1 #LyX 1.6.6svn 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}
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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 % for the Fourier transformation symbol
88 % center multirows (e.g. in sec. 13.3)
89 \renewcommand{\multirowsetup}{\centering}
91 % define a color, used in sec.9.3
92 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
94 % declare operators (see sec. 10.4 and sec. 15.2)
95 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
96 \DeclareMathOperator{\sgn}{sgn}
98 \newcommand{\spce}{\textvisiblespace}
100 % example definitions for sec. 20.1
101 \newcommand{\gr}{\Longrightarrow}
102 \newcommand{\us}[1]{\underline{#1}}
103 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
104 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
105 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
107 % example macro from sec. 19.4
108 %\def\tagform@#1{\maketag@@@{|#1|}}
110 % macro from sec. 10.2
111 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
112 \def\mathclap {\mathpalette \mathclapinternal}
113 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
115 % redefine the greyed out note
116 \renewenvironment{lyxgreyedout}
117 {\textcolor{blue}\bgroup}{\egroup}
119 % ------------------------------------
120 % used to check for needed LaTeX packages
123 % check for package eurosym
124 % used for the Euro symbol
126 \IfFileExists{eurosym.sty}
127 {\usepackage[gennarrow]{eurosym}
128 \setboolean{eurosym}{true}}
129 {\setboolean{eurosym}{false}}
131 % check for package braket
132 % used for physical vectors
134 \IfFileExists{braket.sty}
136 \setboolean{braket}{true}}
137 {\setboolean{braket}{false}}
139 % check for package cancel
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143 \setboolean{cancel}{true}}
144 {\setboolean{cancel}{false}}
146 % check for package upgreek
148 \IfFileExists{upgreek.sty}
149 {\usepackage{upgreek}
150 \setboolean{upgreek}{true}}
151 {\setboolean{upgreek}{false}}
153 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
154 \use_default_options false
159 \font_typewriter default
160 \font_default_family default
170 \pdf_title "LyX's Math Manual"
171 \pdf_author "LyX Team, Uwe Stöhr"
172 \pdf_subject "LyX-documentation about math"
173 \pdf_keywords "LyX, Mathed"
175 \pdf_bookmarksnumbered true
176 \pdf_bookmarksopen true
177 \pdf_bookmarksopenlevel 1
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183 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
190 \paperorientation portrait
193 \paragraph_separation skip
195 \quotes_language english
198 \paperpagestyle plain
202 \tracking_changes false
203 \output_changes false
211 LyX's detailed Math manual
219 \begin_layout Plain Layout
221 If you have comments or error corrections, please send them to the LyX Documenta
225 \begin_inset CommandInset href
227 name "lyx-docs@lists.lyx.org"
228 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
239 \begin_inset Note Note
242 \begin_layout Plain Layout
249 \begin_inset Newline newline
253 \begin_inset Newline newline
261 \begin_layout Standard
262 \begin_inset CommandInset toc
263 LatexCommand tableofcontents
270 \begin_layout Standard
271 \begin_inset Note Note
274 \begin_layout Plain Layout
275 To export this document to PDF, PS or DVI the LaTeX-packages
277 braket, cancel, eurosym,
288 If they are not installed the document can be export anyway but the sections
289 where the packages are required will not appear in the output.
294 ; if it is not installed, this file cannot be exported.
297 \begin_layout Plain Layout
298 The latest PDF-version of this document can be found here:
299 \begin_inset Newline newline
304 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
312 \begin_layout Standard
313 \begin_inset Newpage newpage
319 \begin_layout Section
323 \begin_layout Standard
324 This document explains LyX's math features and is furthermore a collection
325 of LaTeX-commands used for mathematical characters and constructs.
326 The explanations are designed for the usage of commands.
327 It is therefore required that you have read the section
338 \begin_layout Standard
339 Most of the characters and many constructs explained in this manual are
340 also accessible via the menu
344 \SpecialChar \menuseparator
360 But everybody who has to write lots of formulas will notice that it is
361 much faster to use commands instead of the math toolbar.
362 Therefore this manual is focused on commands but also mentions the correspondin
363 g toolbar buttons when available.
366 \begin_layout Standard
367 If not specially mentioned the commands are only available within formulas.
368 To be able to use all commands explained in this document, the option
372 must be used in the document settings (menu
374 Document\SpecialChar \menuseparator
375 Settings\SpecialChar \menuseparator
386 \begin_layout Plain Layout
389 Use AMS math package automatically
395 \begin_layout Plain Layout
404 -math when math constructs are found that are supported by LyX.
412 \begin_layout Standard
413 This document doesn't list all
417 \begin_layout Plain Layout
430 \begin_layout Plain Layout
435 \begin_layout Plain Layout
444 -math commands is in the file
447 \begin_inset CommandInset href
450 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
456 , which is part of every LaTeX standard installation.
461 for lucidity reasons.
464 \begin_layout Section
468 \begin_layout Standard
469 To create an inline formula
473 \begin_layout Plain Layout
479 that is embedded into a text line, use one of the shortcuts
485 or the toolbar button
486 \begin_inset Graphics
487 filename ../images/math-mode.png
493 \begin_inset Newline newline
496 To create a display style formula
500 \begin_layout Plain Layout
501 Formula ! display style
506 that will appear bigger and in an own paragraph, use one of these shortcuts:
516 \begin_layout Standard
517 To change a display style formula to an inline formula, set the cursor into
518 the formula and use one of the shortcuts
526 Edit\SpecialChar \menuseparator
527 Math\SpecialChar \menuseparator
531 The same way is used to change an inline formula to a display style formula.
534 \begin_layout Standard
535 To display parts of an inline formula in the size of a display style formula,
546 \begin_layout Plain Layout
555 Then a new blue box appears in which the desired formula part is inserted.
558 \begin_layout Standard
559 Only inline formulas are allowed inside tables.
562 \begin_layout Standard
567 can be turned on in the menu
569 View\SpecialChar \menuseparator
573 When you click there on
574 \begin_inset Quotes eld
578 \begin_inset Quotes erd
581 the toolbar will be shown permanently at the bottom; this state is visualized
586 menu with a checkmark.
587 When you click in this state again on
588 \begin_inset Quotes eld
592 \begin_inset Quotes erd
603 is only shown when the cursor is within a formula; this state is visualized
604 by the renaming of the menu entry from
605 \begin_inset Quotes eld
609 \begin_inset Quotes erd
613 \begin_inset Quotes eld
621 \begin_inset Quotes erd
627 \begin_layout Standard
632 \begin_layout Plain Layout
638 is invoked by pressing the toolbar button
639 \begin_inset Graphics
640 filename ../images/ert-insert.png
647 Insert\SpecialChar \menuseparator
652 \begin_layout Plain Layout
668 \begin_inset Note Note
671 \begin_layout Plain Layout
672 In LyX there are three
673 \begin_inset Quotes eld
677 \begin_inset Quotes erd
680 that appear in the output with sub- and superscript letters: TeX, LaTeX
684 \begin_layout Plain Layout
685 To avoid that these names are recognized as proper names, a TeX-brace pair
694 \begin_layout Standard
695 To change the LaTeX-preamble
699 \begin_layout Plain Layout
707 Document\SpecialChar \menuseparator
708 Settings\SpecialChar \menuseparator
713 \begin_layout Plain Layout
729 \begin_layout Standard
730 To edit matrices, case differentiations and multiline formulas subsequently,
733 Edit\SpecialChar \menuseparator
738 Edit\SpecialChar \menuseparator
740 \begin_inset space \thinspace{}
744 \begin_inset space \thinspace{}
754 When lines and columns are swapped via the menu, the column or line where
755 the cursor is in is exchanged with the column to the right or the line
757 Is the cursor in the last column or row, the exchange is done with the
758 column to the left or the line above.
761 \begin_layout Standard
762 To write text in formulas
766 \begin_layout Plain Layout
767 For multiline formulas the command
774 \begin_inset CommandInset ref
776 reference "sub:Text-in-multiline"
793 \begin_layout Plain Layout
803 \begin_layout Plain Layout
810 This mode is invoked with the shortcut
816 or by the insertion of the command
826 \begin_layout Plain Layout
835 The text appears black in LyX and can therefore be distinguished from the
836 other formula parts that appear blue.
837 In the output mathematical text is set upright, in contrary to other formula
841 \begin_layout Subsection*
845 \begin_layout Standard
846 Most of the LaTeX-commands for math constructs have the following scheme:
849 \begin_layout Standard
865 \begin_layout Standard
866 A command starts always with a backslash
867 \begin_inset Quotes gld
877 \begin_inset Quotes grd
881 To omit optional arguments, also omit the associated brackets.
882 The braces around the required arguments are named in this document as
887 \begin_layout Plain Layout
894 If you add in a formula a left brace to a command name, LyX creates automatical
896 In all other cases TeX-braces are created in formulas with the command
904 TeX-braces appear red in LyX, in contrary to normal braces that appear
906 In TeX-mode no command is needed to get TeX-braces.
907 TeX-braces don't appear in the output.
910 \begin_layout Standard
911 When commands without arguments, like commands for symbols are entered in
912 TeX-mode, a space character must
916 be behind the command to end it.
917 This space doesn't appear in the output.
918 When the space should appear in the output, the space must be followed
919 by a protected space in normal text.
922 \begin_layout Standard
923 A protected space is inserted with
926 arg "space-insert protected"
932 \begin_layout Subsection*
933 \begin_inset Newpage newpage
939 \begin_layout Itemize
944 \begin_layout Plain Layout
945 This visible space character can be created with the command
955 \begin_layout Plain Layout
963 , inserted in TeX-mode.
972 \begin_layout Plain Layout
985 denotes a space character to be input.
988 \begin_layout Itemize
990 \begin_inset Formula $\to$
993 denotes the usage of the corresponding arrow key on the keyboard.
996 \begin_layout Subsection*
1000 \begin_layout Standard
1002 \begin_inset Float table
1008 \begin_layout Plain Layout
1010 \begin_inset Caption
1012 \begin_layout Plain Layout
1013 \begin_inset CommandInset label
1015 name "tab:Available-units"
1027 \begin_layout Plain Layout
1029 \begin_inset Tabular
1030 <lyxtabular version="3" rows="13" columns="2">
1032 <column alignment="center" valignment="top" width="0">
1033 <column alignment="center" valignment="top" width="0">
1035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1038 \begin_layout Plain Layout
1044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1047 \begin_layout Plain Layout
1055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1058 \begin_layout Plain Layout
1064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1067 \begin_layout Plain Layout
1075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1078 \begin_layout Plain Layout
1084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1087 \begin_layout Plain Layout
1095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1098 \begin_layout Plain Layout
1104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1107 \begin_layout Plain Layout
1109 \begin_inset space \thinspace{}
1113 \begin_inset space \thinspace{}
1123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1126 \begin_layout Plain Layout
1132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1135 \begin_layout Plain Layout
1137 \begin_inset space \thinspace{}
1141 \begin_inset space \thinspace{}
1151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1154 \begin_layout Plain Layout
1160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1163 \begin_layout Plain Layout
1165 \begin_inset space \thinspace{}
1169 \begin_inset space \thinspace{}
1179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1182 \begin_layout Plain Layout
1188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1191 \begin_layout Plain Layout
1193 \begin_inset space \thinspace{}
1197 \begin_inset space \thinspace{}
1207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1210 \begin_layout Plain Layout
1216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1219 \begin_layout Plain Layout
1221 \begin_inset space \thinspace{}
1225 \begin_inset space \thinspace{}
1235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1238 \begin_layout Plain Layout
1244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1247 \begin_layout Plain Layout
1249 \begin_inset space \thinspace{}
1253 \begin_inset Formula $\approx$
1257 \begin_inset space \thinspace{}
1267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1270 \begin_layout Plain Layout
1276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1279 \begin_layout Plain Layout
1281 \begin_inset space \thinspace{}
1285 \begin_inset space \thinspace{}
1295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1298 \begin_layout Plain Layout
1304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1307 \begin_layout Plain Layout
1311 \begin_inset Quotes eld
1317 \begin_inset Quotes erd
1327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1330 \begin_layout Plain Layout
1336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1339 \begin_layout Plain Layout
1341 \begin_inset Quotes eld
1349 \begin_inset Quotes erd
1359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1362 \begin_layout Plain Layout
1368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1371 \begin_layout Plain Layout
1373 \begin_inset space \thinspace{}
1377 \begin_inset Formula $\nicefrac{1}{18}$
1381 \begin_inset space \thinspace{}
1402 \begin_layout Standard
1403 \begin_inset Newpage newpage
1409 \begin_layout Section
1413 \begin_layout Subsection
1418 \begin_layout Plain Layout
1428 \begin_layout Plain Layout
1438 \begin_layout Plain Layout
1443 \begin_layout Plain Layout
1454 \begin_layout Plain Layout
1470 \begin_layout Plain Layout
1475 \begin_layout Plain Layout
1486 \begin_layout Plain Layout
1501 \begin_layout Standard
1502 Indices are created with an underscore
1503 \begin_inset Quotes eld
1507 \begin_inset Quotes erd
1510 or via the math toolbar button
1511 \begin_inset Graphics
1512 filename ../images/math-subscript.png
1517 , exponents with a caret
1518 \begin_inset Quotes eld
1522 \begin_inset Quotes erd
1525 or via the math toolbar button
1526 \begin_inset Graphics
1527 filename ../images/math-superscript.png
1535 \begin_layout Standard
1537 \begin_inset Tabular
1538 <lyxtabular version="3" rows="4" columns="2">
1540 <column alignment="center" valignment="top" width="0pt">
1541 <column alignment="center" valignment="top" width="0pt">
1543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1546 \begin_layout Plain Layout
1552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1555 \begin_layout Plain Layout
1557 \begin_inset Note Note
1560 \begin_layout Plain Layout
1567 is only used as spacer.
1579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1582 \begin_layout Plain Layout
1588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1591 \begin_layout Plain Layout
1592 \begin_inset Formula $B_{V}$
1602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1605 \begin_layout Plain Layout
1611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1614 \begin_layout Plain Layout
1615 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1628 \begin_layout Plain Layout
1633 \begin_layout Plain Layout
1647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1650 \begin_layout Plain Layout
1651 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1667 \begin_layout Standard
1668 As the caret is in some languages an accent, vowels will be accentuated
1669 in this case and not set as exponents
1673 \begin_layout Plain Layout
1674 Depending on the used keyboard settings this can also happen for other character
1681 To get in this case exponents, press
1685 after the caret as in the last example.
1688 \begin_layout Subsection
1690 \begin_inset CommandInset label
1692 name "sub:Fractions"
1700 \begin_layout Plain Layout
1709 \begin_layout Standard
1710 Fractions are generated with the command
1720 \begin_layout Plain Layout
1728 or via the math toolbar button
1729 \begin_inset Graphics
1730 filename ../images/math/frac.png
1736 The font size is adjusted automatically, depending on whether the fraction
1737 is in an inline or display style formula.
1738 With the math toolbar button
1739 \begin_inset Graphics
1740 filename ../images/math/frac-square.png
1745 you can select different fraction types.
1748 \begin_layout Standard
1757 \begin_layout Plain Layout
1767 a fraction can be created that has in any case the size of a display style
1777 \begin_layout Plain Layout
1787 the fraction appears always with the size of an inline formula.
1791 \begin_layout Standard
1792 A line with the fraction
1793 \begin_inset Formula $\frac{1}{2}$
1796 that was created with the command
1805 \begin_layout Standard
1806 A line with the fraction
1807 \begin_inset Formula $\dfrac{1}{2}$
1810 that was created with the command
1819 \begin_layout Standard
1821 \begin_inset Tabular
1822 <lyxtabular version="3" rows="4" columns="2">
1824 <column alignment="center" valignment="top" width="0pt">
1825 <column alignment="center" valignment="top" width="0pt">
1827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1830 \begin_layout Plain Layout
1836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1839 \begin_layout Plain Layout
1841 \begin_inset Note Note
1844 \begin_layout Plain Layout
1851 is only used as spacer.
1863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1866 \begin_layout Plain Layout
1873 \begin_layout Plain Layout
1883 \begin_inset Formula $\downarrow$
1891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1894 \begin_layout Plain Layout
1895 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1908 \begin_layout Plain Layout
1915 \begin_layout Plain Layout
1925 \begin_inset Formula $\downarrow$
1933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1936 \begin_layout Plain Layout
1937 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1950 \begin_layout Plain Layout
1957 \begin_layout Plain Layout
1970 \begin_layout Plain Layout
1985 \begin_layout Plain Layout
1995 \begin_inset Formula $\downarrow$
1999 \begin_inset Formula $\downarrow\downarrow$
2007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2010 \begin_layout Plain Layout
2011 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2027 \begin_layout Standard
2028 \begin_inset VSpace bigskip
2032 \begin_inset Newpage newpage
2035 For nested fractions the command
2045 \begin_layout Plain Layout
2055 \begin_inset VSpace -3mm
2061 \begin_layout Standard
2062 \begin_inset Formula \begin{align*}
2063 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2064 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2071 \begin_layout Standard
2072 The command for the example above is:
2075 \begin_layout Standard
2084 \begin_layout Plain Layout
2094 \begin_inset Formula $\downarrow$
2103 \begin_layout Plain Layout
2118 \begin_layout Plain Layout
2128 \begin_inset Formula $\downarrow$
2132 \begin_inset Formula $\downarrow$
2138 \begin_layout Standard
2139 \begin_inset VSpace medskip
2145 \begin_layout Standard
2152 sets the fraction always in the size of a displayed formula, also when
2153 it is part of another fraction.
2156 \begin_layout Standard
2157 It is possible to specify the alignment of the numerator.
2164 is used to left align it, the command
2177 centers the numerator.
2178 These fractions demonstrate the different alignments:
2181 \begin_layout Standard
2182 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2186 \begin_inset Formula $\cfrac{A}{B+C}$
2190 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2196 \begin_layout Standard
2197 \begin_inset Note Greyedout
2200 \begin_layout Plain Layout
2217 are no real LaTeX commands but represent the command
2221 cfrac[alignment]{numerator}{denominator}
2224 Therefore you cannot use them in TeX code.
2232 \begin_layout Standard
2233 \begin_inset VSpace medskip
2236 It is often advantageous to combine
2249 \begin_inset Formula \[
2250 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2257 \begin_layout Standard
2258 For inline fractions with a sloped fraction stroke you can use the command
2269 \begin_layout Plain Layout
2278 \begin_inset Formula $\nicefrac{5}{31}$
2291 \begin_layout Plain Layout
2300 \begin_inset Formula $\unitfrac{5}{31}$
2303 There is furthermore the command
2309 that offers to write a fraction in combination with a number:
2310 \begin_inset Formula $\unitfrac[2]{1}{3}$
2316 \begin_layout Standard
2317 \begin_inset Note Greyedout
2320 \begin_layout Plain Layout
2331 is not a real LaTeX command but the command
2332 \begin_inset Newline newline
2339 unitfrac[number]{numerator}{denominator}
2342 Therefore you cannot use it in TeX code.
2350 \begin_layout Standard
2351 How to define own fractions where the fraction stroke can be changed, is
2353 \begin_inset CommandInset ref
2355 reference "sub:Self-defined-Fractions"
2362 \begin_layout Subsection
2367 \begin_layout Plain Layout
2376 \begin_layout Standard
2377 Square roots are created with
2387 \begin_layout Plain Layout
2395 or the math toolbar button
2396 \begin_inset Graphics
2397 filename ../images/math/sqrt.png
2402 , all other roots with the command
2412 \begin_layout Plain Layout
2420 or with the math toolbar button
2421 \begin_inset Graphics
2422 filename ../images/math/root.png
2430 \begin_layout Standard
2432 \begin_inset Tabular
2433 <lyxtabular version="3" rows="3" columns="2">
2435 <column alignment="center" valignment="top" width="0pt">
2436 <column alignment="center" valignment="top" width="0pt">
2438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2441 \begin_layout Plain Layout
2447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2450 \begin_layout Plain Layout
2452 \begin_inset Note Note
2455 \begin_layout Plain Layout
2462 is only used as spacer.
2474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2477 \begin_layout Plain Layout
2484 \begin_layout Plain Layout
2498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2501 \begin_layout Plain Layout
2502 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2512 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2515 \begin_layout Plain Layout
2522 \begin_layout Plain Layout
2532 \begin_inset Formula $\downarrow$
2540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2543 \begin_layout Plain Layout
2544 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2560 \begin_layout Standard
2561 A square root can also be created with
2567 when the root index field is left empty.
2570 \begin_layout Standard
2571 With certain indices the distance to the root is too small, like in this
2573 \begin_inset Formula $\sqrt[\beta]{B}$
2577 \begin_inset Newline newline
2581 \begin_inset Formula $\beta$
2585 To avoid this, the commands
2595 \begin_layout Plain Layout
2613 \begin_layout Plain Layout
2621 are used with the following scheme:
2624 \begin_layout Standard
2638 \begin_layout Standard
2639 Distance is the number of Big Points (unit bp;
2640 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2643 ), that the index should be moved to the left or top, resp..
2644 The commands are written to the index.
2645 This way the command
2646 \begin_inset Newline newline
2656 \begin_inset Formula $\to$
2662 \begin_inset Formula $\to$
2671 \begin_layout Plain Layout
2681 \begin_inset Formula $\to$
2685 \begin_inset Newline newline
2690 produces a correct typeset formula:
2691 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2697 \begin_layout Subsection
2698 Binomial Coefficients
2702 \begin_layout Plain Layout
2703 Binomial coefficients
2711 \begin_layout Standard
2712 Binomial coefficients are inserted with the command
2722 \begin_layout Plain Layout
2730 or with the submenu of the math toolbar button
2731 \begin_inset Graphics
2732 filename ../images/math/frac-square.png
2738 Analog to fractions (
2758 \begin_layout Plain Layout
2778 \begin_layout Plain Layout
2787 For other brackets around binomial coeficients there are the commands
2797 \begin_layout Plain Layout
2815 \begin_layout Plain Layout
2826 \begin_layout Standard
2828 \begin_inset Tabular
2829 <lyxtabular version="3" rows="6" columns="2">
2831 <column alignment="center" valignment="top" width="0pt">
2832 <column alignment="center" valignment="top" width="0pt">
2834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2837 \begin_layout Plain Layout
2843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2846 \begin_layout Plain Layout
2848 \begin_inset Note Note
2851 \begin_layout Plain Layout
2858 is only used as spacer.
2870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2873 \begin_layout Plain Layout
2880 \begin_layout Plain Layout
2890 \begin_inset Formula $\downarrow$
2898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2901 \begin_layout Plain Layout
2902 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2915 \begin_layout Plain Layout
2922 \begin_layout Plain Layout
2932 \begin_inset Formula $\downarrow$
2940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2943 \begin_layout Plain Layout
2944 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2957 \begin_layout Plain Layout
2964 \begin_layout Plain Layout
2974 \begin_inset Formula $\downarrow$
2982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2985 \begin_layout Plain Layout
2986 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2999 \begin_layout Plain Layout
3006 \begin_layout Plain Layout
3016 \begin_inset Formula $\downarrow$
3024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3027 \begin_layout Plain Layout
3028 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3041 \begin_layout Plain Layout
3048 \begin_layout Plain Layout
3058 \begin_inset Formula $\downarrow$
3066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3069 \begin_layout Plain Layout
3070 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3086 \begin_layout Subsection
3087 Case Differentiations
3091 \begin_layout Plain Layout
3092 Case differentiations
3100 \begin_layout Standard
3102 \begin_inset Tabular
3103 <lyxtabular version="3" rows="3" columns="2">
3105 <column alignment="center" valignment="top" width="0pt">
3106 <column alignment="center" valignment="top" width="0pt">
3108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3111 \begin_layout Plain Layout
3117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3120 \begin_layout Plain Layout
3128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3131 \begin_layout Plain Layout
3138 \begin_layout Plain Layout
3148 \begin_inset Formula $\to$
3155 \begin_layout Plain Layout
3168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3171 \begin_layout Plain Layout
3172 \begin_inset Formula $\begin{cases}
3183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3186 \begin_layout Plain Layout
3193 \begin_layout Plain Layout
3205 arg "newline-insert newline"
3213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3216 \begin_layout Plain Layout
3217 \begin_inset Formula $\begin{cases}
3218 A & \textrm{for }x>0\\
3219 B & \textrm{for }x=0\end{cases}$
3235 \begin_layout Standard
3242 or the usage of the math toolbar button
3243 \begin_inset Graphics
3244 filename ../images/math/cases.png
3249 you can create new lines with the shortcut
3252 arg "newline-insert newline"
3255 or the table toolbar button
3256 \begin_inset Graphics
3257 filename ../images/tabular-feature_append-row.png
3265 \begin_layout Standard
3272 is also available via the menu
3274 Insert\SpecialChar \menuseparator
3275 Math\SpecialChar \menuseparator
3281 \begin_layout Subsection
3286 \begin_layout Plain Layout
3295 \begin_layout Standard
3306 \begin_layout Plain Layout
3314 every character can be displayed canceled.
3315 The characters are quasi accentuated by a slash.
3318 \begin_layout Standard
3320 \begin_inset Tabular
3321 <lyxtabular version="3" rows="4" columns="2">
3323 <column alignment="center" valignment="top" width="0pt">
3324 <column alignment="center" valignment="top" width="0pt">
3326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3329 \begin_layout Plain Layout
3335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3338 \begin_layout Plain Layout
3346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3349 \begin_layout Plain Layout
3357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3360 \begin_layout Plain Layout
3361 \begin_inset Formula $\not=$
3371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3374 \begin_layout Plain Layout
3384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3387 \begin_layout Plain Layout
3388 \begin_inset Formula $\not\le$
3398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3401 \begin_layout Plain Layout
3411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3414 \begin_layout Plain Layout
3415 \begin_inset Formula $\not\parallel$
3431 \begin_layout Standard
3432 The last example shows, that not all negations look good.
3433 Therefore there are for some negations special commands (see
3434 \begin_inset CommandInset ref
3436 reference "sub:Mathematical-Symbols"
3441 \begin_inset CommandInset ref
3443 reference "sec:Relations"
3450 \begin_layout Subsection
3452 \begin_inset CommandInset label
3454 name "sub:Placeholders"
3462 \begin_layout Plain Layout
3472 \begin_layout Plain Layout
3473 Chemical characters ! Isotopes
3482 \begin_layout Plain Layout
3487 \begin_layout Plain Layout
3498 \begin_layout Plain Layout
3513 \begin_layout Standard
3515 \begin_inset space \thinspace{}
3519 \begin_inset space \space{}
3526 \begin_layout Plain Layout
3527 Typesetting isotopes and chemical symbols is described in
3528 \begin_inset CommandInset ref
3530 reference "sub:Chemical-Symbols-and"
3539 the following problem occurs:
3542 \begin_layout Standard
3544 \begin_inset Tabular
3545 <lyxtabular version="3" rows="2" columns="2">
3547 <column alignment="center" valignment="top" width="0pt">
3548 <column alignment="center" valignment="top" width="0pt">
3550 <cell alignment="center" valignment="top" usebox="none">
3553 \begin_layout Plain Layout
3554 Indices created with sub- and superscripts:
3559 <cell alignment="center" valignment="top" usebox="none">
3562 \begin_layout Plain Layout
3563 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3573 <cell alignment="center" valignment="top" usebox="none">
3576 \begin_layout Plain Layout
3582 <cell alignment="center" valignment="top" usebox="none">
3585 \begin_layout Plain Layout
3586 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3600 \begin_inset Note Note
3603 \begin_layout Plain Layout
3610 is only used as spacer.
3618 \begin_layout Standard
3619 The shorter index is by default placed below or above the first character
3620 of the longer index.
3621 To avoid this there is the command
3631 \begin_layout Plain Layout
3639 or the math toolbar button
3640 \begin_inset space \thinspace{}
3647 \begin_layout Plain Layout
3648 can be found in the submenu of the toolbar button
3649 \begin_inset Graphics
3650 filename ../images/math/space.png
3661 \begin_inset Graphics
3662 filename ../images/math/phantom.png
3667 that creates one or more phantom characters.
3674 a small blue box appears that is superposed with two red arrows.
3675 The arrows indicate that the complete width and height of the box content
3676 will be created as placeholder.
3677 Phantom characters are accordingly placeholders with the size of the characters.
3680 \begin_layout Standard
3682 \begin_inset Tabular
3683 <lyxtabular version="3" rows="4" columns="2">
3685 <column alignment="center" valignment="top" width="0">
3686 <column alignment="center" valignment="top" width="0">
3688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3691 \begin_layout Plain Layout
3697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3700 \begin_layout Plain Layout
3702 \begin_inset Note Note
3705 \begin_layout Plain Layout
3712 is only used as spacer.
3724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3727 \begin_layout Plain Layout
3732 \begin_layout Plain Layout
3747 \begin_layout Plain Layout
3757 \begin_inset Formula $\to$
3764 \begin_layout Plain Layout
3778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3781 \begin_layout Plain Layout
3782 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3795 \begin_layout Plain Layout
3800 \begin_layout Plain Layout
3815 \begin_layout Plain Layout
3825 \begin_inset Formula $\to$
3832 \begin_layout Plain Layout
3846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3849 \begin_layout Plain Layout
3850 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3863 \begin_layout Plain Layout
3870 \begin_layout Plain Layout
3885 \begin_layout Plain Layout
3895 \begin_inset Formula $\to$
3902 \begin_layout Plain Layout
3916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3919 \begin_layout Plain Layout
3920 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3936 \begin_layout Standard
3937 Furthermore there are the commands
3947 \begin_layout Plain Layout
3956 \begin_inset space ~
3960 \begin_inset Graphics
3961 filename ../images/math/vphantom.png
3976 \begin_layout Plain Layout
3985 \begin_inset space ~
3989 \begin_inset Graphics
3990 filename ../images/math/hphantom.png
4002 creates only space for the maximal height of the characters in the box
4003 but not for its width.
4010 creates only space for the width of the box content.
4011 Therefore the boxes of both commands have only one red arrow.
4014 \begin_layout Standard
4025 \begin_layout Plain Layout
4040 space for the height of the integral sign,
4044 \begin_layout Plain Layout
4051 creates an integral sign, see
4052 \begin_inset CommandInset ref
4054 reference "sub:Big-Operators"
4063 because this is the larger character.
4064 An example application is in
4065 \begin_inset CommandInset ref
4067 reference "sub:Multiline-Brackets"
4074 \begin_layout Subsection
4079 \begin_layout Plain Layout
4089 \begin_layout Plain Layout
4090 Formula ! underlined
4098 \begin_layout Standard
4100 \begin_inset Tabular
4101 <lyxtabular version="3" rows="4" columns="2">
4103 <column alignment="center" valignment="top" width="0pt">
4104 <column alignment="center" valignment="top" width="0pt">
4106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4109 \begin_layout Plain Layout
4115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4118 \begin_layout Plain Layout
4120 \begin_inset Note Note
4123 \begin_layout Plain Layout
4130 is only used as spacer.
4142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4145 \begin_layout Plain Layout
4152 \begin_layout Plain Layout
4165 \begin_layout Plain Layout
4178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4181 \begin_layout Plain Layout
4182 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4192 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4195 \begin_layout Plain Layout
4202 \begin_layout Plain Layout
4215 \begin_layout Plain Layout
4228 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4231 \begin_layout Plain Layout
4232 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4245 \begin_layout Plain Layout
4252 \begin_layout Plain Layout
4267 \begin_layout Plain Layout
4281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4284 \begin_layout Plain Layout
4285 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4301 \begin_layout Standard
4302 In the last example it doesn't matter if first
4317 \begin_layout Standard
4318 To double underline e.
4319 \begin_inset space \thinspace{}
4323 \begin_inset space \space{}
4335 \begin_layout Standard
4336 It is possible to place up to 6 lines above or below characters.
4339 \begin_layout Standard
4340 \begin_inset VSpace bigskip
4343 Custom lines can be created using the command
4353 \begin_layout Plain Layout
4361 which has the following scheme:
4364 \begin_layout Standard
4369 rule[vertical offset]{length}{thickness}
4372 \begin_layout Standard
4373 The optional vertical offset shifts the line upwards (or downwards, when
4374 the value is negative).
4376 \begin_inset CommandInset ref
4378 reference "tab:Available-units"
4382 can be used for the values.
4383 Here are two example lines created with the commands
4384 \begin_inset Newline newline
4391 rule[-2ex]{3cm}{2pt}
4402 \begin_layout Standard
4404 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4410 \begin_layout Standard
4417 can also be used for text when it is inserted in TeX-mode.
4420 \begin_layout Subsection
4422 \begin_inset CommandInset label
4432 \begin_layout Plain Layout
4441 \begin_layout Standard
4442 There are different types of ellipses available.
4446 \begin_layout Plain Layout
4447 In the math toolbar in the submenu of the button
4448 \begin_inset Graphics
4449 filename ../images/math/ldots.png
4459 For listings dots at the baseline are used (
4469 \begin_layout Plain Layout
4477 ), while for operations dots are needed that are on the same height as the
4488 \begin_layout Plain Layout
4497 When using the command
4507 \begin_layout Plain Layout
4515 , LaTeX decides on the basis of the next character what type is used.
4518 \begin_layout Standard
4520 \begin_inset Tabular
4521 <lyxtabular version="3" rows="8" columns="2">
4523 <column alignment="center" valignment="top" width="0pt">
4524 <column alignment="center" valignment="top" width="0pt">
4526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4529 \begin_layout Plain Layout
4535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4538 \begin_layout Plain Layout
4546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4549 \begin_layout Plain Layout
4554 \begin_layout Plain Layout
4569 \begin_layout Plain Layout
4583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4586 \begin_layout Plain Layout
4587 \begin_inset Formula $A_{1},\dots,A_{n}$
4597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4600 \begin_layout Plain Layout
4605 \begin_layout Plain Layout
4620 \begin_layout Plain Layout
4634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4637 \begin_layout Plain Layout
4638 \begin_inset Formula $A_{1}+\dots+A_{n}$
4648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4651 \begin_layout Plain Layout
4656 \begin_layout Plain Layout
4671 \begin_layout Plain Layout
4685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4688 \begin_layout Plain Layout
4689 \begin_inset Formula $A_{1},\ldots,A_{n}$
4699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4702 \begin_layout Plain Layout
4707 \begin_layout Plain Layout
4722 \begin_layout Plain Layout
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 $A_{1}+\cdots+A_{n}$
4750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4753 \begin_layout Plain Layout
4761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4764 \begin_layout Plain Layout
4765 \begin_inset Formula $\vdots$
4775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4778 \begin_layout Plain Layout
4786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4789 \begin_layout Plain Layout
4790 \begin_inset Formula $\ddots$
4800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4803 \begin_layout Plain Layout
4805 \begin_inset space \thinspace{}
4808 matrix with the different dots
4813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4816 \begin_layout Plain Layout
4817 \begin_inset Formula $\begin{array}{ccc}
4818 A_{11} & \cdots & A_{1m}\\
4819 \vdots & \ddots & \vdots\\
4820 A_{n1} & \cdots & A_{nm}\end{array}$
4836 \begin_layout Standard
4837 The ellipses available in menu
4839 Insert\SpecialChar \menuseparator
4841 \begin_inset space ~
4855 \begin_layout Standard
4856 \begin_inset VSpace medskip
4859 Specially for matrices there are ellipses that span over several columns.
4860 They are created with the command
4870 \begin_layout Plain Layout
4878 , that has the following scheme:
4881 \begin_layout Standard
4886 hdotsfor[distance]{number of columns}
4889 \begin_layout Standard
4890 The number of columns specifies how many columns should be spanned.
4891 Distance is a factor for the distance between the dots.
4894 \begin_layout Standard
4895 In the following matrix the command
4901 was inserted in the first box of the second line, to get an ellipsis with
4902 a dot distance twice as long as with the command
4909 \begin_inset Formula \[
4910 \left(\begin{array}{cccc}
4913 q & w & e & r\end{array}\right)\]
4917 Note that the matrix fields that should be spanned must be empty, otherwise
4918 you get LaTeX-errors.
4921 \begin_layout Standard
4922 \begin_inset VSpace bigskip
4925 Furthermore you can fill with the command
4935 \begin_layout Plain Layout
4943 the rest of a line with dots.
4944 The effect of these commands is the same like with
4951 \begin_inset CommandInset ref
4953 reference "sub:Variable-Space"
4960 \begin_layout Standard
4961 For example the command
4969 \begin_layout Plain Layout
4983 \begin_layout Standard
4984 \begin_inset Formula $A\dotfill B$
4990 \begin_layout Standard
4997 there is for a line the command
5007 \begin_layout Plain Layout
5018 \begin_layout Standard
5019 \begin_inset Formula $A\hrulefill B$
5025 \begin_layout Standard
5026 To use the commands for text, they have to be inserted in TeX-mode.
5029 \begin_layout Section
5031 \begin_inset CommandInset label
5041 \begin_layout Plain Layout
5050 \begin_layout Standard
5051 Matrices can be inserted via the math toolbar button
5052 \begin_inset Graphics
5053 filename ../images/dialog-show_mathmatrix.png
5060 Insert\SpecialChar \menuseparator
5061 Math\SpecialChar \menuseparator
5065 You will be asked for the number of matrix columns and rows and the alignment.
5066 The vertical alignment is hereby only of importance for matrices in inline
5070 \begin_layout Standard
5071 The first matrix is top
5072 \begin_inset Formula $\begin{array}[t]{cccc}
5075 C & F & I & L\end{array}$
5079 \begin_inset Formula $\begin{array}{cccc}
5082 C & F & I & L\end{array}$
5085 and the third bottom
5086 \begin_inset Formula $\begin{array}[b]{cccc}
5089 C & F & I & L\end{array}$
5095 \begin_layout Standard
5096 The horizontal alignment specifies how the column entries should be aligned.
5097 It is set by entering a letter for every column.
5102 denotes left aligned,
5111 To create for example a 4
5116 \begin_inset space ~
5119 matrix where the first column is left aligned, the second and third are
5120 centered and the last one is right aligned, one enters for the horizontal
5126 Normally are in a matrix all columns centered, therefore the default is
5127 for every column is a
5134 \begin_layout Standard
5135 Horizontal alignment:
5138 \begin_layout Standard
5144 \begin_inset Formula $\begin{array}{lll}
5147 C & F & 10000\end{array}$
5155 \begin_inset Formula $\begin{array}{ccc}
5158 C & F & 10000\end{array}$
5166 \begin_inset Formula $\begin{array}{rrr}
5169 C & F & 10000\end{array}$
5175 \begin_layout Standard
5176 To add or delete rows and columns subsequently, the math toolbar buttons
5178 \begin_inset Graphics
5179 filename ../images/tabular-feature_append-row.png
5185 \begin_inset Graphics
5186 filename ../images/tabular-feature_delete-row.png
5192 \begin_inset space \thinspace{}
5197 Edit\SpecialChar \menuseparator
5201 New rows can also be created with
5204 arg "newline-insert newline"
5210 \begin_layout Standard
5211 \begin_inset VSpace bigskip
5214 Parentheses around a matrix can can either be created with the commands
5225 \begin_layout Plain Layout
5243 \begin_layout Plain Layout
5254 \begin_inset space ~
5260 \begin_inset CommandInset ref
5262 reference "sub:Automatic-Bracket-Size"
5266 , or by using the following commands:
5267 \begin_inset VSpace medskip
5273 \begin_layout Standard
5274 \begin_inset space \hfill{}
5278 \begin_inset Tabular
5279 <lyxtabular version="3" rows="4" columns="2">
5281 <column alignment="center" valignment="top" width="0">
5282 <column alignment="center" valignment="top" width="0">
5284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5287 \begin_layout Plain Layout
5293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5296 \begin_layout Plain Layout
5298 \begin_inset Note Note
5301 \begin_layout Plain Layout
5308 is only used as spacer.
5320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5323 \begin_layout Plain Layout
5330 \begin_layout Plain Layout
5344 \begin_inset space \thinspace{}
5352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5355 \begin_layout Plain Layout
5356 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5357 0 & \textrm{-}\mathrm{i}\\
5358 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5371 \begin_layout Plain Layout
5378 \begin_layout Plain Layout
5392 \begin_inset space \thinspace{}
5400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5403 \begin_layout Plain Layout
5404 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5405 0 & \textrm{-}\mathrm{i}\\
5406 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5419 \begin_layout Plain Layout
5426 \begin_layout Plain Layout
5440 \begin_inset space \thinspace{}
5448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5451 \begin_layout Plain Layout
5452 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5453 0 & \textrm{-}\mathrm{i}\\
5454 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5468 \begin_inset space \hfill{}
5472 \begin_inset Tabular
5473 <lyxtabular version="3" rows="4" columns="2">
5475 <column alignment="center" valignment="top" width="0">
5476 <column alignment="center" valignment="top" width="0">
5478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5481 \begin_layout Plain Layout
5487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5490 \begin_layout Plain Layout
5498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5501 \begin_layout Plain Layout
5508 \begin_layout Plain Layout
5522 \begin_inset space \thinspace{}
5530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5533 \begin_layout Plain Layout
5534 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5535 0 & \textrm{-}\mathrm{i}\\
5536 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5549 \begin_layout Plain Layout
5556 \begin_layout Plain Layout
5570 \begin_inset space \thinspace{}
5578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5581 \begin_layout Plain Layout
5582 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5583 0 & \textrm{-}\mathrm{i}\\
5584 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5597 \begin_layout Plain Layout
5604 \begin_layout Plain Layout
5618 \begin_inset space \thinspace{}
5626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5629 \begin_layout Plain Layout
5630 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5631 0 & \textrm{-}\mathrm{i}\\
5632 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5646 \begin_inset space \hfill{}
5652 \begin_layout Standard
5653 \begin_inset VSpace medskip
5657 \begin_inset space \thinspace{}
5661 \begin_inset space \space{}
5670 is inserted, a blue box appears between two vertical lines where the matrix
5674 \begin_layout Standard
5675 \begin_inset VSpace bigskip
5678 As all multiline formulas are matrices, the length
5688 \begin_layout Plain Layout
5696 that is described in
5697 \begin_inset CommandInset ref
5699 reference "sub:Column-Separation"
5703 can also be used to change the column separation of matrices.
5706 \begin_layout Standard
5707 To change the row separation, the command
5717 \begin_layout Plain Layout
5726 It is used as follows:
5729 \begin_layout Standard
5736 arraystretch}{stretch factor}
5740 \begin_layout Plain Layout
5751 \begin_layout Standard
5758 assigns the stretch factor to the predefined command
5766 \begin_inset space \thinspace{}
5770 \begin_inset space \space{}
5773 the row separation, use the factor 2.
5774 This is then used for all following matrices.
5775 To go back to the original separation, assign the factor 1 to
5784 \begin_layout Standard
5785 To set matrices into a text line, the command
5795 \begin_layout Plain Layout
5804 When it is inserted a blue box with two dashed lines appears.
5805 In this box the matrix is inserted.
5808 \begin_layout Standard
5810 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5811 C & D\end{smallmatrix}\right)$
5817 \begin_layout Section
5818 Brackets and Delimiters
5822 \begin_layout Plain Layout
5832 \begin_layout Plain Layout
5841 \begin_layout Subsection
5842 Vertical Brackets and Delimiters
5846 \begin_layout Plain Layout
5855 \begin_layout Standard
5856 \begin_inset space \hfill{}
5860 \begin_inset Tabular
5861 <lyxtabular version="3" rows="9" columns="2">
5863 <column alignment="center" valignment="top" width="0pt">
5864 <column alignment="center" valignment="top" width="0pt">
5866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5869 \begin_layout Plain Layout
5875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5878 \begin_layout Plain Layout
5886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5889 \begin_layout Plain Layout
5895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5898 \begin_layout Plain Layout
5899 \begin_inset Formula $($
5909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5912 \begin_layout Plain Layout
5918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5921 \begin_layout Plain Layout
5922 \begin_inset Formula $\{$
5932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5935 \begin_layout Plain Layout
5941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5944 \begin_layout Plain Layout
5945 \begin_inset Formula $[$
5955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5958 \begin_layout Plain Layout
5966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5969 \begin_layout Plain Layout
5970 \begin_inset Formula $\langle$
5980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5983 \begin_layout Plain Layout
5991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5994 \begin_layout Plain Layout
5995 \begin_inset Formula $\lceil$
6005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6008 \begin_layout Plain Layout
6016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6019 \begin_layout Plain Layout
6020 \begin_inset Formula $\lfloor$
6030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6033 \begin_layout Plain Layout
6039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6042 \begin_layout Plain Layout
6043 \begin_inset Formula $/$
6053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6056 \begin_layout Plain Layout
6062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6065 \begin_layout Plain Layout
6066 \begin_inset Formula $|$
6080 \begin_inset space \hfill{}
6084 \begin_inset Tabular
6085 <lyxtabular version="3" rows="9" columns="2">
6087 <column alignment="center" valignment="top" width="0pt">
6088 <column alignment="center" valignment="top" width="0pt">
6090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6093 \begin_layout Plain Layout
6099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6102 \begin_layout Plain Layout
6110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6113 \begin_layout Plain Layout
6119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6122 \begin_layout Plain Layout
6123 \begin_inset Formula $)$
6133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6136 \begin_layout Plain Layout
6142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6145 \begin_layout Plain Layout
6146 \begin_inset Formula $\}$
6156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6159 \begin_layout Plain Layout
6165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6168 \begin_layout Plain Layout
6169 \begin_inset Formula $]$
6179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6182 \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 $\rangle$
6204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6207 \begin_layout Plain Layout
6215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6218 \begin_layout Plain Layout
6219 \begin_inset Formula $\rceil$
6229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6232 \begin_layout Plain Layout
6240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6243 \begin_layout Plain Layout
6244 \begin_inset Formula $\rfloor$
6254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6257 \begin_layout Plain Layout
6267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6270 \begin_layout Plain Layout
6271 \begin_inset Formula $\backslash$
6281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6284 \begin_layout Plain Layout
6292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6295 \begin_layout Plain Layout
6296 \begin_inset Formula $\|$
6310 \begin_inset space \hfill{}
6316 \begin_layout Standard
6319 \begin_inset Note Greyedout
6322 \begin_layout Plain Layout
6327 In TeX-mode the command
6337 \begin_layout Plain Layout
6345 must be used for the backslash, because the command
6353 produces there a line break.
6361 \begin_layout Standard
6362 For all characters listed above the size can be adjusted with the commands
6363 described in the following two subsections.
6364 When using these commands, the characters < and > can directly be used
6365 instead of the commands
6380 \begin_layout Subsubsection
6382 \begin_inset CommandInset label
6384 name "sub:Manual-Bracket-Size"
6392 \begin_layout Plain Layout
6393 Bracket size ! manual
6401 \begin_layout Standard
6402 The bracket size can be specified manually by the LaTeX-commands
6412 \begin_layout Plain Layout
6445 denotes the smallest and
6451 the largest bracket size.
6454 \begin_layout Standard
6455 These commands are used to emphasize levels of brackets:
6458 \begin_layout Standard
6460 \begin_inset Tabular
6461 <lyxtabular version="3" rows="2" columns="2">
6463 <column alignment="center" valignment="top" width="0pt">
6464 <column alignment="center" valignment="top" width="0pt">
6466 <cell alignment="center" valignment="top" usebox="none">
6469 \begin_layout Plain Layout
6470 all brackets in the same size:
6475 <cell alignment="center" valignment="top" usebox="none">
6478 \begin_layout Plain Layout
6479 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6489 <cell alignment="center" valignment="top" usebox="none">
6492 \begin_layout Plain Layout
6498 <cell alignment="center" valignment="top" usebox="none">
6501 \begin_layout Plain Layout
6502 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6516 \begin_inset Note Note
6519 \begin_layout Plain Layout
6526 is only used as spacer.
6534 \begin_layout Standard
6535 For the second formula the command
6545 \begin_layout Plain Layout
6559 \begin_layout Standard
6560 Here is an overview about all bracket sizes:
6563 \begin_layout Standard
6583 \begin_layout Plain Layout
6600 \begin_layout Plain Layout
6613 \begin_layout Plain Layout
6629 \begin_layout Standard
6631 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6637 \begin_layout Standard
6644 -commands there is the variant
6654 \begin_layout Plain Layout
6662 that adds a bit more space between the bracket and its content, and the
6679 \begin_layout Plain Layout
6689 , that don't add additional space.
6694 at the end of the command
6700 is for a left bracket; for a right bracket this will be replaced by an
6706 A left or right bracket can each be an opening or closing bracket.
6709 \begin_layout Standard
6710 In the following table is a comparison of the variants:
6713 \begin_layout Standard
6715 \begin_inset Tabular
6716 <lyxtabular version="3" rows="5" columns="2">
6718 <column alignment="center" valignment="middle" width="0">
6719 <column alignment="center" valignment="middle" width="0">
6721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6724 \begin_layout Plain Layout
6730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6733 \begin_layout Plain Layout
6735 \begin_inset Note Note
6738 \begin_layout Plain Layout
6745 is only used as spacer.
6757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6760 \begin_layout Plain Layout
6775 \begin_layout Plain Layout
6793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6796 \begin_layout Plain Layout
6797 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6810 \begin_layout Plain Layout
6825 \begin_layout Plain Layout
6843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6846 \begin_layout Plain Layout
6847 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6860 \begin_layout Plain Layout
6875 \begin_layout Plain Layout
6893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6896 \begin_layout Plain Layout
6897 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6910 \begin_layout Plain Layout
6922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6925 \begin_layout Plain Layout
6926 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6942 \begin_layout Subsubsection
6943 Automatic Bracket Size
6944 \begin_inset CommandInset label
6946 name "sub:Automatic-Bracket-Size"
6954 \begin_layout Plain Layout
6955 Bracket size ! automatic
6963 \begin_layout Standard
6964 Brackets with variable size can be inserted with the commands
6974 \begin_layout Plain Layout
6992 \begin_layout Plain Layout
7000 or via the math toolbar button
7001 \begin_inset Graphics
7002 filename ../images/dialog-show_mathdelimiter.png
7020 the wanted bracket must be inserted.
7021 The bracket size will then automatically be calculated for the output.
7024 \begin_layout Standard
7026 normal bracket: The command
7036 \begin_layout Plain Layout
7046 \begin_inset Formula $\downarrow$
7053 \begin_layout Plain Layout
7065 \begin_inset Formula \[
7073 \begin_layout Standard
7075 multiline bracket: The command
7087 \begin_layout Plain Layout
7097 \begin_inset Formula $\downarrow$
7104 \begin_layout Plain Layout
7118 \begin_inset Formula \[
7119 \ln\left(\frac{A}{C}\right)\]
7126 \begin_layout Standard
7142 \begin_inset space ~
7148 This has the advantage that you can see in LyX immediately the real bracket
7149 size and that the matching right bracket will be created too.
7150 \begin_inset Newline newline
7153 The command for the last example would then be:
7167 \begin_layout Plain Layout
7177 \begin_inset Formula $\downarrow$
7183 \begin_layout Standard
7184 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7185 For example the command
7195 \begin_layout Plain Layout
7205 \begin_inset Formula $\downarrow$
7212 \begin_layout Plain Layout
7228 \begin_inset Formula \[
7229 \left.\frac{A}{B}\right\} \]
7247 will be converted by LyX to brackets in the right size when the document
7248 is reloaded and an omitted bracket will appear as dashed line.
7251 \begin_layout Standard
7252 \begin_inset VSpace bigskip
7255 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7266 \begin_layout Plain Layout
7274 is additionally available for all brackets and limits.
7275 With this command the height of the following character is adapted to the
7276 one of the surrounding brackets, what is e.
7277 \begin_inset space \thinspace{}
7281 \begin_inset space \space{}
7284 needed for physical vectors:
7285 \begin_inset Formula \[
7286 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7290 For physical vectors there is a special LaTeX-package, described in
7291 \begin_inset CommandInset ref
7293 reference "sub:Physical-Vectors"
7300 \begin_layout Subsection
7305 \begin_layout Plain Layout
7306 Brackets ! horizontal
7314 \begin_layout Standard
7316 \begin_inset Tabular
7317 <lyxtabular version="3" rows="4" columns="2">
7319 <column alignment="center" valignment="top" width="0pt">
7320 <column alignment="center" valignment="top" width="0pt">
7322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7325 \begin_layout Plain Layout
7327 \begin_inset Note Note
7330 \begin_layout Plain Layout
7337 is only used as spacer.
7347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7350 \begin_layout Plain Layout
7358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7361 \begin_layout Plain Layout
7365 \begin_layout Plain Layout
7380 \begin_layout Plain Layout
7393 \begin_layout Plain Layout
7406 \begin_layout Plain Layout
7419 \begin_layout Plain Layout
7430 \begin_layout Plain Layout
7443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7446 \begin_layout Plain Layout
7447 \begin_inset Formula $\overbrace{A+B}^{3}$
7457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7460 \begin_layout Plain Layout
7464 \begin_layout Plain Layout
7479 \begin_layout Plain Layout
7492 \begin_layout Plain Layout
7505 \begin_layout Plain Layout
7516 \begin_layout Plain Layout
7529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7532 \begin_layout Plain Layout
7533 \begin_inset Formula $\underbrace{A+B}_{5}$
7543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7546 \begin_layout Plain Layout
7553 \begin_layout Plain Layout
7568 \begin_layout Plain Layout
7581 \begin_layout Plain Layout
7594 \begin_layout Plain Layout
7607 \begin_layout Plain Layout
7620 \begin_layout Plain Layout
7633 \begin_layout Plain Layout
7647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7650 \begin_layout Plain Layout
7651 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7667 \begin_layout Standard
7668 In the last example it doesn't matter if
7680 is inserted at first.
7683 \begin_layout Standard
7684 \begin_inset VSpace bigskip
7687 When brackets are needed that overlap each other, multiline formulas, as
7689 \begin_inset CommandInset ref
7691 reference "sec:Multiline-Formulas"
7696 \begin_inset Formula \begin{eqnarray*}
7697 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7698 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7702 In the first row the formula is inserted together with the first brace.
7703 It is hereby important that the space command
7707 \begin_layout Plain Layout
7708 Space commands are explained in
7709 \begin_inset CommandInset ref
7711 reference "sub:Predefined-Space"
7726 is inserted before the first
7727 \begin_inset Formula $d$
7730 , because the brace that ends behind the
7731 \begin_inset Formula $q$
7734 prevents that the following
7735 \begin_inset Quotes eld
7739 \begin_inset Quotes erd
7742 is surrounded by space.
7746 \begin_layout Plain Layout
7747 because a bracket is not handled as character, see
7748 \begin_inset CommandInset ref
7750 reference "sub:Binary-Operators"
7759 In the second row the second brace is inserted.
7760 As it should begin before the
7761 \begin_inset Formula $b$
7776 \begin_layout Plain Layout
7784 \begin_inset CommandInset ref
7786 reference "sub:Placeholders"
7795 This space is needed because the
7796 \begin_inset Quotes eld
7800 \begin_inset Quotes erd
7803 is also surrounded by space in the formula.
7804 The brace is placed under the command
7813 \begin_layout Standard
7814 It gets more complicated when brackets overlap each other, like in the following
7819 \begin_layout Plain Layout
7831 \begin_inset Formula \begin{eqnarray*}
7832 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7833 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7841 \begin_layout Plain Layout
7852 The first formula row is the same as the second row of the previous example,
7853 with the difference that the brace is above.
7854 The second row contains the formula together with the second brace.
7855 To avoid that there is space between the upper brace in the first row and
7856 the formula, the row spacing need to be reduced.
7857 This is not easily possible due to a bug in LyX
7861 \begin_layout Plain Layout
7862 \begin_inset CommandInset href
7864 name "LyX-bug #1505"
7865 target "http://www.lyx.org/trac/ticket/1505"
7875 As solution for the problem, the global formula row separation
7885 \begin_layout Plain Layout
7893 must be changed to -6
7894 \begin_inset space \thinspace{}
7897 pt before the formula with the command
7912 is set back after the formula to the standard value of 3
7913 \begin_inset space \thinspace{}
7916 pt using the same command.
7917 More about the row separation in formulas is explained in
7918 \begin_inset CommandInset ref
7920 reference "sub:Line-Separation"
7927 \begin_layout Section
7932 \begin_layout Plain Layout
7941 \begin_layout Standard
7942 Arrows can be inserted via the math toolbar button
7943 \begin_inset Graphics
7944 filename ../images/math/leftarrow.png
7949 or the commands listed in the following subsections.
7952 \begin_layout Standard
7953 \begin_inset Newpage newpage
7959 \begin_layout Subsection
7964 \begin_layout Plain Layout
7973 \begin_layout Standard
7974 \begin_inset space \hfill{}
7978 \begin_inset Tabular
7979 <lyxtabular version="3" rows="8" columns="2">
7981 <column alignment="center" valignment="top" width="0pt">
7982 <column alignment="center" valignment="top" width="0pt">
7984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7987 \begin_layout Plain Layout
7993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7996 \begin_layout Plain Layout
8004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8007 \begin_layout Plain Layout
8015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8018 \begin_layout Plain Layout
8019 \begin_inset Formula $\gets$
8029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8032 \begin_layout Plain Layout
8040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8043 \begin_layout Plain Layout
8044 \begin_inset Formula $\Leftarrow$
8054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8057 \begin_layout Plain Layout
8065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8068 \begin_layout Plain Layout
8069 \begin_inset Formula $\longleftarrow$
8079 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8082 \begin_layout Plain Layout
8090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8093 \begin_layout Plain Layout
8094 \begin_inset Formula $\Longleftarrow$
8104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8107 \begin_layout Plain Layout
8115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8118 \begin_layout Plain Layout
8119 \begin_inset Formula $\leftharpoonup$
8129 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8132 \begin_layout Plain Layout
8140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8143 \begin_layout Plain Layout
8144 \begin_inset Formula $\leftharpoondown$
8154 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8157 \begin_layout Plain Layout
8165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8168 \begin_layout Plain Layout
8169 \begin_inset Formula $\hookleftarrow$
8183 \begin_inset space \hfill{}
8187 \begin_inset Tabular
8188 <lyxtabular version="3" rows="8" columns="2">
8190 <column alignment="center" valignment="top" width="0pt">
8191 <column alignment="center" valignment="top" width="0pt">
8193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8196 \begin_layout Plain Layout
8202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8205 \begin_layout Plain Layout
8213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8216 \begin_layout Plain Layout
8224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8227 \begin_layout Plain Layout
8228 \begin_inset Formula $\to$
8238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8241 \begin_layout Plain Layout
8249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8252 \begin_layout Plain Layout
8253 \begin_inset Formula $\Rightarrow$
8263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8266 \begin_layout Plain Layout
8274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8277 \begin_layout Plain Layout
8278 \begin_inset Formula $\longrightarrow$
8288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8291 \begin_layout Plain Layout
8299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8302 \begin_layout Plain Layout
8303 \begin_inset Formula $\Longrightarrow$
8313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8316 \begin_layout Plain Layout
8324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8327 \begin_layout Plain Layout
8328 \begin_inset Formula $\rightharpoonup$
8338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8341 \begin_layout Plain Layout
8349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8352 \begin_layout Plain Layout
8353 \begin_inset Formula $\rightharpoondown$
8363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8366 \begin_layout Plain Layout
8374 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8377 \begin_layout Plain Layout
8378 \begin_inset Formula $\hookrightarrow$
8392 \begin_inset space \hfill{}
8398 \begin_layout Standard
8399 \begin_inset space \hfill{}
8403 \begin_inset Tabular
8404 <lyxtabular version="3" rows="6" columns="2">
8406 <column alignment="center" valignment="top" width="0pt">
8407 <column alignment="center" valignment="top" width="0pt">
8409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8412 \begin_layout Plain Layout
8418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8421 \begin_layout Plain Layout
8429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8432 \begin_layout Plain Layout
8440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8443 \begin_layout Plain Layout
8444 \begin_inset Formula $\leftrightarrow$
8454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8457 \begin_layout Plain Layout
8465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8468 \begin_layout Plain Layout
8469 \begin_inset Formula $\Leftrightarrow$
8479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8482 \begin_layout Plain Layout
8490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8493 \begin_layout Plain Layout
8494 \begin_inset Formula $\longleftrightarrow$
8504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8507 \begin_layout Plain Layout
8515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8518 \begin_layout Plain Layout
8519 \begin_inset Formula $\Longleftrightarrow$
8529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8532 \begin_layout Plain Layout
8540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8543 \begin_layout Plain Layout
8544 \begin_inset Formula $\rightleftharpoons$
8558 \begin_inset space \hspace{}
8563 \begin_inset space \hfill{}
8567 \begin_inset Tabular
8568 <lyxtabular version="3" rows="5" columns="2">
8570 <column alignment="center" valignment="top" width="0pt">
8571 <column alignment="center" valignment="top" width="0pt">
8573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8576 \begin_layout Plain Layout
8582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8585 \begin_layout Plain Layout
8593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8596 \begin_layout Plain Layout
8604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8607 \begin_layout Plain Layout
8608 \begin_inset Formula $\mapsto$
8618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8621 \begin_layout Plain Layout
8629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8632 \begin_layout Plain Layout
8633 \begin_inset Formula $\longmapsto$
8643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8646 \begin_layout Plain Layout
8654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8657 \begin_layout Plain Layout
8658 \begin_inset Formula $\leadsto$
8668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8671 \begin_layout Plain Layout
8679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8682 \begin_layout Plain Layout
8683 \begin_inset Formula $\dasharrow$
8697 \begin_inset space \hfill{}
8703 \begin_layout Standard
8704 \begin_inset VSpace medskip
8707 Arrows used as accent like e.
8708 \begin_inset space \thinspace{}
8712 \begin_inset space \space{}
8715 vector arrows are listed in
8716 \begin_inset CommandInset ref
8718 reference "sec:Accents"
8725 \begin_layout Standard
8726 \begin_inset VSpace bigskip
8729 Furthermore there are the labeled arrows
8733 \begin_layout Plain Layout
8749 \begin_layout Plain Layout
8767 \begin_layout Plain Layout
8774 \begin_layout Plain Layout
8789 When inserting one of these commands in a formula, an arrow with two blue
8790 boxes appear where the label can be inserted.
8791 The length of the arrow adapts to the label width.
8794 \begin_layout Standard
8796 \begin_inset Tabular
8797 <lyxtabular version="3" rows="3" columns="2">
8799 <column alignment="center" valignment="top" width="0pt">
8800 <column alignment="center" valignment="top" width="0pt">
8802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8805 \begin_layout Plain Layout
8811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8814 \begin_layout Plain Layout
8816 \begin_inset Note Note
8819 \begin_layout Plain Layout
8826 is only used as spacer.
8838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8841 \begin_layout Plain Layout
8848 \begin_layout Plain Layout
8858 \begin_inset Formula $\downarrow$
8862 \begin_inset Formula $\to$
8870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8873 \begin_layout Plain Layout
8874 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8887 \begin_layout Plain Layout
8894 \begin_layout Plain Layout
8904 \begin_inset Formula $\downarrow$
8908 \begin_inset Formula $\to$
8916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8919 \begin_layout Plain Layout
8920 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8936 \begin_layout Subsection
8937 Vertical and diagonal Arrows
8941 \begin_layout Plain Layout
8951 \begin_layout Plain Layout
8960 \begin_layout Standard
8961 \begin_inset space \hfill{}
8965 \begin_inset Tabular
8966 <lyxtabular version="3" rows="7" columns="2">
8968 <column alignment="center" valignment="top" width="0pt">
8969 <column alignment="center" valignment="top" width="0pt">
8971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8974 \begin_layout Plain Layout
8980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8983 \begin_layout Plain Layout
8991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8994 \begin_layout Plain Layout
9002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9005 \begin_layout Plain Layout
9006 \begin_inset Formula $\uparrow$
9016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9019 \begin_layout Plain Layout
9027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9030 \begin_layout Plain Layout
9031 \begin_inset Formula $\Uparrow$
9041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9044 \begin_layout Plain Layout
9052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9055 \begin_layout Plain Layout
9056 \begin_inset Formula $\updownarrow$
9066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9069 \begin_layout Plain Layout
9077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9080 \begin_layout Plain Layout
9081 \begin_inset Formula $\Updownarrow$
9091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9094 \begin_layout Plain Layout
9102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9105 \begin_layout Plain Layout
9106 \begin_inset Formula $\Downarrow$
9116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9119 \begin_layout Plain Layout
9127 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9130 \begin_layout Plain Layout
9131 \begin_inset Formula $\downarrow$
9145 \begin_inset space \hfill{}
9149 \begin_inset Tabular
9150 <lyxtabular version="3" rows="5" columns="2">
9152 <column alignment="center" valignment="top" width="0pt">
9153 <column alignment="center" valignment="top" width="0pt">
9155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9158 \begin_layout Plain Layout
9164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9167 \begin_layout Plain Layout
9175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9178 \begin_layout Plain Layout
9186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9189 \begin_layout Plain Layout
9190 \begin_inset Formula $\nearrow$
9200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9203 \begin_layout Plain Layout
9211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9214 \begin_layout Plain Layout
9215 \begin_inset Formula $\searrow$
9225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9228 \begin_layout Plain Layout
9236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9239 \begin_layout Plain Layout
9240 \begin_inset Formula $\swarrow$
9250 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9253 \begin_layout Plain Layout
9261 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9264 \begin_layout Plain Layout
9265 \begin_inset Formula $\nwarrow$
9279 \begin_inset space \hfill{}
9285 \begin_layout Standard
9286 \begin_inset VSpace medskip
9289 Vertical arrows can be used also as delimiter together with the commands
9291 \begin_inset CommandInset ref
9293 reference "sub:Manual-Bracket-Size"
9298 \begin_inset CommandInset ref
9300 reference "sub:Automatic-Bracket-Size"
9307 \begin_layout Standard
9308 \begin_inset Newpage newpage
9314 \begin_layout Section
9316 \begin_inset CommandInset label
9326 \begin_layout Plain Layout
9335 \begin_layout Standard
9336 Accents can be inserted via the math toolbar button
9337 \begin_inset Graphics
9338 filename ../images/math/hat.png
9343 or the commands listed in the following subsections.
9346 \begin_layout Subsection
9347 Accents for one Character
9351 \begin_layout Plain Layout
9364 \begin_layout Plain Layout
9366 \begin_inset CommandInset ref
9368 reference "sub:Accents-in-Text"
9381 \begin_layout Plain Layout
9389 \begin_inset Note Note
9392 \begin_layout Plain Layout
9395 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9398 \begin_layout Plain Layout
9401 texorpdfstring is in section
9402 \begin_inset CommandInset ref
9404 reference "sub:Formulas-in-Section"
9414 \begin_inset CommandInset label
9416 name "sub:Accents-for-one"
9424 \begin_layout Plain Layout
9425 Accents ! for one character
9433 \begin_layout Standard
9434 \begin_inset space \hfill{}
9438 \begin_inset Tabular
9439 <lyxtabular version="3" rows="8" columns="2">
9441 <column alignment="center" valignment="top" width="0pt">
9442 <column alignment="center" valignment="top" width="0pt">
9444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9447 \begin_layout Plain Layout
9453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9456 \begin_layout Plain Layout
9458 \begin_inset Note Note
9461 \begin_layout Plain Layout
9468 is only used as spacer.
9480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9483 \begin_layout Plain Layout
9490 \begin_layout Plain Layout
9504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9507 \begin_layout Plain Layout
9508 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9521 \begin_layout Plain Layout
9528 \begin_layout Plain Layout
9542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9545 \begin_layout Plain Layout
9546 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9556 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9559 \begin_layout Plain Layout
9566 \begin_layout Plain Layout
9580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9583 \begin_layout Plain Layout
9584 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9597 \begin_layout Plain Layout
9605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9608 \begin_layout Plain Layout
9609 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9619 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9622 \begin_layout Plain Layout
9629 \begin_layout Plain Layout
9642 \begin_layout Plain Layout
9653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9656 \begin_layout Plain Layout
9657 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9667 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9670 \begin_layout Plain Layout
9677 \begin_layout Plain Layout
9691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9694 \begin_layout Plain Layout
9695 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9708 \begin_layout Plain Layout
9715 \begin_layout Plain Layout
9729 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9732 \begin_layout Plain Layout
9733 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9747 \begin_inset space \hfill{}
9751 \begin_inset Tabular
9752 <lyxtabular version="3" rows="7" columns="2">
9754 <column alignment="center" valignment="top" width="0pt">
9755 <column alignment="center" valignment="top" width="0pt">
9757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9760 \begin_layout Plain Layout
9766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9769 \begin_layout Plain Layout
9777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9780 \begin_layout Plain Layout
9787 \begin_layout Plain Layout
9801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9804 \begin_layout Plain Layout
9805 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9818 \begin_layout Plain Layout
9825 \begin_layout Plain Layout
9839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9842 \begin_layout Plain Layout
9843 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9853 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9856 \begin_layout Plain Layout
9863 \begin_layout Plain Layout
9877 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9880 \begin_layout Plain Layout
9881 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9891 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9894 \begin_layout Plain Layout
9901 \begin_layout Plain Layout
9915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9918 \begin_layout Plain Layout
9919 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9929 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9932 \begin_layout Plain Layout
9939 \begin_layout Plain Layout
9953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9956 \begin_layout Plain Layout
9957 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9967 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9970 \begin_layout Plain Layout
9977 \begin_layout Plain Layout
9991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9994 \begin_layout Plain Layout
9995 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10009 \begin_inset space \hfill{}
10015 \begin_layout Standard
10016 \begin_inset VSpace bigskip
10022 \begin_layout Standard
10023 You can directly insert accents like é to formulas.
10024 LyX will transform them to the corresponding accent command.
10029 \begin_layout Plain Layout
10035 it is better to insert a quotation mark before the vowel.
10036 These two characters are then treated by LaTeX as
10040 character when the formula part with the umlaut is marked as German.
10048 \begin_inset Quotes eld
10052 \begin_inset Quotes erd
10055 umlauts are created as demonstrated in the following example:
10058 \begin_layout Standard
10059 \begin_inset VSpace -2mm
10065 \begin_layout Standard
10067 \begin_inset Tabular
10068 <lyxtabular version="3" rows="3" columns="2">
10070 <column alignment="center" valignment="top" width="0">
10071 <column alignment="center" valignment="top" width="0">
10073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10076 \begin_layout Plain Layout
10082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10085 \begin_layout Plain Layout
10087 \begin_inset Note Note
10090 \begin_layout Plain Layout
10098 \begin_inset space \thinspace{}
10101 pt space are only used as spacer.
10113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10116 \begin_layout Plain Layout
10119 \begin_inset Quotes grd
10127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10130 \begin_layout Plain Layout
10131 \begin_inset space \hspace{}
10138 \begin_inset Formula $"i$
10148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10151 \begin_layout Plain Layout
10158 \begin_layout Plain Layout
10172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10175 \begin_layout Plain Layout
10176 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10192 \begin_layout Standard
10193 Another advantage to
10199 is that umlauts can directly be converted to mathematical text because
10200 the accent commands above are
10206 in mathematical text
10209 To convert an accented character to mathematical text, only the character
10210 under the accent may be converted.
10211 This applies also for all other conversions, e.
10212 \begin_inset space \thinspace{}
10216 \begin_inset space \space{}
10222 \begin_layout Standard
10223 In mathematical text, umlauts and other accented characters can directly
10227 \begin_layout Subsection
10228 Accents for Operators
10232 \begin_layout Plain Layout
10233 Accents ! for operators
10241 \begin_layout Standard
10252 \begin_layout Plain Layout
10270 \begin_layout Plain Layout
10278 characters can be placed above or below an operator, respectively, to accent
10290 \begin_layout Plain Layout
10298 characters can be set before and behind an operator.
10299 The command scheme is:
10302 \begin_layout Standard
10318 \begin_layout Standard
10325 must always be before the operator that should be accented.
10326 You can accent with several characters and even with other operators and
10334 for example only characters behind an operator, write nothing between the
10335 first braces but don't omit the braces.
10338 \begin_layout Standard
10339 For example the command
10344 \begin_inset Formula $\to$
10354 \begin_inset Formula $\to$
10363 \begin_layout Plain Layout
10379 \begin_inset Formula \[
10380 \sideset{}{'}\sum_{k=1}^{n}\]
10387 \begin_layout Standard
10396 \begin_layout Plain Layout
10411 \begin_layout Plain Layout
10423 \begin_inset Formula $\uparrow$
10431 \begin_inset Formula \[
10432 \overset{a}{\maltese}\]
10436 As seen in the last example, with
10448 also symbols and characters can be accented; with
10454 this is not possible.
10457 \begin_layout Subsection
10458 Accents for several Characters
10462 \begin_layout Plain Layout
10463 Accents ! for several characters
10471 \begin_layout Standard
10472 \begin_inset space \hfill{}
10476 \begin_inset Tabular
10477 <lyxtabular version="3" rows="5" columns="2">
10479 <column alignment="center" valignment="top" width="0pt">
10480 <column alignment="center" valignment="top" width="0pt">
10482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10485 \begin_layout Plain Layout
10491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10494 \begin_layout Plain Layout
10496 \begin_inset Note Note
10499 \begin_layout Plain Layout
10506 is only used as spacer.
10518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10521 \begin_layout Plain Layout
10528 \begin_layout Plain Layout
10542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10545 \begin_layout Plain Layout
10546 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10556 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10559 \begin_layout Plain Layout
10566 \begin_layout Plain Layout
10580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10583 \begin_layout Plain Layout
10584 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10597 \begin_layout Plain Layout
10604 \begin_layout Plain Layout
10618 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10621 \begin_layout Plain Layout
10622 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10632 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10635 \begin_layout Plain Layout
10638 underleftrightarrow
10642 \begin_layout Plain Layout
10656 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10659 \begin_layout Plain Layout
10660 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10674 \begin_inset space \hfill{}
10678 \begin_inset Tabular
10679 <lyxtabular version="3" rows="5" columns="2">
10681 <column alignment="center" valignment="top" width="0pt">
10682 <column alignment="center" valignment="top" width="0pt">
10684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10687 \begin_layout Plain Layout
10693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10696 \begin_layout Plain Layout
10704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10707 \begin_layout Plain Layout
10714 \begin_layout Plain Layout
10728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10731 \begin_layout Plain Layout
10732 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10745 \begin_layout Plain Layout
10752 \begin_layout Plain Layout
10766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10769 \begin_layout Plain Layout
10770 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10780 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10783 \begin_layout Plain Layout
10790 \begin_layout Plain Layout
10804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10807 \begin_layout Plain Layout
10808 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10818 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10821 \begin_layout Plain Layout
10828 \begin_layout Plain Layout
10842 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10845 \begin_layout Plain Layout
10846 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10860 \begin_inset space \hfill{}
10866 \begin_layout Standard
10867 \begin_inset VSpace medskip
10870 With these commands as many characters as you like can be accented.
10883 will only be set in the output with a length of three characters, as shown
10884 in the following example:
10885 \begin_inset Formula \[
10886 \widetilde{A+B=C-D}\]
10893 \begin_layout Standard
10904 \begin_layout Plain Layout
10922 \begin_layout Plain Layout
10930 described in the previous subsection it is also possible to accent several
10940 \begin_layout Plain Layout
10950 \begin_inset Formula $\downarrow$
10956 \begin_inset Formula \[
10957 \underset{***}{A=B}\]
10964 \begin_layout Section
10966 \begin_inset CommandInset label
10976 \begin_layout Plain Layout
10985 \begin_layout Subsection
10987 \begin_inset CommandInset label
10989 name "sub:Predefined-Space"
10997 \begin_layout Plain Layout
10998 Space ! horizontal ! predefined
11006 \begin_layout Standard
11007 Sometimes it is necessary to insert horizontal space to a formula.
11008 This is done by inserting a protected space (shortcut
11011 arg "space-insert protected"
11016 \begin_inset Quotes eld
11025 \begin_layout Plain Layout
11037 \begin_inset Quotes erd
11040 appears and by pressing
11044 several times one can select one of eight different space sizes.
11045 The spaces can also be inserted using the math toolbar button
11046 \begin_inset Graphics
11047 filename ../images/math/space.png
11052 or special commands.
11053 Independent from the inserted command, one can select the size again by
11061 \begin_layout Standard
11064 \begin_inset VSpace -5mm
11068 \begin_inset Tabular
11069 <lyxtabular version="3" rows="3" columns="7">
11071 <column alignment="center" valignment="middle" width="6.8cm">
11072 <column alignment="center" valignment="top" width="0">
11073 <column alignment="center" valignment="top" width="0">
11074 <column alignment="center" valignment="top" width="0">
11075 <column alignment="center" valignment="top" width="0">
11076 <column alignment="center" valignment="top" width="0">
11077 <column alignment="center" valignment="top" width="0">
11079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11082 \begin_layout Plain Layout
11088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11091 \begin_layout Plain Layout
11099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11102 \begin_layout Plain Layout
11110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11113 \begin_layout Plain Layout
11121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11124 \begin_layout Plain Layout
11132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11135 \begin_layout Plain Layout
11143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11146 \begin_layout Plain Layout
11156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11159 \begin_layout Plain Layout
11164 keystrokes after inserting the protected space
11169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11172 \begin_layout Plain Layout
11178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11181 \begin_layout Plain Layout
11187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11190 \begin_layout Plain Layout
11196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11199 \begin_layout Plain Layout
11205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11208 \begin_layout Plain Layout
11214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11217 \begin_layout Plain Layout
11225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11228 \begin_layout Plain Layout
11234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11237 \begin_layout Plain Layout
11238 \begin_inset Formula $A\, B$
11246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11249 \begin_layout Plain Layout
11250 \begin_inset Formula $A\: B$
11258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11261 \begin_layout Plain Layout
11262 \begin_inset Formula $A\; B$
11270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11273 \begin_layout Plain Layout
11274 \begin_inset Formula $A\quad B$
11282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11285 \begin_layout Plain Layout
11286 \begin_inset Formula $A\qquad B$
11294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11297 \begin_layout Plain Layout
11298 \begin_inset Formula $A\! B$
11314 \begin_layout Standard
11315 The last size seem to produce no space.
11316 It is displayed red in LyX contrary to the other sizes, because it is a
11318 There are two more negative spaces:
11321 \begin_layout Standard
11323 \begin_inset Tabular
11324 <lyxtabular version="3" rows="3" columns="3">
11326 <column alignment="center" valignment="middle" width="6.8cm">
11327 <column alignment="center" valignment="top" width="0pt">
11328 <column alignment="center" valignment="top" width="0pt">
11330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11333 \begin_layout Plain Layout
11339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11342 \begin_layout Plain Layout
11350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11353 \begin_layout Plain Layout
11363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11366 \begin_layout Plain Layout
11371 keystrokes after inserting the protected space
11376 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11379 \begin_layout Plain Layout
11385 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11388 \begin_layout Plain Layout
11396 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11399 \begin_layout Plain Layout
11405 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11408 \begin_layout Plain Layout
11409 \begin_inset Formula $A\negmedspace B$
11417 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11420 \begin_layout Plain Layout
11421 \begin_inset Formula $A\negthickspace B$
11437 \begin_layout Standard
11438 Negative spaces can lead to characters overlapping each other.
11439 Thus they can be used to enforce ligatures, what is e.
11440 \begin_inset space \thinspace{}
11444 \begin_inset space \space{}
11447 useful for summation operators:
11450 \begin_layout Standard
11452 \begin_inset Tabular
11453 <lyxtabular version="3" rows="3" columns="2">
11455 <column alignment="center" valignment="top" width="0">
11456 <column alignment="center" valignment="top" width="0">
11458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11461 \begin_layout Plain Layout
11467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11470 \begin_layout Plain Layout
11472 \begin_inset Note Note
11475 \begin_layout Plain Layout
11482 is only used as spacer.
11494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11497 \begin_layout Plain Layout
11506 \begin_layout Plain Layout
11520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11523 \begin_layout Plain Layout
11524 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11537 \begin_layout Plain Layout
11548 \begin_layout Plain Layout
11562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11565 \begin_layout Plain Layout
11566 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11582 \begin_layout Standard
11583 Relations like for example equal signs, are always surrounded by space.
11584 To suppress this, the equal sign is placed into a TeX-brace.
11585 The following example demonstrates this:
11588 \begin_layout Standard
11590 \begin_inset Tabular
11591 <lyxtabular version="3" rows="2" columns="2">
11593 <column alignment="center" valignment="top" width="0pt">
11594 <column alignment="center" valignment="top" width="0pt">
11596 <cell alignment="center" valignment="top" usebox="none">
11599 \begin_layout Plain Layout
11605 <cell alignment="center" valignment="top" usebox="none">
11608 \begin_layout Plain Layout
11609 \begin_inset Formula $A=B$
11619 <cell alignment="center" valignment="top" usebox="none">
11622 \begin_layout Plain Layout
11623 \begin_inset Note Note
11626 \begin_layout Plain Layout
11633 is only used as spacer.
11639 \begin_inset Formula $\raisebox{5mm}{}$
11642 equation without space
11647 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11650 \begin_layout Plain Layout
11651 \begin_inset Formula $A{=}B$
11667 \begin_layout Standard
11669 The command for the last formula is:
11674 \begin_inset Formula $\to$
11680 \begin_layout Standard
11681 \begin_inset VSpace bigskip
11684 Spaces are needed for physical units, because the space between the value
11685 and the unit is the smallest one and not a normal space.
11686 For units in text, the smallest space is inserted via the menu
11688 Insert\SpecialChar \menuseparator
11689 Formatting\SpecialChar \menuseparator
11691 \begin_inset space ~
11699 arg "space-insert thin"
11705 \begin_layout Standard
11706 An example to visualize the difference:
11709 \begin_layout Standard
11710 \begin_inset Tabular
11711 <lyxtabular version="3" rows="2" columns="2">
11713 <column alignment="left" valignment="top" width="0">
11714 <column alignment="left" valignment="top" width="0">
11716 <cell alignment="center" valignment="top" usebox="none">
11719 \begin_layout Plain Layout
11721 \begin_inset Formula $\cdot$
11729 <cell alignment="center" valignment="top" usebox="none">
11732 \begin_layout Plain Layout
11733 space between value and unit
11740 <cell alignment="center" valignment="top" usebox="none">
11743 \begin_layout Plain Layout
11745 \begin_inset space \thinspace{}
11749 \begin_inset Formula $\cdot$
11757 <cell alignment="center" valignment="top" usebox="none">
11760 \begin_layout Plain Layout
11761 smallest space between value and unit
11774 \begin_layout Subsection
11779 \begin_layout Plain Layout
11792 \begin_layout Plain Layout
11793 for vertical space in formulas see
11794 \begin_inset CommandInset ref
11796 reference "sub:Line-Separation"
11809 \begin_layout Plain Layout
11817 \begin_inset Note Note
11820 \begin_layout Plain Layout
11823 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11826 \begin_layout Plain Layout
11829 texorpdfstring is in section
11830 \begin_inset CommandInset ref
11832 reference "sub:Formulas-in-Section"
11842 \begin_inset CommandInset label
11844 name "sub:Variable-Space"
11852 \begin_layout Plain Layout
11853 Space ! horizontal ! variable
11861 \begin_layout Standard
11862 Space with a defined length can be inserted with the command
11872 \begin_layout Plain Layout
11882 \begin_inset Quotes eld
11891 \begin_layout Plain Layout
11903 \begin_inset Quotes erd
11907 The length can be specified by left-clicking on the
11908 \begin_inset Quotes eld
11917 \begin_layout Plain Layout
11929 \begin_inset Quotes erd
11933 The length may also be negative.
11934 To insert so many space that the formula uses all available space, the
11945 \begin_layout Plain Layout
11956 \begin_layout Standard
11957 \begin_inset VSpace -1mm
11963 \begin_layout Standard
11965 \begin_inset Tabular
11966 <lyxtabular version="3" rows="4" columns="2">
11968 <column alignment="center" valignment="top" width="0">
11969 <column alignment="center" valignment="top" width="0">
11971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11974 \begin_layout Plain Layout
11982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11985 \begin_layout Plain Layout
11993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11996 \begin_layout Plain Layout
12003 \begin_layout Plain Layout
12013 \begin_inset Formula $\to$
12019 \begin_inset space \thinspace{}
12027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12030 \begin_layout Plain Layout
12031 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12044 \begin_layout Plain Layout
12051 \begin_layout Plain Layout
12061 \begin_inset Formula $\to$
12067 \begin_inset space \thinspace{}
12075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12078 \begin_layout Plain Layout
12079 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12092 \begin_layout Plain Layout
12099 \begin_layout Plain Layout
12113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12116 \begin_layout Plain Layout
12117 \begin_inset Formula $A=A\hfill B=B$
12133 \begin_layout Standard
12134 In the last example the available space is given by the longest column entry
12136 In an inline formula the space depends on the length of the line in which
12144 Thus, when the line uses the full width, no space will be created.
12151 only has an effect on displayed formulas when the formula style
12156 (Formula styles are explained in
12157 \begin_inset CommandInset ref
12159 reference "sec:Formula-Styles"
12166 \begin_layout Standard
12173 , there are the commands
12185 that fill the space with a pattern, see
12186 \begin_inset CommandInset ref
12188 reference "sub:Ellipses"
12195 \begin_layout Standard
12196 For text, variable space can be inserted via the menu
12198 Insert\SpecialChar \menuseparator
12199 Formatting\SpecialChar \menuseparator
12201 \begin_inset space ~
12209 \begin_layout Standard
12210 This is a line with
12211 \begin_inset space \hspace{}
12216 \begin_inset space \thinspace{}
12222 \begin_layout Standard
12223 This is a line with
12224 \begin_inset space \hfill{}
12230 \begin_layout Subsection
12231 Space besides inline Formulas
12235 \begin_layout Plain Layout
12236 Space ! besides inline formulas
12244 \begin_layout Standard
12245 The space that surrounds inline formulas can be adjusted with the length
12254 \begin_layout Plain Layout
12265 The value of a length is set with the command
12273 \begin_layout Plain Layout
12283 that has the following scheme:
12286 \begin_layout Standard
12291 setlength{length name}{value}
12294 \begin_layout Standard
12302 \begin_inset space \thinspace{}
12308 \begin_layout Standard
12318 \begin_layout Standard
12319 is inserted in TeX-mode.
12321 \begin_inset space \thinspace{}
12324 mm space will now be set around all inline formulas:
12328 \begin_layout Plain Layout
12342 \begin_layout Standard
12343 This is a line with an inline formula
12344 \begin_inset Formula $A=B$
12348 \begin_inset space \thinspace{}
12351 mm surrounding space.
12355 \begin_layout Plain Layout
12369 \begin_layout Standard
12370 To return to the predefined value,
12376 is set to the value 0
12377 \begin_inset space \thinspace{}
12383 \begin_layout Section
12388 \begin_layout Plain Layout
12398 \begin_layout Plain Layout
12403 \begin_layout Plain Layout
12414 \begin_layout Plain Layout
12429 \begin_layout Standard
12430 Boxes for text are described in chapter
12437 \begin_inset space ~
12445 \begin_layout Subsection
12447 \begin_inset CommandInset label
12449 name "sub:Boxes-with-Frame"
12457 \begin_layout Plain Layout
12466 \begin_layout Standard
12467 It is possible to frame formulas or parts of it with the commands
12477 \begin_layout Plain Layout
12495 \begin_layout Plain Layout
12506 \begin_layout Standard
12507 When one of these commands is inserted to a formula, a blue box appears
12508 within a frame to enter formula parts.
12515 an additional formula has to be created by
12519 within this box, because the box content will otherwise be treated as mathemati
12527 is used, a new formula is automatically created inside the frame.
12530 \begin_layout Standard
12537 is not suitable to frame displayed formulas because the formula will always
12538 be set in the size of the text.
12545 is in contrary not suitable to frame inline formulas, because the formula
12546 will always be set in the size of a displayed formula.
12549 \begin_layout Standard
12556 there is the command
12566 \begin_layout Plain Layout
12574 where additionally the frame width and the alignment can be specified.
12581 is used in the following scheme:
12584 \begin_layout Standard
12589 framebox[frame width][position]{box content}
12592 \begin_layout Standard
12593 The position can either be
12610 right aligns the formula in the box.
12611 When no position is given, the formula will be centered.
12612 \begin_inset Newline newline
12615 Is no width given, also no position can be given.
12616 In this case the frame width is adjusted to the box content like for
12625 \begin_layout Standard
12632 is inserted, a box appears containing three blue boxes.
12633 The first two boxes are surrounded by brackets and denote the two optional
12635 The third box is for formula parts like for
12644 \begin_layout Standard
12646 \begin_inset Tabular
12647 <lyxtabular version="3" rows="5" columns="2">
12649 <column alignment="center" valignment="top" width="0">
12650 <column alignment="center" valignment="top" width="0">
12652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12655 \begin_layout Plain Layout
12661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12664 \begin_layout Plain Layout
12666 \begin_inset Note Note
12669 \begin_layout Plain Layout
12676 is only used as spacer.
12688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12691 \begin_layout Plain Layout
12698 \begin_layout Plain Layout
12717 \begin_layout Plain Layout
12731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12734 \begin_layout Plain Layout
12735 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12748 \begin_layout Plain Layout
12755 \begin_layout Plain Layout
12770 \begin_layout Plain Layout
12784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12787 \begin_layout Plain Layout
12788 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12801 \begin_layout Plain Layout
12808 \begin_layout Plain Layout
12822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12825 \begin_layout Plain Layout
12826 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12839 \begin_layout Plain Layout
12846 \begin_layout Plain Layout
12856 \begin_inset Formula $\to$
12860 \begin_inset Formula $\to$
12873 \begin_layout Plain Layout
12883 \begin_inset Formula $\downarrow$
12891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12894 \begin_layout Plain Layout
12895 \begin_inset Formula $\raisebox{6mm}{}$
12899 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12903 \begin_inset Formula $\raisebox{-4mm}{}$
12919 \begin_layout Standard
12920 The frame thickness can also be adjusted.
12921 To do this the following commands have to be inserted in TeX-mode before
12925 \begin_layout Standard
12935 \begin_inset Quotes eld
12939 \begin_inset Quotes erd
12953 \begin_inset Quotes eld
12957 \begin_inset Quotes erd
12963 \begin_layout Standard
12964 \begin_inset Quotes eld
12968 \begin_inset Quotes erd
12971 specifies the minimal distance between the frame and the first character
12973 An example for this is the following framed formula:
12977 \begin_layout Plain Layout
12989 \begin_inset Formula \[
12994 Before this formula the commands
12997 \begin_layout Standard
13019 \begin_layout Standard
13020 were inserted in TeX-mode.
13021 The given values are used for all following boxes.
13024 \begin_layout Standard
13025 To return to the standard frame size, the command
13028 \begin_layout Standard
13053 \begin_layout Plain Layout
13067 \begin_layout Standard
13068 is inserted in TeX-mode before the next formula.
13071 \begin_layout Subsection
13072 Boxes without Frame
13073 \begin_inset CommandInset label
13075 name "sub:Boxes-without-Frame"
13083 \begin_layout Plain Layout
13084 Boxes ! without frame
13092 \begin_layout Standard
13093 For boxes without a frame there are the following box commands:
13103 \begin_layout Plain Layout
13121 \begin_layout Plain Layout
13139 \begin_layout Plain Layout
13150 \begin_layout Standard
13157 a box can be super- or subscripted.
13158 But in contrary to normal super- and subscripting, the characters in the
13159 box keep their font size.
13166 is used in the following scheme:
13169 \begin_layout Standard
13174 raisebox{height}{box content}
13177 \begin_layout Standard
13178 When the box should contain a formula, an extra formula is needed like for
13189 \begin_inset Note Greyedout
13192 \begin_layout Plain Layout
13203 this extra formula is created by pressing
13207 twice instead of once because LyX doesn't yet support
13221 \begin_layout Standard
13223 \begin_inset Tabular
13224 <lyxtabular version="3" rows="4" columns="2">
13226 <column alignment="center" valignment="top" width="0">
13227 <column alignment="center" valignment="top" width="0">
13229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13232 \begin_layout Plain Layout
13238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13241 \begin_layout Plain Layout
13249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13252 \begin_layout Plain Layout
13256 \begin_inset Formula $\to$
13262 \begin_inset Formula $\to$
13270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13273 \begin_layout Plain Layout
13274 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13287 \begin_layout Plain Layout
13291 \begin_inset Formula $\to$
13297 \begin_inset Formula $\to$
13305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13308 \begin_layout Plain Layout
13309 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13322 \begin_layout Plain Layout
13326 \begin_inset Formula $\to$
13345 \begin_layout Plain Layout
13359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13362 \begin_layout Plain Layout
13363 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13379 \begin_layout Standard
13404 , with the difference that there is no frame.
13407 \begin_layout Subsection
13409 \begin_inset CommandInset label
13411 name "sub:Colored-Boxes"
13419 \begin_layout Plain Layout
13428 \begin_layout Standard
13429 To be able to use all commands explained in this section, the LaTeX-package
13438 \begin_layout Plain Layout
13443 is part of every LaTeX standard installation.
13452 \begin_layout Plain Layout
13458 has to be loaded in the LaTeX-preamble with the line
13462 \begin_layout Plain Layout
13463 When text is colored somewhere in the document with a predefined color,
13464 LyX loads the LaTeX-package
13469 Thus it is possible that the package is loaded twice, but this doesn't
13476 \begin_inset Note Note
13479 \begin_layout Plain Layout
13480 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13489 \begin_layout Standard
13497 \begin_layout Standard
13498 \begin_inset VSpace medskip
13501 To color boxes, the command
13511 \begin_layout Plain Layout
13519 is used in the following scheme:
13522 \begin_layout Standard
13527 colorbox{color}{box content}
13530 \begin_layout Standard
13531 The box content can also be a box and a
13537 can also be part of another box (see the 2nd and 3rd example).
13538 When the box should contain a formula, an extra formula has to be created,
13539 the same way as for
13549 \begin_layout Plain Layout
13550 This also applies for the command
13564 \begin_layout Standard
13565 One of the following predefined colors can be chosen:
13568 \begin_layout Standard
13602 \begin_layout Standard
13604 \begin_inset Tabular
13605 <lyxtabular version="3" rows="4" columns="2">
13607 <column alignment="center" valignment="top" width="0">
13608 <column alignment="center" valignment="top" width="0">
13610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13613 \begin_layout Plain Layout
13619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13622 \begin_layout Plain Layout
13624 \begin_inset Note Note
13627 \begin_layout Plain Layout
13634 is only used as spacer.
13646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13649 \begin_layout Plain Layout
13653 \begin_inset Formula $\to$
13663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13666 \begin_layout Plain Layout
13667 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13680 \begin_layout Plain Layout
13684 \begin_inset Formula $\to$
13695 \begin_layout Plain Layout
13709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13712 \begin_layout Plain Layout
13713 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13726 \begin_layout Plain Layout
13733 \begin_layout Plain Layout
13745 \begin_inset Formula $\to$
13764 \begin_layout Plain Layout
13778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13781 \begin_layout Plain Layout
13782 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13798 \begin_layout Standard
13805 only colors the box but not the characters in the box.
13806 To color all characters, the whole formula is highlighted and the wanted
13807 color is chosen in the
13810 \begin_inset space ~
13816 The dialog can be called with the toolbar button
13817 \begin_inset Graphics
13818 filename ../images/dialog-show_character.png
13825 Edit\SpecialChar \menuseparator
13827 \begin_inset space ~
13830 Style\SpecialChar \menuseparator
13834 The formula number has then the same color as the formula.
13835 When the formula number should get another color than the formula characters,
13836 the color must be changed within the formula.
13839 \begin_layout Standard
13843 \begin_layout Standard
13846 \begin_inset Formula \begin{equation}
13847 \int A=B\label{eq:red}\end{equation}
13854 \begin_inset Formula \begin{equation}
13855 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13862 \begin_layout Standard
13864 \begin_inset CommandInset ref
13870 is completely colored red.
13871 \begin_inset Newline newline
13875 \begin_inset CommandInset ref
13877 reference "eq:redgreen"
13881 was first completely colored green to set the color for the formula number.
13882 Subsequently the formula characters were colored red.
13885 \begin_layout Standard
13886 \begin_inset VSpace bigskip
13889 To color the frame different than the rest of the box, the command
13899 \begin_layout Plain Layout
13907 is used in the following scheme:
13910 \begin_layout Standard
13915 fcolorbox{frame color}{color}{box content}
13918 \begin_layout Standard
13925 is an extension of the command
13932 The frame width is set, like for
13955 \begin_layout Plain Layout
13967 \begin_inset Formula \[
13968 \fcolorbox{cyan}{magenta}{A=B}\]
13976 \begin_layout Plain Layout
13990 \begin_layout Standard
13991 This formula was created with the command
13992 \begin_inset Newline newline
14000 \begin_inset Formula $\to$
14006 \begin_inset Formula $\to$
14016 \begin_layout Standard
14017 \begin_inset VSpace bigskip
14020 To use other colors than the predefined ones, they have to be defined first.
14023 \begin_layout Standard
14024 One can for example define the color
14025 \begin_inset Quotes eld
14033 \begin_inset Quotes erd
14036 with the LaTeX-preamble line:
14039 \begin_layout Standard
14044 definecolor{darkgreen}{cmyk}{0.5,
14062 \begin_layout Plain Layout
14073 \begin_layout Standard
14078 is the color space that denotes the colors
14095 The four comma separated numbers are the portion factor for the corresponding
14096 colors of the color space.
14097 The factors can be in the range of 0
14098 \begin_inset space \thinspace{}
14102 \begin_inset space \thinspace{}
14110 also the color space
14114 can be used for definitions.
14131 , so that there are in this case three portion factors for the corresponding
14133 Furthermore there is the color space
14137 with one portion factor for the gray value.
14140 \begin_layout Standard
14141 As example a framed box with the new defined color
14145 where the characters have been colored
14150 \begin_inset Formula \begin{equation}
14151 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14158 \begin_layout Standard
14159 Self-defined colors can also be used for text with the help of the command
14170 \begin_layout Plain Layout
14179 \begin_layout Standard
14183 \begin_layout Plain Layout
14187 textcolor{darkgreen}{
14193 \begin_inset Quotes eld
14197 \begin_inset Quotes erd
14204 \begin_layout Plain Layout
14214 \begin_layout Standard
14225 \begin_layout Plain Layout
14233 is used in the scheme
14237 textcolor{color}{characters to color}
14242 \begin_layout Subsection
14244 \begin_inset CommandInset label
14246 name "sub:Paragraph-Boxes"
14254 \begin_layout Plain Layout
14255 Boxes ! as paragraph
14263 \begin_layout Standard
14264 A box that can contain several lines and paragraphs, a so called paragraph
14265 box (parbox), can be created with the menu
14267 Insert\SpecialChar \menuseparator
14270 or the toolbar button
14271 \begin_inset Graphics
14272 filename ../images/box-insert.png
14280 \begin_layout Standard
14281 The following example shows a framed parbox in a line:
14284 \begin_layout Standard
14285 \begin_inset VSpace medskip
14289 \begin_inset Box Boxed
14298 height_special "totalheight"
14301 \begin_layout Plain Layout
14302 This is a paragraph box.
14304 \begin_inset space \thinspace{}
14307 cm long and can also contain formulas:
14308 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14319 \begin_layout Standard
14320 \begin_inset VSpace medskip
14326 \begin_layout Standard
14327 Such a box is created by right-clicking on the gray box inset.
14328 A dialog pops up showing the box properties.
14342 \begin_inset space \thinspace{}
14347 Vertical Box Alignment
14352 \begin_layout Standard
14353 \begin_inset VSpace medskip
14356 In LaTeX a parbox is created with the command
14366 \begin_layout Plain Layout
14374 that has the following scheme:
14377 \begin_layout Standard
14382 parbox[position]{width}{box content}
14385 \begin_layout Standard
14399 for bottom means that the box is aligned within the surrounding text with
14405 for top this is done with the first line.
14406 When no position is given, the box will be vertically centered, see section
14414 \begin_inset space ~
14419 manual for examples.
14422 \begin_layout Standard
14423 \begin_inset VSpace bigskip
14426 To frame formulas completely, including the formula number, the formula
14427 must be set into a parbox.
14428 To do this, the command
14442 is inserted in TeX-mode before the formula.
14451 \begin_layout Plain Layout
14461 is hereby the line width set for the document.
14462 Because the frame is outside the parbox, 2
14463 \begin_inset space \thinspace{}
14466 times the frame separation and the frame thickness must be subtracted from
14468 As this is not automatically done by LyX due to a bug
14472 \begin_layout Plain Layout
14473 \begin_inset CommandInset href
14475 name "LyX-bug #4483"
14476 target "http://www.lyx.org/trac/ticket/4483"
14485 , TeX-mode has to be used.
14486 To be able to multiply and subtract in arguments, the LaTeX-package
14494 \begin_layout Plain Layout
14499 is part of every LaTeX standard installation.
14508 \begin_layout Plain Layout
14514 must be loaded in the LaTeX-preamble with the line
14517 \begin_layout Standard
14525 \begin_layout Standard
14526 Behind the formula both boxes are closed by entering
14531 Here is an example:
14535 \begin_layout Plain Layout
14549 \begin_layout Standard
14553 \begin_layout Plain Layout
14571 \begin_inset Formula \begin{equation}
14572 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14580 \begin_layout Plain Layout
14591 \begin_layout Plain Layout
14605 \begin_layout Standard
14606 \begin_inset VSpace medskip
14609 As a parbox is used as argument of
14615 , there is in this case no difference between
14630 \begin_layout Standard
14631 \begin_inset VSpace bigskip
14634 Paragraph boxes are very useful to comment formulas directly.
14641 is used in combination with the command
14655 \begin_inset CommandInset ref
14657 reference "sub:User-defined-Numbering"
14664 \begin_layout Standard
14665 An example of a formula commented with
14674 \begin_layout Standard
14678 \begin_layout Plain Layout
14691 This is a description.
14692 It is distinctly separated from the formula and multiline.
14696 \begin_layout Plain Layout
14708 \begin_layout Standard
14709 Such a formula must be inserted completely in TeX-mode because LyX does
14710 not yet support the command
14717 The formula is created with the following command sequence:
14720 \begin_layout Standard
14733 is inserted in TeX-mode.
14737 \begin_layout Plain Layout
14738 When the formula style
14750 can also be replaced by
14757 (formula styles see
14758 \begin_inset CommandInset ref
14760 reference "sec:Formula-Styles"
14769 Then the description follows as normal text and finally
14775 is inserted in TeX-mode.
14788 hereby create a displayed formula.
14791 \begin_layout Standard
14798 can be seen in this example that was
14799 \begin_inset Quotes eld
14803 \begin_inset Quotes erd
14806 using the mathematical textmode:
14807 \begin_inset Formula \[
14808 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14815 \begin_layout Section
14820 \begin_layout Plain Layout
14829 \begin_layout Subsection
14831 \begin_inset CommandInset label
14833 name "sub:Big-Operators"
14841 \begin_layout Plain Layout
14851 \begin_layout Plain Layout
14861 \begin_layout Plain Layout
14870 \begin_layout Standard
14871 To be able to use all integral operators listed here, the option
14873 Use esint package automatically
14875 must be set in the document settings under
14878 \begin_inset space ~
14886 \begin_layout Standard
14887 \begin_inset space \hfill{}
14891 \begin_inset Tabular
14892 <lyxtabular version="3" rows="11" columns="2">
14894 <column alignment="center" valignment="top" width="0pt">
14895 <column alignment="center" valignment="top" width="0pt">
14897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14900 \begin_layout Plain Layout
14906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14909 \begin_layout Plain Layout
14917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14920 \begin_layout Plain Layout
14927 \begin_layout Plain Layout
14940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14943 \begin_layout Plain Layout
14944 \begin_inset Formula $\int$
14954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14957 \begin_layout Plain Layout
14965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14968 \begin_layout Plain Layout
14969 \begin_inset Formula $\oint$
14979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14982 \begin_layout Plain Layout
14990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14993 \begin_layout Plain Layout
14994 \begin_inset Formula $\ointctrclockwise$
15004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15007 \begin_layout Plain Layout
15015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15018 \begin_layout Plain Layout
15019 \begin_inset Formula $\ointclockwise$
15029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15032 \begin_layout Plain Layout
15040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15043 \begin_layout Plain Layout
15044 \begin_inset Formula $\sqint$
15054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15057 \begin_layout Plain Layout
15065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15068 \begin_layout Plain Layout
15070 \begin_inset Formula $\fint$
15080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15083 \begin_layout Plain Layout
15091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15094 \begin_layout Plain Layout
15096 \begin_inset Formula $\landupint$
15106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15109 \begin_layout Plain Layout
15117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15120 \begin_layout Plain Layout
15122 \begin_inset Formula $\landdownint$
15132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15135 \begin_layout Plain Layout
15143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15146 \begin_layout Plain Layout
15147 \begin_inset Formula $\bigcap$
15157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15160 \begin_layout Plain Layout
15168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15171 \begin_layout Plain Layout
15172 \begin_inset Formula $\bigcup$
15186 \begin_inset space \hfill{}
15190 \begin_inset Tabular
15191 <lyxtabular version="3" rows="11" columns="2">
15193 <column alignment="center" valignment="top" width="0pt">
15194 <column alignment="center" valignment="top" width="0pt">
15196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15199 \begin_layout Plain Layout
15205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15208 \begin_layout Plain Layout
15216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15219 \begin_layout Plain Layout
15226 \begin_layout Plain Layout
15239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15242 \begin_layout Plain Layout
15243 \begin_inset Formula $\sum$
15253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15256 \begin_layout Plain Layout
15263 \begin_layout Plain Layout
15276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15279 \begin_layout Plain Layout
15280 \begin_inset Formula $\prod$
15290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15293 \begin_layout Plain Layout
15301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15304 \begin_layout Plain Layout
15305 \begin_inset Formula $\coprod$
15315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15318 \begin_layout Plain Layout
15326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15329 \begin_layout Plain Layout
15330 \begin_inset Formula $\bigodot$
15340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15343 \begin_layout Plain Layout
15351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15354 \begin_layout Plain Layout
15355 \begin_inset Formula $\bigotimes$
15365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15368 \begin_layout Plain Layout
15376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15379 \begin_layout Plain Layout
15380 \begin_inset Formula $\bigoplus$
15390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15393 \begin_layout Plain Layout
15401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15404 \begin_layout Plain Layout
15405 \begin_inset Formula $\bigwedge$
15415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15418 \begin_layout Plain Layout
15426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15429 \begin_layout Plain Layout
15430 \begin_inset Formula $\bigvee$
15440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15443 \begin_layout Plain Layout
15451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15454 \begin_layout Plain Layout
15455 \begin_inset Formula $\bigsqcup$
15465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15468 \begin_layout Plain Layout
15476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15479 \begin_layout Plain Layout
15480 \begin_inset Formula $\biguplus$
15494 \begin_inset space \hfill{}
15500 \begin_layout Standard
15501 All big operators can also be inserted via the math toolbar button
15502 \begin_inset Graphics
15503 filename ../images/math/intop.png
15511 \begin_layout Standard
15512 The operators are called big because they are bigger than the sometimes
15513 equal looking binary operators.
15514 All big operators can have limits as described in the next subsection.
15517 \begin_layout Standard
15518 For all integral operators there is a second version available, ending on
15536 These operators are different from
15543 \begin_inset space \space{}
15546 in the style the operator limits are displayed, see
15547 \begin_inset CommandInset ref
15549 reference "sub:Operator-Limits"
15557 \begin_layout Subsubsection*
15558 Advice for Integrals
15561 \begin_layout Standard
15566 in an integral is an operator, that therefore has to be set upright.
15567 This is done by highlighting the
15571 and using the keyboard shortcut
15581 \begin_layout Plain Layout
15587 \begin_inset CommandInset ref
15589 reference "sub:Font-Styles"
15599 Finally the smallest space is inserted before the
15603 , as this is usual for operators.
15607 \begin_layout Standard
15609 \begin_inset Formula $\int A(x)dx$
15613 \begin_inset Newline newline
15620 \begin_layout Plain Layout
15630 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15636 \begin_layout Standard
15637 For multiple integrals there are the following commands:
15638 \begin_inset VSpace medskip
15644 \begin_layout Standard
15645 \begin_inset space \hfill{}
15649 \begin_inset Tabular
15650 <lyxtabular version="3" rows="4" columns="2">
15652 <column alignment="center" valignment="top" width="0">
15653 <column alignment="center" valignment="top" width="0">
15655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15658 \begin_layout Plain Layout
15664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15667 \begin_layout Plain Layout
15669 \begin_inset Note Note
15672 \begin_layout Plain Layout
15679 is only used as spacer.
15691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15694 \begin_layout Plain Layout
15702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15705 \begin_layout Plain Layout
15706 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15719 \begin_layout Plain Layout
15727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15730 \begin_layout Plain Layout
15731 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15744 \begin_layout Plain Layout
15752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15755 \begin_layout Plain Layout
15756 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15770 \begin_inset space \hfill{}
15774 \begin_inset Tabular
15775 <lyxtabular version="3" rows="4" columns="2">
15777 <column alignment="center" valignment="top" width="0">
15778 <column alignment="center" valignment="top" width="0">
15780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15783 \begin_layout Plain Layout
15789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15792 \begin_layout Plain Layout
15800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15803 \begin_layout Plain Layout
15811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15814 \begin_layout Plain Layout
15815 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15828 \begin_layout Plain Layout
15836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15839 \begin_layout Plain Layout
15840 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15853 \begin_layout Plain Layout
15861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15864 \begin_layout Plain Layout
15865 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15879 \begin_inset space \hfill{}
15885 \begin_layout Subsection
15887 \begin_inset CommandInset label
15889 name "sub:Operator-Limits"
15897 \begin_layout Plain Layout
15906 \begin_layout Standard
15907 Limits are created by super- and subscripts:
15910 \begin_layout Standard
15912 \begin_inset Tabular
15913 <lyxtabular version="3" rows="2" columns="2">
15915 <column alignment="center" valignment="top" width="0pt">
15916 <column alignment="center" valignment="top" width="0pt">
15918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15921 \begin_layout Plain Layout
15927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15930 \begin_layout Plain Layout
15932 \begin_inset Note Note
15935 \begin_layout Plain Layout
15942 is only used as spacer.
15954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15957 \begin_layout Plain Layout
15966 \begin_layout Plain Layout
15976 \begin_inset Formula $\to$
15980 \begin_inset Formula $\to$
15988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15991 \begin_layout Plain Layout
15992 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16008 \begin_layout Standard
16009 Limits of inline formulas are set right beside the operator.
16010 Limits in displayed formulas are set above or below the operator, except
16011 for integral limits.
16014 \begin_layout Standard
16015 To force that the limits are set beside the operator, the cursor is set
16016 directly behind the operator and the limits type is changed with the menu
16019 Edit\SpecialChar \menuseparator
16020 Math\SpecialChar \menuseparator
16039 \begin_layout Standard
16040 The default limits type is this:
16041 \begin_inset Formula \[
16042 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16046 This is how it looks when the limits type was changed to
16053 \begin_inset Formula \[
16054 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16058 For integrals, except those ending with
16074 etc., the limits are by default set beside the operator.
16075 But for multiple integrals the limits are often set below the operator.
16076 In the following example the limits type was therefore set to
16080 and so set below the integrals:
16081 \begin_inset Formula \begin{equation}
16082 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16089 \begin_layout Standard
16090 \begin_inset VSpace medskip
16093 To specify conditions for limits, the commands
16103 \begin_layout Plain Layout
16121 \begin_layout Plain Layout
16130 To create for example this expression
16131 \begin_inset Formula \begin{equation}
16132 \sum_{\begin{subarray}{c}
16134 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16141 \begin_layout Standard
16142 the following has to be done:
16143 \begin_inset Newline newline
16158 \begin_layout Plain Layout
16170 One is now in a blue box under the summation operator and insert there
16179 \begin_layout Plain Layout
16191 The blue box is now within a purple box and now several lines can be written
16193 A new line is created by inserting a line break (
16196 arg "newline-insert newline"
16201 \begin_inset Newline newline
16206 0<k<1000 Ctrl+Return
16207 \begin_inset Newline newline
16212 is typed in, a new box appears below for the new line.
16215 \begin_layout Standard
16216 The alignment of the lines can be changed to left aligned with the
16226 Edit\SpecialChar \menuseparator
16230 To get right alignment,
16238 \begin_layout Plain Layout
16249 is inserted at the beginning of the line.
16252 \begin_layout Standard
16265 with the difference that the lines are always centered.
16268 \begin_layout Standard
16269 \begin_inset VSpace bigskip
16273 \begin_inset CommandInset ref
16275 reference "eq:substack"
16279 there can be too much space beside an operator, because the characters
16280 following the operator are set beside the limits.
16283 \begin_layout Standard
16284 To avoid this, the following macro can be used in the LaTeX-preamble:
16287 \begin_layout Standard
16301 \begin_inset Newline newline
16313 \begin_inset Newline newline
16320 mathclapinternal #1#2{
16324 mathsurround =0pt #1{#2}$}}
16327 \begin_layout Standard
16328 This defines the command
16338 \begin_layout Plain Layout
16346 that sets the width of the limit to 0
16347 \begin_inset space \thinspace{}
16351 The command scheme is
16354 \begin_layout Standard
16362 \begin_layout Standard
16363 where the limit can consist of several conditions.
16366 \begin_layout Standard
16368 \begin_inset CommandInset ref
16370 reference "eq:substack"
16374 , one uses the command
16377 \begin_layout Standard
16390 \begin_layout Plain Layout
16399 0<k<1000 Ctrl+Return
16402 \begin_layout Standard
16403 to create the lower limit.
16404 The summand is now directly behind the summation operator:
16405 \begin_inset Formula \[
16406 \sum_{\mathclap{\substack{0<k<1000\\
16407 \\k\,\in\,\mathbb{N}}
16415 \begin_layout Standard
16416 \begin_inset VSpace bigskip
16419 How to use one limit for several operators is described in
16420 \begin_inset CommandInset ref
16422 reference "sub:Self-defined-Operators"
16429 \begin_layout Subsection
16431 \begin_inset CommandInset label
16433 name "sub:Binary-Operators"
16441 \begin_layout Plain Layout
16450 \begin_layout Standard
16451 Binary operators are surrounded by space when there is a character before
16453 \begin_inset VSpace medskip
16459 \begin_layout Standard
16460 \begin_inset space \hfill{}
16464 \begin_inset Tabular
16465 <lyxtabular version="3" rows="13" columns="2">
16467 <column alignment="center" valignment="top" width="0pt">
16468 <column alignment="center" valignment="top" width="0pt">
16470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16473 \begin_layout Plain Layout
16475 \begin_inset Note Note
16478 \begin_layout Plain Layout
16485 is only used as spacer.
16495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16498 \begin_layout Plain Layout
16506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16509 \begin_layout Plain Layout
16515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16518 \begin_layout Plain Layout
16519 \begin_inset Formula $+$
16529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16532 \begin_layout Plain Layout
16538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16541 \begin_layout Plain Layout
16542 \begin_inset Formula $-$
16552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16555 \begin_layout Plain Layout
16563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16566 \begin_layout Plain Layout
16567 \begin_inset Formula $\pm$
16577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16580 \begin_layout Plain Layout
16588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16591 \begin_layout Plain Layout
16592 \begin_inset Formula $\mp$
16602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16605 \begin_layout Plain Layout
16613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16616 \begin_layout Plain Layout
16617 \begin_inset Formula $\cdot$
16627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16630 \begin_layout Plain Layout
16638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16641 \begin_layout Plain Layout
16642 \begin_inset Formula $\times$
16652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16655 \begin_layout Plain Layout
16663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16666 \begin_layout Plain Layout
16667 \begin_inset Formula $\div$
16677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16680 \begin_layout Plain Layout
16684 \begin_layout Plain Layout
16697 \begin_layout Plain Layout
16709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16712 \begin_layout Plain Layout
16713 \begin_inset Formula $*$
16723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16726 \begin_layout Plain Layout
16734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16737 \begin_layout Plain Layout
16738 \begin_inset Formula $\star$
16748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16751 \begin_layout Plain Layout
16759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16762 \begin_layout Plain Layout
16763 \begin_inset Formula $\circ$
16773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16776 \begin_layout Plain Layout
16784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16787 \begin_layout Plain Layout
16788 \begin_inset Formula $\diamond$
16798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16801 \begin_layout Plain Layout
16809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16812 \begin_layout Plain Layout
16813 \begin_inset Formula $\bullet$
16827 \begin_inset space \hfill{}
16831 \begin_inset Tabular
16832 <lyxtabular version="3" rows="13" columns="2">
16834 <column alignment="center" valignment="top" width="0pt">
16835 <column alignment="center" valignment="top" width="0pt">
16837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16840 \begin_layout Plain Layout
16846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16849 \begin_layout Plain Layout
16857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16860 \begin_layout Plain Layout
16868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16871 \begin_layout Plain Layout
16872 \begin_inset Formula $\nabla$
16882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16885 \begin_layout Plain Layout
16893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16896 \begin_layout Plain Layout
16897 \begin_inset Formula $\bigtriangledown$
16907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16910 \begin_layout Plain Layout
16918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16921 \begin_layout Plain Layout
16922 \begin_inset Formula $\bigtriangleup$
16932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16935 \begin_layout Plain Layout
16943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16946 \begin_layout Plain Layout
16947 \begin_inset Formula $\Box$
16957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16960 \begin_layout Plain Layout
16968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16971 \begin_layout Plain Layout
16972 \begin_inset Formula $\cap$
16982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16985 \begin_layout Plain Layout
16993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16996 \begin_layout Plain Layout
16997 \begin_inset Formula $\cup$
17007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17010 \begin_layout Plain Layout
17018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17021 \begin_layout Plain Layout
17022 \begin_inset Formula $\dagger$
17032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17035 \begin_layout Plain Layout
17043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17046 \begin_layout Plain Layout
17047 \begin_inset Formula $\ddagger$
17057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17060 \begin_layout Plain Layout
17068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17071 \begin_layout Plain Layout
17072 \begin_inset Formula $\wr$
17082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17085 \begin_layout Plain Layout
17093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17096 \begin_layout Plain Layout
17097 \begin_inset Formula $\bigcirc$
17107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17110 \begin_layout Plain Layout
17118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17121 \begin_layout Plain Layout
17122 \begin_inset Formula $\wedge$
17132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17135 \begin_layout Plain Layout
17143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17146 \begin_layout Plain Layout
17147 \begin_inset Formula $\vee$
17161 \begin_inset space \hfill{}
17165 \begin_inset Tabular
17166 <lyxtabular version="3" rows="13" columns="2">
17168 <column alignment="center" valignment="top" width="0pt">
17169 <column alignment="center" valignment="top" width="0pt">
17171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17174 \begin_layout Plain Layout
17180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17183 \begin_layout Plain Layout
17191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17194 \begin_layout Plain Layout
17202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17205 \begin_layout Plain Layout
17206 \begin_inset Formula $\oplus$
17216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17219 \begin_layout Plain Layout
17227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17230 \begin_layout Plain Layout
17231 \begin_inset Formula $\ominus$
17241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17244 \begin_layout Plain Layout
17252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17255 \begin_layout Plain Layout
17256 \begin_inset Formula $\otimes$
17266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17269 \begin_layout Plain Layout
17277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17280 \begin_layout Plain Layout
17281 \begin_inset Formula $\oslash$
17291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17294 \begin_layout Plain Layout
17302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17305 \begin_layout Plain Layout
17306 \begin_inset Formula $\odot$
17316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17319 \begin_layout Plain Layout
17327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17330 \begin_layout Plain Layout
17331 \begin_inset Formula $\amalg$
17341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17344 \begin_layout Plain Layout
17352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17355 \begin_layout Plain Layout
17356 \begin_inset Formula $\uplus$
17366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17369 \begin_layout Plain Layout
17377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17380 \begin_layout Plain Layout
17381 \begin_inset Formula $\setminus$
17391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17394 \begin_layout Plain Layout
17402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17405 \begin_layout Plain Layout
17406 \begin_inset Formula $\sqcap$
17416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17419 \begin_layout Plain Layout
17427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17430 \begin_layout Plain Layout
17431 \begin_inset Formula $\sqcup$
17441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17444 \begin_layout Plain Layout
17452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17455 \begin_layout Plain Layout
17456 \begin_inset Formula $\triangleleft$
17466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17469 \begin_layout Plain Layout
17477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17480 \begin_layout Plain Layout
17481 \begin_inset Formula $\triangleright$
17495 \begin_inset space \hfill{}
17501 \begin_layout Standard
17502 All binary operators can also be inserted via the math toolbar button
17503 \begin_inset Graphics
17504 filename ../images/math/pm.png
17512 \begin_layout Standard
17513 To typeset the Laplace operator also
17530 \begin_inset Formula $\nabla^{2}$
17533 ) can be used instead of
17542 \begin_layout Standard
17549 Insert\SpecialChar \menuseparator
17561 \begin_layout Subsection
17562 Self-defined Operators
17563 \begin_inset CommandInset label
17565 name "sub:Self-defined-Operators"
17573 \begin_layout Plain Layout
17574 Operators ! self-defined
17582 \begin_layout Standard
17583 With the help of the command
17587 DeclareMathOperator
17593 \begin_layout Plain Layout
17598 DeclareMathOperator
17603 custom operators can be defined in the LaTeX-preamble.
17604 Its command scheme is:
17607 \begin_layout Standard
17612 DeclareMathOperator{new command}{display}
17615 \begin_layout Standard
17616 Display can be characters or symbols that define how the operator looks
17618 To define a big operator a * is set behind the command.
17619 All self-defined big operators can have limits as described in
17620 \begin_inset CommandInset ref
17622 reference "sub:Operator-Limits"
17629 \begin_layout Standard
17630 For example the LaTeX-preamble line
17633 \begin_layout Standard
17638 DeclareMathOperator*{
17645 \begin_layout Standard
17646 defines the command
17652 , that inserts a big operator consisting of the lozenge symbol from
17653 \begin_inset CommandInset ref
17655 reference "sub:Miscellaneous-Symbols"
17660 \begin_inset Formula \[
17661 \Lozenge_{n=1}^{\infty}\]
17665 The command for this formula is:
17676 \begin_inset Formula $\to$
17682 \begin_layout Standard
17683 \begin_inset VSpace bigskip
17686 When self-defined operators are not used several times in the document,
17687 they can also be defined with the commands
17697 \begin_layout Plain Layout
17715 \begin_layout Plain Layout
17723 , which have the following scheme:
17726 \begin_layout Standard
17740 \begin_layout Standard
17747 defines big operators,
17756 \begin_layout Standard
17764 \begin_inset space \thinspace{}
17768 \begin_inset space \space{}
17771 be used to use one limit for several operators:
17774 \begin_layout Standard
17775 \begin_inset Formula \[
17776 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17783 \begin_layout Standard
17784 The command for the formula above is:
17785 \begin_inset Newline newline
17804 \begin_layout Plain Layout
17816 \begin_inset Formula $\to$
17825 \begin_layout Plain Layout
17839 \begin_layout Section
17844 \begin_layout Plain Layout
17853 \begin_layout Subsection
17855 \begin_inset CommandInset label
17857 name "sub:Font-Styles"
17865 \begin_layout Plain Layout
17874 \begin_layout Standard
17875 Latin letters in formulas can be set in one of the following font styles:
17876 \begin_inset VSpace -2mm
17882 \begin_layout Standard
17884 \begin_inset Tabular
17885 <lyxtabular version="3" rows="6" columns="3">
17887 <column alignment="center" valignment="top" width="0">
17888 <column alignment="center" valignment="top" width="0">
17889 <column alignment="center" valignment="top" width="0">
17891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17894 \begin_layout Plain Layout
17900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17903 \begin_layout Plain Layout
17909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17912 \begin_layout Plain Layout
17920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17923 \begin_layout Plain Layout
17932 \begin_layout Plain Layout
17948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17951 \begin_layout Plain Layout
17952 \begin_inset Formula $\mathbb{ABC}$
17960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17963 \begin_layout Plain Layout
17976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17979 \begin_layout Plain Layout
17988 \begin_layout Plain Layout
18004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18007 \begin_layout Plain Layout
18008 \begin_inset Formula $\mathbf{AbC}$
18016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18019 \begin_layout Plain Layout
18032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18035 \begin_layout Plain Layout
18044 \begin_layout Plain Layout
18060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18063 \begin_layout Plain Layout
18064 \begin_inset Formula $\boldsymbol{AbC}$
18072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18075 \begin_layout Plain Layout
18078 arg "font-boldsymbol"
18088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18091 \begin_layout Plain Layout
18100 \begin_layout Plain Layout
18116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18119 \begin_layout Plain Layout
18120 \begin_inset Formula $\mathcal{ABC}$
18128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18131 \begin_layout Plain Layout
18144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18147 \begin_layout Plain Layout
18156 \begin_layout Plain Layout
18172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18175 \begin_layout Plain Layout
18176 \begin_inset Formula $\mathfrak{AbC}$
18184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18187 \begin_layout Plain Layout
18201 \begin_layout Standard
18203 \begin_inset Tabular
18204 <lyxtabular version="3" rows="5" columns="3">
18206 <column alignment="center" valignment="top" width="0">
18207 <column alignment="center" valignment="top" width="0">
18208 <column alignment="center" valignment="top" width="0">
18210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18213 \begin_layout Plain Layout
18219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18222 \begin_layout Plain Layout
18228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18231 \begin_layout Plain Layout
18239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18242 \begin_layout Plain Layout
18251 \begin_layout Plain Layout
18267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18270 \begin_layout Plain Layout
18271 \begin_inset Formula $\mathit{AbC}$
18279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18282 \begin_layout Plain Layout
18290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18293 \begin_layout Plain Layout
18302 \begin_layout Plain Layout
18318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18321 \begin_layout Plain Layout
18322 \begin_inset Formula $\mathrm{AbC}$
18330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18333 \begin_layout Plain Layout
18346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18349 \begin_layout Plain Layout
18358 \begin_layout Plain Layout
18374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18377 \begin_layout Plain Layout
18378 \begin_inset Formula $\mathsf{AbC}$
18386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18389 \begin_layout Plain Layout
18402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18405 \begin_layout Plain Layout
18414 \begin_layout Plain Layout
18430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18433 \begin_layout Plain Layout
18434 \begin_inset Formula $\mathtt{AbC}$
18442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18445 \begin_layout Plain Layout
18448 arg "font-typewriter"
18464 \begin_layout Standard
18465 \begin_inset Note Greyedout
18468 \begin_layout Plain Layout
18485 can only be used for big letters.
18493 \begin_layout Standard
18494 Predefined is the style
18503 \begin_layout Standard
18504 The style commands work also for letters in mathematical constructs:
18505 \begin_inset Formula \[
18506 \mathfrak{A=\frac{b}{C}}\]
18513 \begin_layout Standard
18514 Characters in mathematical text don't appear in a math font style but in
18515 the text font style
18522 That their style can't be set correctly via the text style dialog is a
18527 \begin_layout Plain Layout
18528 \begin_inset CommandInset href
18530 name "LyX-bug #4629"
18531 target "http://www.lyx.org/trac/ticket/4629"
18543 \begin_layout Standard
18544 Instead of the style commands the dialog
18546 Edit\SpecialChar \menuseparator
18547 Math\SpecialChar \menuseparator
18550 or the toolbar button
18551 \begin_inset Graphics
18552 filename ../images/math/font.png
18560 \begin_layout Subsection
18562 \begin_inset CommandInset label
18564 name "sub:Bold-Formulas"
18572 \begin_layout Plain Layout
18581 \begin_layout Standard
18582 To make a complete formula bold, the command
18588 from the previous subsection cannot be used, because it doesn't work for
18589 small Greek letters.
18590 Furthermore it prints Latin letters always upright, like in the following
18594 \begin_layout Standard
18595 \begin_inset Formula \[
18596 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18603 \begin_layout Standard
18604 To display the formula correctly, the command
18611 \begin_inset Formula \[
18612 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18616 It is also possible to set the formula in a
18618 boldmath environment
18621 This environment is created by inserting the command
18629 \begin_layout Plain Layout
18640 To end the environment, the command
18648 \begin_layout Plain Layout
18658 is inserted in TeX-mode.
18662 \begin_layout Plain Layout
18672 \begin_inset Formula \[
18673 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18681 \begin_layout Plain Layout
18693 \begin_layout Subsection
18698 \begin_layout Plain Layout
18707 \begin_layout Standard
18708 Formulas can be colored like normal text: Highlight a formula or a formula
18714 Here is a formula in magenta:
18715 \begin_inset Formula \[
18716 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18723 \begin_layout Standard
18724 You can also define your own colors as described in
18725 \begin_inset CommandInset ref
18727 reference "sub:Colored-Boxes"
18732 They can be used with the TeX code command
18742 \begin_layout Plain Layout
18753 \begin_layout Standard
18758 textcolor{color}{characters or formula}
18761 \begin_layout Standard
18762 The following example was colored completely dark green and partly red:
18765 \begin_layout Standard
18769 \begin_layout Plain Layout
18773 textcolor{darkgreen}{
18779 \begin_inset Formula \[
18780 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18788 \begin_layout Plain Layout
18798 \begin_layout Standard
18799 Due to a bug in LyX only complete formulas can be colored with self-defined
18804 \begin_layout Plain Layout
18805 \begin_inset CommandInset href
18807 name "LyX-bug #5269"
18808 target "http://www.lyx.org/trac/ticket/5269"
18820 \begin_layout Subsection
18822 \begin_inset CommandInset label
18824 name "sub:Font-Sizes"
18832 \begin_layout Plain Layout
18841 \begin_layout Standard
18842 For characters in formulas there are, analog to characters in text, the
18843 following size commands:
18846 \begin_layout Standard
18890 \begin_inset Newline newline
18912 \begin_layout Standard
18913 The size produced by the commands depends on the document font size, that
18914 corresponds with the command
18921 The other commands produce smaller or larger sizes than
18928 The font size can however not exceed a certain value.
18929 Is for example the document font size 12
18930 \begin_inset space \thinspace{}
18939 switches to the same size as
18949 \begin_layout Standard
18950 A size command is inserted in TeX-mode before the formula and sets the size
18951 for all following formula and text characters.
18952 To switch back to the initial size, the command
18958 is inserted behind the formula in TeX-mode.
18961 \begin_layout Standard
18962 \begin_inset Newpage newpage
18968 \begin_layout Standard
18969 Within a formula the size can be changed using the following size commands:
18972 \begin_layout Standard
18975 \begin_inset Tabular
18976 <lyxtabular version="3" rows="5" columns="2">
18978 <column alignment="center" valignment="top" width="0">
18979 <column alignment="center" valignment="top" width="0">
18981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18984 \begin_layout Plain Layout
18990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18993 \begin_layout Plain Layout
18995 \begin_inset Note Note
18998 \begin_layout Plain Layout
19005 is only used as spacer.
19017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19020 \begin_layout Plain Layout
19027 \begin_layout Plain Layout
19040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19043 \begin_layout Plain Layout
19044 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19057 \begin_layout Plain Layout
19065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19068 \begin_layout Plain Layout
19069 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19082 \begin_layout Plain Layout
19090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19093 \begin_layout Plain Layout
19094 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19107 \begin_layout Plain Layout
19115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19118 \begin_layout Plain Layout
19119 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19135 \begin_layout Standard
19136 After entering these commands, a blue box appears in which the formula parts
19140 \begin_layout Standard
19141 There is a further method to change the font size, that though only works
19142 for symbols or letters in mathematical text.
19143 To use it, one of the above text size commands is inserted in mathematical
19145 All following characters until the end of the mathematical text or until
19146 another size command will have the selected size.
19148 \begin_inset VSpace -2mm
19154 \begin_layout Standard
19158 \begin_layout Plain Layout
19168 \begin_inset Formula \[
19169 A=\frac{B}{c}\cdot\maltese\]
19174 \begin_inset Formula \[
19175 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19183 \begin_layout Plain Layout
19195 \begin_layout Standard
19196 \begin_inset VSpace medskip
19199 Before both formulas the command
19206 The command for the second formula is:
19207 \begin_inset Newline newline
19218 \begin_layout Plain Layout
19233 \begin_layout Plain Layout
19248 \begin_layout Plain Layout
19263 \begin_layout Plain Layout
19273 \begin_inset Formula $\to$
19277 \begin_inset Formula $\to$
19281 \begin_inset Newline newline
19285 \begin_inset space \hspace*{}
19299 \begin_layout Plain Layout
19314 \begin_layout Plain Layout
19329 \begin_layout Plain Layout
19341 \begin_layout Standard
19342 If a symbol cannot be displayed in different sizes, it will always be displayed
19343 in the default size.
19346 \begin_layout Standard
19347 \begin_inset Newpage newpage
19353 \begin_layout Section
19358 \begin_layout Plain Layout
19367 \begin_layout Standard
19368 All Greek letters can also be inserted via the toolbar button
19369 \begin_inset Graphics
19370 filename ../images/math/alpha.png
19378 \begin_layout Subsection
19383 \begin_layout Plain Layout
19384 Greek letters ! small
19392 \begin_layout Standard
19393 \begin_inset space \hfill{}
19397 \begin_inset Tabular
19398 <lyxtabular version="3" rows="11" columns="2">
19400 <column alignment="center" valignment="top" width="0pt">
19401 <column alignment="center" valignment="top" width="0pt">
19403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19406 \begin_layout Plain Layout
19412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19415 \begin_layout Plain Layout
19423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19426 \begin_layout Plain Layout
19434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19437 \begin_layout Plain Layout
19438 \begin_inset Formula $\alpha$
19448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19451 \begin_layout Plain Layout
19459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19462 \begin_layout Plain Layout
19463 \begin_inset Formula $\beta$
19473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19476 \begin_layout Plain Layout
19484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19487 \begin_layout Plain Layout
19488 \begin_inset Formula $\gamma$
19498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19501 \begin_layout Plain Layout
19509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19512 \begin_layout Plain Layout
19513 \begin_inset Formula $\delta$
19523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19526 \begin_layout Plain Layout
19534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19537 \begin_layout Plain Layout
19538 \begin_inset Formula $\epsilon$
19548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19551 \begin_layout Plain Layout
19559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19562 \begin_layout Plain Layout
19563 \begin_inset Formula $\varepsilon$
19573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19576 \begin_layout Plain Layout
19584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19587 \begin_layout Plain Layout
19588 \begin_inset Formula $\zeta$
19598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19601 \begin_layout Plain Layout
19609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19612 \begin_layout Plain Layout
19613 \begin_inset Formula $\eta$
19623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19626 \begin_layout Plain Layout
19634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19637 \begin_layout Plain Layout
19638 \begin_inset Formula $\theta$
19648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19651 \begin_layout Plain Layout
19659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19662 \begin_layout Plain Layout
19663 \begin_inset Formula $\vartheta$
19677 \begin_inset space \hfill{}
19681 \begin_inset Tabular
19682 <lyxtabular version="3" rows="12" columns="2">
19684 <column alignment="center" valignment="top" width="0pt">
19685 <column alignment="center" valignment="top" width="0pt">
19687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19690 \begin_layout Plain Layout
19696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19699 \begin_layout Plain Layout
19707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19710 \begin_layout Plain Layout
19718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19721 \begin_layout Plain Layout
19722 \begin_inset Formula $\iota$
19732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19735 \begin_layout Plain Layout
19743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19746 \begin_layout Plain Layout
19747 \begin_inset Formula $\kappa$
19757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19760 \begin_layout Plain Layout
19768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19771 \begin_layout Plain Layout
19772 \begin_inset Formula $\varkappa$
19782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19785 \begin_layout Plain Layout
19793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19796 \begin_layout Plain Layout
19797 \begin_inset Formula $\lambda$
19807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19810 \begin_layout Plain Layout
19818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19821 \begin_layout Plain Layout
19822 \begin_inset Formula $\mu$
19832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19835 \begin_layout Plain Layout
19843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19846 \begin_layout Plain Layout
19847 \begin_inset Formula $\nu$
19857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19860 \begin_layout Plain Layout
19868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19871 \begin_layout Plain Layout
19872 \begin_inset Formula $\xi$
19882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19885 \begin_layout Plain Layout
19891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19894 \begin_layout Plain Layout
19895 \begin_inset Formula $o$
19905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19908 \begin_layout Plain Layout
19916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19919 \begin_layout Plain Layout
19920 \begin_inset Formula $\pi$
19930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19933 \begin_layout Plain Layout
19941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19944 \begin_layout Plain Layout
19945 \begin_inset Formula $\varpi$
19955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19958 \begin_layout Plain Layout
19966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19969 \begin_layout Plain Layout
19970 \begin_inset Formula $\rho$
19984 \begin_inset space \hfill{}
19988 \begin_inset Tabular
19989 <lyxtabular version="3" rows="11" columns="2">
19991 <column alignment="center" valignment="top" width="0pt">
19992 <column alignment="center" valignment="top" width="0pt">
19994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19997 \begin_layout Plain Layout
20003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20006 \begin_layout Plain Layout
20014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20017 \begin_layout Plain Layout
20025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20028 \begin_layout Plain Layout
20029 \begin_inset Formula $\varrho$
20039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20042 \begin_layout Plain Layout
20050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20053 \begin_layout Plain Layout
20054 \begin_inset Formula $\sigma$
20064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20067 \begin_layout Plain Layout
20075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20078 \begin_layout Plain Layout
20079 \begin_inset Formula $\varsigma$
20089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20092 \begin_layout Plain Layout
20100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20103 \begin_layout Plain Layout
20104 \begin_inset Formula $\tau$
20114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20117 \begin_layout Plain Layout
20125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20128 \begin_layout Plain Layout
20129 \begin_inset Formula $\upsilon$
20139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20142 \begin_layout Plain Layout
20150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20153 \begin_layout Plain Layout
20154 \begin_inset Formula $\phi$
20164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20167 \begin_layout Plain Layout
20175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20178 \begin_layout Plain Layout
20179 \begin_inset Formula $\varphi$
20189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20192 \begin_layout Plain Layout
20200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20203 \begin_layout Plain Layout
20204 \begin_inset Formula $\chi$
20214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20217 \begin_layout Plain Layout
20225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20228 \begin_layout Plain Layout
20229 \begin_inset Formula $\psi$
20239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20242 \begin_layout Plain Layout
20250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20253 \begin_layout Plain Layout
20254 \begin_inset Formula $\omega$
20268 \begin_inset space \hfill{}
20274 \begin_layout Standard
20275 \begin_inset VSpace medskip
20281 \begin_layout Standard
20282 How to create upright Greek letters is explained in
20283 \begin_inset CommandInset ref
20285 reference "sub:Upright-small-Greek"
20292 \begin_layout Subsection
20297 \begin_layout Plain Layout
20298 Greek letters ! big
20306 \begin_layout Standard
20307 \begin_inset space \hfill{}
20311 \begin_inset Tabular
20312 <lyxtabular version="3" rows="7" columns="2">
20314 <column alignment="center" valignment="top" width="0pt">
20315 <column alignment="center" valignment="top" width="0pt">
20317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20320 \begin_layout Plain Layout
20326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20329 \begin_layout Plain Layout
20337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20340 \begin_layout Plain Layout
20348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20351 \begin_layout Plain Layout
20352 \begin_inset Formula $\Gamma$
20362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20365 \begin_layout Plain Layout
20373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20376 \begin_layout Plain Layout
20377 \begin_inset Formula $\Delta$
20387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20390 \begin_layout Plain Layout
20398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20401 \begin_layout Plain Layout
20402 \begin_inset Formula $\Theta$
20412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20415 \begin_layout Plain Layout
20423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20426 \begin_layout Plain Layout
20427 \begin_inset Formula $\Lambda$
20437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20440 \begin_layout Plain Layout
20448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20451 \begin_layout Plain Layout
20452 \begin_inset Formula $\Xi$
20462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20465 \begin_layout Plain Layout
20473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20476 \begin_layout Plain Layout
20477 \begin_inset Formula $\Pi$
20491 \begin_inset space \hfill{}
20495 \begin_inset Tabular
20496 <lyxtabular version="3" rows="6" columns="2">
20498 <column alignment="center" valignment="top" width="0pt">
20499 <column alignment="center" valignment="top" width="0pt">
20501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20504 \begin_layout Plain Layout
20510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20513 \begin_layout Plain Layout
20521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20524 \begin_layout Plain Layout
20532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20535 \begin_layout Plain Layout
20536 \begin_inset Formula $\Sigma$
20546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20549 \begin_layout Plain Layout
20557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20560 \begin_layout Plain Layout
20561 \begin_inset Formula $\Upsilon$
20571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20574 \begin_layout Plain Layout
20582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20585 \begin_layout Plain Layout
20586 \begin_inset Formula $\Phi$
20596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20599 \begin_layout Plain Layout
20607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20610 \begin_layout Plain Layout
20611 \begin_inset Formula $\Psi$
20621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20624 \begin_layout Plain Layout
20632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20635 \begin_layout Plain Layout
20636 \begin_inset Formula $\Omega$
20650 \begin_inset space \hfill{}
20656 \begin_layout Standard
20657 \begin_inset VSpace medskip
20660 That the big Greek letters appear upright is caused by a design bug when
20662 To get correct italic big letters, begin every command with
20667 For example the command
20674 \begin_inset Formula $\varGamma$
20680 \begin_layout Subsection
20685 \begin_layout Plain Layout
20686 Greek letters ! bold
20694 \begin_layout Standard
20695 Greek letters cannot be set with different font styles like Latin letters.
20696 They can only be made bold with the command
20706 \begin_layout Plain Layout
20717 \begin_layout Standard
20719 \begin_inset Tabular
20720 <lyxtabular version="3" rows="3" columns="2">
20722 <column alignment="center" valignment="top" width="0">
20723 <column alignment="center" valignment="top" width="0">
20725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20728 \begin_layout Plain Layout
20734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20737 \begin_layout Plain Layout
20745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20748 \begin_layout Plain Layout
20760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20763 \begin_layout Plain Layout
20764 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20777 \begin_layout Plain Layout
20789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20792 \begin_layout Plain Layout
20793 \begin_inset Formula $\theta\boldsymbol{\theta}$
20809 \begin_layout Section
20814 \begin_layout Plain Layout
20827 \begin_layout Plain Layout
20828 A list with all symbols of most of the LaTeX-packages can be found in
20829 \begin_inset CommandInset citation
20844 \begin_layout Plain Layout
20852 \begin_inset Note Note
20855 \begin_layout Plain Layout
20858 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20861 \begin_layout Plain Layout
20864 texorpdfstring is in section
20865 \begin_inset CommandInset ref
20867 reference "sub:Formulas-in-Section"
20880 \begin_layout Plain Layout
20889 \begin_layout Standard
20890 Many of the symbols listed in this section can also be inserted via the
20892 \begin_inset Graphics
20893 filename ../images/math/nabla.png
20899 \begin_inset Graphics
20900 filename ../images/math/digamma.png
20908 \begin_layout Subsection
20909 Mathematical Symbols
20910 \begin_inset CommandInset label
20912 name "sub:Mathematical-Symbols"
20920 \begin_layout Plain Layout
20921 Symbols ! mathematical
20929 \begin_layout Standard
20930 \begin_inset space \hfill{}
20934 \begin_inset Tabular
20935 <lyxtabular version="3" rows="10" columns="2">
20937 <column alignment="center" valignment="top" width="0pt">
20938 <column alignment="center" valignment="top" width="0pt">
20940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20943 \begin_layout Plain Layout
20949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20952 \begin_layout Plain Layout
20960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20963 \begin_layout Plain Layout
20971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20974 \begin_layout Plain Layout
20975 \begin_inset Formula $\neg$
20985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20988 \begin_layout Plain Layout
20996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20999 \begin_layout Plain Layout
21000 \begin_inset Formula $\Im$
21010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21013 \begin_layout Plain Layout
21021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21024 \begin_layout Plain Layout
21025 \begin_inset Formula $\Re$
21035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21038 \begin_layout Plain Layout
21046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21049 \begin_layout Plain Layout
21050 \begin_inset Formula $\aleph$
21060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21063 \begin_layout Plain Layout
21071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21074 \begin_layout Plain Layout
21075 \begin_inset Formula $\partial$
21085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21088 \begin_layout Plain Layout
21096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21099 \begin_layout Plain Layout
21100 \begin_inset Formula $\infty$
21110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21113 \begin_layout Plain Layout
21121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21124 \begin_layout Plain Layout
21125 \begin_inset Formula $\wp$
21135 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21138 \begin_layout Plain Layout
21146 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21149 \begin_layout Plain Layout
21150 \begin_inset Formula $\imath$
21160 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21163 \begin_layout Plain Layout
21171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21174 \begin_layout Plain Layout
21175 \begin_inset Formula $\jmath$
21189 \begin_inset space \hfill{}
21193 \begin_inset Tabular
21194 <lyxtabular version="3" rows="10" columns="2">
21196 <column alignment="center" valignment="top" width="0pt">
21197 <column alignment="center" valignment="top" width="0pt">
21199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21202 \begin_layout Plain Layout
21208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21211 \begin_layout Plain Layout
21213 \begin_inset Note Note
21216 \begin_layout Plain Layout
21223 is only used as spacer.
21235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21238 \begin_layout Plain Layout
21246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21249 \begin_layout Plain Layout
21250 \begin_inset Formula $\forall$
21260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21263 \begin_layout Plain Layout
21271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21274 \begin_layout Plain Layout
21275 \begin_inset Formula $\exists$
21285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21288 \begin_layout Plain Layout
21296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21299 \begin_layout Plain Layout
21300 \begin_inset Formula $\nexists$
21310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21313 \begin_layout Plain Layout
21321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21324 \begin_layout Plain Layout
21325 \begin_inset Formula $\emptyset$
21335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21338 \begin_layout Plain Layout
21346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21349 \begin_layout Plain Layout
21350 \begin_inset Formula $\varnothing$
21360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21363 \begin_layout Plain Layout
21371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21374 \begin_layout Plain Layout
21375 \begin_inset Formula $\dag$
21385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21388 \begin_layout Plain Layout
21396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21399 \begin_layout Plain Layout
21400 \begin_inset Formula $\ddag$
21410 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21413 \begin_layout Plain Layout
21421 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21424 \begin_layout Plain Layout
21428 \begin_layout Plain Layout
21438 \begin_inset Formula $\complement$
21445 \begin_layout Plain Layout
21459 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21462 \begin_layout Plain Layout
21470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21473 \begin_layout Plain Layout
21474 \begin_inset Formula $\Bbbk$
21488 \begin_inset space \hfill{}
21492 \begin_inset Tabular
21493 <lyxtabular version="3" rows="10" columns="2">
21495 <column alignment="center" valignment="top" width="0pt">
21496 <column alignment="center" valignment="top" width="0pt">
21498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21501 \begin_layout Plain Layout
21507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21510 \begin_layout Plain Layout
21518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21521 \begin_layout Plain Layout
21529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21532 \begin_layout Plain Layout
21533 \begin_inset Formula $\prime$
21543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21546 \begin_layout Plain Layout
21554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21557 \begin_layout Plain Layout
21558 \begin_inset Formula $\backprime$
21568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21571 \begin_layout Plain Layout
21579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21582 \begin_layout Plain Layout
21583 \begin_inset Formula $\mho$
21593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21596 \begin_layout Plain Layout
21604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21607 \begin_layout Plain Layout
21608 \begin_inset Formula $\triangle$
21618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21621 \begin_layout Plain Layout
21629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21632 \begin_layout Plain Layout
21633 \begin_inset Formula $\angle$
21643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21646 \begin_layout Plain Layout
21654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21657 \begin_layout Plain Layout
21658 \begin_inset Formula $\measuredangle$
21668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21671 \begin_layout Plain Layout
21679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21682 \begin_layout Plain Layout
21683 \begin_inset Formula $\sphericalangle$
21693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21696 \begin_layout Plain Layout
21704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21707 \begin_layout Plain Layout
21708 \begin_inset Formula $\top$
21718 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21721 \begin_layout Plain Layout
21729 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21732 \begin_layout Plain Layout
21733 \begin_inset Formula $\bot$
21747 \begin_inset space \hfill{}
21753 \begin_layout Subsection
21754 Miscellaneous Symbols
21755 \begin_inset CommandInset label
21757 name "sub:Miscellaneous-Symbols"
21765 \begin_layout Plain Layout
21766 Symbols ! miscellaneous
21774 \begin_layout Standard
21777 \begin_inset Tabular
21778 <lyxtabular version="3" rows="10" columns="2">
21780 <column alignment="center" valignment="top" width="0pt">
21781 <column alignment="center" valignment="top" width="0pt">
21783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21786 \begin_layout Plain Layout
21792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21795 \begin_layout Plain Layout
21803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21806 \begin_layout Plain Layout
21814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21817 \begin_layout Plain Layout
21818 \begin_inset Formula $\flat$
21828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21831 \begin_layout Plain Layout
21839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21842 \begin_layout Plain Layout
21843 \begin_inset Formula $\natural$
21853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21856 \begin_layout Plain Layout
21864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21867 \begin_layout Plain Layout
21868 \begin_inset Formula $\sharp$
21878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21881 \begin_layout Plain Layout
21889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21892 \begin_layout Plain Layout
21893 \begin_inset Formula $\surd$
21903 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21906 \begin_layout Plain Layout
21914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21917 \begin_layout Plain Layout
21918 \begin_inset Formula $\checkmark$
21928 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21931 \begin_layout Plain Layout
21939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21942 \begin_layout Plain Layout
21943 \begin_inset Formula $\yen$
21953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21956 \begin_layout Plain Layout
21964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21967 \begin_layout Plain Layout
21968 \begin_inset Formula $\pounds$
21978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21981 \begin_layout Plain Layout
21987 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21990 \begin_layout Plain Layout
21991 \begin_inset Formula $\$$
22001 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22004 \begin_layout Plain Layout
22010 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22013 \begin_layout Plain Layout
22014 \begin_inset Formula $§$
22028 \begin_inset Tabular
22029 <lyxtabular version="3" rows="10" columns="2">
22031 <column alignment="center" valignment="top" width="0">
22032 <column alignment="center" valignment="top" width="0">
22034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22037 \begin_layout Plain Layout
22043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22046 \begin_layout Plain Layout
22054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22057 \begin_layout Plain Layout
22065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22068 \begin_layout Plain Layout
22069 \begin_inset Formula $\hbar$
22079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22082 \begin_layout Plain Layout
22090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22093 \begin_layout Plain Layout
22094 \begin_inset Formula $\hslash$
22104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22107 \begin_layout Plain Layout
22115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22118 \begin_layout Plain Layout
22119 \begin_inset Formula $\clubsuit$
22129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22132 \begin_layout Plain Layout
22140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22143 \begin_layout Plain Layout
22144 \begin_inset Formula $\spadesuit$
22154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22157 \begin_layout Plain Layout
22165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22168 \begin_layout Plain Layout
22169 \begin_inset Formula $\bigstar$
22179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22182 \begin_layout Plain Layout
22190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22193 \begin_layout Plain Layout
22194 \begin_inset Formula $\blacklozenge$
22204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22207 \begin_layout Plain Layout
22215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22218 \begin_layout Plain Layout
22219 \begin_inset Formula $\blacktriangle$
22229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22232 \begin_layout Plain Layout
22240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22243 \begin_layout Plain Layout
22244 \begin_inset Formula $\blacktriangledown$
22254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22257 \begin_layout Plain Layout
22265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22268 \begin_layout Plain Layout
22269 \begin_inset Formula $\bullet$
22283 \begin_inset Tabular
22284 <lyxtabular version="3" rows="10" columns="2">
22286 <column alignment="center" valignment="top" width="0pt">
22287 <column alignment="center" valignment="top" width="0pt">
22289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22292 \begin_layout Plain Layout
22298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22301 \begin_layout Plain Layout
22309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22312 \begin_layout Plain Layout
22320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22323 \begin_layout Plain Layout
22324 \begin_inset Formula $\diamondsuit$
22334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22337 \begin_layout Plain Layout
22345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22348 \begin_layout Plain Layout
22349 \begin_inset Formula $\Diamond$
22359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22362 \begin_layout Plain Layout
22370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22373 \begin_layout Plain Layout
22374 \begin_inset Formula $\heartsuit$
22384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22387 \begin_layout Plain Layout
22395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22398 \begin_layout Plain Layout
22399 \begin_inset Formula $\P$
22409 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22412 \begin_layout Plain Layout
22420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22423 \begin_layout Plain Layout
22424 \begin_inset Formula $\copyright$
22434 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22437 \begin_layout Plain Layout
22445 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22448 \begin_layout Plain Layout
22449 \begin_inset Formula $\circledR$
22459 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22462 \begin_layout Plain Layout
22470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22473 \begin_layout Plain Layout
22474 \begin_inset Formula $\maltese$
22484 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22487 \begin_layout Plain Layout
22495 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22498 \begin_layout Plain Layout
22499 \begin_inset Formula $\diagup$
22509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22512 \begin_layout Plain Layout
22520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22523 \begin_layout Plain Layout
22524 \begin_inset Formula $\diagdown$
22540 \begin_layout Standard
22541 \begin_inset VSpace medskip
22544 More symbols are listed in
22545 \begin_inset CommandInset ref
22547 reference "sub:Miscellaneous-special-Characters"
22554 \begin_layout Standard
22555 Some symbols can be displayed in different sizes, see
22556 \begin_inset CommandInset ref
22558 reference "sub:Font-Sizes"
22565 \begin_layout Subsection
22570 \begin_layout Plain Layout
22571 Symbols ! Euro-symbol
22580 \begin_layout Plain Layout
22587 \begin_layout Plain Layout
22604 \begin_layout Standard
22605 To use the Euro symbol in formulas, the LaTeX-package
22613 \begin_layout Plain Layout
22619 must be installed and loaded with the LaTeX-preamble line
22622 \begin_layout Standard
22627 usepackage[gennarrow]{eurosym}
22630 \begin_layout Standard
22631 The Euro symbol can now be inserted with the command
22641 \begin_layout Plain Layout
22652 \begin_layout Standard
22653 The Euro symbol can directly be inserted with the € key in mathematical
22654 text, without having
22669 can also be inserted in TeX-mode.
22670 The official currency symbol can then be inserted with the command
22680 \begin_layout Plain Layout
22688 , that is only available in TeX-mode.
22691 \begin_layout Standard
22695 \begin_layout Plain Layout
22705 \begin_inset Note Note
22708 \begin_layout Plain Layout
22709 The following table will only be displayed when the LaTeX-package
22721 \begin_layout Standard
22722 An overview about the different Euro symbols:
22725 \begin_layout Standard
22727 \begin_inset Tabular
22728 <lyxtabular version="3" rows="4" columns="3">
22730 <column alignment="center" valignment="top" width="0pt">
22731 <column alignment="center" valignment="top" width="0pt">
22732 <column alignment="center" valignment="top" width="0pt">
22734 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22737 \begin_layout Plain Layout
22743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22746 \begin_layout Plain Layout
22752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22755 \begin_layout Plain Layout
22763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22766 \begin_layout Plain Layout
22772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22775 \begin_layout Plain Layout
22783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22786 \begin_layout Plain Layout
22787 \begin_inset Formula $\euro$
22797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22800 \begin_layout Plain Layout
22806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22809 \begin_layout Plain Layout
22815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22818 \begin_layout Plain Layout
22819 \begin_inset Formula $\mbox{€}$
22829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22832 \begin_layout Plain Layout
22838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22841 \begin_layout Plain Layout
22849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22852 \begin_layout Plain Layout
22856 \begin_layout Plain Layout
22878 \begin_layout Standard
22882 \begin_layout Plain Layout
22892 \begin_inset Note Note
22895 \begin_layout Plain Layout
22896 The following will be displayed when the LaTeX-package
22908 \begin_layout Standard
22909 You need to install the LaTeX-package
22913 to see the rest of this subsection in the output.
22916 \begin_layout Standard
22920 \begin_layout Plain Layout
22932 \begin_layout Section
22934 \begin_inset CommandInset label
22936 name "sec:Relations"
22944 \begin_layout Plain Layout
22954 \begin_layout Plain Layout
22959 \begin_layout Plain Layout
22970 \begin_layout Plain Layout
22985 \begin_layout Standard
22986 All relations can also be inserted via the toolbar button
22987 \begin_inset Graphics
22988 filename ../images/math/leq.png
22996 \begin_layout Standard
22997 \begin_inset space \hfill{}
23001 \begin_inset Tabular
23002 <lyxtabular version="3" rows="17" columns="2">
23004 <column alignment="center" valignment="top" width="0pt">
23005 <column alignment="center" valignment="top" width="0pt">
23007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23010 \begin_layout Plain Layout
23016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23019 \begin_layout Plain Layout
23027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23030 \begin_layout Plain Layout
23036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23039 \begin_layout Plain Layout
23040 \begin_inset Formula $<$
23050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23053 \begin_layout Plain Layout
23061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23064 \begin_layout Plain Layout
23065 \begin_inset Formula $\le$
23075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23078 \begin_layout Plain Layout
23086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23089 \begin_layout Plain Layout
23090 \begin_inset Formula $\ll$
23100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23103 \begin_layout Plain Layout
23111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23114 \begin_layout Plain Layout
23115 \begin_inset Formula $\prec$
23125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23128 \begin_layout Plain Layout
23136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23139 \begin_layout Plain Layout
23140 \begin_inset Formula $\preceq$
23150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23153 \begin_layout Plain Layout
23161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23164 \begin_layout Plain Layout
23165 \begin_inset Formula $\subset$
23175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23178 \begin_layout Plain Layout
23186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23189 \begin_layout Plain Layout
23190 \begin_inset Formula $\subseteq$
23200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23203 \begin_layout Plain Layout
23211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23214 \begin_layout Plain Layout
23215 \begin_inset Formula $\sqsubseteq$
23225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23228 \begin_layout Plain Layout
23236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23239 \begin_layout Plain Layout
23240 \begin_inset Formula $\in$
23250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23253 \begin_layout Plain Layout
23261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23264 \begin_layout Plain Layout
23265 \begin_inset Formula $\vdash$
23275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23278 \begin_layout Plain Layout
23286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23289 \begin_layout Plain Layout
23290 \begin_inset Formula $\smile$
23300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23303 \begin_layout Plain Layout
23311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23314 \begin_layout Plain Layout
23315 \begin_inset Formula $\lhd$
23325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23328 \begin_layout Plain Layout
23336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23339 \begin_layout Plain Layout
23340 \begin_inset Formula $\unlhd$
23350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23353 \begin_layout Plain Layout
23361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23364 \begin_layout Plain Layout
23365 \begin_inset Formula $\gtrless$
23375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23378 \begin_layout Plain Layout
23386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23389 \begin_layout Plain Layout
23390 \begin_inset Formula $\mid$
23400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23403 \begin_layout Plain Layout
23411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23414 \begin_layout Plain Layout
23415 \begin_inset Formula $\nmid$
23429 \begin_inset space \hfill{}
23433 \begin_inset Tabular
23434 <lyxtabular version="3" rows="17" columns="2">
23436 <column alignment="center" valignment="top" width="0pt">
23437 <column alignment="center" valignment="top" width="0pt">
23439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23442 \begin_layout Plain Layout
23448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23451 \begin_layout Plain Layout
23459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23462 \begin_layout Plain Layout
23468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23471 \begin_layout Plain Layout
23472 \begin_inset Formula $=$
23482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23485 \begin_layout Plain Layout
23493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23496 \begin_layout Plain Layout
23497 \begin_inset Formula $\not=$
23507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23510 \begin_layout Plain Layout
23518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23521 \begin_layout Plain Layout
23522 \begin_inset Formula $\equiv$
23532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23535 \begin_layout Plain Layout
23543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23546 \begin_layout Plain Layout
23547 \begin_inset Formula $\sim$
23557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23560 \begin_layout Plain Layout
23568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23571 \begin_layout Plain Layout
23572 \begin_inset Formula $\simeq$
23582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23585 \begin_layout Plain Layout
23593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23596 \begin_layout Plain Layout
23597 \begin_inset Formula $\approx$
23607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23610 \begin_layout Plain Layout
23618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23621 \begin_layout Plain Layout
23622 \begin_inset Formula $\cong$
23632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23635 \begin_layout Plain Layout
23643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23646 \begin_layout Plain Layout
23647 \begin_inset Formula $\bowtie$
23657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23660 \begin_layout Plain Layout
23668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23671 \begin_layout Plain Layout
23672 \begin_inset Formula $\notin$
23682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23685 \begin_layout Plain Layout
23693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23696 \begin_layout Plain Layout
23697 \begin_inset Formula $\perp$
23707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23710 \begin_layout Plain Layout
23718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23721 \begin_layout Plain Layout
23722 \begin_inset Formula $\propto$
23732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23735 \begin_layout Plain Layout
23743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23746 \begin_layout Plain Layout
23747 \begin_inset Formula $\asymp$
23757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23760 \begin_layout Plain Layout
23768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23771 \begin_layout Plain Layout
23772 \begin_inset Formula $\doteq$
23782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23785 \begin_layout Plain Layout
23793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23796 \begin_layout Plain Layout
23797 \begin_inset Formula $\circeq$
23807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23810 \begin_layout Plain Layout
23818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23821 \begin_layout Plain Layout
23822 \begin_inset Formula $\models$
23832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23835 \begin_layout Plain Layout
23843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23846 \begin_layout Plain Layout
23847 \begin_inset Formula $\widehat{=}$
23861 \begin_inset space \hfill{}
23865 \begin_inset Tabular
23866 <lyxtabular version="3" rows="17" columns="2">
23868 <column alignment="center" valignment="top" width="0pt">
23869 <column alignment="center" valignment="top" width="0pt">
23871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23874 \begin_layout Plain Layout
23880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23883 \begin_layout Plain Layout
23891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23894 \begin_layout Plain Layout
23900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23903 \begin_layout Plain Layout
23904 \begin_inset Formula $>$
23914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23917 \begin_layout Plain Layout
23925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23928 \begin_layout Plain Layout
23929 \begin_inset Formula $\ge$
23939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23942 \begin_layout Plain Layout
23950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23953 \begin_layout Plain Layout
23954 \begin_inset Formula $\gg$
23964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23967 \begin_layout Plain Layout
23975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23978 \begin_layout Plain Layout
23979 \begin_inset Formula $\succ$
23989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23992 \begin_layout Plain Layout
24000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24003 \begin_layout Plain Layout
24004 \begin_inset Formula $\succeq$
24014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24017 \begin_layout Plain Layout
24025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24028 \begin_layout Plain Layout
24029 \begin_inset Formula $\supset$
24039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24042 \begin_layout Plain Layout
24050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24053 \begin_layout Plain Layout
24054 \begin_inset Formula $\supseteq$
24064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24067 \begin_layout Plain Layout
24075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24078 \begin_layout Plain Layout
24079 \begin_inset Formula $\sqsupseteq$
24089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24092 \begin_layout Plain Layout
24100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24103 \begin_layout Plain Layout
24104 \begin_inset Formula $\ni$
24114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24117 \begin_layout Plain Layout
24125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24128 \begin_layout Plain Layout
24129 \begin_inset Formula $\dashv$
24139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24142 \begin_layout Plain Layout
24150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24153 \begin_layout Plain Layout
24154 \begin_inset Formula $\frown$
24164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24167 \begin_layout Plain Layout
24175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24178 \begin_layout Plain Layout
24179 \begin_inset Formula $\rhd$
24189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24192 \begin_layout Plain Layout
24200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24203 \begin_layout Plain Layout
24204 \begin_inset Formula $\unrhd$
24214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24217 \begin_layout Plain Layout
24225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24228 \begin_layout Plain Layout
24229 \begin_inset Formula $\lessgtr$
24239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24242 \begin_layout Plain Layout
24250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24253 \begin_layout Plain Layout
24254 \begin_inset Formula $\parallel$
24264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24267 \begin_layout Plain Layout
24275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24278 \begin_layout Plain Layout
24279 \begin_inset Formula $\nparallel$
24293 \begin_inset space \hfill{}
24299 \begin_layout Standard
24300 \begin_inset VSpace medskip
24315 are bigger than the equal looking operators
24330 \begin_layout Standard
24331 Relations are, in contrary to symbols, always surrounded by space.
24334 \begin_layout Standard
24335 Relations with labels can be created with the command
24345 \begin_layout Plain Layout
24356 \begin_layout Standard
24358 \begin_inset Tabular
24359 <lyxtabular version="3" rows="2" columns="2">
24361 <column alignment="center" valignment="top" width="0">
24362 <column alignment="center" valignment="top" width="0">
24364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24367 \begin_layout Plain Layout
24373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24376 \begin_layout Plain Layout
24378 \begin_inset Note Note
24381 \begin_layout Plain Layout
24388 is only used as spacer.
24400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24403 \begin_layout Plain Layout
24410 \begin_layout Plain Layout
24427 \begin_layout Plain Layout
24437 \begin_inset Formula $\downarrow$
24446 \begin_layout Plain Layout
24459 \begin_layout Plain Layout
24473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24476 \begin_layout Plain Layout
24477 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24493 \begin_layout Section
24497 \begin_layout Subsection
24498 Predefined Functions
24499 \begin_inset CommandInset label
24501 name "sub:Predefined-Functions"
24509 \begin_layout Plain Layout
24510 Functions ! predefined
24518 \begin_layout Standard
24519 In general, variables are set
24523 in mathematical expressions, but not function names, because
24524 \begin_inset Formula $sin$
24527 could be misunderstood as
24528 \begin_inset Formula $s\cdot i\cdot n$
24532 Therefore there are predefined functions, that are additionally a bit separated
24534 They are inserted as commands starting with a backslash before their name.
24537 \begin_layout Standard
24539 \begin_inset Tabular
24540 <lyxtabular version="3" rows="2" columns="4">
24542 <column alignment="center" valignment="top" width="0pt">
24543 <column alignment="center" valignment="top" width="0pt">
24544 <column alignment="center" valignment="top" width="0pt">
24545 <column alignment="center" valignment="top" width="0pt">
24547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24550 \begin_layout Plain Layout
24556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24559 \begin_layout Plain Layout
24565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24568 \begin_layout Plain Layout
24574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24577 \begin_layout Plain Layout
24585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24588 \begin_layout Plain Layout
24594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24597 \begin_layout Plain Layout
24598 \begin_inset Formula $Asin(x)+B$
24606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24609 \begin_layout Plain Layout
24617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24620 \begin_layout Plain Layout
24621 \begin_inset Formula $A\sin(x)+B$
24637 \begin_layout Standard
24638 The following functions are predefined:
24641 \begin_layout Standard
24642 \begin_inset VSpace -2mm
24648 \begin_layout Standard
24650 \begin_inset Tabular
24651 <lyxtabular version="3" rows="9" columns="4">
24653 <column alignment="center" valignment="top" width="0pt">
24654 <column alignment="center" valignment="top" width="0pt">
24655 <column alignment="center" valignment="top" width="0pt">
24656 <column alignment="center" valignment="top" width="0pt">
24658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24661 \begin_layout Plain Layout
24667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24670 \begin_layout Plain Layout
24676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24679 \begin_layout Plain Layout
24685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="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" usebox="none">
24721 \begin_layout Plain Layout
24729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24732 \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" usebox="none">
24767 \begin_layout Plain Layout
24775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24778 \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" usebox="none">
24813 \begin_layout Plain Layout
24821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24824 \begin_layout Plain Layout
24834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24837 \begin_layout Plain Layout
24845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24848 \begin_layout Plain Layout
24856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24859 \begin_layout Plain Layout
24867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24870 \begin_layout Plain Layout
24880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24883 \begin_layout Plain Layout
24891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24894 \begin_layout Plain Layout
24902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24905 \begin_layout Plain Layout
24913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24916 \begin_layout Plain Layout
24926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24929 \begin_layout Plain Layout
24937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24940 \begin_layout Plain Layout
24948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24951 \begin_layout Plain Layout
24959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24962 \begin_layout Plain Layout
24972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24975 \begin_layout Plain Layout
24983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24986 \begin_layout Plain Layout
24994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24997 \begin_layout Plain Layout
25005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25008 \begin_layout Plain Layout
25018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25021 \begin_layout Plain Layout
25029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25032 \begin_layout Plain Layout
25040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25043 \begin_layout Plain Layout
25051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25054 \begin_layout Plain Layout
25070 \begin_layout Standard
25071 They can also be inserted with the math toolbar button
25072 \begin_inset Graphics
25073 filename ../images/math/functions.png
25081 \begin_layout Subsection
25082 Self-defined Functions
25086 \begin_layout Plain Layout
25087 Functions ! self-defined
25095 \begin_layout Standard
25096 To use a function that is not predefined, like for example the sign function
25097 sgn(x), there are two possibilities:
25100 \begin_layout Itemize
25101 Define the function by inserting the following line to the LaTeX-preamble
25105 \begin_layout Plain Layout
25110 DeclareMathOperator
25113 \begin_inset CommandInset ref
25115 reference "sub:Self-defined-Operators"
25125 \begin_inset Newline newline
25129 \begin_inset VSpace -3mm
25133 \begin_inset Newline newline
25140 DeclareMathOperator{
25148 \begin_layout Plain Layout
25153 DeclareMathOperator
25159 \begin_inset Newline newline
25163 \begin_inset VSpace -2mm
25167 \begin_inset Newline newline
25170 Now the new defined function can be called with the command
25179 \begin_layout Itemize
25180 Write the formula as usual, mark the formula name, in our example the letters
25185 , and change it to mathematical text.
25186 At last a space is inserted between prefactor and function.
25189 \begin_layout Standard
25190 The result is the same with both methods as with a predefined function
25194 \begin_layout Plain Layout
25195 In LyX self-defined functions are displayed red, predefined ones black.
25203 \begin_layout Standard
25205 \begin_inset Tabular
25206 <lyxtabular version="3" rows="3" columns="2">
25208 <column alignment="center" valignment="top" width="0pt">
25209 <column alignment="center" valignment="top" width="0pt">
25211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25214 \begin_layout Plain Layout
25220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25223 \begin_layout Plain Layout
25231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25234 \begin_layout Plain Layout
25242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25245 \begin_layout Plain Layout
25246 \begin_inset Formula $A\sgn(x)+B$
25256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25259 \begin_layout Plain Layout
25263 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25274 \begin_layout Plain Layout
25275 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25291 \begin_layout Standard
25292 The first method is more suitable when the self-defined function should
25293 be used several times.
25296 \begin_layout Subsection
25301 \begin_layout Plain Layout
25310 \begin_layout Standard
25311 For limits there are defined besides
25321 \begin_layout Plain Layout
25341 furthermore the following functions:
25344 \begin_layout Standard
25346 \begin_inset Tabular
25347 <lyxtabular version="3" rows="5" columns="2">
25349 <column alignment="center" valignment="top" width="0">
25350 <column alignment="center" valignment="top" width="0">
25352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25355 \begin_layout Plain Layout
25361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25364 \begin_layout Plain Layout
25366 \begin_inset Note Note
25369 \begin_layout Plain Layout
25376 is only used as spacer.
25388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25391 \begin_layout Plain Layout
25399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25402 \begin_layout Plain Layout
25403 \begin_inset Formula $\varliminf$
25413 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25416 \begin_layout Plain Layout
25424 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25427 \begin_layout Plain Layout
25428 \begin_inset Formula $\varlimsup$
25438 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25441 \begin_layout Plain Layout
25449 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25452 \begin_layout Plain Layout
25453 \begin_inset Formula $\varprojlim$
25463 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25466 \begin_layout Plain Layout
25474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25477 \begin_layout Plain Layout
25478 \begin_inset Formula $\varinjlim$
25482 \begin_inset Formula $\raisebox{-2.5mm}{}$
25498 \begin_layout Standard
25499 \begin_inset VSpace medskip
25502 The limit is created by inserting a subscript.
25503 It is set right beside the function in an inline formula:
25506 \begin_layout Standard
25508 \begin_inset Tabular
25509 <lyxtabular version="3" rows="2" columns="2">
25511 <column alignment="center" valignment="top" width="0pt">
25512 <column alignment="center" valignment="top" width="0pt">
25514 <cell alignment="center" valignment="top" usebox="none">
25517 \begin_layout Plain Layout
25523 <cell alignment="center" valignment="top" usebox="none">
25526 \begin_layout Plain Layout
25527 \begin_inset space \hspace{}
25532 \begin_inset Note Note
25535 \begin_layout Plain Layout
25542 are used here as spacer.
25554 <cell alignment="center" valignment="top" usebox="none">
25557 \begin_layout Plain Layout
25566 \begin_layout Plain Layout
25579 \begin_layout Plain Layout
25593 <cell alignment="center" valignment="top" usebox="none">
25596 \begin_layout Plain Layout
25597 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25613 \begin_layout Standard
25614 In a displayed formula the limit is set below the formula, as usual:
25615 \begin_inset Formula \[
25623 \begin_layout Subsection
25628 \begin_layout Plain Layout
25629 Functions ! modulo-
25637 \begin_layout Standard
25638 The modulo-function is special, because it exists in four variants.
25641 \begin_layout Standard
25642 The variants in a displayed formula:
25643 \begin_inset Formula \begin{align*}
25644 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25645 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25646 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25647 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25648 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25655 \begin_layout Standard
25656 In an inline formula less space is set before the function names for all
25660 \begin_layout Section
25665 \begin_layout Plain Layout
25674 \begin_layout Subsection
25675 Special Characters in Mathematical Text
25678 \begin_layout Standard
25679 The following commands can only be used in mathematical text or in TeX-mode:
25682 \begin_layout Standard
25683 \begin_inset space \hfill{}
25687 \begin_inset Tabular
25688 <lyxtabular version="3" rows="8" columns="2">
25690 <column alignment="block" valignment="top" width="0">
25691 <column alignment="block" valignment="top" width="0">
25693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25696 \begin_layout Plain Layout
25702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25705 \begin_layout Plain Layout
25713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25716 \begin_layout Plain Layout
25724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25727 \begin_layout Plain Layout
25728 \begin_inset Formula $\textrm{œ}$
25738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25741 \begin_layout Plain Layout
25749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25752 \begin_layout Plain Layout
25753 \begin_inset Formula $\textrm{Œ}$
25763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25766 \begin_layout Plain Layout
25774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25777 \begin_layout Plain Layout
25778 \begin_inset Formula $\textrm{æ}$
25788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25791 \begin_layout Plain Layout
25799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25802 \begin_layout Plain Layout
25803 \begin_inset Formula $\textrm{Æ}$
25813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25816 \begin_layout Plain Layout
25824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25827 \begin_layout Plain Layout
25828 \begin_inset Formula $\textrm{\aa}$
25838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25841 \begin_layout Plain Layout
25848 \begin_layout Plain Layout
25855 \begin_layout Plain Layout
25876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25879 \begin_layout Plain Layout
25880 \begin_inset Formula $\textrm{Å}$
25890 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25893 \begin_layout Plain Layout
25901 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25904 \begin_layout Plain Layout
25905 \begin_inset Formula $\textrm{ı}$
25919 \begin_inset space \hfill{}
25923 \begin_inset Tabular
25924 <lyxtabular version="3" rows="8" columns="2">
25926 <column alignment="block" valignment="top" width="0">
25927 <column alignment="center" valignment="top" width="0">
25929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25932 \begin_layout Plain Layout
25934 \begin_inset Note Note
25937 \begin_layout Plain Layout
25939 \begin_inset space \thinspace{}
25942 mm is used for separation, because otherwise the output will be ¡ and ¿
25953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25956 \begin_layout Plain Layout
25964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25967 \begin_layout Plain Layout
25975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25978 \begin_layout Plain Layout
25979 \begin_inset Formula $\textrm{ø}$
25989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25992 \begin_layout Plain Layout
26000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26003 \begin_layout Plain Layout
26004 \begin_inset Formula $\textrm{Ø}$
26014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26017 \begin_layout Plain Layout
26025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26028 \begin_layout Plain Layout
26029 \begin_inset Formula $\textrm{ł}$
26039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26042 \begin_layout Plain Layout
26050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26053 \begin_layout Plain Layout
26054 \begin_inset Formula $\textrm{Ł}$
26064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26067 \begin_layout Plain Layout
26069 \begin_inset space \hspace{}
26077 \begin_layout Plain Layout
26091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26094 \begin_layout Plain Layout
26095 \begin_inset Formula $\textrm{!`}$
26105 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26108 \begin_layout Plain Layout
26110 \begin_inset space \hspace{}
26118 \begin_layout Plain Layout
26132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26135 \begin_layout Plain Layout
26136 \begin_inset Formula $\textrm{?`}$
26146 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26149 \begin_layout Plain Layout
26157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26160 \begin_layout Plain Layout
26161 \begin_inset Formula $\textrm{ȷ}$
26175 \begin_inset space \hfill{}
26181 \begin_layout Standard
26183 \begin_inset Formula $\textrm{\textrm{Å}}$
26187 \begin_inset Formula $\textrm{\textrm{Ø}}$
26190 can also be inserted via the math toolbar button
26191 \begin_inset Graphics
26192 filename ../images/math/digamma.png
26200 \begin_layout Standard
26201 An exception are the commands
26204 \begin_inset space \hspace{}
26213 \begin_inset space \hspace{}
26219 , because they can be inserted in LyX directly to text.
26222 \begin_layout Subsection
26224 \begin_inset CommandInset label
26226 name "sub:Accents-in-Text"
26234 \begin_layout Plain Layout
26243 \begin_layout Standard
26244 With the following commands all letters can be accented.
26245 The commands must be inserted in TeX-mode.
26248 \begin_layout Standard
26249 \begin_inset space \hfill{}
26253 \begin_inset Tabular
26254 <lyxtabular version="3" rows="8" columns="2">
26256 <column alignment="block" valignment="top" width="0">
26257 <column alignment="block" valignment="top" width="0">
26259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26262 \begin_layout Plain Layout
26268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26271 \begin_layout Plain Layout
26279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26282 \begin_layout Plain Layout
26286 \begin_inset Quotes grd
26294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26297 \begin_layout Plain Layout
26301 \begin_layout Plain Layout
26317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26320 \begin_layout Plain Layout
26328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26331 \begin_layout Plain Layout
26335 \begin_layout Plain Layout
26351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26354 \begin_layout Plain Layout
26361 \begin_layout Plain Layout
26375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26378 \begin_layout Plain Layout
26382 \begin_layout Plain Layout
26398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26401 \begin_layout Plain Layout
26409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26412 \begin_layout Plain Layout
26416 \begin_layout Plain Layout
26432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26435 \begin_layout Plain Layout
26442 \begin_layout Plain Layout
26456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26459 \begin_layout Plain Layout
26463 \begin_layout Plain Layout
26479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26482 \begin_layout Plain Layout
26489 \begin_layout Plain Layout
26503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26506 \begin_layout Plain Layout
26510 \begin_layout Plain Layout
26526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26529 \begin_layout Plain Layout
26536 \begin_layout Plain Layout
26550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26553 \begin_layout Plain Layout
26557 \begin_layout Plain Layout
26577 \begin_inset space \hfill{}
26581 \begin_inset Tabular
26582 <lyxtabular version="3" rows="8" columns="2">
26584 <column alignment="block" valignment="top" width="0">
26585 <column alignment="center" valignment="top" width="0">
26587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26590 \begin_layout Plain Layout
26596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26599 \begin_layout Plain Layout
26607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26610 \begin_layout Plain Layout
26617 \begin_layout Plain Layout
26631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26634 \begin_layout Plain Layout
26638 \begin_layout Plain Layout
26654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26657 \begin_layout Plain Layout
26665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26668 \begin_layout Plain Layout
26672 \begin_layout Plain Layout
26688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26691 \begin_layout Plain Layout
26698 \begin_layout Plain Layout
26709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26712 \begin_layout Plain Layout
26716 \begin_layout Plain Layout
26732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26735 \begin_layout Plain Layout
26743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26746 \begin_layout Plain Layout
26750 \begin_layout Plain Layout
26766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26769 \begin_layout Plain Layout
26776 \begin_layout Plain Layout
26790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26793 \begin_layout Plain Layout
26797 \begin_layout Plain Layout
26813 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26816 \begin_layout Plain Layout
26823 \begin_layout Plain Layout
26837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26840 \begin_layout Plain Layout
26844 \begin_layout Plain Layout
26860 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26863 \begin_layout Plain Layout
26870 \begin_layout Plain Layout
26884 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26887 \begin_layout Plain Layout
26891 \begin_layout Plain Layout
26911 \begin_inset space \hfill{}
26917 \begin_layout Standard
26918 \begin_inset VSpace medskip
26927 also two different characters can be accented.
26936 \begin_layout Plain Layout
26951 \begin_layout Plain Layout
26963 \begin_layout Standard
26976 can in combination with vowels directly be inserted with the keyboard without
26978 The same applies for the tilde
26982 \begin_layout Plain Layout
26983 This only applies for keyboards where the tilde is defined as accent.
26992 in combination with
27007 \begin_layout Standard
27050 and accents that are inserted directly with the keyboard are also available
27051 in mathematical text.
27052 For the other accents there are special math commands to be used in formulas,
27054 \begin_inset CommandInset ref
27056 reference "sub:Accents-for-one"
27063 \begin_layout Standard
27064 \begin_inset VSpace bigskip
27067 Furthermore, with the command
27077 \begin_layout Plain Layout
27085 all numbers and letters can be set into a circle, quasi accented with a
27086 circle, similar to the copyright symbol.
27089 \begin_layout Standard
27091 \begin_inset Tabular
27092 <lyxtabular version="3" rows="3" columns="2">
27094 <column alignment="center" valignment="top" width="0">
27095 <column alignment="center" valignment="top" width="0">
27097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27100 \begin_layout Plain Layout
27106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27109 \begin_layout Plain Layout
27111 \begin_inset Note Note
27114 \begin_layout Plain Layout
27121 is only used as spacer.
27133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27136 \begin_layout Plain Layout
27144 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27147 \begin_layout Plain Layout
27151 \begin_layout Plain Layout
27167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27170 \begin_layout Plain Layout
27181 raisebox{-1.5pt}{W}}
27186 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27189 \begin_layout Plain Layout
27190 \begin_inset Formula $\raisebox{4.5mm}{}$
27197 \begin_layout Plain Layout
27215 \begin_inset Formula $\raisebox{-2mm}{}$
27231 \begin_layout Standard
27232 One has to take care that the character fits in the circle.
27243 \begin_layout Plain Layout
27245 \begin_inset CommandInset ref
27247 reference "sub:Font-Sizes"
27256 specifies thereby the size of the circle.
27267 \begin_layout Plain Layout
27269 \begin_inset CommandInset ref
27271 reference "sub:Boxes-without-Frame"
27280 the character can be centered.
27283 \begin_layout Subsection
27288 \begin_layout Plain Layout
27297 \begin_layout Standard
27298 Minuscule numbers are created with the command
27308 \begin_layout Plain Layout
27317 The command can be used in formulas and in TeX-mode.
27318 The command scheme is:
27321 \begin_layout Standard
27326 oldstylenums{number}
27329 \begin_layout Standard
27334 oldstylenums{0123456789
27337 \begin_inset Formula $\oldstylenums{0123456789}$
27343 \begin_layout Subsection
27344 Miscellaneous special Characters
27345 \begin_inset CommandInset label
27347 name "sub:Miscellaneous-special-Characters"
27355 \begin_layout Plain Layout
27356 Special characters ! miscellaneous
27364 \begin_layout Standard
27365 The following characters can only be inserted to formulas by using commands:
27368 \begin_layout Standard
27370 \begin_inset Tabular
27371 <lyxtabular version="3" rows="4" columns="2">
27373 <column alignment="center" valignment="top" width="0">
27374 <column alignment="center" valignment="top" width="0">
27376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27379 \begin_layout Plain Layout
27385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27388 \begin_layout Plain Layout
27396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27399 \begin_layout Plain Layout
27406 \begin_layout Plain Layout
27420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27423 \begin_layout Plain Layout
27424 \begin_inset Formula $\mathcircumflex$
27434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27437 \begin_layout Plain Layout
27445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27448 \begin_layout Plain Layout
27449 \begin_inset Formula $\_$
27459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27462 \begin_layout Plain Layout
27467 \begin_layout Plain Layout
27482 \begin_layout Plain Layout
27495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27498 \begin_layout Plain Layout
27499 \begin_inset Formula $^{\circ}$
27515 \begin_layout Standard
27516 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27517 contains the following line
27521 \begin_layout Plain Layout
27522 More about this is described in
27523 \begin_inset CommandInset ref
27525 reference "sub:Text-Characters-in"
27537 \begin_layout Standard
27542 DeclareInputtext{176}{
27555 \begin_layout Section
27557 \begin_inset CommandInset label
27559 name "sec:Formula-Styles"
27567 \begin_layout Plain Layout
27576 \begin_layout Itemize
27577 There are two different alignment styles:
27581 \begin_layout Description
27582 Centered is the predefined standard
27585 \begin_layout Description
27586 Indented for this the option
27590 must be inserted in the menu
27592 Document\SpecialChar \menuseparator
27598 \begin_inset space ~
27604 \begin_layout Standard
27609 is used, the indentation can be adjusted with the length
27619 \begin_layout Plain Layout
27628 Should the distance be 15
27629 \begin_inset space \thinspace{}
27632 mm, the following command line is inserted in the LaTeX-preamble
27635 \begin_layout Standard
27645 \begin_layout Standard
27646 When no length is specified, the predefined value of 30
27647 \begin_inset space \thinspace{}
27654 \begin_layout Itemize
27655 And two different numbering styles:
27659 \begin_layout Description
27660 Right is the predefined standard
27663 \begin_layout Description
27664 Left for this the option
27668 must be inserted in the menu
27670 Document\SpecialChar \menuseparator
27676 \begin_inset space ~
27683 \begin_layout Standard
27692 can also be used together.
27693 In this case both options are inserted, separated by a comma.
27696 \begin_layout Standard
27697 The chosen styles are used for all displayed formulas of the document.
27698 When both, centered and indented formulas should be created in a document,
27704 The indented formulas are then set in a flalign environment, see
27705 \begin_inset CommandInset ref
27707 reference "sub:Flalign-Environment"
27714 \begin_layout Section
27716 \begin_inset CommandInset label
27718 name "sec:Multiline-Formulas"
27726 \begin_layout Plain Layout
27727 Formula ! multiline
27735 \begin_layout Subsection
27739 \begin_layout Standard
27740 In LyX multiline formulas are created by pressing
27745 arg "newline-insert newline"
27751 This creates either an
27753 eqnarray environment
27755 that is described in
27756 \begin_inset CommandInset ref
27758 reference "sub:Eqnarray-Environment"
27762 or, when the option
27764 Use AMS math package
27766 in the document settings is selected, an
27770 that is described in
27771 \begin_inset CommandInset ref
27773 reference "sub:Standard-align-Environment"
27780 \begin_layout Standard
27781 There are other multiline formula environments that can be created via the
27784 Insert\SpecialChar \menuseparator
27788 These environments are described in the following sections.
27791 \begin_layout Standard
27792 In all multiline formula environments a new line is created by pressing
27796 arg "newline-insert newline"
27800 To add or delete lines, the math toolbar buttons
27801 \begin_inset Graphics
27802 filename ../images/tabular-feature_append-row.png
27808 \begin_inset Graphics
27809 filename ../images/tabular-feature_delete-row.png
27814 , respectively, or the menu
27816 Edit\SpecialChar \menuseparator
27822 \begin_layout Subsubsection
27824 \begin_inset CommandInset label
27826 name "sub:Line-Separation"
27834 \begin_layout Plain Layout
27835 Formula ! multiline ! Line separation
27843 \begin_layout Standard
27844 There is sometimes not enough space in multiline formulas between the lines:
27845 \begin_inset Formula \begin{eqnarray*}
27846 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}\\
27847 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*}
27854 \begin_layout Standard
27855 In LaTeX additional line space is specified as optional argument of the
27857 This is not yet possible in LyX
27861 \begin_layout Plain Layout
27863 \begin_inset CommandInset href
27865 name "LyX-bug #1505"
27866 target "http://www.lyx.org/trac/ticket/1505"
27875 , therefore the whole formula must be inserted in TeX-mode.
27876 To add in our example space, the command
27884 is inserted at the end of the first line.
27889 \begin_layout Plain Layout
27896 \begin_layout Plain Layout
27898 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27901 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27908 \begin_layout Plain Layout
27912 left(B^{2}+x_{0}^{2}
27920 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27925 \begin_layout Plain Layout
27937 \begin_layout Standard
27938 \begin_inset VSpace bigskip
27941 To set the line separation for all lines in a formula, the length
27951 \begin_layout Plain Layout
27961 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27972 \begin_inset space \thinspace{}
27977 \begin_inset space \thinspace{}
27980 mm additional line separation as in the previous example, the command
27983 \begin_layout Standard
27993 \begin_layout Standard
27994 is inserted in TeX-mode before the formula.
27995 This requires that the LaTeX-package
28003 \begin_layout Plain Layout
28008 is part of every LaTeX standard installation.
28017 \begin_layout Plain Layout
28023 was loaded in LaTeX-preamble with the line
28026 \begin_layout Standard
28034 \begin_layout Standard
28039 \begin_layout Plain Layout
28051 \begin_inset Formula \begin{eqnarray*}
28052 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}\\
28053 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*}
28060 \begin_layout Standard
28064 \begin_layout Plain Layout
28075 To get back to the predefined distance,
28081 is set to the value 3
28082 \begin_inset space \thinspace{}
28088 \begin_layout Subsubsection
28090 \begin_inset CommandInset label
28092 name "sub:Column-Separation"
28100 \begin_layout Plain Layout
28101 Formula ! multiline ! Column separation
28109 \begin_layout Standard
28110 Multiline formulas form a matrix.
28111 A formula in the eqnarray environment is for example a matrix with three
28113 By changing the column separation in this environment, the space beside
28114 the relation sign can be changed.
28117 \begin_layout Standard
28118 The column separation is specified with the length
28128 \begin_layout Plain Layout
28137 \begin_inset Newline newline
28140 column separation = 2
28141 \begin_inset space \thinspace{}
28151 \begin_inset Newline newline
28157 \begin_layout Standard
28167 \begin_layout Standard
28168 inserted in TeX-mode, sets for all following formulas a column separation
28170 \begin_inset space \thinspace{}
28174 To get back to the predefined distance,
28181 \begin_inset space \thinspace{}
28187 \begin_layout Standard
28189 \begin_inset space \thinspace{}
28192 cm column separation:
28196 \begin_layout Plain Layout
28208 \begin_inset Formula \begin{eqnarray*}
28210 C & \ne & A\end{eqnarray*}
28214 A formula with the predefined column separation for matrices of 10
28215 \begin_inset space \thinspace{}
28222 \begin_layout Plain Layout
28234 \begin_inset Formula \begin{eqnarray*}
28236 C & \ne & A\end{eqnarray*}
28243 \begin_layout Subsubsection
28248 \begin_layout Plain Layout
28257 \begin_layout Standard
28258 Long formulas can be typeset using these methods:
28261 \begin_layout Itemize
28262 When one side of the equation is much shorther than the line width, this
28263 one is chosen for the left side and the right side is typeset over two
28265 \begin_inset Formula \begin{eqnarray}
28266 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 \\
28267 & & -\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}
28271 The minus sign at the beginning of the second line does normally not appear
28272 as operator because it is the first character of the line.
28273 Thus it would not be surrounded by space and could not be distinguished
28274 from the fraction bar.
28276 \begin_inset space \thinspace{}
28279 pt space was inserted behind the minus sign with the command
28289 \begin_layout Plain Layout
28297 \begin_inset CommandInset ref
28299 reference "sub:Variable-Space"
28312 \begin_layout Plain Layout
28323 \begin_layout Itemize
28324 When both sides of the equation are too long, the command
28334 \begin_layout Plain Layout
28343 It is inserted to the first column of the first line and effects that all
28344 further insertions overwrite the following columns:
28345 \begin_inset Formula \begin{eqnarray}
28346 \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 \\
28347 & & -\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 \\
28348 & & =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}
28352 After the insertion of
28358 , the cursor is in a purple box that is a bit shifted to the left from the
28360 In this the formula is inserted.
28361 \begin_inset Newline newline
28364 The content of the further lines is inserted to the second or another formula
28366 The greater the column number where it was inserted, the larger the indentation.
28367 \begin_inset VSpace medskip
28371 \begin_inset Newline newline
28375 \begin_inset Note Greyedout
28378 \begin_layout Plain Layout
28379 Note the following when using
28388 \begin_layout Itemize
28389 The formula doesn't use the full page width.
28391 \begin_inset space \thinspace{}
28395 \begin_inset space \space{}
28399 \begin_inset Formula $-B^{2}$
28402 is added to the first line in the above example, it would have been outside
28404 To better use the width, negative space can be inserted at the beginning
28408 \begin_layout Itemize
28409 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28414 \begin_layout Plain Layout
28415 \begin_inset CommandInset href
28417 name "LyX-bug #1429"
28418 target "http://www.lyx.org/trac/ticket/1429"
28427 One can only set the cursor at the beginning of the line and move it with
28436 \begin_layout Itemize
28437 Other methods to set long formulas are offered by the environments described
28439 \begin_inset CommandInset ref
28441 reference "sub:Multline-Environment"
28446 \begin_inset CommandInset ref
28448 reference "sub:Multiline-Formula-Parts"
28455 \begin_layout Subsubsection
28457 \begin_inset CommandInset label
28459 name "sub:Multiline-Brackets"
28467 \begin_layout Plain Layout
28468 Brackets ! for multiline expressions
28476 \begin_layout Standard
28477 For brackets spanning multiple lines the following problem occurs:
28478 \begin_inset Formula \begin{eqnarray*}
28479 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28480 & & \left.\cdots+B-D\right]\end{eqnarray*}
28487 \begin_layout Standard
28488 The closing bracket is smaller than the opening bracket because brackets
28489 with variable size may not span multiple lines.
28492 \begin_layout Standard
28493 To set the bracket size for the second line correctly, the first line is
28504 \begin_layout Plain Layout
28512 and the second line with
28520 \begin_layout Plain Layout
28534 \begin_inset CommandInset ref
28536 reference "sub:Automatic-Bracket-Size"
28551 \begin_layout Plain Layout
28577 \begin_layout Plain Layout
28596 \begin_layout Plain Layout
28615 \begin_layout Plain Layout
28627 \begin_inset Formula $\downarrow$
28636 \begin_layout Plain Layout
28644 is inserted, because the multiplication operator with its limits is the
28645 largest symbol in the first line and this should be the size for the bracket
28646 in the second line.
28649 \begin_layout Standard
28650 The result is this:
28651 \begin_inset Formula \begin{eqnarray*}
28652 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28653 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28660 \begin_layout Subsection
28664 \begin_layout Standard
28665 Align environments can be used for every kind of multiline formulas.
28666 They are specially useful to set several formulas side by side.
28669 \begin_layout Standard
28670 Align environments consist of columns.
28671 The odd columns are right aligned, the even ones left aligned.
28672 Every line in an Align environment can be numbered.
28675 \begin_layout Standard
28676 Align environments are created via the menu
28678 Insert\SpecialChar \menuseparator
28684 Edit\SpecialChar \menuseparator
28685 Math\SpecialChar \menuseparator
28686 Change Formula Type
28688 already existing formulas can be converted to Align environments.
28691 \begin_layout Standard
28692 To add or delete columns, the math toolbar buttons
28693 \begin_inset Graphics
28694 filename ../images/tabular-feature_append-column.png
28700 \begin_inset Graphics
28701 filename ../images/tabular-feature_delete-column.png
28706 , respectively, or the menu
28708 Edit\SpecialChar \menuseparator
28714 \begin_layout Subsubsection
28715 Standard align Environment
28716 \begin_inset CommandInset label
28718 name "sub:Standard-align-Environment"
28726 \begin_layout Plain Layout
28727 Formula ! multiline ! align environment
28735 \begin_layout Standard
28736 This Align environment is created by presssing
28739 arg "newline-insert newline"
28742 in a formula or by the menu
28744 Insert\SpecialChar \menuseparator
28745 Math\SpecialChar \menuseparator
28746 AMS align Environment
28751 \begin_layout Standard
28752 An example for two formulas set side by side, that are created with a four
28753 column align environment:
28754 \begin_inset Formula \begin{align*}
28755 A & =\sin(B) & C & =D\\
28756 C & \ne A & B & \ne D\end{align*}
28760 As it can be seen, the formulas in this environment are placed so as if
28769 \begin_layout Plain Layout
28777 \begin_inset CommandInset ref
28779 reference "sub:Variable-Space"
28790 before the first and after every even column.
28791 When the formula style
28797 \begin_layout Plain Layout
28799 \begin_inset CommandInset ref
28801 reference "sec:Formula-Styles"
28812 is used, the formula is set without the
28818 before the first column.
28821 \begin_layout Subsubsection
28822 Alignat Environment
28826 \begin_layout Plain Layout
28827 Formula ! multiline ! alignat environment
28835 \begin_layout Standard
28836 The alignat environment has no predefined column separation.
28837 It can be inserted manually with the spaces that are described
28838 \begin_inset CommandInset ref
28840 reference "sub:Space"
28847 \begin_layout Standard
28848 The above example in the alignat environment where 1
28849 \begin_inset space \thinspace{}
28852 cm space was inserted at the beginning of the second formula:
28853 \begin_inset Formula \begin{alignat*}{2}
28854 A & =\sin(B) & \hspace{1cm}C & =D\\
28855 C & \ne A & B & \ne D\end{alignat*}
28859 Because the column separation can be set separately for every column, this
28860 environment is especially suitable to set three and more formulas side
28864 \begin_layout Subsubsection
28865 Flalign Environment
28866 \begin_inset CommandInset label
28868 name "sub:Flalign-Environment"
28876 \begin_layout Plain Layout
28877 Formula ! multiline ! flalign environment
28885 \begin_layout Standard
28886 In this environment the first two columns are always set as much as possible
28887 to the left and the last two ones to the right.
28889 \begin_inset Formula \begin{flalign*}
28890 A & =1 & B & =2 & C & =3\\
28891 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28898 \begin_layout Standard
28899 By creating a flalign environment with an odd number of columns where an
28900 empty TeX-brace is inserted to the last column, several formulas in a document
28901 can be set to the left, although the formula style
28906 As example the indented formula
28907 \begin_inset CommandInset ref
28909 reference "eq:VolInt"
28914 \begin_inset Formula \begin{flalign}
28915 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28919 The first two columns contain the formula.
28920 To indent it as with the formula style
28925 \begin_inset space \thinspace{}
28928 pt space was inserted at the beginning of the first column.
28931 \begin_layout Subsection
28932 Eqnarray Environment
28933 \begin_inset CommandInset label
28935 name "sub:Eqnarray-Environment"
28943 \begin_layout Plain Layout
28944 Formula ! multiline ! eqnarray environment
28952 \begin_layout Standard
28953 When this environment has been created, three blue boxes appear.
28954 The content of the first box is right aligned, the content of the last
28956 The content of the middle box appears centered and a bit smaller, because
28957 it is designed to insert there only relation characters.
28958 \begin_inset Formula \begin{eqnarray*}
28959 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28961 A & = & A\end{eqnarray*}
28968 \begin_layout Subsection
28973 \begin_layout Plain Layout
28974 Formula ! multiline ! gather environment
28982 \begin_layout Standard
28983 This environment consists of only one centered column.
28984 Every line can be numbered.
28985 \begin_inset Formula \begin{gather}
28987 X=\textrm{-}1\end{gather}
28994 \begin_layout Subsection
28995 Multline Environment
28996 \begin_inset CommandInset label
28998 name "sub:Multline-Environment"
29006 \begin_layout Plain Layout
29007 Formula ! multiline ! multline environment
29015 \begin_layout Standard
29016 The multline environment consists, like the gather environment, of only
29018 But the first line is left aligned, the last one right aligned.
29019 All other lines are centered.
29020 Therefore this environment is suitable for long formulas.
29022 \begin_inset CommandInset ref
29024 reference "eq:lefteqn"
29028 in the multline environment:
29029 \begin_inset Formula \begin{multline}
29030 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}\\
29031 -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}\\
29032 =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}
29039 \begin_layout Standard
29040 In the output only the last (first) line of a multline environment appears
29041 numbered when the document numbering is right (left).
29045 \begin_layout Plain Layout
29046 numbering styles see
29047 \begin_inset CommandInset ref
29049 reference "sec:Formula-Styles"
29061 \begin_layout Standard
29070 \begin_layout Plain Layout
29088 \begin_layout Plain Layout
29098 a centered line can be right or left aligned, respectively.
29099 The commands are used as follows:
29102 \begin_layout Standard
29107 shoveright{line content}
29113 shoveleft{line content}
29116 \begin_layout Standard
29117 \begin_inset VSpace medskip
29128 \begin_layout Plain Layout
29138 specifies the distance of the first line from the left page margin.
29139 Predefined is the length 0
29140 \begin_inset space \thinspace{}
29146 \begin_layout Standard
29147 As example the above formula where the command
29150 \begin_layout Standard
29160 \begin_layout Standard
29161 was inserted in TeX-mode before:
29165 \begin_layout Plain Layout
29177 \begin_inset Formula \begin{multline}
29178 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}\\
29179 \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}}\\
29180 =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}
29188 \begin_layout Plain Layout
29199 The second line was left aligned using
29208 \begin_layout Subsection
29209 Multiline Formula Parts
29210 \begin_inset CommandInset label
29212 name "sub:Multiline-Formula-Parts"
29220 \begin_layout Plain Layout
29221 Formula ! multiline ! formula parts
29229 \begin_layout Standard
29230 To display only parts of a formula with multiple lines, one of the following
29231 environments are used:
29248 They can be inserted via the menu
29250 Insert\SpecialChar \menuseparator
29253 or by using the commands described in this section.
29256 \begin_layout Standard
29257 The first three have the same properties as the corresponding multiline
29258 formula environments, but it is possible to set further formula parts beside
29261 \begin_inset Formula \[
29262 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29263 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29264 \right\} \textrm{Uncertainty relations}\]
29271 \begin_layout Standard
29272 To get this formula, a displayed formula is created where the command
29280 \begin_layout Plain Layout
29291 A purple box appears around the blue formula box where now columns and
29292 lines can be added.
29293 Outside the multiline environment other formula parts can be set, like
29297 \begin_layout Standard
29298 The aligned environment is also suitable for long formulas whose lines are
29299 horizontally aligned.
29300 Using aligned in a displayed formula has the advantage that the formula
29301 number is vertically centered behind the lines.
29303 \begin_inset CommandInset ref
29305 reference "eq:shortlong"
29309 in the aligned environment:
29310 \begin_inset Formula \begin{equation}
29311 \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}|}\\
29312 & -\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}
29320 \begin_layout Standard
29321 To use the environments
29343 \begin_layout Plain Layout
29361 \begin_layout Plain Layout
29379 \begin_layout Plain Layout
29387 are inserted, respectively.
29388 The split environment has the same properties as the aligned environment
29389 but it can only have two columns.
29392 \begin_layout Subsection
29393 Text in multiline Formulas
29394 \begin_inset CommandInset label
29396 name "sub:Text-in-multiline"
29404 \begin_layout Plain Layout
29414 \begin_layout Plain Layout
29415 Formula ! multiline ! text
29423 \begin_layout Standard
29424 In the Align environments, and the multline and gather environment, text
29425 can be inserted that will appear in a separate line and doesn't affect
29426 the column alignment.
29427 To do this, the command
29435 \begin_layout Plain Layout
29445 is used in the following scheme:
29448 \begin_layout Standard
29456 \begin_layout Standard
29457 The text should not be longer than a line because it cannot be hyphenated.
29458 As LyX doesn't yet support
29464 directly, the text is written as mathematical text.
29471 must hereby be at the beginning of a line and appears in the output above
29473 An example where the text was inserted at the beginning of the second line:
29474 \begin_inset Formula \begin{align}
29475 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29476 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29483 \begin_layout Section
29488 \begin_layout Plain Layout
29498 \begin_layout Plain Layout
29499 Formula ! numbering|see
29503 \begin_layout Plain Layout
29514 \begin_layout Plain Layout
29529 \begin_layout Subsection
29533 \begin_layout Standard
29534 Numbered formulas can be created with the menu
29536 Insert\SpecialChar \menuseparator
29537 Math\SpecialChar \menuseparator
29539 \begin_inset space ~
29547 \begin_inset space ~
29553 Existing formulas can be numbered with the menu
29555 Edit\SpecialChar \menuseparator
29556 Math\SpecialChar \menuseparator
29558 \begin_inset space ~
29566 arg "math-number-toggle"
29570 The formula number is displayed in LyX behind the formula as number sign
29572 The number sign is replaced in the output by the formula number.
29575 \begin_layout Standard
29576 When numbering is turned on in multiline formulas, all lines will be numbered.
29577 But the numbering can be controlled with the menu
29579 Edit\SpecialChar \menuseparator
29580 Math\SpecialChar \menuseparator
29582 \begin_inset space ~
29586 \begin_inset space ~
29590 \begin_inset space ~
29598 arg "math-number-line-toggle"
29604 \begin_layout Standard
29605 Except for inline formulas, all formulas can be numbered with two different
29607 \begin_inset CommandInset ref
29609 reference "sec:Formula-Styles"
29616 \begin_layout Subsection
29621 \begin_layout Plain Layout
29622 Cross-references ! to formulas
29630 \begin_layout Standard
29631 All labeled formulas can be cross-referenced.
29632 A label is added by the menu
29634 Insert\SpecialChar \menuseparator
29637 or the toolbar button
29638 \begin_inset Graphics
29639 filename ../images/label-insert.png
29645 The cursor must hereby be inside a displayed formula.
29646 A dialog pops up displaying the prefix
29651 The label is inserted there behind the prefix.
29652 The predefined prefix means
29653 \begin_inset Quotes eld
29657 \begin_inset Quotes erd
29660 and makes it easier to find labels in large documents because it marks
29661 it as formula label to divide it from e.
29662 \begin_inset space \thinspace{}
29666 \begin_inset space \space{}
29670 To change a label, the menu
29672 Insert\SpecialChar \menuseparator
29678 \begin_layout Standard
29679 The name of the label is displayed in LyX within two parentheses behind
29681 A formula with a label is always numbered.
29684 \begin_layout Standard
29685 Cross-references are inserted via the menu
29687 Insert\SpecialChar \menuseparator
29690 or with the toolbar button
29691 \begin_inset Graphics
29692 filename ../images/dialog-show-new-inset_ref.png
29698 A formula cross-reference appears in the output as formula number.
29699 When in the cross-reference dialog window the format
29703 is chosen, the cross-reference appears in the output as formula number
29705 \begin_inset Newline newline
29708 By right-clicking on a cross-reference in LyX, one jumps to the formula
29709 that is referenced.
29712 \begin_layout Standard
29713 Here are as examples cross-references to formulas of the following subsections:
29714 \begin_inset Note Note
29717 \begin_layout Plain Layout
29718 Note the different cross-reference types.
29726 \begin_layout Standard
29728 \begin_inset CommandInset ref
29735 \begin_inset CommandInset ref
29743 \begin_inset CommandInset ref
29749 ) big Latin letters are used for the numbering in contrary to (
29750 \begin_inset CommandInset ref
29759 \begin_layout Standard
29760 \begin_inset VSpace medskip
29763 When the argument of
29771 \begin_layout Plain Layout
29779 \begin_inset CommandInset ref
29781 reference "sub:User-defined-Numbering"
29792 contains a box like in
29793 \begin_inset CommandInset ref
29795 reference "sub:Paragraph-Boxes"
29799 , the formula cannot be referenced.
29802 \begin_layout Subsection
29807 \begin_layout Plain Layout
29808 Formula numbering ! subnumbering
29816 \begin_layout Standard
29817 With the help of the commands
29821 begin{subequations}
29829 formulas can be subnumbered.
29830 Both commands are inserted in TeX-mode.
29833 \begin_layout Standard
29835 \begin_inset Formula \begin{equation}
29836 A=C-B\label{eq:a}\end{equation}
29844 \begin_layout Plain Layout
29848 addtocounter{equation}{-1}
29857 \begin_layout Plain Layout
29861 begin{subequations}
29867 \begin_inset VSpace -5mm
29871 \begin_inset Formula \begin{equation}
29872 B=C-A\label{eq:b}\end{equation}
29877 \begin_inset Formula \begin{equation}
29878 C=A+B\label{eq:c}\end{equation}
29885 \begin_layout Standard
29889 \begin_layout Plain Layout
29901 \begin_layout Standard
29902 To create the example, the following is done:
29905 \begin_layout Enumerate
29906 first formula is inserted
29909 \begin_layout Enumerate
29914 addtocounter{equation}{-1}
29916 begin{subequations}
29920 \begin_layout Plain Layout
29929 \begin_inset Newline newline
29934 is inserted after the first formula
29937 \begin_layout Enumerate
29938 second formula is inserted
29941 \begin_layout Enumerate
29942 third formula is inserted
29945 \begin_layout Enumerate
29952 is inserted after the third formula
29955 \begin_layout Standard
29956 Every formula between the commands
29968 is subnumbered as a, b,
29969 \begin_inset Newline linebreak
29972 c, \SpecialChar \ldots{}
29973 For multiline formulas every line will be subnumbered.
29974 All subnumbered formulas are treated as
29979 But as every numbered formula increases the counter
29983 by one, the command
29989 is needed to decrease it.
29990 Otherwise the formulas
29991 \begin_inset CommandInset ref
29998 \begin_inset CommandInset ref
30005 \begin_inset CommandInset ref
30011 would be numbered as
30012 \begin_inset CommandInset ref
30019 \begin_inset CommandInset ref
30026 \begin_inset CommandInset ref
30035 \begin_layout Standard
30036 By inserting the commands in TeX-mode, a space is created between the first
30039 \begin_inset space \thinspace{}
30042 mm vertical space is inserted after the command
30046 begin{subequations}
30049 When the formula style
30055 \begin_layout Plain Layout
30057 \begin_inset CommandInset ref
30059 reference "sec:Formula-Styles"
30071 \begin_inset space \thinspace{}
30074 mm space is inserted instead.
30077 \begin_layout Standard
30078 Here is an example for a multiline formula where the numbering was turned
30079 off for the second line:
30083 \begin_layout Plain Layout
30087 begin{subequations}
30093 \begin_inset Formula \begin{eqnarray}
30094 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30095 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30096 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
30104 \begin_layout Plain Layout
30116 \begin_layout Subsection
30117 User-defined Numbering
30118 \begin_inset CommandInset label
30120 name "sub:User-defined-Numbering"
30128 \begin_layout Plain Layout
30129 Formula numbering ! user-defined
30137 \begin_layout Standard
30141 \begin_layout Plain Layout
30142 Formula numbering ! self-defined delimiters
30147 With the standard numbering parentheses are set around the formula number.
30148 To replace the parentheses for example by vertical bars, the following
30149 line is added to the LaTeX-preamble:
30152 \begin_layout Standard
30164 \begin_inset Note Note
30167 \begin_layout Plain Layout
30168 This macro is already declared in the LaTeX-preamble for testing.
30169 To activate it, remove the percent sign at the beginning.
30177 \begin_layout Standard
30178 To use other characters, the vertical bars besides the
30182 are replaced by one ore more characters.
30183 To get only the formula number the vertical bars are omitted.
30186 \begin_layout Standard
30187 \begin_inset VSpace bigskip
30190 When there should be an expression of your choice instead of the consecutive
30191 formula number in parentheses behind the formula, the command
30201 \begin_layout Plain Layout
30210 \begin_inset Formula \begin{equation}
30211 A+B=C\tag{something}\label{eq:tag}\end{equation}
30215 In this example the command
30223 \begin_layout Plain Layout
30234 was inserted to the formula.
30237 \begin_layout Standard
30246 \begin_layout Plain Layout
30257 is inserted instead, the star prevents the parentheses around the expression:
30258 \begin_inset Formula \[
30259 A+B=C\tag*{something}\]
30266 \begin_layout Standard
30267 \begin_inset VSpace bigskip
30270 To restart the formula numbering with new document parts or sections, the
30271 following command is used:
30274 \begin_layout Standard
30279 @addtoreset{equation}{part}
30285 \begin_layout Plain Layout
30290 \begin_layout Plain Layout
30301 \begin_layout Plain Layout
30314 \begin_layout Plain Layout
30325 \begin_layout Plain Layout
30338 \begin_inset Newline newline
30342 \begin_inset Newline newline
30349 @addtoreset{equation}{section}
30352 \begin_layout Standard
30353 To be able to use these commands in TeX-mode, the
30354 \begin_inset Quotes eld
30358 \begin_inset Quotes erd
30361 character has to be made
30362 \begin_inset Quotes eld
30366 \begin_inset Quotes erd
30369 for LaTeX using the command
30383 So the command sequence in TeX-mode is:
30386 \begin_layout Standard
30392 \begin_inset Newline newline
30397 @addtoreset{equation}{section}
30398 \begin_inset Newline newline
30406 \begin_layout Standard
30407 In the LaTeX-preamble
30419 can be omitted as they are automatically internally inserted by LyX.
30422 \begin_layout Standard
30437 \begin_layout Plain Layout
30442 is part of the LaTeX-package
30450 \begin_layout Plain Layout
30451 Packages ! carlisle
30456 that is part of every LaTeX standard installation.
30465 \begin_layout Plain Layout
30466 Packages ! remreset
30471 has to be loaded in the LaTeX-preamble with the line
30474 \begin_layout Standard
30479 usepackage{remreset}
30482 \begin_layout Standard
30493 \begin_layout Plain Layout
30498 \begin_layout Plain Layout
30509 \begin_layout Plain Layout
30522 \begin_layout Plain Layout
30533 \begin_layout Plain Layout
30545 can be used with the same scheme as
30554 \begin_layout Standard
30555 \begin_inset VSpace bigskip
30558 Sometimes formulas should be numbered in the following form:
30561 \begin_layout Standard
30564 (section number.formula number)
30567 \begin_layout Standard
30568 The formula number should start with every section with
30569 \begin_inset Quotes eld
30573 \begin_inset Quotes erd
30579 \begin_layout Standard
30580 For this case there is the command
30590 \begin_layout Plain Layout
30598 , which is used with the following scheme:
30601 \begin_layout Standard
30606 numberwithin{counter}{sectioning}
30609 \begin_layout Standard
30610 Counter denotes what kind of numbering is affected, sectioning denotes what
30611 number is before the dot.
30614 \begin_layout Standard
30615 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30618 \begin_layout Standard
30623 numberwithin{equation}{section}
30626 \begin_layout Standard
30627 This is the result:
30631 \begin_layout Plain Layout
30635 numberwithin{equation}{section}
30641 \begin_inset Formula \begin{equation}
30642 A+B=C\end{equation}
30649 \begin_layout Standard
30651 \begin_inset space \thinspace{}
30655 \begin_inset space \space{}
30658 tables so that the number of the part is the sectioning,
30659 \begin_inset Newline newline
30666 numberwithin{table}{part}
30671 \begin_layout Standard
30672 To go back to the standard numbering or to prevent this kind of numbering
30673 when it is defined by the document class, the following command is inserted
30674 as TeX-Code or to the LaTeX-preamble:
30677 \begin_layout Standard
30690 \begin_layout Plain Layout
30704 \begin_layout Plain Layout
30720 \begin_inset Newline newline
30728 \begin_inset Newline newline
30740 \begin_layout Standard
30747 uses internally the command
30753 , described above, that also needs to be reverted.
30757 \begin_layout Plain Layout
30764 \begin_layout Plain Layout
30768 @removefromreset{equation}{section}
30771 \begin_layout Plain Layout
30783 \begin_layout Subsection
30784 Numbering with Roman Numbers and Letters
30788 \begin_layout Plain Layout
30789 Formula numbering ! with letters
30798 \begin_layout Plain Layout
30799 Formula numbering ! with Roman numbers
30807 \begin_layout Standard
30808 Formulas can also be numbered with Roman numbers and Latin letters.
30809 To number for example with small Roman numbers, the command
30812 \begin_layout Standard
30824 \begin_layout Standard
30825 is inserted before the formula in TeX-mode.
30836 \begin_layout Plain Layout
30844 redefines the predefined command
30860 \begin_layout Plain Layout
30867 has the same scheme like the command
30873 that is described in
30874 \begin_inset CommandInset ref
30876 reference "sub:The-Command-newcommand"
30889 is the formula counter.
30896 is used as prefix for a counter, the value of the counter is output as
30898 When a formula is numbered, LaTeX sets internally the command
30904 behind the formula.
30913 \begin_layout Plain Layout
30923 outputs the counter as small Roman number.
30926 \begin_layout Standard
30927 All formulas behind the command
30937 are now numbered Roman.
30938 To switch to numbering with big Roman numbers, the command is inserted
30955 \begin_layout Plain Layout
30967 \begin_inset Quotes eld
30971 \begin_inset Quotes erd
30974 with small Latin letters there is the command
30984 \begin_layout Plain Layout
30992 , for big ones there is the command
31002 \begin_layout Plain Layout
31015 \begin_layout Standard
31016 \begin_inset Note Greyedout
31019 \begin_layout Plain Layout
31024 Only maximal 26 formulas can be numbered with Latin letters in one document.
31032 \begin_layout Standard
31036 \begin_layout Plain Layout
31052 \begin_layout Standard
31053 \begin_inset Formula \begin{equation}
31054 A=\textrm{small roman}\end{equation}
31062 \begin_layout Plain Layout
31076 \begin_inset Formula \begin{equation}
31077 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
31085 \begin_layout Plain Layout
31099 \begin_inset Formula \begin{equation}
31100 C=\textrm{small Latin}\end{equation}
31108 \begin_layout Plain Layout
31122 \begin_inset Formula \begin{equation}
31123 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31130 \begin_layout Standard
31131 To switch back to the default numbering, insert the command:
31134 \begin_layout Standard
31147 \begin_layout Plain Layout
31158 \begin_layout Standard
31162 \begin_layout Plain Layout
31176 \begin_inset Formula \begin{equation}
31177 E=\textrm{Arabic}\end{equation}
31184 \begin_layout Standard
31185 \begin_inset VSpace medskip
31188 As you see, formulas are numbered serially independent from the numbering
31190 When then numbering should start with
31191 \begin_inset Quotes eld
31195 \begin_inset Quotes erd
31198 when the style is changed, new equation counters have to be defined.
31199 A description about this can be found in the file
31200 \begin_inset CommandInset href
31202 name "Formula-numbering.lyx"
31203 target "run:Formula-numbering.lyx"
31210 \begin_layout Section
31211 Chemical Symbols and Equations
31212 \begin_inset CommandInset label
31214 name "sub:Chemical-Symbols-and"
31222 \begin_layout Plain Layout
31223 Chemical characters ! Symbols
31232 \begin_layout Plain Layout
31242 \begin_layout Plain Layout
31251 \begin_layout Standard
31252 An example text from chemistry:
31255 \begin_layout Quote
31257 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31260 -ion reacts with two
31261 \begin_inset Formula $\mathrm{Na^{+}}$
31264 -ions to sodium sulfate
31265 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31269 The chemical equation for this is:
31270 \begin_inset Formula \begin{equation}
31271 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31278 \begin_layout Standard
31279 This chemical equation can directly be created as formula.
31280 To avoid that the symbols appear italic, everything is highlighted and
31281 changed by the shortcut
31287 to the upright font style.
31291 \begin_layout Plain Layout
31297 \begin_inset CommandInset ref
31299 reference "sub:Font-Styles"
31311 \begin_layout Standard
31312 A more convenient way to typeset chemical formulas is to use the command
31323 \begin_layout Plain Layout
31331 that is available when the LaTeX-package
31339 \begin_layout Plain Layout
31352 to a formula a new blue box appears where chemical formulas can be inserted
31353 in an intuitive way.
31356 \begin_layout Standard
31358 \begin_inset Tabular
31359 <lyxtabular version="3" rows="9" columns="2">
31361 <column alignment="center" valignment="top" width="0">
31362 <column alignment="center" valignment="top" width="0">
31364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31367 \begin_layout Plain Layout
31373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31376 \begin_layout Plain Layout
31378 \begin_inset Note Note
31381 \begin_layout Plain Layout
31388 is only used as spacer.
31400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31403 \begin_layout Plain Layout
31410 \begin_layout Plain Layout
31424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31427 \begin_layout Plain Layout
31428 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31441 \begin_layout Plain Layout
31448 \begin_layout Plain Layout
31462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31465 \begin_layout Plain Layout
31466 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31479 \begin_layout Plain Layout
31486 \begin_layout Plain Layout
31500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31503 \begin_layout Plain Layout
31504 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31517 \begin_layout Plain Layout
31524 \begin_layout Plain Layout
31538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31541 \begin_layout Plain Layout
31542 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31555 \begin_layout Plain Layout
31562 \begin_layout Plain Layout
31577 \begin_layout Plain Layout
31592 \begin_layout Plain Layout
31606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31609 \begin_layout Plain Layout
31610 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31623 \begin_layout Plain Layout
31630 \begin_layout Plain Layout
31640 \begin_inset Formula $\downarrow$
31644 \begin_inset Formula $\to$
31652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31655 \begin_layout Plain Layout
31656 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31669 \begin_layout Plain Layout
31676 \begin_layout Plain Layout
31689 \begin_layout Plain Layout
31702 \begin_layout Plain Layout
31715 \begin_layout Plain Layout
31728 \begin_layout Plain Layout
31742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31745 \begin_layout Plain Layout
31746 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31759 \begin_layout Plain Layout
31766 \begin_layout Plain Layout
31779 \begin_layout Plain Layout
31792 \begin_layout Plain Layout
31805 \begin_layout Plain Layout
31822 \begin_layout Plain Layout
31836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31839 \begin_layout Plain Layout
31840 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
31856 \begin_layout Standard
31857 \begin_inset Note Greyedout
31860 \begin_layout Plain Layout
31865 Inserting a formula to a
31871 box will lead to LaTeX errors.
31872 In this case TeX code has to be used like for
31886 \begin_layout Plain Layout
31907 \begin_layout Standard
31914 the command for equation
31915 \begin_inset space ~
31919 \begin_inset CommandInset ref
31921 reference "eq:chem-reaction"
31926 \begin_inset Newline newline
31937 \begin_layout Plain Layout
31950 \begin_layout Plain Layout
31963 \begin_layout Plain Layout
31976 \begin_layout Plain Layout
31989 \begin_layout Plain Layout
32002 \begin_layout Plain Layout
32014 \begin_layout Standard
32015 To create multiline chemical equations first a multiline formula is created
32017 \begin_inset CommandInset ref
32019 reference "sec:Multiline-Formulas"
32024 Afterwards the command
32030 is used in every small blue box of the formula.
32032 \begin_inset CommandInset ref
32034 reference "eq:TEOS-reaction-1"
32039 \begin_inset CommandInset ref
32041 reference "eq:TEOS-reaction-2"
32045 are an example of a multi-stage chemical reaction where every equation
32046 has its own number.
32047 \begin_inset Formula \begin{eqnarray}
32048 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32049 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}\end{eqnarray}
32056 \begin_layout Standard
32067 package provides the command
32077 \begin_layout Plain Layout
32085 that has to be used for special cases.
32086 For more information about
32092 and more examples have a look at the documentation of
32097 \begin_inset CommandInset citation
32106 \begin_layout Standard
32107 \begin_inset Newpage newpage
32113 \begin_layout Section
32117 \begin_layout Standard
32118 LyX supports two types of commutative diagrams:
32126 that are explained in the following.
32129 \begin_layout Subsection
32134 \begin_layout Plain Layout
32143 \begin_layout Standard
32144 Diagrams of this type visualize relations by vertical and horizontal lines
32146 \begin_inset Formula \[
32147 \begin{CD}A@>>>B@>>>C\\
32149 F@<<<E@<<<D\end{CD}\]
32156 \begin_layout Standard
32157 To get them, the command
32165 \begin_layout Plain Layout
32175 is inserted to a formula.
32176 A blue box appears with two dashed lines where further commands can be
32181 arg "newline-insert newline"
32184 a new line is created.
32185 Horizontal relations are inserted in odd, vertical in even formula lines.
32188 \begin_layout Standard
32189 To create the relations there are the following commands:
32192 \begin_layout Itemize
32197 creates a left arrow,
32208 \begin_layout Itemize
32213 creates an up arrow,
32221 a vertical equal sign
32224 \begin_layout Itemize
32230 is a placeholder for non-existent relations
32233 \begin_layout Standard
32234 All arrows can be labeled as follows:
32237 \begin_layout Itemize
32238 Is text inserted between the first and second < or >, resp., it is placed
32240 When it is inserted between the second and third one, it appears under
32244 \begin_layout Itemize
32245 When text for vertical arrows is inserted between the first and second A
32246 or V, resp., it is placed left beside the arrow.
32247 When it is inserted between the second and third one, it appears right
32249 If the text contains an A or V, these letters must be set into a TeX-brace.
32252 \begin_layout Standard
32253 As example a diagram with all possible relations:
32256 \begin_layout Standard
32257 \begin_inset Formula \[
32258 \begin{CD}A@>j>>B@>>k>C@=F\\
32260 D@<<j<E@>k>>F@=C\end{CD}\]
32267 \begin_layout Standard
32268 The command for this is:
32269 \begin_inset Newline newline
32280 \begin_layout Plain Layout
32289 A@>j>>B@>>k>C@=F Ctrl+Return
32290 \begin_inset Newline newline
32297 \begin_layout Plain Layout
32312 \begin_layout Plain Layout
32325 \begin_layout Plain Layout
32337 \begin_inset Formula $\to$
32343 \begin_inset Newline newline
32350 \begin_layout Plain Layout
32365 \begin_layout Plain Layout
32378 \begin_layout Plain Layout
32388 \begin_layout Subsection
32393 \begin_layout Plain Layout
32394 Diagrams ! xymatrix
32402 \begin_layout Standard
32403 To be able to use xymatrices, the LaTeX-package
32408 A xymatrix is created by inserting the command
32415 Then you are able to add new matrix columns and rows like for normal matrices,
32417 \begin_inset CommandInset ref
32419 reference "sec:Matrices"
32426 \begin_layout Standard
32427 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32429 All possibilities to create commutative diagrams and decorations are explained
32434 that you find in the menu
32436 Help\SpecialChar \menuseparator
32438 \begin_inset space ~
32441 Manuals\SpecialChar \menuseparator
32443 \begin_inset space ~
32451 \begin_layout Section
32452 User-defined Commands
32456 \begin_layout Plain Layout
32457 User-defined commands
32465 \begin_layout Standard
32466 \begin_inset Note Greyedout
32469 \begin_layout Plain Layout
32474 The names of user-defined commands and macros may only consist of Latin
32483 \begin_layout Subsection
32487 \begin_inset CommandInset label
32489 name "sub:The-Command-newcommand"
32497 \begin_layout Plain Layout
32498 User-defined commands !
32509 \begin_layout Plain Layout
32520 \begin_layout Standard
32521 Many LaTeX-commands are too long to be used frequently.
32522 But it is possible to define with the command
32528 new shorter commands.
32531 \begin_layout Standard
32532 The command scheme of
32541 \begin_layout Standard
32546 newcommand{new command name}[number of arguments][optional
32551 \begin_inset Newline newline
32558 \begin_layout Plain Layout
32573 \begin_layout Plain Layout
32580 {command definition}
32583 \begin_layout Standard
32584 \begin_inset Note Greyedout
32587 \begin_layout Plain Layout
32592 Assure that the name of the new command is not already used in your document
32593 or by LaTeX-packages that you use.
32594 When you for example define the command
32606 , you get an error message because
32612 is already defined as command for
32613 \begin_inset Quotes eld
32617 \begin_inset Formula $\le$
32621 \begin_inset Quotes erd
32632 \begin_layout Standard
32633 The number of arguments is an integer in the range 0
32634 \begin_inset space \thinspace{}
32638 \begin_inset space \thinspace{}
32641 9 and specifies how many arguments the new command should have.
32642 With the optional value a value for an optional argument can be predefined.
32643 When this is done, the
32651 rgument of the new command is automatically an optional one.
32654 \begin_layout Standard
32655 Here are some examples:
32658 \begin_layout Itemize
32659 To define the command
32671 , the LaTeX-preamble line is:
32672 \begin_inset VSpace medskip
32676 \begin_inset Newline newline
32690 \begin_layout Itemize
32691 To define the command
32703 , the argument (that should be underlined) must be taken into account.
32704 For this the preamble line is:
32705 \begin_inset VSpace medskip
32709 \begin_inset Newline newline
32723 \begin_inset VSpace medskip
32727 \begin_inset Newline newline
32734 acts as argument placeholder, the
32738 behind it denotes that it is the placeholder for the first argument.
32741 \begin_layout Itemize
32749 \begin_inset space \thinspace{}
32753 \begin_inset space \space{}
32763 \begin_inset VSpace medskip
32767 \begin_inset Newline newline
32778 framebox#1#2{$#3$}}
32781 \begin_inset VSpace medskip
32785 \begin_inset Newline newline
32788 The two Dollar signs creates the extra formula needed for
32795 \begin_inset CommandInset ref
32797 reference "sub:Boxes-with-Frame"
32804 \begin_layout Itemize
32805 To create a new command for
32811 where the color for the box needn't to be specified, the argument for the
32812 color is defined optional:
32813 \begin_inset VSpace medskip
32817 \begin_inset Newline newline
32828 fcolorbox{#2}{#1}{$#3$}}
32831 \begin_inset VSpace medskip
32835 \begin_inset Newline newline
32838 When the color is not specified when using
32844 , the predefined color
32851 \begin_layout Standard
32852 A test of the new defined commands:
32855 \begin_layout Standard
32857 \begin_inset Tabular
32858 <lyxtabular version="3" rows="6" columns="2">
32860 <column alignment="center" valignment="top" width="0">
32861 <column alignment="center" valignment="top" width="0">
32863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32866 \begin_layout Plain Layout
32872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32875 \begin_layout Plain Layout
32877 \begin_inset Note Note
32880 \begin_layout Plain Layout
32887 is only used as spacer.
32899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32902 \begin_layout Plain Layout
32909 \begin_layout Plain Layout
32923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32926 \begin_layout Plain Layout
32927 \begin_inset Formula $A\gr B$
32937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32940 \begin_layout Plain Layout
32948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32951 \begin_layout Plain Layout
32952 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32965 \begin_layout Plain Layout
32969 \begin_inset Formula $\to$
32975 \begin_inset Formula $\to$
32986 \begin_layout Plain Layout
33000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33003 \begin_layout Plain Layout
33004 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33017 \begin_layout Plain Layout
33021 \begin_inset Formula $\to$
33032 \begin_layout Plain Layout
33046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33049 \begin_layout Plain Layout
33050 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33063 \begin_layout Plain Layout
33069 \begin_inset Formula $\to$
33080 \begin_layout Plain Layout
33094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33097 \begin_layout Plain Layout
33098 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33114 \begin_layout Subsection
33119 \begin_layout Plain Layout
33120 User-defined commands! Math macros
33129 \begin_layout Plain Layout
33138 \begin_layout Standard
33139 User-defined commands are especially convenient for complex expressions.
33140 When you are for example dealing in a document with quadratic equations,
33141 the same solution type occurs several times.
33142 The general form of a quadratic equation is
33143 \begin_inset Formula \[
33144 0=\lambda^{2}+p\lambda+q\]
33148 The general form of the solution is
33149 \begin_inset Formula \[
33150 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33157 \begin_layout Standard
33158 To define a command for the solution formula where only the three parameters
33160 \begin_inset Formula $\lambda$
33164 \begin_inset Formula $p$
33168 \begin_inset Formula $q$
33171 need to be specified and the index of
33172 \begin_inset Formula $\lambda$
33175 can be given optionally, the LaTeX-preamble line is
33176 \begin_inset Newline newline
33192 \begin_inset Newline newline
33199 \begin_layout Plain Layout
33214 \begin_layout Plain Layout
33225 frac{#3^{2}}{4}-#4}}
33228 \begin_layout Standard
33229 To create with this the solution formula, the command
33230 \begin_inset Newline newline
33240 \begin_inset Formula $\to$
33246 \begin_inset Formula $\to$
33253 is inserted to a formula
33258 \begin_layout Standard
33259 The definition of the new command is unintuitive because one has to know
33260 the schemes of all used LaTeX commands, e.
33261 \begin_inset space \thinspace{}
33265 \begin_inset space \space{}
33268 that a fraction is inserted in LaTeX as
33272 frac{numerator}{denominator}
33275 Furthermore one can easily forget a brace in the definition and cannot
33276 see in LyX what the new command is doing.
33277 To avoid these problems LyX offers the possibility to use math macros instead
33287 \begin_layout Standard
33288 A math macro is created by using the menu
33290 Insert\SpecialChar \menuseparator
33291 Math\SpecialChar \menuseparator
33294 or the toolbar button
33295 \begin_inset Graphics
33296 filename ../images/math-macro_newmacroname_newcommand.png
33302 The math macro toolbar appears together with the following box where the
33304 \begin_inset Newline newline
33308 \begin_inset space \hspace*{\fill}
33312 \begin_inset Graphics
33313 filename clipart/macrobox.png
33318 \begin_inset space \hspace*{\fill}
33322 \begin_inset Newline newline
33326 \begin_inset FormulaMacro
33327 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33332 newmacroname is the default name of the macro that should be changed to
33333 something sensible.
33334 The wanted formula is inserted in the first blue box.
33335 An argument placeholder is inserted with the command
33342 \begin_inset space \thinspace{}
33346 \begin_inset space \space{}
33355 or by using the macro toolbar button
33356 \begin_inset Graphics
33357 filename ../images/math-macro-add-param.png
33363 Argument placeholders are displayed red.
33364 Maximum 9 arguments are possible.
33365 Optional arguments are created with the toolbar button
33366 \begin_inset Graphics
33367 filename ../images/math-macro-add-optional-param.png
33373 The first non-optional argument can be transformed to an optional one with
33375 \begin_inset Graphics
33376 filename ../images/math-macro-make-optional.png
33382 In the second blue box the appearance of the macro in LyX can be defined.
33383 Normally you want to see it as it is defined, so the box is kept empty.
33384 But when you have created a macro that needs lot of space on the screen,
33385 you can insert in the box for example
33386 \begin_inset Newline newline
33416 \begin_inset Newline newline
33421 For the macro only the arguments with the macro name in front of them will
33422 then be displayed in LyX, leading to a better overview.
33423 The formula appears in the output as defined in the first box.
33424 \begin_inset Newline newline
33427 The appearance of macros in formulas can furthermore be changed for single
33428 macros by setting the cursor in the macro and using the menu
33430 View\SpecialChar \menuseparator
33432 \begin_inset space ~
33436 \begin_inset space ~
33444 \begin_layout Standard
33445 To use a macro, the macro name is inserted as command to a formula, in our
33453 Our macro looks in LyX like this:
33454 \begin_inset Newline newline
33458 \begin_inset space \hspace*{\fill}
33462 \begin_inset Graphics
33463 filename clipart/macrouse.png
33468 \begin_inset space \hspace*{\fill}
33472 \begin_inset Newline newline
33475 Here is our macro example with the arguments
33476 \begin_inset Formula $x$
33480 \begin_inset Formula $\ln(x)$
33484 \begin_inset Formula $B$
33490 \begin_layout Standard
33491 \begin_inset Formula \[
33499 \begin_layout Standard
33500 LyX offers in the menu
33502 Tools\SpecialChar \menuseparator
33503 Preferences\SpecialChar \menuseparator
33504 Editing\SpecialChar \menuseparator
33507 different styles to edit macros.
33508 To find the style that suits you the most, choose a style and set the cursor
33509 in a macro formula to see the difference.
33512 \begin_layout Standard
33513 A math macro is transformed internally to a
33519 command when exporting the document.
33526 command is not placed in the LaTeX-preamble, therefore macros can only
33527 be used in formulas that are in the document below the macro definition
33531 \begin_layout Standard
33532 Math macros can also be directly be created from a
33539 When writing for example the command
33542 \begin_inset Newline newline
33551 xleftarrow[#2]{#1}}
33552 \begin_inset Newline newline
33557 in LyX as normal text, highlighting it completely and using then the shortcut
33562 , the command will be transformed to a math macro.
33563 Using this method you need to be careful that the
33569 command is typed correctly, otherwise you get a faulty macro leading to
33573 \begin_layout Standard
33574 Math macros currently yet have the problem that further formulas in macro
33575 definitions are handled wrongly.
33576 Therefore the example
33583 \begin_inset CommandInset ref
33585 reference "sub:The-Command-newcommand"
33589 cannot be created as macro.
33592 \begin_layout Standard
33593 When the cursor is in a macro definition box, you will see the macro toolbar
33597 \begin_layout Standard
33598 \begin_inset VSpace defskip
33604 \begin_layout Standard
33605 \begin_inset Graphics
33606 filename clipart/MacroToolbar.png
33614 \begin_layout Plain Layout
33623 \begin_layout Standard
33624 \begin_inset VSpace defskip
33630 \begin_layout Standard
33631 The macro toolbar contains from left to right the following buttons:
33634 \begin_layout Standard
33635 \begin_inset VSpace defskip
33641 \begin_layout Standard
33642 \begin_inset Tabular
33643 <lyxtabular version="3" rows="9" columns="2">
33644 <features islongtable="true">
33645 <column alignment="left" valignment="top" width="0">
33646 <column alignment="left" valignment="top" width="85col%">
33647 <row interlinespace="2.5mm">
33648 <cell alignment="center" valignment="top" usebox="none">
33651 \begin_layout Plain Layout
33652 \begin_inset Graphics
33653 filename ../images/math-macro-remove-param.png
33654 BoundingBox 0bp 5bp 20bp 25bp
33655 rotateOrigin center
33664 <cell alignment="center" valignment="top" usebox="none">
33667 \begin_layout Plain Layout
33670 Edit\SpecialChar \menuseparator
33671 Math\SpecialChar \menuseparator
33673 \begin_inset space ~
33676 Definition\SpecialChar \menuseparator
33677 Remove Last Argument
33683 <row interlinespace="2.5mm">
33684 <cell alignment="center" valignment="top" usebox="none">
33687 \begin_layout Plain Layout
33688 \begin_inset Graphics
33689 filename ../images/math-macro-add-param.png
33690 BoundingBox 0bp 5bp 20bp 25bp
33691 rotateOrigin center
33700 <cell alignment="center" valignment="top" usebox="none">
33703 \begin_layout Plain Layout
33706 Edit\SpecialChar \menuseparator
33707 Math\SpecialChar \menuseparator
33709 \begin_inset space ~
33712 Definition\SpecialChar \menuseparator
33719 <row interlinespace="2.5mm">
33720 <cell alignment="center" valignment="top" usebox="none">
33723 \begin_layout Plain Layout
33724 \begin_inset Graphics
33725 filename ../images/math-macro-make-optional.png
33726 BoundingBox 0bp 5bp 20bp 25bp
33727 rotateOrigin center
33736 <cell alignment="center" valignment="top" usebox="none">
33739 \begin_layout Plain Layout
33742 Edit\SpecialChar \menuseparator
33743 Math\SpecialChar \menuseparator
33745 \begin_inset space ~
33748 Definition\SpecialChar \menuseparator
33749 Make First Non-Optional into
33750 \begin_inset Newline newline
33757 \begin_layout Plain Layout
33766 Edit\SpecialChar \menuseparator
33767 Math\SpecialChar \menuseparator
33769 \begin_inset space ~
33772 Definition\SpecialChar \menuseparator
33777 \begin_layout Plain Layout
33790 <row interlinespace="2.5mm">
33791 <cell alignment="center" valignment="top" usebox="none">
33794 \begin_layout Plain Layout
33795 \begin_inset Graphics
33796 filename ../images/math-macro-make-nonoptional.png
33797 BoundingBox 0bp 5bp 20bp 25bp
33798 rotateOrigin center
33807 <cell alignment="center" valignment="top" usebox="none">
33810 \begin_layout Plain Layout
33813 Edit\SpecialChar \menuseparator
33814 Math\SpecialChar \menuseparator
33816 \begin_inset space ~
33819 Definition\SpecialChar \menuseparator
33820 Make Last Optional into
33821 \begin_inset Newline newline
33828 \begin_layout Plain Layout
33837 Edit\SpecialChar \menuseparator
33838 Math\SpecialChar \menuseparator
33840 \begin_inset space ~
33843 Definition\SpecialChar \menuseparator
33848 \begin_layout Plain Layout
33855 Non-Optional Argument
33861 <row interlinespace="2.5mm">
33862 <cell alignment="center" valignment="top" usebox="none">
33865 \begin_layout Plain Layout
33866 \begin_inset Graphics
33867 filename ../images/math-macro-remove-optional-param.png
33868 BoundingBox 0bp 5bp 20bp 25bp
33869 rotateOrigin center
33878 <cell alignment="center" valignment="top" usebox="none">
33881 \begin_layout Plain Layout
33884 Edit\SpecialChar \menuseparator
33885 Math\SpecialChar \menuseparator
33887 \begin_inset space ~
33890 Definition\SpecialChar \menuseparator
33891 Remove Optional Argument
33897 <row interlinespace="2.5mm">
33898 <cell alignment="center" valignment="top" usebox="none">
33901 \begin_layout Plain Layout
33902 \begin_inset Graphics
33903 filename ../images/math-macro-add-optional-param.png
33904 BoundingBox 0bp 5bp 20bp 25bp
33905 rotateOrigin center
33914 <cell alignment="center" valignment="top" usebox="none">
33917 \begin_layout Plain Layout
33920 Edit\SpecialChar \menuseparator
33921 Math\SpecialChar \menuseparator
33923 \begin_inset space ~
33926 Definition\SpecialChar \menuseparator
33927 Insert Optional Argument
33933 <row interlinespace="2.5mm">
33934 <cell alignment="center" valignment="top" usebox="none">
33937 \begin_layout Plain Layout
33938 \begin_inset Graphics
33939 filename ../images/math-macro-remove-greedy-param.png
33940 BoundingBox 0bp 5bp 20bp 25bp
33941 rotateOrigin center
33950 <cell alignment="center" valignment="top" usebox="none">
33953 \begin_layout Plain Layout
33956 Edit\SpecialChar \menuseparator
33957 Math\SpecialChar \menuseparator
33959 \begin_inset space ~
33962 Definition\SpecialChar \menuseparator
33963 Remove Last Argument
33964 \begin_inset Newline newline
33971 \begin_layout Plain Layout
33980 Edit\SpecialChar \menuseparator
33981 Math\SpecialChar \menuseparator
33983 \begin_inset space ~
33986 Definition\SpecialChar \menuseparator
33991 \begin_layout Plain Layout
33998 Spitting Out To The Right
34004 <row interlinespace="2.5mm">
34005 <cell alignment="center" valignment="top" usebox="none">
34008 \begin_layout Plain Layout
34009 \begin_inset Graphics
34010 filename ../images/math-macro-append-greedy-param.png
34011 BoundingBox 0bp 5bp 20bp 25bp
34012 rotateOrigin center
34021 <cell alignment="center" valignment="top" usebox="none">
34024 \begin_layout Plain Layout
34027 Edit\SpecialChar \menuseparator
34028 Math\SpecialChar \menuseparator
34030 \begin_inset space ~
34033 Definition\SpecialChar \menuseparator
34035 \begin_inset Newline newline
34042 \begin_layout Plain Layout
34051 Edit\SpecialChar \menuseparator
34052 Math\SpecialChar \menuseparator
34054 \begin_inset space ~
34057 Definition\SpecialChar \menuseparator
34062 \begin_layout Plain Layout
34069 Eating From The Right
34075 <row interlinespace="2.5mm">
34076 <cell alignment="center" valignment="top" usebox="none">
34079 \begin_layout Plain Layout
34080 \begin_inset Graphics
34081 filename ../images/math-macro-add-greedy-optional-param.png
34082 BoundingBox 0bp 5bp 20bp 25bp
34083 rotateOrigin center
34092 <cell alignment="center" valignment="top" usebox="none">
34095 \begin_layout Plain Layout
34098 Edit\SpecialChar \menuseparator
34099 Math\SpecialChar \menuseparator
34101 \begin_inset space ~
34104 Definition\SpecialChar \menuseparator
34105 Append Optional Argument
34106 \begin_inset Newline newline
34113 \begin_layout Plain Layout
34122 Edit\SpecialChar \menuseparator
34123 Math\SpecialChar \menuseparator
34125 \begin_inset space ~
34128 Definition\SpecialChar \menuseparator
34133 \begin_layout Plain Layout
34140 Eating From The Right
34153 \begin_layout Standard
34154 \begin_inset Newpage newpage
34160 \begin_layout Section
34165 \begin_layout Plain Layout
34174 \begin_layout Subsection
34179 \begin_layout Plain Layout
34188 \begin_layout Standard
34189 Negative numbers often look ugly in formulas because the minus sign before
34190 the number is set with the same length as the minus operator sign.
34191 When writing the negative number in normal text, the minus sign appears
34195 \begin_layout Standard
34196 Thus, the problem disappears when converting the minus sign to mathematical
34200 \begin_layout Standard
34201 An example to visualize the problem:
34204 \begin_layout Standard
34206 \begin_inset Tabular
34207 <lyxtabular version="3" rows="3" columns="2">
34209 <column alignment="right" valignment="top" width="0">
34210 <column alignment="left" valignment="top" width="0">
34212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34215 \begin_layout Plain Layout
34221 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34224 \begin_layout Plain Layout
34232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34235 \begin_layout Plain Layout
34241 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34244 \begin_layout Plain Layout
34245 \begin_inset Formula $x=-2$
34255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34258 \begin_layout Plain Layout
34264 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34267 \begin_layout Plain Layout
34268 \begin_inset Formula $x=\textrm{-}2$
34284 \begin_layout Subsection
34285 Comma as decimal Separator
34289 \begin_layout Plain Layout
34298 \begin_layout Standard
34299 In LaTeX a comma inside a formula is used, according to the English convention,
34300 as number group separator.
34301 So there will be space added behind all commas in formulas.
34304 \begin_layout Standard
34305 To avoid this, the comma is highlighted and changed to mathematical text
34315 \begin_layout Standard
34316 To use all formula commas in the document as decimal separator, the file
34325 \begin_layout Plain Layout
34330 is part of the LaTeX-package
34338 \begin_layout Plain Layout
34343 \begin_layout Plain Layout
34366 \begin_layout Plain Layout
34372 is loaded with the LaTeX-preamble line
34375 \begin_layout Standard
34383 \begin_layout Subsection
34385 \begin_inset CommandInset label
34387 name "sub:Physical-Vectors"
34395 \begin_layout Plain Layout
34404 \begin_layout Standard
34405 Predefined vectors are offered by the LaTeX-package
34413 \begin_layout Plain Layout
34419 that is loaded with the LaTeX-preamble line
34422 \begin_layout Standard
34430 \begin_layout Standard
34434 \begin_layout Plain Layout
34444 \begin_inset Note Note
34447 \begin_layout Plain Layout
34448 The following table will only be displayed when the LaTeX-package
34460 \begin_layout Standard
34461 The following commands are defined:
34464 \begin_layout Standard
34466 \begin_inset Tabular
34467 <lyxtabular version="3" rows="4" columns="2">
34469 <column alignment="center" valignment="top" width="0">
34470 <column alignment="center" valignment="top" width="0">
34472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34475 \begin_layout Plain Layout
34481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34484 \begin_layout Plain Layout
34492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34495 \begin_layout Plain Layout
34505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34508 \begin_layout Plain Layout
34509 \begin_inset Formula $\Bra{\psi}$
34519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34522 \begin_layout Plain Layout
34532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34535 \begin_layout Plain Layout
34536 \begin_inset Formula $\Ket{\psi}$
34546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34549 \begin_layout Plain Layout
34561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34564 \begin_layout Plain Layout
34565 \begin_inset Formula $\Braket{\psi|\phi}$
34581 \begin_layout Standard
34588 assures that all vertical bars are set in the size of the surrounding brackets:
34589 \begin_inset Formula \[
34590 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34598 \begin_layout Plain Layout
34608 \begin_inset Note Note
34611 \begin_layout Plain Layout
34612 The following will be displayed when the LaTeX-package
34624 \begin_layout Standard
34625 You need to install the LaTeX-package
34629 to see the rest of this subsection in the output.
34632 \begin_layout Standard
34636 \begin_layout Plain Layout
34648 \begin_layout Standard
34655 can also be achieved using the command
34661 , that is described in
34662 \begin_inset CommandInset ref
34664 reference "sub:Automatic-Bracket-Size"
34671 \begin_layout Subsection
34672 Self-defined Fractions
34673 \begin_inset CommandInset label
34675 name "sub:Self-defined-Fractions"
34683 \begin_layout Plain Layout
34684 Fractions ! self-defined
34692 \begin_layout Standard
34693 To define custom commands for fractions, the command
34703 \begin_layout Plain Layout
34711 is used in the following scheme:
34714 \begin_layout Standard
34727 bracket}{fraction bar thickness}{style}
34728 \begin_inset Newline newline
34735 \begin_layout Plain Layout
34750 \begin_layout Plain Layout
34757 {numerator}{denominator}
34760 \begin_layout Standard
34761 The style is a number in the range of 0
34762 \begin_inset space \thinspace{}
34766 \begin_inset space \thinspace{}
34772 \begin_layout Standard
34774 \begin_inset Tabular
34775 <lyxtabular version="3" rows="5" columns="2">
34777 <column alignment="center" valignment="top" width="0">
34778 <column alignment="center" valignment="top" width="0">
34780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34783 \begin_layout Plain Layout
34789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34792 \begin_layout Plain Layout
34800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34803 \begin_layout Plain Layout
34809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34812 \begin_layout Plain Layout
34813 display style formula
34820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34823 \begin_layout Plain Layout
34829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34832 \begin_layout Plain Layout
34840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34843 \begin_layout Plain Layout
34849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34852 \begin_layout Plain Layout
34860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34863 \begin_layout Plain Layout
34869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34872 \begin_layout Plain Layout
34886 \begin_layout Standard
34887 When no style is given, the size is adjusted to the surrounding environment
34888 like for the command
34897 \begin_layout Standard
34898 When no fraction bar thickness is given, the predefined value of 0.4
34899 \begin_inset space \thinspace{}
34905 \begin_layout Standard
34906 \begin_inset VSpace medskip
34909 For example, the commands
34922 \begin_inset CommandInset ref
34924 reference "sub:Fractions"
34928 are defined with the commands
34931 \begin_layout Standard
34940 genfrac{}{}{}{0}{#1}{#2}}
34943 \begin_layout Standard
34947 \begin_layout Standard
34956 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34959 \begin_layout Standard
34960 \begin_inset VSpace medskip
34963 To define a fraction where the fraction bar thickness can be given as optional
34964 argument, the following line is inserted to the LaTeX-preamble:
34967 \begin_layout Standard
34976 genfrac{}{}{#1}{}{#2}{#3}}
34979 \begin_layout Standard
34981 \begin_inset Formula \begin{align*}
34982 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34983 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34987 As one can see, the distance of the numerator and the denominator to the
34988 fraction bar is round about three times the bar thickness.
34991 \begin_layout Subsection
34996 \begin_layout Plain Layout
35005 \begin_layout Standard
35006 To cancel formulas or formula parts, the LaTeX-package
35014 \begin_layout Plain Layout
35020 has to be loaded with the LaTeX-preamble line
35023 \begin_layout Standard
35028 usepackage[samesize]{cancel}
35031 \begin_layout Standard
35035 \begin_layout Plain Layout
35045 \begin_inset Note Note
35048 \begin_layout Plain Layout
35049 The following table will only be displayed when the LaTeX-package
35061 \begin_layout Standard
35062 There are four ways to cancel formulas:
35065 \begin_layout Standard
35067 \begin_inset Tabular
35068 <lyxtabular version="3" rows="5" columns="2">
35070 <column alignment="center" valignment="top" width="0">
35071 <column alignment="center" valignment="top" width="0">
35073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35076 \begin_layout Plain Layout
35082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35085 \begin_layout Plain Layout
35087 \begin_inset Note Note
35090 \begin_layout Plain Layout
35097 are used here as spacer.
35109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35112 \begin_layout Plain Layout
35121 \begin_layout Plain Layout
35135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35138 \begin_layout Plain Layout
35139 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35152 \begin_layout Plain Layout
35161 \begin_layout Plain Layout
35175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35178 \begin_layout Plain Layout
35179 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35192 \begin_layout Plain Layout
35201 \begin_layout Plain Layout
35215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35218 \begin_layout Plain Layout
35219 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35232 \begin_layout Plain Layout
35236 \begin_inset Formula $\to$
35247 \begin_layout Plain Layout
35261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35264 \begin_layout Plain Layout
35265 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35281 \begin_layout Standard
35288 is especially suitable to visualize the reduction of fractions within formulas:
35289 \begin_inset Formula \[
35290 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35297 \begin_layout Standard
35301 \begin_layout Plain Layout
35311 \begin_inset Note Note
35314 \begin_layout Plain Layout
35315 The following will be displayed when the LaTeX-package
35327 \begin_layout Standard
35328 You need to install the LaTeX-package
35332 to see the rest of this subsection in the output.
35335 \begin_layout Standard
35339 \begin_layout Plain Layout
35351 \begin_layout Subsection
35352 Formulas in Section Headings
35353 \begin_inset CommandInset label
35355 name "sub:Formulas-in-Section"
35363 \begin_layout Plain Layout
35364 Formula ! in section headings
35372 \begin_layout Standard
35373 When formulas are used in section headings, the following has to be taken
35377 \begin_layout Standard
35378 \begin_inset Note Greyedout
35381 \begin_layout Plain Layout
35390 \begin_layout Plain Layout
35391 Packages ! hyperref
35396 support is enabled in the document settings dialog under
35399 \begin_inset space ~
35404 , PDF-bookmarks are created for every section heading in the table of contents.
35405 If a section heading contains formulas, they are incorrectly displayed
35406 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35415 \begin_layout Standard
35416 Both problems can be solved by inserting at the end of the section heading
35417 a short title with the menu
35419 Insert\SpecialChar \menuseparator
35421 \begin_inset space ~
35427 Short titles are used as alternative for multiline section headings to
35428 keep the table of contents clearly arranged.
35429 Only the short title appears in the table of contents and therefore also
35430 in the PDF-bookmark.
35433 \begin_layout Standard
35434 When formulas should be used in the table of contents but
35438 is used, one can use the following command in TeX-mode:
35441 \begin_layout Standard
35446 texorpdfstring{part}{alternative}
35450 \begin_layout Plain Layout
35461 \begin_layout Standard
35462 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35463 This can be characters, formulas, footnotes, but also cross-references.
35464 The alternative is used instead of the part for the bookmark.
35467 \begin_layout Standard
35468 Here are two example headings:
35469 \begin_inset VSpace -3mm
35476 \begin_layout Plain Layout
35488 \begin_layout Subsubsection
35489 Heading without formula in table of contents
35490 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35494 \begin_inset OptArg
35497 \begin_layout Plain Layout
35498 Heading without formula in table of contents
35506 \begin_layout Subsubsection
35507 Heading with formula in table of contents
35511 \begin_layout Plain Layout
35521 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35528 \begin_layout Plain Layout
35538 \begin_layout Standard
35542 \begin_layout Plain Layout
35551 In the first heading a short title was used, in the second one
35560 \begin_layout Standard
35561 To get the same formatting as for the other headings, the complete heading
35570 \begin_layout Plain Layout
35572 \begin_inset CommandInset ref
35574 reference "sub:Bold-Formulas"
35586 \begin_layout Subsection
35587 Formulas in multi-column Text
35591 \begin_layout Plain Layout
35592 Formula ! in multi-column text
35600 \begin_layout Standard
35601 Formulas in multi-column text are often too wide to fit into a column and
35602 thus need to be set over the whole page width.
35603 This is done by using the LaTeX-package
35611 \begin_layout Plain Layout
35616 is part of every LaTeX standard installation.
35625 \begin_layout Plain Layout
35626 Packages ! multicol
35631 , that is loaded with the LaTeX-preamble line
35634 \begin_layout Standard
35639 usepackage{multicol}
35642 \begin_layout Standard
35643 \begin_inset Note Greyedout
35646 \begin_layout Plain Layout
35647 Note herby that the setting
35650 \begin_inset space ~
35657 Document\SpecialChar \menuseparator
35663 \begin_inset space ~
35683 \begin_layout Standard
35684 Before the multi-column text the command
35687 \begin_layout Standard
35692 begin{multicols}{column number}
35695 \begin_layout Standard
35696 is written in TeX-mode.
35697 The column number is a number in the range of 2
35698 \begin_inset space \thinspace{}
35702 \begin_inset space \thinspace{}
35706 Before the formula the multi-column text is ended by inserting the command
35709 \begin_layout Standard
35717 \begin_layout Standard
35721 \begin_layout Standard
35722 Due to the command some space is automatically added before the formula.
35724 \begin_inset space \thinspace{}
35727 mm vertical space is inserted before the formula.
35728 When the formula style
35734 \begin_layout Plain Layout
35736 \begin_inset CommandInset ref
35738 reference "sec:Formula-Styles"
35750 \begin_inset space \thinspace{}
35753 mm space is inserted instead.
35756 \begin_layout Standard
35757 As example a multi-column text with a displayed formula:
35760 \begin_layout Standard
35766 \begin_layout Plain Layout
35770 begin{multicols}{2}
35775 Das Spektrum wird fouriertransformiert.
35776 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35777 , Lösungsmittel) zu trennen.
35778 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35779 nun das Aussehen des Ausgangssignals.
35780 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35781 über alle Phasen integrieren muss.
35783 \begin_inset Formula $S$
35786 unser normiertes Ausgangssignal und
35787 \begin_inset Formula $P$
35790 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35794 \begin_layout Plain Layout
35804 \begin_inset VSpace -6mm
35808 \begin_inset Formula \begin{equation}
35809 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35817 \begin_layout Plain Layout
35821 begin{multicols}{2}
35827 \begin_inset Formula $S_{0}$
35830 das Signal ohne Gradient ist und die Normierungsbedingung
35831 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35835 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35837 \begin_inset Formula $\nicefrac{\pi}{2}$
35841 \begin_inset space \thinspace{}
35844 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35845 das Signal zusätzlich abschwächt.
35846 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35848 \begin_inset Formula $T_{2}$
35854 \begin_layout Standard
35860 \begin_layout Plain Layout
35872 \begin_layout Subsection
35873 Formulas with Description of Variables
35877 \begin_layout Plain Layout
35878 Formula ! with description of variables
35886 \begin_layout Standard
35887 To describe variables within a formula, like in formula
35888 \begin_inset CommandInset ref
35890 reference "eq:within"
35899 \begin_inset Formula $n$
35903 \begin_inset space ~
35906 matrix is used with left aligned columns for the
35907 \begin_inset Formula $n$
35914 \begin_layout Plain Layout
35916 \begin_inset CommandInset ref
35918 reference "sec:Matrices"
35927 To set the description in a smaller size, before the matrix e.
35928 \begin_inset space \thinspace{}
35932 \begin_inset space \space{}
35945 \begin_layout Plain Layout
35947 \begin_inset CommandInset ref
35949 reference "sub:Font-Sizes"
35961 \begin_layout Standard
35962 When the formula style
35968 \begin_layout Plain Layout
35970 \begin_inset CommandInset ref
35972 reference "sec:Formula-Styles"
35993 \begin_layout Plain Layout
36000 only works in formulas with the style
36005 \begin_inset CommandInset ref
36007 reference "sub:Variable-Space"
36016 is inserted before and after the matrix to have the same separation of
36017 the matrix from the equation and the side margin.
36020 \begin_layout Standard
36021 When the formula style
36025 is used, the method described in
36026 \begin_inset CommandInset ref
36028 reference "sub:Flalign-Environment"
36032 is used to indent formulas.
36034 \begin_inset CommandInset ref
36036 reference "eq:within"
36040 consists of five columns whereas in the first two columns contain the equation,
36041 the third the matrix and the last one an empty TeX-brace.
36042 \begin_inset Formula \begin{flalign}
36043 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36044 \rho & \textrm{density}\\
36045 V & \textrm{volume}\\
36046 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
36053 \begin_layout Subsection
36054 Upright small Greek Letters
36055 \begin_inset CommandInset label
36057 name "sub:Upright-small-Greek"
36065 \begin_layout Plain Layout
36066 Greek letters ! upright
36074 \begin_layout Standard
36075 Most of the math fonts only provide italic small Greek letters.
36076 But for symbols of elementary particles like pions and neutrinos, upright
36077 Greek letters are needed.
36086 \begin_layout Plain Layout
36091 is part of the LaTeX-package
36099 \begin_layout Plain Layout
36104 \begin_layout Plain Layout
36127 \begin_layout Plain Layout
36133 that is loaded with the LaTeX-preamble line
36136 \begin_layout Standard
36141 usepackage{upgreek}
36144 \begin_layout Standard
36150 \begin_layout Plain Layout
36160 \begin_inset Note Note
36163 \begin_layout Plain Layout
36164 The following table will only be displayed when the LaTeX-package
36173 They are created when the command for a small Greek letters is started
36179 For example the command
36186 \begin_inset Formula $\uptau$
36192 \begin_layout Standard
36193 With these commands reactions of elementary particles can be typeset:
36194 \begin_inset Formula \[
36195 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36202 \begin_layout Standard
36203 The upright letters are more bold and wider than the italic ones.
36204 They should therefore not be used for units like
36205 \begin_inset Quotes eld
36209 \begin_inset Quotes erd
36215 \begin_layout Standard
36219 \begin_layout Plain Layout
36229 \begin_inset Note Note
36232 \begin_layout Plain Layout
36233 The following will be displayed when the LaTeX-package
36245 \begin_layout Standard
36246 You need to install the LaTeX-package
36250 to see the rest of this subsection in the output.
36253 \begin_layout Standard
36257 \begin_layout Plain Layout
36269 \begin_layout Subsection
36270 Text Characters in Formulas
36271 \begin_inset CommandInset label
36273 name "sub:Text-Characters-in"
36281 \begin_layout Plain Layout
36290 \begin_layout Standard
36291 In some cases you might want to insert text characters directly into formulas.
36292 When for example the centered dot · is often used in formulas like
36293 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36296 , one would have to insert the command
36306 \begin_layout Plain Layout
36308 \begin_inset CommandInset ref
36310 reference "sub:Binary-Operators"
36319 all the time, because this character is defined in all encodings as text
36321 But the encoding can be changed by this LaTeX-preamble line:
36324 \begin_layout Standard
36329 Declare Inputtext{183}{
36339 f\SpecialChar \textcompwordmark{}
36343 \begin_layout Standard
36344 The character encoding (menu
36346 Document\SpecialChar \menuseparator
36347 Settings\SpecialChar \menuseparator
36350 ) specifies what character appears when a keyboard key is pressed.
36351 When the key for the character '·' is pressed, internally the command
36358 But this command is not available in a formula so that you would get LaTeX-erro
36360 With the changed encoding the right command is chosen automatically, depending
36361 on if the character was inserted into a formula or not.
36364 \begin_layout Standard
36365 The encoding of several characters is saved in definition files.
36366 Fore example the encoding
36370 is defined in the file
36374 that is in the installation folder of LaTeX.
36375 Encodings should only be changed via the LaTeX-preamble and not in the
36377 Otherwise own documents could not be edited by other LyX users working
36378 on other computers.
36381 \begin_layout Standard
36382 \begin_inset VSpace medskip
36385 Besides the centered dot, in this document the degree sign ° is defined
36386 with the following LaTeX-preamble line so that it can directly be inserted
36390 \begin_layout Standard
36395 DeclareInputtext{176}{
36405 f\SpecialChar \textcompwordmark{}
36409 \begin_layout Standard
36410 \begin_inset Newpage newpage
36416 \begin_layout Section
36422 \begin_layout Plain Layout
36431 \begin_layout Standard
36432 This section is a summary of the most important typographic rules, listed
36437 \begin_layout Plain Layout
36438 This collection was partly taken from the German semi-official dictionary
36440 \begin_inset Quotes eld
36444 \begin_inset Quotes erd
36448 \begin_inset CommandInset citation
36454 that lists some of the ISO rules.
36455 More rules are listed in
36456 \begin_inset CommandInset citation
36470 \begin_layout Itemize
36479 \begin_layout Plain Layout
36480 done with font styles, see
36481 \begin_inset CommandInset ref
36483 reference "sub:Font-Styles"
36492 , no matter if they appear in italic text: 30
36493 \begin_inset space \thinspace{}
36497 \begin_inset Newline newline
36500 Between the value and the unit is the smallest space, see
36501 \begin_inset CommandInset ref
36503 reference "sub:Predefined-Space"
36508 \begin_inset Newline newline
36511 This convention is automatically fulfilled when the command
36518 When it is entered to a formula, two boxes appear.
36519 In the first one the value is inserted, in the second one the unit, and
36521 \begin_inset Formula $\unit[30]{km/h}$
36525 \begin_inset space \thinspace{}
36535 is not a real LaTeX command but the command
36541 , therefore you cannot use it in TeX code.
36544 \begin_layout Itemize
36545 Percent and perthousand signs are set like physical units:
36546 \begin_inset Newline newline
36550 \begin_inset space \thinspace{}
36556 \begin_layout Itemize
36557 The degree sign follows directly on the value: 15°, but not when it is used
36559 \begin_inset space \thinspace{}
36565 \begin_layout Itemize
36566 In numbers with more than four digits the smallest space is inserted before
36567 every third digit to group them:
36577 \begin_inset space \thinspace{}
36581 \begin_inset space \thinspace{}
36587 \begin_layout Itemize
36588 For dimensions like 120×90×40
36589 \begin_inset space \thinspace{}
36592 cm the multiplication sign
36593 \begin_inset Quotes eld
36597 \begin_inset Quotes erd
36601 It is available either via the command
36609 Insert\SpecialChar \menuseparator
36610 Special Character\SpecialChar \menuseparator
36616 \begin_layout Itemize
36617 Functions with names consisting of several letters are set upright to avoid
36619 \begin_inset CommandInset ref
36621 reference "sub:Predefined-Functions"
36628 \begin_layout Itemize
36629 Indices consisting of several letters, are set upright:
36630 \begin_inset Formula $E_{\mathrm{kin}}$
36634 \begin_inset Newline newline
36637 Components of matrices are set italic:
36638 \begin_inset Formula $\hat{H}_{kl}$
36644 \begin_layout Itemize
36645 The differentiation/integration operator 'd', the Euler's number 'e' and
36646 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36650 \begin_layout Itemize
36651 The character that denotes a
36655 transformation is inserted either by the command
36663 \begin_layout Plain Layout
36680 \begin_layout Plain Layout
36690 Insert\SpecialChar \menuseparator
36691 Special Character\SpecialChar \menuseparator
36692 Symbols\SpecialChar \menuseparator
36694 \begin_inset space ~
36700 \begin_inset Formula $\mathscr{F}$
36704 \begin_inset Newline newline
36707 To be able to use the command
36713 , the LaTeX package
36721 \begin_layout Plain Layout
36722 Packages ! mathrsfs
36727 needs to be loaded with the LaTeX-preamble line
36731 usepackage{mathrsfs}
36736 \begin_layout Standard
36737 \begin_inset Newpage newpage
36743 \begin_layout Section
36748 \begin_layout Plain Layout
36757 \begin_layout Standard
36758 Some characters and symbols can be created with several commands.
36759 Here is a list of the synonym commands:
36762 \begin_layout Standard
36763 \begin_inset VSpace bigskip
36767 \begin_inset space \hfill{}
36771 \begin_inset Tabular
36772 <lyxtabular version="3" rows="12" columns="2">
36774 <column alignment="center" valignment="top" width="0pt">
36775 <column alignment="center" valignment="top" width="0pt">
36777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36780 \begin_layout Plain Layout
36786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36789 \begin_layout Plain Layout
36791 \begin_inset Note Note
36794 \begin_layout Plain Layout
36801 is only used as spacer.
36813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36816 \begin_layout Plain Layout
36824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36827 \begin_layout Plain Layout
36831 \begin_layout Plain Layout
36844 \begin_layout Plain Layout
36858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36861 \begin_layout Plain Layout
36869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36872 \begin_layout Plain Layout
36882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36885 \begin_layout Plain Layout
36893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36896 \begin_layout Plain Layout
36906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36909 \begin_layout Plain Layout
36917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36920 \begin_layout Plain Layout
36928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36931 \begin_layout Plain Layout
36939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36942 \begin_layout Plain Layout
36950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36953 \begin_layout Plain Layout
36961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36964 \begin_layout Plain Layout
36974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36977 \begin_layout Plain Layout
36985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36988 \begin_layout Plain Layout
36998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37001 \begin_layout Plain Layout
37009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37012 \begin_layout Plain Layout
37022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37025 \begin_layout Plain Layout
37033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37036 \begin_layout Plain Layout
37046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37049 \begin_layout Plain Layout
37057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37060 \begin_layout Plain Layout
37068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37071 \begin_layout Plain Layout
37079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37082 \begin_layout Plain Layout
37094 \begin_inset space \hfill{}
37098 \begin_inset Tabular
37099 <lyxtabular version="3" rows="12" columns="2">
37101 <column alignment="center" valignment="top" width="0pt">
37102 <column alignment="center" valignment="top" width="0pt">
37104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37107 \begin_layout Plain Layout
37113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37116 \begin_layout Plain Layout
37124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37127 \begin_layout Plain Layout
37135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37138 \begin_layout Plain Layout
37150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37153 \begin_layout Plain Layout
37161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37164 \begin_layout Plain Layout
37174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37177 \begin_layout Plain Layout
37185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37188 \begin_layout Plain Layout
37198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37201 \begin_layout Plain Layout
37209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37212 \begin_layout Plain Layout
37220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37223 \begin_layout Plain Layout
37231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37234 \begin_layout Plain Layout
37242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37245 \begin_layout Plain Layout
37253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37256 \begin_layout Plain Layout
37266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37269 \begin_layout Plain Layout
37277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37280 \begin_layout Plain Layout
37290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37293 \begin_layout Plain Layout
37301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37304 \begin_layout Plain Layout
37314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37317 \begin_layout Plain Layout
37325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37328 \begin_layout Plain Layout
37338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37341 \begin_layout Plain Layout
37349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37352 \begin_layout Plain Layout
37362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37365 \begin_layout Plain Layout
37373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37376 \begin_layout Plain Layout
37390 \begin_inset space \hfill{}
37396 \begin_layout Standard
37397 \begin_inset Newpage newpage
37403 \begin_layout Bibliography
37404 \begin_inset CommandInset bibitem
37405 LatexCommand bibitem
37417 The LaTeX Companion
37420 Addison Wesley, 2004
37423 \begin_layout Bibliography
37424 \begin_inset CommandInset bibitem
37425 LatexCommand bibitem
37431 \begin_inset CommandInset href
37434 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37438 of LaTeX's math abilities
37441 \begin_layout Bibliography
37442 \begin_inset CommandInset bibitem
37443 LatexCommand bibitem
37449 \begin_inset CommandInset href
37452 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37460 \begin_layout Plain Layout
37472 \begin_layout Bibliography
37473 \begin_inset CommandInset bibitem
37474 LatexCommand bibitem
37480 \begin_inset CommandInset href
37483 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37487 of all symbols available with LaTeX-packages
37490 \begin_layout Bibliography
37491 \begin_inset CommandInset bibitem
37492 LatexCommand bibitem
37498 \begin_inset CommandInset href
37500 name "Documentation"
37501 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37505 of the LaTeX-package
37513 \begin_layout Plain Layout
37514 Packages ! hyperref
37522 \begin_layout Bibliography
37523 \begin_inset CommandInset bibitem
37524 LatexCommand bibitem
37530 \begin_inset CommandInset href
37532 name "Documentation"
37533 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37537 of the LaTeX-package
37545 \begin_layout Plain Layout
37554 \begin_layout Bibliography
37555 \begin_inset CommandInset bibitem
37556 LatexCommand bibitem
37562 \begin_inset CommandInset href
37565 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37576 \begin_inset CommandInset ref
37578 reference "sub:Operator-Limits"
37586 \begin_layout Plain Layout
37597 \begin_layout Bibliography
37598 \begin_inset CommandInset bibitem
37599 LatexCommand bibitem
37610 Auflage, Duden 2001
37613 \begin_layout Bibliography
37614 \begin_inset CommandInset bibitem
37615 LatexCommand bibitem
37621 \begin_inset CommandInset href
37624 target "http://physics.nist.gov/Document/checklist.pdf"
37628 for reviewing manuscripts
37631 \begin_layout Standard
37632 \begin_inset CommandInset index_print
37633 LatexCommand printindex