyX loads the 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 LaTeX-pre
-amble.
-\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 color boxes, the command
-\series bold
-
-\backslash
-colorbox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-colorbox
-\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
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="4" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\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" topline="true" 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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
-\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
-colorbox{green
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-{
-\backslash
-fbox
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=B
-\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 $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
-\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
-
-\backslash
-fbox
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-C=D
-\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 $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-colorbox
-\series default
- only colors the box but 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 Graphics
- filename ../images/dialog-show_character.png
- scale 85
-
-\end_inset
-
- or the menu
-\family sans
-Edit\SpecialChar \menuseparator
-Text
-\begin_inset space ~
-\end_inset
-
-Style\SpecialChar \menuseparator
-Customized
-\family default
-.
- The formula number then has the same color as the formula.
- When the formula number should get another color than the formula characters,
- 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"
-
-\end_inset
-
- is completely colored red.
-\begin_inset Newline newline
-\end_inset
-
-Formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:redgreen"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! F !
-\backslash
-fcolorbox
-\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 other colors than the predefined ones, they have to 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 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-definecolor
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-cmyk
-\series default
- is the color space that denotes 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 factor 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
- also the color space
-\series bold
-rgb
-\series default
- can 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 that there are in this case 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 example a framed box with the new 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
-status collapsed
-
-\begin_layout Plain Layout
-Text ! colored
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-textcolor
-\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 "sub:Paragraph-Boxes"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Boxes ! as paragraph
-\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 Graphics
- filename ../images/box-insert.png
- scale 85
-
-\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"
-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 LaTeX a parbox is created with the command
-\series bold
-
-\backslash
-parbox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! P !
-\backslash
-parbox
-\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 TeX-mode before the formula.
-
-\series bold
-
-\backslash
-linewidth
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-linewidth
-\end_layout
-
-\end_inset
-
- is hereby the line width set for the document.
- Because the frame is outside the parbox, 2
-\begin_inset space \thinspace{}
-\end_inset
-
-times the frame separation and the frame thickness must be subtracted from
- the line width.
- As this is not automatically done by LyX due to a bug
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-\begin_inset CommandInset href
-LatexCommand href
-name "LyX-bug #4483"
-target "http://www.lyx.org/trac/ticket/4483"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-, TeX-mode has to be used.
- To be able to multiply and subtract in arguments, the 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 LaTeX standard installation.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! calc
-\end_layout
-
-\end_inset
-
- must be loaded in the 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 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 "sub:User-defined-Numbering"
-
-\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 TeX-mode because 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 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"
-
-\end_inset
-
-)
-\end_layout
-
-\end_inset
-
- Then the description follows as normal text and finally
-\series bold
-}}
-\backslash
-]
-\series default
- is inserted in TeX-mode.
- The commands
-\series bold
-
-\backslash
-[
-\series default
- and
-\series bold
-
-\backslash
-]
-\series default
- hereby 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
-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 "sub:Big-Operators"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Operators ! big
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Sums
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Integrals
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To be able to use all integral operators listed here, the option
-\family sans
-Use esint package automatically
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-int
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! I !
-\backslash
-int
-\end_layout
-
-\end_inset
-
-
-\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 $\int$
-\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
-oint
-\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 $\oint$
-\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
-ointctrclockwise
-\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 $\ointctrclockwise$
-\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
-ointclockwise
-\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 $\ointclockwise$
-\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
-sqint
-\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 $\sqint$
-\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
-fint
-\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 $\fint$
-\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
-landupint
-\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 $\landupint$
-\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
-landdownint
-\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 $\landdownint$
-\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
-bigcap
-\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 $\bigcap$
-\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
-
-\backslash
-bigcup
-\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 $\bigcup$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sum
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-sum
-\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
-\begin_inset Formula $\sum$
-\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
-prod
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! P !
-\backslash
-prod
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-vspace{4mm}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\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 $\prod$
-\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
-coprod
-\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 $\coprod$
-\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
-bigodot
-\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 $\bigodot$
-\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
-bigotimes
-\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 $\bigotimes$
-\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
-bigoplus
-\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 $\bigoplus$
-\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
-bigwedge
-\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 $\bigwedge$
-\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
-bigvee
-\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 $\bigvee$
-\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
-bigsqcup
-\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 $\bigsqcup$
-\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
-
-\backslash
-biguplus
-\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 $\biguplus$
-\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 Graphics
- filename ../images/math/intop.png
- scale 85
-
-\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 are different from
-\series bold
-
-\backslash
-int
-\series default
- etc.
-\begin_inset space \space{}
-\end_inset
-
-in the style the operator limits are displayed, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Operator-Limits"
-
-\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 therefore 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 "sub:Font-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-.
- Finally 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
-For multiple integrals there are 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 tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-iint
-\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 $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
-\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
-oiint
-\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 $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
-\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
-
-\backslash
-sqiint
-\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 $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
-\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 tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-iiint
-\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 $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
-\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
-iiiint
-\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 $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
-\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
-
-\backslash
-dotsint
-\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 $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Operator Limits
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Operator-Limits"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Operators ! Limits
-\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 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
-\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" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-prod^
-\backslash
-infty
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Limits of inline formulas are set right beside the operator.
- Limits in displayed formulas are set above or below the operator, except
- for integral limits.
-\end_layout
-
-\begin_layout Standard
-To force that the limits are set beside the operator, the cursor is set
- 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 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 was 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 are by default set beside the operator.
- But for multiple integrals the limits are often set below the operator.
- In the following example the limits type was therefore 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-subarray
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-substack
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-substack
-\end_layout
-
-\end_inset
-
- are used.
- To create for example 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 has to be done:
-\begin_inset Newline newline
-\end_inset
-
-First the command
-\series bold
-
-\backslash
-sum
-\series default
-^
-\series bold
-n
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-_
-\series default
- is typed in.
- One is now in a blue box under the summation operator and insert there
- the command
-\series bold
-
-\backslash
-subarray
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-.
- The blue box is now within a purple box and now several lines can be written
- among each other.
- A new line is created by inserting a line break (
-\begin_inset Info
-type "shortcut"
-arg "newline-insert newline"
-\end_inset
-
-).
- When now
-\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 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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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
-
-Like in formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:substack"
-
-\end_inset
-
- there can be too much space beside an operator, because the characters
- following the operator are set beside the limits.
-\end_layout
-
-\begin_layout Standard
-To avoid this, the following macro can be used in the LaTeX-preamble:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-def
-\backslash
-clap#1{
-\backslash
-hbox to 0pt{
-\backslash
-hss #1
-\backslash
-hss}}
-\begin_inset Newline newline
-\end_inset
-
-
-\backslash
-def
-\backslash
-mathclap {
-\backslash
-mathpalette
-\backslash
-mathclapinternal}
-\begin_inset Newline newline
-\end_inset
-
-
-\backslash
-def
-\backslash
-mathclapinternal #1#2{
-\backslash
-clap{$
-\backslash
-mathsurround =0pt #1{#2}$}}
-\end_layout
-
-\begin_layout Standard
-This defines the command
-\series bold
-
-\backslash
-mathclap
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-mathclap
-\end_layout
-
-\end_inset
-
- that sets the width of the limit to 0
-\begin_inset space \thinspace{}
-\end_inset
-
-pt.
- The command scheme is
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-mathclap{limit}
-\end_layout
-
-\begin_layout Standard
-where the limit can consist of several conditions.
-\end_layout
-
-\begin_layout Standard
-Applied on formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:substack"
-
-\end_inset
-
-, one uses the command
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-sum_
-\backslash
-mathclap{
-\backslash
-substack
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-0<k<1000 Ctrl+Return
-\end_layout
-
-\begin_layout Standard
-to create the lower limit.
- The summand is now directly behind the summation operator:
-\begin_inset Formula
-\[
-\sum_{\mathclap{\substack{0<k<1000\\
-\\
-k\,\in\,\mathbb{N}
-}
-}}^{n}k^{-2}
-\]
-
-\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 "sub:Self-defined-Operators"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Decoration for Operators
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Operators ! Decoration
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-With the commands
-\series bold
-
-\backslash
-overset
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! O !
-\backslash
-overset
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-underset
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! U !
-\backslash
-underset
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-sideset
-\end_layout
-
-\end_inset
-
- characters can be set before and behind a big operator.
- The command scheme is:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-sideset{character
-\series default
-
-\series bold
-before}{character
-\series default
-
-\series bold
-behind}
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-sideset
-\series default
- must always be before the operator.
- You can decorate with several characters and even with other operators
- and symbols.
- To place for example only characters behind a big operator, write nothing
- between the first braces but don't omit the braces.
-\end_layout
-
-\begin_layout Standard
-For example the command
-\series bold
-
-\backslash
-sideset{
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-{
-\series default
-'
-\series bold
-
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-sum_k=1
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-maltese
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 "sub:Binary-Operators"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Operators ! binary
-\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 space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="13" 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" 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-+
-\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 $+$
-\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
--
-\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 $-$
-\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
-pm
-\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 $\pm$
-\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
-mp
-\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 $\mp$
-\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
-cdot
-\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 $\cdot$
-\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
-times
-\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 $\times$
-\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
-div
-\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 $\div$
-\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
-\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" topline="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>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-star
-\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 $\star$
-\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
-circ
-\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 $\circ$
-\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
-diamond
-\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 $\diamond$
-\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
-
-\backslash
-bullet
-\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 $\bullet$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-nabla
-\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 $\nabla$
-\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
-bigtriangledown
-\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 $\bigtriangledown$
-\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
-bigtriangleup
-\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 $\bigtriangleup$
-\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
-Box
-\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 $\Box$
-\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
-cap
-\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 $\cap$
-\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
-cup
-\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 $\cup$
-\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
-dagger
-\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 $\dagger$
-\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
-ddagger
-\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 $\ddagger$
-\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
-wr
-\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 $\wr$
-\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
-bigcirc
-\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 $\bigcirc$
-\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
-wedge
-\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 $\wedge$
-\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
-
-\backslash
-vee
-\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 $\vee$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-oplus
-\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 $\oplus$
-\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
-ominus
-\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 $\ominus$
-\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
-otimes
-\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 $\otimes$
-\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
-oslash
-\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 $\oslash$
-\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
-odot
-\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 $\odot$
-\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
-amalg
-\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 $\amalg$
-\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
-uplus
-\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 $\uplus$
-\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
-setminus
-\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 $\setminus$
-\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
-sqcap
-\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 $\sqcap$
-\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
-sqcup
-\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 $\sqcup$
-\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
-triangleleft
-\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 $\triangleleft$
-\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
-
-\backslash
-triangleright
-\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 $\triangleright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-All binary operators can also be inserted via the math toolbar button
-\begin_inset Graphics
- filename ../images/math/pm.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-To typeset the Laplace operator also
-\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 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 "sub:Self-defined-Operators"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Operators ! self-defined
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-dbinom@
-\backslash
-DeclareMathOperator
-\end_layout
-
-\end_inset
-
- custom operators can be defined in the 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 "sub:Operator-Limits"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-For example the 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 lozenge symbol from
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Miscellaneous-Symbols"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-mathop
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-mathbin
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-mathbin
-\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 e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series bold
-
-\begin_inset Formula $\to$
-\end_inset
-
-^N
-\series default
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series bold
-_i,j=1
-\end_layout
-
-\begin_layout Section
-Fonts
-\begin_inset Index idx
-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 "sub:Font-Styles"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Font ! style
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Latin letters in formulas can be set in one of the following font styles:
-\begin_inset VSpace -2mm
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="7" columns="3">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-Result
-\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
-shortcut
-\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
-mathbb
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-ABC
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-noun"
-\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
-mathbf
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-AbC
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-bold"
-\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
-boldsymbol
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-AbC
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-boldsymbol"
-\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
-mathcal
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-ABC
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-emph"
-\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
-mathfrak
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-AbC
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
--
-\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
-
-\backslash
-mathscr
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-AbC
-\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
-\begin_inset Formula $\mathscr{AbC}$
-\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
--
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="5" columns="3">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-Result
-\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
-shortcut
-\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
-mathit
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-AbC
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
--
-\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
-mathrm
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-AbC
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-roman"
-\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
-mathsf
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-AbC
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="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" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-sans"
-\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
-
-\backslash
-mathtt
-\series bold
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-AbC
-\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
-\begin_inset Formula $\mathtt{AbC}$
-\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
-\begin_inset Info
-type "shortcuts"
-arg "font-typewriter"
-\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
- The styles
-\series bold
-
-\backslash
-mathbb
-\series default
- and
-\series bold
-
-\backslash
-mathcal
-\series default
- can only be used for big letters.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Predefined is the style
-\series bold
-
-\backslash
-mathnormal
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-The style commands work also 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
-.
- That their style can't be set correctly via the text style dialog is a
- bug in LyX.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-\begin_inset CommandInset href
-LatexCommand href
-name "LyX-bug #4629"
-target "http://www.lyx.org/trac/ticket/4629"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Instead of the style commands the dialog
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Text Style
-\family default
- or the toolbar button
-\begin_inset Graphics
- filename ../images/math/font.png
- scale 85
-
-\end_inset
-
- can be used.
-\end_layout
-
-\begin_layout Subsection
-Bold Formulas
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Bold-Formulas"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! bold
-\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.
- Furthermore it prints Latin letters always upright, like 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-boldmath
-\end_layout
-
-\end_inset
-
- in TeX-mode.
- To end the environment, the command
-\series bold
-
-\backslash
-unboldmath
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! U !
-\backslash
-unboldmath
-\end_layout
-
-\end_inset
-
- is inserted in 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
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! colored
-\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 "sub:Colored-Boxes"
-
-\end_inset
-
-.
- They can be used with the TeX code command
-\series bold
-
-\backslash
-textcolor
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-textcolor
-\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 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 "http://www.lyx.org/trac/ticket/5269"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Font Sizes
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Font-Sizes"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Font ! size
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-For characters in formulas there are, analog to characters in text, the
- following size commands:
-\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 size produced by the commands depends on the document font size, which
- corresponds to the command
-\series bold
-
-\backslash
-normalsize
-\series default
-.
- The other commands produce smaller or larger sizes than
-\series bold
-
-\backslash
-normalsize
-\series default
-.
- The font size can however not exceed a certain value.
- Is for example the document font size 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 TeX-mode before the formula and sets the size
- for all following formula and text characters.
- To switch back to the initial size, the command
-\series bold
-
-\backslash
-normalsize
-\series default
- is inserted behind the formula in TeX-mode.
-\end_layout
-
-\begin_layout Standard
-Within a formula the size can be changed using the following size commands:
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="5" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-displaystyle
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-displaystyle
-\end_layout
-
-\end_inset
-
-
-\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 $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
-\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
-textstyle
-\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 $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
-\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
-scriptstyle
-\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 $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
-\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
-
-\backslash
-scriptscriptstyle
-\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 $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
-\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 a further method to change the font size, that though only works
- for symbols or letters in mathematical text.
- To use it, one of the above text size commands is inserted in mathematical
- text.
- All following 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
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-Before both formulas 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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A Alt+M M
-\backslash
-Large
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-maltese
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-textit
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-maltese
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-textit
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Greek letters
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Greek letters can also be inserted via the toolbar button
-\begin_inset Graphics
- filename ../images/math/alpha.png
- scale 85
-
-\end_inset
-
-.
- 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
-status collapsed
-
-\begin_layout Plain Layout
-Greek letters ! small
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-alpha
-\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 $\alpha$
-\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
-beta
-\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 $\beta$
-\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
-gamma
-\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 $\gamma$
-\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
-delta
-\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 $\delta$
-\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
-epsilon
-\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 $\epsilon$
-\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
-varepsilon
-\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 $\varepsilon$
-\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
-zeta
-\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 $\zeta$
-\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
-eta
-\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 $\eta$
-\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
-theta
-\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 $\theta$
-\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
-
-\backslash
-vartheta
-\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 $\vartheta$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-iota
-\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 $\iota$
-\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
-kappa
-\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 $\kappa$
-\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
-varkappa
-\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 $\varkappa$
-\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
-lambda
-\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 $\lambda$
-\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
-mu
-\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 $\mu$
-\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
-nu
-\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 $\nu$
-\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
-xi
-\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 $\xi$
-\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
-o
-\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 $o$
-\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
-pi
-\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 $\pi$
-\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
-varpi
-\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 $\varpi$
-\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
-
-\backslash
-rho
-\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 $\rho$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varrho
-\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 $\varrho$
-\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
-sigma
-\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 $\sigma$
-\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
-varsigma
-\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 $\varsigma$
-\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
-tau
-\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 $\tau$
-\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
-upsilon
-\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 $\upsilon$
-\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
-phi
-\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 $\phi$
-\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
-varphi
-\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 $\varphi$
-\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
-chi
-\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 $\chi$
-\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
-psi
-\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 $\psi$
-\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
-
-\backslash
-omega
-\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 $\omega$
-\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
-How to create special upright Greek letters is explained in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Upright-small-Greek"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Big Letters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Greek letters ! big
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Gamma
-\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 $\Gamma$
-\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
-Delta
-\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 $\Delta$
-\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
-Theta
-\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 $\Theta$
-\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
-Lambda
-\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 $\Lambda$
-\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
-Xi
-\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 $\Xi$
-\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
-
-\backslash
-Pi
-\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 $\Pi$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Sigma
-\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 $\Sigma$
-\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
-Upsilon
-\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 $\Upsilon$
-\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
-Phi
-\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 $\Phi$
-\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
-Psi
-\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 $\Psi$
-\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
-
-\backslash
-Omega
-\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 $\Omega$
-\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
-
-That the big Greek letters appear upright is caused by a design bug when
- TeX was developed.
- To get 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 LaTeX-package
-\series bold
-was
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! was
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-vspace{4mm}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! fixmath
-\end_layout
-
-\end_inset
-
- with the 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
-status collapsed
-
-\begin_layout Plain Layout
-Greek letters ! bold
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-boldsymbol
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="3" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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" topline="true" 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" topline="true" 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" topline="true" 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" topline="true" 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 LaTeX-packages can be found in
-\begin_inset CommandInset citation
-LatexCommand cite
-key "Symbols"
-
-\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 "sub:Formulas-in-Section"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-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 Graphics
- filename ../images/math/nabla.png
- scale 85
-
-\end_inset
-
- and
-\begin_inset Graphics
- filename ../images/math/digamma.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Mathematical Symbols
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Mathematical-Symbols"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Symbols ! mathematical
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="10" 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" 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-neg
-\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 $\neg$
-\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
-Im
-\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 $\Im$
-\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
-Re
-\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 $\Re$
-\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
-aleph
-\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 $\aleph$
-\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
-partial
-\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 $\partial$
-\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
-infty
-\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 $\infty$
-\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
-
-\backslash
-wp
-\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 $\wp$
-\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
-imath
-\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 $\imath$
-\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 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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-forall
-\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 $\forall$
-\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
-exists
-\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 $\exists$
-\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
-nexists
-\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 $\nexists$
-\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
-emptyset
-\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 $\emptyset$
-\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
-varnothing
-\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 $\varnothing$
-\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
-dag
-\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 $\dag$
-\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
-
-\backslash
-ddag
-\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 $\ddag$
-\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
-complement
-\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
-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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-prime
-\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 $\prime$
-\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
-backprime
-\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 $\backprime$
-\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
-mho
-\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 $\mho$
-\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
-triangle
-\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 $\triangle$
-\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
-angle
-\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 $\angle$
-\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
-measuredangle
-\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 $\measuredangle$
-\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
-
-\backslash
-sphericalangle
-\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 $\sphericalangle$
-\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
-top
-\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 $\top$
-\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
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Miscellaneous Symbols
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Miscellaneous-Symbols"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Symbols ! miscellaneous
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="10" 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" 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-flat
-\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 $\flat$
-\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
-natural
-\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 $\natural$
-\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
-sharp
-\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 $\sharp$
-\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
-
-\backslash
-surd
-\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 $\surd$
-\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
-checkmark
-\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 $\checkmark$
-\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
-yen
-\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 $\yen$
-\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
-pounds
-\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 $\pounds$
-\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
-$
-\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>
-<row>
-<cell alignment="center" valignment="top" bottomline="true" leftline="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 Tabular
-<lyxtabular version="3" rows="10" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-hbar
-\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 $\hbar$
-\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
-hslash
-\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 $\hslash$
-\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
-clubsuit
-\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 $\clubsuit$
-\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
-spadesuit
-\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 $\spadesuit$
-\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
-bigstar
-\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 $\bigstar$
-\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
-blacklozenge
-\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 $\blacklozenge$
-\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
-blacktriangle
-\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 $\blacktriangle$
-\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
-blacktiangledown
-\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 $\blacktriangledown$
-\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
-
-\backslash
-bullet
-\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 $\bullet$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="10" 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" 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-diamondsuit
-\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 $\diamondsuit$
-\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
-Diamond
-\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 $\Diamond$
-\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
-heartsuit
-\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 $\heartsuit$
-\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
-
-\backslash
-P
-\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 $\P$
-\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
-copyright
-\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 $\copyright$
-\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
-circledR
-\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 $\circledR$
-\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
-maltese
-\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 $\maltese$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
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-\begin_inset Text
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-
-\backslash
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-
-\end_inset
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-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\diagup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-\begin_layout Plain Layout
-
-\backslash
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-
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\diagdown$
-\end_inset
-
-
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-
-\end_inset
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-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-More symbols are listed in
-\begin_inset CommandInset ref
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-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-Some symbols can be displayed in different sizes, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Font-Sizes"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-The Euro-Symbol €
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Symbols ! Euro-symbol
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-
-\backslash
-@
-\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 LaTeX-package
-\series bold
-eurosym
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! eurosym
-\end_layout
-
-\end_inset
-
- must be installed and loaded with the 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! E !
-\backslash
-euro
-\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 TeX-mode.
- The official currency symbol can then be inserted with the command
-\series bold
-
-\backslash
-officialeuro
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! O !
-\backslash
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-\end_layout
-
-\end_inset
-
-, that is only available in TeX-mode.
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-ifeurosym
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-
-\end_inset
-
-
-\begin_inset Note Note
-status open
-
-\begin_layout Plain Layout
-The following table will only be displayed when the 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
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-<lyxtabular version="3" rows="4" columns="3">
-<features tabularvalignment="middle">
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-
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-
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-\begin_inset Text
-
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-Command
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-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
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-
-\end_inset
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-
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-
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
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-
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\euro$
-\end_inset
-
-
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-
-\end_inset
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-
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-
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-€
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-
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mbox{€}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-
-\end_inset
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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
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
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-
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
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-
-\end_inset
-
-
-\begin_inset Note Note
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-
-\begin_layout Plain Layout
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-\series bold
-eurosym
-\series default
- is not installed:
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-You need to install the 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
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-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
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-Relations
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
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-
-\begin_layout Plain Layout
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-
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-
-{
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-
-\end_inset
-
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-\begin_inset ERT
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-
-\begin_layout Plain Layout
-
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-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-All relations can also be inserted via the toolbar button
-\begin_inset Graphics
- filename ../images/math/leq.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
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-\begin_inset Text
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-
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-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
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-<row>
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-\begin_inset Text
-
-\begin_layout Plain Layout
-<
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-
-\end_inset
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $<$
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-
-
-\end_layout
-
-\end_inset
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-\begin_inset Text
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-
-\backslash
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-
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-\begin_inset Text
-
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-\begin_inset Formula $\le$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
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-
-\backslash
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-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\ll$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-<row>
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-\begin_inset Text
-
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-
-\backslash
-prec
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-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\prec$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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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
-\begin_inset Formula $\preceq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
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-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\subset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-subseteq
-\end_layout
-
-\end_inset
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\subseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-<row>
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
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-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\sqsubseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-in
-\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 $\in$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-vdash
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-
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\vdash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-smile
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\smile$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-<row>
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-lhd
-\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 $\lhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-<row>
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-unlhd
-\end_layout
-
-\end_inset
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\unlhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-<row>
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-gtrless
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\gtrless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-mid
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-nmid
-\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 $\nmid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
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-<features tabularvalignment="middle">
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-\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
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-<row>
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-\begin_inset Text
-
-\begin_layout Plain Layout
-=
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-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $=$
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-
-
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-not=
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-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\not=$
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-
-
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-equiv
-\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 $\equiv$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-<row>
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sim
-\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 $\sim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-simeq
-\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 $\simeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-approx
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\approx$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-cong
-\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 $\cong$
-\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
-bowtie
-\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 $\bowtie$
-\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
-notin
-\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 $\notin$
-\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
-perp
-\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 $\perp$
-\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
-propto
-\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 $\propto$
-\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
-asymp
-\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 $\asymp$
-\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
-doteq
-\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 $\doteq$
-\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
-circeq
-\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 $\circeq$
-\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
-models
-\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 $\models$
-\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
-
-\backslash
-widehat=
-\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 $\widehat{=}$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
->
-\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 $>$
-\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
-ge
-\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 $\ge$
-\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
-gg
-\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 $\gg$
-\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
-succ
-\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 $\succ$
-\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
-succeq
-\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 $\succeq$
-\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
-supset
-\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 $\supset$
-\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
-supseteq
-\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 $\supseteq$
-\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
-sqsupseteq
-\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 $\sqsupseteq$
-\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
-ni
-\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 $\ni$
-\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
-dashv
-\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 $\dashv$
-\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
-frown
-\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 $\frown$
-\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
-rhd
-\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 $\rhd$
-\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
-unrhd
-\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 $\unrhd$
-\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
-lessgtr
-\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 $\lessgtr$
-\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
-parallel
-\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 $\parallel$
-\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
-
-\backslash
-nparallel
-\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 $\nparallel$
-\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 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
-Relations are, in contrary to symbols, 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-stackrel
-\end_layout
-
-\end_inset
-
-:
-\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="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\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" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-A(r)
-\backslash
-stackrel
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-r
-\backslash
-to
-\backslash
-infty
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\begin_inset Formula $\downarrow$
-\end_inset
-
-
-\backslash
-approx
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
-\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 "sub:Predefined-Functions"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Functions ! predefined
-\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
-
-.
- Therefore there are predefined functionswhich are additionally a bit separated
- from prefactors.
- 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="4">
-<features 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" 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" 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" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Asin(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 $Asin(x)+B$
-\end_inset
-
-
-\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
-A
-\backslash
-sin(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 $A\sin(x)+B$
-\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 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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sin
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sinh
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-arcsin
-\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
-
-\backslash
-sup
-\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
-cos
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-cosh
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-arccos
-\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
-
-\backslash
-inf
-\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
-tan
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-tanh
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-arctan
-\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
-
-\backslash
-lim
-\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
-cot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-coth
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-arg
-\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
-
-\backslash
-liminf
-\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
-sec
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-min
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-deg
-\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
-
-\backslash
-limsup
-\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
-csc
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-max
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-det
-\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
-
-\backslash
-Pr
-\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
-ln
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-exp
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-dim
-\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
-
-\backslash
-hom
-\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
-
-\backslash
-lg
-\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
-log
-\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
-ker
-\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
-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 Graphics
- filename ../images/math/functions.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Self-defined Functions
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Functions ! self-defined
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To use a function that is not predefined, like for example the sign function
- sgn(x), there are two possibilities:
-\end_layout
-
-\begin_layout Itemize
-Define the function by inserting the following line to the 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 "sub:Self-defined-Operators"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-dbinom@
-\backslash
-DeclareMathOperator
-\end_layout
-
-\end_inset
-
-
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset VSpace -2mm
-\end_inset
-
-
-\begin_inset Newline newline
-\end_inset
-
-Now the new 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, a space is inserted between 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 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 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" topline="true" bottomline="true" 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" topline="true" bottomline="true" 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 should
- be used several times.
-\end_layout
-
-\begin_layout Subsection
-Limits
-\begin_inset Index idx
-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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-lim
-\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 tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varliminf
-\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 $\varliminf$
-\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
-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>
-<cell alignment="center" valignment="top" leftline="true" 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>
-<cell alignment="center" valignment="top" bottomline="true" leftline="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
-
-
-\begin_inset Formula $\raisebox{-2.5mm}{}$
-\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 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
-Command
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset space \hspace{}
-\length 1cm
-\end_inset
-
-Result
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-The space and
-\series bold
-
-\backslash
-raisebox
-\series default
- are used here as spacer.
-\end_layout
-
-\end_inset
-
-
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
-\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 Subsection
-Modulo-Functions
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Functions ! modulo-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The modulo-function is special, because it exists in four variants.
- The variants in a displayed formula are:
-\begin_inset Formula
-\begin{align*}
-\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
-\mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
-\mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
-\mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
-\mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
-\end{align*}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In an inline formula less space is set before the function names for all
- variants.
- By default the modulo-functions take only the first following character
- into account.
- To use more than one character, one has to put them into TeX-braces:
-\begin_inset Formula
-\begin{align*}
-\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
-\mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
-\mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
-\end{align*}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Special Characters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Special characters
-\end_layout
-
-\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 TeX-mode:
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="8" columns="2">
-<features tabularvalignment="middle">
-<column alignment="block" valignment="top" width="0">
-<column alignment="block" valignment="top" width="0">
-<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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-oe
-\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 $\textrm{œ}$
-\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
-OE
-\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 $\textrm{Œ}$
-\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
-ae
-\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 $\textrm{æ}$
-\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
-AE
-\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 $\textrm{Æ}$
-\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
-aa
-\end_layout
-
-\end_inset
-</cell>
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{\aa}$
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-
-
-\end_layout
-
-\end_inset
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-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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-
-\begin_layout Plain Layout
-
-\backslash
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-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-
-\backslash
-@
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-textrm{
-\backslash
-AA}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
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-
-
-\end_layout
-
-\end_inset
-</cell>
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-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-i
-\end_layout
-
-\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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-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
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-\begin_layout Plain Layout
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-\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
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-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
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-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-o
-\end_layout
-
-\end_inset
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{ø}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-O
-\end_layout
-
-\end_inset
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-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{Ø}$
-\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
-l
-\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 $\textrm{ł}$
-\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
-L
-\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 $\textrm{Ł}$
-\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
-!
-\begin_inset space \hspace{}
-\length 0mm
-\end_inset
-
-`
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\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
-\begin_inset Formula $\textrm{!`}$
-\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
-?
-\begin_inset space \hspace{}
-\length 0mm
-\end_inset
-
-`
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\textrm{?`}$
-\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
-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 $\textrm{\textrm{Å}}$
-\end_inset
-
- and
-\begin_inset Formula $\textrm{\textrm{Ø}}$
-\end_inset
-
- can also be inserted via the math toolbar button
-\begin_inset Graphics
- filename ../images/math/digamma.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-An exception are 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
-, because they can be inserted in LyX directly to text.
-\end_layout
-
-\begin_layout Subsection
-Accents in Text
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Accents-in-Text"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Accents ! in text
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-With the following commands all letters can be accented.
- The commands must be inserted in TeX-mode.
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="8" columns="2">
-<features tabularvalignment="middle">
-<column alignment="block" valignment="top" width="0">
-<column alignment="block" valignment="top" width="0">
-<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" topline="true" 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" topline="true" 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="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-`e
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-`e
-\end_layout
-
-\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
-^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-e
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-^e
-\end_layout
-
-\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
-=e
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-=e
-\end_layout
-
-\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
-u
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-e
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-u e
-\end_layout
-
-\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
-
-\backslash
-b
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-e
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-b e
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
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-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-t
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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>
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-</lyxtabular>
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="8" columns="2">
-<features tabularvalignment="middle">
-<column alignment="block" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-H
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-e
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-H e
-\end_layout
-
-\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
-'e
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-'e
-\end_layout
-
-\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
-~e
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Tilde
-\end_layout
-
-\end_inset
-
-
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-~e
-\end_layout
-
-\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
-.e
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-.e
-\end_layout
-
-\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
-
-\backslash
-v
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-e
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-v e
-\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
-d
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-e
-\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
-d e
-\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
-c
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-e
-\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
-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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 directly be inserted with the keyboard without
- using 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 to be used in formulas,
- see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Accents-for-one"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-Furthermore, with the command
-\series bold
-
-\backslash
-textcircled
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-textcircled
-\end_layout
-
-\end_inset
-
- all numbers and letters 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 tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\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" topline="true" 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" topline="true" 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>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="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" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}$
-\end_inset
-
-
-\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
-
-
-\begin_inset Formula $\raisebox{-2mm}{}$
-\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 in 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 "sub:Font-Sizes"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- specifies thereby 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 "sub:Boxes-without-Frame"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- the character can be centered.
-\end_layout
-
-\begin_layout Subsection
-Old-style Figures
-\begin_inset Index idx
-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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! O !
-\backslash
-oldstylenums
-\end_layout
-
-\end_inset
-
-.
- The command can be used in formulas and in 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 Subsection
-Miscellaneous special Characters
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Miscellaneous-special-Characters"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Special characters ! miscellaneous
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The following characters can only be inserted to formulas by using commands:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="4" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\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 $\mathcircumflex$
-\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
-_
-\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 $\_$
-\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
-^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-circ
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-
-\backslash
-@°
-\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
-\begin_inset Formula $^{\circ}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
- contains the following line
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-More about this is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Text-Characters-in"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-DeclareInputtext{176}{
-\backslash
-ifmmode^
-\backslash
-circ
-\backslash
-else
-\backslash
-textdegree
-\backslash
-fi}
-\end_layout
-
-\begin_layout Section
-Formula Styles
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Formula-Styles"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! styles
-\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 for this the option
-\series bold
-fleqn
-\series default
- must be inserted in the menu
-\family sans
-Document\SpecialChar \menuseparator
-Settings
-\family default
- under
-\family sans
-Document
-\begin_inset space ~
-\end_inset
-
-Class
-\end_layout
-
-\begin_layout Standard
-When
-\series bold
-Indented
-\series default
- is used, the indentation can be adjusted with the length
-\series bold
-
-\backslash
-mathindent
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-mathindent
-\end_layout
-
-\end_inset
-
-.
- Should the distance be 15
-\begin_inset space \thinspace{}
-\end_inset
-
-mm, the following command line is inserted in the LaTeX-preamble
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-setlength{
-\backslash
-mathindent}{15mm}
-\end_layout
-
-\begin_layout Standard
-When no length is specified, the predefined value of 30
-\begin_inset space \thinspace{}
-\end_inset
-
-pt will be used.
-\end_layout
-
-\end_deeper
-\begin_layout Itemize
-And two different numbering styles:
-\end_layout
-
-\begin_deeper
-\begin_layout Description
-Right is the predefined standard
-\end_layout
-
-\begin_layout Description
-Left for this the option
-\series bold
-leqno
-\series default
- must be inserted in the menu
-\family sans
-Document\SpecialChar \menuseparator
-Settings
-\family default
- under
-\family sans
-Document
-\begin_inset space ~
-\end_inset
-
-Class
-\end_layout
-
-\end_deeper
-\begin_layout Standard
-
-\series bold
-fleqn
-\series default
- and
-\series bold
-leqno
-\series default
- can also be used together.
- In this case both options are inserted, separated by a comma.
-\end_layout
-
-\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 "sub:Flalign-Environment"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-General
-\end_layout
-
-\begin_layout Standard
-In LyX multiline formulas are created by pressing
-\series bold
-
-\begin_inset Info
-type "shortcut"
-arg "newline-insert newline"
-\end_inset
-
-
-\series default
- inside a formula.
- This creates either an
-\series bold
-eqnarray environment
-\series default
- that is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Eqnarray-Environment"
-
-\end_inset
-
- or, when the option
-\family sans
-Use AMS math package
-\family default
- in the document settings is selected, an
-\series bold
-align environment
-\series default
- that is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Standard-align-Environment"
-
-\end_inset
-
-.
- The align environment is recommended because it provides in any case a
- typographically correct output.
-\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, the math toolbar buttons
-\begin_inset Graphics
- filename ../images/tabular-feature_append-row.png
- scale 85
-
-\end_inset
-
- or
-\begin_inset Graphics
- filename ../images/tabular-feature_delete-row.png
- scale 85
-
-\end_inset
-
-, respectively, or the menu
-\family sans
-Edit\SpecialChar \menuseparator
-Rows & Columns
-\family default
- can be used.
-\end_layout
-
-\begin_layout Subsubsection
-Line Separation
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Line-Separation"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! Line separation
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-There is sometimes 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 LaTeX additional line space is specified as optional argument of the
- new line command.
- This is not yet possible in LyX
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-see
-\begin_inset CommandInset href
-LatexCommand href
-name "LyX-bug #1505"
-target "http://www.lyx.org/trac/ticket/1505"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-, therefore the whole formula must be inserted in 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 collapsed
-
-\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
-\series bold
-
-\backslash
-jot
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! J !
-\backslash
-jot
-\end_layout
-
-\end_inset
-
- is changed.
- The definition is:
-\begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
-\end_inset
-
-.
- Predefined for
-\series bold
-
-\backslash
-jot
-\series default
- is the value 3
-\begin_inset space \thinspace{}
-\end_inset
-
-pt.
- To create 3
-\begin_inset space \thinspace{}
-\end_inset
-
-mm 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 TeX-mode before the formula.
- This requires that the 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 LaTeX standard installation.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! calc
-\end_layout
-
-\end_inset
-
- was loaded in 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 back to the predefined distance,
-\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 "sub:Column-Separation"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! Column separation
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Multiline formulas form a matrix.
- A formula in the eqnarray environment is for example 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-arraycolsep
-\end_layout
-
-\end_inset
-
- according to:
-\begin_inset Newline newline
-\end_inset
-
-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 TeX-mode, sets for all following formulas a column separation
- of 2
-\begin_inset space \thinspace{}
-\end_inset
-
-cm.
- To get back 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 collapsed
-
-\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 collapsed
-
-\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 Subsubsection
-Long Formulas
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! long
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Long formulas can be typeset using these methods:
-\end_layout
-
-\begin_layout Itemize
-When one side of the equation is much shorter than the line width, this
- one 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, 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 "sub:Variable-Space"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! H !
-\backslash
-hspace
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Itemize
-When both sides of the equation are too long, the command
-\series bold
-
-\backslash
-lefteqn
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-lefteqn
-\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 a bit shifted to the left from the
- blue one.
- In this the formula is inserted.
-\begin_inset Newline newline
-\end_inset
-
-The content of the further lines is inserted to the second or another formula
- column.
- The greater the column number where it was inserted, 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 LyX the cursor cannot be set with the mouse into the first
- line.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-\begin_inset CommandInset href
-LatexCommand href
-name "LyX-bug #1429"
-target "http://www.lyx.org/trac/ticket/1429"
-
-\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 "sub:Multline-Environment"
-
-\end_inset
-
- and
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Multiline-Formula-Parts"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsubsection
-Multiline Brackets
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Multiline-Brackets"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Brackets ! for multiline expressions
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-right
-\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 "sub:Automatic-Bracket-Size"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-left
-\end_layout
-
-\end_inset
-
-.
- After
-\series bold
-
-\backslash
-left.
-
-\series default
- the command
-\series bold
-
-\backslash
-vphantom
-\series default
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series bold
-
-\backslash
-prod
-\series default
-^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series bold
-
-\backslash
-infty
-\series default
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series bold
-
-\begin_inset Formula $\downarrow$
-\end_inset
-
-_R=1}
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! V !
-\backslash
-vphantom
-\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
- already existing formulas can be converted to Align environments.
-\end_layout
-
-\begin_layout Standard
-To add or delete columns, the math toolbar buttons
-\begin_inset Graphics
- filename ../images/tabular-feature_append-column.png
- scale 85
-
-\end_inset
-
- or
-\begin_inset Graphics
- filename ../images/tabular-feature_delete-column.png
- scale 85
-
-\end_inset
-
-, respectively, or the menu
-\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 "sub:Standard-align-Environment"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! align environment
-\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 collapsed
-
-\begin_layout Plain Layout
-more about
-\series bold
-
-\backslash
-hfill
-\series default
- see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Variable-Space"
-
-\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 collapsed
-
-\begin_layout Plain Layout
-formula styles see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! alignat environment
-\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
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Space"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-The above example 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 and more formulas side
- by side.
-\end_layout
-
-\begin_layout Subsubsection
-Flalign Environment
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Flalign-Environment"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! flalign environment
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In this environment the first two columns are always set as much as possible
- to the left and the last two ones 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 TeX-brace is inserted to 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"
-
-\end_inset
-
-:
-\begin_inset Formula
-\begin{flalign}
-\hspace{30pt}\iiint\limits _{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
-, 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 "sub:Eqnarray-Environment"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! eqnarray environment
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-When this environment has been created, three blue boxes appear.
- The content of the first box is right aligned, the content of the last
- one left aligned.
- The content of the middle box appears centered and a bit smaller, because
- it is designed to insert there only relation characters.
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! gather environment
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-This environment consists of only 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 "sub:Multline-Environment"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! multline environment
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The multline environment consists, like the gather environment, of only
- 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.
- As example formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:lefteqn"
-
-\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 (first) line of a multline environment appears
- numbered when the document numbering is right (left).
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-numbering styles see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-With the commands
-\series bold
-
-\backslash
-shoveright
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-shoveright
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-shoveleft
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-shoveleft
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-multlinegap
-\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 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 "sub:Multiline-Formula-Parts"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! formula parts
-\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 further 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-aligned
-\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.
- As example formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:shortlong"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-alignedat
-\end_layout
-
-\end_inset
-
-
-\series bold
-
-\backslash
-gathered
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! G !
-\backslash
-gathered
-\end_layout
-
-\end_inset
-
-, or
-\series bold
-
-\backslash
-split
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-split
-\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 "sub:Text-in-multiline"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Text ! in formulas
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! text
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In the Align environments, and 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! I !
-\backslash
-intertext
-\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 LyX doesn't yet support
-\series bold
-
-\backslash
-intertext
-\series default
- directly, the text is written as mathematical text.
-
-\series bold
-
-\backslash
-intertext
-\series default
- must hereby be at the beginning of a line and appears 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 Section
-Formula Numbering
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula numbering
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! numbering|see
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
-Formula numbering
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\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
-\family sans
-Ctrl+Alt
-\begin_inset space ~
-\end_inset
-
-N
-\family default
-).
- Existing formulas can be numbered with the menu
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Toggle
-\begin_inset space ~
-\end_inset
-
-Numbering
-\family default
- (shortcut
-\begin_inset Info
-type "shortcut"
-arg "math-number-toggle"
-\end_inset
-
-).
- The formula number is displayed in LyX behind the formula as a number sign
- in parentheses.
- The number sign is replaced in the output by the formula number.
-\end_layout
-
-\begin_layout Standard
-When numbering is turned on in multiline formulas, all lines will be numbered.
- But the numbering can be controlled with the menu
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Toggle
-\begin_inset space ~
-\end_inset
-
-Numbering
-\begin_inset space ~
-\end_inset
-
-of
-\begin_inset space ~
-\end_inset
-
-Line
-\family default
- (shortcut
-\begin_inset Info
-type "shortcut"
-arg "math-number-line-toggle"
-\end_inset
-
-) for every line.
-\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"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Cross-References
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Cross-references ! to formulas
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-All labeled formulas can be cross-referenced.
- A label is added by the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Label
-\family default
- or the toolbar button
-\begin_inset Graphics
- filename ../images/label-insert.png
- scale 85
-
-\end_inset
-
-.
- The cursor must hereby 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 there 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 formula label to divide 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 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 LyX within two parentheses behind
- formula.
- 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 Graphics
- filename ../images/dialog-show-new-inset_ref.png
- scale 85
-
-\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 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"
-
-\end_inset
-
- and
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:c"
-
-\end_inset
-
- are equivalent.
- In (
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "eq:Lat"
-
-\end_inset
-
-) big Latin letters are used for the numbering in contrary to (
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "eq:Rom"
-
-\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 "sub:User-defined-Numbering"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\series default
- contains a box like in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Paragraph-Boxes"
-
-\end_inset
-
-, the formula cannot be referenced.
-\end_layout
-
-\begin_layout Subsection
-Subnumbering
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula numbering ! subnumbering
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-With the help of the commands
-\series bold
-
-\backslash
-begin{subequations}
-\series default
- and
-\series bold
-
-\backslash
-end{subequations}
-\series default
- formulas can be subnumbered.
- Both commands are inserted in TeX-mode.
-\end_layout
-
-\begin_layout Standard
-An example:
-\begin_inset Formula
-\begin{equation}
-A=C-B\label{eq:a}
-\end{equation}
-
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-addtocounter{equation}{-1}
-\end_layout
-
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-begin{subequations}
-\end_layout
-
-\end_inset
-
-
-\begin_inset VSpace -5mm
-\end_inset
-
-
-\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
-
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-end{subequations}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To create the example, the following is done:
-\end_layout
-
-\begin_layout Enumerate
-first formula is inserted
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-
-\backslash
-addtocounter{equation}{-1}
-\backslash
-begin{subequations}
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-addtocounter
-\end_layout
-
-\end_inset
-
-
-\begin_inset Newline newline
-\end_inset
-
-
-\series default
-is inserted after the first formula
-\end_layout
-
-\begin_layout Enumerate
-second formula is inserted
-\end_layout
-
-\begin_layout Enumerate
-third formula is inserted
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-
-\backslash
-end{subequations}
-\series default
- is inserted after the third formula
-\end_layout
-
-\begin_layout Standard
-Every formula between the commands
-\series bold
-
-\backslash
-begin
-\series default
- and
-\series bold
-
-\backslash
-end
-\series default
- is subnumbered as a, b,
-\begin_inset Newline linebreak
-\end_inset
-
-c, \SpecialChar \ldots{}
- For multiline formulas every line will be subnumbered.
- All subnumbered formulas are treated as
-\emph on
-one
-\emph default
- numbered formula.
- But as every numbered formula increases the counter
-\series bold
-equation
-\series default
- by one, the command
-\series bold
-
-\backslash
-addtocounter
-\series default
- is needed to decrease it.
- Otherwise the formulas
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:a"
-
-\end_inset
-
-,
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:b"
-
-\end_inset
-
-,
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:c"
-
-\end_inset
-
- would be numbered as
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:a"
-
-\end_inset
-
-,
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:d"
-
-\end_inset
-
-,
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:f"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-By inserting the commands in TeX-mode, a space is created between the first
- two formulas.
- To revert this -5
-\begin_inset space \thinspace{}
-\end_inset
-
-mm vertical space is inserted after the command
-\series bold
-
-\backslash
-begin{subequations}
-\series default
-.
- When the formula style
-\series bold
-Indented
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-formula styles see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\series default
- is used, -7
-\begin_inset space \thinspace{}
-\end_inset
-
-mm space is inserted instead.
-\end_layout
-
-\begin_layout Standard
-Here is an example for a multiline formula where the numbering was turned
- off for the second line:
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-begin{subequations}
-\end_layout
-
-\end_inset
-
-
-\begin_inset Formula
-\begin{eqnarray}
-A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
- & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
- & = & B^{2}-2BZ+Z^{2}\label{eq:f}
-\end{eqnarray}
-
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-end{subequations}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-User-defined Numbering
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:User-defined-Numbering"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula numbering ! user-defined
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula numbering ! self-defined delimiters
-\end_layout
-
-\end_inset
-
-With the standard numbering parentheses are set around the formula number.
- To replace the parentheses for example by vertical bars, the following
- line is added to the LaTeX-preamble:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\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 LaTeX-preamble for testing.
- To activate it, remove the percent sign 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 ore more characters.
- To get 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-tag
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-something
-\series default
- was inserted in the formula.
-\end_layout
-
-\begin_layout Standard
-When the command
-\series bold
-
-\backslash
-tag*
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-something
-\series default
- is inserted instead, the star prevents the parentheses around the expression:
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands !
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-"
-\end_layout
-
-\end_inset
-
-@
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-"
-\end_layout
-
-\end_inset
-
- !
-\backslash
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-"
-\end_layout
-
-\end_inset
-
-@
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-"
-\end_layout
-
-\end_inset
-
-addtoreset
-\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 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 LaTeX using the command
-\series bold
-
-\backslash
-makeatletter.
-
-\series default
- The command
-\series bold
-
-\backslash
-makeatother
-\series default
- reverts this.
- So the command sequence in 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 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 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 LaTeX-package
-\series bold
-carlisle
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! carlisle
-\end_layout
-
-\end_inset
-
- that is part of every LaTeX standard installation.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! remreset
-\end_layout
-
-\end_inset
-
- has to be loaded in the 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands !
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-"
-\end_layout
-
-\end_inset
-
-@
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-"
-\end_layout
-
-\end_inset
-
- !
-\backslash
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-"
-\end_layout
-
-\end_inset
-
-@
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-"
-\end_layout
-
-\end_inset
-
-removefromreset
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! N !
-\backslash
-numberwithin
-\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
- number is before the dot.
-\end_layout
-
-\begin_layout Standard
-Thus in our case the following LaTeX-preamble or 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 TeX code or to the LaTeX-preamble:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-renewcommand{
-\backslash
-theequation}{
-\backslash
-arabic{equation}}
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-arabic
-\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
- uses internally the command
-\series bold
-
-\backslash
-@addtoreset
-\series default
-, described above, that also needs to be reverted.
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-
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-
-
-\backslash
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-
-\begin_layout Plain Layout
-
-
-\backslash
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-
-\begin_layout Plain Layout
-
-
-\backslash
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-
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-
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-
-\begin_layout Subsection
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-
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-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula numbering ! with Roman numbers
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Formulas can also be numbered with Roman numbers and Latin letters.
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-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-renewcommand{
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-\backslash
-roman{equation}}
-\end_layout
-
-\begin_layout Standard
-is inserted before the formula in TeX-mode.
-
-\series bold
-
-\backslash
-renewcommand
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-renewcommand
-\end_layout
-
-\end_inset
-
- redefines the predefined command
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-
-\backslash
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-\series default
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-\series bold
-
-\backslash
-roman{equation}
-\series default
-.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-The command
-\series bold
-
-\backslash
-renewcommand
-\series default
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-\series bold
-
-\backslash
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-\series default
- that is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:The-Command-newcommand"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\series bold
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- When the command
-\series bold
-
-\backslash
-the
-\series default
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-\series bold
-
-\backslash
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-\series default
- behind the formula.
-
-\series bold
-
-\backslash
-roman{equation}
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
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-\end_layout
-
-\end_inset
-
-
-\series default
- outputs the counter as small Roman number.
-\end_layout
-
-\begin_layout Standard
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-\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
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-\series bold
-
-\backslash
-roman
-\series default
- is replaced by
-\series bold
-
-\backslash
-Roman
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-roman@
-\backslash
-Roman
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-alph
-\end_layout
-
-\end_inset
-
-, for big ones there is the command
-\series bold
-
-\backslash
-Alph
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-alph@
-\backslash
-Alph
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Greyedout
-status open
-
-\begin_layout Plain Layout
-
-\series bold
-\color none
-Note:
-\series default
- Only maximal 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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-arabic
-\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 about this can be found in the file
-\begin_inset CommandInset href
-LatexCommand href
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-target "run:Formula-numbering.lyx"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Chemical Symbols and Equations
-\begin_inset CommandInset label
-LatexCommand label
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-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Chemical characters ! Symbols
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Chemical equations
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Symbols ! chemical
-\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
-This chemical equation can directly be created as formula.
- To avoid that the symbols appear 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
-font styles
-\series bold
-
-\series default
-see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Font-Styles"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-ce
-\end_layout
-
-\end_inset
-
- that is available when the LaTeX-package
-\series bold
-mhchem
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! mhchem
-\end_layout
-
-\end_inset
-
- is installed.
- After inserting
-\series bold
-
-\backslash
-ce
-\series default
- to 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="9" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
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-<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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ce
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-H2CO3
-\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 $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
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-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ce
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-SO4^2-
-\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 $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
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-(NH4)2S
-\end_layout
-
-\end_inset
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-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-KCr(SO4)2.12H2O
-\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 $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
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-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
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-\begin_layout Plain Layout
-
-\backslash
-ce
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A-B
-\backslash
-dbond
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-C
-\backslash
-tbond
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-D
-\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 $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
-\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
-
-\backslash
-ce
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-CO2
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-+
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-C
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-<=>
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
-\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
-
-\backslash
-ce
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-CO2
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-+
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-C
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-->[
-\backslash
-alpha][
-\backslash
-beta]
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-2CO}
-\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 $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
-\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
-\color none
-Note:
-\series default
- Inserting a formula to a
-\series bold
-
-\backslash
-ce
-\series default
- box will lead to LaTeX errors due to a LyX bug.
-\color inherit
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-\begin_inset CommandInset href
-LatexCommand href
-name "LyX-bug #8566"
-target "http://www.lyx.org/trac/ticket/8566"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\color none
- In this case TeX code has to be used like for
-\series bold
-
-\backslash
-ce{$
-\backslash
-mu
-\backslash
-hyphen$Cl}
-\series default
-:
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-ce{$
-\backslash
-mu
-\backslash
-hyphen$Cl}
-\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
-\color none
-Note:
-\series default
- It is not possible in 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"
-
-\end_inset
-
- is:
-\begin_inset Newline newline
-\end_inset
-
-
-\series bold
-
-\backslash
-ce
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-2Na+
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-+
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-SO4^2-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-->
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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"
-
-\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"
-
-\end_inset
-
- and
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:TEOS-reaction-2"
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-cf
-\end_layout
-
-\end_inset
-
- that has to be 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"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Section
-Diagrams
-\end_layout
-
-\begin_layout Standard
-LyX supports two types of commutative diagrams:
-\series bold
-amscd
-\series default
- and
-\series bold
-xymatrix
-\series default
- that are explained in the following.
-\end_layout
-
-\begin_layout Subsection
-Amscd Diagrams
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Diagrams ! amscd
-\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 get them, the command
-\series bold
-
-\backslash
-CD
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-CD
-\end_layout
-
-\end_inset
-
-
-\series default
- is inserted to a formula.
- A blue box appears with two dashed lines where further 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, vertical in even formula lines.
-\end_layout
-
-\begin_layout Standard
-To create the relations there are 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 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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-D@<<j<E@>k>>F@=C
-\end_layout
-
-\begin_layout Subsection
-Xymatrix Diagrams
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Diagrams ! xymatrix
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To be able to use xymatrices, the 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"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
- and much more.
- All possibilities to create commutative diagrams and decorations are explained
- in detail in the
-\emph on
-XY-pic manual
-\emph default
- that you find 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
-status collapsed
-
-\begin_layout Plain Layout
-Diagrams ! Feynman
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To be able to use
-\noun on
-Feynman
-\noun default
--diagrams, the 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 are able to add new matrix columns and rows like for normal matrices,
- see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Matrices"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-Examples how to create
-\noun on
-Feynman-
-\noun default
-diagrams in LyX is given in the
-\emph on
-Feynman-diagram manual
-\emph default
- that you find in the menu
-\family sans
-Help\SpecialChar \menuseparator
-Specific
-\begin_inset space ~
-\end_inset
-
-Manuals
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-User-defined Commands
-\begin_inset Index idx
-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 "sub:The-Command-newcommand"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-User-defined commands !
-\backslash
-newcommand
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! N !
-\backslash
-newcommand
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Many 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
- Assure that the name of the new command is not already used in your document
- or by LaTeX-packages that you use.
- When you for example define the command
-\series bold
-
-\backslash
-le
-\series default
- for
-\series bold
-
-\backslash
-Leftarrow
-\series default
-, you 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 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 "sub:Boxes-with-Frame"
-
-\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 tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-A
-\backslash
-gr
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-B
-\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 $A\gr B$
-\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
-us{ABcd
-\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 $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
-\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
-fb{[2cm]
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-{
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-{
-\backslash
-int
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=B
-\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 $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
-\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
-cb{red
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-{
-\backslash
-int
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=B
-\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 $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
-\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
-
-\backslash
-cb[green]
-\backslash
-{red
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-{
-\backslash
-int
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=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 $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Math Macros
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-User-defined commands! Math macros
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-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.
- When you are for example 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 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 LaTeX commands, e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-that a fraction is inserted in LaTeX as
-\series bold
-
-\backslash
-frac{numerator}{denominator}
-\series default
-.
- Furthermore one can easily forget a brace in the definition and cannot
- see in LyX what the new command is doing.
- To avoid these problems 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 Graphics
- filename ../images/math-macro_newmacroname_newcommand.png
- scale 85
-
-\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
-
-\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 Graphics
- filename ../images/math-macro-add-param.png
- scale 85
-
-\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 Graphics
- filename ../images/math-macro-add-optional-param.png
- scale 85
-
-\end_inset
-
-.
- The first non-optional argument can be transformed to an optional one with
- the toolbar button
-\begin_inset Graphics
- filename ../images/math-macro-make-optional.png
- scale 85
-
-\end_inset
-
-.
- In the second blue box the appearance of the macro in 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 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 LyX like this:
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset space \hspace*{\fill}
-\end_inset
-
-
-\begin_inset Graphics
- filename clipart/macrouse.png
-
-\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
-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 the most, 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 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 LyX as normal text, highlighting it completely and using then 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
- LaTeX errors.
-\end_layout
-
-\begin_layout Standard
-Math macros currently have the problem that further formulas in macro definition
-s are handled wrongly.
- Therefore the example
-\series bold
-
-\backslash
-fb
-\series default
- from
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:The-Command-newcommand"
-
-\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 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
-status collapsed
-
-\begin_layout Plain Layout
-Macros ! Toolbar
-\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" width="0">
-<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 Graphics
- filename ../images/math-macro-remove-param.png
- rotateOrigin center
-
-\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 Graphics
- filename ../images/math-macro-add-param.png
- rotateOrigin center
-
-\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 Graphics
- filename ../images/math-macro-make-optional.png
- rotateOrigin center
-
-\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
-Make First Non-Optional into
-\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 Graphics
- filename ../images/math-macro-make-nonoptional.png
- rotateOrigin center
-
-\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
-Make Last Optional into
-\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 Graphics
- filename ../images/math-macro-remove-optional-param.png
- rotateOrigin center
-
-\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 Graphics
- filename ../images/math-macro-add-optional-param.png
- rotateOrigin center
-
-\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 Graphics
- filename ../images/math-macro-remove-greedy-param.png
- rotateOrigin center
-
-\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 Graphics
- filename ../images/math-macro-append-greedy-param.png
- rotateOrigin center
-
-\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 Graphics
- filename ../images/math-macro-add-greedy-optional-param.png
- rotateOrigin center
-
-\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 Section
-Computer Algebra Systems
-\end_layout
-
-\begin_layout Standard
-LyX offers the exchange between mathematical expressions written in 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 $\det\left[\begin{array}{ccc}
-1 & 6 & 7\\
-2 & 5 & 8\\
-3 & 4 & 17
-\end{array}\right]=-56$
-\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 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
- LyX function (see the
-\family sans
-\emph on
-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 break-paragraph;math-extern maxima
-\end_layout
-
-\begin_layout Section
-Miscellaneous
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Miscellaneous
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Negative Numbers
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Numbers ! negative
-\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 tabularvalignment="middle">
-<column alignment="right" valignment="top" width="0">
-<column alignment="left" valignment="top" width="0">
-<row>
-<cell alignment="center" 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="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-formula:
-\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 $x=-2$
-\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
-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
-status collapsed
-
-\begin_layout Plain Layout
-Comma
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In 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 LaTeX-package
-\series bold
-was
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! was
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-vspace{4mm}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! icomma
-\end_layout
-
-\end_inset
-
- is loaded with the 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 "sub:Physical-Vectors"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Vectors ! physical
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Predefined vectors are offered by the LaTeX-package
-\series bold
-braket
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! braket
-\end_layout
-
-\end_inset
-
- that is loaded with the 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 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 tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Bra{
-\backslash
-psi
-\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 $\Bra{\psi}$
-\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
-Ket{
-\backslash
-psi
-\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 $\Ket{\psi}$
-\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
-
-\backslash
-Braket{
-\backslash
-psi|
-\backslash
-phi
-\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 $\Braket{\psi|\phi}$
-\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 LaTeX-package
-\series bold
-braket
-\series default
- is not installed:
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-You need to install the 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 "sub:Automatic-Bracket-Size"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Self-defined Fractions
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Self-defined-Fractions"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Fractions ! self-defined
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! G !
-\backslash
-genfrac
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-vspace{4mm}
-\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 tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<row>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="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" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Style (Size)
-\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
-0
-\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
-display style formula
-\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
-1
-\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
-inline formula
-\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
-2
-\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
-small
-\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
-3
-\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
-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 "sub:Fractions"
-
-\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 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
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! canceled
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To cancel formulas or formula parts, the LaTeX-package
-\series bold
-cancel
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! cancel
-\end_layout
-
-\end_inset
-
- has to be loaded with the LaTeX-preamble line
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-usepackage{cancel}
-\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 LaTeX-package
-\series bold
-cancel
-\series default
- is installed.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-There are four ways to cancel formulas:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="5" columns="2">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<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
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-The space and
-\series bold
-
-\backslash
-raisebox
-\series default
- are used here as spacer.
-\end_layout
-
-\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
-cancel{
-\backslash
-int
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=B
-\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 $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
-\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
-bcancel{
-\backslash
-int
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=B
-\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 $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
-\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
-
-\backslash
-xcancel{
-\backslash
-int
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=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 $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
-\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
-
-\backslash
-cancelto{1
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-{
-\backslash
-int
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-A=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 $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
-\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 load the package
-\series bold
-cancel
-\series default
- with either the option
-\series bold
-samesize
-\series default
- which leads to the same size as for the canceled value or with the option
-
-\series bold
-Smaller
-\series default
- which makes is it a bit smaller than the size one gets without using a
- package option.
- In this document
-\series bold
-cancel
-\series default
- was loaded with this line:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-usepackage[samesize]{cancel}
-\end_layout
-
-\begin_layout Standard
-To color the cancellation bar one adds this command as 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"
-
-\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 LaTeX-package
-\series bold
-cancel
-\series default
- is not installed:
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-You need to install the 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 Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Formulas in Section Headings
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Formulas-in-Section"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! in section headings
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! hyperref
-\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 convention
-s.
-\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 TeX-mode:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-texorpdfstring{part}{alternative}
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-texorpdfstring
-\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
-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 collapsed
-
-\begin_layout Plain Layout
-see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Bold-Formulas"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Formulas in multi-column Text
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! in multi-column text
-\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 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 LaTeX standard installation.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! multicol
-\end_layout
-
-\end_inset
-
-, that is loaded with the 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 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 TeX-mode.
-\end_layout
-
-\begin_layout Standard
-Due to the command some space is automatically added before the formula.
- To revert 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 collapsed
-
-\begin_layout Plain Layout
-formula styles see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\series default
- is used, -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 german
-\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 german
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! with description of variables
-\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"
-
-\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
-matrices see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Matrices"
-
-\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
-font sizes see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Font-Sizes"
-
-\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
-formula styles see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\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 "sub:Variable-Space"
-
-\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 "sub:Flalign-Environment"
-
-\end_inset
-
- is used to indent formulas.
- Formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:within"
-
-\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 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 "sub:Upright-small-Greek"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Greek letters ! upright
-\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 LaTeX-package
-\series bold
-was
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! was
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-vspace{4mm}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! upgreek
-\end_layout
-
-\end_inset
-
- that is loaded with the 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 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 LaTeX-package
-\series bold
-upgreek
-\series default
- is not installed:
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-You need to install the 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 CommandInset label
-LatexCommand label
-name "sub:Text-Characters-in"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Text ! in formulas
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In some cases you might want to insert text characters directly into formulas.
- When 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 "sub:Binary-Operators"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- all the time, because this character is defined in all encodings as text
- character.
- But the encoding can be changed by this 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 \textcompwordmark{}
-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 LaTeX-erro
-rs.
- With the changed encoding the right 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 LaTeX.
- Encodings should only be changed via the LaTeX-preamble and not in the
- definition files.
- Otherwise documents could not be edited by other 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 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 \textcompwordmark{}
-i}
-\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
-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"
-
-\end_inset
-
- that lists some of the ISO rules.
- More rules are listed in
-\begin_inset CommandInset citation
-LatexCommand cite
-key "Checklist"
-
-\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 "sub:Font-Styles"
-
-\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 "sub:Predefined-Space"
-
-\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 to a formula, two boxes appear.
- In the first one the value is inserted, in the second one the unit, and
- one gets 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 LaTeX command but the command
-\series bold
-
-\backslash
-unit[value]{unit}
-\series default
-, therefore you cannot use it in 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 directly on the value: 15°, but not 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 "sub:Predefined-Functions"
-
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\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
-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 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
-equivalent to
-\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" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ast
-\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 ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-raisebox{-1.2mm}{
-\end_layout
-
-\end_inset
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+#LyX 2.0 created this file. For more info see http://www.lyx.org/\r
+\lyxformat 413\r
+\begin_document\r
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+%\r
+% This preamble is designed to ensure that the file prints\r
+% out as advertised. If you mess with this preamble,\r
+% parts of this document may not print out as expected. If you\r
+% have problems LaTeXing this file, please contact \r
+% the documentation team\r
+% email: lyx-docs@lists.lyx.org\r
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+% To be able to enter the character ° and · directly in LyX,\r
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+% increase link area for cross-references and autoname them,\r
+\AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}\r
+\@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}\r
+\addto\extrasenglish{%\r
+ \renewcommand*{\equationautorefname}[1]{}\r
+ \renewcommand{\sectionautorefname}{sec.\negthinspace}\r
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+% see first footnote in sec. 9.3\r
+\@ifundefined{textcolor}{\usepackage{color}}{}\r
+\r
+% the pages of the TOC are numbered roman\r
+% and a PDF-bookmark for the TOC is added\r
+\pagenumbering{roman}\r
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+\renewcommand{\tableofcontents}{%\r
+ \vspace{1cm}\r
+ \pdfbookmark[1]{\contentsname}{}\r
+ \myTOC\r
+ \cleardoublepage\r
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+% insert additional vertical space of 1.5 mm between footnotes,\r
+\let\myFoot\footnote\r
+\renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}\r
+\r
+% provides caption formatting\r
+\setkomafont{captionlabel}{\bfseries}\r
+\r
+% used in sec. 24.5\r
+\usepackage[samesize]{cancel}\r
+\r
+% enables calculation of values\r
+\usepackage{calc}\r
+\r
+% for multiple columns used in sec. 24.7\r
+\usepackage{multicol}\r
+\r
+% needed in sec. 19.4\r
+\usepackage{remreset}\r
+\r
+% for the Fourier transformation symbol\r
+\usepackage{mathrsfs}\r
+\r
+% define a color, used in sec.9.3\r
+\definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}\r
+\r
+% declare operators (see sec. 10.4 and sec. 15.2)\r
+\DeclareMathOperator*{\Lozenge}{\blacklozenge}\r
+\DeclareMathOperator{\sgn}{sgn}\r
+\r
+\newcommand{\spce}{\textvisiblespace}\r
+\r
+% example definitions for sec. 20.1 \r
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+\newcommand{\us}[1]{\underline{#1}}\r
+\newcommand{\fb}[3]{\framebox#1#2{$#3$}}\r
+\newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}\r
+\newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}\r
+\r
+% example macro from sec. 19.4\r
+%\def\tagform@#1{\maketag@@@{|#1|}}\r
+\r
+% macro from sec. 10.2\r
+\def\clap#1{\hbox to 0pt{\hss #1\hss}}\r
+\def\mathclap {\mathpalette \mathclapinternal}\r
+\def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}\r
+\r
+\r
+% ------------------------------------\r
+% used to check for needed LaTeX packages\r
+\usepackage{ifthen}\r
+\r
+% check for package eurosym\r
+% used for the Euro symbol\r
+\newboolean{eurosym}\r
+\IfFileExists{eurosym.sty}\r
+ {\usepackage[gennarrow]{eurosym}\r
+ \setboolean{eurosym}{true}}\r
+ {\setboolean{eurosym}{false}}\r
+\r
+% check for package braket\r
+% used for physical vectors\r
+\newboolean{braket}\r
+\IfFileExists{braket.sty}\r
+ {\usepackage{braket}\r
+ \setboolean{braket}{true}}\r
+ {\setboolean{braket}{false}}\r
+\r
+% check for package cancel\r
+\newboolean{cancel}\r
+\IfFileExists{cancel.sty}\r
+ {\usepackage{cancel}\r
+ \setboolean{cancel}{true}}\r
+ {\setboolean{cancel}{false}}\r
+\r
+% check for package upgreek\r
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+\IfFileExists{upgreek.sty}\r
+ {\usepackage{upgreek}\r
+ \setboolean{upgreek}{true}}\r
+ {\setboolean{upgreek}{false}}\r
+\end_preamble\r
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+\spacing single\r
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+\pdf_title "LyX's Math Manual"\r
+\pdf_author "LyX Team, Uwe Stöhr"\r
+\pdf_subject "LyX-documentation about math"\r
+\pdf_keywords "LyX, Mathed"\r
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+\pdf_backref false\r
+\pdf_pdfusetitle false\r
+\pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"\r
+\papersize a4paper\r
+\use_geometry false\r
+\use_amsmath 2\r
+\use_esint 1\r
+\use_mhchem 1\r
+\use_mathdots 1\r
+\cite_engine basic\r
+\use_bibtopic false\r
+\use_indices false\r
+\paperorientation portrait\r
+\suppress_date false\r
+\use_refstyle 0\r
+\notefontcolor #0000ff\r
+\index Index\r
+\shortcut idx\r
+\color #008000\r
+\end_index\r
+\secnumdepth 4\r
+\tocdepth 3\r
+\paragraph_separation skip\r
+\defskip medskip\r
+\quotes_language english\r
+\papercolumns 1\r
+\papersides 2\r
+\paperpagestyle plain\r
+\bullet 1 0 6 -1\r
+\bullet 2 2 35 -1\r
+\bullet 3 2 7 -1\r
+\tracking_changes false\r
+\output_changes false\r
+\html_math_output 0\r
+\html_css_as_file 0\r
+\html_be_strict false\r
+\end_header\r
+\r
+\begin_body\r
+\r
+\begin_layout Title\r
+LyX's detailed Math manual\r
+\end_layout\r
+\r
+\begin_layout Author\r
+by the LyX Team\r
+\begin_inset Foot\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+\noindent\r
+If you have comments or error corrections, please send them to the LyX Documenta\r
+tion mailing list: \r
+\family typewriter\r
+\r
+\begin_inset CommandInset href\r
+LatexCommand href\r
+name "lyx-docs@lists.lyx.org"\r
+target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"\r
+type "mailto:"\r
+\r
+\end_inset\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
+author: Uwe Stöhr\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+\r
+\begin_inset Newline newline\r
+\end_inset\r
+\r
+\r
+\begin_inset Newline newline\r
+\end_inset\r
+\r
+\r
+\family sans\r
+Version 2.0.x\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+\begin_inset CommandInset toc\r
+LatexCommand tableofcontents\r
+\r
+\end_inset\r
+\r
+\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+\begin_inset Note Note\r
+status open\r
+\r
+\begin_layout Plain Layout\r
+To export this document to PDF, PS or DVI the LaTeX-packages \r
+\series bold\r
+braket, cancel, eurosym, mathdots, mhchem\r
+\series default\r
+ and \r
+\series bold\r
+was\r
+\series default\r
+ should be installed.\r
+ If they are not installed the document can be exported anyway but the sections\r
+ where the packages are required will not appear in the output.\r
+ An exception is \r
+\series bold\r
+mhchem\r
+\series default\r
+; if it is not installed, this file cannot be exported.\r
+\end_layout\r
+\r
+\begin_layout Plain Layout\r
+The latest PDF-version of this document can be found here:\r
+\begin_inset Newline newline\r
+\end_inset\r
+\r
+\r
+\series bold\r
+http://wiki.lyx.org/LyX/DocumentationDevelopment#Math\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
+Introduction\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+This document explains LyX's math features and is furthermore a collection\r
+ of LaTeX-commands used for mathematical characters and constructs.\r
+ The explanations are designed for the usage of commands.\r
+ It is therefore required that you have read the section \r
+\family typewriter\r
+Mathematical\r
+\begin_inset space ~\r
+\end_inset\r
+\r
+Formulas\r
+\family default\r
+ of the User's Guide.\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+Most of the characters and many constructs explained in this manual are\r
+ also accessible via the menu \r
+\family sans\r
+Insert\r
+\series bold\r
+\SpecialChar \menuseparator\r
+\r
+\series default\r
+Math\r
+\family default\r
+ or the \r
+\family sans\r
+math\r
+\family default\r
+\series bold\r
+ \r
+\family sans\r
+\series default\r
+toolbar\r
+\family default\r
+.\r
+ But everybody who has to write lots of formulas will notice that it is\r
+ much faster to use commands instead of the math toolbar.\r
+ Therefore this manual is focused on commands but also mentions the correspondin\r
+g toolbar buttons when available.\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+If not specially mentioned the commands are only available within formulas.\r
+ To be able to use all commands explained in this document, the option \r
+\family sans\r
+Use AMS math package\r
+\family default\r
+ must be checked in the document settings (menu \r
+\family sans\r
+Document\SpecialChar \menuseparator\r
+Settings\SpecialChar \menuseparator\r
+Math\r
+\begin_inset space ~\r
+\end_inset\r
+\r
+Options\r
+\family default\r
+).\r
+\begin_inset Foot\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+The option \r
+\family sans\r
+Use AMS math package automatically\r
+\family default\r
+ only uses \r
+\begin_inset ERT\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+\r
+\r
+\backslash\r
+AmS \r
+\end_layout\r
+\r
+\end_inset\r
+\r
+-math when math constructs are found that are supported by LyX.\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+This document doesn't list all \r
+\begin_inset ERT\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+\r
+\r
+\backslash\r
+AmS \r
+\end_layout\r
+\r
+\end_inset\r
+\r
+-math commands\r
+\begin_inset Foot\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+A list with all \r
+\begin_inset ERT\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+\r
+\r
+\backslash\r
+AmS\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+-math commands is in the file \r
+\family sans\r
+\r
+\begin_inset CommandInset href\r
+LatexCommand href\r
+name "amsguide.ps"\r
+target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"\r
+\r
+\end_inset\r
+\r
+\r
+\family default\r
+, which is part of every LaTeX standard installation.\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+ for lucidity reasons.\r
+\end_layout\r
+\r
+\begin_layout Section\r
+General Instructions\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+To create an inline formula\r
+\begin_inset Index idx\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+Formula ! inline\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+ that is embedded into a text line, use one of the shortcuts \r
+\begin_inset Info\r
+type "shortcuts"\r
+arg "math-mode"\r
+\end_inset\r
+\r
+ or the toolbar button \r
+\begin_inset Graphics\r
+ filename ../images/math-mode.png\r
+ scale 85\r
+\r
+\end_inset\r
+\r
+.\r
+\begin_inset Newline newline\r
+\end_inset\r
+\r
+To create a display style formula\r
+\begin_inset Index idx\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+Formula ! display style\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+ which will appear bigger, has a different format, and will be in a separate\r
+ paragraph, use one of these shortcuts: \r
+\begin_inset Info\r
+type "shortcuts"\r
+arg "math-display"\r
+\end_inset\r
+\r
+.\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+To change a display style formula to an inline formula, set the cursor into\r
+ the formula and use one of the shortcuts \r
+\begin_inset Info\r
+type "shortcuts"\r
+arg "math-mode"\r
+\end_inset\r
+\r
+ or the menu \r
+\family sans\r
+Edit\SpecialChar \menuseparator\r
+Math\SpecialChar \menuseparator\r
+Change formula type\r
+\family default\r
+.\r
+ The same way is used to change an inline formula to a display style formula.\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+To display parts of an inline formula in the size of a display style formula,\r
+ enter the command \r
+\series bold\r
+\r
+\backslash\r
+displaystyle\r
+\series default\r
+\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
+ to a formula.\r
+ Then a new blue box appears in which the desired formula part is inserted.\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+Only inline formulas are allowed inside tables.\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+The \r
+\family sans\r
+math toolbar\r
+\family default\r
+ can be turned on in the menu \r
+\family sans\r
+View\SpecialChar \menuseparator\r
+Toolbars\r
+\family default\r
+.\r
+ When you click there on \r
+\begin_inset Quotes eld\r
+\end_inset\r
+\r
+Math\r
+\begin_inset Quotes erd\r
+\end_inset\r
+\r
+ the toolbar will be shown permanently at the bottom; this state is visualized\r
+ in the \r
+\family sans\r
+Toolbars\r
+\family default\r
+ menu with a checkmark.\r
+ When you click in this state again on \r
+\begin_inset Quotes eld\r
+\end_inset\r
+\r
+Math\r
+\begin_inset Quotes erd\r
+\end_inset\r
+\r
+ in the \r
+\family sans\r
+Toolbars\r
+\family default\r
+ menu, the \r
+\family sans\r
+math toolbar\r
+\family default\r
+ is only shown when the cursor is within a formula; this state is visualized\r
+ by the renaming of the menu entry from \r
+\begin_inset Quotes eld\r
+\end_inset\r
+\r
+Math\r
+\begin_inset Quotes erd\r
+\end_inset\r
+\r
+ to \r
+\begin_inset Quotes eld\r
+\end_inset\r
+\r
+Math\r
+\begin_inset space ~\r
+\end_inset\r
+\r
+(auto)\r
+\begin_inset Quotes erd\r
+\end_inset\r
+\r
+.\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+The TeX-mode\r
+\begin_inset Index idx\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+T@TeX-mode\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+ is invoked by pressing the toolbar button \r
+\begin_inset Graphics\r
+ filename ../images/ert-insert.png\r
+ scale 85\r
+\r
+\end_inset\r
+\r
+ or by using the menu \r
+\family sans\r
+Insert\SpecialChar \menuseparator\r
+Te\r
+\begin_inset ERT\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+\r
+{}\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+X Code\r
+\family default\r
+ (shortcut \r
+\begin_inset Info\r
+type "shortcut"\r
+arg "ert-insert"\r
+\end_inset\r
+\r
+).\r
+\begin_inset Note Note\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+In LyX there are three \r
+\begin_inset Quotes eld\r
+\end_inset\r
+\r
+proper names\r
+\begin_inset Quotes erd\r
+\end_inset\r
+\r
+ that appear in the output with sub- and superscript letters: TeX, LaTeX\r
+ and LyX\r
+\end_layout\r
+\r
+\begin_layout Plain Layout\r
+To avoid that these names are recognized as proper names, a TeX-brace pair\r
+ is inserted.\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+To change the LaTeX-preamble\r
+\begin_inset Index idx\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+L@LaTeX-preamble\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+, use the menu \r
+\family sans\r
+Document\SpecialChar \menuseparator\r
+Settings\SpecialChar \menuseparator\r
+LaT\r
+\begin_inset ERT\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+\r
+{}\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+eX\r
+\family default\r
+ \r
+\family sans\r
+Preamble\r
+\family default\r
+.\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+To edit matrices, case differentiations and multiline formulas subsequently,\r
+ use the menus \r
+\family sans\r
+Edit\SpecialChar \menuseparator\r
+Math\r
+\family default\r
+ and \r
+\family sans\r
+Edit\SpecialChar \menuseparator\r
+Rows\r
+\begin_inset space \thinspace{}\r
+\end_inset\r
+\r
+&\r
+\begin_inset space \thinspace{}\r
+\end_inset\r
+\r
+Columns,\r
+\family default\r
+ or the \r
+\family sans\r
+table toolbar\r
+\family default\r
+.\r
+ When lines and columns are swapped via the menu, the column or line where\r
+ the cursor is in is exchanged with the column to the right or the line\r
+ below, respectively.\r
+ Is the cursor in the last column or row, the exchange is done with the\r
+ column to the left or the line above.\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+To write text in formulas\r
+\begin_inset Foot\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+For multiline formulas the command \r
+\series bold\r
+\r
+\backslash\r
+intertext\r
+\series default\r
+ is used, see \r
+\begin_inset CommandInset ref\r
+LatexCommand ref\r
+reference "sub:Text-in-multiline"\r
+\r
+\end_inset\r
+\r
+.\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+ \r
+\emph on\r
+mathematical text\r
+\emph default\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
+Mathematical text\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+ is used.\r
+ This mode is invoked with the shortcut \r
+\begin_inset Info\r
+type "shortcut"\r
+arg "font-default"\r
+\end_inset\r
+\r
+ or by the insertion of the command \r
+\series bold\r
+\r
+\backslash\r
+text\r
+\series default\r
+\r
+\begin_inset Index idx\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
+Commands ! T ! \r
+\backslash\r
+text\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+.\r
+ The text appears black in LyX and can therefore be distinguished from the\r
+ other formula parts which appear blue.\r
+ In the output mathematical text is set upright, in contrary to other formula\r
+ parts.\r
+\end_layout\r
+\r
+\begin_layout Subsection*\r
+Command Scheme\r
+\end_layout\r
+\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
+argument}\r
+\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
+ The braces around the required arguments are named in this document as\r
+ TeX-braces\r
+\begin_inset Index idx\r
+status collapsed\r
+\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\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 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 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 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 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 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 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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 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 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 tabularvalignment="middle">\r
+<column alignment="center" valignment="middle" width="0">\r
+<column alignment="center" valignment="middle" width="0">\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 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 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 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 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 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 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 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 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 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 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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 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 tabularvalignment="middle">\r
+<column alignment="center" valignment="middle" width="6.8cm">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 tabularvalignment="middle">\r
+<column alignment="left" valignment="top" width="0">\r
+<column alignment="left" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 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
+<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
+pm\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 $\pm$\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
+mp\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 $\mp$\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
+cdot\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 $\cdot$\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
+times\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 $\times$\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
+div\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 $\div$\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
+\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
+<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
+star\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 $\star$\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
+circ\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 $\circ$\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" 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 space \hfill{}\r
+\end_inset\r
+\r
+\r
+\begin_inset Tabular\r
+<lyxtabular version="3" rows="13" columns="2">\r
+<features 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
+nabla\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 $\nabla$\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
+bigtriangledown\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 $\bigtriangledown$\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
+bigtriangleup\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 $\bigtriangleup$\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
+Box\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 $\Box$\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
+cap \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 $\cap$\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
+cup\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 $\cup$\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
+dagger\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 $\dagger$\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
+ddagger\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 $\ddagger$\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
+wr\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 $\wr$\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
+bigcirc\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 $\bigcirc$\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
+wedge\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 $\wedge$\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
+vee\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 $\vee$\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="13" columns="2">\r
+<features 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
+oplus\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 $\oplus$\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
+ominus\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 $\ominus$\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
+otimes\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 $\otimes$\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
+oslash\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 $\oslash$\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
+odot\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 $\odot$\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
+amalg\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 $\amalg$\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
+uplus\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 $\uplus$\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
+setminus\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 $\setminus$\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
+sqcap\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 $\sqcap$\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
+sqcup\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 $\sqcup$\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 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 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 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 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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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
+</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 $\jmath$\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 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
+forall\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 $\forall$\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
+exists\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 $\exists$\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
+nexists\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 $\nexists$\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
+emptyset\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 $\emptyset$\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
+varnothing\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 $\varnothing$\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
+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
+</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
+ddag\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 $\ddag$\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
+complement\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
+raisebox{-0.8mm}{\r
+\end_layout\r
+\r
+\end_inset\r
+\r
+\r
+\begin_inset Formula $\complement$\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" 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 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
+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
+\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
+backprime\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 $\backprime$\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
+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
+\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
+triangle\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 $\triangle$\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
+</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
+sphericalangle\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 $\sphericalangle$\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
+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
+</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
+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
+</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 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
+\end_layout\r
+\r
+\end_inset\r
+\r
+\r
+\end_layout\r
+\r
+\begin_layout Standard\r
+\noindent\r
+\align center\r
+\begin_inset Tabular\r
+<lyxtabular version="3" rows="10" columns="2">\r
+<features 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
+flat\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 $\flat$\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
+natural\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 $\natural$\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
+sharp\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 $\sharp$\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
+surd\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 $\surd$\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
+checkmark\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 $\checkmark$\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
+yen\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 $\yen$\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
+pounds\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 $\pounds$\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
+\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
+\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
+\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
+\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 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 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
+\backslash\r
+le\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 $\le$\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" leftline="true" usebox="none">\r
+\begin_inset Text\r
+\r
+\begin_layout Plain Layout\r
+\r
+\backslash\r
+ll\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 $\ll$\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
+prec\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 $\prec$\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
+preceq\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 $\preceq$\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
+subset\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 $\subset$\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
+subseteq\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 $\subseteq$\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
+sqsubseteq\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 $\sqsubseteq$\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
+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
+\begin_inset Formula $\in$\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
+vdash\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
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+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
+\begin_inset Text\r
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+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
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+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
+\begin_inset Text\r
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+mid\r
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+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
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+\begin_inset Text\r
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+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
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+\end_inset\r
+\r
+\r
+\begin_inset space \hfill{}\r
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+\r
+\r
+\begin_inset Tabular\r
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+<features 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
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+</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
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+</cell>\r
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
+\begin_inset Text\r
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+\begin_layout Plain Layout\r
+\begin_inset Formula $=$\r
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+\r
+\r
+\end_layout\r
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+</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
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+\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
+\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
+equiv\r
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+\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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+\end_inset\r
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+</row>\r
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+<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
+sim\r
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+\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
+\begin_inset Formula $\sim$\r
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+\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
+simeq\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 $\simeq$\r
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+\end_layout\r
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+</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
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+\backslash\r
+approx\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 $\approx$\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
+cong\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 $\cong$\r
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+\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
+bowtie\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 $\bowtie$\r
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+\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
+notin\r
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+\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
+\begin_inset Formula $\notin$\r
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+\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
+perp\r
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+\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
+\begin_inset Formula $\perp$\r
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+<row>\r
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
+\begin_inset Text\r
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+\backslash\r
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+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
+\begin_inset Text\r
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+\begin_layout Plain Layout\r
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+\end_layout\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
+asymp\r
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+\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
+\begin_inset Formula $\asymp$\r
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+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
+\begin_inset Text\r
+\r
+\begin_layout Plain Layout\r
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+\backslash\r
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+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
+\begin_inset Text\r
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+\begin_layout Plain Layout\r
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+</row>\r
+<row>\r
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
+\begin_inset Text\r
+\r
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+\r
+\backslash\r
+circeq\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 $\circeq$\r
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+\end_layout\r
+\r
+\end_inset\r
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+</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
+models\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 $\models$\r
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+</row>\r
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+\begin_inset Text\r
+\r
+\begin_layout Plain Layout\r
+\r
+\backslash\r
+widehat=\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 $\widehat{=}$\r
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+\r
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+\end_inset\r
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+</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="17" columns="2">\r
+<features 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
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+\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
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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
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+\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
+<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
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+\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
+\begin_inset Formula $\ge$\r
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+\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
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+\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
+\begin_inset Formula $\gg$\r
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+\end_layout\r
+\r
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+</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
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+\backslash\r
+succ\r
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+\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
+\begin_inset Formula $\succ$\r
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+\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
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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
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+\begin_layout Plain Layout\r
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+\end_layout\r
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+</row>\r
+<row>\r
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
+\begin_inset Text\r
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+\begin_layout Plain Layout\r
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+\backslash\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
+\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
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+\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
+\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
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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 $\sqsupseteq$\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
+ni\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 $\ni$\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
+dashv\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 $\dashv$\r
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+\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
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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 $\frown$\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 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 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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 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 tabularvalignment="middle">\r
+<column alignment="block" valignment="top" width="0">\r
+<column alignment="block" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="block" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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
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+\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
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+\backslash\r
+L\r
+\end_layout\r
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+\end_inset\r
+</cell>\r
+<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
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+\begin_layout Plain Layout\r
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+\begin_inset space \hspace{}\r
+\length 0mm\r
+\end_inset\r
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+`\r
+\begin_inset ERT\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
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+\r
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+\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
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+\begin_inset space \hspace{}\r
+\length 0mm\r
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+`\r
+\begin_inset ERT\r
+status collapsed\r
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+\begin_layout Plain Layout\r
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+\r
+\backslash\r
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+\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 tabularvalignment="middle">\r
+<column alignment="block" valignment="top" width="0">\r
+<column alignment="block" valignment="top" width="0">\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
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+\begin_layout Plain Layout\r
+\begin_inset ERT\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
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+\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
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+\begin_layout Plain Layout\r
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+status collapsed\r
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+\begin_layout Plain Layout\r
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+^e\r
+\end_layout\r
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+\end_inset\r
+\r
+\r
+\end_layout\r
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+\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
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+\begin_layout Plain Layout\r
+\begin_inset ERT\r
+status collapsed\r
+\r
+\begin_layout Plain Layout\r
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+\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
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+\begin_layout Plain Layout\r
+\begin_inset ERT\r
+status collapsed\r
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+\begin_layout Plain Layout\r
+\r
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+\backslash\r
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+\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
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+\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 tabularvalignment="middle">\r
+<column alignment="block" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 islongtable="true" longtabularalignment="center">\r
+<column alignment="left" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="right" valignment="top" width="0">\r
+<column alignment="left" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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 tabularvalignment="middle">\r
+<column alignment="center" valignment="top" width="0">\r
+<column alignment="center" valignment="top" width="0">\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\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
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projects / lyx.git / commitdiff