1 #LyX 1.6.2svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
45 \renewcommand{\equationautorefname}{\hspace{-\abc}}
46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
73 \usepackage[samesize]{cancel}
75 % enables calculation of values,
78 % for multiple table row and column cells
85 % center multirows (e.g. in sec. 13.3)
86 \renewcommand{\multirowsetup}{\centering}
88 % define a color, used in sec.9.3
89 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
91 % declare operators (see sec. 10.4 and sec. 15.2)
92 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
93 \DeclareMathOperator{\sgn}{sgn}
95 \newcommand{\spce}{\textvisiblespace}
97 % example definitions for sec. 20.1
98 \newcommand{\gr}{\Longrightarrow}
99 \newcommand{\us}[1]{\underline{#1}}
100 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
101 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
102 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
104 % example macro from sec. 19.4
105 %\def\tagform@#1{\maketag@@@{|#1|}}
107 % macro from sec. 10.2
108 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
109 \def\mathclap {\mathpalette \mathclapinternal}
110 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
112 % redefine the greyed out note
113 \renewenvironment{lyxgreyedout}
114 {\textcolor{blue}\bgroup}{\egroup}
116 % ------------------------------------
117 % used to check for needed LaTeX packages
120 % check for package eurosym
121 % used for the Euro symbol
123 \IfFileExists{eurosym.sty}
124 {\usepackage[gennarrow]{eurosym}
125 \setboolean{eurosym}{true}}
126 {\setboolean{eurosym}{false}}
128 % needed in sec. 22.4
129 % check for package braket
131 \IfFileExists{braket.sty}
133 \setboolean{braket}{true}}
134 {\setboolean{braket}{false}}
136 % needed in sec. 22.10
137 % check for package upgreek
139 \IfFileExists{upgreek.sty}
140 {\usepackage{upgreek}
141 \setboolean{upgreek}{true}}
142 {\setboolean{upgreek}{false}}
144 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
145 \use_default_options false
150 \font_typewriter default
151 \font_default_family default
161 \pdf_title "LyX's Math Manual"
162 \pdf_author "LyX Team, Uwe Stöhr"
163 \pdf_subject "LyX-documentation about math"
164 \pdf_keywords "LyX, Mathed"
166 \pdf_bookmarksnumbered true
167 \pdf_bookmarksopen true
168 \pdf_bookmarksopenlevel 1
169 \pdf_breaklinks false
173 \pdf_pdfusetitle false
174 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
181 \paperorientation portrait
184 \paragraph_separation skip
186 \quotes_language english
189 \paperpagestyle plain
193 \tracking_changes false
194 \output_changes false
202 LyX's detailed Math manual
210 \begin_layout Plain Layout
212 If you have comments or error corrections, please send them to the LyX Documenta
216 \begin_inset CommandInset href
218 name "lyx-docs@lists.lyx.org"
219 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
230 \begin_inset Note Note
233 \begin_layout Plain Layout
240 \begin_inset Newline newline
244 \begin_inset Newline newline
252 \begin_layout Standard
253 \begin_inset CommandInset toc
254 LatexCommand tableofcontents
261 \begin_layout Standard
262 \begin_inset Note Note
265 \begin_layout Plain Layout
266 To export this document to PDF, PS, or DVI the LaTeX-packages
279 If they are not installed you can export the document anyway but the sections
280 where the packages are required won't appear in the output.
283 \begin_layout Plain Layout
284 The latest PDF-version of this document can be found here:
285 \begin_inset Newline newline
290 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
298 \begin_layout Standard
299 \begin_inset Newpage newpage
305 \begin_layout Section
309 \begin_layout Standard
310 This document explains LyX's math features and is furthermore a collection
311 of LaTeX-commands used for mathematical characters and constructs.
312 The explanations are designed for the usage of commands.
313 It is therefore required that you have read the section
324 \begin_layout Standard
325 Most of the characters and many constructs explained in this manual are
326 also accessible via the menu
330 \SpecialChar \menuseparator
346 But everybody who has to write lots of formulas will notice that it is
347 much faster to use commands instead of the math toolbar.
348 Therefore this manual is focused on commands but also mentions the correspondin
349 g toolbar buttons when available.
352 \begin_layout Standard
353 If not specially mentioned the commands are only available within formulas.
354 To be able to use all commands explained in this document, the option
358 must be used in the document settings (menu
360 Document\SpecialChar \menuseparator
361 Settings\SpecialChar \menuseparator
372 \begin_layout Plain Layout
375 Use AMS math package automatically
381 \begin_layout Plain Layout
390 -math when math constructs are found that are supported by LyX.
398 \begin_layout Standard
399 This document doesn't list all
403 \begin_layout Plain Layout
416 \begin_layout Plain Layout
421 \begin_layout Plain Layout
430 -math commands is in the file
433 \begin_inset CommandInset href
436 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
442 , which is part of every LaTeX standard installation.
447 for lucidity reasons.
450 \begin_layout Section
454 \begin_layout Standard
455 To create an inline formula
459 \begin_layout Plain Layout
465 that is embedded into a text line, use one of the shortcuts
471 or the toolbar button
472 \begin_inset Graphics
473 filename ../images/math-mode.png
479 \begin_inset Newline newline
482 To create a display style formula
486 \begin_layout Plain Layout
487 Formula ! display style
492 that will appear bigger and in an own paragraph, use one of these shortcuts:
502 \begin_layout Standard
503 To change a display style formula to an inline formula, set the cursor into
504 the formula and use one of the shortcuts
512 Edit\SpecialChar \menuseparator
513 Math\SpecialChar \menuseparator
517 The same way is used to change an inline formula to a display style formula.
520 \begin_layout Standard
521 To display parts of an inline formula in the size of a display style formula,
530 \begin_layout Plain Layout
541 Then a new blue box appears in which the desired formula part is inserted.
544 \begin_layout Standard
545 Only inline formulas are allowed inside tables.
548 \begin_layout Standard
553 can be turned on in the menu
555 View\SpecialChar \menuseparator
559 When you click there on
560 \begin_inset Quotes eld
564 \begin_inset Quotes erd
567 the toolbar will be shown permanently at the bottom; this state is visualized
572 menu with a checkmark.
573 When you click in this state again on
574 \begin_inset Quotes eld
578 \begin_inset Quotes erd
589 is only shown when the cursor is within a formula; this state is visualized
590 by the renaming of the menu entry from
591 \begin_inset Quotes eld
595 \begin_inset Quotes erd
599 \begin_inset Quotes eld
607 \begin_inset Quotes erd
613 \begin_layout Standard
618 \begin_layout Plain Layout
624 is invoked by pressing the toolbar button
625 \begin_inset Graphics
626 filename ../images/ert-insert.png
633 Insert\SpecialChar \menuseparator
638 \begin_layout Plain Layout
654 \begin_inset Note Note
657 \begin_layout Plain Layout
658 In LyX there are three
659 \begin_inset Quotes eld
663 \begin_inset Quotes erd
666 that appear in the output with sub- and superscript letters: TeX, LaTeX,
670 \begin_layout Plain Layout
671 To avoid that these names are recognized as proper names, a TeX-brace pair
680 \begin_layout Standard
681 To change the LaTeX-preamble
685 \begin_layout Plain Layout
693 Document\SpecialChar \menuseparator
694 Settings\SpecialChar \menuseparator
699 \begin_layout Plain Layout
715 \begin_layout Standard
716 To edit matrices, case differentiations, and multiline formulas subsequently,
719 Edit\SpecialChar \menuseparator
724 Edit\SpecialChar \menuseparator
726 \begin_inset space \thinspace{}
730 \begin_inset space \thinspace{}
740 When lines and columns are swapped via the menu, the column or line where
741 the cursor is in is exchanged with the column to the right or the line
743 Is the cursor in the last column or row, the exchange is done with the
744 column to the left or the line above.
747 \begin_layout Standard
748 To write text in formulas
752 \begin_layout Plain Layout
753 For multiline formulas the command
760 \begin_inset CommandInset ref
762 reference "sub:Text-in-multiline"
779 \begin_layout Plain Layout
789 \begin_layout Plain Layout
796 This mode is invoked with the the shortcut
802 or by the insertion of the command
810 \begin_layout Plain Layout
821 The text appears black in LyX and can therefore be distinguished from the
822 other formula parts that appear blue.
823 In the output mathematical text is set upright, in contrary to other formula
827 \begin_layout Subsection*
831 \begin_layout Standard
832 Most of the LaTeX-commands for math constructs have the following scheme:
835 \begin_layout Standard
851 \begin_layout Standard
852 A command starts always with a backslash
853 \begin_inset Quotes gld
863 \begin_inset Quotes grd
867 To omit optional arguments, also omit the associated brackets.
868 The braces around the required arguments are named in this document as
873 \begin_layout Plain Layout
880 If you add in a formula a left brace to a command name, LyX creates automatical
882 In all other cases TeX-braces are created in formulas with the command
890 TeX-braces appear red in LyX, in contrary to normal braces that appear
892 In TeX-mode no command is needed to get TeX-braces.
893 TeX-braces don't appear in the output.
896 \begin_layout Standard
897 When commands without arguments, like commands for symbols are entered in
898 TeX-mode, a space character must
902 be behind the command to end it.
903 This space doesn't appear in the output.
904 When the space should appear in the output, the space must be followed
905 by a protected space in normal text.
908 \begin_layout Standard
909 A protected space is inserted with
912 arg "space-insert protected"
918 \begin_layout Subsection*
919 \begin_inset Newpage newpage
925 \begin_layout Itemize
930 \begin_layout Plain Layout
931 This visible space character can be created with the command
941 \begin_layout Plain Layout
949 , inserted in TeX-mode.
958 \begin_layout Plain Layout
971 denotes a space character to be input.
974 \begin_layout Itemize
976 \begin_inset Formula $\to$
979 denotes the usage of the corresponding arrow key on the keyboard.
982 \begin_layout Subsection*
986 \begin_layout Standard
988 \begin_inset Float table
994 \begin_layout Plain Layout
998 \begin_layout Plain Layout
999 \begin_inset CommandInset label
1001 name "tab:Available-units"
1013 \begin_layout Plain Layout
1015 \begin_inset Tabular
1016 <lyxtabular version="3" rows="13" columns="2">
1018 <column alignment="center" valignment="top" width="0">
1019 <column alignment="center" valignment="top" width="0">
1021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1024 \begin_layout Plain Layout
1030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1033 \begin_layout Plain Layout
1041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1044 \begin_layout Plain Layout
1050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1053 \begin_layout Plain Layout
1061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1064 \begin_layout Plain Layout
1070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1073 \begin_layout Plain Layout
1081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1084 \begin_layout Plain Layout
1090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1093 \begin_layout Plain Layout
1095 \begin_inset space \thinspace{}
1099 \begin_inset space \thinspace{}
1109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1112 \begin_layout Plain Layout
1118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1121 \begin_layout Plain Layout
1123 \begin_inset space \thinspace{}
1127 \begin_inset space \thinspace{}
1137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1140 \begin_layout Plain Layout
1146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1149 \begin_layout Plain Layout
1151 \begin_inset space \thinspace{}
1155 \begin_inset space \thinspace{}
1165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1168 \begin_layout Plain Layout
1174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1177 \begin_layout Plain Layout
1179 \begin_inset space \thinspace{}
1183 \begin_inset space \thinspace{}
1193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1196 \begin_layout Plain Layout
1202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1205 \begin_layout Plain Layout
1207 \begin_inset space \thinspace{}
1211 \begin_inset space \thinspace{}
1221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1224 \begin_layout Plain Layout
1230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1233 \begin_layout Plain Layout
1235 \begin_inset space \thinspace{}
1239 \begin_inset Formula $\approx$
1243 \begin_inset space \thinspace{}
1253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1256 \begin_layout Plain Layout
1262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1265 \begin_layout Plain Layout
1267 \begin_inset space \thinspace{}
1271 \begin_inset space \thinspace{}
1281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1284 \begin_layout Plain Layout
1290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1293 \begin_layout Plain Layout
1297 \begin_inset Quotes eld
1303 \begin_inset Quotes erd
1313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1316 \begin_layout Plain Layout
1322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1325 \begin_layout Plain Layout
1327 \begin_inset Quotes eld
1335 \begin_inset Quotes erd
1345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1348 \begin_layout Plain Layout
1354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1357 \begin_layout Plain Layout
1359 \begin_inset space \thinspace{}
1363 \begin_inset Formula $\nicefrac{1}{18}$
1367 \begin_inset space \thinspace{}
1388 \begin_layout Standard
1389 \begin_inset Newpage newpage
1395 \begin_layout Section
1399 \begin_layout Subsection
1404 \begin_layout Plain Layout
1414 \begin_layout Plain Layout
1424 \begin_layout Plain Layout
1429 \begin_layout Plain Layout
1440 \begin_layout Plain Layout
1456 \begin_layout Plain Layout
1461 \begin_layout Plain Layout
1472 \begin_layout Plain Layout
1487 \begin_layout Standard
1488 Indices are created with an underscore
1489 \begin_inset Quotes eld
1493 \begin_inset Quotes erd
1496 or via the math toolbar button
1497 \begin_inset Graphics
1498 filename ../images/math-subscript.png
1503 , exponents with a caret
1504 \begin_inset Quotes eld
1508 \begin_inset Quotes erd
1511 or via the math toolbar button
1512 \begin_inset Graphics
1513 filename ../images/math-superscript.png
1521 \begin_layout Standard
1523 \begin_inset Tabular
1524 <lyxtabular version="3" rows="4" columns="2">
1526 <column alignment="center" valignment="top" width="0pt">
1527 <column alignment="center" valignment="top" width="0pt">
1529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1532 \begin_layout Plain Layout
1538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1541 \begin_layout Plain Layout
1543 \begin_inset Note Note
1546 \begin_layout Plain Layout
1553 is only used as spacer.
1565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1568 \begin_layout Plain Layout
1574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1577 \begin_layout Plain Layout
1578 \begin_inset Formula $B_{V}$
1588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1591 \begin_layout Plain Layout
1597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1600 \begin_layout Plain Layout
1601 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1614 \begin_layout Plain Layout
1619 \begin_layout Plain Layout
1633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1636 \begin_layout Plain Layout
1637 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1653 \begin_layout Standard
1654 As the caret is in some languages an accent, vowels will be accentuated
1655 in this case and not set as exponents
1659 \begin_layout Plain Layout
1660 Depending on the used keyboard settings this can also happen for other character
1667 To get in this case exponents, press
1671 after the caret as in the last example.
1674 \begin_layout Subsection
1676 \begin_inset CommandInset label
1678 name "sub:Fractions"
1686 \begin_layout Plain Layout
1695 \begin_layout Standard
1696 Fractions are generated with the command
1706 \begin_layout Plain Layout
1714 or via the math toolbar button
1715 \begin_inset Graphics
1716 filename ../images/math/frac.png
1722 The font size is adjusted automatically, depending on whether the fraction
1723 is in an inline or display style formula.
1724 With the math toolbar button
1725 \begin_inset Graphics
1726 filename ../images/math/frac-square.png
1731 you can select different fraction types.
1734 \begin_layout Standard
1743 \begin_layout Plain Layout
1753 a fraction can be created that has in any case the size of a display style
1763 \begin_layout Plain Layout
1773 the fraction appears always with the size of an inline formula.
1777 \begin_layout Standard
1778 A line with the fraction
1779 \begin_inset Formula $\frac{1}{2}$
1782 that was created with the command
1791 \begin_layout Standard
1792 A line with the fraction
1793 \begin_inset Formula $\dfrac{1}{2}$
1796 that was created with the command
1805 \begin_layout Standard
1807 \begin_inset Tabular
1808 <lyxtabular version="3" rows="4" columns="2">
1810 <column alignment="center" valignment="top" width="0pt">
1811 <column alignment="center" valignment="top" width="0pt">
1813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1816 \begin_layout Plain Layout
1822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1825 \begin_layout Plain Layout
1827 \begin_inset Note Note
1830 \begin_layout Plain Layout
1837 is only used as spacer.
1849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1852 \begin_layout Plain Layout
1859 \begin_layout Plain Layout
1869 \begin_inset Formula $\downarrow$
1877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1880 \begin_layout Plain Layout
1881 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1894 \begin_layout Plain Layout
1901 \begin_layout Plain Layout
1911 \begin_inset Formula $\downarrow$
1919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1922 \begin_layout Plain Layout
1923 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1936 \begin_layout Plain Layout
1943 \begin_layout Plain Layout
1956 \begin_layout Plain Layout
1971 \begin_layout Plain Layout
1981 \begin_inset Formula $\downarrow$
1985 \begin_inset Formula $\downarrow\downarrow$
1993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1996 \begin_layout Plain Layout
1997 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2013 \begin_layout Standard
2014 \begin_inset VSpace bigskip
2018 \begin_inset Newpage newpage
2021 For nested fractions the command
2031 \begin_layout Plain Layout
2041 \begin_inset VSpace -3mm
2047 \begin_layout Standard
2048 \begin_inset Formula \begin{align*}
2049 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2050 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2057 \begin_layout Standard
2058 The command for the example above is:
2061 \begin_layout Standard
2067 \begin_inset Formula $\to$
2077 \begin_inset Formula $\to$
2083 \begin_inset Formula $\to\to$
2091 \begin_layout Standard
2092 \begin_inset VSpace medskip
2098 \begin_layout Standard
2105 sets the fraction always in the size of a displayed formula, also when
2106 it is part of another fraction.
2113 has the following command scheme:
2116 \begin_layout Standard
2121 cfrac[numerator position]{numerator}{denominator}
2124 \begin_layout Standard
2125 The numerator position can be
2138 l or r aligns the numerator to the left or right, resp.
2139 \begin_inset space ~
2142 with the fraction stroke.
2147 or no position is given, the numerator appears centered.
2148 These fractions demonstrate the different alignments:
2149 \begin_inset Newline newline
2155 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2159 \begin_inset Formula $\cfrac{A}{B+C}$
2163 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2169 \begin_layout Standard
2170 \begin_inset VSpace medskip
2173 It is often advantageous to combine
2186 \begin_inset Formula \[
2187 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2194 \begin_layout Standard
2195 For inline fractions with a sloped fraction stroke you can use the command
2206 \begin_layout Plain Layout
2215 \begin_inset Formula $\nicefrac{5}{31}$
2228 \begin_layout Plain Layout
2237 \begin_inset Formula $\unitfrac{5}{31}$
2240 There is furthermore the command
2246 that offers to write a fraction in combination with a number:
2247 \begin_inset Formula $\unitfrac[2]{1}{3}$
2251 \begin_inset Newline newline
2260 is not a real LaTeX command but the command
2261 \begin_inset Newline newline
2268 unitfrac[number]{numerator}{denominator}
2270 , therefore you cannot use it in TeX code.
2273 \begin_layout Standard
2274 How to define own fractions where the fraction stroke can be changed, is
2276 \begin_inset CommandInset ref
2278 reference "sub:Self-defined-Fractions"
2285 \begin_layout Subsection
2290 \begin_layout Plain Layout
2299 \begin_layout Standard
2300 Square roots are created with
2310 \begin_layout Plain Layout
2318 or the math toolbar button
2319 \begin_inset Graphics
2320 filename ../images/math/sqrt.png
2325 , all other roots with the command
2335 \begin_layout Plain Layout
2343 or with the math toolbar button
2344 \begin_inset Graphics
2345 filename ../images/math/root.png
2353 \begin_layout Standard
2355 \begin_inset Tabular
2356 <lyxtabular version="3" rows="3" columns="2">
2358 <column alignment="center" valignment="top" width="0pt">
2359 <column alignment="center" valignment="top" width="0pt">
2361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2364 \begin_layout Plain Layout
2370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2373 \begin_layout Plain Layout
2375 \begin_inset Note Note
2378 \begin_layout Plain Layout
2385 is only used as spacer.
2397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2400 \begin_layout Plain Layout
2407 \begin_layout Plain Layout
2421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2424 \begin_layout Plain Layout
2425 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2435 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2438 \begin_layout Plain Layout
2445 \begin_layout Plain Layout
2455 \begin_inset Formula $\downarrow$
2463 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2466 \begin_layout Plain Layout
2467 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2483 \begin_layout Standard
2484 A square root can also be created with
2490 when the root index field is left empty.
2493 \begin_layout Standard
2494 With certain indices the distance to the root is too small, like in this
2496 \begin_inset Formula $\sqrt[\beta]{B}$
2500 \begin_inset Newline newline
2504 \begin_inset Formula $\beta$
2508 To avoid this, the commands
2518 \begin_layout Plain Layout
2536 \begin_layout Plain Layout
2544 are used with the following scheme:
2547 \begin_layout Standard
2561 \begin_layout Standard
2562 Distance is the number of Big Points (unit bp;
2563 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2566 ), that the index should be moved to the left or top, resp..
2567 The commands are written to the index.
2568 This way the command
2569 \begin_inset Newline newline
2579 \begin_inset Formula $\to$
2585 \begin_inset Formula $\to$
2594 \begin_layout Plain Layout
2604 \begin_inset Formula $\to$
2608 \begin_inset Newline newline
2613 produces a correct typeset formula:
2614 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2620 \begin_layout Subsection
2621 Binomial Coefficients
2625 \begin_layout Plain Layout
2626 Binomial coefficients
2634 \begin_layout Standard
2635 Binomial coefficients are inserted with the command
2645 \begin_layout Plain Layout
2653 or with the submenu of the math toolbar button
2654 \begin_inset Graphics
2655 filename ../images/math/frac-square.png
2661 Analog to fractions (
2681 \begin_layout Plain Layout
2701 \begin_layout Plain Layout
2710 For other brackets around binomial coeficients there are the commands
2720 \begin_layout Plain Layout
2738 \begin_layout Plain Layout
2749 \begin_layout Standard
2751 \begin_inset Tabular
2752 <lyxtabular version="3" rows="6" columns="2">
2754 <column alignment="center" valignment="top" width="0pt">
2755 <column alignment="center" valignment="top" width="0pt">
2757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2760 \begin_layout Plain Layout
2766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2769 \begin_layout Plain Layout
2771 \begin_inset Note Note
2774 \begin_layout Plain Layout
2781 is only used as spacer.
2793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2796 \begin_layout Plain Layout
2803 \begin_layout Plain Layout
2813 \begin_inset Formula $\downarrow$
2821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2824 \begin_layout Plain Layout
2825 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2838 \begin_layout Plain Layout
2845 \begin_layout Plain Layout
2855 \begin_inset Formula $\downarrow$
2863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2866 \begin_layout Plain Layout
2867 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2880 \begin_layout Plain Layout
2887 \begin_layout Plain Layout
2897 \begin_inset Formula $\downarrow$
2905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2908 \begin_layout Plain Layout
2909 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2922 \begin_layout Plain Layout
2929 \begin_layout Plain Layout
2939 \begin_inset Formula $\downarrow$
2947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2950 \begin_layout Plain Layout
2951 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2964 \begin_layout Plain Layout
2971 \begin_layout Plain Layout
2981 \begin_inset Formula $\downarrow$
2989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2992 \begin_layout Plain Layout
2993 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3009 \begin_layout Subsection
3010 Case Differentiations
3014 \begin_layout Plain Layout
3015 Case differentiations
3023 \begin_layout Standard
3025 \begin_inset Tabular
3026 <lyxtabular version="3" rows="3" columns="2">
3028 <column alignment="center" valignment="top" width="0pt">
3029 <column alignment="center" valignment="top" width="0pt">
3031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3034 \begin_layout Plain Layout
3040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3043 \begin_layout Plain Layout
3051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3054 \begin_layout Plain Layout
3061 \begin_layout Plain Layout
3071 \begin_inset Formula $\to$
3078 \begin_layout Plain Layout
3091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3094 \begin_layout Plain Layout
3095 \begin_inset Formula $\begin{cases}
3106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3109 \begin_layout Plain Layout
3116 \begin_layout Plain Layout
3128 arg "newline-insert newline"
3136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3139 \begin_layout Plain Layout
3140 \begin_inset Formula $\begin{cases}
3141 A & \textrm{for }x>0\\
3142 B & \textrm{for }x=0\end{cases}$
3158 \begin_layout Standard
3165 or the usage of the math toolbar button
3166 \begin_inset Graphics
3167 filename ../images/math/cases.png
3172 you can create new lines with the shortcut
3175 arg "newline-insert newline"
3178 or the table toolbar button
3179 \begin_inset Graphics
3180 filename ../images/tabular-feature_append-row.png
3188 \begin_layout Standard
3195 is also available via the menu
3197 Insert\SpecialChar \menuseparator
3198 Math\SpecialChar \menuseparator
3204 \begin_layout Subsection
3209 \begin_layout Plain Layout
3218 \begin_layout Standard
3229 \begin_layout Plain Layout
3237 every character can be displayed canceled.
3238 The characters are quasi accentuated by a slash.
3241 \begin_layout Standard
3243 \begin_inset Tabular
3244 <lyxtabular version="3" rows="4" columns="2">
3246 <column alignment="center" valignment="top" width="0pt">
3247 <column alignment="center" valignment="top" width="0pt">
3249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3252 \begin_layout Plain Layout
3258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3261 \begin_layout Plain Layout
3269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3272 \begin_layout Plain Layout
3280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3283 \begin_layout Plain Layout
3284 \begin_inset Formula $\not=$
3294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3297 \begin_layout Plain Layout
3307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3310 \begin_layout Plain Layout
3311 \begin_inset Formula $\not\le$
3321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3324 \begin_layout Plain Layout
3334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3337 \begin_layout Plain Layout
3338 \begin_inset Formula $\not\parallel$
3354 \begin_layout Standard
3355 The last example shows, that not all negations look good.
3356 Therefore there are for some negations special commands (see
3357 \begin_inset CommandInset ref
3359 reference "sub:Mathematical-Symbols"
3364 \begin_inset CommandInset ref
3366 reference "sec:Relations"
3373 \begin_layout Subsection
3375 \begin_inset CommandInset label
3377 name "sub:Placeholders"
3385 \begin_layout Plain Layout
3395 \begin_layout Plain Layout
3396 Chemical characters ! Isotopes
3405 \begin_layout Plain Layout
3410 \begin_layout Plain Layout
3421 \begin_layout Plain Layout
3436 \begin_layout Standard
3438 \begin_inset space \thinspace{}
3442 \begin_inset space \space{}
3449 \begin_layout Plain Layout
3450 More about chemical symbols is written in
3451 \begin_inset CommandInset ref
3453 reference "sub:Chemical-Symbols-and"
3462 the following problem occurs:
3465 \begin_layout Standard
3467 \begin_inset Tabular
3468 <lyxtabular version="3" rows="2" columns="2">
3470 <column alignment="center" valignment="top" width="0pt">
3471 <column alignment="center" valignment="top" width="0pt">
3473 <cell alignment="center" valignment="top" usebox="none">
3476 \begin_layout Plain Layout
3477 Indices created with sub- and superscripts:
3482 <cell alignment="center" valignment="top" usebox="none">
3485 \begin_layout Plain Layout
3486 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3496 <cell alignment="center" valignment="top" usebox="none">
3499 \begin_layout Plain Layout
3505 <cell alignment="center" valignment="top" usebox="none">
3508 \begin_layout Plain Layout
3509 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3523 \begin_inset Note Note
3526 \begin_layout Plain Layout
3533 is only used as spacer.
3541 \begin_layout Standard
3542 The shorter index is by default placed below or above the first character
3543 of the longer index.
3544 To avoid this there is the command
3554 \begin_layout Plain Layout
3562 or the math toolbar button
3563 \begin_inset space \thinspace{}
3570 \begin_layout Plain Layout
3571 can be found in the submenu of the toolbar button
3572 \begin_inset Graphics
3573 filename ../images/math/space.png
3584 \begin_inset Graphics
3585 filename ../images/math/phantom.png
3590 that creates one or more phantom characters.
3597 a small blue box appears that is superposed with two red arrows.
3598 The arrows indicate that the complete width and height of the box content
3599 will be created as placeholder.
3600 Phantom characters are accordingly placeholders with the size of the characters.
3603 \begin_layout Standard
3605 \begin_inset Tabular
3606 <lyxtabular version="3" rows="4" columns="2">
3608 <column alignment="center" valignment="top" width="0">
3609 <column alignment="center" valignment="top" width="0">
3611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3614 \begin_layout Plain Layout
3620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3623 \begin_layout Plain Layout
3625 \begin_inset Note Note
3628 \begin_layout Plain Layout
3635 is only used as spacer.
3647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3650 \begin_layout Plain Layout
3655 \begin_layout Plain Layout
3670 \begin_layout Plain Layout
3680 \begin_inset Formula $\to$
3687 \begin_layout Plain Layout
3701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3704 \begin_layout Plain Layout
3705 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3718 \begin_layout Plain Layout
3723 \begin_layout Plain Layout
3738 \begin_layout Plain Layout
3748 \begin_inset Formula $\to$
3755 \begin_layout Plain Layout
3769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3772 \begin_layout Plain Layout
3773 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3786 \begin_layout Plain Layout
3793 \begin_layout Plain Layout
3808 \begin_layout Plain Layout
3818 \begin_inset Formula $\to$
3825 \begin_layout Plain Layout
3839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3842 \begin_layout Plain Layout
3843 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3859 \begin_layout Standard
3860 Furthermore there are the commands
3870 \begin_layout Plain Layout
3879 \begin_inset space ~
3883 \begin_inset Graphics
3884 filename ../images/math/vphantom.png
3899 \begin_layout Plain Layout
3908 \begin_inset space ~
3912 \begin_inset Graphics
3913 filename ../images/math/hphantom.png
3925 creates only space for the maximal height of the characters in the box
3926 but not for its width.
3933 creates only space for the width of the box content.
3934 Therefore the boxes of both commands have only one red arrow.
3937 \begin_layout Standard
3948 \begin_layout Plain Layout
3963 space for the height of the integral sign,
3967 \begin_layout Plain Layout
3974 creates an integral sign, see
3975 \begin_inset CommandInset ref
3977 reference "sub:Big-Operators"
3986 because this is the larger character.
3987 An example application is in
3988 \begin_inset CommandInset ref
3990 reference "sub:Multiline-Brackets"
3997 \begin_layout Subsection
4002 \begin_layout Plain Layout
4012 \begin_layout Plain Layout
4013 Formula ! underlined
4021 \begin_layout Standard
4023 \begin_inset Tabular
4024 <lyxtabular version="3" rows="4" columns="2">
4026 <column alignment="center" valignment="top" width="0pt">
4027 <column alignment="center" valignment="top" width="0pt">
4029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4032 \begin_layout Plain Layout
4038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4041 \begin_layout Plain Layout
4043 \begin_inset Note Note
4046 \begin_layout Plain Layout
4053 is only used as spacer.
4065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4068 \begin_layout Plain Layout
4075 \begin_layout Plain Layout
4088 \begin_layout Plain Layout
4101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4104 \begin_layout Plain Layout
4105 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4118 \begin_layout Plain Layout
4125 \begin_layout Plain Layout
4138 \begin_layout Plain Layout
4151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4154 \begin_layout Plain Layout
4155 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4168 \begin_layout Plain Layout
4175 \begin_layout Plain Layout
4190 \begin_layout Plain Layout
4204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4207 \begin_layout Plain Layout
4208 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4224 \begin_layout Standard
4225 In the last example it doesn't matter if first
4240 \begin_layout Standard
4241 To double underline e.
4242 \begin_inset space \thinspace{}
4246 \begin_inset space \space{}
4258 \begin_layout Standard
4259 It is possible to place up to 6 lines above or below characters.
4262 \begin_layout Standard
4263 \begin_inset VSpace bigskip
4266 Custom lines can be created using the command
4276 \begin_layout Plain Layout
4284 which has the following scheme:
4287 \begin_layout Standard
4292 rule[vertical offset]{length}{thickness}
4295 \begin_layout Standard
4296 The optional vertical offset shifts the line upwards (or downwards, when
4297 the value is negative).
4299 \begin_inset CommandInset ref
4301 reference "tab:Available-units"
4305 can be used for the values.
4306 Here are two example lines created with the commands
4307 \begin_inset Newline newline
4314 rule[-2ex]{3cm}{2pt}
4325 \begin_layout Standard
4327 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4333 \begin_layout Standard
4340 can also be used for text when it is inserted in TeX-mode.
4343 \begin_layout Subsection
4345 \begin_inset CommandInset label
4355 \begin_layout Plain Layout
4364 \begin_layout Standard
4365 There are different types of ellipses available.
4369 \begin_layout Plain Layout
4370 In the math toolbar in the submenu of the button
4371 \begin_inset Graphics
4372 filename ../images/math/ldots.png
4382 For listings dots at the baseline are used (
4392 \begin_layout Plain Layout
4400 ), while for operations dots are needed that are on the same height as the
4411 \begin_layout Plain Layout
4420 When using the command
4430 \begin_layout Plain Layout
4438 , LaTeX decides on the basis of the next character what type is used.
4441 \begin_layout Standard
4443 \begin_inset Tabular
4444 <lyxtabular version="3" rows="8" columns="2">
4446 <column alignment="center" valignment="top" width="0pt">
4447 <column alignment="center" valignment="top" width="0pt">
4449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4452 \begin_layout Plain Layout
4458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4461 \begin_layout Plain Layout
4469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4472 \begin_layout Plain Layout
4477 \begin_layout Plain Layout
4492 \begin_layout Plain Layout
4506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4509 \begin_layout Plain Layout
4510 \begin_inset Formula $A_{1},\dots,A_{n}$
4520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4523 \begin_layout Plain Layout
4528 \begin_layout Plain Layout
4543 \begin_layout Plain Layout
4557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4560 \begin_layout Plain Layout
4561 \begin_inset Formula $A_{1}+\dots+A_{n}$
4571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4574 \begin_layout Plain Layout
4579 \begin_layout Plain Layout
4594 \begin_layout Plain Layout
4608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4611 \begin_layout Plain Layout
4612 \begin_inset Formula $A_{1},\ldots,A_{n}$
4622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4625 \begin_layout Plain Layout
4630 \begin_layout Plain Layout
4645 \begin_layout Plain Layout
4659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4662 \begin_layout Plain Layout
4663 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4676 \begin_layout Plain Layout
4684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4687 \begin_layout Plain Layout
4688 \begin_inset Formula $\vdots$
4698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4701 \begin_layout Plain Layout
4709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4712 \begin_layout Plain Layout
4713 \begin_inset Formula $\ddots$
4723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4726 \begin_layout Plain Layout
4728 \begin_inset space \thinspace{}
4731 matrix with the different dots
4736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4739 \begin_layout Plain Layout
4740 \begin_inset Formula $\begin{array}{ccc}
4741 A_{11} & \cdots & A_{1m}\\
4742 \vdots & \ddots & \vdots\\
4743 A_{n1} & \cdots & A_{nm}\end{array}$
4759 \begin_layout Standard
4760 The ellipses available in menu
4762 Insert\SpecialChar \menuseparator
4764 \begin_inset space ~
4778 \begin_layout Standard
4779 \begin_inset VSpace medskip
4782 Specially for matrices there are ellipses that span over several columns.
4783 They are created with the command
4793 \begin_layout Plain Layout
4801 , that has the following scheme:
4804 \begin_layout Standard
4809 hdotsfor[distance]{number of columns}
4812 \begin_layout Standard
4813 The number of columns specifies how many columns should be spanned.
4814 Distance is a factor for the distance between the dots.
4817 \begin_layout Standard
4818 In the following matrix the command
4824 was inserted in the first box of the second line, to get an ellipsis with
4825 a dot distance twice as long as with the command
4832 \begin_inset Formula \[
4833 \left(\begin{array}{cccc}
4836 q & w & e & r\end{array}\right)\]
4840 Note that the matrix fields that should be spanned must be empty, otherwise
4841 you get LaTeX-errors.
4844 \begin_layout Standard
4845 \begin_inset VSpace bigskip
4848 Furthermore you can fill with the command
4858 \begin_layout Plain Layout
4866 the rest of a line with dots.
4867 The effect of these commands is the same like with
4874 \begin_inset CommandInset ref
4876 reference "sub:Variable-Space"
4883 \begin_layout Standard
4884 For example the command
4892 \begin_layout Plain Layout
4906 \begin_layout Standard
4907 \begin_inset Formula $A\dotfill B$
4913 \begin_layout Standard
4920 there is for a line the command
4930 \begin_layout Plain Layout
4941 \begin_layout Standard
4942 \begin_inset Formula $A\hrulefill B$
4948 \begin_layout Standard
4949 To use the commands for text, they have to be inserted in TeX-mode.
4952 \begin_layout Section
4954 \begin_inset CommandInset label
4964 \begin_layout Plain Layout
4973 \begin_layout Standard
4974 Matrices can be inserted via the math toolbar button
4975 \begin_inset Graphics
4976 filename ../images/dialog-show_mathmatrix.png
4983 Insert\SpecialChar \menuseparator
4984 Math\SpecialChar \menuseparator
4988 You will be asked for the number of matrix columns and rows, and the alignment.
4989 The vertical alignment is hereby only of importance for matrices in inline
4993 \begin_layout Standard
4994 The first matrix is top
4995 \begin_inset Formula $\begin{array}[t]{cccc}
4998 C & F & I & L\end{array}$
5002 \begin_inset Formula $\begin{array}{cccc}
5005 C & F & I & L\end{array}$
5008 , and the third bottom
5009 \begin_inset Formula $\begin{array}[b]{cccc}
5012 C & F & I & L\end{array}$
5018 \begin_layout Standard
5019 The horizontal alignment specifies how the column entries should be aligned.
5020 It is set by entering a letter for every column.
5025 denotes left aligned,
5034 To create for example a 4
5039 \begin_inset space ~
5042 matrix where the first column is left aligned, the second and third are
5043 centered, and the last one is right aligned, one enters for the horizontal
5049 Normally are in a matrix all columns centered, therefore the default is
5050 for every column is a
5057 \begin_layout Standard
5058 Horizontal alignment:
5061 \begin_layout Standard
5067 \begin_inset Formula $\begin{array}{lll}
5070 C & F & 10000\end{array}$
5078 \begin_inset Formula $\begin{array}{ccc}
5081 C & F & 10000\end{array}$
5089 \begin_inset Formula $\begin{array}{rrr}
5092 C & F & 10000\end{array}$
5098 \begin_layout Standard
5099 To add or delete rows and columns subsequently, the math toolbar buttons
5101 \begin_inset Graphics
5102 filename ../images/tabular-feature_append-row.png
5108 \begin_inset Graphics
5109 filename ../images/tabular-feature_delete-row.png
5115 \begin_inset space \thinspace{}
5120 Edit\SpecialChar \menuseparator
5124 New rows can also be created with
5127 arg "newline-insert newline"
5133 \begin_layout Standard
5134 \begin_inset VSpace bigskip
5137 Parentheses around a matrix can can either be created with the commands
5148 \begin_layout Plain Layout
5166 \begin_layout Plain Layout
5177 \begin_inset space ~
5183 \begin_inset CommandInset ref
5185 reference "sub:Automatic-Bracket-Size"
5189 , or by using the following commands:
5190 \begin_inset VSpace medskip
5196 \begin_layout Standard
5197 \begin_inset space \hfill{}
5201 \begin_inset Tabular
5202 <lyxtabular version="3" rows="4" columns="2">
5204 <column alignment="center" valignment="top" width="0">
5205 <column alignment="center" valignment="top" width="0">
5207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5210 \begin_layout Plain Layout
5216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5219 \begin_layout Plain Layout
5221 \begin_inset Note Note
5224 \begin_layout Plain Layout
5231 is only used as spacer.
5243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5246 \begin_layout Plain Layout
5253 \begin_layout Plain Layout
5267 \begin_inset space \thinspace{}
5275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5278 \begin_layout Plain Layout
5279 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5280 0 & \textrm{-}\mathrm{i}\\
5281 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5294 \begin_layout Plain Layout
5301 \begin_layout Plain Layout
5315 \begin_inset space \thinspace{}
5323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5326 \begin_layout Plain Layout
5327 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5328 0 & \textrm{-}\mathrm{i}\\
5329 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5342 \begin_layout Plain Layout
5349 \begin_layout Plain Layout
5363 \begin_inset space \thinspace{}
5371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5374 \begin_layout Plain Layout
5375 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5376 0 & \textrm{-}\mathrm{i}\\
5377 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5391 \begin_inset space \hfill{}
5395 \begin_inset Tabular
5396 <lyxtabular version="3" rows="4" columns="2">
5398 <column alignment="center" valignment="top" width="0">
5399 <column alignment="center" valignment="top" width="0">
5401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5404 \begin_layout Plain Layout
5410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5413 \begin_layout Plain Layout
5421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5424 \begin_layout Plain Layout
5431 \begin_layout Plain Layout
5445 \begin_inset space \thinspace{}
5453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5456 \begin_layout Plain Layout
5457 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5458 0 & \textrm{-}\mathrm{i}\\
5459 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5472 \begin_layout Plain Layout
5479 \begin_layout Plain Layout
5493 \begin_inset space \thinspace{}
5501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5504 \begin_layout Plain Layout
5505 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5506 0 & \textrm{-}\mathrm{i}\\
5507 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5520 \begin_layout Plain Layout
5527 \begin_layout Plain Layout
5541 \begin_inset space \thinspace{}
5549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5552 \begin_layout Plain Layout
5553 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5554 0 & \textrm{-}\mathrm{i}\\
5555 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5569 \begin_inset space \hfill{}
5575 \begin_layout Standard
5576 \begin_inset VSpace medskip
5580 \begin_inset space \thinspace{}
5584 \begin_inset space \space{}
5593 is inserted, a blue box appears between two vertical lines where the matrix
5597 \begin_layout Standard
5598 \begin_inset VSpace bigskip
5601 As all multiline formulas are matrices, the length
5611 \begin_layout Plain Layout
5619 that is described in
5620 \begin_inset CommandInset ref
5622 reference "sub:Column-Separation"
5626 can also be used to change the column separation of matrices.
5629 \begin_layout Standard
5630 To change the row separation, the command
5640 \begin_layout Plain Layout
5649 It is used as follows:
5652 \begin_layout Standard
5659 arraystretch}{stretch factor}
5663 \begin_layout Plain Layout
5674 \begin_layout Standard
5681 assigns the stretch factor to the predefined command
5689 \begin_inset space \thinspace{}
5693 \begin_inset space \space{}
5696 the row separation, use the factor 2.
5697 This is then used for all following matrices.
5698 To go back to the original separation, assign the factor 1 to
5707 \begin_layout Standard
5708 To set matrices into a text line, the command
5718 \begin_layout Plain Layout
5727 When it is inserted a blue box with two dashed lines appears.
5728 In this box the matrix is inserted.
5731 \begin_layout Standard
5733 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5734 C & D\end{smallmatrix}\right)$
5740 \begin_layout Section
5741 Brackets and Delimiters
5745 \begin_layout Plain Layout
5755 \begin_layout Plain Layout
5764 \begin_layout Subsection
5765 Vertical Brackets and Delimiters
5769 \begin_layout Plain Layout
5778 \begin_layout Standard
5779 \begin_inset space \hfill{}
5783 \begin_inset Tabular
5784 <lyxtabular version="3" rows="9" columns="2">
5786 <column alignment="center" valignment="top" width="0pt">
5787 <column alignment="center" valignment="top" width="0pt">
5789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5792 \begin_layout Plain Layout
5798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5801 \begin_layout Plain Layout
5809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5812 \begin_layout Plain Layout
5818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5821 \begin_layout Plain Layout
5822 \begin_inset Formula $($
5832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5835 \begin_layout Plain Layout
5841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5844 \begin_layout Plain Layout
5845 \begin_inset Formula $\{$
5855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5858 \begin_layout Plain Layout
5864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5867 \begin_layout Plain Layout
5868 \begin_inset Formula $[$
5878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5881 \begin_layout Plain Layout
5889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5892 \begin_layout Plain Layout
5893 \begin_inset Formula $\langle$
5903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5906 \begin_layout Plain Layout
5914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5917 \begin_layout Plain Layout
5918 \begin_inset Formula $\lceil$
5928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5931 \begin_layout Plain Layout
5939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5942 \begin_layout Plain Layout
5943 \begin_inset Formula $\lfloor$
5953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5956 \begin_layout Plain Layout
5962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5965 \begin_layout Plain Layout
5966 \begin_inset Formula $/$
5976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5979 \begin_layout Plain Layout
5985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5988 \begin_layout Plain Layout
5989 \begin_inset Formula $|$
6003 \begin_inset space \hfill{}
6007 \begin_inset Tabular
6008 <lyxtabular version="3" rows="9" columns="2">
6010 <column alignment="center" valignment="top" width="0pt">
6011 <column alignment="center" valignment="top" width="0pt">
6013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6016 \begin_layout Plain Layout
6022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6025 \begin_layout Plain Layout
6033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6036 \begin_layout Plain Layout
6042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6045 \begin_layout Plain Layout
6046 \begin_inset Formula $)$
6056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6059 \begin_layout Plain Layout
6065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6068 \begin_layout Plain Layout
6069 \begin_inset Formula $\}$
6079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6082 \begin_layout Plain Layout
6088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6091 \begin_layout Plain Layout
6092 \begin_inset Formula $]$
6102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6105 \begin_layout Plain Layout
6113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6116 \begin_layout Plain Layout
6117 \begin_inset Formula $\rangle$
6127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6130 \begin_layout Plain Layout
6138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6141 \begin_layout Plain Layout
6142 \begin_inset Formula $\rceil$
6152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6155 \begin_layout Plain Layout
6163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6166 \begin_layout Plain Layout
6167 \begin_inset Formula $\rfloor$
6177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6180 \begin_layout Plain Layout
6190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6193 \begin_layout Plain Layout
6194 \begin_inset Formula $\backslash$
6204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6207 \begin_layout Plain Layout
6215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6218 \begin_layout Plain Layout
6219 \begin_inset Formula $\|$
6233 \begin_inset space \hfill{}
6239 \begin_layout Standard
6242 \begin_inset Note Greyedout
6245 \begin_layout Plain Layout
6250 In TeX-mode the command
6260 \begin_layout Plain Layout
6268 must be used for the backslash, because the command
6276 produces there a line break.
6284 \begin_layout Standard
6285 For all characters listed above the size can be adjusted with the commands
6286 described in the following two subsections.
6287 When using these commands, the characters < and > can directly be used
6288 instead of the commands
6303 \begin_layout Subsubsection
6305 \begin_inset CommandInset label
6307 name "sub:Manual-Bracket-Size"
6315 \begin_layout Plain Layout
6316 Bracket size ! manual
6324 \begin_layout Standard
6325 The bracket size can be specified manually by the LaTeX-commands
6335 \begin_layout Plain Layout
6368 denotes the smallest and
6374 the largest bracket size.
6377 \begin_layout Standard
6378 These commands are used to emphasize levels of brackets:
6381 \begin_layout Standard
6383 \begin_inset Tabular
6384 <lyxtabular version="3" rows="2" columns="2">
6386 <column alignment="center" valignment="top" width="0pt">
6387 <column alignment="center" valignment="top" width="0pt">
6389 <cell alignment="center" valignment="top" usebox="none">
6392 \begin_layout Plain Layout
6393 all brackets in the same size:
6398 <cell alignment="center" valignment="top" usebox="none">
6401 \begin_layout Plain Layout
6402 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6412 <cell alignment="center" valignment="top" usebox="none">
6415 \begin_layout Plain Layout
6421 <cell alignment="center" valignment="top" usebox="none">
6424 \begin_layout Plain Layout
6425 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6439 \begin_inset Note Note
6442 \begin_layout Plain Layout
6449 is only used as spacer.
6457 \begin_layout Standard
6458 For the second formula the command
6468 \begin_layout Plain Layout
6482 \begin_layout Standard
6483 Here is an overview about all bracket sizes:
6486 \begin_layout Standard
6506 \begin_layout Plain Layout
6523 \begin_layout Plain Layout
6536 \begin_layout Plain Layout
6552 \begin_layout Standard
6554 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6560 \begin_layout Standard
6567 -commands there is the variant
6577 \begin_layout Plain Layout
6585 that adds a bit more space between the bracket and its content, and the
6602 \begin_layout Plain Layout
6612 , that don't add additional space.
6617 at the end of the command
6623 is for a left bracket; for a right bracket this will be replaced by an
6629 A left or right bracket can each be an opening or closing bracket.
6632 \begin_layout Standard
6633 In the following table is a comparison of the variants:
6636 \begin_layout Standard
6638 \begin_inset Tabular
6639 <lyxtabular version="3" rows="5" columns="2">
6641 <column alignment="center" valignment="middle" width="0">
6642 <column alignment="center" valignment="middle" width="0">
6644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6647 \begin_layout Plain Layout
6653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6656 \begin_layout Plain Layout
6658 \begin_inset Note Note
6661 \begin_layout Plain Layout
6668 is only used as spacer.
6680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6683 \begin_layout Plain Layout
6698 \begin_layout Plain Layout
6716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6719 \begin_layout Plain Layout
6720 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6733 \begin_layout Plain Layout
6748 \begin_layout Plain Layout
6766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6769 \begin_layout Plain Layout
6770 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6783 \begin_layout Plain Layout
6798 \begin_layout Plain Layout
6816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6819 \begin_layout Plain Layout
6820 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6833 \begin_layout Plain Layout
6845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6848 \begin_layout Plain Layout
6849 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6865 \begin_layout Subsubsection
6866 Automatic Bracket Size
6867 \begin_inset CommandInset label
6869 name "sub:Automatic-Bracket-Size"
6877 \begin_layout Plain Layout
6878 Bracket size ! automatic
6886 \begin_layout Standard
6887 Brackets with variable size can be inserted with the commands
6897 \begin_layout Plain Layout
6915 \begin_layout Plain Layout
6923 or via the math toolbar button
6924 \begin_inset Graphics
6925 filename ../images/dialog-show_mathdelimiter.png
6943 the wanted bracket must be inserted.
6944 The bracket size will then automatically be calculated for the output.
6947 \begin_layout Standard
6949 normal bracket: The command
6959 \begin_layout Plain Layout
6969 \begin_inset Formula $\downarrow$
6976 \begin_layout Plain Layout
6988 \begin_inset Formula \[
6996 \begin_layout Standard
6998 multiline bracket: The command
7010 \begin_layout Plain Layout
7020 \begin_inset Formula $\downarrow$
7027 \begin_layout Plain Layout
7041 \begin_inset Formula \[
7042 \ln\left(\frac{A}{C}\right)\]
7049 \begin_layout Standard
7065 \begin_inset space ~
7071 This has the advantage that you can see in LyX immediately the real bracket
7072 size and that the matching right bracket will be created too.
7073 \begin_inset Newline newline
7076 The command for the last example would then be:
7090 \begin_layout Plain Layout
7100 \begin_inset Formula $\downarrow$
7106 \begin_layout Standard
7107 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7108 For example the command
7118 \begin_layout Plain Layout
7128 \begin_inset Formula $\downarrow$
7135 \begin_layout Plain Layout
7151 \begin_inset Formula \[
7152 \left.\frac{A}{B}\right\} \]
7170 will be converted by LyX to brackets in the right size when the document
7171 is reloaded and an omitted bracket will appear as dashed line.
7174 \begin_layout Standard
7175 \begin_inset VSpace bigskip
7178 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7189 \begin_layout Plain Layout
7197 is additionally available for all brackets and limits.
7198 With this command the height of the following character is adapted to the
7199 one of the surrounding brackets, what is e.
7200 \begin_inset space \thinspace{}
7204 \begin_inset space \space{}
7207 needed for physical vectors:
7208 \begin_inset Formula \[
7209 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7213 For physical vectors there is a special LaTeX-package, described in
7214 \begin_inset CommandInset ref
7216 reference "sub:Physical-Vectors"
7223 \begin_layout Subsection
7228 \begin_layout Plain Layout
7229 Brackets ! horizontal
7237 \begin_layout Standard
7239 \begin_inset Tabular
7240 <lyxtabular version="3" rows="4" columns="2">
7242 <column alignment="center" valignment="top" width="0pt">
7243 <column alignment="center" valignment="top" width="0pt">
7245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7248 \begin_layout Plain Layout
7250 \begin_inset Note Note
7253 \begin_layout Plain Layout
7260 is only used as spacer.
7270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7273 \begin_layout Plain Layout
7281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7284 \begin_layout Plain Layout
7288 \begin_layout Plain Layout
7303 \begin_layout Plain Layout
7316 \begin_layout Plain Layout
7329 \begin_layout Plain Layout
7342 \begin_layout Plain Layout
7353 \begin_layout Plain Layout
7366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7369 \begin_layout Plain Layout
7370 \begin_inset Formula $\overbrace{A+B}^{3}$
7380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7383 \begin_layout Plain Layout
7387 \begin_layout Plain Layout
7402 \begin_layout Plain Layout
7415 \begin_layout Plain Layout
7428 \begin_layout Plain Layout
7439 \begin_layout Plain Layout
7452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7455 \begin_layout Plain Layout
7456 \begin_inset Formula $\underbrace{A+B}_{5}$
7466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7469 \begin_layout Plain Layout
7476 \begin_layout Plain Layout
7491 \begin_layout Plain Layout
7504 \begin_layout Plain Layout
7517 \begin_layout Plain Layout
7530 \begin_layout Plain Layout
7543 \begin_layout Plain Layout
7556 \begin_layout Plain Layout
7570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7573 \begin_layout Plain Layout
7574 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7590 \begin_layout Standard
7591 In the last example it doesn't matter if
7603 is inserted at first.
7606 \begin_layout Standard
7607 \begin_inset VSpace bigskip
7610 When brackets are needed that overlap each other, multiline formulas, as
7612 \begin_inset CommandInset ref
7614 reference "sec:Multiline-Formulas"
7619 \begin_inset Formula \begin{eqnarray*}
7620 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7621 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7625 In the first row the formula is inserted together with the first brace.
7626 It is hereby important that the space command
7630 \begin_layout Plain Layout
7631 Space commands are explained in
7632 \begin_inset CommandInset ref
7634 reference "sub:Predefined-Space"
7649 is inserted before the first
7650 \begin_inset Formula $d$
7653 , because the brace that ends behind the
7654 \begin_inset Formula $q$
7657 prevents that the following
7658 \begin_inset Quotes eld
7662 \begin_inset Quotes erd
7665 is surrounded by space.
7669 \begin_layout Plain Layout
7670 because a bracket is not handled as character, see
7671 \begin_inset CommandInset ref
7673 reference "sub:Binary-Operators"
7682 In the second row the second brace is inserted.
7683 As it should begin before the
7684 \begin_inset Formula $b$
7699 \begin_layout Plain Layout
7707 \begin_inset CommandInset ref
7709 reference "sub:Placeholders"
7718 This space is needed because the
7719 \begin_inset Quotes eld
7723 \begin_inset Quotes erd
7726 is also surrounded by space in the formula.
7727 The brace is placed under the command
7736 \begin_layout Standard
7737 It gets more complicated when brackets overlap each other, like in the following
7742 \begin_layout Plain Layout
7754 \begin_inset Formula \begin{eqnarray*}
7755 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7756 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7764 \begin_layout Plain Layout
7775 The first formula row is the same as the second row of the previous example,
7776 with the difference that the brace is above.
7777 The second row contains the formula together with the second brace.
7778 To avoid that there is space between the upper brace in the first row and
7779 the formula, the row spacing need to be reduced.
7780 This is not easily possible due to a bug in LyX
7784 \begin_layout Plain Layout
7785 \begin_inset CommandInset href
7787 name "LyX-bug #1505"
7788 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7798 As solution for the problem, the global formula row separation
7808 \begin_layout Plain Layout
7816 must be changed to -6
7817 \begin_inset space \thinspace{}
7820 pt before the formula with the command
7835 is set back after the formula to the standard value of 3
7836 \begin_inset space \thinspace{}
7839 pt using the same command.
7840 More about the row separation in formulas is explained in
7841 \begin_inset CommandInset ref
7843 reference "sub:Line-Separation"
7850 \begin_layout Section
7855 \begin_layout Plain Layout
7864 \begin_layout Standard
7865 Arrows can be inserted via the math toolbar button
7866 \begin_inset Graphics
7867 filename ../images/math/leftarrow.png
7872 or the commands listed in the following subsections.
7875 \begin_layout Standard
7876 \begin_inset Newpage newpage
7882 \begin_layout Subsection
7887 \begin_layout Plain Layout
7896 \begin_layout Standard
7897 \begin_inset space \hfill{}
7901 \begin_inset Tabular
7902 <lyxtabular version="3" rows="8" columns="2">
7904 <column alignment="center" valignment="top" width="0pt">
7905 <column alignment="center" valignment="top" width="0pt">
7907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7910 \begin_layout Plain Layout
7916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7919 \begin_layout Plain Layout
7927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7930 \begin_layout Plain Layout
7938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7941 \begin_layout Plain Layout
7942 \begin_inset Formula $\gets$
7952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7955 \begin_layout Plain Layout
7963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7966 \begin_layout Plain Layout
7967 \begin_inset Formula $\Leftarrow$
7977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7980 \begin_layout Plain Layout
7988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7991 \begin_layout Plain Layout
7992 \begin_inset Formula $\longleftarrow$
8002 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8005 \begin_layout Plain Layout
8013 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8016 \begin_layout Plain Layout
8017 \begin_inset Formula $\Longleftarrow$
8027 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8030 \begin_layout Plain Layout
8038 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8041 \begin_layout Plain Layout
8042 \begin_inset Formula $\leftharpoonup$
8052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8055 \begin_layout Plain Layout
8063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8066 \begin_layout Plain Layout
8067 \begin_inset Formula $\leftharpoondown$
8077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8080 \begin_layout Plain Layout
8088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8091 \begin_layout Plain Layout
8092 \begin_inset Formula $\hookleftarrow$
8106 \begin_inset space \hfill{}
8110 \begin_inset Tabular
8111 <lyxtabular version="3" rows="8" columns="2">
8113 <column alignment="center" valignment="top" width="0pt">
8114 <column alignment="center" valignment="top" width="0pt">
8116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8119 \begin_layout Plain Layout
8125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8128 \begin_layout Plain Layout
8136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8139 \begin_layout Plain Layout
8147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8150 \begin_layout Plain Layout
8151 \begin_inset Formula $\to$
8161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8164 \begin_layout Plain Layout
8172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8175 \begin_layout Plain Layout
8176 \begin_inset Formula $\Rightarrow$
8186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8189 \begin_layout Plain Layout
8197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8200 \begin_layout Plain Layout
8201 \begin_inset Formula $\longrightarrow$
8211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8214 \begin_layout Plain Layout
8222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8225 \begin_layout Plain Layout
8226 \begin_inset Formula $\Longrightarrow$
8236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8239 \begin_layout Plain Layout
8247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8250 \begin_layout Plain Layout
8251 \begin_inset Formula $\rightharpoonup$
8261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8264 \begin_layout Plain Layout
8272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8275 \begin_layout Plain Layout
8276 \begin_inset Formula $\rightharpoondown$
8286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8289 \begin_layout Plain Layout
8297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8300 \begin_layout Plain Layout
8301 \begin_inset Formula $\hookrightarrow$
8315 \begin_inset space \hfill{}
8321 \begin_layout Standard
8322 \begin_inset space \hfill{}
8326 \begin_inset Tabular
8327 <lyxtabular version="3" rows="6" columns="2">
8329 <column alignment="center" valignment="top" width="0pt">
8330 <column alignment="center" valignment="top" width="0pt">
8332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8335 \begin_layout Plain Layout
8341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8344 \begin_layout Plain Layout
8352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8355 \begin_layout Plain Layout
8363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8366 \begin_layout Plain Layout
8367 \begin_inset Formula $\leftrightarrow$
8377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8380 \begin_layout Plain Layout
8388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8391 \begin_layout Plain Layout
8392 \begin_inset Formula $\Leftrightarrow$
8402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8405 \begin_layout Plain Layout
8413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8416 \begin_layout Plain Layout
8417 \begin_inset Formula $\longleftrightarrow$
8427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8430 \begin_layout Plain Layout
8438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8441 \begin_layout Plain Layout
8442 \begin_inset Formula $\Longleftrightarrow$
8452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8455 \begin_layout Plain Layout
8463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8466 \begin_layout Plain Layout
8467 \begin_inset Formula $\rightleftharpoons$
8481 \begin_inset space \hspace{}
8486 \begin_inset space \hfill{}
8490 \begin_inset Tabular
8491 <lyxtabular version="3" rows="5" columns="2">
8493 <column alignment="center" valignment="top" width="0pt">
8494 <column alignment="center" valignment="top" width="0pt">
8496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8499 \begin_layout Plain Layout
8505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8508 \begin_layout Plain Layout
8516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8519 \begin_layout Plain Layout
8527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8530 \begin_layout Plain Layout
8531 \begin_inset Formula $\mapsto$
8541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8544 \begin_layout Plain Layout
8552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8555 \begin_layout Plain Layout
8556 \begin_inset Formula $\longmapsto$
8566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8569 \begin_layout Plain Layout
8577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8580 \begin_layout Plain Layout
8581 \begin_inset Formula $\leadsto$
8591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8594 \begin_layout Plain Layout
8602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8605 \begin_layout Plain Layout
8606 \begin_inset Formula $\dasharrow$
8620 \begin_inset space \hfill{}
8626 \begin_layout Standard
8627 \begin_inset VSpace medskip
8630 Arrows used as accent like e.
8631 \begin_inset space \thinspace{}
8635 \begin_inset space \space{}
8638 vector arrows are listed in
8639 \begin_inset CommandInset ref
8641 reference "sec:Accents"
8648 \begin_layout Standard
8649 \begin_inset VSpace bigskip
8652 Furthermore there are the labeled arrows
8656 \begin_layout Plain Layout
8672 \begin_layout Plain Layout
8690 \begin_layout Plain Layout
8697 \begin_layout Plain Layout
8712 When inserting one of these commands in a formula, an arrow with two blue
8713 boxes appear where the label can be inserted.
8714 The length of the arrow adapts to the label width.
8717 \begin_layout Standard
8719 \begin_inset Tabular
8720 <lyxtabular version="3" rows="3" columns="2">
8722 <column alignment="center" valignment="top" width="0pt">
8723 <column alignment="center" valignment="top" width="0pt">
8725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8728 \begin_layout Plain Layout
8734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8737 \begin_layout Plain Layout
8739 \begin_inset Note Note
8742 \begin_layout Plain Layout
8749 is only used as spacer.
8761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8764 \begin_layout Plain Layout
8771 \begin_layout Plain Layout
8781 \begin_inset Formula $\downarrow$
8785 \begin_inset Formula $\to$
8793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8796 \begin_layout Plain Layout
8797 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8810 \begin_layout Plain Layout
8817 \begin_layout Plain Layout
8827 \begin_inset Formula $\downarrow$
8831 \begin_inset Formula $\to$
8839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8842 \begin_layout Plain Layout
8843 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8859 \begin_layout Subsection
8860 Vertical and diagonal Arrows
8864 \begin_layout Plain Layout
8874 \begin_layout Plain Layout
8883 \begin_layout Standard
8884 \begin_inset space \hfill{}
8888 \begin_inset Tabular
8889 <lyxtabular version="3" rows="7" columns="2">
8891 <column alignment="center" valignment="top" width="0pt">
8892 <column alignment="center" valignment="top" width="0pt">
8894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8897 \begin_layout Plain Layout
8903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8906 \begin_layout Plain Layout
8914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8917 \begin_layout Plain Layout
8925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8928 \begin_layout Plain Layout
8929 \begin_inset Formula $\uparrow$
8939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8942 \begin_layout Plain Layout
8950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8953 \begin_layout Plain Layout
8954 \begin_inset Formula $\Uparrow$
8964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8967 \begin_layout Plain Layout
8975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8978 \begin_layout Plain Layout
8979 \begin_inset Formula $\updownarrow$
8989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8992 \begin_layout Plain Layout
9000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9003 \begin_layout Plain Layout
9004 \begin_inset Formula $\Updownarrow$
9014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9017 \begin_layout Plain Layout
9025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9028 \begin_layout Plain Layout
9029 \begin_inset Formula $\Downarrow$
9039 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9042 \begin_layout Plain Layout
9050 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9053 \begin_layout Plain Layout
9054 \begin_inset Formula $\downarrow$
9068 \begin_inset space \hfill{}
9072 \begin_inset Tabular
9073 <lyxtabular version="3" rows="5" columns="2">
9075 <column alignment="center" valignment="top" width="0pt">
9076 <column alignment="center" valignment="top" width="0pt">
9078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9081 \begin_layout Plain Layout
9087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9090 \begin_layout Plain Layout
9098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9101 \begin_layout Plain Layout
9109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9112 \begin_layout Plain Layout
9113 \begin_inset Formula $\nearrow$
9123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9126 \begin_layout Plain Layout
9134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9137 \begin_layout Plain Layout
9138 \begin_inset Formula $\searrow$
9148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9151 \begin_layout Plain Layout
9159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9162 \begin_layout Plain Layout
9163 \begin_inset Formula $\swarrow$
9173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9176 \begin_layout Plain Layout
9184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9187 \begin_layout Plain Layout
9188 \begin_inset Formula $\nwarrow$
9202 \begin_inset space \hfill{}
9208 \begin_layout Standard
9209 \begin_inset VSpace medskip
9212 Vertical arrows can be used also as delimiter together with the commands
9214 \begin_inset CommandInset ref
9216 reference "sub:Manual-Bracket-Size"
9221 \begin_inset CommandInset ref
9223 reference "sub:Automatic-Bracket-Size"
9230 \begin_layout Standard
9231 \begin_inset Newpage newpage
9237 \begin_layout Section
9239 \begin_inset CommandInset label
9249 \begin_layout Plain Layout
9258 \begin_layout Standard
9259 Accents can be inserted via the math toolbar button
9260 \begin_inset Graphics
9261 filename ../images/math/hat.png
9266 or the commands listed in the following subsections.
9269 \begin_layout Subsection
9270 Accents for one Character
9274 \begin_layout Plain Layout
9287 \begin_layout Plain Layout
9289 \begin_inset CommandInset ref
9291 reference "sub:Accents-in-Text"
9304 \begin_layout Plain Layout
9312 \begin_inset Note Note
9315 \begin_layout Plain Layout
9318 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9321 \begin_layout Plain Layout
9324 texorpdfstring is in section
9325 \begin_inset CommandInset ref
9327 reference "sub:Formulas-in-Section"
9337 \begin_inset CommandInset label
9339 name "sub:Accents-for-one"
9347 \begin_layout Plain Layout
9348 Accents ! for one character
9356 \begin_layout Standard
9357 \begin_inset space \hfill{}
9361 \begin_inset Tabular
9362 <lyxtabular version="3" rows="8" columns="2">
9364 <column alignment="center" valignment="top" width="0pt">
9365 <column alignment="center" valignment="top" width="0pt">
9367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9370 \begin_layout Plain Layout
9376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9379 \begin_layout Plain Layout
9381 \begin_inset Note Note
9384 \begin_layout Plain Layout
9391 is only used as spacer.
9403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9406 \begin_layout Plain Layout
9413 \begin_layout Plain Layout
9427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9430 \begin_layout Plain Layout
9431 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9441 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9444 \begin_layout Plain Layout
9451 \begin_layout Plain Layout
9465 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9468 \begin_layout Plain Layout
9469 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9482 \begin_layout Plain Layout
9489 \begin_layout Plain Layout
9503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9506 \begin_layout Plain Layout
9507 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9520 \begin_layout Plain Layout
9528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9531 \begin_layout Plain Layout
9532 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9545 \begin_layout Plain Layout
9552 \begin_layout Plain Layout
9565 \begin_layout Plain Layout
9576 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9579 \begin_layout Plain Layout
9580 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9593 \begin_layout Plain Layout
9600 \begin_layout Plain Layout
9614 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9617 \begin_layout Plain Layout
9618 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9628 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9631 \begin_layout Plain Layout
9638 \begin_layout Plain Layout
9652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9655 \begin_layout Plain Layout
9656 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9670 \begin_inset space \hfill{}
9674 \begin_inset Tabular
9675 <lyxtabular version="3" rows="7" columns="2">
9677 <column alignment="center" valignment="top" width="0pt">
9678 <column alignment="center" valignment="top" width="0pt">
9680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9683 \begin_layout Plain Layout
9689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9692 \begin_layout Plain Layout
9700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9703 \begin_layout Plain Layout
9710 \begin_layout Plain Layout
9724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9727 \begin_layout Plain Layout
9728 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9741 \begin_layout Plain Layout
9748 \begin_layout Plain Layout
9762 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9765 \begin_layout Plain Layout
9766 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9779 \begin_layout Plain Layout
9786 \begin_layout Plain Layout
9800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9803 \begin_layout Plain Layout
9804 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9817 \begin_layout Plain Layout
9824 \begin_layout Plain Layout
9838 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9841 \begin_layout Plain Layout
9842 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9852 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9855 \begin_layout Plain Layout
9862 \begin_layout Plain Layout
9876 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9879 \begin_layout Plain Layout
9880 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9890 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9893 \begin_layout Plain Layout
9900 \begin_layout Plain Layout
9914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9917 \begin_layout Plain Layout
9918 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9932 \begin_inset space \hfill{}
9938 \begin_layout Standard
9939 \begin_inset VSpace bigskip
9945 \begin_layout Standard
9946 You can directly insert accents like é to formulas.
9947 LyX will transform them to the corresponding accent command.
9952 \begin_layout Plain Layout
9958 it is better to insert a quotation mark before the vowel.
9959 These two characters are then treated by LaTeX as
9963 character when the formula part with the umlaut is marked as German.
9971 \begin_inset Quotes eld
9975 \begin_inset Quotes erd
9978 umlauts are created as demonstrated in the following example:
9981 \begin_layout Standard
9982 \begin_inset VSpace -2mm
9988 \begin_layout Standard
9990 \begin_inset Tabular
9991 <lyxtabular version="3" rows="3" columns="2">
9993 <column alignment="center" valignment="top" width="0">
9994 <column alignment="center" valignment="top" width="0">
9996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9999 \begin_layout Plain Layout
10005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10008 \begin_layout Plain Layout
10010 \begin_inset Note Note
10013 \begin_layout Plain Layout
10021 \begin_inset space \thinspace{}
10024 pt space are only used as spacer.
10036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10039 \begin_layout Plain Layout
10042 \begin_inset Quotes grd
10050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10053 \begin_layout Plain Layout
10054 \begin_inset space \hspace{}
10061 \begin_inset Formula $"i$
10071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10074 \begin_layout Plain Layout
10081 \begin_layout Plain Layout
10095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10098 \begin_layout Plain Layout
10099 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10115 \begin_layout Standard
10116 Another advantage to
10122 is that umlauts can directly be converted to mathematical text because
10123 the accent commands above are
10129 in mathematical text
10132 To convert an accented character to mathematical text, only the character
10133 under the accent may be converted.
10134 This applies also for all other conversions, e.
10135 \begin_inset space \thinspace{}
10139 \begin_inset space \space{}
10145 \begin_layout Standard
10146 In mathematical text, umlauts and other accented characters can directly
10150 \begin_layout Subsection
10151 Accents for Operators
10155 \begin_layout Plain Layout
10156 Accents ! for operators
10164 \begin_layout Standard
10175 \begin_layout Plain Layout
10193 \begin_layout Plain Layout
10201 characters can be placed above or below an operator, respectively, to accent
10213 \begin_layout Plain Layout
10221 characters can be set before and behind an operator.
10222 The command scheme is:
10225 \begin_layout Standard
10241 \begin_layout Standard
10248 must always be before the operator that should be accented.
10249 You can accent with several characters and even with other operators and
10257 for example only characters behind an operator, write nothing between the
10258 first braces but don't omit the braces.
10261 \begin_layout Standard
10262 For example the command
10267 \begin_inset Formula $\to$
10277 \begin_inset Formula $\to$
10286 \begin_layout Plain Layout
10302 \begin_inset Formula \[
10303 \sideset{}{'}\sum_{k=1}^{n}\]
10310 \begin_layout Standard
10319 \begin_layout Plain Layout
10334 \begin_layout Plain Layout
10346 \begin_inset Formula $\uparrow$
10354 \begin_inset Formula \[
10355 \overset{a}{\maltese}\]
10359 As seen in the last example, with
10371 also symbols and characters can be accented; with
10377 this is not possible.
10380 \begin_layout Subsection
10381 Accents for several Characters
10385 \begin_layout Plain Layout
10386 Accents ! for several characters
10394 \begin_layout Standard
10395 \begin_inset space \hfill{}
10399 \begin_inset Tabular
10400 <lyxtabular version="3" rows="5" columns="2">
10402 <column alignment="center" valignment="top" width="0pt">
10403 <column alignment="center" valignment="top" width="0pt">
10405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10408 \begin_layout Plain Layout
10414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10417 \begin_layout Plain Layout
10419 \begin_inset Note Note
10422 \begin_layout Plain Layout
10429 is only used as spacer.
10441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10444 \begin_layout Plain Layout
10451 \begin_layout Plain Layout
10465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10468 \begin_layout Plain Layout
10469 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10482 \begin_layout Plain Layout
10489 \begin_layout Plain Layout
10503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10506 \begin_layout Plain Layout
10507 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10520 \begin_layout Plain Layout
10527 \begin_layout Plain Layout
10541 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10544 \begin_layout Plain Layout
10545 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10558 \begin_layout Plain Layout
10561 underleftrightarrow
10565 \begin_layout Plain Layout
10579 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10582 \begin_layout Plain Layout
10583 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10597 \begin_inset space \hfill{}
10601 \begin_inset Tabular
10602 <lyxtabular version="3" rows="5" columns="2">
10604 <column alignment="center" valignment="top" width="0pt">
10605 <column alignment="center" valignment="top" width="0pt">
10607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10610 \begin_layout Plain Layout
10616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10619 \begin_layout Plain Layout
10627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10630 \begin_layout Plain Layout
10637 \begin_layout Plain Layout
10651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10654 \begin_layout Plain Layout
10655 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10665 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10668 \begin_layout Plain Layout
10675 \begin_layout Plain Layout
10689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10692 \begin_layout Plain Layout
10693 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10703 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10706 \begin_layout Plain Layout
10713 \begin_layout Plain Layout
10727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10730 \begin_layout Plain Layout
10731 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10744 \begin_layout Plain Layout
10751 \begin_layout Plain Layout
10765 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10768 \begin_layout Plain Layout
10769 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10783 \begin_inset space \hfill{}
10789 \begin_layout Standard
10790 \begin_inset VSpace medskip
10793 With these commands as many characters as you like can be accented.
10806 will only be set in the output with a length of three characters, as shown
10807 in the following example:
10808 \begin_inset Formula \[
10809 \widetilde{A+B=C-D}\]
10816 \begin_layout Standard
10827 \begin_layout Plain Layout
10845 \begin_layout Plain Layout
10853 described in the previous subsection it is also possible to accent several
10863 \begin_layout Plain Layout
10873 \begin_inset Formula $\downarrow$
10879 \begin_inset Formula \[
10880 \underset{***}{A=B}\]
10887 \begin_layout Section
10889 \begin_inset CommandInset label
10899 \begin_layout Plain Layout
10908 \begin_layout Subsection
10910 \begin_inset CommandInset label
10912 name "sub:Predefined-Space"
10920 \begin_layout Plain Layout
10921 Space ! horizontal ! predefined
10929 \begin_layout Standard
10930 Sometimes it is necessary to insert horizontal space to a formula.
10931 This is done by inserting a protected space (shortcut
10934 arg "space-insert protected"
10939 \begin_inset Quotes eld
10948 \begin_layout Plain Layout
10960 \begin_inset Quotes erd
10963 appears and by pressing
10967 several times one can select one of eight different space sizes.
10968 The spaces can also be inserted using the math toolbar button
10969 \begin_inset Graphics
10970 filename ../images/math/space.png
10975 or special commands.
10976 Independent from the inserted command, one can select the size again by
10984 \begin_layout Standard
10987 \begin_inset VSpace -5mm
10991 \begin_inset Tabular
10992 <lyxtabular version="3" rows="3" columns="7">
10994 <column alignment="center" valignment="middle" width="6.8cm">
10995 <column alignment="center" valignment="top" width="0">
10996 <column alignment="center" valignment="top" width="0">
10997 <column alignment="center" valignment="top" width="0">
10998 <column alignment="center" valignment="top" width="0">
10999 <column alignment="center" valignment="top" width="0">
11000 <column alignment="center" valignment="top" width="0">
11002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11005 \begin_layout Plain Layout
11011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11014 \begin_layout Plain Layout
11022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11025 \begin_layout Plain Layout
11033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11036 \begin_layout Plain Layout
11044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11047 \begin_layout Plain Layout
11055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11058 \begin_layout Plain Layout
11066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11069 \begin_layout Plain Layout
11079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11082 \begin_layout Plain Layout
11087 keystrokes after inserting the protected space
11092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11095 \begin_layout Plain Layout
11101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11104 \begin_layout Plain Layout
11110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11113 \begin_layout Plain Layout
11119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11122 \begin_layout Plain Layout
11128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11131 \begin_layout Plain Layout
11137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11140 \begin_layout Plain Layout
11148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11151 \begin_layout Plain Layout
11157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11160 \begin_layout Plain Layout
11161 \begin_inset Formula $A\, B$
11169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11172 \begin_layout Plain Layout
11173 \begin_inset Formula $A\: B$
11181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11184 \begin_layout Plain Layout
11185 \begin_inset Formula $A\; B$
11193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11196 \begin_layout Plain Layout
11197 \begin_inset Formula $A\quad B$
11205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11208 \begin_layout Plain Layout
11209 \begin_inset Formula $A\qquad B$
11217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11220 \begin_layout Plain Layout
11221 \begin_inset Formula $A\! B$
11237 \begin_layout Standard
11238 The last size seem to produce no space.
11239 It is displayed red in LyX contrary to the other sizes, because it is a
11241 There are two more negative spaces:
11244 \begin_layout Standard
11246 \begin_inset Tabular
11247 <lyxtabular version="3" rows="3" columns="3">
11249 <column alignment="center" valignment="middle" width="6.8cm">
11250 <column alignment="center" valignment="top" width="0pt">
11251 <column alignment="center" valignment="top" width="0pt">
11253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11256 \begin_layout Plain Layout
11262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11265 \begin_layout Plain Layout
11273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11276 \begin_layout Plain Layout
11286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11289 \begin_layout Plain Layout
11294 keystrokes after inserting the protected space
11299 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11302 \begin_layout Plain Layout
11308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11311 \begin_layout Plain Layout
11319 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11322 \begin_layout Plain Layout
11328 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11331 \begin_layout Plain Layout
11332 \begin_inset Formula $A\negmedspace B$
11340 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11343 \begin_layout Plain Layout
11344 \begin_inset Formula $A\negthickspace B$
11360 \begin_layout Standard
11361 Negative spaces can lead to characters overlapping each other.
11362 Thus they can be used to enforce ligatures, what is e.
11363 \begin_inset space \thinspace{}
11367 \begin_inset space \space{}
11370 useful for summation operators:
11373 \begin_layout Standard
11375 \begin_inset Tabular
11376 <lyxtabular version="3" rows="3" columns="2">
11378 <column alignment="center" valignment="top" width="0">
11379 <column alignment="center" valignment="top" width="0">
11381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11384 \begin_layout Plain Layout
11390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11393 \begin_layout Plain Layout
11395 \begin_inset Note Note
11398 \begin_layout Plain Layout
11405 is only used as spacer.
11417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11420 \begin_layout Plain Layout
11429 \begin_layout Plain Layout
11443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11446 \begin_layout Plain Layout
11447 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11460 \begin_layout Plain Layout
11471 \begin_layout Plain Layout
11485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11488 \begin_layout Plain Layout
11489 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11505 \begin_layout Standard
11506 Relations like for example equal signs, are always surrounded by space.
11507 To suppress this, the equal sign is placed into a TeX-brace.
11508 The following example demonstrates this:
11511 \begin_layout Standard
11513 \begin_inset Tabular
11514 <lyxtabular version="3" rows="2" columns="2">
11516 <column alignment="center" valignment="top" width="0pt">
11517 <column alignment="center" valignment="top" width="0pt">
11519 <cell alignment="center" valignment="top" usebox="none">
11522 \begin_layout Plain Layout
11528 <cell alignment="center" valignment="top" usebox="none">
11531 \begin_layout Plain Layout
11532 \begin_inset Formula $A=B$
11542 <cell alignment="center" valignment="top" usebox="none">
11545 \begin_layout Plain Layout
11546 \begin_inset Note Note
11549 \begin_layout Plain Layout
11556 is only used as spacer.
11562 \begin_inset Formula $\raisebox{5mm}{}$
11565 equation without space
11570 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11573 \begin_layout Plain Layout
11574 \begin_inset Formula $A{=}B$
11590 \begin_layout Standard
11592 The command for the last formula is:
11597 \begin_inset Formula $\to$
11603 \begin_layout Standard
11604 \begin_inset VSpace bigskip
11607 Spaces are needed for physical units, because the space between the value
11608 and the unit is the smallest one and not a normal space.
11609 For units in text, the smallest space is inserted via the menu
11611 Insert\SpecialChar \menuseparator
11612 Formatting\SpecialChar \menuseparator
11614 \begin_inset space ~
11622 arg "space-insert thin"
11628 \begin_layout Standard
11629 An example to visualize the difference:
11632 \begin_layout Standard
11633 \begin_inset Tabular
11634 <lyxtabular version="3" rows="2" columns="2">
11636 <column alignment="left" valignment="top" width="0">
11637 <column alignment="left" valignment="top" width="0">
11639 <cell alignment="center" valignment="top" usebox="none">
11642 \begin_layout Plain Layout
11644 \begin_inset Formula $\cdot$
11652 <cell alignment="center" valignment="top" usebox="none">
11655 \begin_layout Plain Layout
11656 space between value and unit
11663 <cell alignment="center" valignment="top" usebox="none">
11666 \begin_layout Plain Layout
11668 \begin_inset space \thinspace{}
11672 \begin_inset Formula $\cdot$
11680 <cell alignment="center" valignment="top" usebox="none">
11683 \begin_layout Plain Layout
11684 smallest space between value and unit
11697 \begin_layout Subsection
11702 \begin_layout Plain Layout
11715 \begin_layout Plain Layout
11716 for vertical space in formulas see
11717 \begin_inset CommandInset ref
11719 reference "sub:Line-Separation"
11732 \begin_layout Plain Layout
11740 \begin_inset Note Note
11743 \begin_layout Plain Layout
11746 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11749 \begin_layout Plain Layout
11752 texorpdfstring is in section
11753 \begin_inset CommandInset ref
11755 reference "sub:Formulas-in-Section"
11765 \begin_inset CommandInset label
11767 name "sub:Variable-Space"
11775 \begin_layout Plain Layout
11776 Space ! horizontal ! variable
11784 \begin_layout Standard
11785 Space with a defined length can be inserted with the command
11795 \begin_layout Plain Layout
11805 \begin_inset Quotes eld
11814 \begin_layout Plain Layout
11826 \begin_inset Quotes erd
11830 The length can be specified by left-clicking on the
11831 \begin_inset Quotes eld
11840 \begin_layout Plain Layout
11852 \begin_inset Quotes erd
11856 The length may also be negative.
11857 To insert so many space that the formula uses all available space, the
11868 \begin_layout Plain Layout
11879 \begin_layout Standard
11880 \begin_inset VSpace -1mm
11886 \begin_layout Standard
11888 \begin_inset Tabular
11889 <lyxtabular version="3" rows="4" columns="2">
11891 <column alignment="center" valignment="top" width="0">
11892 <column alignment="center" valignment="top" width="0">
11894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11897 \begin_layout Plain Layout
11905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11908 \begin_layout Plain Layout
11916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11919 \begin_layout Plain Layout
11926 \begin_layout Plain Layout
11936 \begin_inset Formula $\to$
11942 \begin_inset space \thinspace{}
11950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11953 \begin_layout Plain Layout
11954 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11967 \begin_layout Plain Layout
11974 \begin_layout Plain Layout
11984 \begin_inset Formula $\to$
11990 \begin_inset space \thinspace{}
11998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12001 \begin_layout Plain Layout
12002 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12015 \begin_layout Plain Layout
12022 \begin_layout Plain Layout
12036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12039 \begin_layout Plain Layout
12040 \begin_inset Formula $A=A\hfill B=B$
12056 \begin_layout Standard
12057 In the last example the available space is given by the longest column entry
12059 In an inline formula the space depends on the length of the line in which
12067 Thus, when the line uses the full width, no space will be created.
12074 only has an effect on displayed formulas when the formula style
12079 (Formula styles are explained in
12080 \begin_inset CommandInset ref
12082 reference "sec:Formula-Styles"
12089 \begin_layout Standard
12096 , there are the commands
12108 that fill the space with a pattern, see
12109 \begin_inset CommandInset ref
12111 reference "sub:Ellipses"
12118 \begin_layout Standard
12119 For text, variable space can be inserted via the menu
12121 Insert\SpecialChar \menuseparator
12122 Formatting\SpecialChar \menuseparator
12124 \begin_inset space ~
12132 \begin_layout Standard
12133 This is a line with
12134 \begin_inset space \hspace{}
12139 \begin_inset space \thinspace{}
12145 \begin_layout Standard
12146 This is a line with
12147 \begin_inset space \hfill{}
12153 \begin_layout Subsection
12154 Space besides inline Formulas
12158 \begin_layout Plain Layout
12159 Space ! besides inline formulas
12167 \begin_layout Standard
12168 The space that surrounds inline formulas can be adjusted with the length
12177 \begin_layout Plain Layout
12188 The value of a length is set with the command
12196 \begin_layout Plain Layout
12206 that has the following scheme:
12209 \begin_layout Standard
12214 setlength{length name}{value}
12217 \begin_layout Standard
12225 \begin_inset space \thinspace{}
12231 \begin_layout Standard
12241 \begin_layout Standard
12242 is inserted in TeX-mode.
12244 \begin_inset space \thinspace{}
12247 mm space will now be set around all inline formulas:
12251 \begin_layout Plain Layout
12265 \begin_layout Standard
12266 This is a line with an inline formula
12267 \begin_inset Formula $A=B$
12271 \begin_inset space \thinspace{}
12274 mm surrounding space.
12278 \begin_layout Plain Layout
12292 \begin_layout Standard
12293 To return to the predefined value,
12299 is set to the value 0
12300 \begin_inset space \thinspace{}
12306 \begin_layout Section
12311 \begin_layout Plain Layout
12321 \begin_layout Plain Layout
12326 \begin_layout Plain Layout
12337 \begin_layout Plain Layout
12352 \begin_layout Standard
12353 Boxes for text are described in chapter
12360 \begin_inset space ~
12368 \begin_layout Subsection
12370 \begin_inset CommandInset label
12372 name "sub:Boxes-with-Frame"
12380 \begin_layout Plain Layout
12389 \begin_layout Standard
12390 It is possible to frame formulas or parts of it with the commands
12400 \begin_layout Plain Layout
12418 \begin_layout Plain Layout
12429 \begin_layout Standard
12430 When one of these commands is inserted to a formula, a blue box appears
12431 within a frame to enter formula parts.
12438 an additional formula has to be created by
12446 \begin_layout Plain Layout
12447 Due to a bug in LyX it is not possible to create a new formula with
12452 \begin_inset CommandInset href
12454 name "LyX-bug #1435"
12455 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12464 , because the box content will otherwise be treated as mathematical text.
12471 is used, a new formula is automatically created inside the frame.
12474 \begin_layout Standard
12481 is not suitable to frame displayed formulas, because the formula will always
12482 be set in the size of the text.
12489 is in contrary not suitable to frame inline formulas, because the formula
12490 will always be set in the size of a displayed formula.
12493 \begin_layout Standard
12500 there is the command
12510 \begin_layout Plain Layout
12518 where additionally the frame width and the alignment can be specified.
12525 is used in the following scheme:
12528 \begin_layout Standard
12533 framebox[frame width][position]{box content}
12536 \begin_layout Standard
12537 The position can either be
12554 right aligns the formula in the box.
12555 When no position is given, the formula will be centered.
12556 \begin_inset Newline newline
12559 Is no width given, also no position can be given.
12560 In this case the frame width is adjusted to the box content like for
12569 \begin_layout Standard
12576 is inserted, a box appears containing three blue boxes.
12577 The first two boxes are surrounded by brackets and denote the two optional
12579 The third box is for formula parts like for
12588 \begin_layout Standard
12590 \begin_inset Note Note
12593 \begin_layout Plain Layout
12594 The table has been set into a minipage to make the footnote appearing.
12595 Otherwise the footnote text would not be displayed.
12601 \begin_inset Box Frameless
12610 height_special "totalheight"
12613 \begin_layout Plain Layout
12615 \begin_inset Tabular
12616 <lyxtabular version="3" rows="5" columns="2">
12618 <column alignment="center" valignment="top" width="0">
12619 <column alignment="center" valignment="top" width="0">
12621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12624 \begin_layout Plain Layout
12629 \begin_layout Plain Layout
12630 Due to a bug in LyX it is not possible to create a new formula with
12635 \begin_inset CommandInset href
12637 name "LyX-bug #1435"
12638 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12655 \begin_layout Plain Layout
12657 \begin_inset Note Note
12660 \begin_layout Plain Layout
12667 is only used as spacer.
12679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12682 \begin_layout Plain Layout
12689 \begin_layout Plain Layout
12708 \begin_layout Plain Layout
12722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12725 \begin_layout Plain Layout
12726 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12739 \begin_layout Plain Layout
12746 \begin_layout Plain Layout
12761 \begin_layout Plain Layout
12775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12778 \begin_layout Plain Layout
12779 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12792 \begin_layout Plain Layout
12799 \begin_layout Plain Layout
12813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12816 \begin_layout Plain Layout
12817 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12830 \begin_layout Plain Layout
12837 \begin_layout Plain Layout
12847 \begin_inset Formula $\to$
12851 \begin_inset Formula $\to$
12864 \begin_layout Plain Layout
12874 \begin_inset Formula $\downarrow$
12882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12885 \begin_layout Plain Layout
12886 \begin_inset Formula $\raisebox{6mm}{}$
12890 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12894 \begin_inset Formula $\raisebox{-4mm}{}$
12915 \begin_layout Standard
12916 The frame thickness can also be adjusted.
12917 To do this the following commands have to be inserted in TeX-mode before
12921 \begin_layout Standard
12931 \begin_inset Quotes eld
12935 \begin_inset Quotes erd
12949 \begin_inset Quotes eld
12953 \begin_inset Quotes erd
12959 \begin_layout Standard
12960 \begin_inset Quotes eld
12964 \begin_inset Quotes erd
12967 specifies the minimal distance between the frame and the first character
12969 An example for this is the following framed formula:
12973 \begin_layout Plain Layout
12985 \begin_inset Formula \[
12990 Before this formula the commands
12993 \begin_layout Standard
13015 \begin_layout Standard
13016 were inserted in TeX-mode.
13017 The given values are used for all following boxes.
13020 \begin_layout Standard
13021 To return to the standard frame size, the command
13024 \begin_layout Standard
13049 \begin_layout Plain Layout
13063 \begin_layout Standard
13064 is inserted in TeX-mode before the next formula.
13067 \begin_layout Subsection
13068 Boxes without Frame
13069 \begin_inset CommandInset label
13071 name "sub:Boxes-without-Frame"
13079 \begin_layout Plain Layout
13080 Boxes ! without frame
13088 \begin_layout Standard
13089 For boxes without a frame there are the following box commands:
13099 \begin_layout Plain Layout
13117 \begin_layout Plain Layout
13135 \begin_layout Plain Layout
13146 \begin_layout Standard
13153 a box can be super- or subscripted.
13154 But in contrary to normal super- and subscripting, the characters in the
13155 box keep their font size.
13162 is used in the following scheme:
13165 \begin_layout Standard
13170 raisebox{height}{box content}
13173 \begin_layout Standard
13174 When the box should contain a formula, an extra formula is needed like for
13184 \begin_layout Standard
13186 \begin_inset Tabular
13187 <lyxtabular version="3" rows="4" columns="2">
13189 <column alignment="center" valignment="top" width="0">
13190 <column alignment="center" valignment="top" width="0">
13192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13195 \begin_layout Plain Layout
13201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13204 \begin_layout Plain Layout
13212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13215 \begin_layout Plain Layout
13219 \begin_inset Formula $\to$
13225 \begin_inset Formula $\to$
13233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13236 \begin_layout Plain Layout
13237 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13250 \begin_layout Plain Layout
13254 \begin_inset Formula $\to$
13260 \begin_inset Formula $\to$
13268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13271 \begin_layout Plain Layout
13272 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13285 \begin_layout Plain Layout
13289 \begin_inset Formula $\to$
13304 \begin_layout Plain Layout
13318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13321 \begin_layout Plain Layout
13325 \begin_layout Plain Layout
13349 \begin_layout Standard
13350 The last formula can currently only be created using TeX-mode because LyX
13351 inserts a box instead of the needed extra formula.
13355 \begin_layout Plain Layout
13357 \begin_inset CommandInset href
13359 name "LyX-bug #1435"
13360 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13372 \begin_layout Standard
13397 , with the difference that there is no frame.
13400 \begin_layout Subsection
13402 \begin_inset CommandInset label
13404 name "sub:Colored-Boxes"
13412 \begin_layout Plain Layout
13421 \begin_layout Standard
13422 To be able to use all commands explained in this section, the LaTeX-package
13431 \begin_layout Plain Layout
13436 is part of every LaTeX standard installation.
13445 \begin_layout Plain Layout
13451 has to be loaded in the LaTeX-preamble with the line
13455 \begin_layout Plain Layout
13456 When text is colored somewhere in the document with a predefined color,
13457 LyX loads the LaTeX-package
13462 Thus it is possible that the package is loaded twice, but this doesn't
13469 \begin_inset Note Note
13472 \begin_layout Plain Layout
13473 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13482 \begin_layout Standard
13490 \begin_layout Standard
13491 \begin_inset VSpace medskip
13494 To color boxes, the command
13504 \begin_layout Plain Layout
13512 is used in the following scheme:
13515 \begin_layout Standard
13520 colorbox{color}{box content}
13523 \begin_layout Standard
13524 The box content can also be a box and a
13530 can also be part of another box (see the 2nd and 3rd example).
13531 When the box should contain a formula, an extra formula has to be created,
13542 \begin_layout Plain Layout
13543 This also applies for the command
13551 \begin_inset CommandInset href
13553 name "LyX-bug #1435"
13554 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13566 \begin_layout Standard
13567 One of the following predefined colors can be chosen:
13570 \begin_layout Standard
13604 \begin_layout Standard
13606 \begin_inset Tabular
13607 <lyxtabular version="3" rows="4" columns="2">
13609 <column alignment="center" valignment="top" width="0">
13610 <column alignment="center" valignment="top" width="0">
13612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13615 \begin_layout Plain Layout
13621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13624 \begin_layout Plain Layout
13626 \begin_inset Note Note
13629 \begin_layout Plain Layout
13636 is only used as spacer.
13648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13651 \begin_layout Plain Layout
13655 \begin_inset Formula $\to$
13665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13668 \begin_layout Plain Layout
13669 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13682 \begin_layout Plain Layout
13686 \begin_inset Formula $\to$
13697 \begin_layout Plain Layout
13711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13714 \begin_layout Plain Layout
13715 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13728 \begin_layout Plain Layout
13735 \begin_layout Plain Layout
13747 \begin_inset Formula $\to$
13757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13760 \begin_layout Plain Layout
13761 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13777 \begin_layout Standard
13784 only colors the box but not the characters in the box.
13785 To color all characters, the whole formula is highlighted and the wanted
13786 color is chosen in the
13789 \begin_inset space ~
13795 The dialog can be called with the toolbar button
13796 \begin_inset Graphics
13797 filename ../images/dialog-show_character.png
13804 Edit\SpecialChar \menuseparator
13806 \begin_inset space ~
13809 Style\SpecialChar \menuseparator
13813 The formula number has then the same color as the formula.
13814 When the formula number should get another color than the formula characters,
13815 the color must be changed within the formula.
13818 \begin_layout Standard
13822 \begin_layout Standard
13825 \begin_inset Formula \begin{equation}
13826 \int A=B\label{eq:red}\end{equation}
13833 \begin_inset Formula \begin{equation}
13834 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13841 \begin_layout Standard
13843 \begin_inset CommandInset ref
13849 is completely colored red.
13850 \begin_inset Newline newline
13854 \begin_inset CommandInset ref
13856 reference "eq:redgreen"
13860 was first completely colored green to set the color for the formula number.
13861 Subsequently the formula characters were colored red.
13864 \begin_layout Standard
13865 \begin_inset VSpace bigskip
13868 To color the frame different than the rest of the box, the command
13878 \begin_layout Plain Layout
13886 is used in the following scheme:
13889 \begin_layout Standard
13894 fcolorbox{frame color}{color}{box content}
13897 \begin_layout Standard
13904 is an extension of the command
13911 The frame width is set, like for
13934 \begin_layout Plain Layout
13946 \begin_inset Formula \[
13947 \fcolorbox{cyan}{magenta}{A=B}\]
13955 \begin_layout Plain Layout
13969 \begin_layout Standard
13970 This formula was created with the command
13971 \begin_inset Newline newline
13979 \begin_inset Formula $\to$
13985 \begin_inset Formula $\to$
13995 \begin_layout Standard
13996 \begin_inset VSpace bigskip
13999 To use other colors than the predefined ones, they have to be defined first.
14002 \begin_layout Standard
14003 One can for example define the color
14004 \begin_inset Quotes eld
14012 \begin_inset Quotes erd
14015 with the LaTeX-preamble line:
14018 \begin_layout Standard
14023 definecolor{darkgreen}{cmyk}{0.5,
14041 \begin_layout Plain Layout
14052 \begin_layout Standard
14057 is the color space that denotes the colors
14074 The four comma separated numbers are the portion factor for the corresponding
14075 colors of the color space.
14076 The factors can be in the range of 0
14077 \begin_inset space \thinspace{}
14081 \begin_inset space \thinspace{}
14089 also the color space
14093 can be used for definitions.
14110 , so that there are in this case three portion factors for the corresponding
14112 Furthermore there is the color space
14116 with one portion factor for the gray value.
14119 \begin_layout Standard
14120 As example a framed box with the new defined color
14124 where the characters have been colored
14129 \begin_inset Formula \begin{equation}
14130 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14137 \begin_layout Standard
14138 Self-defined colors can also be used for text with the help of the command
14149 \begin_layout Plain Layout
14158 \begin_layout Standard
14162 \begin_layout Plain Layout
14166 textcolor{darkgreen}{
14172 \begin_inset Quotes eld
14176 \begin_inset Quotes erd
14183 \begin_layout Plain Layout
14193 \begin_layout Standard
14204 \begin_layout Plain Layout
14212 is used in the scheme
14216 textcolor{color}{characters to color}
14221 \begin_layout Subsection
14223 \begin_inset CommandInset label
14225 name "sub:Paragraph-Boxes"
14233 \begin_layout Plain Layout
14234 Boxes ! as paragraph
14242 \begin_layout Standard
14243 A box that can contain several lines and paragraphs, a so called paragraph
14244 box (parbox), can be created with the menu
14246 Insert\SpecialChar \menuseparator
14249 or the toolbar button
14250 \begin_inset Graphics
14251 filename ../images/box-insert.png
14259 \begin_layout Standard
14260 The following example shows a framed parbox in a line:
14263 \begin_layout Standard
14264 \begin_inset VSpace medskip
14268 \begin_inset Box Boxed
14277 height_special "totalheight"
14280 \begin_layout Plain Layout
14281 This is a paragraph box.
14283 \begin_inset space \thinspace{}
14286 cm long and can also contain formulas:
14287 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14298 \begin_layout Standard
14299 \begin_inset VSpace medskip
14305 \begin_layout Standard
14306 Such a box is created by right-clicking on the gray box inset.
14307 A dialog pops up showing the box properties.
14321 \begin_inset space \thinspace{}
14326 Vertical Box Alignment
14331 \begin_layout Standard
14332 \begin_inset VSpace medskip
14335 In LaTeX a parbox is created with the command
14345 \begin_layout Plain Layout
14353 that has the following scheme:
14356 \begin_layout Standard
14361 parbox[position]{width}{box content}
14364 \begin_layout Standard
14378 for bottom means that the box is aligned within the surrounding text with
14384 for top this is done with the first line.
14385 When no position is given, the box will be vertically centered, see section
14393 \begin_inset space ~
14398 manual for examples.
14401 \begin_layout Standard
14402 \begin_inset VSpace bigskip
14405 To frame formulas completely, including the formula number, the formula
14406 must be set into a parbox.
14407 To do this, the command
14421 is inserted in TeX-mode before the formula.
14430 \begin_layout Plain Layout
14440 is hereby the line width set for the document.
14441 Because the frame is outside the parbox, 2
14442 \begin_inset space \thinspace{}
14445 times the frame separation and the frame thickness must be subtracted from
14447 As this is not automatically done by LyX due to a bug
14451 \begin_layout Plain Layout
14452 \begin_inset CommandInset href
14454 name "LyX-bug #4483"
14455 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14464 , TeX-mode has to be used.
14465 To be able to multiply and subtract in arguments, the LaTeX-package
14473 \begin_layout Plain Layout
14478 is part of every LaTeX standard installation.
14487 \begin_layout Plain Layout
14493 must be loaded in the LaTeX-preamble with the line
14496 \begin_layout Standard
14504 \begin_layout Standard
14505 Behind the formula both boxes are closed by entering
14510 Here is an example:
14514 \begin_layout Plain Layout
14528 \begin_layout Standard
14532 \begin_layout Plain Layout
14550 \begin_inset Formula \begin{equation}
14551 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14559 \begin_layout Plain Layout
14570 \begin_layout Plain Layout
14584 \begin_layout Standard
14585 \begin_inset VSpace medskip
14588 As a parbox is used as argument of
14594 , there is in this case no difference between
14609 \begin_layout Standard
14610 \begin_inset VSpace bigskip
14613 Paragraph boxes are very useful to comment formulas directly.
14620 is used in combination with the command
14634 \begin_inset CommandInset ref
14636 reference "sub:User-defined-Numbering"
14643 \begin_layout Standard
14644 An example of a formula commented with
14653 \begin_layout Standard
14657 \begin_layout Plain Layout
14670 This is a description.
14671 It is distinctly separated from the formula and multiline.
14675 \begin_layout Plain Layout
14687 \begin_layout Standard
14688 Such a formula must be inserted completely in TeX-mode because LyX does
14689 not yet support the command
14696 The formula is created with the following command sequence:
14699 \begin_layout Standard
14712 is inserted in TeX-mode.
14716 \begin_layout Plain Layout
14717 When the formula style
14729 can also be replaced by
14736 (formula styles see
14737 \begin_inset CommandInset ref
14739 reference "sec:Formula-Styles"
14748 Then the description follows as normal text, and finally
14754 is inserted in TeX-mode.
14767 hereby create a displayed formula.
14770 \begin_layout Standard
14777 can be seen in this example that was
14778 \begin_inset Quotes eld
14782 \begin_inset Quotes erd
14785 using the mathematical textmode:
14786 \begin_inset Formula \[
14787 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14794 \begin_layout Section
14799 \begin_layout Plain Layout
14808 \begin_layout Subsection
14810 \begin_inset CommandInset label
14812 name "sub:Big-Operators"
14820 \begin_layout Plain Layout
14830 \begin_layout Plain Layout
14840 \begin_layout Plain Layout
14849 \begin_layout Standard
14850 To be able to use all integral operators listed here, the option
14852 Use esint package automatically
14854 must be set in the document settings under
14857 \begin_inset space ~
14865 \begin_layout Standard
14866 \begin_inset space \hfill{}
14870 \begin_inset Tabular
14871 <lyxtabular version="3" rows="12" columns="2">
14873 <column alignment="center" valignment="top" width="0pt">
14874 <column alignment="center" valignment="top" width="0pt">
14876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14879 \begin_layout Plain Layout
14885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14888 \begin_layout Plain Layout
14896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14899 \begin_layout Plain Layout
14906 \begin_layout Plain Layout
14919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14922 \begin_layout Plain Layout
14923 \begin_inset Formula $\sum$
14933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14936 \begin_layout Plain Layout
14943 \begin_layout Plain Layout
14956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14959 \begin_layout Plain Layout
14960 \begin_inset Formula $\int$
14970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14973 \begin_layout Plain Layout
14981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14984 \begin_layout Plain Layout
14985 \begin_inset Formula $\oint$
14995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14998 \begin_layout Plain Layout
15006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15009 \begin_layout Plain Layout
15010 \begin_inset Formula $\ointctrclockwise$
15020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15023 \begin_layout Plain Layout
15031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15034 \begin_layout Plain Layout
15035 \begin_inset Formula $\ointclockwise$
15045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15048 \begin_layout Plain Layout
15056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15059 \begin_layout Plain Layout
15060 \begin_inset Formula $\sqint$
15070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15073 \begin_layout Plain Layout
15081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15084 \begin_layout Plain Layout
15086 \begin_inset Formula $\fint$
15096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15099 \begin_layout Plain Layout
15107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15110 \begin_layout Plain Layout
15112 \begin_inset Formula $\landupint$
15122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15125 \begin_layout Plain Layout
15133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15136 \begin_layout Plain Layout
15138 \begin_inset Formula $\landdownint$
15148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15151 \begin_layout Plain Layout
15159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15162 \begin_layout Plain Layout
15163 \begin_inset Formula $\bigcap$
15173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15176 \begin_layout Plain Layout
15184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15187 \begin_layout Plain Layout
15188 \begin_inset Formula $\bigcup$
15202 \begin_inset space \hfill{}
15206 \begin_inset Tabular
15207 <lyxtabular version="3" rows="10" columns="2">
15209 <column alignment="center" valignment="top" width="0pt">
15210 <column alignment="center" valignment="top" width="0pt">
15212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15215 \begin_layout Plain Layout
15221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15224 \begin_layout Plain Layout
15232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15235 \begin_layout Plain Layout
15242 \begin_layout Plain Layout
15255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15258 \begin_layout Plain Layout
15259 \begin_inset Formula $\prod$
15269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15272 \begin_layout Plain Layout
15280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15283 \begin_layout Plain Layout
15284 \begin_inset Formula $\coprod$
15294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15297 \begin_layout Plain Layout
15305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15308 \begin_layout Plain Layout
15309 \begin_inset Formula $\bigodot$
15319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15322 \begin_layout Plain Layout
15330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15333 \begin_layout Plain Layout
15334 \begin_inset Formula $\bigotimes$
15344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15347 \begin_layout Plain Layout
15355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15358 \begin_layout Plain Layout
15359 \begin_inset Formula $\bigoplus$
15369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15372 \begin_layout Plain Layout
15380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15383 \begin_layout Plain Layout
15384 \begin_inset Formula $\bigwedge$
15394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15397 \begin_layout Plain Layout
15405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15408 \begin_layout Plain Layout
15409 \begin_inset Formula $\bigvee$
15419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15422 \begin_layout Plain Layout
15430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15433 \begin_layout Plain Layout
15434 \begin_inset Formula $\bigsqcup$
15444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15447 \begin_layout Plain Layout
15455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15458 \begin_layout Plain Layout
15459 \begin_inset Formula $\biguplus$
15473 \begin_inset space \hfill{}
15479 \begin_layout Standard
15480 All big operators can also be inserted via the math toolbar button
15481 \begin_inset Graphics
15482 filename ../images/math/intop.png
15490 \begin_layout Standard
15491 The operators are called big because they are bigger than the sometimes
15492 equal looking binary operators.
15493 All big operators can have limits as described in the next subsection.
15496 \begin_layout Standard
15497 For all integral operators there is a second version available, ending on
15515 These operators are different from
15528 \begin_inset space ~
15531 in the style the operator limits are displayed, see
15532 \begin_inset CommandInset ref
15534 reference "sub:Operator-Limits"
15542 \begin_layout Subsubsection*
15543 Advices for Integrals
15546 \begin_layout Standard
15551 in an integral is an operator, that therefore has to be set upright.
15552 This is done by highlighting the
15556 and using the keyboard shortcut
15566 \begin_layout Plain Layout
15572 \begin_inset CommandInset ref
15574 reference "sub:Font-Styles"
15584 Finally the smallest space is inserted before the
15588 , as this is usual for operators.
15592 \begin_layout Standard
15594 \begin_inset Formula $\int A(x)dx$
15598 \begin_inset Newline newline
15605 \begin_layout Plain Layout
15615 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15621 \begin_layout Standard
15622 For multiple integrals there are the following commands:
15623 \begin_inset VSpace medskip
15629 \begin_layout Standard
15630 \begin_inset space \hfill{}
15634 \begin_inset Tabular
15635 <lyxtabular version="3" rows="4" columns="2">
15637 <column alignment="center" valignment="top" width="0">
15638 <column alignment="center" valignment="top" width="0">
15640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15643 \begin_layout Plain Layout
15649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15652 \begin_layout Plain Layout
15654 \begin_inset Note Note
15657 \begin_layout Plain Layout
15664 is only used as spacer.
15676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15679 \begin_layout Plain Layout
15687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15690 \begin_layout Plain Layout
15691 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15704 \begin_layout Plain Layout
15712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15715 \begin_layout Plain Layout
15716 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15729 \begin_layout Plain Layout
15737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15740 \begin_layout Plain Layout
15741 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15755 \begin_inset space \hfill{}
15759 \begin_inset Tabular
15760 <lyxtabular version="3" rows="4" columns="2">
15762 <column alignment="center" valignment="top" width="0">
15763 <column alignment="center" valignment="top" width="0">
15765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15768 \begin_layout Plain Layout
15774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15777 \begin_layout Plain Layout
15785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15788 \begin_layout Plain Layout
15796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15799 \begin_layout Plain Layout
15800 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15813 \begin_layout Plain Layout
15821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15824 \begin_layout Plain Layout
15825 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15838 \begin_layout Plain Layout
15846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15849 \begin_layout Plain Layout
15850 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15864 \begin_inset space \hfill{}
15870 \begin_layout Subsection
15872 \begin_inset CommandInset label
15874 name "sub:Operator-Limits"
15882 \begin_layout Plain Layout
15891 \begin_layout Standard
15892 Limits are created by super- and subscripts:
15895 \begin_layout Standard
15897 \begin_inset Tabular
15898 <lyxtabular version="3" rows="2" columns="2">
15900 <column alignment="center" valignment="top" width="0pt">
15901 <column alignment="center" valignment="top" width="0pt">
15903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15906 \begin_layout Plain Layout
15912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15915 \begin_layout Plain Layout
15917 \begin_inset Note Note
15920 \begin_layout Plain Layout
15927 is only used as spacer.
15939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15942 \begin_layout Plain Layout
15951 \begin_layout Plain Layout
15961 \begin_inset Formula $\to$
15965 \begin_inset Formula $\to$
15973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15976 \begin_layout Plain Layout
15977 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15993 \begin_layout Standard
15994 Limits of inline formulas are set right beside the operator.
15995 Limits in displayed formulas are set above or below the operator, except
15996 of integral limits.
15999 \begin_layout Standard
16000 To force that the limits are set beside the operator, the cursor is set
16001 directly behind the operator and the limits type is changed with the menu
16004 Edit\SpecialChar \menuseparator
16005 Math\SpecialChar \menuseparator
16024 \begin_layout Standard
16025 The default limits type is this:
16026 \begin_inset Formula \[
16027 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16031 This is how it looks when the limits type was changed to
16038 \begin_inset Formula \[
16039 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16043 For integrals, except those ending with
16059 , the limits are by default set beside the operator.
16060 But for multiple integrals the limits are often set below the operator.
16061 In the following example the limits type was therefore set to
16065 and so set below the integrals:
16066 \begin_inset Formula \begin{equation}
16067 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16074 \begin_layout Standard
16075 \begin_inset VSpace medskip
16078 To specify conditions for limits, the commands
16088 \begin_layout Plain Layout
16106 \begin_layout Plain Layout
16115 To create for example this expression
16116 \begin_inset Formula \begin{equation}
16117 \sum_{\begin{subarray}{c}
16119 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16126 \begin_layout Standard
16127 the following has to be done:
16128 \begin_inset Newline newline
16143 \begin_layout Plain Layout
16155 One is now in a blue box under the summation operator and insert there
16164 \begin_layout Plain Layout
16176 The blue box is now within a purple box and now several lines can be written
16178 A new line is created by inserting a line break (
16181 arg "newline-insert newline"
16186 \begin_inset Newline newline
16191 0<k<1000 Ctrl+Return
16192 \begin_inset Newline newline
16197 is typed in, a new box appears below for the new line.
16200 \begin_layout Standard
16201 The alignment of the lines can be changed to left aligned with the
16211 Edit\SpecialChar \menuseparator
16215 To get right alignment,
16223 \begin_layout Plain Layout
16234 is inserted at the beginning of the line.
16237 \begin_layout Standard
16250 with the difference that the lines are always centered.
16253 \begin_layout Standard
16254 \begin_inset VSpace bigskip
16258 \begin_inset CommandInset ref
16260 reference "eq:substack"
16264 there can be too much space beside an operator, because the characters
16265 following the operator are set beside the limits.
16268 \begin_layout Standard
16269 To avoid this, the following macro can be used in the LaTeX-preamble:
16272 \begin_layout Standard
16286 \begin_inset Newline newline
16298 \begin_inset Newline newline
16305 mathclapinternal #1#2{
16309 mathsurround =0pt #1{#2}$}}
16312 \begin_layout Standard
16313 This defines the command
16323 \begin_layout Plain Layout
16331 that sets the width of the limit to 0
16332 \begin_inset space \thinspace{}
16336 The command scheme is
16339 \begin_layout Standard
16347 \begin_layout Standard
16348 where the limit can consist of several conditions.
16351 \begin_layout Standard
16353 \begin_inset CommandInset ref
16355 reference "eq:substack"
16359 , one uses the command
16362 \begin_layout Standard
16375 \begin_layout Plain Layout
16384 0<k<1000 Ctrl+Return
16387 \begin_layout Standard
16388 to create the lower limit.
16389 The summand is now directly behind the summation operator:
16390 \begin_inset Formula \[
16391 \sum_{\mathclap{\substack{0<k<1000\\
16392 \\k\,\in\,\mathbb{N}}
16400 \begin_layout Standard
16401 \begin_inset VSpace bigskip
16404 How to use one limit for several operators is described in
16405 \begin_inset CommandInset ref
16407 reference "sub:Self-defined-Operators"
16414 \begin_layout Standard
16415 \begin_inset Newpage newpage
16421 \begin_layout Subsection
16423 \begin_inset CommandInset label
16425 name "sub:Binary-Operators"
16433 \begin_layout Plain Layout
16442 \begin_layout Standard
16443 Binary operators are surrounded by space when there is a character before
16445 \begin_inset VSpace medskip
16451 \begin_layout Standard
16452 \begin_inset space \hfill{}
16456 \begin_inset Tabular
16457 <lyxtabular version="3" rows="13" columns="2">
16459 <column alignment="center" valignment="top" width="0pt">
16460 <column alignment="center" valignment="top" width="0pt">
16462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16465 \begin_layout Plain Layout
16467 \begin_inset Note Note
16470 \begin_layout Plain Layout
16477 is only used as spacer.
16487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16490 \begin_layout Plain Layout
16498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16501 \begin_layout Plain Layout
16507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16510 \begin_layout Plain Layout
16511 \begin_inset Formula $+$
16521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16524 \begin_layout Plain Layout
16530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16533 \begin_layout Plain Layout
16534 \begin_inset Formula $-$
16544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16547 \begin_layout Plain Layout
16555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16558 \begin_layout Plain Layout
16559 \begin_inset Formula $\pm$
16569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16572 \begin_layout Plain Layout
16580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16583 \begin_layout Plain Layout
16584 \begin_inset Formula $\mp$
16594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16597 \begin_layout Plain Layout
16605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16608 \begin_layout Plain Layout
16609 \begin_inset Formula $\cdot$
16619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16622 \begin_layout Plain Layout
16630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16633 \begin_layout Plain Layout
16634 \begin_inset Formula $\times$
16644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16647 \begin_layout Plain Layout
16655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16658 \begin_layout Plain Layout
16659 \begin_inset Formula $\div$
16669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16672 \begin_layout Plain Layout
16676 \begin_layout Plain Layout
16689 \begin_layout Plain Layout
16701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16704 \begin_layout Plain Layout
16705 \begin_inset Formula $*$
16715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16718 \begin_layout Plain Layout
16726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16729 \begin_layout Plain Layout
16730 \begin_inset Formula $\star$
16740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16743 \begin_layout Plain Layout
16751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16754 \begin_layout Plain Layout
16755 \begin_inset Formula $\circ$
16765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16768 \begin_layout Plain Layout
16776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16779 \begin_layout Plain Layout
16780 \begin_inset Formula $\diamond$
16790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16793 \begin_layout Plain Layout
16801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16804 \begin_layout Plain Layout
16805 \begin_inset Formula $\bullet$
16819 \begin_inset space \hfill{}
16823 \begin_inset Tabular
16824 <lyxtabular version="3" rows="13" columns="2">
16826 <column alignment="center" valignment="top" width="0pt">
16827 <column alignment="center" valignment="top" width="0pt">
16829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16832 \begin_layout Plain Layout
16838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16841 \begin_layout Plain Layout
16849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16852 \begin_layout Plain Layout
16860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16863 \begin_layout Plain Layout
16864 \begin_inset Formula $\nabla$
16874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16877 \begin_layout Plain Layout
16885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16888 \begin_layout Plain Layout
16889 \begin_inset Formula $\bigtriangledown$
16899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16902 \begin_layout Plain Layout
16910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16913 \begin_layout Plain Layout
16914 \begin_inset Formula $\bigtriangleup$
16924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16927 \begin_layout Plain Layout
16935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16938 \begin_layout Plain Layout
16939 \begin_inset Formula $\Box$
16949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16952 \begin_layout Plain Layout
16960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16963 \begin_layout Plain Layout
16964 \begin_inset Formula $\cap$
16974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16977 \begin_layout Plain Layout
16985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16988 \begin_layout Plain Layout
16989 \begin_inset Formula $\cup$
16999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17002 \begin_layout Plain Layout
17010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17013 \begin_layout Plain Layout
17014 \begin_inset Formula $\dagger$
17024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17027 \begin_layout Plain Layout
17035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17038 \begin_layout Plain Layout
17039 \begin_inset Formula $\ddagger$
17049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17052 \begin_layout Plain Layout
17060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17063 \begin_layout Plain Layout
17064 \begin_inset Formula $\wr$
17074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17077 \begin_layout Plain Layout
17085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17088 \begin_layout Plain Layout
17089 \begin_inset Formula $\bigcirc$
17099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17102 \begin_layout Plain Layout
17110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17113 \begin_layout Plain Layout
17114 \begin_inset Formula $\wedge$
17124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17127 \begin_layout Plain Layout
17135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17138 \begin_layout Plain Layout
17139 \begin_inset Formula $\vee$
17153 \begin_inset space \hfill{}
17157 \begin_inset Tabular
17158 <lyxtabular version="3" rows="13" columns="2">
17160 <column alignment="center" valignment="top" width="0pt">
17161 <column alignment="center" valignment="top" width="0pt">
17163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17166 \begin_layout Plain Layout
17172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17175 \begin_layout Plain Layout
17183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17186 \begin_layout Plain Layout
17194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17197 \begin_layout Plain Layout
17198 \begin_inset Formula $\oplus$
17208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17211 \begin_layout Plain Layout
17219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17222 \begin_layout Plain Layout
17223 \begin_inset Formula $\ominus$
17233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17236 \begin_layout Plain Layout
17244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17247 \begin_layout Plain Layout
17248 \begin_inset Formula $\otimes$
17258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17261 \begin_layout Plain Layout
17269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17272 \begin_layout Plain Layout
17273 \begin_inset Formula $\oslash$
17283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17286 \begin_layout Plain Layout
17294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17297 \begin_layout Plain Layout
17298 \begin_inset Formula $\odot$
17308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17311 \begin_layout Plain Layout
17319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17322 \begin_layout Plain Layout
17323 \begin_inset Formula $\amalg$
17333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17336 \begin_layout Plain Layout
17344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17347 \begin_layout Plain Layout
17348 \begin_inset Formula $\uplus$
17358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17361 \begin_layout Plain Layout
17369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17372 \begin_layout Plain Layout
17373 \begin_inset Formula $\setminus$
17383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17386 \begin_layout Plain Layout
17394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17397 \begin_layout Plain Layout
17398 \begin_inset Formula $\sqcap$
17408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17411 \begin_layout Plain Layout
17419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17422 \begin_layout Plain Layout
17423 \begin_inset Formula $\sqcup$
17433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17436 \begin_layout Plain Layout
17444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17447 \begin_layout Plain Layout
17448 \begin_inset Formula $\triangleleft$
17458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17461 \begin_layout Plain Layout
17469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17472 \begin_layout Plain Layout
17473 \begin_inset Formula $\triangleright$
17487 \begin_inset space \hfill{}
17493 \begin_layout Standard
17494 All binary operators can also be inserted via the math toolbar button
17495 \begin_inset Graphics
17496 filename ../images/math/pm.png
17504 \begin_layout Standard
17505 To typeset the Laplace operator also
17522 \begin_inset Formula $\nabla^{2}$
17525 ) can be used instead of
17534 \begin_layout Standard
17541 Insert\SpecialChar \menuseparator
17553 \begin_layout Subsection
17554 Self-defined Operators
17555 \begin_inset CommandInset label
17557 name "sub:Self-defined-Operators"
17565 \begin_layout Plain Layout
17566 Operators ! self-defined
17574 \begin_layout Standard
17575 With the help of the command
17579 DeclareMathOperator
17585 \begin_layout Plain Layout
17590 DeclareMathOperator
17595 custom operators can be defined in the LaTeX-preamble.
17596 Its command scheme is:
17599 \begin_layout Standard
17604 DeclareMathOperator{new command}{display}
17607 \begin_layout Standard
17608 Display can be characters or symbols that define how the operator looks
17610 To define a big operator a * is set behind the command.
17611 All self-defined big operators can have limits as described in
17612 \begin_inset CommandInset ref
17614 reference "sub:Operator-Limits"
17621 \begin_layout Standard
17622 For example the LaTeX-preamble line
17625 \begin_layout Standard
17630 DeclareMathOperator*{
17637 \begin_layout Standard
17638 defines the command
17644 , that inserts a big operator consisting of the lozenge symbol from
17645 \begin_inset CommandInset ref
17647 reference "sub:Miscellaneous-Symbols"
17652 \begin_inset Formula \[
17653 \Lozenge_{n=1}^{\infty}\]
17657 The command for this formula is:
17668 \begin_inset Formula $\to$
17674 \begin_layout Standard
17675 \begin_inset VSpace bigskip
17678 When self-defined operators are not used several times in the document,
17679 they can also be defined with the commands
17689 \begin_layout Plain Layout
17707 \begin_layout Plain Layout
17715 , which have the following scheme:
17718 \begin_layout Standard
17732 \begin_layout Standard
17739 defines big operators,
17748 \begin_layout Standard
17756 \begin_inset space \thinspace{}
17760 \begin_inset space \space{}
17763 be used to use one limit for several operators:
17766 \begin_layout Standard
17767 \begin_inset Formula \[
17768 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17775 \begin_layout Standard
17776 The command for the formula above is:
17777 \begin_inset Newline newline
17796 \begin_layout Plain Layout
17808 \begin_inset Formula $\to$
17817 \begin_layout Plain Layout
17831 \begin_layout Section
17836 \begin_layout Plain Layout
17845 \begin_layout Subsection
17847 \begin_inset CommandInset label
17849 name "sub:Font-Styles"
17857 \begin_layout Plain Layout
17866 \begin_layout Standard
17867 Latin letters in formulas can be set in one of the following font styles:
17868 \begin_inset VSpace -2mm
17874 \begin_layout Standard
17876 \begin_inset Tabular
17877 <lyxtabular version="3" rows="6" columns="3">
17879 <column alignment="center" valignment="top" width="0">
17880 <column alignment="center" valignment="top" width="0">
17881 <column alignment="center" valignment="top" width="0">
17883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17886 \begin_layout Plain Layout
17892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17895 \begin_layout Plain Layout
17901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17904 \begin_layout Plain Layout
17912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17915 \begin_layout Plain Layout
17924 \begin_layout Plain Layout
17940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17943 \begin_layout Plain Layout
17944 \begin_inset Formula $\mathbb{ABC}$
17952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17955 \begin_layout Plain Layout
17968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17971 \begin_layout Plain Layout
17980 \begin_layout Plain Layout
17996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17999 \begin_layout Plain Layout
18000 \begin_inset Formula $\mathbf{AbC}$
18008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18011 \begin_layout Plain Layout
18024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18027 \begin_layout Plain Layout
18036 \begin_layout Plain Layout
18052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18055 \begin_layout Plain Layout
18056 \begin_inset Formula $\boldsymbol{AbC}$
18064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18067 \begin_layout Plain Layout
18070 arg "font-boldsymbol"
18080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18083 \begin_layout Plain Layout
18092 \begin_layout Plain Layout
18108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18111 \begin_layout Plain Layout
18112 \begin_inset Formula $\mathcal{ABC}$
18120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18123 \begin_layout Plain Layout
18136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18139 \begin_layout Plain Layout
18148 \begin_layout Plain Layout
18164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18167 \begin_layout Plain Layout
18168 \begin_inset Formula $\mathfrak{AbC}$
18176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18179 \begin_layout Plain Layout
18193 \begin_layout Standard
18195 \begin_inset Tabular
18196 <lyxtabular version="3" rows="5" columns="3">
18198 <column alignment="center" valignment="top" width="0">
18199 <column alignment="center" valignment="top" width="0">
18200 <column alignment="center" valignment="top" width="0">
18202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18205 \begin_layout Plain Layout
18211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18214 \begin_layout Plain Layout
18220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18223 \begin_layout Plain Layout
18231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18234 \begin_layout Plain Layout
18243 \begin_layout Plain Layout
18259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18262 \begin_layout Plain Layout
18263 \begin_inset Formula $\mathit{AbC}$
18271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18274 \begin_layout Plain Layout
18282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18285 \begin_layout Plain Layout
18294 \begin_layout Plain Layout
18310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18313 \begin_layout Plain Layout
18314 \begin_inset Formula $\mathrm{AbC}$
18322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18325 \begin_layout Plain Layout
18338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18341 \begin_layout Plain Layout
18350 \begin_layout Plain Layout
18366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18369 \begin_layout Plain Layout
18370 \begin_inset Formula $\mathsf{AbC}$
18378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18381 \begin_layout Plain Layout
18394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18397 \begin_layout Plain Layout
18406 \begin_layout Plain Layout
18422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18425 \begin_layout Plain Layout
18426 \begin_inset Formula $\mathtt{AbC}$
18434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18437 \begin_layout Plain Layout
18440 arg "font-typewriter"
18456 \begin_layout Standard
18457 \begin_inset Note Greyedout
18460 \begin_layout Plain Layout
18477 can only be used for big letters.
18485 \begin_layout Standard
18486 Predefined is the style
18495 \begin_layout Standard
18496 The style commands work also for letters in mathematical constructs:
18497 \begin_inset Formula \[
18498 \mathfrak{A=\frac{b}{C}}\]
18505 \begin_layout Standard
18506 Characters in mathematical text don't appear in a math font style but in
18507 the text font style
18514 That their style can't be set correctly via the text style dialog is a
18519 \begin_layout Plain Layout
18520 \begin_inset CommandInset href
18522 name "LyX-bug #4091"
18523 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18535 \begin_layout Standard
18536 Instead of the style commands the dialog
18538 Edit\SpecialChar \menuseparator
18539 Math\SpecialChar \menuseparator
18542 or the toolbar button
18543 \begin_inset Graphics
18544 filename ../images/math/font.png
18552 \begin_layout Subsection
18554 \begin_inset CommandInset label
18556 name "sub:Bold-Formulas"
18564 \begin_layout Plain Layout
18573 \begin_layout Standard
18574 To make a complete formula bold, the command
18580 from the previous subsection cannot be used, because it doesn't work for
18581 small Greek letters.
18582 Furthermore it prints Latin letters always upright, like in the following
18586 \begin_layout Standard
18587 \begin_inset Formula \[
18588 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18595 \begin_layout Standard
18596 To display the formula correctly, the command
18603 \begin_inset Formula \[
18604 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18608 It is also possible to set the formula in a
18610 boldmath environment
18613 This environment is created by inserting the command
18621 \begin_layout Plain Layout
18632 To end the environment, the command
18640 \begin_layout Plain Layout
18650 is inserted in TeX-mode.
18654 \begin_layout Plain Layout
18664 \begin_inset Formula \[
18665 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18673 \begin_layout Plain Layout
18685 \begin_layout Subsection
18690 \begin_layout Plain Layout
18699 \begin_layout Standard
18700 Formulas can be colored like normal text: Highlight a formula or a formula
18706 Here is a formula in magenta:
18707 \begin_inset Formula \[
18708 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18715 \begin_layout Standard
18716 You can also define your own colors as described in
18717 \begin_inset CommandInset ref
18719 reference "sub:Colored-Boxes"
18724 They can be used with the TeX code command
18734 \begin_layout Plain Layout
18745 \begin_layout Standard
18750 textcolor{color}{characters or formula}
18753 \begin_layout Standard
18754 The following example was colored completely dark green and partly red:
18757 \begin_layout Standard
18761 \begin_layout Plain Layout
18765 textcolor{darkgreen}{
18771 \begin_inset Formula \[
18772 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18780 \begin_layout Plain Layout
18790 \begin_layout Standard
18791 Due to a bug in LyX only complete formulas can be colored with self-defined
18796 \begin_layout Plain Layout
18797 \begin_inset CommandInset href
18799 name "LyX-bug #5269"
18800 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18812 \begin_layout Subsection
18814 \begin_inset CommandInset label
18816 name "sub:Font-Sizes"
18824 \begin_layout Plain Layout
18833 \begin_layout Standard
18834 For characters in formulas there are, analog to characters in text, the
18835 following size commands:
18838 \begin_layout Standard
18882 \begin_inset Newline newline
18904 \begin_layout Standard
18905 The size produced by the commands depends on the document font size, that
18906 corresponds with the command
18913 The other commands produce smaller or larger sizes than
18920 The font size can however not exceed a certain value.
18921 Is for example the document font size 12
18922 \begin_inset space \thinspace{}
18931 switches to the same size as
18941 \begin_layout Standard
18942 A size command is inserted in TeX-mode before the formula and sets the size
18943 for all following formula and text characters.
18944 To switch back to the initial size, the command
18950 is inserted behind the formula in TeX-mode.
18953 \begin_layout Standard
18954 Within a formula the size can only be changed for symbols or letters in
18956 To do this, the size command is inserted in mathematical text.
18957 All following characters until the end of the mathematical text or until
18958 another size command will have the selected size.
18960 \begin_inset VSpace -2mm
18966 \begin_layout Standard
18970 \begin_layout Plain Layout
18980 \begin_inset Formula \[
18981 A=\frac{B}{c}\cdot\maltese\]
18986 \begin_inset Formula \[
18987 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18995 \begin_layout Plain Layout
19007 \begin_layout Standard
19008 \begin_inset VSpace medskip
19011 Before both formulas the command
19018 The command for the second formula is:
19019 \begin_inset Newline newline
19030 \begin_layout Plain Layout
19045 \begin_layout Plain Layout
19060 \begin_layout Plain Layout
19075 \begin_layout Plain Layout
19085 \begin_inset Formula $\to$
19089 \begin_inset Formula $\to$
19093 \begin_inset Newline newline
19097 \begin_inset space \hspace*{}
19111 \begin_layout Plain Layout
19126 \begin_layout Plain Layout
19141 \begin_layout Plain Layout
19153 \begin_layout Standard
19154 If a symbol cannot be displayed in different sizes, it will always be displayed
19155 in the default size.
19158 \begin_layout Section
19163 \begin_layout Plain Layout
19172 \begin_layout Standard
19173 All Greek letters can also be inserted via the toolbar button
19174 \begin_inset Graphics
19175 filename ../images/math/alpha.png
19183 \begin_layout Subsection
19188 \begin_layout Plain Layout
19189 Greek letters ! small
19197 \begin_layout Standard
19198 \begin_inset space \hfill{}
19202 \begin_inset Tabular
19203 <lyxtabular version="3" rows="11" columns="2">
19205 <column alignment="center" valignment="top" width="0pt">
19206 <column alignment="center" valignment="top" width="0pt">
19208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19211 \begin_layout Plain Layout
19217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19220 \begin_layout Plain Layout
19228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19231 \begin_layout Plain Layout
19239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19242 \begin_layout Plain Layout
19243 \begin_inset Formula $\alpha$
19253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19256 \begin_layout Plain Layout
19264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19267 \begin_layout Plain Layout
19268 \begin_inset Formula $\beta$
19278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19281 \begin_layout Plain Layout
19289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19292 \begin_layout Plain Layout
19293 \begin_inset Formula $\gamma$
19303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19306 \begin_layout Plain Layout
19314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19317 \begin_layout Plain Layout
19318 \begin_inset Formula $\delta$
19328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19331 \begin_layout Plain Layout
19339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19342 \begin_layout Plain Layout
19343 \begin_inset Formula $\epsilon$
19353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19356 \begin_layout Plain Layout
19364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19367 \begin_layout Plain Layout
19368 \begin_inset Formula $\varepsilon$
19378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19381 \begin_layout Plain Layout
19389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19392 \begin_layout Plain Layout
19393 \begin_inset Formula $\zeta$
19403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19406 \begin_layout Plain Layout
19414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19417 \begin_layout Plain Layout
19418 \begin_inset Formula $\eta$
19428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19431 \begin_layout Plain Layout
19439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19442 \begin_layout Plain Layout
19443 \begin_inset Formula $\theta$
19453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19456 \begin_layout Plain Layout
19464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19467 \begin_layout Plain Layout
19468 \begin_inset Formula $\vartheta$
19482 \begin_inset space \hfill{}
19486 \begin_inset Tabular
19487 <lyxtabular version="3" rows="12" columns="2">
19489 <column alignment="center" valignment="top" width="0pt">
19490 <column alignment="center" valignment="top" width="0pt">
19492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19495 \begin_layout Plain Layout
19501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19504 \begin_layout Plain Layout
19512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19515 \begin_layout Plain Layout
19523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19526 \begin_layout Plain Layout
19527 \begin_inset Formula $\iota$
19537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19540 \begin_layout Plain Layout
19548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19551 \begin_layout Plain Layout
19552 \begin_inset Formula $\kappa$
19562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19565 \begin_layout Plain Layout
19573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19576 \begin_layout Plain Layout
19577 \begin_inset Formula $\varkappa$
19587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19590 \begin_layout Plain Layout
19598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19601 \begin_layout Plain Layout
19602 \begin_inset Formula $\lambda$
19612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19615 \begin_layout Plain Layout
19623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19626 \begin_layout Plain Layout
19627 \begin_inset Formula $\mu$
19637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19640 \begin_layout Plain Layout
19648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19651 \begin_layout Plain Layout
19652 \begin_inset Formula $\nu$
19662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19665 \begin_layout Plain Layout
19673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19676 \begin_layout Plain Layout
19677 \begin_inset Formula $\xi$
19687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19690 \begin_layout Plain Layout
19696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19699 \begin_layout Plain Layout
19700 \begin_inset Formula $o$
19710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19713 \begin_layout Plain Layout
19721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19724 \begin_layout Plain Layout
19725 \begin_inset Formula $\pi$
19735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19738 \begin_layout Plain Layout
19746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19749 \begin_layout Plain Layout
19750 \begin_inset Formula $\varpi$
19760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19763 \begin_layout Plain Layout
19771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19774 \begin_layout Plain Layout
19775 \begin_inset Formula $\rho$
19789 \begin_inset space \hfill{}
19793 \begin_inset Tabular
19794 <lyxtabular version="3" rows="11" columns="2">
19796 <column alignment="center" valignment="top" width="0pt">
19797 <column alignment="center" valignment="top" width="0pt">
19799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19802 \begin_layout Plain Layout
19808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19811 \begin_layout Plain Layout
19819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19822 \begin_layout Plain Layout
19830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19833 \begin_layout Plain Layout
19834 \begin_inset Formula $\varrho$
19844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19847 \begin_layout Plain Layout
19855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19858 \begin_layout Plain Layout
19859 \begin_inset Formula $\sigma$
19869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19872 \begin_layout Plain Layout
19880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19883 \begin_layout Plain Layout
19884 \begin_inset Formula $\varsigma$
19894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19897 \begin_layout Plain Layout
19905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19908 \begin_layout Plain Layout
19909 \begin_inset Formula $\tau$
19919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19922 \begin_layout Plain Layout
19930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19933 \begin_layout Plain Layout
19934 \begin_inset Formula $\upsilon$
19944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19947 \begin_layout Plain Layout
19955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19958 \begin_layout Plain Layout
19959 \begin_inset Formula $\phi$
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19972 \begin_layout Plain Layout
19980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19983 \begin_layout Plain Layout
19984 \begin_inset Formula $\varphi$
19994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19997 \begin_layout Plain Layout
20005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20008 \begin_layout Plain Layout
20009 \begin_inset Formula $\chi$
20019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20022 \begin_layout Plain Layout
20030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20033 \begin_layout Plain Layout
20034 \begin_inset Formula $\psi$
20044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20047 \begin_layout Plain Layout
20055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20058 \begin_layout Plain Layout
20059 \begin_inset Formula $\omega$
20073 \begin_inset space \hfill{}
20079 \begin_layout Standard
20080 \begin_inset VSpace medskip
20086 \begin_layout Standard
20087 How to create upright Greek letters is explained in
20088 \begin_inset CommandInset ref
20090 reference "sub:Upright-small-Greek"
20097 \begin_layout Subsection
20102 \begin_layout Plain Layout
20103 Greek letters ! big
20111 \begin_layout Standard
20112 \begin_inset space \hfill{}
20116 \begin_inset Tabular
20117 <lyxtabular version="3" rows="7" columns="2">
20119 <column alignment="center" valignment="top" width="0pt">
20120 <column alignment="center" valignment="top" width="0pt">
20122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20125 \begin_layout Plain Layout
20131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20134 \begin_layout Plain Layout
20142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20145 \begin_layout Plain Layout
20153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20156 \begin_layout Plain Layout
20157 \begin_inset Formula $\Gamma$
20167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20170 \begin_layout Plain Layout
20178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20181 \begin_layout Plain Layout
20182 \begin_inset Formula $\Delta$
20192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20195 \begin_layout Plain Layout
20203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20206 \begin_layout Plain Layout
20207 \begin_inset Formula $\Theta$
20217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20220 \begin_layout Plain Layout
20228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20231 \begin_layout Plain Layout
20232 \begin_inset Formula $\Lambda$
20242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20245 \begin_layout Plain Layout
20253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20256 \begin_layout Plain Layout
20257 \begin_inset Formula $\Xi$
20267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20270 \begin_layout Plain Layout
20278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20281 \begin_layout Plain Layout
20282 \begin_inset Formula $\Pi$
20296 \begin_inset space \hfill{}
20300 \begin_inset Tabular
20301 <lyxtabular version="3" rows="6" columns="2">
20303 <column alignment="center" valignment="top" width="0pt">
20304 <column alignment="center" valignment="top" width="0pt">
20306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20309 \begin_layout Plain Layout
20315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20318 \begin_layout Plain Layout
20326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20329 \begin_layout Plain Layout
20337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20340 \begin_layout Plain Layout
20341 \begin_inset Formula $\Sigma$
20351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20354 \begin_layout Plain Layout
20362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20365 \begin_layout Plain Layout
20366 \begin_inset Formula $\Upsilon$
20376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20379 \begin_layout Plain Layout
20387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20390 \begin_layout Plain Layout
20391 \begin_inset Formula $\Phi$
20401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20404 \begin_layout Plain Layout
20412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20415 \begin_layout Plain Layout
20416 \begin_inset Formula $\Psi$
20426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20429 \begin_layout Plain Layout
20437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20440 \begin_layout Plain Layout
20441 \begin_inset Formula $\Omega$
20455 \begin_inset space \hfill{}
20461 \begin_layout Standard
20462 \begin_inset VSpace medskip
20465 That the big Greek letters appear upright is caused by a design bug when
20467 To get correct italic big letters, begin every command with
20472 For example the command
20479 \begin_inset Formula $\varGamma$
20485 \begin_layout Subsection
20490 \begin_layout Plain Layout
20491 Greek letters ! bold
20499 \begin_layout Standard
20500 Greek letters cannot be set with different font styles like Latin letters.
20501 They can only be made bold with the command
20511 \begin_layout Plain Layout
20522 \begin_layout Standard
20524 \begin_inset Tabular
20525 <lyxtabular version="3" rows="3" columns="2">
20527 <column alignment="center" valignment="top" width="0">
20528 <column alignment="center" valignment="top" width="0">
20530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20533 \begin_layout Plain Layout
20539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20542 \begin_layout Plain Layout
20550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20553 \begin_layout Plain Layout
20565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20568 \begin_layout Plain Layout
20569 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20582 \begin_layout Plain Layout
20594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20597 \begin_layout Plain Layout
20598 \begin_inset Formula $\theta\boldsymbol{\theta}$
20614 \begin_layout Section
20619 \begin_layout Plain Layout
20632 \begin_layout Plain Layout
20633 A list with all symbols of most of the LaTeX-packages can be found in
20634 \begin_inset CommandInset citation
20649 \begin_layout Plain Layout
20657 \begin_inset Note Note
20660 \begin_layout Plain Layout
20663 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20666 \begin_layout Plain Layout
20669 texorpdfstring is in section
20670 \begin_inset CommandInset ref
20672 reference "sub:Formulas-in-Section"
20685 \begin_layout Plain Layout
20694 \begin_layout Standard
20695 Many of the symbols listed in this section can also be inserted via the
20697 \begin_inset Graphics
20698 filename ../images/math/nabla.png
20704 \begin_inset Graphics
20705 filename ../images/math/digamma.png
20713 \begin_layout Subsection
20714 Mathematical Symbols
20715 \begin_inset CommandInset label
20717 name "sub:Mathematical-Symbols"
20725 \begin_layout Plain Layout
20726 Symbols ! mathematical
20734 \begin_layout Standard
20735 \begin_inset space \hfill{}
20739 \begin_inset Tabular
20740 <lyxtabular version="3" rows="10" columns="2">
20742 <column alignment="center" valignment="top" width="0pt">
20743 <column alignment="center" valignment="top" width="0pt">
20745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20748 \begin_layout Plain Layout
20754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20757 \begin_layout Plain Layout
20765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20768 \begin_layout Plain Layout
20776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20779 \begin_layout Plain Layout
20780 \begin_inset Formula $\neg$
20790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20793 \begin_layout Plain Layout
20801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20804 \begin_layout Plain Layout
20805 \begin_inset Formula $\Im$
20815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20818 \begin_layout Plain Layout
20826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20829 \begin_layout Plain Layout
20830 \begin_inset Formula $\Re$
20840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20843 \begin_layout Plain Layout
20851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20854 \begin_layout Plain Layout
20855 \begin_inset Formula $\aleph$
20865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20868 \begin_layout Plain Layout
20876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20879 \begin_layout Plain Layout
20880 \begin_inset Formula $\partial$
20890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20893 \begin_layout Plain Layout
20901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20904 \begin_layout Plain Layout
20905 \begin_inset Formula $\infty$
20915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20918 \begin_layout Plain Layout
20926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20929 \begin_layout Plain Layout
20930 \begin_inset Formula $\wp$
20940 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20943 \begin_layout Plain Layout
20951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20954 \begin_layout Plain Layout
20955 \begin_inset Formula $\imath$
20965 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20968 \begin_layout Plain Layout
20976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20979 \begin_layout Plain Layout
20980 \begin_inset Formula $\jmath$
20994 \begin_inset space \hfill{}
20998 \begin_inset Tabular
20999 <lyxtabular version="3" rows="10" columns="2">
21001 <column alignment="center" valignment="top" width="0pt">
21002 <column alignment="center" valignment="top" width="0pt">
21004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21007 \begin_layout Plain Layout
21013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21016 \begin_layout Plain Layout
21018 \begin_inset Note Note
21021 \begin_layout Plain Layout
21028 is only used as spacer.
21040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21043 \begin_layout Plain Layout
21051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21054 \begin_layout Plain Layout
21055 \begin_inset Formula $\forall$
21065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21068 \begin_layout Plain Layout
21076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21079 \begin_layout Plain Layout
21080 \begin_inset Formula $\exists$
21090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21093 \begin_layout Plain Layout
21101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21104 \begin_layout Plain Layout
21105 \begin_inset Formula $\nexists$
21115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21118 \begin_layout Plain Layout
21126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21129 \begin_layout Plain Layout
21130 \begin_inset Formula $\emptyset$
21140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21143 \begin_layout Plain Layout
21151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21154 \begin_layout Plain Layout
21155 \begin_inset Formula $\varnothing$
21165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21168 \begin_layout Plain Layout
21176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21179 \begin_layout Plain Layout
21180 \begin_inset Formula $\dag$
21190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21193 \begin_layout Plain Layout
21201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21204 \begin_layout Plain Layout
21205 \begin_inset Formula $\ddag$
21215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21218 \begin_layout Plain Layout
21226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21229 \begin_layout Plain Layout
21233 \begin_layout Plain Layout
21243 \begin_inset Formula $\complement$
21250 \begin_layout Plain Layout
21264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21267 \begin_layout Plain Layout
21275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21278 \begin_layout Plain Layout
21279 \begin_inset Formula $\Bbbk$
21293 \begin_inset space \hfill{}
21297 \begin_inset Tabular
21298 <lyxtabular version="3" rows="10" columns="2">
21300 <column alignment="center" valignment="top" width="0pt">
21301 <column alignment="center" valignment="top" width="0pt">
21303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21306 \begin_layout Plain Layout
21312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21315 \begin_layout Plain Layout
21323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21326 \begin_layout Plain Layout
21334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21337 \begin_layout Plain Layout
21338 \begin_inset Formula $\prime$
21348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21351 \begin_layout Plain Layout
21359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21362 \begin_layout Plain Layout
21363 \begin_inset Formula $\backprime$
21373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21376 \begin_layout Plain Layout
21384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21387 \begin_layout Plain Layout
21388 \begin_inset Formula $\mho$
21398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21401 \begin_layout Plain Layout
21409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21412 \begin_layout Plain Layout
21413 \begin_inset Formula $\triangle$
21423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21426 \begin_layout Plain Layout
21434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21437 \begin_layout Plain Layout
21438 \begin_inset Formula $\angle$
21448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21451 \begin_layout Plain Layout
21459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21462 \begin_layout Plain Layout
21463 \begin_inset Formula $\measuredangle$
21473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21476 \begin_layout Plain Layout
21484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21487 \begin_layout Plain Layout
21488 \begin_inset Formula $\sphericalangle$
21498 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21501 \begin_layout Plain Layout
21509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21512 \begin_layout Plain Layout
21513 \begin_inset Formula $\top$
21523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21526 \begin_layout Plain Layout
21534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21537 \begin_layout Plain Layout
21538 \begin_inset Formula $\bot$
21552 \begin_inset space \hfill{}
21558 \begin_layout Subsection
21559 Miscellaneous Symbols
21560 \begin_inset CommandInset label
21562 name "sub:Miscellaneous-Symbols"
21570 \begin_layout Plain Layout
21571 Symbols ! miscellaneous
21579 \begin_layout Standard
21582 \begin_inset Tabular
21583 <lyxtabular version="3" rows="10" columns="2">
21585 <column alignment="center" valignment="top" width="0pt">
21586 <column alignment="center" valignment="top" width="0pt">
21588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21591 \begin_layout Plain Layout
21597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21600 \begin_layout Plain Layout
21608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21611 \begin_layout Plain Layout
21619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21622 \begin_layout Plain Layout
21623 \begin_inset Formula $\flat$
21633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21636 \begin_layout Plain Layout
21644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21647 \begin_layout Plain Layout
21648 \begin_inset Formula $\natural$
21658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21661 \begin_layout Plain Layout
21669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21672 \begin_layout Plain Layout
21673 \begin_inset Formula $\sharp$
21683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21686 \begin_layout Plain Layout
21694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21697 \begin_layout Plain Layout
21698 \begin_inset Formula $\surd$
21708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21711 \begin_layout Plain Layout
21719 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21722 \begin_layout Plain Layout
21723 \begin_inset Formula $\checkmark$
21733 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21736 \begin_layout Plain Layout
21744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21747 \begin_layout Plain Layout
21748 \begin_inset Formula $\yen$
21758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21761 \begin_layout Plain Layout
21769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21772 \begin_layout Plain Layout
21773 \begin_inset Formula $\pounds$
21783 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21786 \begin_layout Plain Layout
21792 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21795 \begin_layout Plain Layout
21796 \begin_inset Formula $\$$
21806 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21809 \begin_layout Plain Layout
21815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21818 \begin_layout Plain Layout
21819 \begin_inset Formula $§$
21833 \begin_inset Tabular
21834 <lyxtabular version="3" rows="10" columns="2">
21836 <column alignment="center" valignment="top" width="0">
21837 <column alignment="center" valignment="top" width="0">
21839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21842 \begin_layout Plain Layout
21848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21851 \begin_layout Plain Layout
21859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21862 \begin_layout Plain Layout
21870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21873 \begin_layout Plain Layout
21874 \begin_inset Formula $\hbar$
21884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21887 \begin_layout Plain Layout
21895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21898 \begin_layout Plain Layout
21899 \begin_inset Formula $\hslash$
21909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21912 \begin_layout Plain Layout
21920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21923 \begin_layout Plain Layout
21924 \begin_inset Formula $\clubsuit$
21934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21937 \begin_layout Plain Layout
21945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21948 \begin_layout Plain Layout
21949 \begin_inset Formula $\spadesuit$
21959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21962 \begin_layout Plain Layout
21970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21973 \begin_layout Plain Layout
21974 \begin_inset Formula $\bigstar$
21984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21987 \begin_layout Plain Layout
21995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21998 \begin_layout Plain Layout
21999 \begin_inset Formula $\blacklozenge$
22009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22012 \begin_layout Plain Layout
22020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22023 \begin_layout Plain Layout
22024 \begin_inset Formula $\blacktriangle$
22034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22037 \begin_layout Plain Layout
22045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22048 \begin_layout Plain Layout
22049 \begin_inset Formula $\blacktriangledown$
22059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22062 \begin_layout Plain Layout
22070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22073 \begin_layout Plain Layout
22074 \begin_inset Formula $\bullet$
22088 \begin_inset Tabular
22089 <lyxtabular version="3" rows="10" columns="2">
22091 <column alignment="center" valignment="top" width="0pt">
22092 <column alignment="center" valignment="top" width="0pt">
22094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22097 \begin_layout Plain Layout
22103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22106 \begin_layout Plain Layout
22114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22117 \begin_layout Plain Layout
22125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22128 \begin_layout Plain Layout
22129 \begin_inset Formula $\diamondsuit$
22139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22142 \begin_layout Plain Layout
22150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22153 \begin_layout Plain Layout
22154 \begin_inset Formula $\Diamond$
22164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22167 \begin_layout Plain Layout
22175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22178 \begin_layout Plain Layout
22179 \begin_inset Formula $\heartsuit$
22189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22192 \begin_layout Plain Layout
22200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22203 \begin_layout Plain Layout
22204 \begin_inset Formula $\P$
22214 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22217 \begin_layout Plain Layout
22225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22228 \begin_layout Plain Layout
22229 \begin_inset Formula $\copyright$
22239 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22242 \begin_layout Plain Layout
22250 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22253 \begin_layout Plain Layout
22254 \begin_inset Formula $\circledR$
22264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22267 \begin_layout Plain Layout
22275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22278 \begin_layout Plain Layout
22279 \begin_inset Formula $\maltese$
22289 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22292 \begin_layout Plain Layout
22300 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22303 \begin_layout Plain Layout
22304 \begin_inset Formula $\diagup$
22314 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22317 \begin_layout Plain Layout
22325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22328 \begin_layout Plain Layout
22329 \begin_inset Formula $\diagdown$
22345 \begin_layout Standard
22346 \begin_inset VSpace medskip
22349 More symbols are listed in
22350 \begin_inset CommandInset ref
22352 reference "sub:Miscellaneous-special-Characters"
22359 \begin_layout Standard
22360 Some symbols can be displayed in different sizes, see
22361 \begin_inset CommandInset ref
22363 reference "sub:Font-Sizes"
22370 \begin_layout Subsection
22375 \begin_layout Plain Layout
22376 Symbols ! Euro-symbol
22385 \begin_layout Plain Layout
22392 \begin_layout Plain Layout
22409 \begin_layout Standard
22410 To use the Euro symbol in formulas, the LaTeX-package
22418 \begin_layout Plain Layout
22424 must be installed and loaded with the LaTeX-preamble line
22427 \begin_layout Standard
22432 usepackage[gennarrow]{eurosym}
22435 \begin_layout Standard
22436 The Euro symbol can now be inserted with the command
22446 \begin_layout Plain Layout
22457 \begin_layout Standard
22458 The Euro symbol can directly be inserted with the € key in mathematical
22459 text, without having
22474 can also be inserted in TeX-mode.
22475 The official currency symbol can then be inserted with the command
22485 \begin_layout Plain Layout
22493 , that is only available in TeX-mode.
22496 \begin_layout Standard
22500 \begin_layout Plain Layout
22510 \begin_inset Note Note
22513 \begin_layout Plain Layout
22514 The following table will only be displayed when the LaTeX-package
22526 \begin_layout Standard
22527 An overview about the different Euro symbols:
22530 \begin_layout Standard
22532 \begin_inset Tabular
22533 <lyxtabular version="3" rows="4" columns="3">
22535 <column alignment="center" valignment="top" width="0pt">
22536 <column alignment="center" valignment="top" width="0pt">
22537 <column alignment="center" valignment="top" width="0pt">
22539 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22542 \begin_layout Plain Layout
22548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22551 \begin_layout Plain Layout
22557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22560 \begin_layout Plain Layout
22568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22571 \begin_layout Plain Layout
22577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22580 \begin_layout Plain Layout
22588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22591 \begin_layout Plain Layout
22592 \begin_inset Formula $\euro$
22602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22605 \begin_layout Plain Layout
22611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22614 \begin_layout Plain Layout
22620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22623 \begin_layout Plain Layout
22624 \begin_inset Formula $\mbox{€}$
22634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22637 \begin_layout Plain Layout
22643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22646 \begin_layout Plain Layout
22654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22657 \begin_layout Plain Layout
22661 \begin_layout Plain Layout
22683 \begin_layout Standard
22687 \begin_layout Plain Layout
22697 \begin_inset Note Note
22700 \begin_layout Plain Layout
22701 The following will be displayed when the LaTeX-package
22713 \begin_layout Standard
22714 You need to install the LaTeX-package
22718 to see the rest of this subsection in the output.
22721 \begin_layout Standard
22725 \begin_layout Plain Layout
22737 \begin_layout Section
22739 \begin_inset CommandInset label
22741 name "sec:Relations"
22749 \begin_layout Plain Layout
22759 \begin_layout Plain Layout
22764 \begin_layout Plain Layout
22775 \begin_layout Plain Layout
22790 \begin_layout Standard
22791 All relations can also be inserted via the toolbar button
22792 \begin_inset Graphics
22793 filename ../images/math/leq.png
22801 \begin_layout Standard
22802 \begin_inset space \hfill{}
22806 \begin_inset Tabular
22807 <lyxtabular version="3" rows="17" columns="2">
22809 <column alignment="center" valignment="top" width="0pt">
22810 <column alignment="center" valignment="top" width="0pt">
22812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22815 \begin_layout Plain Layout
22821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22824 \begin_layout Plain Layout
22832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22835 \begin_layout Plain Layout
22841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22844 \begin_layout Plain Layout
22845 \begin_inset Formula $<$
22855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22858 \begin_layout Plain Layout
22866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22869 \begin_layout Plain Layout
22870 \begin_inset Formula $\le$
22880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22883 \begin_layout Plain Layout
22891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22894 \begin_layout Plain Layout
22895 \begin_inset Formula $\ll$
22905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22908 \begin_layout Plain Layout
22916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22919 \begin_layout Plain Layout
22920 \begin_inset Formula $\prec$
22930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22933 \begin_layout Plain Layout
22941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22944 \begin_layout Plain Layout
22945 \begin_inset Formula $\preceq$
22955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22958 \begin_layout Plain Layout
22966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22969 \begin_layout Plain Layout
22970 \begin_inset Formula $\subset$
22980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22983 \begin_layout Plain Layout
22991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22994 \begin_layout Plain Layout
22995 \begin_inset Formula $\subseteq$
23005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23008 \begin_layout Plain Layout
23016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23019 \begin_layout Plain Layout
23020 \begin_inset Formula $\sqsubseteq$
23030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23033 \begin_layout Plain Layout
23041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23044 \begin_layout Plain Layout
23045 \begin_inset Formula $\in$
23055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23058 \begin_layout Plain Layout
23066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23069 \begin_layout Plain Layout
23070 \begin_inset Formula $\vdash$
23080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23083 \begin_layout Plain Layout
23091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23094 \begin_layout Plain Layout
23095 \begin_inset Formula $\smile$
23105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23108 \begin_layout Plain Layout
23116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23119 \begin_layout Plain Layout
23120 \begin_inset Formula $\lhd$
23130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23133 \begin_layout Plain Layout
23141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23144 \begin_layout Plain Layout
23145 \begin_inset Formula $\unlhd$
23155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23158 \begin_layout Plain Layout
23166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23169 \begin_layout Plain Layout
23170 \begin_inset Formula $\gtrless$
23180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23183 \begin_layout Plain Layout
23191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23194 \begin_layout Plain Layout
23195 \begin_inset Formula $\mid$
23205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23208 \begin_layout Plain Layout
23216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23219 \begin_layout Plain Layout
23220 \begin_inset Formula $\nmid$
23234 \begin_inset space \hfill{}
23238 \begin_inset Tabular
23239 <lyxtabular version="3" rows="17" columns="2">
23241 <column alignment="center" valignment="top" width="0pt">
23242 <column alignment="center" valignment="top" width="0pt">
23244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23247 \begin_layout Plain Layout
23253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23256 \begin_layout Plain Layout
23264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23267 \begin_layout Plain Layout
23273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23276 \begin_layout Plain Layout
23277 \begin_inset Formula $=$
23287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23290 \begin_layout Plain Layout
23298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23301 \begin_layout Plain Layout
23302 \begin_inset Formula $\not=$
23312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23315 \begin_layout Plain Layout
23323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23326 \begin_layout Plain Layout
23327 \begin_inset Formula $\equiv$
23337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23340 \begin_layout Plain Layout
23348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23351 \begin_layout Plain Layout
23352 \begin_inset Formula $\sim$
23362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23365 \begin_layout Plain Layout
23373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23376 \begin_layout Plain Layout
23377 \begin_inset Formula $\simeq$
23387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23390 \begin_layout Plain Layout
23398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23401 \begin_layout Plain Layout
23402 \begin_inset Formula $\approx$
23412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23415 \begin_layout Plain Layout
23423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23426 \begin_layout Plain Layout
23427 \begin_inset Formula $\cong$
23437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23440 \begin_layout Plain Layout
23448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23451 \begin_layout Plain Layout
23452 \begin_inset Formula $\bowtie$
23462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23465 \begin_layout Plain Layout
23473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23476 \begin_layout Plain Layout
23477 \begin_inset Formula $\notin$
23487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23490 \begin_layout Plain Layout
23498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23501 \begin_layout Plain Layout
23502 \begin_inset Formula $\perp$
23512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23515 \begin_layout Plain Layout
23523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23526 \begin_layout Plain Layout
23527 \begin_inset Formula $\propto$
23537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23540 \begin_layout Plain Layout
23548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23551 \begin_layout Plain Layout
23552 \begin_inset Formula $\asymp$
23562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23565 \begin_layout Plain Layout
23573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23576 \begin_layout Plain Layout
23577 \begin_inset Formula $\doteq$
23587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23590 \begin_layout Plain Layout
23598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23601 \begin_layout Plain Layout
23602 \begin_inset Formula $\circeq$
23612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23615 \begin_layout Plain Layout
23623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23626 \begin_layout Plain Layout
23627 \begin_inset Formula $\models$
23637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23640 \begin_layout Plain Layout
23648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23651 \begin_layout Plain Layout
23652 \begin_inset Formula $\widehat{=}$
23666 \begin_inset space \hfill{}
23670 \begin_inset Tabular
23671 <lyxtabular version="3" rows="17" columns="2">
23673 <column alignment="center" valignment="top" width="0pt">
23674 <column alignment="center" valignment="top" width="0pt">
23676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23679 \begin_layout Plain Layout
23685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23688 \begin_layout Plain Layout
23696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23699 \begin_layout Plain Layout
23705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23708 \begin_layout Plain Layout
23709 \begin_inset Formula $>$
23719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23722 \begin_layout Plain Layout
23730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23733 \begin_layout Plain Layout
23734 \begin_inset Formula $\ge$
23744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23747 \begin_layout Plain Layout
23755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23758 \begin_layout Plain Layout
23759 \begin_inset Formula $\gg$
23769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23772 \begin_layout Plain Layout
23780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23783 \begin_layout Plain Layout
23784 \begin_inset Formula $\succ$
23794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23797 \begin_layout Plain Layout
23805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23808 \begin_layout Plain Layout
23809 \begin_inset Formula $\succeq$
23819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23822 \begin_layout Plain Layout
23830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23833 \begin_layout Plain Layout
23834 \begin_inset Formula $\supset$
23844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23847 \begin_layout Plain Layout
23855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23858 \begin_layout Plain Layout
23859 \begin_inset Formula $\supseteq$
23869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23872 \begin_layout Plain Layout
23880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23883 \begin_layout Plain Layout
23884 \begin_inset Formula $\sqsupseteq$
23894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23897 \begin_layout Plain Layout
23905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23908 \begin_layout Plain Layout
23909 \begin_inset Formula $\ni$
23919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23922 \begin_layout Plain Layout
23930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23933 \begin_layout Plain Layout
23934 \begin_inset Formula $\dashv$
23944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23947 \begin_layout Plain Layout
23955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23958 \begin_layout Plain Layout
23959 \begin_inset Formula $\frown$
23969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23972 \begin_layout Plain Layout
23980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23983 \begin_layout Plain Layout
23984 \begin_inset Formula $\rhd$
23994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23997 \begin_layout Plain Layout
24005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24008 \begin_layout Plain Layout
24009 \begin_inset Formula $\unrhd$
24019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24022 \begin_layout Plain Layout
24030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24033 \begin_layout Plain Layout
24034 \begin_inset Formula $\lessgtr$
24044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24047 \begin_layout Plain Layout
24055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24058 \begin_layout Plain Layout
24059 \begin_inset Formula $\parallel$
24069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24072 \begin_layout Plain Layout
24080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24083 \begin_layout Plain Layout
24084 \begin_inset Formula $\nparallel$
24098 \begin_inset space \hfill{}
24104 \begin_layout Standard
24105 \begin_inset VSpace medskip
24120 are bigger than the equal looking operators
24135 \begin_layout Standard
24136 Relations are, in contrary to symbols, always surrounded by space.
24139 \begin_layout Standard
24140 Relations with labels can be created with the command
24150 \begin_layout Plain Layout
24161 \begin_layout Standard
24163 \begin_inset Tabular
24164 <lyxtabular version="3" rows="2" columns="2">
24166 <column alignment="center" valignment="top" width="0">
24167 <column alignment="center" valignment="top" width="0">
24169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24172 \begin_layout Plain Layout
24178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24181 \begin_layout Plain Layout
24183 \begin_inset Note Note
24186 \begin_layout Plain Layout
24193 is only used as spacer.
24205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24208 \begin_layout Plain Layout
24215 \begin_layout Plain Layout
24232 \begin_layout Plain Layout
24242 \begin_inset Formula $\downarrow$
24251 \begin_layout Plain Layout
24264 \begin_layout Plain Layout
24278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24281 \begin_layout Plain Layout
24282 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24298 \begin_layout Section
24302 \begin_layout Subsection
24303 Predefined Functions
24304 \begin_inset CommandInset label
24306 name "sub:Predefined-Functions"
24314 \begin_layout Plain Layout
24315 Functions ! predefined
24323 \begin_layout Standard
24324 In general, variables are set
24328 in mathematical expressions, but not function names, because
24329 \begin_inset Formula $sin$
24332 could be misunderstood as
24333 \begin_inset Formula $s\cdot i\cdot n$
24337 Therefore there are predefined functions, that are additionally a bit separated
24339 They are inserted as commands starting with a backslash before their name.
24342 \begin_layout Standard
24344 \begin_inset Tabular
24345 <lyxtabular version="3" rows="2" columns="4">
24347 <column alignment="center" valignment="top" width="0pt">
24348 <column alignment="center" valignment="top" width="0pt">
24349 <column alignment="center" valignment="top" width="0pt">
24350 <column alignment="center" valignment="top" width="0pt">
24352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24355 \begin_layout Plain Layout
24361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24364 \begin_layout Plain Layout
24370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24373 \begin_layout Plain Layout
24379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24382 \begin_layout Plain Layout
24390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24393 \begin_layout Plain Layout
24399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24402 \begin_layout Plain Layout
24403 \begin_inset Formula $Asin(x)+B$
24411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24414 \begin_layout Plain Layout
24422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24425 \begin_layout Plain Layout
24426 \begin_inset Formula $A\sin(x)+B$
24442 \begin_layout Standard
24443 The following functions are predefined:
24446 \begin_layout Standard
24447 \begin_inset VSpace -2mm
24453 \begin_layout Standard
24455 \begin_inset Tabular
24456 <lyxtabular version="3" rows="9" columns="4">
24458 <column alignment="center" valignment="top" width="0pt">
24459 <column alignment="center" valignment="top" width="0pt">
24460 <column alignment="center" valignment="top" width="0pt">
24461 <column alignment="center" valignment="top" width="0pt">
24463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24466 \begin_layout Plain Layout
24472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24475 \begin_layout Plain Layout
24481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24484 \begin_layout Plain Layout
24490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24493 \begin_layout Plain Layout
24501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24504 \begin_layout Plain Layout
24512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24515 \begin_layout Plain Layout
24523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24526 \begin_layout Plain Layout
24534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24537 \begin_layout Plain Layout
24547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24550 \begin_layout Plain Layout
24558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24561 \begin_layout Plain Layout
24569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24572 \begin_layout Plain Layout
24580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24583 \begin_layout Plain Layout
24593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24596 \begin_layout Plain Layout
24604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24607 \begin_layout Plain Layout
24615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24618 \begin_layout Plain Layout
24626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24629 \begin_layout Plain Layout
24639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24642 \begin_layout Plain Layout
24650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24653 \begin_layout Plain Layout
24661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24664 \begin_layout Plain Layout
24672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24675 \begin_layout Plain Layout
24685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24688 \begin_layout Plain Layout
24696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24699 \begin_layout Plain Layout
24707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24710 \begin_layout Plain Layout
24718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24721 \begin_layout Plain Layout
24731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24734 \begin_layout Plain Layout
24742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24745 \begin_layout Plain Layout
24753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24756 \begin_layout Plain Layout
24764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24767 \begin_layout Plain Layout
24777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24780 \begin_layout Plain Layout
24788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24791 \begin_layout Plain Layout
24799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24802 \begin_layout Plain Layout
24810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24813 \begin_layout Plain Layout
24823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24826 \begin_layout Plain Layout
24834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24837 \begin_layout Plain Layout
24845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24848 \begin_layout Plain Layout
24856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24859 \begin_layout Plain Layout
24875 \begin_layout Standard
24876 They can also be inserted with the math toolbar button
24877 \begin_inset Graphics
24878 filename ../images/math/functions.png
24886 \begin_layout Subsection
24887 Self-defined Functions
24891 \begin_layout Plain Layout
24892 Functions ! self-defined
24900 \begin_layout Standard
24901 To use a function that is not predefined, like for example the sign function
24902 sgn(x), there are two possibilities:
24905 \begin_layout Itemize
24906 Define the function by inserting the following line to the LaTeX-preamble
24910 \begin_layout Plain Layout
24915 DeclareMathOperator
24918 \begin_inset CommandInset ref
24920 reference "sub:Self-defined-Operators"
24930 \begin_inset Newline newline
24934 \begin_inset VSpace -3mm
24938 \begin_inset Newline newline
24945 DeclareMathOperator{
24953 \begin_layout Plain Layout
24958 DeclareMathOperator
24964 \begin_inset Newline newline
24968 \begin_inset VSpace -2mm
24972 \begin_inset Newline newline
24975 Now the new defined function can be called with the command
24984 \begin_layout Itemize
24985 Write the the formula as usual, mark the formula name, in our example the
24990 , and change it to mathematical text.
24991 At last a space is inserted between prefactor and function.
24994 \begin_layout Standard
24995 The result is the same with both methods as with a predefined function
24999 \begin_layout Plain Layout
25000 In LyX self-defined functions are displayed red, predefined ones black.
25008 \begin_layout Standard
25010 \begin_inset Tabular
25011 <lyxtabular version="3" rows="3" columns="2">
25013 <column alignment="center" valignment="top" width="0pt">
25014 <column alignment="center" valignment="top" width="0pt">
25016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25019 \begin_layout Plain Layout
25025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25028 \begin_layout Plain Layout
25036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25039 \begin_layout Plain Layout
25047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25050 \begin_layout Plain Layout
25051 \begin_inset Formula $A\sgn(x)+B$
25061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25064 \begin_layout Plain Layout
25068 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25079 \begin_layout Plain Layout
25080 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25096 \begin_layout Standard
25097 The first method is more suitable when the self-defined function should
25098 be used several times.
25101 \begin_layout Subsection
25106 \begin_layout Plain Layout
25115 \begin_layout Standard
25116 For limits there are defined besides
25126 \begin_layout Plain Layout
25146 furthermore the following functions:
25149 \begin_layout Standard
25151 \begin_inset Tabular
25152 <lyxtabular version="3" rows="5" columns="2">
25154 <column alignment="center" valignment="top" width="0">
25155 <column alignment="center" valignment="top" width="0">
25157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25160 \begin_layout Plain Layout
25166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25169 \begin_layout Plain Layout
25171 \begin_inset Note Note
25174 \begin_layout Plain Layout
25181 is only used as spacer.
25193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25196 \begin_layout Plain Layout
25204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25207 \begin_layout Plain Layout
25208 \begin_inset Formula $\varliminf$
25218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25221 \begin_layout Plain Layout
25229 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25232 \begin_layout Plain Layout
25233 \begin_inset Formula $\varlimsup$
25243 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25246 \begin_layout Plain Layout
25254 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25257 \begin_layout Plain Layout
25258 \begin_inset Formula $\varprojlim$
25268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25271 \begin_layout Plain Layout
25279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25282 \begin_layout Plain Layout
25283 \begin_inset Formula $\varinjlim$
25287 \begin_inset Formula $\raisebox{-2.5mm}{}$
25303 \begin_layout Standard
25304 \begin_inset VSpace medskip
25307 The limit is created by inserting a subscript.
25308 It is set right beside the function in an inline formula:
25311 \begin_layout Standard
25313 \begin_inset Tabular
25314 <lyxtabular version="3" rows="2" columns="2">
25316 <column alignment="center" valignment="top" width="0pt">
25317 <column alignment="center" valignment="top" width="0pt">
25319 <cell alignment="center" valignment="top" usebox="none">
25322 \begin_layout Plain Layout
25328 <cell alignment="center" valignment="top" usebox="none">
25331 \begin_layout Plain Layout
25332 \begin_inset space \hspace{}
25337 \begin_inset Note Note
25340 \begin_layout Plain Layout
25353 are used here as spacer.
25365 <cell alignment="center" valignment="top" usebox="none">
25368 \begin_layout Plain Layout
25377 \begin_layout Plain Layout
25390 \begin_layout Plain Layout
25404 <cell alignment="center" valignment="top" usebox="none">
25407 \begin_layout Plain Layout
25408 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25424 \begin_layout Standard
25425 In a displayed formula the limit is set below the formula, as usual:
25426 \begin_inset Formula \[
25434 \begin_layout Subsection
25439 \begin_layout Plain Layout
25440 Functions ! modulo-
25448 \begin_layout Standard
25449 The modulo-function is special, because it exists in four variants.
25452 \begin_layout Standard
25453 The variants in a displayed formula:
25454 \begin_inset Formula \begin{align*}
25455 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25456 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25457 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25458 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25459 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25466 \begin_layout Standard
25467 In an inline formula less space is set before the function names for all
25471 \begin_layout Section
25476 \begin_layout Plain Layout
25485 \begin_layout Subsection
25486 Special Characters in Mathematical Text
25489 \begin_layout Standard
25490 The following commands can only be used in mathematical text or in TeX-mode:
25493 \begin_layout Standard
25494 \begin_inset space \hfill{}
25498 \begin_inset Tabular
25499 <lyxtabular version="3" rows="8" columns="2">
25501 <column alignment="block" valignment="top" width="0">
25502 <column alignment="block" valignment="top" width="0">
25504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25507 \begin_layout Plain Layout
25513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25516 \begin_layout Plain Layout
25524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25527 \begin_layout Plain Layout
25535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25538 \begin_layout Plain Layout
25539 \begin_inset Formula $\textrm{œ}$
25549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25552 \begin_layout Plain Layout
25560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25563 \begin_layout Plain Layout
25564 \begin_inset Formula $\textrm{Œ}$
25574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25577 \begin_layout Plain Layout
25585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25588 \begin_layout Plain Layout
25589 \begin_inset Formula $\textrm{æ}$
25599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25602 \begin_layout Plain Layout
25610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25613 \begin_layout Plain Layout
25614 \begin_inset Formula $\textrm{Æ}$
25624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25627 \begin_layout Plain Layout
25635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25638 \begin_layout Plain Layout
25639 \begin_inset Formula $\textrm{\aa}$
25649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25652 \begin_layout Plain Layout
25659 \begin_layout Plain Layout
25666 \begin_layout Plain Layout
25687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25690 \begin_layout Plain Layout
25691 \begin_inset Formula $\textrm{Å}$
25701 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25704 \begin_layout Plain Layout
25712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25715 \begin_layout Plain Layout
25716 \begin_inset Formula $\textrm{ı}$
25730 \begin_inset space \hfill{}
25734 \begin_inset Tabular
25735 <lyxtabular version="3" rows="8" columns="2">
25737 <column alignment="block" valignment="top" width="0">
25738 <column alignment="center" valignment="top" width="0">
25740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25743 \begin_layout Plain Layout
25745 \begin_inset Note Note
25748 \begin_layout Plain Layout
25755 is used for separation, because otherwise the output will be ¡ and ¿ respective
25766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25769 \begin_layout Plain Layout
25777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25780 \begin_layout Plain Layout
25788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25791 \begin_layout Plain Layout
25792 \begin_inset Formula $\textrm{ø}$
25802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25805 \begin_layout Plain Layout
25813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25816 \begin_layout Plain Layout
25817 \begin_inset Formula $\textrm{Ø}$
25827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25830 \begin_layout Plain Layout
25838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25841 \begin_layout Plain Layout
25842 \begin_inset Formula $\textrm{ł}$
25852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25855 \begin_layout Plain Layout
25863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25866 \begin_layout Plain Layout
25867 \begin_inset Formula $\textrm{Ł}$
25877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25880 \begin_layout Plain Layout
25882 \begin_inset space \hspace{}
25890 \begin_layout Plain Layout
25904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25907 \begin_layout Plain Layout
25908 \begin_inset Formula $\textrm{!`}$
25918 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25921 \begin_layout Plain Layout
25923 \begin_inset space \hspace{}
25931 \begin_layout Plain Layout
25945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25948 \begin_layout Plain Layout
25949 \begin_inset Formula $\textrm{?`}$
25959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25962 \begin_layout Plain Layout
25970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25973 \begin_layout Plain Layout
25974 \begin_inset Formula $\textrm{ȷ}$
25988 \begin_inset space \hfill{}
25994 \begin_layout Standard
25996 \begin_inset Formula $\textrm{\textrm{Å}}$
26000 \begin_inset Formula $\textrm{\textrm{Ø}}$
26003 can also be inserted via the math toolbar button
26004 \begin_inset Graphics
26005 filename ../images/math/digamma.png
26013 \begin_layout Standard
26014 An exception are the commands
26017 \begin_inset space \hspace{}
26026 \begin_inset space \hspace{}
26032 , because they can be inserted in LyX directly to text.
26035 \begin_layout Subsection
26037 \begin_inset CommandInset label
26039 name "sub:Accents-in-Text"
26047 \begin_layout Plain Layout
26056 \begin_layout Standard
26057 With the following commands all letters can be accented.
26058 The commands must be inserted in TeX-mode.
26061 \begin_layout Standard
26062 \begin_inset space \hfill{}
26066 \begin_inset Tabular
26067 <lyxtabular version="3" rows="8" columns="2">
26069 <column alignment="block" valignment="top" width="0">
26070 <column alignment="block" valignment="top" width="0">
26072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26075 \begin_layout Plain Layout
26081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26084 \begin_layout Plain Layout
26092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26095 \begin_layout Plain Layout
26099 \begin_inset Quotes grd
26107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26110 \begin_layout Plain Layout
26114 \begin_layout Plain Layout
26130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26133 \begin_layout Plain Layout
26141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26144 \begin_layout Plain Layout
26148 \begin_layout Plain Layout
26164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26167 \begin_layout Plain Layout
26174 \begin_layout Plain Layout
26188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26191 \begin_layout Plain Layout
26195 \begin_layout Plain Layout
26211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26214 \begin_layout Plain Layout
26222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26225 \begin_layout Plain Layout
26229 \begin_layout Plain Layout
26245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26248 \begin_layout Plain Layout
26255 \begin_layout Plain Layout
26269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26272 \begin_layout Plain Layout
26276 \begin_layout Plain Layout
26292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26295 \begin_layout Plain Layout
26302 \begin_layout Plain Layout
26316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26319 \begin_layout Plain Layout
26323 \begin_layout Plain Layout
26339 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26342 \begin_layout Plain Layout
26349 \begin_layout Plain Layout
26363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26366 \begin_layout Plain Layout
26370 \begin_layout Plain Layout
26390 \begin_inset space \hfill{}
26394 \begin_inset Tabular
26395 <lyxtabular version="3" rows="8" columns="2">
26397 <column alignment="block" valignment="top" width="0">
26398 <column alignment="center" valignment="top" width="0">
26400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26403 \begin_layout Plain Layout
26409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26412 \begin_layout Plain Layout
26420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26423 \begin_layout Plain Layout
26430 \begin_layout Plain Layout
26444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26447 \begin_layout Plain Layout
26451 \begin_layout Plain Layout
26467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26470 \begin_layout Plain Layout
26478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26481 \begin_layout Plain Layout
26485 \begin_layout Plain Layout
26501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26504 \begin_layout Plain Layout
26511 \begin_layout Plain Layout
26522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26525 \begin_layout Plain Layout
26529 \begin_layout Plain Layout
26545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26548 \begin_layout Plain Layout
26556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26559 \begin_layout Plain Layout
26563 \begin_layout Plain Layout
26579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26582 \begin_layout Plain Layout
26589 \begin_layout Plain Layout
26603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26606 \begin_layout Plain Layout
26610 \begin_layout Plain Layout
26626 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26629 \begin_layout Plain Layout
26636 \begin_layout Plain Layout
26650 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26653 \begin_layout Plain Layout
26657 \begin_layout Plain Layout
26673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26676 \begin_layout Plain Layout
26683 \begin_layout Plain Layout
26697 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26700 \begin_layout Plain Layout
26704 \begin_layout Plain Layout
26724 \begin_inset space \hfill{}
26730 \begin_layout Standard
26731 \begin_inset VSpace medskip
26740 also two different characters can be accented.
26749 \begin_layout Plain Layout
26764 \begin_layout Plain Layout
26776 \begin_layout Standard
26789 can in combination with vowels directly be inserted with the keyboard without
26791 The same applies for the tilde
26795 \begin_layout Plain Layout
26796 This only applies for keyboards where the tilde is defined as accent.
26805 in combination with
26820 \begin_layout Standard
26863 , and accents inserted directly with the keyboard are also available in
26865 For the other accents there are special math commands to be used in formulas,
26867 \begin_inset CommandInset ref
26869 reference "sub:Accents-for-one"
26876 \begin_layout Standard
26877 \begin_inset VSpace bigskip
26880 Furthermore, with the command
26890 \begin_layout Plain Layout
26898 all numbers and letters can be set into a circle, quasi accented with a
26899 circle, similar to the the copyright symbol.
26902 \begin_layout Standard
26904 \begin_inset Tabular
26905 <lyxtabular version="3" rows="3" columns="2">
26907 <column alignment="center" valignment="top" width="0">
26908 <column alignment="center" valignment="top" width="0">
26910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26913 \begin_layout Plain Layout
26919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26922 \begin_layout Plain Layout
26924 \begin_inset Note Note
26927 \begin_layout Plain Layout
26934 is only used as spacer.
26946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26949 \begin_layout Plain Layout
26957 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26960 \begin_layout Plain Layout
26964 \begin_layout Plain Layout
26980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26983 \begin_layout Plain Layout
26994 raisebox{-1.5pt}{W}}
26999 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27002 \begin_layout Plain Layout
27003 \begin_inset Formula $\raisebox{4.5mm}{}$
27010 \begin_layout Plain Layout
27028 \begin_inset Formula $\raisebox{-2mm}{}$
27044 \begin_layout Standard
27045 One has to take care that the character fits in the circle.
27056 \begin_layout Plain Layout
27058 \begin_inset CommandInset ref
27060 reference "sub:Font-Sizes"
27069 specifies thereby the size of the circle.
27080 \begin_layout Plain Layout
27082 \begin_inset CommandInset ref
27084 reference "sub:Boxes-without-Frame"
27093 the character can be centered.
27096 \begin_layout Subsection
27101 \begin_layout Plain Layout
27110 \begin_layout Standard
27111 Minuscule numbers are created with the command
27121 \begin_layout Plain Layout
27130 The command can be used in formulas and in TeX-mode.
27131 The command scheme is:
27134 \begin_layout Standard
27139 oldstylenums{number}
27142 \begin_layout Standard
27147 oldstylenums{0123456789
27150 \begin_inset Formula $\oldstylenums{0123456789}$
27156 \begin_layout Subsection
27157 Miscellaneous special Characters
27158 \begin_inset CommandInset label
27160 name "sub:Miscellaneous-special-Characters"
27168 \begin_layout Plain Layout
27169 Special characters ! miscellaneous
27177 \begin_layout Standard
27178 The following characters can only be inserted to formulas by using commands:
27181 \begin_layout Standard
27183 \begin_inset Tabular
27184 <lyxtabular version="3" rows="4" columns="2">
27186 <column alignment="center" valignment="top" width="0">
27187 <column alignment="center" valignment="top" width="0">
27189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27192 \begin_layout Plain Layout
27198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27201 \begin_layout Plain Layout
27209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27212 \begin_layout Plain Layout
27219 \begin_layout Plain Layout
27233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27236 \begin_layout Plain Layout
27237 \begin_inset Formula $\mathcircumflex$
27247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27250 \begin_layout Plain Layout
27258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27261 \begin_layout Plain Layout
27262 \begin_inset Formula $\_$
27272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27275 \begin_layout Plain Layout
27280 \begin_layout Plain Layout
27295 \begin_layout Plain Layout
27308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27311 \begin_layout Plain Layout
27312 \begin_inset Formula $^{\circ}$
27328 \begin_layout Standard
27329 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27330 contains the following line
27334 \begin_layout Plain Layout
27335 More about this is described in
27336 \begin_inset CommandInset ref
27338 reference "sub:Text-Characters-in"
27350 \begin_layout Standard
27355 DeclareInputtext{176}{
27368 \begin_layout Section
27370 \begin_inset CommandInset label
27372 name "sec:Formula-Styles"
27380 \begin_layout Plain Layout
27389 \begin_layout Itemize
27390 There are two different alignment styles:
27394 \begin_layout Description
27395 Centered is the predefined standard
27398 \begin_layout Description
27399 Indented for this the option
27403 must be inserted in the menu
27405 Document\SpecialChar \menuseparator
27411 \begin_inset space ~
27417 \begin_layout Standard
27422 is used, the indentation can be adjusted with the length
27432 \begin_layout Plain Layout
27441 Should the distance be 15
27442 \begin_inset space \thinspace{}
27445 mm, the following command line is inserted in the LaTeX-preamble
27448 \begin_layout Standard
27458 \begin_layout Standard
27459 When no length is specified, the predefined value of 30
27460 \begin_inset space \thinspace{}
27467 \begin_layout Itemize
27468 And two different numbering styles:
27472 \begin_layout Description
27473 Right is the predefined standard
27476 \begin_layout Description
27477 Left for this the option
27481 must be inserted in the menu
27483 Document\SpecialChar \menuseparator
27489 \begin_inset space ~
27496 \begin_layout Standard
27505 can also be used together.
27506 In this case both options are inserted, separated by a comma.
27509 \begin_layout Standard
27510 The chosen styles are used for all displayed formulas of the document.
27511 When both, centered and indented formulas should be created in a document,
27517 The indented formulas are then set in a flalign environment, see
27518 \begin_inset CommandInset ref
27520 reference "sub:Flalign-Environment"
27527 \begin_layout Section
27529 \begin_inset CommandInset label
27531 name "sec:Multiline-Formulas"
27539 \begin_layout Plain Layout
27540 Formula ! multiline
27548 \begin_layout Subsection
27552 \begin_layout Standard
27553 In LyX multiline formulas are created by pressing
27558 arg "newline-insert newline"
27564 This creates either an
27566 eqnarray environment
27568 that is described in
27569 \begin_inset CommandInset ref
27571 reference "sub:Eqnarray-Environment"
27575 or, when the option
27577 Use AMS math package
27579 in the document settings is selected, an
27583 that is described in
27584 \begin_inset CommandInset ref
27586 reference "sub:Standard-align-Environment"
27593 \begin_layout Standard
27594 There are other multiline formula environments that can be created via the
27597 Insert\SpecialChar \menuseparator
27601 These environments are described in the following sections.
27604 \begin_layout Standard
27605 In all multiline formula environments a new line is created by pressing
27609 arg "newline-insert newline"
27613 To add or delete lines, the math toolbar buttons
27614 \begin_inset Graphics
27615 filename ../images/tabular-feature_append-row.png
27621 \begin_inset Graphics
27622 filename ../images/tabular-feature_delete-row.png
27627 , respectively, or the menu
27629 Edit\SpecialChar \menuseparator
27635 \begin_layout Subsubsection
27637 \begin_inset CommandInset label
27639 name "sub:Line-Separation"
27647 \begin_layout Plain Layout
27648 Formula ! multiline ! Line separation
27656 \begin_layout Standard
27657 There is sometimes not enough space in multiline formulas between the lines:
27658 \begin_inset Formula \begin{eqnarray*}
27659 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}\\
27660 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*}
27667 \begin_layout Standard
27668 In LaTeX additional line space is specified as optional argument of the
27670 This is not yet possible in LyX
27674 \begin_layout Plain Layout
27676 \begin_inset CommandInset href
27678 name "LyX-bug #1505"
27679 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27688 , therefore the whole formula must be inserted in TeX-mode.
27689 To add in our example space, the command
27697 is inserted at the end of the first line.
27702 \begin_layout Plain Layout
27709 \begin_layout Plain Layout
27711 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27714 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27721 \begin_layout Plain Layout
27725 left(B^{2}+x_{0}^{2}
27733 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27738 \begin_layout Plain Layout
27750 \begin_layout Standard
27751 \begin_inset VSpace bigskip
27754 To set the the line separation for all lines in a formula, the length
27764 \begin_layout Plain Layout
27774 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27785 \begin_inset space \thinspace{}
27790 \begin_inset space \thinspace{}
27793 mm additional line separation as in the previous example, the command
27796 \begin_layout Standard
27806 \begin_layout Standard
27807 is inserted in TeX-mode before the formula.
27808 This requires that the LaTeX-package
27816 \begin_layout Plain Layout
27821 is part of every LaTeX standard installation.
27830 \begin_layout Plain Layout
27836 was loaded in LaTeX-preamble with the line
27839 \begin_layout Standard
27847 \begin_layout Standard
27852 \begin_layout Plain Layout
27864 \begin_inset Formula \begin{eqnarray*}
27865 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}\\
27866 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*}
27873 \begin_layout Standard
27877 \begin_layout Plain Layout
27888 To get back to the predefined distance,
27894 is set to the value 3
27895 \begin_inset space \thinspace{}
27901 \begin_layout Subsubsection
27903 \begin_inset CommandInset label
27905 name "sub:Column-Separation"
27913 \begin_layout Plain Layout
27914 Formula ! multiline ! Column separation
27922 \begin_layout Standard
27923 Multiline formulas form a matrix.
27924 A formula in the eqnarray environment is for example a matrix with three
27926 By changing the column separation in this environment, the space beside
27927 the relation sign can be changed.
27930 \begin_layout Standard
27931 The column separation is specified with the length
27941 \begin_layout Plain Layout
27950 \begin_inset Newline newline
27953 column separation = 2
27954 \begin_inset space \thinspace{}
27964 \begin_inset Newline newline
27970 \begin_layout Standard
27980 \begin_layout Standard
27981 inserted in TeX-mode, sets for all following formulas a column separation
27983 \begin_inset space \thinspace{}
27987 To get back to the predefined distance,
27994 \begin_inset space \thinspace{}
28000 \begin_layout Standard
28002 \begin_inset space \thinspace{}
28005 cm column separation:
28009 \begin_layout Plain Layout
28021 \begin_inset Formula \begin{eqnarray*}
28023 C & \ne & A\end{eqnarray*}
28027 A formula with the predefined column separation for matrices of 10
28028 \begin_inset space \thinspace{}
28035 \begin_layout Plain Layout
28047 \begin_inset Formula \begin{eqnarray*}
28049 C & \ne & A\end{eqnarray*}
28056 \begin_layout Subsubsection
28061 \begin_layout Plain Layout
28070 \begin_layout Standard
28071 Long formulas can be typeset using these methods:
28074 \begin_layout Itemize
28075 When one side of the equation is much shorther than the line width, this
28076 one is chosen for the left side and the right side is typeset over two
28081 \begin_layout Plain Layout
28091 \begin_inset Formula \begin{eqnarray}
28092 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 \\
28093 & & -\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}
28101 \begin_layout Plain Layout
28111 \begin_inset Newline newline
28114 The minus sign at the beginning of the second line does normally not appear
28115 as operator because it is the first character of the line.
28116 Thus it would not be surrounded by space and could not be distinguished
28117 from the fraction bar.
28118 To avoid this, space was inserted behind the minus sign with the command
28129 \begin_layout Plain Layout
28137 \begin_inset CommandInset ref
28139 reference "sub:Variable-Space"
28152 \begin_layout Plain Layout
28163 \begin_layout Itemize
28164 When both sides of the equation are too long, the command
28174 \begin_layout Plain Layout
28183 It is inserted to the first column of the first line and effects that all
28184 further insertions overwrite the following columns:
28188 \begin_layout Plain Layout
28198 \begin_inset Formula \begin{eqnarray}
28199 \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 \\
28200 & & -\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 \\
28201 & & =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}
28209 \begin_layout Plain Layout
28219 \begin_inset Newline newline
28222 After the insertion of
28228 , the cursor is in a purple box that is a bit shifted to the left from the
28230 In this the formula is inserted.
28234 \begin_layout Plain Layout
28244 \begin_inset Newline newline
28247 The content of the further lines is inserted to the second or another formula
28249 The greater the column number where it was inserted, the larger the indentation.
28253 \begin_layout Plain Layout
28263 \begin_inset Newline newline
28267 \begin_inset Note Greyedout
28270 \begin_layout Plain Layout
28271 Note the following when using
28280 \begin_layout Itemize
28281 The formula doesn't use the full page width.
28283 \begin_inset space \thinspace{}
28287 \begin_inset space \space{}
28291 \begin_inset Formula $-B^{2}$
28294 is added to the first line in the above example, it would have been outside
28296 To better use the width, negative space can be inserted at the beginning
28300 \begin_layout Itemize
28301 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28306 \begin_layout Plain Layout
28307 \begin_inset CommandInset href
28309 name "LyX-bug #1429"
28310 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28319 One can only set the cursor at the beginning of the line and move it with
28328 \begin_layout Itemize
28329 Other methods to set long formulas are offered by the environments described
28331 \begin_inset CommandInset ref
28333 reference "sub:Multline-Environment"
28338 \begin_inset CommandInset ref
28340 reference "sub:Multiline-Formula-Parts"
28347 \begin_layout Subsubsection
28349 \begin_inset CommandInset label
28351 name "sub:Multiline-Brackets"
28359 \begin_layout Plain Layout
28360 Brackets ! for multiline expressions
28368 \begin_layout Standard
28369 For brackets spanning multiple lines the following problem occurs:
28370 \begin_inset Formula \begin{eqnarray*}
28371 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28372 & & \left.\cdots+B-D\right]\end{eqnarray*}
28379 \begin_layout Standard
28380 The closing bracket is smaller than the opening bracket because brackets
28381 with variable size may not span multiple lines.
28384 \begin_layout Standard
28385 To set the bracket size for the second line correctly, the first line is
28396 \begin_layout Plain Layout
28404 and the second line with
28412 \begin_layout Plain Layout
28426 \begin_inset CommandInset ref
28428 reference "sub:Automatic-Bracket-Size"
28443 \begin_layout Plain Layout
28469 \begin_layout Plain Layout
28488 \begin_layout Plain Layout
28507 \begin_layout Plain Layout
28519 \begin_inset Formula $\downarrow$
28528 \begin_layout Plain Layout
28536 is inserted, because the multiplication operator with its limits is the
28537 largest symbol in the first line and this should be the size for the bracket
28538 in the second line.
28541 \begin_layout Standard
28542 The result is this:
28543 \begin_inset Formula \begin{eqnarray*}
28544 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28545 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28552 \begin_layout Subsection
28556 \begin_layout Standard
28557 Align environments can be used for every kind of multiline formulas.
28558 They are specially useful to set several formulas side by side.
28561 \begin_layout Standard
28562 Align environments consist of columns.
28563 The odd columns are right aligned, the even ones left aligned.
28564 Every line in an Align environment can be numbered.
28567 \begin_layout Standard
28568 Align environments are created via the menu
28570 Insert\SpecialChar \menuseparator
28576 Edit\SpecialChar \menuseparator
28577 Math\SpecialChar \menuseparator
28578 Change Formula Type
28580 already existing formulas can be converted to Align environments.
28583 \begin_layout Standard
28584 To add or delete columns, the math toolbar buttons
28585 \begin_inset Graphics
28586 filename ../images/tabular-feature_append-column.png
28592 \begin_inset Graphics
28593 filename ../images/tabular-feature_delete-column.png
28598 , respectively, or the menu
28600 Edit\SpecialChar \menuseparator
28606 \begin_layout Subsubsection
28607 Standard align Environment
28608 \begin_inset CommandInset label
28610 name "sub:Standard-align-Environment"
28618 \begin_layout Plain Layout
28619 Formula ! multiline ! align environment
28627 \begin_layout Standard
28628 This Align environment is created by presssing
28631 arg "newline-insert newline"
28634 in a formula or by the menu
28636 Insert\SpecialChar \menuseparator
28637 Math\SpecialChar \menuseparator
28638 AMS align Environment
28643 \begin_layout Standard
28644 An example for two formulas set side by side, that are created with a four
28645 column align environment:
28646 \begin_inset Formula \begin{align*}
28647 A & =\sin(B) & C & =D\\
28648 C & \ne A & B & \ne D\end{align*}
28652 As it can be seen, the formulas in this environment are placed so as if
28661 \begin_layout Plain Layout
28669 \begin_inset CommandInset ref
28671 reference "sub:Variable-Space"
28682 before the first and after every even column.
28683 When the formula style
28689 \begin_layout Plain Layout
28691 \begin_inset CommandInset ref
28693 reference "sec:Formula-Styles"
28704 is used, the formula is set without the
28710 before the first column.
28713 \begin_layout Subsubsection
28714 Alignat Environment
28718 \begin_layout Plain Layout
28719 Formula ! multiline ! alignat environment
28727 \begin_layout Standard
28728 The alignat environment has no predefined column separation.
28729 It can be inserted manually with the spaces that are described
28730 \begin_inset CommandInset ref
28732 reference "sub:Space"
28739 \begin_layout Standard
28740 The above example in the alignat environment where 1
28741 \begin_inset space \thinspace{}
28744 cm space was inserted at the beginning of the second formula:
28745 \begin_inset Formula \begin{alignat*}{2}
28746 A & =\sin(B) & \hspace{1cm}C & =D\\
28747 C & \ne A & B & \ne D\end{alignat*}
28751 Because the column separation can be set separately for every column, this
28752 environment is especially suitable to set three and more formulas side
28756 \begin_layout Subsubsection
28757 Flalign Environment
28758 \begin_inset CommandInset label
28760 name "sub:Flalign-Environment"
28768 \begin_layout Plain Layout
28769 Formula ! multiline ! flalign environment
28777 \begin_layout Standard
28778 In this environment the first two columns are always set as much as possible
28779 to the left and the last two ones to the right.
28781 \begin_inset Formula \begin{flalign*}
28782 A & =1 & B & =2 & C & =3\\
28783 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28790 \begin_layout Standard
28791 By creating a flalign environment with an odd number of columns where an
28792 empty TeX-brace is inserted to the last column, several formulas in a document
28793 can be set to the left, although the formula style
28798 As example the indented formula
28799 \begin_inset CommandInset ref
28801 reference "eq:VolInt"
28806 \begin_inset Formula \begin{flalign}
28807 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28811 The first two columns contain the formula.
28812 To indent it as with the formula style
28817 \begin_inset space \thinspace{}
28820 pt space was inserted at the beginning of the first column.
28823 \begin_layout Subsection
28824 Eqnarray Environment
28825 \begin_inset CommandInset label
28827 name "sub:Eqnarray-Environment"
28835 \begin_layout Plain Layout
28836 Formula ! multiline ! eqnarray environment
28844 \begin_layout Standard
28845 When this environment has been created, three blue boxes appear.
28846 The content of the first box is right aligned, the content of the last
28848 The content of the middle box appears centered and a bit smaller, because
28849 it is designed to insert there only relation characters.
28850 \begin_inset Formula \begin{eqnarray*}
28851 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28853 A & = & A\end{eqnarray*}
28860 \begin_layout Subsection
28865 \begin_layout Plain Layout
28866 Formula ! multiline ! gather environment
28874 \begin_layout Standard
28875 This environment consists of only one centered column.
28876 Every line can be numbered.
28877 \begin_inset Formula \begin{gather}
28879 X=\textrm{-}1\end{gather}
28886 \begin_layout Subsection
28887 Multline Environment
28888 \begin_inset CommandInset label
28890 name "sub:Multline-Environment"
28898 \begin_layout Plain Layout
28899 Formula ! multiline ! multline environment
28907 \begin_layout Standard
28908 The multline environment consists, like the gather environment, of only
28910 But the first line is left aligned, the last one right aligned.
28911 All other lines are centered.
28912 Therefore this environment is suitable for long formulas.
28914 \begin_inset CommandInset ref
28916 reference "eq:lefteqn"
28920 in the multline environment:
28921 \begin_inset Formula \begin{multline}
28922 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}\\
28923 -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}\\
28924 =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}
28931 \begin_layout Standard
28932 In the output only the last (first) line of a multline environment appears
28933 numbered when the document numbering is right (left).
28937 \begin_layout Plain Layout
28938 numbering styles see
28939 \begin_inset CommandInset ref
28941 reference "sec:Formula-Styles"
28953 \begin_layout Standard
28962 \begin_layout Plain Layout
28980 \begin_layout Plain Layout
28990 a centered line can be right or left aligned, respectively.
28991 The commands are used as follows:
28994 \begin_layout Standard
28999 shoveright{line content}
29005 shoveleft{line content}
29008 \begin_layout Standard
29009 \begin_inset VSpace medskip
29020 \begin_layout Plain Layout
29030 specifies the distance of the first line from the left page margin.
29031 Predefined is the length 0
29032 \begin_inset space \thinspace{}
29038 \begin_layout Standard
29039 As example the above formula where the command
29042 \begin_layout Standard
29052 \begin_layout Standard
29053 was inserted in TeX-mode before:
29057 \begin_layout Plain Layout
29069 \begin_inset Formula \begin{multline}
29070 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}\\
29071 \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}}\\
29072 =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}
29080 \begin_layout Plain Layout
29091 The second line was left aligned using
29100 \begin_layout Subsection
29101 Multiline Formula Parts
29102 \begin_inset CommandInset label
29104 name "sub:Multiline-Formula-Parts"
29112 \begin_layout Plain Layout
29113 Formula ! multiline ! formula parts
29121 \begin_layout Standard
29122 To display only parts of a formula with multiple lines, one of the following
29123 environments are used:
29140 They can be inserted via the menu
29142 Insert\SpecialChar \menuseparator
29145 or by using the commands described in this section.
29148 \begin_layout Standard
29149 The first three have the same properties as the corresponding multiline
29150 formula environments, but it is possible to set further formula parts beside
29153 \begin_inset Formula \[
29154 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29155 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29156 \right\} \textrm{Uncertainty relations}\]
29163 \begin_layout Standard
29164 To get this formula, a displayed formula is created where the command
29172 \begin_layout Plain Layout
29183 A purple box appears around the blue formula box where now columns and
29184 lines can be added.
29185 Outside the multiline environment other formula parts can be set, like
29189 \begin_layout Standard
29190 The aligned environment is also suitable for long formulas whose lines are
29191 horizontally aligned.
29192 Using aligned in a displayed formula has the advantage that the formula
29193 number is vertically centered behind the lines.
29195 \begin_inset CommandInset ref
29197 reference "eq:shortlong"
29201 in the aligned environment:
29202 \begin_inset Formula \begin{equation}
29203 \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}|}\\
29204 & -\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}
29212 \begin_layout Standard
29213 To use the environments
29235 \begin_layout Plain Layout
29253 \begin_layout Plain Layout
29271 \begin_layout Plain Layout
29279 are inserted, respectively.
29280 The split environment has the same properties as the aligned environment
29281 but it can only have two columns.
29284 \begin_layout Subsection
29285 Text in multiline Formulas
29286 \begin_inset CommandInset label
29288 name "sub:Text-in-multiline"
29296 \begin_layout Plain Layout
29306 \begin_layout Plain Layout
29307 Formula ! multiline ! text
29315 \begin_layout Standard
29316 In the Align environments, and the multline and gather environment, text
29317 can be inserted that will appear in a separate line and doesn't affect
29318 the column alignment.
29319 To do this, the command
29327 \begin_layout Plain Layout
29337 is used in the following scheme:
29340 \begin_layout Standard
29348 \begin_layout Standard
29349 The text should not be longer than a line because it cannot be hyphenated.
29350 As LyX doesn't yet support
29356 directly, the text is written as mathematical text.
29363 must hereby be at the beginning of a line and appears in the output above
29365 An example where the text was inserted at the beginning of the second line:
29366 \begin_inset Formula \begin{align}
29367 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29368 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29375 \begin_layout Section
29380 \begin_layout Plain Layout
29390 \begin_layout Plain Layout
29391 Formula ! numbering|see
29395 \begin_layout Plain Layout
29406 \begin_layout Plain Layout
29421 \begin_layout Subsection
29425 \begin_layout Standard
29426 Numbered formulas can be created with the menu
29428 Insert\SpecialChar \menuseparator
29429 Math\SpecialChar \menuseparator
29431 \begin_inset space ~
29439 \begin_inset space ~
29445 Existing formulas can be numbered with the menu
29447 Edit\SpecialChar \menuseparator
29448 Math\SpecialChar \menuseparator
29450 \begin_inset space ~
29458 arg "math-number-toggle"
29462 The formula number is displayed in LyX behind the formula as number sign
29464 The number sign is replaced in the output by the formula number.
29467 \begin_layout Standard
29468 When numbering is turned on in multiline formulas, all lines will be numbered.
29469 But the numbering can be controlled with the menu
29471 Edit\SpecialChar \menuseparator
29472 Math\SpecialChar \menuseparator
29474 \begin_inset space ~
29478 \begin_inset space ~
29482 \begin_inset space ~
29490 arg "math-number-line-toggle"
29496 \begin_layout Standard
29497 Except of inline formulas, all formulas can be numbered with two different
29499 \begin_inset CommandInset ref
29501 reference "sec:Formula-Styles"
29508 \begin_layout Subsection
29513 \begin_layout Plain Layout
29514 Cross-references ! to formulas
29522 \begin_layout Standard
29523 All labeled formulas can be cross-referenced.
29524 A label is added by the menu
29526 Insert\SpecialChar \menuseparator
29529 or the toolbar button
29530 \begin_inset Graphics
29531 filename ../images/label-insert.png
29537 The cursor must hereby be inside a displayed formula.
29538 A dialog pops up displaying the prefix
29543 The label is inserted there behind the prefix.
29544 The predefined prefix means
29545 \begin_inset Quotes eld
29549 \begin_inset Quotes erd
29552 and makes it easier to find labels in large documents because it marks
29553 it as formula label to divide it from e.
29554 \begin_inset space \thinspace{}
29558 \begin_inset space \space{}
29562 To change a label, the menu
29564 Insert\SpecialChar \menuseparator
29570 \begin_layout Standard
29571 The name of the label is displayed in LyX within two parentheses behind
29573 A formula with a label is always numbered.
29576 \begin_layout Standard
29577 Cross-references are inserted via the menu
29579 Insert\SpecialChar \menuseparator
29582 or with the toolbar button
29583 \begin_inset Graphics
29584 filename ../images/dialog-show-new-inset_ref.png
29590 A formula cross-reference appears in the output as formula number.
29591 When in the cross-reference dialog window the format
29595 is chosen, the cross-reference appears in the output as formula number
29597 \begin_inset Newline newline
29600 By right-clicking on a cross-reference in LyX, one jumps to the formula
29601 that is referenced.
29604 \begin_layout Standard
29605 Here are as examples cross-references to formulas of the following subsections:
29606 \begin_inset Note Note
29609 \begin_layout Plain Layout
29610 Note the different cross-reference types.
29618 \begin_layout Standard
29620 \begin_inset CommandInset ref
29627 \begin_inset CommandInset ref
29635 \begin_inset CommandInset ref
29641 ) big Latin letters are used for the numbering in contrary to (
29642 \begin_inset CommandInset ref
29651 \begin_layout Standard
29652 \begin_inset VSpace medskip
29655 When the argument of
29663 \begin_layout Plain Layout
29671 \begin_inset CommandInset ref
29673 reference "sub:User-defined-Numbering"
29684 contains a box like in
29685 \begin_inset CommandInset ref
29687 reference "sub:Paragraph-Boxes"
29691 , the formula cannot be referenced.
29694 \begin_layout Subsection
29699 \begin_layout Plain Layout
29700 Formula numbering ! subnumbering
29708 \begin_layout Standard
29709 With the help of the commands
29713 begin{subequations}
29721 formulas can be subnumbered.
29722 Both commands are inserted in TeX-mode.
29725 \begin_layout Standard
29727 \begin_inset Formula \begin{equation}
29728 A=C-B\label{eq:a}\end{equation}
29736 \begin_layout Plain Layout
29740 addtocounter{equation}{-1}
29749 \begin_layout Plain Layout
29753 begin{subequations}
29759 \begin_inset VSpace -5mm
29763 \begin_inset Formula \begin{equation}
29764 B=C-A\label{eq:b}\end{equation}
29769 \begin_inset Formula \begin{equation}
29770 C=A+B\label{eq:c}\end{equation}
29777 \begin_layout Standard
29781 \begin_layout Plain Layout
29793 \begin_layout Standard
29794 To create the example, the following is done:
29797 \begin_layout Enumerate
29798 first formula is inserted
29801 \begin_layout Enumerate
29806 addtocounter{equation}{-1}
29808 begin{subequations}
29812 \begin_layout Plain Layout
29821 \begin_inset Newline newline
29826 is inserted after the first formula
29829 \begin_layout Enumerate
29830 second formula is inserted
29833 \begin_layout Enumerate
29834 third formula is inserted
29837 \begin_layout Enumerate
29844 is inserted after the third formula
29847 \begin_layout Standard
29848 Every formula between the commands
29860 is subnumbered as a, b,
29861 \begin_inset Newline linebreak
29864 c, \SpecialChar \ldots{}
29865 For multiline formulas every line will be subnumbered.
29866 All subnumbered formulas are treated as
29871 But as every numbered formula increases the counter
29875 by one, the command
29881 is needed to decrease it.
29882 Otherwise the formulas
29883 \begin_inset CommandInset ref
29890 \begin_inset CommandInset ref
29897 \begin_inset CommandInset ref
29903 would be numbered as
29904 \begin_inset CommandInset ref
29911 \begin_inset CommandInset ref
29918 \begin_inset CommandInset ref
29927 \begin_layout Standard
29928 By inserting the commands in TeX-mode, a space is created between the first
29931 \begin_inset space \thinspace{}
29934 mm vertical space is inserted after the command
29938 begin{subequations}
29941 When the formula style
29947 \begin_layout Plain Layout
29949 \begin_inset CommandInset ref
29951 reference "sec:Formula-Styles"
29963 \begin_inset space \thinspace{}
29966 mm space is inserted instead.
29969 \begin_layout Standard
29970 Here is an example for a multiline formula where the numbering was turned
29971 off for the second line:
29975 \begin_layout Plain Layout
29979 begin{subequations}
29985 \begin_inset Formula \begin{eqnarray}
29986 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29987 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29988 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29996 \begin_layout Plain Layout
30008 \begin_layout Subsection
30009 User-defined Numbering
30010 \begin_inset CommandInset label
30012 name "sub:User-defined-Numbering"
30020 \begin_layout Plain Layout
30021 Formula numbering ! user-defined
30029 \begin_layout Standard
30033 \begin_layout Plain Layout
30034 Formula numbering ! self-defined delimiters
30039 With the standard numbering parentheses are set around the formula number.
30040 To replace the parentheses for example by vertical bars, the following
30041 line is added to the LaTeX-preamble:
30044 \begin_layout Standard
30056 \begin_inset Note Note
30059 \begin_layout Plain Layout
30060 This macro is already declared in the LaTeX-preamble for testing.
30061 To activate it, remove the percent sign at the beginning.
30069 \begin_layout Standard
30070 To use other characters, the vertical bars besides the
30074 are replaced by one ore more characters.
30075 To get only the formula number the vertical bars are omitted.
30078 \begin_layout Standard
30079 \begin_inset VSpace bigskip
30082 When there should be an expression of your choice instead of the consecutive
30083 formula number in parentheses behind the formula, the command
30093 \begin_layout Plain Layout
30102 \begin_inset Formula \begin{equation}
30103 A+B=C\tag{something}\label{eq:tag}\end{equation}
30107 In this example the command
30115 \begin_layout Plain Layout
30126 was inserted to the formula.
30129 \begin_layout Standard
30138 \begin_layout Plain Layout
30149 is inserted instead, the star prevents the parentheses around the expression:
30150 \begin_inset Formula \[
30151 A+B=C\tag*{something}\]
30158 \begin_layout Standard
30159 \begin_inset VSpace bigskip
30162 To restart the formula numbering with new document parts or sections, the
30163 following command is used:
30166 \begin_layout Standard
30171 @addtoreset{equation}{part}
30177 \begin_layout Plain Layout
30182 \begin_layout Plain Layout
30193 \begin_layout Plain Layout
30206 \begin_layout Plain Layout
30217 \begin_layout Plain Layout
30230 \begin_inset Newline newline
30234 \begin_inset Newline newline
30241 @addtoreset{equation}{section}
30244 \begin_layout Standard
30245 To be able to use these commands in TeX-mode, the
30246 \begin_inset Quotes eld
30250 \begin_inset Quotes erd
30253 character has to be made
30254 \begin_inset Quotes eld
30258 \begin_inset Quotes erd
30261 for LaTeX using the command
30275 So the command sequence in TeX-mode is:
30278 \begin_layout Standard
30284 \begin_inset Newline newline
30289 @addtoreset{equation}{section}
30290 \begin_inset Newline newline
30298 \begin_layout Standard
30299 In the LaTeX-preamble
30311 can be omitted as they are automatically internally inserted by LyX.
30314 \begin_layout Standard
30329 \begin_layout Plain Layout
30334 is part of the LaTeX-package
30342 \begin_layout Plain Layout
30343 Packages ! carlisle
30348 that is part of every LaTeX standard installation.
30357 \begin_layout Plain Layout
30358 Packages ! remreset
30363 has to be loaded in the LaTeX-preamble with the line
30366 \begin_layout Standard
30371 usepackage{remreset}
30374 \begin_layout Standard
30385 \begin_layout Plain Layout
30390 \begin_layout Plain Layout
30401 \begin_layout Plain Layout
30414 \begin_layout Plain Layout
30425 \begin_layout Plain Layout
30437 can be used with the same scheme as
30446 \begin_layout Standard
30447 \begin_inset VSpace bigskip
30450 Sometimes formulas should be numbered in the following form:
30453 \begin_layout Standard
30456 (section number.formula number)
30459 \begin_layout Standard
30460 The formula number should start with every section with
30461 \begin_inset Quotes eld
30465 \begin_inset Quotes erd
30471 \begin_layout Standard
30472 For this case there is the command
30482 \begin_layout Plain Layout
30490 , which is used with the following scheme:
30493 \begin_layout Standard
30498 numberwithin{counter}{sectioning}
30501 \begin_layout Standard
30502 Counter denotes what kind of numbering is affected, sectioning denotes what
30503 number is before the dot.
30506 \begin_layout Standard
30507 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30510 \begin_layout Standard
30515 numberwithin{equation}{section}
30518 \begin_layout Standard
30519 This is the result:
30523 \begin_layout Plain Layout
30527 numberwithin{equation}{section}
30533 \begin_inset Formula \begin{equation}
30534 A+B=C\end{equation}
30541 \begin_layout Standard
30543 \begin_inset space \thinspace{}
30547 \begin_inset space \space{}
30550 tables so that the number of the part is the sectioning,
30551 \begin_inset Newline newline
30558 numberwithin{table}{part}
30563 \begin_layout Standard
30564 To go back to the standard numbering or to prevent this kind of numbering
30565 when it is defined by the document class, the following command is inserted
30566 as TeX-Code or to the LaTeX-preamble:
30569 \begin_layout Standard
30582 \begin_layout Plain Layout
30596 \begin_layout Plain Layout
30612 \begin_inset Newline newline
30620 \begin_inset Newline newline
30632 \begin_layout Standard
30639 uses internally the command
30645 , described above, that also needs to be reverted.
30649 \begin_layout Plain Layout
30656 \begin_layout Plain Layout
30660 @removefromreset{equation}{section}
30663 \begin_layout Plain Layout
30675 \begin_layout Subsection
30676 Numbering with Roman Numbers and Letters
30680 \begin_layout Plain Layout
30681 Formula numbering ! with letters
30690 \begin_layout Plain Layout
30691 Formula numbering ! with Roman numbers
30699 \begin_layout Standard
30700 Formulas can also be numbered with Roman numbers and Latin letters.
30701 To number for example with small Roman numbers, the command
30704 \begin_layout Standard
30716 \begin_layout Standard
30717 is inserted before the formula in TeX-mode.
30728 \begin_layout Plain Layout
30736 redefines the predefined command
30752 \begin_layout Plain Layout
30759 has the same scheme like the command
30765 that is described in
30766 \begin_inset CommandInset ref
30768 reference "sub:The-Command-newcommand"
30781 is the formula counter.
30788 is used as prefix for a counter, the value of the counter is output as
30790 When a formula is numbered, LaTeX sets internally the command
30796 behind the formula.
30805 \begin_layout Plain Layout
30815 outputs the counter as small Roman number.
30818 \begin_layout Standard
30819 All formulas behind the command
30829 are now numbered Roman.
30830 To switch to numbering with big Roman numbers, the command is inserted
30847 \begin_layout Plain Layout
30859 \begin_inset Quotes eld
30863 \begin_inset Quotes erd
30866 with small Latin letters there is the command
30876 \begin_layout Plain Layout
30884 , for big ones there is the command
30894 \begin_layout Plain Layout
30907 \begin_layout Standard
30908 \begin_inset Note Greyedout
30911 \begin_layout Plain Layout
30916 Only maximal 26 formulas can be numbered with Latin letters in one document.
30924 \begin_layout Standard
30928 \begin_layout Plain Layout
30944 \begin_layout Standard
30945 \begin_inset Formula \begin{equation}
30946 A=\textrm{small roman}\label{eq:rom}\end{equation}
30954 \begin_layout Plain Layout
30968 \begin_inset Formula \begin{equation}
30969 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30977 \begin_layout Plain Layout
30991 \begin_inset Formula \begin{equation}
30992 C=\textrm{small Latin}\label{eq:lat}\end{equation}
31000 \begin_layout Plain Layout
31014 \begin_inset Formula \begin{equation}
31015 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31022 \begin_layout Standard
31023 To switch back to the default numbering, insert the command:
31026 \begin_layout Standard
31039 \begin_layout Plain Layout
31050 \begin_layout Standard
31054 \begin_layout Plain Layout
31068 \begin_inset Formula \begin{equation}
31069 E=\textrm{Arabic}\label{eq:arab}\end{equation}
31076 \begin_layout Standard
31077 \begin_inset VSpace medskip
31080 As you see, formulas are numbered serially independent from the numbering
31082 When then numbering should start with
31083 \begin_inset Quotes eld
31087 \begin_inset Quotes erd
31090 when the style is changed, new equation counters have to be defined.
31091 A description about this can be found in the file
31092 \begin_inset CommandInset href
31094 target "Formula-numbering.lyx"
31101 \begin_layout Section
31102 User-defined Commands
31106 \begin_layout Plain Layout
31107 User-defined commands
31115 \begin_layout Standard
31116 \begin_inset Note Greyedout
31119 \begin_layout Plain Layout
31124 The names of user-defined commands and macros may only consist of Latin
31133 \begin_layout Subsection
31137 \begin_inset CommandInset label
31139 name "sub:The-Command-newcommand"
31147 \begin_layout Plain Layout
31148 User-defined commands !
31159 \begin_layout Plain Layout
31170 \begin_layout Standard
31171 Many LaTeX-commands are too long to be used frequently.
31172 But it is possible to define with the command
31178 new shorter commands.
31181 \begin_layout Standard
31182 The command scheme of
31191 \begin_layout Standard
31196 newcommand{new command name}[number of arguments][optional
31201 \begin_inset Newline newline
31208 \begin_layout Plain Layout
31223 \begin_layout Plain Layout
31230 {command definition}
31233 \begin_layout Standard
31234 \begin_inset Note Greyedout
31237 \begin_layout Plain Layout
31242 Assure that the name of the new command is not already used in your document
31243 or by LaTeX-packages that you use.
31244 When you for example define the command
31256 , you get an error message because
31262 is already defined as command for
31263 \begin_inset Quotes eld
31267 \begin_inset Formula $\le$
31271 \begin_inset Quotes erd
31282 \begin_layout Standard
31283 The number of arguments is an integer in the range 0
31284 \begin_inset space \thinspace{}
31288 \begin_inset space \thinspace{}
31291 9 and specifies how many arguments the new command should have.
31292 With the optional value a value for an optional argument can be predefined.
31293 When this is done, the
31301 rgument of the new command is automatically an optional one.
31304 \begin_layout Standard
31305 Here are some examples:
31308 \begin_layout Itemize
31309 To define the command
31321 , the LaTeX-preamble line is:
31325 \begin_layout Plain Layout
31337 \begin_inset Newline newline
31349 \begin_layout Itemize
31350 To define the command
31362 , the argument (that should be underlined) must be taken into account.
31363 For this the preamble line is:
31367 \begin_layout Plain Layout
31379 \begin_inset Newline newline
31394 \begin_layout Plain Layout
31406 \begin_inset Newline newline
31415 acts as argument placeholder, the
31419 behind it denotes that it is the placeholder for the first argument.
31422 \begin_layout Itemize
31430 \begin_inset space \thinspace{}
31434 \begin_inset space \space{}
31447 \begin_layout Plain Layout
31459 \begin_inset Newline newline
31468 framebox#1#2{$#3$}}
31474 \begin_layout Plain Layout
31486 \begin_inset Newline newline
31491 The two Dollar signs creates the extra formula needed for
31498 \begin_inset CommandInset ref
31500 reference "sub:Boxes-with-Frame"
31507 \begin_layout Itemize
31508 To create a new command for
31514 where the color for the box needn't to be specified, the argument for the
31515 color is defined optional:
31519 \begin_layout Plain Layout
31531 \begin_inset Newline newline
31540 fcolorbox{#2}{#1}{$#3$}}
31546 \begin_layout Plain Layout
31556 \begin_inset Newline newline
31559 When the color is not specified when using
31565 , the predefined color
31572 \begin_layout Standard
31573 A test of the new defined commands:
31576 \begin_layout Standard
31578 \begin_inset Tabular
31579 <lyxtabular version="3" rows="6" columns="2">
31581 <column alignment="center" valignment="top" width="0">
31582 <column alignment="center" valignment="top" width="0">
31584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31587 \begin_layout Plain Layout
31593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31596 \begin_layout Plain Layout
31598 \begin_inset Note Note
31601 \begin_layout Plain Layout
31608 is only used as spacer.
31620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31623 \begin_layout Plain Layout
31630 \begin_layout Plain Layout
31644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31647 \begin_layout Plain Layout
31648 \begin_inset Formula $A\gr B$
31658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31661 \begin_layout Plain Layout
31669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31672 \begin_layout Plain Layout
31673 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31686 \begin_layout Plain Layout
31690 \begin_inset Formula $\to$
31696 \begin_inset Formula $\to$
31707 \begin_layout Plain Layout
31721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31724 \begin_layout Plain Layout
31725 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31738 \begin_layout Plain Layout
31742 \begin_inset Formula $\to$
31753 \begin_layout Plain Layout
31767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31770 \begin_layout Plain Layout
31771 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31784 \begin_layout Plain Layout
31790 \begin_inset Formula $\to$
31801 \begin_layout Plain Layout
31815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31818 \begin_layout Plain Layout
31819 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31835 \begin_layout Subsection
31840 \begin_layout Plain Layout
31841 User-defined commands! Math macros
31850 \begin_layout Plain Layout
31859 \begin_layout Standard
31860 User-defined commands are especially convenient for complex expressions.
31861 When you are for example dealing in a document with quadratic equations,
31862 the same solution type occurs several times.
31863 The general form of a quadratic equation is
31864 \begin_inset Formula \[
31865 0=\lambda^{2}+p\lambda+q\]
31869 The general form of the solution is
31870 \begin_inset Formula \[
31871 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
31878 \begin_layout Standard
31879 To define a command for the solution formula where only the three parameters
31881 \begin_inset Formula $\lambda$
31885 \begin_inset Formula $p$
31889 \begin_inset Formula $q$
31892 need to be specified and the index of
31893 \begin_inset Formula $\lambda$
31896 can be given optionally, the LaTeX-preamble line is
31897 \begin_inset Newline newline
31913 \begin_inset Newline newline
31920 \begin_layout Plain Layout
31935 \begin_layout Plain Layout
31946 frac{#3^{2}}{4}-#4}}
31949 \begin_layout Standard
31950 To create with this the solution formula, the command
31951 \begin_inset Newline newline
31961 \begin_inset Formula $\to$
31967 \begin_inset Formula $\to$
31974 is inserted to a formula
31979 \begin_layout Standard
31980 The definition of the new command is unintuitive because one has to know
31981 the schemes of all used LaTeX commands, e.
31982 \begin_inset space \thinspace{}
31986 \begin_inset space \space{}
31989 that a fraction is inserted in LaTeX as
31993 frac{numerator}{denominator}
31996 Furthermore one can easily forget a brace in the definition and cannot
31997 see in LyX what the new command is doing.
31998 To avoid these problems LyX offers the possibility to use math macros instead
32008 \begin_layout Standard
32009 A math macro is created by using the menu
32011 Insert\SpecialChar \menuseparator
32012 Math\SpecialChar \menuseparator
32015 or the toolbar button
32016 \begin_inset Graphics
32017 filename ../images/math-macro_newmacroname_newcommand.png
32023 The math macro toolbar appears together with the following box where the
32025 \begin_inset Newline newline
32029 \begin_inset space \hspace*{\fill}
32033 \begin_inset Graphics
32034 filename clipart/macrobox.png
32041 \begin_inset space \hspace*{\fill}
32045 \begin_inset Newline newline
32049 \begin_inset FormulaMacro
32050 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
32055 newmacroname is the default name of the macro that should be changed to
32056 something sensible.
32057 The wanted formula is inserted in the first blue box.
32058 An argument placeholder is inserted with the command
32065 \begin_inset space \thinspace{}
32069 \begin_inset space \space{}
32078 or by using the macro toolbar button
32079 \begin_inset Graphics
32080 filename ../images/math-macro-add-param.png
32086 Argument placeholders are displayed red.
32087 Maximum 9 arguments are possible.
32088 Optional arguments are created with the toolbar button
32089 \begin_inset Graphics
32090 filename ../images/math-macro-add-optional-param.png
32096 The first non-optional argument can be transformed to an optional one with
32098 \begin_inset Graphics
32099 filename ../images/math-macro-make-optional.png
32105 In the second blue box the appearance of the macro in LyX can be defined.
32106 Normally you want to see it as it is defined, so the box is kept empty.
32107 But when you have created a macro that needs lot of space on the screen,
32108 you can insert in the box for example
32109 \begin_inset Newline newline
32139 \begin_inset Newline newline
32144 For the macro only the arguments with the macro name in front of them will
32145 then be displayed in LyX, leading to a better overview.
32146 The formula appears in the output as defined in the first box.
32147 \begin_inset Newline newline
32150 The appearance of macros in formulas can furthermore be changed for single
32151 macros by setting the cursor in the macro and using the menu
32153 View\SpecialChar \menuseparator
32155 \begin_inset space ~
32159 \begin_inset space ~
32167 \begin_layout Standard
32168 To use a macro, the macro name is inserted as command to a formula, in our
32176 Our macro looks in LyX like this:
32177 \begin_inset Newline newline
32181 \begin_inset space \hspace*{\fill}
32185 \begin_inset Graphics
32186 filename clipart/macrouse.png
32193 \begin_inset space \hspace*{\fill}
32197 \begin_inset Newline newline
32200 Here is our macro example with the arguments
32201 \begin_inset Formula $x$
32205 \begin_inset Formula $\ln(x)$
32209 \begin_inset Formula $B$
32215 \begin_layout Standard
32216 \begin_inset Formula \[
32224 \begin_layout Standard
32225 A math macro is transformed internally to a
32231 command when exporting the document.
32238 command is not placed in the LaTeX-preamble, therefore macros can only
32239 be used in formulas that are in the document below the macro definition
32243 \begin_layout Standard
32244 Math macros can also be directly be created from a
32251 When writing for example the command
32254 \begin_inset Newline newline
32263 xleftarrow[#2]{#1}}
32264 \begin_inset Newline newline
32269 in LyX as normal text, highlighting it completely and using then the shortcut
32274 , the command will be transformed to a math macro.
32275 Using this method you need to be careful that the
32281 command is typed correctly, otherwise you get a faulty macro leading to
32285 \begin_layout Standard
32286 Math macros currently yet have the problem that further formulas in macro
32287 definitions are handled wrongly.
32288 Therefore the example
32295 \begin_inset CommandInset ref
32297 reference "sub:The-Command-newcommand"
32301 cannot be created as macro.
32304 \begin_layout Standard
32305 When the cursor is in a macro definition box, you will see the macro toolbar
32309 \begin_layout Standard
32310 \begin_inset VSpace defskip
32316 \begin_layout Standard
32317 \begin_inset Graphics
32318 filename clipart/MacroToolbar.png
32326 \begin_layout Plain Layout
32335 \begin_layout Standard
32336 \begin_inset VSpace defskip
32342 \begin_layout Standard
32343 The macro toolbar contains from left to right the following buttons:
32346 \begin_layout Standard
32347 \begin_inset VSpace defskip
32353 \begin_layout Standard
32354 \begin_inset Tabular
32355 <lyxtabular version="3" rows="9" columns="2">
32356 <features islongtable="true">
32357 <column alignment="left" valignment="top" width="0">
32358 <column alignment="left" valignment="top" width="85col%">
32359 <row interlinespace="2.5mm">
32360 <cell alignment="center" valignment="top" usebox="none">
32363 \begin_layout Plain Layout
32364 \begin_inset Graphics
32365 filename ../images/math-macro-remove-param.png
32366 BoundingBox 0bp 5bp 20bp 25bp
32367 rotateOrigin center
32376 <cell alignment="center" valignment="top" usebox="none">
32379 \begin_layout Plain Layout
32382 Edit\SpecialChar \menuseparator
32383 Math\SpecialChar \menuseparator
32385 \begin_inset space ~
32388 Definition\SpecialChar \menuseparator
32395 <row interlinespace="2.5mm">
32396 <cell alignment="center" valignment="top" usebox="none">
32399 \begin_layout Plain Layout
32400 \begin_inset Graphics
32401 filename ../images/math-macro-add-param.png
32402 BoundingBox 0bp 5bp 20bp 25bp
32403 rotateOrigin center
32412 <cell alignment="center" valignment="top" usebox="none">
32415 \begin_layout Plain Layout
32418 Edit\SpecialChar \menuseparator
32419 Math\SpecialChar \menuseparator
32421 \begin_inset space ~
32424 Definition\SpecialChar \menuseparator
32425 Append Last Argument
32431 <row interlinespace="2.5mm">
32432 <cell alignment="center" valignment="top" usebox="none">
32435 \begin_layout Plain Layout
32436 \begin_inset Graphics
32437 filename ../images/math-macro-make-optional.png
32438 BoundingBox 0bp 5bp 20bp 25bp
32439 rotateOrigin center
32448 <cell alignment="center" valignment="top" usebox="none">
32451 \begin_layout Plain Layout
32454 Edit\SpecialChar \menuseparator
32455 Math\SpecialChar \menuseparator
32457 \begin_inset space ~
32460 Definition\SpecialChar \menuseparator
32461 Make First Non-Optional into
32462 \begin_inset Newline newline
32469 \begin_layout Plain Layout
32478 Edit\SpecialChar \menuseparator
32479 Math\SpecialChar \menuseparator
32481 \begin_inset space ~
32484 Definition\SpecialChar \menuseparator
32489 \begin_layout Plain Layout
32502 <row interlinespace="2.5mm">
32503 <cell alignment="center" valignment="top" usebox="none">
32506 \begin_layout Plain Layout
32507 \begin_inset Graphics
32508 filename ../images/math-macro-make-nonoptional.png
32509 BoundingBox 0bp 5bp 20bp 25bp
32510 rotateOrigin center
32519 <cell alignment="center" valignment="top" usebox="none">
32522 \begin_layout Plain Layout
32525 Edit\SpecialChar \menuseparator
32526 Math\SpecialChar \menuseparator
32528 \begin_inset space ~
32531 Definition\SpecialChar \menuseparator
32532 Make Last Optional into
32533 \begin_inset Newline newline
32540 \begin_layout Plain Layout
32549 Edit\SpecialChar \menuseparator
32550 Math\SpecialChar \menuseparator
32552 \begin_inset space ~
32555 Definition\SpecialChar \menuseparator
32560 \begin_layout Plain Layout
32567 Non-Optional Argument
32573 <row interlinespace="2.5mm">
32574 <cell alignment="center" valignment="top" usebox="none">
32577 \begin_layout Plain Layout
32578 \begin_inset Graphics
32579 filename ../images/math-macro-remove-optional-param.png
32580 BoundingBox 0bp 5bp 20bp 25bp
32581 rotateOrigin center
32590 <cell alignment="center" valignment="top" usebox="none">
32593 \begin_layout Plain Layout
32596 Edit\SpecialChar \menuseparator
32597 Math\SpecialChar \menuseparator
32599 \begin_inset space ~
32602 Definition\SpecialChar \menuseparator
32603 Remove Optional Argument
32609 <row interlinespace="2.5mm">
32610 <cell alignment="center" valignment="top" usebox="none">
32613 \begin_layout Plain Layout
32614 \begin_inset Graphics
32615 filename ../images/math-macro-add-optional-param.png
32616 BoundingBox 0bp 5bp 20bp 25bp
32617 rotateOrigin center
32626 <cell alignment="center" valignment="top" usebox="none">
32629 \begin_layout Plain Layout
32632 Edit\SpecialChar \menuseparator
32633 Math\SpecialChar \menuseparator
32635 \begin_inset space ~
32638 Definition\SpecialChar \menuseparator
32639 Insert Optional Argument
32645 <row interlinespace="2.5mm">
32646 <cell alignment="center" valignment="top" usebox="none">
32649 \begin_layout Plain Layout
32650 \begin_inset Graphics
32651 filename ../images/math-macro-remove-greedy-param.png
32652 BoundingBox 0bp 5bp 20bp 25bp
32653 rotateOrigin center
32662 <cell alignment="center" valignment="top" usebox="none">
32665 \begin_layout Plain Layout
32668 Edit\SpecialChar \menuseparator
32669 Math\SpecialChar \menuseparator
32671 \begin_inset space ~
32674 Definition\SpecialChar \menuseparator
32675 Remove Last Argument
32676 \begin_inset Newline newline
32683 \begin_layout Plain Layout
32692 Edit\SpecialChar \menuseparator
32693 Math\SpecialChar \menuseparator
32695 \begin_inset space ~
32698 Definition\SpecialChar \menuseparator
32703 \begin_layout Plain Layout
32710 Spitting Out To The Right
32716 <row interlinespace="2.5mm">
32717 <cell alignment="center" valignment="top" usebox="none">
32720 \begin_layout Plain Layout
32721 \begin_inset Graphics
32722 filename ../images/math-macro-append-greedy-param.png
32723 BoundingBox 0bp 5bp 20bp 25bp
32724 rotateOrigin center
32733 <cell alignment="center" valignment="top" usebox="none">
32736 \begin_layout Plain Layout
32739 Edit\SpecialChar \menuseparator
32740 Math\SpecialChar \menuseparator
32742 \begin_inset space ~
32745 Definition\SpecialChar \menuseparator
32747 \begin_inset Newline newline
32754 \begin_layout Plain Layout
32763 Edit\SpecialChar \menuseparator
32764 Math\SpecialChar \menuseparator
32766 \begin_inset space ~
32769 Definition\SpecialChar \menuseparator
32774 \begin_layout Plain Layout
32781 Eating From The Right
32787 <row interlinespace="2.5mm">
32788 <cell alignment="center" valignment="top" usebox="none">
32791 \begin_layout Plain Layout
32792 \begin_inset Graphics
32793 filename ../images/math-macro-add-greedy-optional-param.png
32794 BoundingBox 0bp 5bp 20bp 25bp
32795 rotateOrigin center
32804 <cell alignment="center" valignment="top" usebox="none">
32807 \begin_layout Plain Layout
32810 Edit\SpecialChar \menuseparator
32811 Math\SpecialChar \menuseparator
32813 \begin_inset space ~
32816 Definition\SpecialChar \menuseparator
32817 Append Optional Argument
32818 \begin_inset Newline newline
32825 \begin_layout Plain Layout
32834 Edit\SpecialChar \menuseparator
32835 Math\SpecialChar \menuseparator
32837 \begin_inset space ~
32840 Definition\SpecialChar \menuseparator
32845 \begin_layout Plain Layout
32852 Eating From The Right
32865 \begin_layout Standard
32866 \begin_inset Newpage newpage
32872 \begin_layout Section
32876 \begin_layout Standard
32877 LyX supports two types of commutative diagrams:
32885 that are explained in the following.
32888 \begin_layout Subsection
32893 \begin_layout Plain Layout
32902 \begin_layout Standard
32903 Diagrams of this type visualize relations by vertical and horizontal lines
32905 \begin_inset Formula \[
32906 \begin{CD}A@>>>B@>>>C\\
32908 F@<<<E@<<<D\end{CD}\]
32915 \begin_layout Standard
32916 To get them, the command
32924 \begin_layout Plain Layout
32934 is inserted to a formula.
32935 A blue box appears with two dashed lines where further commands can be
32940 arg "newline-insert newline"
32943 a new line is created.
32944 Horizontal relations are inserted in odd, vertical in even formula lines.
32947 \begin_layout Standard
32948 To create the relations there are the following commands:
32951 \begin_layout Itemize
32956 creates a left arrow,
32967 \begin_layout Itemize
32972 creates an up arrow,
32980 a vertical equal sign
32983 \begin_layout Itemize
32989 is a placeholder for non-existent relations
32992 \begin_layout Standard
32993 All arrows can be labeled as follows:
32996 \begin_layout Itemize
32997 Is text inserted between the first and second < or >, resp., it is placed
32999 When it is inserted between the second and third one, it appears under
33003 \begin_layout Itemize
33004 When text for vertical arrows is inserted between the first and second A
33005 or V, resp., it is placed left beside the arrow.
33006 When it is inserted between the second and third one, it appears right
33008 If the text contains an A or V, these letters must be set into a TeX-brace.
33011 \begin_layout Standard
33012 As example a diagram with all possible relations:
33015 \begin_layout Standard
33016 \begin_inset Formula \[
33017 \begin{CD}A@>j>>B@>>k>C@=F\\
33019 D@<<j<E@>k>>F@=C\end{CD}\]
33026 \begin_layout Standard
33027 The command for this is:
33028 \begin_inset Newline newline
33039 \begin_layout Plain Layout
33048 A@>j>>B@>>k>C@=F Ctrl+Return
33049 \begin_inset Newline newline
33056 \begin_layout Plain Layout
33071 \begin_layout Plain Layout
33084 \begin_layout Plain Layout
33096 \begin_inset Formula $\to$
33102 \begin_inset Newline newline
33109 \begin_layout Plain Layout
33124 \begin_layout Plain Layout
33137 \begin_layout Plain Layout
33147 \begin_layout Subsection
33152 \begin_layout Plain Layout
33153 Diagrams ! xymatrix
33161 \begin_layout Standard
33162 To be able to use xymatrices, the LaTeX-package
33167 A xymatrix is created by inserting the command
33174 Then you are able to add new matrix columns and rows like for normal matrices,
33176 \begin_inset CommandInset ref
33178 reference "sec:Matrices"
33185 \begin_layout Standard
33186 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33188 All possibilities to create commutative diagrams and decorations are explained
33193 that you find in the menu
33195 Help\SpecialChar \menuseparator
33197 \begin_inset space ~
33200 Manuals\SpecialChar \menuseparator
33202 \begin_inset space ~
33210 \begin_layout Standard
33211 \begin_inset Newpage newpage
33217 \begin_layout Section
33222 \begin_layout Plain Layout
33235 \begin_layout Plain Layout
33236 Other useful math tips can be found in
33237 \begin_inset CommandInset citation
33252 \begin_layout Plain Layout
33260 \begin_inset Note Note
33263 \begin_layout Plain Layout
33266 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
33269 \begin_layout Plain Layout
33272 texorpdfstring is in section
33273 \begin_inset CommandInset ref
33275 reference "sub:Formulas-in-Section"
33288 \begin_layout Plain Layout
33298 \begin_layout Plain Layout
33303 \begin_layout Plain Layout
33310 Chemical characters
33314 \begin_layout Plain Layout
33329 \begin_layout Subsection
33330 Chemical Symbols and Equations
33331 \begin_inset CommandInset label
33333 name "sub:Chemical-Symbols-and"
33341 \begin_layout Plain Layout
33342 Chemical characters ! Symbols
33351 \begin_layout Plain Layout
33361 \begin_layout Plain Layout
33370 \begin_layout Standard
33371 An example text from chemistry:
33374 \begin_layout Quote
33376 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
33379 -ion reacts with two
33380 \begin_inset Formula $\mathrm{Na^{+}}$
33383 -ions to sodium sulfate
33384 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
33388 The chemical equation for this is:
33389 \begin_inset Formula \[
33390 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
33397 \begin_layout Standard
33398 This chemical equation can directly be created as formula.
33399 To avoid that the symbols appear italic, everything is highlighted and
33400 changed by the shortcut
33406 to the upright font style.
33410 \begin_layout Plain Layout
33416 \begin_inset CommandInset ref
33418 reference "sub:Font-Styles"
33430 \begin_layout Subsection
33435 \begin_layout Plain Layout
33444 \begin_layout Standard
33445 Negative numbers often look ugly in formulas because the minus sign before
33446 the number is set with the same length as the minus operator sign.
33447 When writing the negative number in normal text, the minus sign appears
33451 \begin_layout Standard
33452 Thus, the problem disappears when converting the minus sign to mathematical
33456 \begin_layout Standard
33457 An example to visualize the problem:
33460 \begin_layout Standard
33462 \begin_inset Tabular
33463 <lyxtabular version="3" rows="3" columns="2">
33465 <column alignment="right" valignment="top" width="0">
33466 <column alignment="left" valignment="top" width="0">
33468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33471 \begin_layout Plain Layout
33477 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33480 \begin_layout Plain Layout
33488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33491 \begin_layout Plain Layout
33497 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33500 \begin_layout Plain Layout
33501 \begin_inset Formula $x=-2$
33511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33514 \begin_layout Plain Layout
33520 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33523 \begin_layout Plain Layout
33524 \begin_inset Formula $x=\textrm{-}2$
33540 \begin_layout Subsection
33541 Comma as decimal Separator
33545 \begin_layout Plain Layout
33554 \begin_layout Standard
33555 In LaTeX a comma inside a formula is used, according to the English convention,
33556 as number group separator.
33557 So there will be space added behind all commas in formulas.
33560 \begin_layout Standard
33561 To avoid this, the comma is highlighted and changed to mathematical text
33571 \begin_layout Standard
33572 To use all formula commas in the document as decimal separator, the file
33581 \begin_layout Plain Layout
33586 is part of the LaTeX-package
33594 \begin_layout Plain Layout
33599 \begin_layout Plain Layout
33622 \begin_layout Plain Layout
33628 is loaded with the LaTeX-preamble line
33631 \begin_layout Standard
33639 \begin_layout Subsection
33641 \begin_inset CommandInset label
33643 name "sub:Physical-Vectors"
33651 \begin_layout Plain Layout
33660 \begin_layout Standard
33661 Predefined vectors are offered by the LaTeX-package
33669 \begin_layout Plain Layout
33674 should be part of every LaTeX standard installation.
33683 \begin_layout Plain Layout
33689 that is loaded with the LaTeX-preamble line
33692 \begin_layout Standard
33700 \begin_layout Standard
33704 \begin_layout Plain Layout
33714 \begin_inset Note Note
33717 \begin_layout Plain Layout
33718 The following table will only be displayed when the LaTeX-package
33727 The following commands are defined:
33730 \begin_layout Standard
33732 \begin_inset Tabular
33733 <lyxtabular version="3" rows="4" columns="2">
33735 <column alignment="center" valignment="top" width="0">
33736 <column alignment="center" valignment="top" width="0">
33738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33741 \begin_layout Plain Layout
33747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33750 \begin_layout Plain Layout
33758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33761 \begin_layout Plain Layout
33771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33774 \begin_layout Plain Layout
33775 \begin_inset Formula $\Bra{\psi}$
33785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33788 \begin_layout Plain Layout
33798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33801 \begin_layout Plain Layout
33802 \begin_inset Formula $\Ket{\psi}$
33812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33815 \begin_layout Plain Layout
33827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33830 \begin_layout Plain Layout
33831 \begin_inset Formula $\Braket{\psi|\phi}$
33847 \begin_layout Standard
33854 assures that all vertical bars are set in the size of the surrounding brackets:
33855 \begin_inset Formula \[
33856 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
33864 \begin_layout Plain Layout
33874 \begin_inset Note Note
33877 \begin_layout Plain Layout
33878 The following will be displayed when the LaTeX-package
33890 \begin_layout Standard
33891 You need to install the LaTeX-package
33895 to see the rest of this subsection in the output.
33898 \begin_layout Standard
33902 \begin_layout Plain Layout
33914 \begin_layout Standard
33921 can also be achieved using the command
33927 , that is described in
33928 \begin_inset CommandInset ref
33930 reference "sub:Automatic-Bracket-Size"
33937 \begin_layout Subsection
33938 Self-defined Fractions
33939 \begin_inset CommandInset label
33941 name "sub:Self-defined-Fractions"
33949 \begin_layout Plain Layout
33950 Fractions ! self-defined
33958 \begin_layout Standard
33959 To define custom commands for fractions, the command
33969 \begin_layout Plain Layout
33977 is used in the following scheme:
33980 \begin_layout Standard
33993 bracket}{fraction bar thickness}{style}
33994 \begin_inset Newline newline
34001 \begin_layout Plain Layout
34016 \begin_layout Plain Layout
34023 {numerator}{denominator}
34026 \begin_layout Standard
34027 The style is a number in the range of 0
34028 \begin_inset space \thinspace{}
34032 \begin_inset space \thinspace{}
34038 \begin_layout Standard
34040 \begin_inset Tabular
34041 <lyxtabular version="3" rows="5" columns="2">
34043 <column alignment="center" valignment="top" width="0">
34044 <column alignment="center" valignment="top" width="0">
34046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34049 \begin_layout Plain Layout
34055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34058 \begin_layout Plain Layout
34066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34069 \begin_layout Plain Layout
34075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34078 \begin_layout Plain Layout
34079 display style formula
34086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34089 \begin_layout Plain Layout
34095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34098 \begin_layout Plain Layout
34106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34109 \begin_layout Plain Layout
34115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34118 \begin_layout Plain Layout
34126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34129 \begin_layout Plain Layout
34135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34138 \begin_layout Plain Layout
34152 \begin_layout Standard
34153 When no style is given, the size is adjusted to the surrounding environment
34154 like for the command
34163 \begin_layout Standard
34164 When no fraction bar thickness is given, the predefined value of 0.4
34165 \begin_inset space \thinspace{}
34171 \begin_layout Standard
34172 \begin_inset VSpace medskip
34175 For example, the commands
34188 \begin_inset CommandInset ref
34190 reference "sub:Fractions"
34194 are defined with the commands
34197 \begin_layout Standard
34206 genfrac{}{}{}{0}{#1}{#2}}
34209 \begin_layout Standard
34213 \begin_layout Standard
34222 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34225 \begin_layout Standard
34226 \begin_inset VSpace medskip
34229 To define a fraction where the fraction bar thickness can be given as optional
34230 argument, the following line is inserted to the LaTeX-preamble:
34233 \begin_layout Standard
34242 genfrac{}{}{#1}{}{#2}{#3}}
34245 \begin_layout Standard
34247 \begin_inset Formula \begin{align*}
34248 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34249 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34253 As one can see, the distance of the numerator and the denominator to the
34254 fraction bar is round about three times the bar thickness.
34257 \begin_layout Subsection
34262 \begin_layout Plain Layout
34271 \begin_layout Standard
34272 To cancel formulas or formula parts, the LaTeX-package
34280 \begin_layout Plain Layout
34285 is part of every LaTeX standard installation.
34294 \begin_layout Plain Layout
34300 has to be loaded with the LaTeX-preamble line
34303 \begin_layout Standard
34308 usepackage[samesize]{cancel}
34311 \begin_layout Standard
34312 There are four ways to cancel formulas:
34315 \begin_layout Standard
34317 \begin_inset Tabular
34318 <lyxtabular version="3" rows="5" columns="2">
34320 <column alignment="center" valignment="top" width="0">
34321 <column alignment="center" valignment="top" width="0">
34323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34326 \begin_layout Plain Layout
34332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34335 \begin_layout Plain Layout
34337 \begin_inset Note Note
34340 \begin_layout Plain Layout
34353 are used here as spacer.
34365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34368 \begin_layout Plain Layout
34377 \begin_layout Plain Layout
34391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34394 \begin_layout Plain Layout
34395 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34408 \begin_layout Plain Layout
34417 \begin_layout Plain Layout
34431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34434 \begin_layout Plain Layout
34435 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34448 \begin_layout Plain Layout
34457 \begin_layout Plain Layout
34471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34474 \begin_layout Plain Layout
34475 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34488 \begin_layout Plain Layout
34492 \begin_inset Formula $\to$
34503 \begin_layout Plain Layout
34517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34520 \begin_layout Plain Layout
34521 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34537 \begin_layout Standard
34544 is especially suitable to visualize the reduction of fractions within formulas:
34545 \begin_inset Formula \[
34546 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
34553 \begin_layout Subsection
34554 Formulas in Section Headings
34555 \begin_inset CommandInset label
34557 name "sub:Formulas-in-Section"
34565 \begin_layout Plain Layout
34566 Formula ! in section headings
34574 \begin_layout Standard
34575 When formulas are used in section headings, the following has to be taken
34579 \begin_layout Standard
34580 \begin_inset Note Greyedout
34583 \begin_layout Plain Layout
34592 \begin_layout Plain Layout
34593 Packages ! hyperref
34598 support is enabled in the document settings dialog under
34601 \begin_inset space ~
34606 , PDF-bookmarks are created for every section heading in the table of contents.
34607 If a section heading contains formulas, they are incorrectly displayed
34608 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34617 \begin_layout Standard
34618 Both problems can be solved by inserting at the end of the section heading
34619 a short title with the menu
34621 Insert\SpecialChar \menuseparator
34623 \begin_inset space ~
34629 Short titles are used as alternative for multiline section headings to
34630 keep the table of contents clearly arranged.
34631 Only the short title appears in the table of contents and therefore also
34632 in the PDF-bookmark.
34635 \begin_layout Standard
34636 When formulas should be used in the table of contents but
34640 is used, one can use the following command in TeX-mode:
34643 \begin_layout Standard
34648 texorpdfstring{part}{alternative}
34652 \begin_layout Plain Layout
34663 \begin_layout Standard
34664 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34665 This can be characters, formulas, footnotes, but also cross-references.
34666 The alternative is used instead of the part for the bookmark.
34669 \begin_layout Standard
34670 Here are two example headings:
34671 \begin_inset VSpace -3mm
34678 \begin_layout Plain Layout
34690 \begin_layout Subsubsection
34691 Heading without formula in table of contents
34692 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34696 \begin_inset OptArg
34699 \begin_layout Plain Layout
34700 Heading without formula in table of contents
34708 \begin_layout Subsubsection
34709 Heading with formula in table of contents
34713 \begin_layout Plain Layout
34723 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34730 \begin_layout Plain Layout
34740 \begin_layout Standard
34744 \begin_layout Plain Layout
34753 In the first heading a short title was used, in the second one
34762 \begin_layout Standard
34763 To get the same formatting as for the other headings, the complete heading
34772 \begin_layout Plain Layout
34774 \begin_inset CommandInset ref
34776 reference "sub:Bold-Formulas"
34788 \begin_layout Subsection
34789 Formulas in multi-column Text
34793 \begin_layout Plain Layout
34794 Formula ! in multi-column text
34802 \begin_layout Standard
34803 Formulas in multi-column text are often too wide to fit into a column and
34804 thus need to be set over the whole page width.
34805 This is done by using the LaTeX-package
34813 \begin_layout Plain Layout
34818 is part of every LaTeX standard installation.
34827 \begin_layout Plain Layout
34828 Packages ! multicol
34833 , that is loaded with the LaTeX-preamble line
34836 \begin_layout Standard
34841 usepackage{multicol}
34844 \begin_layout Standard
34845 \begin_inset Note Greyedout
34848 \begin_layout Plain Layout
34849 Note herby that the setting
34852 \begin_inset space ~
34859 Document\SpecialChar \menuseparator
34865 \begin_inset space ~
34885 \begin_layout Standard
34886 Before the multi-column text the command
34889 \begin_layout Standard
34894 begin{multicols}{column number}
34897 \begin_layout Standard
34898 is written in TeX-mode.
34899 The column number is a number in the range of 2
34900 \begin_inset space \thinspace{}
34904 \begin_inset space \thinspace{}
34908 Before the formula the multi-column text is ended by inserting the command
34911 \begin_layout Standard
34919 \begin_layout Standard
34923 \begin_layout Standard
34924 Due to the command some space is automatically added before the formula.
34926 \begin_inset space \thinspace{}
34929 mm vertical space is inserted before the formula.
34930 When the formula style
34936 \begin_layout Plain Layout
34938 \begin_inset CommandInset ref
34940 reference "sec:Formula-Styles"
34952 \begin_inset space \thinspace{}
34955 mm space is inserted instead.
34958 \begin_layout Standard
34959 As example a multi-column text with a displayed formula:
34962 \begin_layout Standard
34966 \begin_layout Plain Layout
34970 begin{multicols}{2}
34975 Das Spektrum wird fouriertransformiert.
34976 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
34977 , Lösungsmittel) zu trennen.
34978 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
34979 nun das Aussehen des Ausgangssignals.
34980 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
34981 über alle Phasen integrieren muss.
34983 \begin_inset Formula $S$
34986 unser normiertes Ausgangssignal and
34987 \begin_inset Formula $P$
34990 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
34994 \begin_layout Plain Layout
35004 \begin_inset VSpace -6mm
35008 \begin_inset Formula \begin{equation}
35009 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35017 \begin_layout Plain Layout
35021 begin{multicols}{2}
35027 \begin_inset Formula $S_{0}$
35030 das Signal ohne Gradient ist and the Normierungsbedingung
35031 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35035 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
35037 \begin_inset Formula $\nicefrac{\pi}{2}$
35041 \begin_inset space \thinspace{}
35044 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
35045 das Signal zusätzlich abschwächt.
35046 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
35048 \begin_inset Formula $T_{2}$
35054 \begin_layout Standard
35058 \begin_layout Plain Layout
35070 \begin_layout Subsection
35071 Formulas with Description of Variables
35075 \begin_layout Plain Layout
35076 Formula ! with description of variables
35084 \begin_layout Standard
35085 To describe variables within a formula, like in formula
35086 \begin_inset CommandInset ref
35088 reference "eq:within"
35097 \begin_inset Formula $n$
35101 \begin_inset space ~
35104 matrix is used with left aligned columns for the
35105 \begin_inset Formula $n$
35112 \begin_layout Plain Layout
35114 \begin_inset CommandInset ref
35116 reference "sec:Matrices"
35125 To set the description in a smaller size, before the matrix e.
35126 \begin_inset space \thinspace{}
35130 \begin_inset space \space{}
35143 \begin_layout Plain Layout
35145 \begin_inset CommandInset ref
35147 reference "sub:Font-Sizes"
35159 \begin_layout Standard
35160 When the formula style
35166 \begin_layout Plain Layout
35168 \begin_inset CommandInset ref
35170 reference "sec:Formula-Styles"
35191 \begin_layout Plain Layout
35198 only works in formulas with the style
35203 \begin_inset CommandInset ref
35205 reference "sub:Variable-Space"
35214 is inserted before and after the matrix to have the same separation of
35215 the matrix from the equation and the side margin.
35218 \begin_layout Standard
35219 When the formula style
35223 is used, the method described in
35224 \begin_inset CommandInset ref
35226 reference "sub:Flalign-Environment"
35230 is used to indent formulas.
35232 \begin_inset CommandInset ref
35234 reference "eq:within"
35238 consists of five columns whereas in the first two columns contain the equation,
35239 the third the matrix, and the last one an empty TeX-brace.
35240 \begin_inset Formula \begin{flalign}
35241 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35242 \rho & \textrm{density}\\
35243 V & \textrm{volume}\\
35244 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35251 \begin_layout Subsection
35252 Upright small Greek Letters
35253 \begin_inset CommandInset label
35255 name "sub:Upright-small-Greek"
35263 \begin_layout Plain Layout
35264 Greek letters ! upright
35272 \begin_layout Standard
35273 Most of the math fonts only provide italic small Greek letters.
35274 But for symbols of elementary particles like pions and neutrinos, upright
35275 Greek letters are needed.
35284 \begin_layout Plain Layout
35289 is part of the LaTeX-package
35297 \begin_layout Plain Layout
35302 \begin_layout Plain Layout
35325 \begin_layout Plain Layout
35331 that is loaded with the LaTeX-preamble line
35334 \begin_layout Standard
35339 usepackage{upgreek}
35342 \begin_layout Standard
35348 \begin_layout Plain Layout
35358 \begin_inset Note Note
35361 \begin_layout Plain Layout
35362 The following table will only be displayed when the LaTeX-package
35371 They are created when the command for a small Greek letters is started
35377 For example the command
35384 \begin_inset Formula $\uptau$
35390 \begin_layout Standard
35391 With these commands reactions of elementary particles can be typeset:
35392 \begin_inset Formula \[
35393 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
35400 \begin_layout Standard
35401 The upright letters are more bold and wider than the italic ones.
35402 They should therefore not be used for units like
35403 \begin_inset Quotes eld
35407 \begin_inset Quotes erd
35413 \begin_layout Standard
35417 \begin_layout Plain Layout
35427 \begin_inset Note Note
35430 \begin_layout Plain Layout
35431 The following will be displayed when the LaTeX-package
35443 \begin_layout Standard
35444 You need to install the LaTeX-package
35448 to see the rest of this subsection in the output.
35451 \begin_layout Standard
35455 \begin_layout Plain Layout
35467 \begin_layout Subsection
35468 Text Characters in Formulas
35469 \begin_inset CommandInset label
35471 name "sub:Text-Characters-in"
35479 \begin_layout Plain Layout
35488 \begin_layout Standard
35489 In some cases you might want to insert text characters directly into formulas.
35490 When for example the centered dot · is often used in formulas like
35491 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35494 , one would have to insert the command
35504 \begin_layout Plain Layout
35506 \begin_inset CommandInset ref
35508 reference "sub:Binary-Operators"
35517 all the time, because this character is defined in all encodings as text
35519 But the encoding can be changed by this LaTeX-preamble line:
35522 \begin_layout Standard
35527 Declare Inputtext{183}{
35537 f\SpecialChar \textcompwordmark{}
35541 \begin_layout Standard
35542 The character encoding (menu
35544 Document\SpecialChar \menuseparator
35545 Settings\SpecialChar \menuseparator
35548 ) specifies what character appears when a keyboard key is pressed.
35549 When the key for the character '·' is pressed, internally the command
35556 But this command is not available in a formula so that you would get LaTeX-erro
35558 With the changed encoding the right command is chosen automatically, depending
35559 on if the character was inserted into a formula or not.
35562 \begin_layout Standard
35563 The encoding of several characters is saved in definition files.
35564 Fore example the encoding
35568 is defined in the file
35572 that is in the installation folder of LaTeX.
35573 Encodings should only be changed via the LaTeX-preamble and not in the
35575 Otherwise own documents could not be edited by other LyX users working
35576 on other computers.
35579 \begin_layout Standard
35580 \begin_inset VSpace medskip
35583 Besides the centered dot, in this document the degree sign ° is defined
35584 with the following LaTeX-preamble line so that it can directly be inserted
35588 \begin_layout Standard
35593 DeclareInputtext{176}{
35603 f\SpecialChar \textcompwordmark{}
35607 \begin_layout Standard
35608 \begin_inset Newpage newpage
35614 \begin_layout Section
35620 \begin_layout Plain Layout
35629 \begin_layout Standard
35630 This section is a summary of the most important typographic rules, listed
35635 \begin_layout Plain Layout
35636 This collection was partly taken from the German semi-official dictionary
35638 \begin_inset Quotes eld
35642 \begin_inset Quotes erd
35646 \begin_inset CommandInset citation
35652 that lists some of the ISO rules.
35660 \begin_layout Itemize
35669 \begin_layout Plain Layout
35670 done with font styles, see
35671 \begin_inset CommandInset ref
35673 reference "sub:Font-Styles"
35683 \begin_inset space \thinspace{}
35687 \begin_inset Newline newline
35690 Between the value and the unit is the smallest space, see
35691 \begin_inset CommandInset ref
35693 reference "sub:Predefined-Space"
35698 \begin_inset Newline newline
35701 This convention is automatically fulfilled when the command
35708 When it is entered to a formula, two boxes appear.
35709 In the first one the value is inserted, in the second one the unit, and
35711 \begin_inset Formula $\unit[30]{km/h}$
35715 \begin_inset space \thinspace{}
35725 is not a real LaTeX command but the command
35731 , therefore you cannot use it in TeX code.
35734 \begin_layout Itemize
35735 Percent and perthousand signs are set like physical units:
35736 \begin_inset Newline newline
35740 \begin_inset space \thinspace{}
35746 \begin_layout Itemize
35747 The degree sign follows directly on the value: 15°, but not when it is used
35749 \begin_inset space \thinspace{}
35755 \begin_layout Itemize
35756 In numbers with more than four digits the smallest space is inserted before
35757 every third digit to group them:
35767 \begin_inset space \thinspace{}
35771 \begin_inset space \thinspace{}
35777 \begin_layout Itemize
35778 For dimensions like 120×90×40
35779 \begin_inset space \thinspace{}
35782 cm the multiplication sign
35783 \begin_inset Quotes eld
35787 \begin_inset Quotes erd
35791 It is available via the menu
35793 Insert\SpecialChar \menuseparator
35794 Special Character\SpecialChar \menuseparator
35798 With some keyboard definitions it can also be inserted directly.
35801 \begin_layout Itemize
35802 Functions with names consisting of several letters are set upright to avoid
35804 \begin_inset CommandInset ref
35806 reference "sub:Predefined-Functions"
35813 \begin_layout Itemize
35814 Indices consisting of several letters, are set upright:
35815 \begin_inset Formula $E_{\mathrm{kin}}$
35819 \begin_inset Newline newline
35822 Components of matrices are set italic:
35823 \begin_inset Formula $\hat{H}_{kl}$
35829 \begin_layout Itemize
35830 The differentiation/integration operator 'd', the Euler's number 'e', and
35831 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35835 \begin_layout Standard
35836 \begin_inset Newpage newpage
35842 \begin_layout Section
35847 \begin_layout Plain Layout
35856 \begin_layout Standard
35857 Some characters and symbols can be created with several commands.
35858 Here is a list of the synonym commands:
35861 \begin_layout Standard
35862 \begin_inset VSpace bigskip
35866 \begin_inset space \hfill{}
35870 \begin_inset Tabular
35871 <lyxtabular version="3" rows="12" columns="2">
35873 <column alignment="center" valignment="top" width="0pt">
35874 <column alignment="center" valignment="top" width="0pt">
35876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35879 \begin_layout Plain Layout
35885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35888 \begin_layout Plain Layout
35890 \begin_inset Note Note
35893 \begin_layout Plain Layout
35900 is only used as spacer.
35912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35915 \begin_layout Plain Layout
35923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35926 \begin_layout Plain Layout
35930 \begin_layout Plain Layout
35943 \begin_layout Plain Layout
35957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35960 \begin_layout Plain Layout
35968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35971 \begin_layout Plain Layout
35981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35984 \begin_layout Plain Layout
35992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35995 \begin_layout Plain Layout
36005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36008 \begin_layout Plain Layout
36016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36019 \begin_layout Plain Layout
36027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36030 \begin_layout Plain Layout
36038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36041 \begin_layout Plain Layout
36049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36052 \begin_layout Plain Layout
36060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36063 \begin_layout Plain Layout
36073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36076 \begin_layout Plain Layout
36084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36087 \begin_layout Plain Layout
36097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36100 \begin_layout Plain Layout
36108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36111 \begin_layout Plain Layout
36121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36124 \begin_layout Plain Layout
36132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36135 \begin_layout Plain Layout
36145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36148 \begin_layout Plain Layout
36156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36159 \begin_layout Plain Layout
36167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36170 \begin_layout Plain Layout
36178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36181 \begin_layout Plain Layout
36193 \begin_inset space \hfill{}
36197 \begin_inset Tabular
36198 <lyxtabular version="3" rows="12" columns="2">
36200 <column alignment="center" valignment="top" width="0pt">
36201 <column alignment="center" valignment="top" width="0pt">
36203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36206 \begin_layout Plain Layout
36212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36215 \begin_layout Plain Layout
36223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36226 \begin_layout Plain Layout
36234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36237 \begin_layout Plain Layout
36249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36252 \begin_layout Plain Layout
36260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36263 \begin_layout Plain Layout
36273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36276 \begin_layout Plain Layout
36284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36287 \begin_layout Plain Layout
36297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36300 \begin_layout Plain Layout
36308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36311 \begin_layout Plain Layout
36319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36322 \begin_layout Plain Layout
36330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36333 \begin_layout Plain Layout
36341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36344 \begin_layout Plain Layout
36352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36355 \begin_layout Plain Layout
36365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36368 \begin_layout Plain Layout
36376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36379 \begin_layout Plain Layout
36389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36392 \begin_layout Plain Layout
36400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36403 \begin_layout Plain Layout
36413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36416 \begin_layout Plain Layout
36424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36427 \begin_layout Plain Layout
36437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36440 \begin_layout Plain Layout
36448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36451 \begin_layout Plain Layout
36461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36464 \begin_layout Plain Layout
36472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36475 \begin_layout Plain Layout
36489 \begin_inset space \hfill{}
36495 \begin_layout Standard
36496 \begin_inset Newpage newpage
36502 \begin_layout Bibliography
36503 \begin_inset CommandInset bibitem
36504 LatexCommand bibitem
36516 The LaTeX Companion
36519 Addison Wesley, 2004
36522 \begin_layout Bibliography
36523 \begin_inset CommandInset bibitem
36524 LatexCommand bibitem
36530 \begin_inset CommandInset href
36533 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
36537 of LaTeX's math abilities
36540 \begin_layout Bibliography
36541 \begin_inset CommandInset bibitem
36542 LatexCommand bibitem
36547 LaTeX tips and tricks-
36548 \begin_inset CommandInset href
36551 target "http://tug.org/TeXnik/"
36558 \begin_layout Bibliography
36559 \begin_inset CommandInset bibitem
36560 LatexCommand bibitem
36566 \begin_inset CommandInset href
36569 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
36577 \begin_layout Plain Layout
36589 \begin_layout Bibliography
36590 \begin_inset CommandInset bibitem
36591 LatexCommand bibitem
36597 \begin_inset CommandInset href
36600 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
36604 of all symbols available with LaTeX-packages
36607 \begin_layout Bibliography
36608 \begin_inset CommandInset bibitem
36609 LatexCommand bibitem
36615 \begin_inset CommandInset href
36617 name "Documentation"
36618 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
36622 of the LaTeX-package
36630 \begin_layout Plain Layout
36631 Packages ! hyperref
36639 \begin_layout Bibliography
36640 \begin_inset CommandInset bibitem
36641 LatexCommand bibitem
36647 \begin_inset CommandInset href
36650 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
36661 \begin_inset CommandInset ref
36663 reference "sub:Operator-Limits"
36671 \begin_layout Plain Layout
36682 \begin_layout Bibliography
36683 \begin_inset CommandInset bibitem
36684 LatexCommand bibitem
36695 Auflage, Duden 2001
36698 \begin_layout Subsubsection*
36699 \begin_inset CommandInset index_print
36700 LatexCommand printindex