1 #LyX 1.6.8svn 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
178 \pdf_breaklinks false
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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
1759 \begin_layout Plain Layout
1767 a fraction can be created that has in any case the size of a display style
1779 \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 (
2760 \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
9604 \begin_layout Plain Layout
9618 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9621 \begin_layout Plain Layout
9622 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9632 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9635 \begin_layout Plain Layout
9642 \begin_layout Plain Layout
9655 \begin_layout Plain Layout
9666 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9669 \begin_layout Plain Layout
9670 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9683 \begin_layout Plain Layout
9690 \begin_layout Plain Layout
9704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9707 \begin_layout Plain Layout
9708 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9718 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9721 \begin_layout Plain Layout
9728 \begin_layout Plain Layout
9742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9745 \begin_layout Plain Layout
9746 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9760 \begin_inset space \hfill{}
9764 \begin_inset Tabular
9765 <lyxtabular version="3" rows="7" columns="2">
9767 <column alignment="center" valignment="top" width="0pt">
9768 <column alignment="center" valignment="top" width="0pt">
9770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9773 \begin_layout Plain Layout
9779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9782 \begin_layout Plain Layout
9790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9793 \begin_layout Plain Layout
9800 \begin_layout Plain Layout
9814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9817 \begin_layout Plain Layout
9818 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9831 \begin_layout Plain Layout
9838 \begin_layout Plain Layout
9852 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9855 \begin_layout Plain Layout
9856 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9869 \begin_layout Plain Layout
9876 \begin_layout Plain Layout
9890 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9893 \begin_layout Plain Layout
9894 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9904 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9907 \begin_layout Plain Layout
9914 \begin_layout Plain Layout
9928 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9931 \begin_layout Plain Layout
9932 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9945 \begin_layout Plain Layout
9952 \begin_layout Plain Layout
9966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9969 \begin_layout Plain Layout
9970 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9983 \begin_layout Plain Layout
9990 \begin_layout Plain Layout
10004 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10007 \begin_layout Plain Layout
10008 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10022 \begin_inset space \hfill{}
10028 \begin_layout Standard
10029 \begin_inset VSpace bigskip
10035 \begin_layout Standard
10036 You can directly insert accents like é to formulas.
10037 LyX will transform them to the corresponding accent command.
10042 \begin_layout Plain Layout
10048 it is better to insert a quotation mark before the vowel.
10049 These two characters are then treated by LaTeX as
10053 character when the formula part with the umlaut is marked as German.
10061 \begin_inset Quotes eld
10065 \begin_inset Quotes erd
10068 umlauts are created as demonstrated in the following example:
10071 \begin_layout Standard
10072 \begin_inset VSpace -2mm
10078 \begin_layout Standard
10080 \begin_inset Tabular
10081 <lyxtabular version="3" rows="3" columns="2">
10083 <column alignment="center" valignment="top" width="0">
10084 <column alignment="center" valignment="top" width="0">
10086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10089 \begin_layout Plain Layout
10095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10098 \begin_layout Plain Layout
10100 \begin_inset Note Note
10103 \begin_layout Plain Layout
10111 \begin_inset space \thinspace{}
10114 pt space are only used as spacer.
10126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10129 \begin_layout Plain Layout
10132 \begin_inset Quotes grd
10140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10143 \begin_layout Plain Layout
10144 \begin_inset space \hspace{}
10151 \begin_inset Formula $"i$
10161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10164 \begin_layout Plain Layout
10171 \begin_layout Plain Layout
10185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10188 \begin_layout Plain Layout
10189 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10205 \begin_layout Standard
10206 Another advantage to
10212 is that umlauts can directly be converted to mathematical text because
10213 the accent commands above are
10219 in mathematical text
10222 To convert an accented character to mathematical text, only the character
10223 under the accent may be converted.
10224 This applies also for all other conversions, e.
10225 \begin_inset space \thinspace{}
10229 \begin_inset space \space{}
10235 \begin_layout Standard
10236 In mathematical text, umlauts and other accented characters can directly
10240 \begin_layout Subsection
10241 Accents for Operators
10245 \begin_layout Plain Layout
10246 Accents ! for operators
10254 \begin_layout Standard
10265 \begin_layout Plain Layout
10283 \begin_layout Plain Layout
10291 characters can be placed above or below an operator, respectively, to accent
10303 \begin_layout Plain Layout
10311 characters can be set before and behind an operator.
10312 The command scheme is:
10315 \begin_layout Standard
10331 \begin_layout Standard
10338 must always be before the operator that should be accented.
10339 You can accent with several characters and even with other operators and
10347 for example only characters behind an operator, write nothing between the
10348 first braces but don't omit the braces.
10351 \begin_layout Standard
10352 For example the command
10357 \begin_inset Formula $\to$
10367 \begin_inset Formula $\to$
10376 \begin_layout Plain Layout
10392 \begin_inset Formula \[
10393 \sideset{}{'}\sum_{k=1}^{n}\]
10400 \begin_layout Standard
10409 \begin_layout Plain Layout
10424 \begin_layout Plain Layout
10436 \begin_inset Formula $\uparrow$
10444 \begin_inset Formula \[
10445 \overset{a}{\maltese}\]
10449 As seen in the last example, with
10461 also symbols and characters can be accented; with
10467 this is not possible.
10470 \begin_layout Subsection
10471 Accents for several Characters
10475 \begin_layout Plain Layout
10476 Accents ! for several characters
10484 \begin_layout Standard
10485 \begin_inset space \hfill{}
10489 \begin_inset Tabular
10490 <lyxtabular version="3" rows="5" columns="2">
10492 <column alignment="center" valignment="top" width="0pt">
10493 <column alignment="center" valignment="top" width="0pt">
10495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10498 \begin_layout Plain Layout
10504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10507 \begin_layout Plain Layout
10509 \begin_inset Note Note
10512 \begin_layout Plain Layout
10519 is only used as spacer.
10531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10534 \begin_layout Plain Layout
10541 \begin_layout Plain Layout
10555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10558 \begin_layout Plain Layout
10559 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10572 \begin_layout Plain Layout
10579 \begin_layout Plain Layout
10593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10596 \begin_layout Plain Layout
10597 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10610 \begin_layout Plain Layout
10617 \begin_layout Plain Layout
10631 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10634 \begin_layout Plain Layout
10635 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10645 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10648 \begin_layout Plain Layout
10651 underleftrightarrow
10655 \begin_layout Plain Layout
10669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10672 \begin_layout Plain Layout
10673 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10687 \begin_inset space \hfill{}
10691 \begin_inset Tabular
10692 <lyxtabular version="3" rows="5" columns="2">
10694 <column alignment="center" valignment="top" width="0pt">
10695 <column alignment="center" valignment="top" width="0pt">
10697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10700 \begin_layout Plain Layout
10706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10709 \begin_layout Plain Layout
10717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10720 \begin_layout Plain Layout
10727 \begin_layout Plain Layout
10741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10744 \begin_layout Plain Layout
10745 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10758 \begin_layout Plain Layout
10765 \begin_layout Plain Layout
10779 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10782 \begin_layout Plain Layout
10783 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10796 \begin_layout Plain Layout
10803 \begin_layout Plain Layout
10817 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10820 \begin_layout Plain Layout
10821 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10831 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10834 \begin_layout Plain Layout
10841 \begin_layout Plain Layout
10855 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10858 \begin_layout Plain Layout
10859 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10873 \begin_inset space \hfill{}
10879 \begin_layout Standard
10880 \begin_inset VSpace medskip
10883 With these commands as many characters as you like can be accented.
10896 will only be set in the output with a length of three characters, as shown
10897 in the following example:
10898 \begin_inset Formula \[
10899 \widetilde{A+B=C-D}\]
10906 \begin_layout Standard
10917 \begin_layout Plain Layout
10935 \begin_layout Plain Layout
10943 described in the previous subsection it is also possible to accent several
10953 \begin_layout Plain Layout
10963 \begin_inset Formula $\downarrow$
10969 \begin_inset Formula \[
10970 \underset{***}{A=B}\]
10977 \begin_layout Section
10979 \begin_inset CommandInset label
10989 \begin_layout Plain Layout
10998 \begin_layout Subsection
11000 \begin_inset CommandInset label
11002 name "sub:Predefined-Space"
11010 \begin_layout Plain Layout
11011 Space ! horizontal ! predefined
11019 \begin_layout Standard
11020 Sometimes it is necessary to insert horizontal space to a formula.
11021 This is done by inserting a protected space (shortcut
11024 arg "space-insert protected"
11029 \begin_inset Quotes eld
11038 \begin_layout Plain Layout
11050 \begin_inset Quotes erd
11053 appears and by pressing
11057 several times one can select one of eight different space sizes.
11058 The spaces can also be inserted using the math toolbar button
11059 \begin_inset Graphics
11060 filename ../images/math/space.png
11065 or special commands.
11066 Independent from the inserted command, one can select the size again by
11074 \begin_layout Standard
11077 \begin_inset VSpace -5mm
11081 \begin_inset Tabular
11082 <lyxtabular version="3" rows="3" columns="7">
11084 <column alignment="center" valignment="middle" width="6.8cm">
11085 <column alignment="center" valignment="top" width="0">
11086 <column alignment="center" valignment="top" width="0">
11087 <column alignment="center" valignment="top" width="0">
11088 <column alignment="center" valignment="top" width="0">
11089 <column alignment="center" valignment="top" width="0">
11090 <column alignment="center" valignment="top" width="0">
11092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11095 \begin_layout Plain Layout
11101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11104 \begin_layout Plain Layout
11112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11115 \begin_layout Plain Layout
11123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11126 \begin_layout Plain Layout
11134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11137 \begin_layout Plain Layout
11145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11148 \begin_layout Plain Layout
11156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11159 \begin_layout Plain Layout
11169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11172 \begin_layout Plain Layout
11177 keystrokes after inserting the protected space
11182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11185 \begin_layout Plain Layout
11191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11194 \begin_layout Plain Layout
11200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11203 \begin_layout Plain Layout
11209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11212 \begin_layout Plain Layout
11218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11221 \begin_layout Plain Layout
11227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11230 \begin_layout Plain Layout
11238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11241 \begin_layout Plain Layout
11247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11250 \begin_layout Plain Layout
11251 \begin_inset Formula $A\, B$
11259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11262 \begin_layout Plain Layout
11263 \begin_inset Formula $A\: B$
11271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11274 \begin_layout Plain Layout
11275 \begin_inset Formula $A\; B$
11283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11286 \begin_layout Plain Layout
11287 \begin_inset Formula $A\quad B$
11295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11298 \begin_layout Plain Layout
11299 \begin_inset Formula $A\qquad B$
11307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11310 \begin_layout Plain Layout
11311 \begin_inset Formula $A\! B$
11327 \begin_layout Standard
11328 The last size seem to produce no space.
11329 It is displayed red in LyX contrary to the other sizes, because it is a
11331 There are two more negative spaces:
11334 \begin_layout Standard
11336 \begin_inset Tabular
11337 <lyxtabular version="3" rows="3" columns="3">
11339 <column alignment="center" valignment="middle" width="6.8cm">
11340 <column alignment="center" valignment="top" width="0pt">
11341 <column alignment="center" valignment="top" width="0pt">
11343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11346 \begin_layout Plain Layout
11352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11355 \begin_layout Plain Layout
11363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11366 \begin_layout Plain Layout
11376 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11379 \begin_layout Plain Layout
11384 keystrokes after inserting the protected space
11389 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11392 \begin_layout Plain Layout
11398 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11401 \begin_layout Plain Layout
11409 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11412 \begin_layout Plain Layout
11418 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11421 \begin_layout Plain Layout
11422 \begin_inset Formula $A\negmedspace B$
11430 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11433 \begin_layout Plain Layout
11434 \begin_inset Formula $A\negthickspace B$
11450 \begin_layout Standard
11451 Negative spaces can lead to characters overlapping each other.
11452 Thus they can be used to enforce ligatures, what is e.
11453 \begin_inset space \thinspace{}
11457 \begin_inset space \space{}
11460 useful for summation operators:
11463 \begin_layout Standard
11465 \begin_inset Tabular
11466 <lyxtabular version="3" rows="3" columns="2">
11468 <column alignment="center" valignment="top" width="0">
11469 <column alignment="center" valignment="top" width="0">
11471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11474 \begin_layout Plain Layout
11480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11483 \begin_layout Plain Layout
11485 \begin_inset Note Note
11488 \begin_layout Plain Layout
11495 is only used as spacer.
11507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11510 \begin_layout Plain Layout
11519 \begin_layout Plain Layout
11533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11536 \begin_layout Plain Layout
11537 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11550 \begin_layout Plain Layout
11561 \begin_layout Plain Layout
11575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11578 \begin_layout Plain Layout
11579 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11595 \begin_layout Standard
11596 Relations like for example equal signs, are always surrounded by space.
11597 To suppress this, the equal sign is placed into a TeX-brace.
11598 The following example demonstrates this:
11601 \begin_layout Standard
11603 \begin_inset Tabular
11604 <lyxtabular version="3" rows="2" columns="2">
11606 <column alignment="center" valignment="top" width="0pt">
11607 <column alignment="center" valignment="top" width="0pt">
11609 <cell alignment="center" valignment="top" usebox="none">
11612 \begin_layout Plain Layout
11618 <cell alignment="center" valignment="top" usebox="none">
11621 \begin_layout Plain Layout
11622 \begin_inset Formula $A=B$
11632 <cell alignment="center" valignment="top" usebox="none">
11635 \begin_layout Plain Layout
11636 \begin_inset Note Note
11639 \begin_layout Plain Layout
11646 is only used as spacer.
11652 \begin_inset Formula $\raisebox{5mm}{}$
11655 equation without space
11660 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11663 \begin_layout Plain Layout
11664 \begin_inset Formula $A{=}B$
11680 \begin_layout Standard
11682 The command for the last formula is:
11687 \begin_inset Formula $\to$
11693 \begin_layout Standard
11694 \begin_inset VSpace bigskip
11697 Spaces are needed for physical units, because the space between the value
11698 and the unit is the smallest one and not a normal space.
11699 For units in text, the smallest space is inserted via the menu
11701 Insert\SpecialChar \menuseparator
11702 Formatting\SpecialChar \menuseparator
11704 \begin_inset space ~
11712 arg "space-insert thin"
11718 \begin_layout Standard
11719 An example to visualize the difference:
11722 \begin_layout Standard
11723 \begin_inset Tabular
11724 <lyxtabular version="3" rows="2" columns="2">
11726 <column alignment="left" valignment="top" width="0">
11727 <column alignment="left" valignment="top" width="0">
11729 <cell alignment="center" valignment="top" usebox="none">
11732 \begin_layout Plain Layout
11734 \begin_inset Formula $\cdot$
11742 <cell alignment="center" valignment="top" usebox="none">
11745 \begin_layout Plain Layout
11746 space between value and unit
11753 <cell alignment="center" valignment="top" usebox="none">
11756 \begin_layout Plain Layout
11758 \begin_inset space \thinspace{}
11762 \begin_inset Formula $\cdot$
11770 <cell alignment="center" valignment="top" usebox="none">
11773 \begin_layout Plain Layout
11774 smallest space between value and unit
11787 \begin_layout Subsection
11792 \begin_layout Plain Layout
11805 \begin_layout Plain Layout
11806 for vertical space in formulas see
11807 \begin_inset CommandInset ref
11809 reference "sub:Line-Separation"
11822 \begin_layout Plain Layout
11830 \begin_inset Note Note
11833 \begin_layout Plain Layout
11836 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11839 \begin_layout Plain Layout
11842 texorpdfstring is in section
11843 \begin_inset CommandInset ref
11845 reference "sub:Formulas-in-Section"
11855 \begin_inset CommandInset label
11857 name "sub:Variable-Space"
11865 \begin_layout Plain Layout
11866 Space ! horizontal ! variable
11874 \begin_layout Standard
11875 Space with a defined length can be inserted with the command
11885 \begin_layout Plain Layout
11895 \begin_inset Quotes eld
11904 \begin_layout Plain Layout
11916 \begin_inset Quotes erd
11920 The length can be specified by left-clicking on the
11921 \begin_inset Quotes eld
11930 \begin_layout Plain Layout
11942 \begin_inset Quotes erd
11946 The length may also be negative.
11947 To insert so many space that the formula uses all available space, the
11958 \begin_layout Plain Layout
11969 \begin_layout Standard
11970 \begin_inset VSpace -1mm
11976 \begin_layout Standard
11978 \begin_inset Tabular
11979 <lyxtabular version="3" rows="4" columns="2">
11981 <column alignment="center" valignment="top" width="0">
11982 <column alignment="center" valignment="top" width="0">
11984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11987 \begin_layout Plain Layout
11995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11998 \begin_layout Plain Layout
12006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12009 \begin_layout Plain Layout
12016 \begin_layout Plain Layout
12026 \begin_inset Formula $\to$
12032 \begin_inset space \thinspace{}
12040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12043 \begin_layout Plain Layout
12044 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12057 \begin_layout Plain Layout
12064 \begin_layout Plain Layout
12074 \begin_inset Formula $\to$
12080 \begin_inset space \thinspace{}
12088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12091 \begin_layout Plain Layout
12092 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12105 \begin_layout Plain Layout
12112 \begin_layout Plain Layout
12126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12129 \begin_layout Plain Layout
12130 \begin_inset Formula $A=A\hfill B=B$
12146 \begin_layout Standard
12147 In the last example the available space is given by the longest column entry
12149 In an inline formula the space depends on the length of the line in which
12157 Thus, when the line uses the full width, no space will be created.
12164 only has an effect on displayed formulas when the formula style
12169 (Formula styles are explained in
12170 \begin_inset CommandInset ref
12172 reference "sec:Formula-Styles"
12179 \begin_layout Standard
12186 , there are the commands
12198 that fill the space with a pattern, see
12199 \begin_inset CommandInset ref
12201 reference "sub:Ellipses"
12208 \begin_layout Standard
12209 For text, variable space can be inserted via the menu
12211 Insert\SpecialChar \menuseparator
12212 Formatting\SpecialChar \menuseparator
12214 \begin_inset space ~
12222 \begin_layout Standard
12223 This is a line with
12224 \begin_inset space \hspace{}
12229 \begin_inset space \thinspace{}
12235 \begin_layout Standard
12236 This is a line with
12237 \begin_inset space \hfill{}
12243 \begin_layout Subsection
12244 Space besides inline Formulas
12248 \begin_layout Plain Layout
12249 Space ! besides inline formulas
12257 \begin_layout Standard
12258 The space that surrounds inline formulas can be adjusted with the length
12269 \begin_layout Plain Layout
12278 The value of a length is set with the command
12288 \begin_layout Plain Layout
12296 that has the following scheme:
12299 \begin_layout Standard
12304 setlength{length name}{value}
12307 \begin_layout Standard
12315 \begin_inset space \thinspace{}
12321 \begin_layout Standard
12331 \begin_layout Standard
12332 is inserted in TeX-mode.
12334 \begin_inset space \thinspace{}
12337 mm space will now be set around all inline formulas:
12341 \begin_layout Plain Layout
12355 \begin_layout Standard
12356 This is a line with an inline formula
12357 \begin_inset Formula $A=B$
12361 \begin_inset space \thinspace{}
12364 mm surrounding space.
12368 \begin_layout Plain Layout
12382 \begin_layout Standard
12383 To return to the predefined value,
12389 is set to the value 0
12390 \begin_inset space \thinspace{}
12396 \begin_layout Section
12401 \begin_layout Plain Layout
12411 \begin_layout Plain Layout
12416 \begin_layout Plain Layout
12427 \begin_layout Plain Layout
12442 \begin_layout Standard
12443 Boxes for text are described in chapter
12450 \begin_inset space ~
12458 \begin_layout Subsection
12460 \begin_inset CommandInset label
12462 name "sub:Boxes-with-Frame"
12470 \begin_layout Plain Layout
12479 \begin_layout Standard
12480 It is possible to frame formulas or parts of it with the commands
12490 \begin_layout Plain Layout
12508 \begin_layout Plain Layout
12519 \begin_layout Standard
12520 When one of these commands is inserted to a formula, a blue box appears
12521 within a frame to enter formula parts.
12528 an additional formula has to be created by
12532 within this box, because the box content will otherwise be treated as mathemati
12540 is used, a new formula is automatically created inside the frame.
12543 \begin_layout Standard
12550 is not suitable to frame displayed formulas because the formula will always
12551 be set in the size of the text.
12558 is in contrary not suitable to frame inline formulas, because the formula
12559 will always be set in the size of a displayed formula.
12562 \begin_layout Standard
12569 there is the command
12579 \begin_layout Plain Layout
12587 where additionally the frame width and the alignment can be specified.
12594 is used in the following scheme:
12597 \begin_layout Standard
12602 framebox[frame width][position]{box content}
12605 \begin_layout Standard
12606 The position can either be
12623 right aligns the formula in the box.
12624 When no position is given, the formula will be centered.
12625 \begin_inset Newline newline
12628 Is no width given, also no position can be given.
12629 In this case the frame width is adjusted to the box content like for
12638 \begin_layout Standard
12645 is inserted, a box appears containing three blue boxes.
12646 The first two boxes are surrounded by brackets and denote the two optional
12648 The third box is for formula parts like for
12657 \begin_layout Standard
12659 \begin_inset Tabular
12660 <lyxtabular version="3" rows="5" columns="2">
12662 <column alignment="center" valignment="top" width="0">
12663 <column alignment="center" valignment="top" width="0">
12665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12668 \begin_layout Plain Layout
12674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12677 \begin_layout Plain Layout
12679 \begin_inset Note Note
12682 \begin_layout Plain Layout
12689 is only used as spacer.
12701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12704 \begin_layout Plain Layout
12711 \begin_layout Plain Layout
12730 \begin_layout Plain Layout
12744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12747 \begin_layout Plain Layout
12748 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12761 \begin_layout Plain Layout
12768 \begin_layout Plain Layout
12783 \begin_layout Plain Layout
12797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12800 \begin_layout Plain Layout
12801 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12814 \begin_layout Plain Layout
12821 \begin_layout Plain Layout
12835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12838 \begin_layout Plain Layout
12839 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12852 \begin_layout Plain Layout
12859 \begin_layout Plain Layout
12869 \begin_inset Formula $\to$
12873 \begin_inset Formula $\to$
12886 \begin_layout Plain Layout
12896 \begin_inset Formula $\downarrow$
12904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12907 \begin_layout Plain Layout
12908 \begin_inset Formula $\raisebox{6mm}{}$
12912 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12916 \begin_inset Formula $\raisebox{-4mm}{}$
12932 \begin_layout Standard
12933 The frame thickness can also be adjusted.
12934 To do this the following commands have to be inserted in TeX-mode before
12938 \begin_layout Standard
12948 \begin_inset Quotes eld
12952 \begin_inset Quotes erd
12966 \begin_inset Quotes eld
12970 \begin_inset Quotes erd
12976 \begin_layout Standard
12977 \begin_inset Quotes eld
12981 \begin_inset Quotes erd
12984 specifies the minimal distance between the frame and the first character
12986 An example for this is the following framed formula:
12990 \begin_layout Plain Layout
13002 \begin_inset Formula \[
13007 Before this formula the commands
13010 \begin_layout Standard
13032 \begin_layout Standard
13033 were inserted in TeX-mode.
13034 The given values are used for all following boxes.
13037 \begin_layout Standard
13038 To return to the standard frame size, the command
13041 \begin_layout Standard
13066 \begin_layout Plain Layout
13080 \begin_layout Standard
13081 is inserted in TeX-mode before the next formula.
13084 \begin_layout Subsection
13085 Boxes without Frame
13086 \begin_inset CommandInset label
13088 name "sub:Boxes-without-Frame"
13096 \begin_layout Plain Layout
13097 Boxes ! without frame
13105 \begin_layout Standard
13106 For boxes without a frame there are the following box commands:
13116 \begin_layout Plain Layout
13134 \begin_layout Plain Layout
13152 \begin_layout Plain Layout
13163 \begin_layout Standard
13170 a box can be super- or subscripted.
13171 But in contrary to normal super- and subscripting, the characters in the
13172 box keep their font size.
13179 is used in the following scheme:
13182 \begin_layout Standard
13187 raisebox{height}{box content}
13190 \begin_layout Standard
13191 When the box should contain a formula, an extra formula is needed like for
13202 \begin_inset Note Greyedout
13205 \begin_layout Plain Layout
13216 this extra formula is created by pressing
13220 twice instead of once because LyX doesn't yet support
13234 \begin_layout Standard
13236 \begin_inset Tabular
13237 <lyxtabular version="3" rows="4" columns="2">
13239 <column alignment="center" valignment="top" width="0">
13240 <column alignment="center" valignment="top" width="0">
13242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13245 \begin_layout Plain Layout
13251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13254 \begin_layout Plain Layout
13262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13265 \begin_layout Plain Layout
13269 \begin_inset Formula $\to$
13275 \begin_inset Formula $\to$
13283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13286 \begin_layout Plain Layout
13287 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13300 \begin_layout Plain Layout
13304 \begin_inset Formula $\to$
13310 \begin_inset Formula $\to$
13318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13321 \begin_layout Plain Layout
13322 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13335 \begin_layout Plain Layout
13339 \begin_inset Formula $\to$
13358 \begin_layout Plain Layout
13372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13375 \begin_layout Plain Layout
13376 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13392 \begin_layout Standard
13417 , with the difference that there is no frame.
13420 \begin_layout Subsection
13422 \begin_inset CommandInset label
13424 name "sub:Colored-Boxes"
13432 \begin_layout Plain Layout
13441 \begin_layout Standard
13442 To be able to use all commands explained in this section, the LaTeX-package
13451 \begin_layout Plain Layout
13456 is part of every LaTeX standard installation.
13465 \begin_layout Plain Layout
13471 has to be loaded in the LaTeX-preamble with the line
13475 \begin_layout Plain Layout
13476 When text is colored somewhere in the document with a predefined color,
13477 LyX loads the LaTeX-package
13482 Thus it is possible that the package is loaded twice, but this doesn't
13489 \begin_inset Note Note
13492 \begin_layout Plain Layout
13493 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13502 \begin_layout Standard
13510 \begin_layout Standard
13511 \begin_inset VSpace medskip
13514 To color boxes, the command
13524 \begin_layout Plain Layout
13532 is used in the following scheme:
13535 \begin_layout Standard
13540 colorbox{color}{box content}
13543 \begin_layout Standard
13544 The box content can also be a box and a
13550 can also be part of another box (see the 2nd and 3rd example).
13551 When the box should contain a formula, an extra formula has to be created,
13552 the same way as for
13562 \begin_layout Plain Layout
13563 This also applies for the command
13577 \begin_layout Standard
13578 One of the following predefined colors can be chosen:
13581 \begin_layout Standard
13615 \begin_layout Standard
13617 \begin_inset Tabular
13618 <lyxtabular version="3" rows="4" columns="2">
13620 <column alignment="center" valignment="top" width="0">
13621 <column alignment="center" valignment="top" width="0">
13623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13626 \begin_layout Plain Layout
13632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13635 \begin_layout Plain Layout
13637 \begin_inset Note Note
13640 \begin_layout Plain Layout
13647 is only used as spacer.
13659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13662 \begin_layout Plain Layout
13666 \begin_inset Formula $\to$
13676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13679 \begin_layout Plain Layout
13680 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13693 \begin_layout Plain Layout
13697 \begin_inset Formula $\to$
13708 \begin_layout Plain Layout
13722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13725 \begin_layout Plain Layout
13726 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13739 \begin_layout Plain Layout
13746 \begin_layout Plain Layout
13758 \begin_inset Formula $\to$
13777 \begin_layout Plain Layout
13791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13794 \begin_layout Plain Layout
13795 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13811 \begin_layout Standard
13818 only colors the box but not the characters in the box.
13819 To color all characters, the whole formula is highlighted and the wanted
13820 color is chosen in the
13823 \begin_inset space ~
13829 The dialog can be called with the toolbar button
13830 \begin_inset Graphics
13831 filename ../images/dialog-show_character.png
13838 Edit\SpecialChar \menuseparator
13840 \begin_inset space ~
13843 Style\SpecialChar \menuseparator
13847 The formula number has then the same color as the formula.
13848 When the formula number should get another color than the formula characters,
13849 the color must be changed within the formula.
13852 \begin_layout Standard
13856 \begin_layout Standard
13859 \begin_inset Formula \begin{equation}
13860 \int A=B\label{eq:red}\end{equation}
13867 \begin_inset Formula \begin{equation}
13868 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13875 \begin_layout Standard
13877 \begin_inset CommandInset ref
13883 is completely colored red.
13884 \begin_inset Newline newline
13888 \begin_inset CommandInset ref
13890 reference "eq:redgreen"
13894 was first completely colored green to set the color for the formula number.
13895 Subsequently the formula characters were colored red.
13898 \begin_layout Standard
13899 \begin_inset VSpace bigskip
13902 To color the frame different than the rest of the box, the command
13912 \begin_layout Plain Layout
13920 is used in the following scheme:
13923 \begin_layout Standard
13928 fcolorbox{frame color}{color}{box content}
13931 \begin_layout Standard
13938 is an extension of the command
13945 The frame width is set, like for
13968 \begin_layout Plain Layout
13980 \begin_inset Formula \[
13981 \fcolorbox{cyan}{magenta}{A=B}\]
13989 \begin_layout Plain Layout
14003 \begin_layout Standard
14004 This formula was created with the command
14005 \begin_inset Newline newline
14013 \begin_inset Formula $\to$
14019 \begin_inset Formula $\to$
14029 \begin_layout Standard
14030 \begin_inset VSpace bigskip
14033 To use other colors than the predefined ones, they have to be defined first.
14036 \begin_layout Standard
14037 One can for example define the color
14038 \begin_inset Quotes eld
14046 \begin_inset Quotes erd
14049 with the LaTeX-preamble line:
14052 \begin_layout Standard
14057 definecolor{darkgreen}{cmyk}{0.5,
14075 \begin_layout Plain Layout
14086 \begin_layout Standard
14091 is the color space that denotes the colors
14108 The four comma separated numbers are the portion factor for the corresponding
14109 colors of the color space.
14110 The factors can be in the range of 0
14111 \begin_inset space \thinspace{}
14115 \begin_inset space \thinspace{}
14123 also the color space
14127 can be used for definitions.
14144 , so that there are in this case three portion factors for the corresponding
14146 Furthermore there is the color space
14150 with one portion factor for the gray value.
14153 \begin_layout Standard
14154 As example a framed box with the new defined color
14158 where the characters have been colored
14163 \begin_inset Formula \begin{equation}
14164 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14171 \begin_layout Standard
14172 Self-defined colors can also be used for text with the help of the command
14183 \begin_layout Plain Layout
14192 \begin_layout Standard
14196 \begin_layout Plain Layout
14200 textcolor{darkgreen}{
14206 \begin_inset Quotes eld
14210 \begin_inset Quotes erd
14217 \begin_layout Plain Layout
14227 \begin_layout Standard
14238 \begin_layout Plain Layout
14246 is used in the scheme
14250 textcolor{color}{characters to color}
14255 \begin_layout Subsection
14257 \begin_inset CommandInset label
14259 name "sub:Paragraph-Boxes"
14267 \begin_layout Plain Layout
14268 Boxes ! as paragraph
14276 \begin_layout Standard
14277 A box that can contain several lines and paragraphs, a so called paragraph
14278 box (parbox), can be created with the menu
14280 Insert\SpecialChar \menuseparator
14283 or the toolbar button
14284 \begin_inset Graphics
14285 filename ../images/box-insert.png
14293 \begin_layout Standard
14294 The following example shows a framed parbox in a line:
14297 \begin_layout Standard
14298 \begin_inset VSpace medskip
14302 \begin_inset Box Boxed
14311 height_special "totalheight"
14314 \begin_layout Plain Layout
14315 This is a paragraph box.
14317 \begin_inset space \thinspace{}
14320 cm long and can also contain formulas:
14321 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14332 \begin_layout Standard
14333 \begin_inset VSpace medskip
14339 \begin_layout Standard
14340 Such a box is created by right-clicking on the gray box inset.
14341 A dialog pops up showing the box properties.
14355 \begin_inset space \thinspace{}
14360 Vertical Box Alignment
14365 \begin_layout Standard
14366 \begin_inset VSpace medskip
14369 In LaTeX a parbox is created with the command
14379 \begin_layout Plain Layout
14387 that has the following scheme:
14390 \begin_layout Standard
14395 parbox[position]{width}{box content}
14398 \begin_layout Standard
14412 for bottom means that the box is aligned within the surrounding text with
14418 for top this is done with the first line.
14419 When no position is given, the box will be vertically centered, see section
14427 \begin_inset space ~
14432 manual for examples.
14435 \begin_layout Standard
14436 \begin_inset VSpace bigskip
14439 To frame formulas completely, including the formula number, the formula
14440 must be set into a parbox.
14441 To do this, the command
14455 is inserted in TeX-mode before the formula.
14466 \begin_layout Plain Layout
14474 is hereby the line width set for the document.
14475 Because the frame is outside the parbox, 2
14476 \begin_inset space \thinspace{}
14479 times the frame separation and the frame thickness must be subtracted from
14481 As this is not automatically done by LyX due to a bug
14485 \begin_layout Plain Layout
14486 \begin_inset CommandInset href
14488 name "LyX-bug #4483"
14489 target "http://www.lyx.org/trac/ticket/4483"
14498 , TeX-mode has to be used.
14499 To be able to multiply and subtract in arguments, the LaTeX-package
14507 \begin_layout Plain Layout
14512 is part of every LaTeX standard installation.
14521 \begin_layout Plain Layout
14527 must be loaded in the LaTeX-preamble with the line
14530 \begin_layout Standard
14538 \begin_layout Standard
14539 Behind the formula both boxes are closed by entering
14544 Here is an example:
14548 \begin_layout Plain Layout
14562 \begin_layout Standard
14566 \begin_layout Plain Layout
14584 \begin_inset Formula \begin{equation}
14585 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14593 \begin_layout Plain Layout
14604 \begin_layout Plain Layout
14618 \begin_layout Standard
14619 \begin_inset VSpace medskip
14622 As a parbox is used as argument of
14628 , there is in this case no difference between
14643 \begin_layout Standard
14644 \begin_inset VSpace bigskip
14647 Paragraph boxes are very useful to comment formulas directly.
14654 is used in combination with the command
14668 \begin_inset CommandInset ref
14670 reference "sub:User-defined-Numbering"
14677 \begin_layout Standard
14678 An example of a formula commented with
14687 \begin_layout Standard
14691 \begin_layout Plain Layout
14704 This is a description.
14705 It is distinctly separated from the formula and multiline.
14709 \begin_layout Plain Layout
14721 \begin_layout Standard
14722 Such a formula must be inserted completely in TeX-mode because LyX does
14723 not yet support the command
14730 The formula is created with the following command sequence:
14733 \begin_layout Standard
14746 is inserted in TeX-mode.
14750 \begin_layout Plain Layout
14751 When the formula style
14763 can also be replaced by
14770 (formula styles see
14771 \begin_inset CommandInset ref
14773 reference "sec:Formula-Styles"
14782 Then the description follows as normal text and finally
14788 is inserted in TeX-mode.
14801 hereby create a displayed formula.
14804 \begin_layout Standard
14811 can be seen in this example that was
14812 \begin_inset Quotes eld
14816 \begin_inset Quotes erd
14819 using the mathematical textmode:
14820 \begin_inset Formula \[
14821 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14828 \begin_layout Section
14833 \begin_layout Plain Layout
14842 \begin_layout Subsection
14844 \begin_inset CommandInset label
14846 name "sub:Big-Operators"
14854 \begin_layout Plain Layout
14864 \begin_layout Plain Layout
14874 \begin_layout Plain Layout
14883 \begin_layout Standard
14884 To be able to use all integral operators listed here, the option
14886 Use esint package automatically
14888 must be set in the document settings under
14891 \begin_inset space ~
14899 \begin_layout Standard
14900 \begin_inset space \hfill{}
14904 \begin_inset Tabular
14905 <lyxtabular version="3" rows="11" columns="2">
14907 <column alignment="center" valignment="top" width="0pt">
14908 <column alignment="center" valignment="top" width="0pt">
14910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14913 \begin_layout Plain Layout
14919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14922 \begin_layout Plain Layout
14930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14933 \begin_layout Plain Layout
14940 \begin_layout Plain Layout
14953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14956 \begin_layout Plain Layout
14957 \begin_inset Formula $\int$
14967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14970 \begin_layout Plain Layout
14978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14981 \begin_layout Plain Layout
14982 \begin_inset Formula $\oint$
14992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14995 \begin_layout Plain Layout
15003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15006 \begin_layout Plain Layout
15007 \begin_inset Formula $\ointctrclockwise$
15017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15020 \begin_layout Plain Layout
15028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15031 \begin_layout Plain Layout
15032 \begin_inset Formula $\ointclockwise$
15042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15045 \begin_layout Plain Layout
15053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15056 \begin_layout Plain Layout
15057 \begin_inset Formula $\sqint$
15067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15070 \begin_layout Plain Layout
15078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15081 \begin_layout Plain Layout
15083 \begin_inset Formula $\fint$
15093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15096 \begin_layout Plain Layout
15104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15107 \begin_layout Plain Layout
15109 \begin_inset Formula $\landupint$
15119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15122 \begin_layout Plain Layout
15130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15133 \begin_layout Plain Layout
15135 \begin_inset Formula $\landdownint$
15145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15148 \begin_layout Plain Layout
15156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15159 \begin_layout Plain Layout
15160 \begin_inset Formula $\bigcap$
15170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15173 \begin_layout Plain Layout
15181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15184 \begin_layout Plain Layout
15185 \begin_inset Formula $\bigcup$
15199 \begin_inset space \hfill{}
15203 \begin_inset Tabular
15204 <lyxtabular version="3" rows="11" columns="2">
15206 <column alignment="center" valignment="top" width="0pt">
15207 <column alignment="center" valignment="top" width="0pt">
15209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15212 \begin_layout Plain Layout
15218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15221 \begin_layout Plain Layout
15229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15232 \begin_layout Plain Layout
15239 \begin_layout Plain Layout
15252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15255 \begin_layout Plain Layout
15256 \begin_inset Formula $\sum$
15266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15269 \begin_layout Plain Layout
15276 \begin_layout Plain Layout
15289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15292 \begin_layout Plain Layout
15293 \begin_inset Formula $\prod$
15303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15306 \begin_layout Plain Layout
15314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15317 \begin_layout Plain Layout
15318 \begin_inset Formula $\coprod$
15328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15331 \begin_layout Plain Layout
15339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15342 \begin_layout Plain Layout
15343 \begin_inset Formula $\bigodot$
15353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15356 \begin_layout Plain Layout
15364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15367 \begin_layout Plain Layout
15368 \begin_inset Formula $\bigotimes$
15378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15381 \begin_layout Plain Layout
15389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15392 \begin_layout Plain Layout
15393 \begin_inset Formula $\bigoplus$
15403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15406 \begin_layout Plain Layout
15414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15417 \begin_layout Plain Layout
15418 \begin_inset Formula $\bigwedge$
15428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15431 \begin_layout Plain Layout
15439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15442 \begin_layout Plain Layout
15443 \begin_inset Formula $\bigvee$
15453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15456 \begin_layout Plain Layout
15464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15467 \begin_layout Plain Layout
15468 \begin_inset Formula $\bigsqcup$
15478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15481 \begin_layout Plain Layout
15489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15492 \begin_layout Plain Layout
15493 \begin_inset Formula $\biguplus$
15507 \begin_inset space \hfill{}
15513 \begin_layout Standard
15514 All big operators can also be inserted via the math toolbar button
15515 \begin_inset Graphics
15516 filename ../images/math/intop.png
15524 \begin_layout Standard
15525 The operators are called big because they are bigger than the sometimes
15526 equal looking binary operators.
15527 All big operators can have limits as described in the next subsection.
15530 \begin_layout Standard
15531 For all integral operators there is a second version available, ending on
15549 These operators are different from
15556 \begin_inset space \space{}
15559 in the style the operator limits are displayed, see
15560 \begin_inset CommandInset ref
15562 reference "sub:Operator-Limits"
15570 \begin_layout Subsubsection*
15571 Advice for Integrals
15574 \begin_layout Standard
15579 in an integral is an operator, that therefore has to be set upright.
15580 This is done by highlighting the
15584 and using the keyboard shortcut
15594 \begin_layout Plain Layout
15600 \begin_inset CommandInset ref
15602 reference "sub:Font-Styles"
15612 Finally the smallest space is inserted before the
15616 , as this is usual for operators.
15620 \begin_layout Standard
15622 \begin_inset Formula $\int A(x)dx$
15626 \begin_inset Newline newline
15633 \begin_layout Plain Layout
15643 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15649 \begin_layout Standard
15650 For multiple integrals there are the following commands:
15651 \begin_inset VSpace medskip
15657 \begin_layout Standard
15658 \begin_inset space \hfill{}
15662 \begin_inset Tabular
15663 <lyxtabular version="3" rows="4" columns="2">
15665 <column alignment="center" valignment="top" width="0">
15666 <column alignment="center" valignment="top" width="0">
15668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15671 \begin_layout Plain Layout
15677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15680 \begin_layout Plain Layout
15682 \begin_inset Note Note
15685 \begin_layout Plain Layout
15692 is only used as spacer.
15704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15707 \begin_layout Plain Layout
15715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15718 \begin_layout Plain Layout
15719 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15732 \begin_layout Plain Layout
15740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15743 \begin_layout Plain Layout
15744 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15757 \begin_layout Plain Layout
15765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15768 \begin_layout Plain Layout
15769 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15783 \begin_inset space \hfill{}
15787 \begin_inset Tabular
15788 <lyxtabular version="3" rows="4" columns="2">
15790 <column alignment="center" valignment="top" width="0">
15791 <column alignment="center" valignment="top" width="0">
15793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15796 \begin_layout Plain Layout
15802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15805 \begin_layout Plain Layout
15813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15816 \begin_layout Plain Layout
15824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15827 \begin_layout Plain Layout
15828 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15841 \begin_layout Plain Layout
15849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15852 \begin_layout Plain Layout
15853 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15866 \begin_layout Plain Layout
15874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15877 \begin_layout Plain Layout
15878 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15892 \begin_inset space \hfill{}
15898 \begin_layout Subsection
15900 \begin_inset CommandInset label
15902 name "sub:Operator-Limits"
15910 \begin_layout Plain Layout
15919 \begin_layout Standard
15920 Limits are created by super- and subscripts:
15923 \begin_layout Standard
15925 \begin_inset Tabular
15926 <lyxtabular version="3" rows="2" columns="2">
15928 <column alignment="center" valignment="top" width="0pt">
15929 <column alignment="center" valignment="top" width="0pt">
15931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15934 \begin_layout Plain Layout
15940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15943 \begin_layout Plain Layout
15945 \begin_inset Note Note
15948 \begin_layout Plain Layout
15955 is only used as spacer.
15967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15970 \begin_layout Plain Layout
15979 \begin_layout Plain Layout
15989 \begin_inset Formula $\to$
15993 \begin_inset Formula $\to$
16001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16004 \begin_layout Plain Layout
16005 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16021 \begin_layout Standard
16022 Limits of inline formulas are set right beside the operator.
16023 Limits in displayed formulas are set above or below the operator, except
16024 for integral limits.
16027 \begin_layout Standard
16028 To force that the limits are set beside the operator, the cursor is set
16029 directly behind the operator and the limits type is changed with the menu
16032 Edit\SpecialChar \menuseparator
16033 Math\SpecialChar \menuseparator
16052 \begin_layout Standard
16053 The default limits type is this:
16054 \begin_inset Formula \[
16055 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16059 This is how it looks when the limits type was changed to
16066 \begin_inset Formula \[
16067 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16071 For integrals, except those ending with
16087 etc., the limits are by default set beside the operator.
16088 But for multiple integrals the limits are often set below the operator.
16089 In the following example the limits type was therefore set to
16093 and so set below the integrals:
16094 \begin_inset Formula \begin{equation}
16095 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16102 \begin_layout Standard
16103 \begin_inset VSpace medskip
16106 To specify conditions for limits, the commands
16116 \begin_layout Plain Layout
16134 \begin_layout Plain Layout
16143 To create for example this expression
16144 \begin_inset Formula \begin{equation}
16145 \sum_{\begin{subarray}{c}
16147 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16154 \begin_layout Standard
16155 the following has to be done:
16156 \begin_inset Newline newline
16171 \begin_layout Plain Layout
16183 One is now in a blue box under the summation operator and insert there
16192 \begin_layout Plain Layout
16204 The blue box is now within a purple box and now several lines can be written
16206 A new line is created by inserting a line break (
16209 arg "newline-insert newline"
16214 \begin_inset Newline newline
16219 0<k<1000 Ctrl+Return
16220 \begin_inset Newline newline
16225 is typed in, a new box appears below for the new line.
16228 \begin_layout Standard
16229 The alignment of the lines can be changed to left aligned with the
16239 Edit\SpecialChar \menuseparator
16243 To get right alignment,
16251 \begin_layout Plain Layout
16262 is inserted at the beginning of the line.
16265 \begin_layout Standard
16278 with the difference that the lines are always centered.
16281 \begin_layout Standard
16282 \begin_inset VSpace bigskip
16286 \begin_inset CommandInset ref
16288 reference "eq:substack"
16292 there can be too much space beside an operator, because the characters
16293 following the operator are set beside the limits.
16296 \begin_layout Standard
16297 To avoid this, the following macro can be used in the LaTeX-preamble:
16300 \begin_layout Standard
16314 \begin_inset Newline newline
16326 \begin_inset Newline newline
16333 mathclapinternal #1#2{
16337 mathsurround =0pt #1{#2}$}}
16340 \begin_layout Standard
16341 This defines the command
16351 \begin_layout Plain Layout
16359 that sets the width of the limit to 0
16360 \begin_inset space \thinspace{}
16364 The command scheme is
16367 \begin_layout Standard
16375 \begin_layout Standard
16376 where the limit can consist of several conditions.
16379 \begin_layout Standard
16381 \begin_inset CommandInset ref
16383 reference "eq:substack"
16387 , one uses the command
16390 \begin_layout Standard
16403 \begin_layout Plain Layout
16412 0<k<1000 Ctrl+Return
16415 \begin_layout Standard
16416 to create the lower limit.
16417 The summand is now directly behind the summation operator:
16418 \begin_inset Formula \[
16419 \sum_{\mathclap{\substack{0<k<1000\\
16420 \\k\,\in\,\mathbb{N}}
16428 \begin_layout Standard
16429 \begin_inset VSpace bigskip
16432 How to use one limit for several operators is described in
16433 \begin_inset CommandInset ref
16435 reference "sub:Self-defined-Operators"
16442 \begin_layout Subsection
16444 \begin_inset CommandInset label
16446 name "sub:Binary-Operators"
16454 \begin_layout Plain Layout
16463 \begin_layout Standard
16464 Binary operators are surrounded by space when there is a character before
16466 \begin_inset VSpace medskip
16472 \begin_layout Standard
16473 \begin_inset space \hfill{}
16477 \begin_inset Tabular
16478 <lyxtabular version="3" rows="13" columns="2">
16480 <column alignment="center" valignment="top" width="0pt">
16481 <column alignment="center" valignment="top" width="0pt">
16483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16486 \begin_layout Plain Layout
16488 \begin_inset Note Note
16491 \begin_layout Plain Layout
16498 is only used as spacer.
16508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16511 \begin_layout Plain Layout
16519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16522 \begin_layout Plain Layout
16528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16531 \begin_layout Plain Layout
16532 \begin_inset Formula $+$
16542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16545 \begin_layout Plain Layout
16551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16554 \begin_layout Plain Layout
16555 \begin_inset Formula $-$
16565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16568 \begin_layout Plain Layout
16576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16579 \begin_layout Plain Layout
16580 \begin_inset Formula $\pm$
16590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16593 \begin_layout Plain Layout
16601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16604 \begin_layout Plain Layout
16605 \begin_inset Formula $\mp$
16615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16618 \begin_layout Plain Layout
16626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16629 \begin_layout Plain Layout
16630 \begin_inset Formula $\cdot$
16640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16643 \begin_layout Plain Layout
16651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16654 \begin_layout Plain Layout
16655 \begin_inset Formula $\times$
16665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16668 \begin_layout Plain Layout
16676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16679 \begin_layout Plain Layout
16680 \begin_inset Formula $\div$
16690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16693 \begin_layout Plain Layout
16697 \begin_layout Plain Layout
16710 \begin_layout Plain Layout
16722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16725 \begin_layout Plain Layout
16726 \begin_inset Formula $*$
16736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16739 \begin_layout Plain Layout
16747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16750 \begin_layout Plain Layout
16751 \begin_inset Formula $\star$
16761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16764 \begin_layout Plain Layout
16772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16775 \begin_layout Plain Layout
16776 \begin_inset Formula $\circ$
16786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16789 \begin_layout Plain Layout
16797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16800 \begin_layout Plain Layout
16801 \begin_inset Formula $\diamond$
16811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16814 \begin_layout Plain Layout
16822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16825 \begin_layout Plain Layout
16826 \begin_inset Formula $\bullet$
16840 \begin_inset space \hfill{}
16844 \begin_inset Tabular
16845 <lyxtabular version="3" rows="13" columns="2">
16847 <column alignment="center" valignment="top" width="0pt">
16848 <column alignment="center" valignment="top" width="0pt">
16850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16853 \begin_layout Plain Layout
16859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16862 \begin_layout Plain Layout
16870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16873 \begin_layout Plain Layout
16881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16884 \begin_layout Plain Layout
16885 \begin_inset Formula $\nabla$
16895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16898 \begin_layout Plain Layout
16906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16909 \begin_layout Plain Layout
16910 \begin_inset Formula $\bigtriangledown$
16920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16923 \begin_layout Plain Layout
16931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16934 \begin_layout Plain Layout
16935 \begin_inset Formula $\bigtriangleup$
16945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16948 \begin_layout Plain Layout
16956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16959 \begin_layout Plain Layout
16960 \begin_inset Formula $\Box$
16970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16973 \begin_layout Plain Layout
16981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16984 \begin_layout Plain Layout
16985 \begin_inset Formula $\cap$
16995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16998 \begin_layout Plain Layout
17006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17009 \begin_layout Plain Layout
17010 \begin_inset Formula $\cup$
17020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17023 \begin_layout Plain Layout
17031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17034 \begin_layout Plain Layout
17035 \begin_inset Formula $\dagger$
17045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17048 \begin_layout Plain Layout
17056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17059 \begin_layout Plain Layout
17060 \begin_inset Formula $\ddagger$
17070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17073 \begin_layout Plain Layout
17081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17084 \begin_layout Plain Layout
17085 \begin_inset Formula $\wr$
17095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17098 \begin_layout Plain Layout
17106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17109 \begin_layout Plain Layout
17110 \begin_inset Formula $\bigcirc$
17120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17123 \begin_layout Plain Layout
17131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17134 \begin_layout Plain Layout
17135 \begin_inset Formula $\wedge$
17145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17148 \begin_layout Plain Layout
17156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17159 \begin_layout Plain Layout
17160 \begin_inset Formula $\vee$
17174 \begin_inset space \hfill{}
17178 \begin_inset Tabular
17179 <lyxtabular version="3" rows="13" columns="2">
17181 <column alignment="center" valignment="top" width="0pt">
17182 <column alignment="center" valignment="top" width="0pt">
17184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17187 \begin_layout Plain Layout
17193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17196 \begin_layout Plain Layout
17204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17207 \begin_layout Plain Layout
17215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17218 \begin_layout Plain Layout
17219 \begin_inset Formula $\oplus$
17229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17232 \begin_layout Plain Layout
17240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17243 \begin_layout Plain Layout
17244 \begin_inset Formula $\ominus$
17254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17257 \begin_layout Plain Layout
17265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17268 \begin_layout Plain Layout
17269 \begin_inset Formula $\otimes$
17279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17282 \begin_layout Plain Layout
17290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17293 \begin_layout Plain Layout
17294 \begin_inset Formula $\oslash$
17304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17307 \begin_layout Plain Layout
17315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17318 \begin_layout Plain Layout
17319 \begin_inset Formula $\odot$
17329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17332 \begin_layout Plain Layout
17340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17343 \begin_layout Plain Layout
17344 \begin_inset Formula $\amalg$
17354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17357 \begin_layout Plain Layout
17365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17368 \begin_layout Plain Layout
17369 \begin_inset Formula $\uplus$
17379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17382 \begin_layout Plain Layout
17390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17393 \begin_layout Plain Layout
17394 \begin_inset Formula $\setminus$
17404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17407 \begin_layout Plain Layout
17415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17418 \begin_layout Plain Layout
17419 \begin_inset Formula $\sqcap$
17429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17432 \begin_layout Plain Layout
17440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17443 \begin_layout Plain Layout
17444 \begin_inset Formula $\sqcup$
17454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17457 \begin_layout Plain Layout
17465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17468 \begin_layout Plain Layout
17469 \begin_inset Formula $\triangleleft$
17479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17482 \begin_layout Plain Layout
17490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17493 \begin_layout Plain Layout
17494 \begin_inset Formula $\triangleright$
17508 \begin_inset space \hfill{}
17514 \begin_layout Standard
17515 All binary operators can also be inserted via the math toolbar button
17516 \begin_inset Graphics
17517 filename ../images/math/pm.png
17525 \begin_layout Standard
17526 To typeset the Laplace operator also
17543 \begin_inset Formula $\nabla^{2}$
17546 ) can be used instead of
17555 \begin_layout Standard
17562 Insert\SpecialChar \menuseparator
17574 \begin_layout Subsection
17575 Self-defined Operators
17576 \begin_inset CommandInset label
17578 name "sub:Self-defined-Operators"
17586 \begin_layout Plain Layout
17587 Operators ! self-defined
17595 \begin_layout Standard
17596 With the help of the command
17600 DeclareMathOperator
17606 \begin_layout Plain Layout
17611 DeclareMathOperator
17616 custom operators can be defined in the LaTeX-preamble.
17617 Its command scheme is:
17620 \begin_layout Standard
17625 DeclareMathOperator{new command}{display}
17628 \begin_layout Standard
17629 Display can be characters or symbols that define how the operator looks
17631 To define a big operator a * is set behind the command.
17632 All self-defined big operators can have limits as described in
17633 \begin_inset CommandInset ref
17635 reference "sub:Operator-Limits"
17642 \begin_layout Standard
17643 For example the LaTeX-preamble line
17646 \begin_layout Standard
17651 DeclareMathOperator*{
17658 \begin_layout Standard
17659 defines the command
17665 , that inserts a big operator consisting of the lozenge symbol from
17666 \begin_inset CommandInset ref
17668 reference "sub:Miscellaneous-Symbols"
17673 \begin_inset Formula \[
17674 \Lozenge_{n=1}^{\infty}\]
17678 The command for this formula is:
17689 \begin_inset Formula $\to$
17695 \begin_layout Standard
17696 \begin_inset VSpace bigskip
17699 When self-defined operators are not used several times in the document,
17700 they can also be defined with the commands
17710 \begin_layout Plain Layout
17728 \begin_layout Plain Layout
17736 , which have the following scheme:
17739 \begin_layout Standard
17753 \begin_layout Standard
17760 defines big operators,
17769 \begin_layout Standard
17777 \begin_inset space \thinspace{}
17781 \begin_inset space \space{}
17784 be used to use one limit for several operators:
17787 \begin_layout Standard
17788 \begin_inset Formula \[
17789 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17796 \begin_layout Standard
17797 The command for the formula above is:
17798 \begin_inset Newline newline
17817 \begin_layout Plain Layout
17829 \begin_inset Formula $\to$
17838 \begin_layout Plain Layout
17852 \begin_layout Section
17857 \begin_layout Plain Layout
17866 \begin_layout Subsection
17868 \begin_inset CommandInset label
17870 name "sub:Font-Styles"
17878 \begin_layout Plain Layout
17887 \begin_layout Standard
17888 Latin letters in formulas can be set in one of the following font styles:
17889 \begin_inset VSpace -2mm
17895 \begin_layout Standard
17897 \begin_inset Tabular
17898 <lyxtabular version="3" rows="6" columns="3">
17900 <column alignment="center" valignment="top" width="0">
17901 <column alignment="center" valignment="top" width="0">
17902 <column alignment="center" valignment="top" width="0">
17904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17907 \begin_layout Plain Layout
17913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17916 \begin_layout Plain Layout
17922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17925 \begin_layout Plain Layout
17933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17936 \begin_layout Plain Layout
17945 \begin_layout Plain Layout
17961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17964 \begin_layout Plain Layout
17965 \begin_inset Formula $\mathbb{ABC}$
17973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17976 \begin_layout Plain Layout
17989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17992 \begin_layout Plain Layout
18001 \begin_layout Plain Layout
18017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18020 \begin_layout Plain Layout
18021 \begin_inset Formula $\mathbf{AbC}$
18029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18032 \begin_layout Plain Layout
18045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18048 \begin_layout Plain Layout
18057 \begin_layout Plain Layout
18073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18076 \begin_layout Plain Layout
18077 \begin_inset Formula $\boldsymbol{AbC}$
18085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18088 \begin_layout Plain Layout
18091 arg "font-boldsymbol"
18101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18104 \begin_layout Plain Layout
18113 \begin_layout Plain Layout
18129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18132 \begin_layout Plain Layout
18133 \begin_inset Formula $\mathcal{ABC}$
18141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18144 \begin_layout Plain Layout
18157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18160 \begin_layout Plain Layout
18169 \begin_layout Plain Layout
18185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18188 \begin_layout Plain Layout
18189 \begin_inset Formula $\mathfrak{AbC}$
18197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18200 \begin_layout Plain Layout
18214 \begin_layout Standard
18216 \begin_inset Tabular
18217 <lyxtabular version="3" rows="5" columns="3">
18219 <column alignment="center" valignment="top" width="0">
18220 <column alignment="center" valignment="top" width="0">
18221 <column alignment="center" valignment="top" width="0">
18223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18226 \begin_layout Plain Layout
18232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18235 \begin_layout Plain Layout
18241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18244 \begin_layout Plain Layout
18252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18255 \begin_layout Plain Layout
18264 \begin_layout Plain Layout
18280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18283 \begin_layout Plain Layout
18284 \begin_inset Formula $\mathit{AbC}$
18292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18295 \begin_layout Plain Layout
18303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18306 \begin_layout Plain Layout
18315 \begin_layout Plain Layout
18331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18334 \begin_layout Plain Layout
18335 \begin_inset Formula $\mathrm{AbC}$
18343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18346 \begin_layout Plain Layout
18359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18362 \begin_layout Plain Layout
18371 \begin_layout Plain Layout
18387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18390 \begin_layout Plain Layout
18391 \begin_inset Formula $\mathsf{AbC}$
18399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18402 \begin_layout Plain Layout
18415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18418 \begin_layout Plain Layout
18427 \begin_layout Plain Layout
18443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18446 \begin_layout Plain Layout
18447 \begin_inset Formula $\mathtt{AbC}$
18455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18458 \begin_layout Plain Layout
18461 arg "font-typewriter"
18477 \begin_layout Standard
18478 \begin_inset Note Greyedout
18481 \begin_layout Plain Layout
18498 can only be used for big letters.
18506 \begin_layout Standard
18507 Predefined is the style
18516 \begin_layout Standard
18517 The style commands work also for letters in mathematical constructs:
18518 \begin_inset Formula \[
18519 \mathfrak{A=\frac{b}{C}}\]
18526 \begin_layout Standard
18527 Characters in mathematical text don't appear in a math font style but in
18528 the text font style
18535 That their style can't be set correctly via the text style dialog is a
18540 \begin_layout Plain Layout
18541 \begin_inset CommandInset href
18543 name "LyX-bug #4629"
18544 target "http://www.lyx.org/trac/ticket/4629"
18556 \begin_layout Standard
18557 Instead of the style commands the dialog
18559 Edit\SpecialChar \menuseparator
18560 Math\SpecialChar \menuseparator
18563 or the toolbar button
18564 \begin_inset Graphics
18565 filename ../images/math/font.png
18573 \begin_layout Subsection
18575 \begin_inset CommandInset label
18577 name "sub:Bold-Formulas"
18585 \begin_layout Plain Layout
18594 \begin_layout Standard
18595 To make a complete formula bold, the command
18601 from the previous subsection cannot be used, because it doesn't work for
18602 small Greek letters.
18603 Furthermore it prints Latin letters always upright, like in the following
18607 \begin_layout Standard
18608 \begin_inset Formula \[
18609 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18616 \begin_layout Standard
18617 To display the formula correctly, the command
18624 \begin_inset Formula \[
18625 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18629 It is also possible to set the formula in a
18631 boldmath environment
18634 This environment is created by inserting the command
18644 \begin_layout Plain Layout
18653 To end the environment, the command
18663 \begin_layout Plain Layout
18671 is inserted in TeX-mode.
18675 \begin_layout Plain Layout
18685 \begin_inset Formula \[
18686 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18694 \begin_layout Plain Layout
18706 \begin_layout Subsection
18711 \begin_layout Plain Layout
18720 \begin_layout Standard
18721 Formulas can be colored like normal text: Highlight a formula or a formula
18727 Here is a formula in magenta:
18728 \begin_inset Formula \[
18729 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18736 \begin_layout Standard
18737 You can also define your own colors as described in
18738 \begin_inset CommandInset ref
18740 reference "sub:Colored-Boxes"
18745 They can be used with the TeX code command
18755 \begin_layout Plain Layout
18766 \begin_layout Standard
18771 textcolor{color}{characters or formula}
18774 \begin_layout Standard
18775 The following example was colored completely dark green and partly red:
18778 \begin_layout Standard
18782 \begin_layout Plain Layout
18786 textcolor{darkgreen}{
18792 \begin_inset Formula \[
18793 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18801 \begin_layout Plain Layout
18811 \begin_layout Standard
18812 Due to a bug in LyX only complete formulas can be colored with self-defined
18817 \begin_layout Plain Layout
18818 \begin_inset CommandInset href
18820 name "LyX-bug #5269"
18821 target "http://www.lyx.org/trac/ticket/5269"
18833 \begin_layout Subsection
18835 \begin_inset CommandInset label
18837 name "sub:Font-Sizes"
18845 \begin_layout Plain Layout
18854 \begin_layout Standard
18855 For characters in formulas there are, analog to characters in text, the
18856 following size commands:
18859 \begin_layout Standard
18903 \begin_inset Newline newline
18925 \begin_layout Standard
18926 The size produced by the commands depends on the document font size, that
18927 corresponds with the command
18934 The other commands produce smaller or larger sizes than
18941 The font size can however not exceed a certain value.
18942 Is for example the document font size 12
18943 \begin_inset space \thinspace{}
18952 switches to the same size as
18962 \begin_layout Standard
18963 A size command is inserted in TeX-mode before the formula and sets the size
18964 for all following formula and text characters.
18965 To switch back to the initial size, the command
18971 is inserted behind the formula in TeX-mode.
18974 \begin_layout Standard
18975 \begin_inset Newpage newpage
18981 \begin_layout Standard
18982 Within a formula the size can be changed using the following size commands:
18985 \begin_layout Standard
18988 \begin_inset Tabular
18989 <lyxtabular version="3" rows="5" columns="2">
18991 <column alignment="center" valignment="top" width="0">
18992 <column alignment="center" valignment="top" width="0">
18994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18997 \begin_layout Plain Layout
19003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19006 \begin_layout Plain Layout
19008 \begin_inset Note Note
19011 \begin_layout Plain Layout
19018 is only used as spacer.
19030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19033 \begin_layout Plain Layout
19040 \begin_layout Plain Layout
19053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19056 \begin_layout Plain Layout
19057 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19070 \begin_layout Plain Layout
19078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19081 \begin_layout Plain Layout
19082 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19095 \begin_layout Plain Layout
19103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19106 \begin_layout Plain Layout
19107 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19120 \begin_layout Plain Layout
19128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19131 \begin_layout Plain Layout
19132 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19148 \begin_layout Standard
19149 After entering these commands, a blue box appears in which the formula parts
19153 \begin_layout Standard
19154 There is a further method to change the font size, that though only works
19155 for symbols or letters in mathematical text.
19156 To use it, one of the above text size commands is inserted in mathematical
19158 All following characters until the end of the mathematical text or until
19159 another size command will have the selected size.
19161 \begin_inset VSpace -2mm
19167 \begin_layout Standard
19171 \begin_layout Plain Layout
19181 \begin_inset Formula \[
19182 A=\frac{B}{c}\cdot\maltese\]
19187 \begin_inset Formula \[
19188 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19196 \begin_layout Plain Layout
19208 \begin_layout Standard
19209 \begin_inset VSpace medskip
19212 Before both formulas the command
19219 The command for the second formula is:
19220 \begin_inset Newline newline
19231 \begin_layout Plain Layout
19246 \begin_layout Plain Layout
19261 \begin_layout Plain Layout
19276 \begin_layout Plain Layout
19286 \begin_inset Formula $\to$
19290 \begin_inset Formula $\to$
19294 \begin_inset Newline newline
19298 \begin_inset space \hspace*{}
19312 \begin_layout Plain Layout
19327 \begin_layout Plain Layout
19342 \begin_layout Plain Layout
19354 \begin_layout Standard
19355 If a symbol cannot be displayed in different sizes, it will always be displayed
19356 in the default size.
19359 \begin_layout Standard
19360 \begin_inset Newpage newpage
19366 \begin_layout Section
19371 \begin_layout Plain Layout
19380 \begin_layout Standard
19381 All Greek letters can also be inserted via the toolbar button
19382 \begin_inset Graphics
19383 filename ../images/math/alpha.png
19391 \begin_layout Subsection
19396 \begin_layout Plain Layout
19397 Greek letters ! small
19405 \begin_layout Standard
19406 \begin_inset space \hfill{}
19410 \begin_inset Tabular
19411 <lyxtabular version="3" rows="11" columns="2">
19413 <column alignment="center" valignment="top" width="0pt">
19414 <column alignment="center" valignment="top" width="0pt">
19416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19419 \begin_layout Plain Layout
19425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19428 \begin_layout Plain Layout
19436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19439 \begin_layout Plain Layout
19447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19450 \begin_layout Plain Layout
19451 \begin_inset Formula $\alpha$
19461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19464 \begin_layout Plain Layout
19472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19475 \begin_layout Plain Layout
19476 \begin_inset Formula $\beta$
19486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19489 \begin_layout Plain Layout
19497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19500 \begin_layout Plain Layout
19501 \begin_inset Formula $\gamma$
19511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19514 \begin_layout Plain Layout
19522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19525 \begin_layout Plain Layout
19526 \begin_inset Formula $\delta$
19536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19539 \begin_layout Plain Layout
19547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19550 \begin_layout Plain Layout
19551 \begin_inset Formula $\epsilon$
19561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19564 \begin_layout Plain Layout
19572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19575 \begin_layout Plain Layout
19576 \begin_inset Formula $\varepsilon$
19586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19589 \begin_layout Plain Layout
19597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19600 \begin_layout Plain Layout
19601 \begin_inset Formula $\zeta$
19611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19614 \begin_layout Plain Layout
19622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19625 \begin_layout Plain Layout
19626 \begin_inset Formula $\eta$
19636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19639 \begin_layout Plain Layout
19647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19650 \begin_layout Plain Layout
19651 \begin_inset Formula $\theta$
19661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19664 \begin_layout Plain Layout
19672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19675 \begin_layout Plain Layout
19676 \begin_inset Formula $\vartheta$
19690 \begin_inset space \hfill{}
19694 \begin_inset Tabular
19695 <lyxtabular version="3" rows="12" columns="2">
19697 <column alignment="center" valignment="top" width="0pt">
19698 <column alignment="center" valignment="top" width="0pt">
19700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19703 \begin_layout Plain Layout
19709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19712 \begin_layout Plain Layout
19720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19723 \begin_layout Plain Layout
19731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19734 \begin_layout Plain Layout
19735 \begin_inset Formula $\iota$
19745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19748 \begin_layout Plain Layout
19756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19759 \begin_layout Plain Layout
19760 \begin_inset Formula $\kappa$
19770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19773 \begin_layout Plain Layout
19781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19784 \begin_layout Plain Layout
19785 \begin_inset Formula $\varkappa$
19795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19798 \begin_layout Plain Layout
19806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19809 \begin_layout Plain Layout
19810 \begin_inset Formula $\lambda$
19820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19823 \begin_layout Plain Layout
19831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19834 \begin_layout Plain Layout
19835 \begin_inset Formula $\mu$
19845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19848 \begin_layout Plain Layout
19856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19859 \begin_layout Plain Layout
19860 \begin_inset Formula $\nu$
19870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19873 \begin_layout Plain Layout
19881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19884 \begin_layout Plain Layout
19885 \begin_inset Formula $\xi$
19895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19898 \begin_layout Plain Layout
19904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19907 \begin_layout Plain Layout
19908 \begin_inset Formula $o$
19918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19921 \begin_layout Plain Layout
19929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19932 \begin_layout Plain Layout
19933 \begin_inset Formula $\pi$
19943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19946 \begin_layout Plain Layout
19954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19957 \begin_layout Plain Layout
19958 \begin_inset Formula $\varpi$
19968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19971 \begin_layout Plain Layout
19979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19982 \begin_layout Plain Layout
19983 \begin_inset Formula $\rho$
19997 \begin_inset space \hfill{}
20001 \begin_inset Tabular
20002 <lyxtabular version="3" rows="11" columns="2">
20004 <column alignment="center" valignment="top" width="0pt">
20005 <column alignment="center" valignment="top" width="0pt">
20007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20010 \begin_layout Plain Layout
20016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20019 \begin_layout Plain Layout
20027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20030 \begin_layout Plain Layout
20038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20041 \begin_layout Plain Layout
20042 \begin_inset Formula $\varrho$
20052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20055 \begin_layout Plain Layout
20063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20066 \begin_layout Plain Layout
20067 \begin_inset Formula $\sigma$
20077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20080 \begin_layout Plain Layout
20088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20091 \begin_layout Plain Layout
20092 \begin_inset Formula $\varsigma$
20102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20105 \begin_layout Plain Layout
20113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20116 \begin_layout Plain Layout
20117 \begin_inset Formula $\tau$
20127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20130 \begin_layout Plain Layout
20138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20141 \begin_layout Plain Layout
20142 \begin_inset Formula $\upsilon$
20152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20155 \begin_layout Plain Layout
20163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20166 \begin_layout Plain Layout
20167 \begin_inset Formula $\phi$
20177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20180 \begin_layout Plain Layout
20188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20191 \begin_layout Plain Layout
20192 \begin_inset Formula $\varphi$
20202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20205 \begin_layout Plain Layout
20213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20216 \begin_layout Plain Layout
20217 \begin_inset Formula $\chi$
20227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20230 \begin_layout Plain Layout
20238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20241 \begin_layout Plain Layout
20242 \begin_inset Formula $\psi$
20252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20255 \begin_layout Plain Layout
20263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20266 \begin_layout Plain Layout
20267 \begin_inset Formula $\omega$
20281 \begin_inset space \hfill{}
20287 \begin_layout Standard
20288 \begin_inset VSpace medskip
20294 \begin_layout Standard
20295 How to create upright Greek letters is explained in
20296 \begin_inset CommandInset ref
20298 reference "sub:Upright-small-Greek"
20305 \begin_layout Subsection
20310 \begin_layout Plain Layout
20311 Greek letters ! big
20319 \begin_layout Standard
20320 \begin_inset space \hfill{}
20324 \begin_inset Tabular
20325 <lyxtabular version="3" rows="7" columns="2">
20327 <column alignment="center" valignment="top" width="0pt">
20328 <column alignment="center" valignment="top" width="0pt">
20330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20333 \begin_layout Plain Layout
20339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20342 \begin_layout Plain Layout
20350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20353 \begin_layout Plain Layout
20361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20364 \begin_layout Plain Layout
20365 \begin_inset Formula $\Gamma$
20375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20378 \begin_layout Plain Layout
20386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20389 \begin_layout Plain Layout
20390 \begin_inset Formula $\Delta$
20400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20403 \begin_layout Plain Layout
20411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20414 \begin_layout Plain Layout
20415 \begin_inset Formula $\Theta$
20425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20428 \begin_layout Plain Layout
20436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20439 \begin_layout Plain Layout
20440 \begin_inset Formula $\Lambda$
20450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20453 \begin_layout Plain Layout
20461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20464 \begin_layout Plain Layout
20465 \begin_inset Formula $\Xi$
20475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20478 \begin_layout Plain Layout
20486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20489 \begin_layout Plain Layout
20490 \begin_inset Formula $\Pi$
20504 \begin_inset space \hfill{}
20508 \begin_inset Tabular
20509 <lyxtabular version="3" rows="6" columns="2">
20511 <column alignment="center" valignment="top" width="0pt">
20512 <column alignment="center" valignment="top" width="0pt">
20514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20517 \begin_layout Plain Layout
20523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20526 \begin_layout Plain Layout
20534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20537 \begin_layout Plain Layout
20545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20548 \begin_layout Plain Layout
20549 \begin_inset Formula $\Sigma$
20559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20562 \begin_layout Plain Layout
20570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20573 \begin_layout Plain Layout
20574 \begin_inset Formula $\Upsilon$
20584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20587 \begin_layout Plain Layout
20595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20598 \begin_layout Plain Layout
20599 \begin_inset Formula $\Phi$
20609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20612 \begin_layout Plain Layout
20620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20623 \begin_layout Plain Layout
20624 \begin_inset Formula $\Psi$
20634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20637 \begin_layout Plain Layout
20645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20648 \begin_layout Plain Layout
20649 \begin_inset Formula $\Omega$
20663 \begin_inset space \hfill{}
20669 \begin_layout Standard
20670 \begin_inset VSpace medskip
20673 That the big Greek letters appear upright is caused by a design bug when
20675 To get correct italic big letters, begin every command with
20680 For example the command
20687 \begin_inset Formula $\varGamma$
20693 \begin_layout Subsection
20698 \begin_layout Plain Layout
20699 Greek letters ! bold
20707 \begin_layout Standard
20708 Greek letters cannot be set with different font styles like Latin letters.
20709 They can only be made bold with the command
20719 \begin_layout Plain Layout
20730 \begin_layout Standard
20732 \begin_inset Tabular
20733 <lyxtabular version="3" rows="3" columns="2">
20735 <column alignment="center" valignment="top" width="0">
20736 <column alignment="center" valignment="top" width="0">
20738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20741 \begin_layout Plain Layout
20747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20750 \begin_layout Plain Layout
20758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20761 \begin_layout Plain Layout
20773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20776 \begin_layout Plain Layout
20777 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20790 \begin_layout Plain Layout
20802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20805 \begin_layout Plain Layout
20806 \begin_inset Formula $\theta\boldsymbol{\theta}$
20822 \begin_layout Section
20827 \begin_layout Plain Layout
20840 \begin_layout Plain Layout
20841 A list with all symbols of most of the LaTeX-packages can be found in
20842 \begin_inset CommandInset citation
20857 \begin_layout Plain Layout
20865 \begin_inset Note Note
20868 \begin_layout Plain Layout
20871 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20874 \begin_layout Plain Layout
20877 texorpdfstring is in section
20878 \begin_inset CommandInset ref
20880 reference "sub:Formulas-in-Section"
20893 \begin_layout Plain Layout
20902 \begin_layout Standard
20903 Many of the symbols listed in this section can also be inserted via the
20905 \begin_inset Graphics
20906 filename ../images/math/nabla.png
20912 \begin_inset Graphics
20913 filename ../images/math/digamma.png
20921 \begin_layout Subsection
20922 Mathematical Symbols
20923 \begin_inset CommandInset label
20925 name "sub:Mathematical-Symbols"
20933 \begin_layout Plain Layout
20934 Symbols ! mathematical
20942 \begin_layout Standard
20943 \begin_inset space \hfill{}
20947 \begin_inset Tabular
20948 <lyxtabular version="3" rows="10" columns="2">
20950 <column alignment="center" valignment="top" width="0pt">
20951 <column alignment="center" valignment="top" width="0pt">
20953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20956 \begin_layout Plain Layout
20962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20965 \begin_layout Plain Layout
20973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20976 \begin_layout Plain Layout
20984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20987 \begin_layout Plain Layout
20988 \begin_inset Formula $\neg$
20998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21001 \begin_layout Plain Layout
21009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21012 \begin_layout Plain Layout
21013 \begin_inset Formula $\Im$
21023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21026 \begin_layout Plain Layout
21034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21037 \begin_layout Plain Layout
21038 \begin_inset Formula $\Re$
21048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21051 \begin_layout Plain Layout
21059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21062 \begin_layout Plain Layout
21063 \begin_inset Formula $\aleph$
21073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21076 \begin_layout Plain Layout
21084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21087 \begin_layout Plain Layout
21088 \begin_inset Formula $\partial$
21098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21101 \begin_layout Plain Layout
21109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21112 \begin_layout Plain Layout
21113 \begin_inset Formula $\infty$
21123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21126 \begin_layout Plain Layout
21134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21137 \begin_layout Plain Layout
21138 \begin_inset Formula $\wp$
21148 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21151 \begin_layout Plain Layout
21159 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21162 \begin_layout Plain Layout
21163 \begin_inset Formula $\imath$
21173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21176 \begin_layout Plain Layout
21184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21187 \begin_layout Plain Layout
21188 \begin_inset Formula $\jmath$
21202 \begin_inset space \hfill{}
21206 \begin_inset Tabular
21207 <lyxtabular version="3" rows="10" columns="2">
21209 <column alignment="center" valignment="top" width="0pt">
21210 <column alignment="center" valignment="top" width="0pt">
21212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21215 \begin_layout Plain Layout
21221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21224 \begin_layout Plain Layout
21226 \begin_inset Note Note
21229 \begin_layout Plain Layout
21236 is only used as spacer.
21248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21251 \begin_layout Plain Layout
21259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21262 \begin_layout Plain Layout
21263 \begin_inset Formula $\forall$
21273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21276 \begin_layout Plain Layout
21284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21287 \begin_layout Plain Layout
21288 \begin_inset Formula $\exists$
21298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21301 \begin_layout Plain Layout
21309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21312 \begin_layout Plain Layout
21313 \begin_inset Formula $\nexists$
21323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21326 \begin_layout Plain Layout
21334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21337 \begin_layout Plain Layout
21338 \begin_inset Formula $\emptyset$
21348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21351 \begin_layout Plain Layout
21359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21362 \begin_layout Plain Layout
21363 \begin_inset Formula $\varnothing$
21373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21376 \begin_layout Plain Layout
21384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21387 \begin_layout Plain Layout
21388 \begin_inset Formula $\dag$
21398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21401 \begin_layout Plain Layout
21409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21412 \begin_layout Plain Layout
21413 \begin_inset Formula $\ddag$
21423 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21426 \begin_layout Plain Layout
21434 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21437 \begin_layout Plain Layout
21441 \begin_layout Plain Layout
21451 \begin_inset Formula $\complement$
21458 \begin_layout Plain Layout
21472 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21475 \begin_layout Plain Layout
21483 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21486 \begin_layout Plain Layout
21487 \begin_inset Formula $\Bbbk$
21501 \begin_inset space \hfill{}
21505 \begin_inset Tabular
21506 <lyxtabular version="3" rows="10" columns="2">
21508 <column alignment="center" valignment="top" width="0pt">
21509 <column alignment="center" valignment="top" width="0pt">
21511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21514 \begin_layout Plain Layout
21520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21523 \begin_layout Plain Layout
21531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21534 \begin_layout Plain Layout
21542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21545 \begin_layout Plain Layout
21546 \begin_inset Formula $\prime$
21556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21559 \begin_layout Plain Layout
21567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21570 \begin_layout Plain Layout
21571 \begin_inset Formula $\backprime$
21581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21584 \begin_layout Plain Layout
21592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21595 \begin_layout Plain Layout
21596 \begin_inset Formula $\mho$
21606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21609 \begin_layout Plain Layout
21617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21620 \begin_layout Plain Layout
21621 \begin_inset Formula $\triangle$
21631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21634 \begin_layout Plain Layout
21642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21645 \begin_layout Plain Layout
21646 \begin_inset Formula $\angle$
21656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21659 \begin_layout Plain Layout
21667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21670 \begin_layout Plain Layout
21671 \begin_inset Formula $\measuredangle$
21681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21684 \begin_layout Plain Layout
21692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21695 \begin_layout Plain Layout
21696 \begin_inset Formula $\sphericalangle$
21706 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21709 \begin_layout Plain Layout
21717 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21720 \begin_layout Plain Layout
21721 \begin_inset Formula $\top$
21731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21734 \begin_layout Plain Layout
21742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21745 \begin_layout Plain Layout
21746 \begin_inset Formula $\bot$
21760 \begin_inset space \hfill{}
21766 \begin_layout Subsection
21767 Miscellaneous Symbols
21768 \begin_inset CommandInset label
21770 name "sub:Miscellaneous-Symbols"
21778 \begin_layout Plain Layout
21779 Symbols ! miscellaneous
21787 \begin_layout Standard
21790 \begin_inset Tabular
21791 <lyxtabular version="3" rows="10" columns="2">
21793 <column alignment="center" valignment="top" width="0pt">
21794 <column alignment="center" valignment="top" width="0pt">
21796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21799 \begin_layout Plain Layout
21805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21808 \begin_layout Plain Layout
21816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21819 \begin_layout Plain Layout
21827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21830 \begin_layout Plain Layout
21831 \begin_inset Formula $\flat$
21841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21844 \begin_layout Plain Layout
21852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21855 \begin_layout Plain Layout
21856 \begin_inset Formula $\natural$
21866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21869 \begin_layout Plain Layout
21877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21880 \begin_layout Plain Layout
21881 \begin_inset Formula $\sharp$
21891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21894 \begin_layout Plain Layout
21902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21905 \begin_layout Plain Layout
21906 \begin_inset Formula $\surd$
21916 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21919 \begin_layout Plain Layout
21927 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21930 \begin_layout Plain Layout
21931 \begin_inset Formula $\checkmark$
21941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21944 \begin_layout Plain Layout
21952 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21955 \begin_layout Plain Layout
21956 \begin_inset Formula $\yen$
21966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21969 \begin_layout Plain Layout
21977 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21980 \begin_layout Plain Layout
21981 \begin_inset Formula $\pounds$
21991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21994 \begin_layout Plain Layout
22000 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22003 \begin_layout Plain Layout
22004 \begin_inset Formula $\$$
22014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22017 \begin_layout Plain Layout
22023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22026 \begin_layout Plain Layout
22027 \begin_inset Formula $§$
22041 \begin_inset Tabular
22042 <lyxtabular version="3" rows="10" columns="2">
22044 <column alignment="center" valignment="top" width="0">
22045 <column alignment="center" valignment="top" width="0">
22047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22050 \begin_layout Plain Layout
22056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22059 \begin_layout Plain Layout
22067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22070 \begin_layout Plain Layout
22078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22081 \begin_layout Plain Layout
22082 \begin_inset Formula $\hbar$
22092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22095 \begin_layout Plain Layout
22103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22106 \begin_layout Plain Layout
22107 \begin_inset Formula $\hslash$
22117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22120 \begin_layout Plain Layout
22128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22131 \begin_layout Plain Layout
22132 \begin_inset Formula $\clubsuit$
22142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22145 \begin_layout Plain Layout
22153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22156 \begin_layout Plain Layout
22157 \begin_inset Formula $\spadesuit$
22167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22170 \begin_layout Plain Layout
22178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22181 \begin_layout Plain Layout
22182 \begin_inset Formula $\bigstar$
22192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22195 \begin_layout Plain Layout
22203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22206 \begin_layout Plain Layout
22207 \begin_inset Formula $\blacklozenge$
22217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22220 \begin_layout Plain Layout
22228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22231 \begin_layout Plain Layout
22232 \begin_inset Formula $\blacktriangle$
22242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22245 \begin_layout Plain Layout
22253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22256 \begin_layout Plain Layout
22257 \begin_inset Formula $\blacktriangledown$
22267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22270 \begin_layout Plain Layout
22278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22281 \begin_layout Plain Layout
22282 \begin_inset Formula $\bullet$
22296 \begin_inset Tabular
22297 <lyxtabular version="3" rows="10" columns="2">
22299 <column alignment="center" valignment="top" width="0pt">
22300 <column alignment="center" valignment="top" width="0pt">
22302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22305 \begin_layout Plain Layout
22311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22314 \begin_layout Plain Layout
22322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22325 \begin_layout Plain Layout
22333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22336 \begin_layout Plain Layout
22337 \begin_inset Formula $\diamondsuit$
22347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22350 \begin_layout Plain Layout
22358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22361 \begin_layout Plain Layout
22362 \begin_inset Formula $\Diamond$
22372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22375 \begin_layout Plain Layout
22383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22386 \begin_layout Plain Layout
22387 \begin_inset Formula $\heartsuit$
22397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22400 \begin_layout Plain Layout
22408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22411 \begin_layout Plain Layout
22412 \begin_inset Formula $\P$
22422 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22425 \begin_layout Plain Layout
22433 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22436 \begin_layout Plain Layout
22437 \begin_inset Formula $\copyright$
22447 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22450 \begin_layout Plain Layout
22458 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22461 \begin_layout Plain Layout
22462 \begin_inset Formula $\circledR$
22472 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22475 \begin_layout Plain Layout
22483 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22486 \begin_layout Plain Layout
22487 \begin_inset Formula $\maltese$
22497 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22500 \begin_layout Plain Layout
22508 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22511 \begin_layout Plain Layout
22512 \begin_inset Formula $\diagup$
22522 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22525 \begin_layout Plain Layout
22533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22536 \begin_layout Plain Layout
22537 \begin_inset Formula $\diagdown$
22553 \begin_layout Standard
22554 \begin_inset VSpace medskip
22557 More symbols are listed in
22558 \begin_inset CommandInset ref
22560 reference "sub:Miscellaneous-special-Characters"
22567 \begin_layout Standard
22568 Some symbols can be displayed in different sizes, see
22569 \begin_inset CommandInset ref
22571 reference "sub:Font-Sizes"
22578 \begin_layout Subsection
22583 \begin_layout Plain Layout
22584 Symbols ! Euro-symbol
22593 \begin_layout Plain Layout
22600 \begin_layout Plain Layout
22617 \begin_layout Standard
22618 To use the Euro symbol in formulas, the LaTeX-package
22626 \begin_layout Plain Layout
22632 must be installed and loaded with the LaTeX-preamble line
22635 \begin_layout Standard
22640 usepackage[gennarrow]{eurosym}
22643 \begin_layout Standard
22644 The Euro symbol can now be inserted with the command
22654 \begin_layout Plain Layout
22665 \begin_layout Standard
22666 The Euro symbol can directly be inserted with the € key in mathematical
22667 text, without having
22682 can also be inserted in TeX-mode.
22683 The official currency symbol can then be inserted with the command
22693 \begin_layout Plain Layout
22701 , that is only available in TeX-mode.
22704 \begin_layout Standard
22708 \begin_layout Plain Layout
22718 \begin_inset Note Note
22721 \begin_layout Plain Layout
22722 The following table will only be displayed when the LaTeX-package
22734 \begin_layout Standard
22735 An overview about the different Euro symbols:
22738 \begin_layout Standard
22740 \begin_inset Tabular
22741 <lyxtabular version="3" rows="4" columns="3">
22743 <column alignment="center" valignment="top" width="0pt">
22744 <column alignment="center" valignment="top" width="0pt">
22745 <column alignment="center" valignment="top" width="0pt">
22747 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22750 \begin_layout Plain Layout
22756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22759 \begin_layout Plain Layout
22765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22768 \begin_layout Plain Layout
22776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22779 \begin_layout Plain Layout
22785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22788 \begin_layout Plain Layout
22796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22799 \begin_layout Plain Layout
22800 \begin_inset Formula $\euro$
22810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22813 \begin_layout Plain Layout
22819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22822 \begin_layout Plain Layout
22828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22831 \begin_layout Plain Layout
22832 \begin_inset Formula $\mbox{€}$
22842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22845 \begin_layout Plain Layout
22851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22854 \begin_layout Plain Layout
22862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22865 \begin_layout Plain Layout
22869 \begin_layout Plain Layout
22891 \begin_layout Standard
22895 \begin_layout Plain Layout
22905 \begin_inset Note Note
22908 \begin_layout Plain Layout
22909 The following will be displayed when the LaTeX-package
22921 \begin_layout Standard
22922 You need to install the LaTeX-package
22926 to see the rest of this subsection in the output.
22929 \begin_layout Standard
22933 \begin_layout Plain Layout
22945 \begin_layout Section
22947 \begin_inset CommandInset label
22949 name "sec:Relations"
22957 \begin_layout Plain Layout
22967 \begin_layout Plain Layout
22972 \begin_layout Plain Layout
22983 \begin_layout Plain Layout
22998 \begin_layout Standard
22999 All relations can also be inserted via the toolbar button
23000 \begin_inset Graphics
23001 filename ../images/math/leq.png
23009 \begin_layout Standard
23010 \begin_inset space \hfill{}
23014 \begin_inset Tabular
23015 <lyxtabular version="3" rows="17" columns="2">
23017 <column alignment="center" valignment="top" width="0pt">
23018 <column alignment="center" valignment="top" width="0pt">
23020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23023 \begin_layout Plain Layout
23029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23032 \begin_layout Plain Layout
23040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23043 \begin_layout Plain Layout
23049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23052 \begin_layout Plain Layout
23053 \begin_inset Formula $<$
23063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23066 \begin_layout Plain Layout
23074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23077 \begin_layout Plain Layout
23078 \begin_inset Formula $\le$
23088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23091 \begin_layout Plain Layout
23099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23102 \begin_layout Plain Layout
23103 \begin_inset Formula $\ll$
23113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23116 \begin_layout Plain Layout
23124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23127 \begin_layout Plain Layout
23128 \begin_inset Formula $\prec$
23138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23141 \begin_layout Plain Layout
23149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23152 \begin_layout Plain Layout
23153 \begin_inset Formula $\preceq$
23163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23166 \begin_layout Plain Layout
23174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23177 \begin_layout Plain Layout
23178 \begin_inset Formula $\subset$
23188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23191 \begin_layout Plain Layout
23199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23202 \begin_layout Plain Layout
23203 \begin_inset Formula $\subseteq$
23213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23216 \begin_layout Plain Layout
23224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23227 \begin_layout Plain Layout
23228 \begin_inset Formula $\sqsubseteq$
23238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23241 \begin_layout Plain Layout
23249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23252 \begin_layout Plain Layout
23253 \begin_inset Formula $\in$
23263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23266 \begin_layout Plain Layout
23274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23277 \begin_layout Plain Layout
23278 \begin_inset Formula $\vdash$
23288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23291 \begin_layout Plain Layout
23299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23302 \begin_layout Plain Layout
23303 \begin_inset Formula $\smile$
23313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23316 \begin_layout Plain Layout
23324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23327 \begin_layout Plain Layout
23328 \begin_inset Formula $\lhd$
23338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23341 \begin_layout Plain Layout
23349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23352 \begin_layout Plain Layout
23353 \begin_inset Formula $\unlhd$
23363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23366 \begin_layout Plain Layout
23374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23377 \begin_layout Plain Layout
23378 \begin_inset Formula $\gtrless$
23388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23391 \begin_layout Plain Layout
23399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23402 \begin_layout Plain Layout
23403 \begin_inset Formula $\mid$
23413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23416 \begin_layout Plain Layout
23424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23427 \begin_layout Plain Layout
23428 \begin_inset Formula $\nmid$
23442 \begin_inset space \hfill{}
23446 \begin_inset Tabular
23447 <lyxtabular version="3" rows="17" columns="2">
23449 <column alignment="center" valignment="top" width="0pt">
23450 <column alignment="center" valignment="top" width="0pt">
23452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23455 \begin_layout Plain Layout
23461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23464 \begin_layout Plain Layout
23472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23475 \begin_layout Plain Layout
23481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23484 \begin_layout Plain Layout
23485 \begin_inset Formula $=$
23495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23498 \begin_layout Plain Layout
23506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23509 \begin_layout Plain Layout
23510 \begin_inset Formula $\not=$
23520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23523 \begin_layout Plain Layout
23531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23534 \begin_layout Plain Layout
23535 \begin_inset Formula $\equiv$
23545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23548 \begin_layout Plain Layout
23556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23559 \begin_layout Plain Layout
23560 \begin_inset Formula $\sim$
23570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23573 \begin_layout Plain Layout
23581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23584 \begin_layout Plain Layout
23585 \begin_inset Formula $\simeq$
23595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23598 \begin_layout Plain Layout
23606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23609 \begin_layout Plain Layout
23610 \begin_inset Formula $\approx$
23620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23623 \begin_layout Plain Layout
23631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23634 \begin_layout Plain Layout
23635 \begin_inset Formula $\cong$
23645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23648 \begin_layout Plain Layout
23656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23659 \begin_layout Plain Layout
23660 \begin_inset Formula $\bowtie$
23670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23673 \begin_layout Plain Layout
23681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23684 \begin_layout Plain Layout
23685 \begin_inset Formula $\notin$
23695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23698 \begin_layout Plain Layout
23706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23709 \begin_layout Plain Layout
23710 \begin_inset Formula $\perp$
23720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23723 \begin_layout Plain Layout
23731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23734 \begin_layout Plain Layout
23735 \begin_inset Formula $\propto$
23745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23748 \begin_layout Plain Layout
23756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23759 \begin_layout Plain Layout
23760 \begin_inset Formula $\asymp$
23770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23773 \begin_layout Plain Layout
23781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23784 \begin_layout Plain Layout
23785 \begin_inset Formula $\doteq$
23795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23798 \begin_layout Plain Layout
23806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23809 \begin_layout Plain Layout
23810 \begin_inset Formula $\circeq$
23820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23823 \begin_layout Plain Layout
23831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23834 \begin_layout Plain Layout
23835 \begin_inset Formula $\models$
23845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23848 \begin_layout Plain Layout
23856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23859 \begin_layout Plain Layout
23860 \begin_inset Formula $\widehat{=}$
23874 \begin_inset space \hfill{}
23878 \begin_inset Tabular
23879 <lyxtabular version="3" rows="17" columns="2">
23881 <column alignment="center" valignment="top" width="0pt">
23882 <column alignment="center" valignment="top" width="0pt">
23884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23887 \begin_layout Plain Layout
23893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23896 \begin_layout Plain Layout
23904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23907 \begin_layout Plain Layout
23913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23916 \begin_layout Plain Layout
23917 \begin_inset Formula $>$
23927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23930 \begin_layout Plain Layout
23938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23941 \begin_layout Plain Layout
23942 \begin_inset Formula $\ge$
23952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23955 \begin_layout Plain Layout
23963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23966 \begin_layout Plain Layout
23967 \begin_inset Formula $\gg$
23977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23980 \begin_layout Plain Layout
23988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23991 \begin_layout Plain Layout
23992 \begin_inset Formula $\succ$
24002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24005 \begin_layout Plain Layout
24013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24016 \begin_layout Plain Layout
24017 \begin_inset Formula $\succeq$
24027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24030 \begin_layout Plain Layout
24038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24041 \begin_layout Plain Layout
24042 \begin_inset Formula $\supset$
24052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24055 \begin_layout Plain Layout
24063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24066 \begin_layout Plain Layout
24067 \begin_inset Formula $\supseteq$
24077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24080 \begin_layout Plain Layout
24088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24091 \begin_layout Plain Layout
24092 \begin_inset Formula $\sqsupseteq$
24102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24105 \begin_layout Plain Layout
24113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24116 \begin_layout Plain Layout
24117 \begin_inset Formula $\ni$
24127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24130 \begin_layout Plain Layout
24138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24141 \begin_layout Plain Layout
24142 \begin_inset Formula $\dashv$
24152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24155 \begin_layout Plain Layout
24163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24166 \begin_layout Plain Layout
24167 \begin_inset Formula $\frown$
24177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24180 \begin_layout Plain Layout
24188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24191 \begin_layout Plain Layout
24192 \begin_inset Formula $\rhd$
24202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24205 \begin_layout Plain Layout
24213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24216 \begin_layout Plain Layout
24217 \begin_inset Formula $\unrhd$
24227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24230 \begin_layout Plain Layout
24238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24241 \begin_layout Plain Layout
24242 \begin_inset Formula $\lessgtr$
24252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24255 \begin_layout Plain Layout
24263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24266 \begin_layout Plain Layout
24267 \begin_inset Formula $\parallel$
24277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24280 \begin_layout Plain Layout
24288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24291 \begin_layout Plain Layout
24292 \begin_inset Formula $\nparallel$
24306 \begin_inset space \hfill{}
24312 \begin_layout Standard
24313 \begin_inset VSpace medskip
24328 are bigger than the equal looking operators
24343 \begin_layout Standard
24344 Relations are, in contrary to symbols, always surrounded by space.
24347 \begin_layout Standard
24348 Relations with labels can be created with the command
24358 \begin_layout Plain Layout
24369 \begin_layout Standard
24371 \begin_inset Tabular
24372 <lyxtabular version="3" rows="2" columns="2">
24374 <column alignment="center" valignment="top" width="0">
24375 <column alignment="center" valignment="top" width="0">
24377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24380 \begin_layout Plain Layout
24386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24389 \begin_layout Plain Layout
24391 \begin_inset Note Note
24394 \begin_layout Plain Layout
24401 is only used as spacer.
24413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24416 \begin_layout Plain Layout
24423 \begin_layout Plain Layout
24440 \begin_layout Plain Layout
24450 \begin_inset Formula $\downarrow$
24459 \begin_layout Plain Layout
24472 \begin_layout Plain Layout
24486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24489 \begin_layout Plain Layout
24490 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24506 \begin_layout Section
24510 \begin_layout Subsection
24511 Predefined Functions
24512 \begin_inset CommandInset label
24514 name "sub:Predefined-Functions"
24522 \begin_layout Plain Layout
24523 Functions ! predefined
24531 \begin_layout Standard
24532 In general, variables are set
24536 in mathematical expressions, but not function names, because
24537 \begin_inset Formula $sin$
24540 could be misunderstood as
24541 \begin_inset Formula $s\cdot i\cdot n$
24545 Therefore there are predefined functions, that are additionally a bit separated
24547 They are inserted as commands starting with a backslash before their name.
24550 \begin_layout Standard
24552 \begin_inset Tabular
24553 <lyxtabular version="3" rows="2" columns="4">
24555 <column alignment="center" valignment="top" width="0pt">
24556 <column alignment="center" valignment="top" width="0pt">
24557 <column alignment="center" valignment="top" width="0pt">
24558 <column alignment="center" valignment="top" width="0pt">
24560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24563 \begin_layout Plain Layout
24569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24572 \begin_layout Plain Layout
24578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24581 \begin_layout Plain Layout
24587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24590 \begin_layout Plain Layout
24598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24601 \begin_layout Plain Layout
24607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24610 \begin_layout Plain Layout
24611 \begin_inset Formula $Asin(x)+B$
24619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24622 \begin_layout Plain Layout
24630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24633 \begin_layout Plain Layout
24634 \begin_inset Formula $A\sin(x)+B$
24650 \begin_layout Standard
24651 The following functions are predefined:
24654 \begin_layout Standard
24655 \begin_inset VSpace -2mm
24661 \begin_layout Standard
24663 \begin_inset Tabular
24664 <lyxtabular version="3" rows="9" columns="4">
24666 <column alignment="center" valignment="top" width="0pt">
24667 <column alignment="center" valignment="top" width="0pt">
24668 <column alignment="center" valignment="top" width="0pt">
24669 <column alignment="center" valignment="top" width="0pt">
24671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24674 \begin_layout Plain Layout
24680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24683 \begin_layout Plain Layout
24689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24692 \begin_layout Plain Layout
24698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24701 \begin_layout Plain Layout
24709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24712 \begin_layout Plain Layout
24720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24723 \begin_layout Plain Layout
24731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24734 \begin_layout Plain Layout
24742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24745 \begin_layout Plain Layout
24755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24758 \begin_layout Plain Layout
24766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24769 \begin_layout Plain Layout
24777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24780 \begin_layout Plain Layout
24788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24791 \begin_layout Plain Layout
24801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24804 \begin_layout Plain Layout
24812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24815 \begin_layout Plain Layout
24823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24826 \begin_layout Plain Layout
24834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24837 \begin_layout Plain Layout
24847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24850 \begin_layout Plain Layout
24858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24861 \begin_layout Plain Layout
24869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24872 \begin_layout Plain Layout
24880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24883 \begin_layout Plain Layout
24893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24896 \begin_layout Plain Layout
24904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24907 \begin_layout Plain Layout
24915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24918 \begin_layout Plain Layout
24926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24929 \begin_layout Plain Layout
24939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24942 \begin_layout Plain Layout
24950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24953 \begin_layout Plain Layout
24961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24964 \begin_layout Plain Layout
24972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24975 \begin_layout Plain Layout
24985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24988 \begin_layout Plain Layout
24996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24999 \begin_layout Plain Layout
25007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25010 \begin_layout Plain Layout
25018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25021 \begin_layout Plain Layout
25031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25034 \begin_layout Plain Layout
25042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25045 \begin_layout Plain Layout
25053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25056 \begin_layout Plain Layout
25064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25067 \begin_layout Plain Layout
25083 \begin_layout Standard
25084 They can also be inserted with the math toolbar button
25085 \begin_inset Graphics
25086 filename ../images/math/functions.png
25094 \begin_layout Subsection
25095 Self-defined Functions
25099 \begin_layout Plain Layout
25100 Functions ! self-defined
25108 \begin_layout Standard
25109 To use a function that is not predefined, like for example the sign function
25110 sgn(x), there are two possibilities:
25113 \begin_layout Itemize
25114 Define the function by inserting the following line to the LaTeX-preamble
25118 \begin_layout Plain Layout
25123 DeclareMathOperator
25126 \begin_inset CommandInset ref
25128 reference "sub:Self-defined-Operators"
25138 \begin_inset Newline newline
25142 \begin_inset VSpace -3mm
25146 \begin_inset Newline newline
25153 DeclareMathOperator{
25161 \begin_layout Plain Layout
25166 DeclareMathOperator
25172 \begin_inset Newline newline
25176 \begin_inset VSpace -2mm
25180 \begin_inset Newline newline
25183 Now the new defined function can be called with the command
25192 \begin_layout Itemize
25193 Write the formula as usual, mark the formula name, in our example the letters
25198 , and change it to mathematical text.
25199 At last a space is inserted between prefactor and function.
25202 \begin_layout Standard
25203 The result is the same with both methods as with a predefined function
25207 \begin_layout Plain Layout
25208 In LyX self-defined functions are displayed red, predefined ones black.
25216 \begin_layout Standard
25218 \begin_inset Tabular
25219 <lyxtabular version="3" rows="3" columns="2">
25221 <column alignment="center" valignment="top" width="0pt">
25222 <column alignment="center" valignment="top" width="0pt">
25224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25227 \begin_layout Plain Layout
25233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25236 \begin_layout Plain Layout
25244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25247 \begin_layout Plain Layout
25255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25258 \begin_layout Plain Layout
25259 \begin_inset Formula $A\sgn(x)+B$
25269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25272 \begin_layout Plain Layout
25276 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25287 \begin_layout Plain Layout
25288 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25304 \begin_layout Standard
25305 The first method is more suitable when the self-defined function should
25306 be used several times.
25309 \begin_layout Subsection
25314 \begin_layout Plain Layout
25323 \begin_layout Standard
25324 For limits there are defined besides
25334 \begin_layout Plain Layout
25354 furthermore the following functions:
25357 \begin_layout Standard
25359 \begin_inset Tabular
25360 <lyxtabular version="3" rows="5" columns="2">
25362 <column alignment="center" valignment="top" width="0">
25363 <column alignment="center" valignment="top" width="0">
25365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25368 \begin_layout Plain Layout
25374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25377 \begin_layout Plain Layout
25379 \begin_inset Note Note
25382 \begin_layout Plain Layout
25389 is only used as spacer.
25401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25404 \begin_layout Plain Layout
25412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25415 \begin_layout Plain Layout
25416 \begin_inset Formula $\varliminf$
25426 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25429 \begin_layout Plain Layout
25437 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25440 \begin_layout Plain Layout
25441 \begin_inset Formula $\varlimsup$
25451 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25454 \begin_layout Plain Layout
25462 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25465 \begin_layout Plain Layout
25466 \begin_inset Formula $\varprojlim$
25476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25479 \begin_layout Plain Layout
25487 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25490 \begin_layout Plain Layout
25491 \begin_inset Formula $\varinjlim$
25495 \begin_inset Formula $\raisebox{-2.5mm}{}$
25511 \begin_layout Standard
25512 \begin_inset VSpace medskip
25515 The limit is created by inserting a subscript.
25516 It is set right beside the function in an inline formula:
25519 \begin_layout Standard
25521 \begin_inset Tabular
25522 <lyxtabular version="3" rows="2" columns="2">
25524 <column alignment="center" valignment="top" width="0pt">
25525 <column alignment="center" valignment="top" width="0pt">
25527 <cell alignment="center" valignment="top" usebox="none">
25530 \begin_layout Plain Layout
25536 <cell alignment="center" valignment="top" usebox="none">
25539 \begin_layout Plain Layout
25540 \begin_inset space \hspace{}
25545 \begin_inset Note Note
25548 \begin_layout Plain Layout
25555 are used here as spacer.
25567 <cell alignment="center" valignment="top" usebox="none">
25570 \begin_layout Plain Layout
25579 \begin_layout Plain Layout
25592 \begin_layout Plain Layout
25606 <cell alignment="center" valignment="top" usebox="none">
25609 \begin_layout Plain Layout
25610 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25626 \begin_layout Standard
25627 In a displayed formula the limit is set below the formula, as usual:
25628 \begin_inset Formula \[
25636 \begin_layout Subsection
25641 \begin_layout Plain Layout
25642 Functions ! modulo-
25650 \begin_layout Standard
25651 The modulo-function is special, because it exists in four variants.
25654 \begin_layout Standard
25655 The variants in a displayed formula:
25656 \begin_inset Formula \begin{align*}
25657 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25658 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25659 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25660 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25661 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25668 \begin_layout Standard
25669 In an inline formula less space is set before the function names for all
25673 \begin_layout Section
25678 \begin_layout Plain Layout
25687 \begin_layout Subsection
25688 Special Characters in Mathematical Text
25691 \begin_layout Standard
25692 The following commands can only be used in mathematical text or in TeX-mode:
25695 \begin_layout Standard
25696 \begin_inset space \hfill{}
25700 \begin_inset Tabular
25701 <lyxtabular version="3" rows="8" columns="2">
25703 <column alignment="block" valignment="top" width="0">
25704 <column alignment="block" valignment="top" width="0">
25706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25709 \begin_layout Plain Layout
25715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25718 \begin_layout Plain Layout
25726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25729 \begin_layout Plain Layout
25737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25740 \begin_layout Plain Layout
25741 \begin_inset Formula $\textrm{œ}$
25751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25754 \begin_layout Plain Layout
25762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25765 \begin_layout Plain Layout
25766 \begin_inset Formula $\textrm{Œ}$
25776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25779 \begin_layout Plain Layout
25787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25790 \begin_layout Plain Layout
25791 \begin_inset Formula $\textrm{æ}$
25801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25804 \begin_layout Plain Layout
25812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25815 \begin_layout Plain Layout
25816 \begin_inset Formula $\textrm{Æ}$
25826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25829 \begin_layout Plain Layout
25837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25840 \begin_layout Plain Layout
25841 \begin_inset Formula $\textrm{\aa}$
25851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25854 \begin_layout Plain Layout
25861 \begin_layout Plain Layout
25868 \begin_layout Plain Layout
25889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25892 \begin_layout Plain Layout
25893 \begin_inset Formula $\textrm{Å}$
25903 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25906 \begin_layout Plain Layout
25914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25917 \begin_layout Plain Layout
25918 \begin_inset Formula $\textrm{ı}$
25932 \begin_inset space \hfill{}
25936 \begin_inset Tabular
25937 <lyxtabular version="3" rows="8" columns="2">
25939 <column alignment="block" valignment="top" width="0">
25940 <column alignment="center" valignment="top" width="0">
25942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25945 \begin_layout Plain Layout
25947 \begin_inset Note Note
25950 \begin_layout Plain Layout
25952 \begin_inset space \thinspace{}
25955 mm is used for separation, because otherwise the output will be ¡ and ¿
25966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25969 \begin_layout Plain Layout
25977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25980 \begin_layout Plain Layout
25988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25991 \begin_layout Plain Layout
25992 \begin_inset Formula $\textrm{ø}$
26002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26005 \begin_layout Plain Layout
26013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26016 \begin_layout Plain Layout
26017 \begin_inset Formula $\textrm{Ø}$
26027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26030 \begin_layout Plain Layout
26038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26041 \begin_layout Plain Layout
26042 \begin_inset Formula $\textrm{ł}$
26052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26055 \begin_layout Plain Layout
26063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26066 \begin_layout Plain Layout
26067 \begin_inset Formula $\textrm{Ł}$
26077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26080 \begin_layout Plain Layout
26082 \begin_inset space \hspace{}
26090 \begin_layout Plain Layout
26104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26107 \begin_layout Plain Layout
26108 \begin_inset Formula $\textrm{!`}$
26118 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26121 \begin_layout Plain Layout
26123 \begin_inset space \hspace{}
26131 \begin_layout Plain Layout
26145 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26148 \begin_layout Plain Layout
26149 \begin_inset Formula $\textrm{?`}$
26159 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26162 \begin_layout Plain Layout
26170 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26173 \begin_layout Plain Layout
26174 \begin_inset Formula $\textrm{ȷ}$
26188 \begin_inset space \hfill{}
26194 \begin_layout Standard
26196 \begin_inset Formula $\textrm{\textrm{Å}}$
26200 \begin_inset Formula $\textrm{\textrm{Ø}}$
26203 can also be inserted via the math toolbar button
26204 \begin_inset Graphics
26205 filename ../images/math/digamma.png
26213 \begin_layout Standard
26214 An exception are the commands
26217 \begin_inset space \hspace{}
26226 \begin_inset space \hspace{}
26232 , because they can be inserted in LyX directly to text.
26235 \begin_layout Subsection
26237 \begin_inset CommandInset label
26239 name "sub:Accents-in-Text"
26247 \begin_layout Plain Layout
26256 \begin_layout Standard
26257 With the following commands all letters can be accented.
26258 The commands must be inserted in TeX-mode.
26261 \begin_layout Standard
26262 \begin_inset space \hfill{}
26266 \begin_inset Tabular
26267 <lyxtabular version="3" rows="8" columns="2">
26269 <column alignment="block" valignment="top" width="0">
26270 <column alignment="block" valignment="top" width="0">
26272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26275 \begin_layout Plain Layout
26281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26284 \begin_layout Plain Layout
26292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26295 \begin_layout Plain Layout
26299 \begin_inset Quotes grd
26307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26310 \begin_layout Plain Layout
26314 \begin_layout Plain Layout
26330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26333 \begin_layout Plain Layout
26341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26344 \begin_layout Plain Layout
26348 \begin_layout Plain Layout
26364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26367 \begin_layout Plain Layout
26374 \begin_layout Plain Layout
26388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26391 \begin_layout Plain Layout
26395 \begin_layout Plain Layout
26411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26414 \begin_layout Plain Layout
26422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26425 \begin_layout Plain Layout
26429 \begin_layout Plain Layout
26445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26448 \begin_layout Plain Layout
26455 \begin_layout Plain Layout
26469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26472 \begin_layout Plain Layout
26476 \begin_layout Plain Layout
26492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26495 \begin_layout Plain Layout
26502 \begin_layout Plain Layout
26516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26519 \begin_layout Plain Layout
26523 \begin_layout Plain Layout
26539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26542 \begin_layout Plain Layout
26549 \begin_layout Plain Layout
26563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26566 \begin_layout Plain Layout
26570 \begin_layout Plain Layout
26590 \begin_inset space \hfill{}
26594 \begin_inset Tabular
26595 <lyxtabular version="3" rows="8" columns="2">
26597 <column alignment="block" valignment="top" width="0">
26598 <column alignment="center" valignment="top" width="0">
26600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26603 \begin_layout Plain Layout
26609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26612 \begin_layout Plain Layout
26620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26623 \begin_layout Plain Layout
26630 \begin_layout Plain Layout
26644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26647 \begin_layout Plain Layout
26651 \begin_layout Plain Layout
26667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26670 \begin_layout Plain Layout
26678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26681 \begin_layout Plain Layout
26685 \begin_layout Plain Layout
26701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26704 \begin_layout Plain Layout
26711 \begin_layout Plain Layout
26722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26725 \begin_layout Plain Layout
26729 \begin_layout Plain Layout
26745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26748 \begin_layout Plain Layout
26756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26759 \begin_layout Plain Layout
26763 \begin_layout Plain Layout
26779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26782 \begin_layout Plain Layout
26789 \begin_layout Plain Layout
26803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26806 \begin_layout Plain Layout
26810 \begin_layout Plain Layout
26826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26829 \begin_layout Plain Layout
26836 \begin_layout Plain Layout
26850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26853 \begin_layout Plain Layout
26857 \begin_layout Plain Layout
26873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26876 \begin_layout Plain Layout
26883 \begin_layout Plain Layout
26897 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26900 \begin_layout Plain Layout
26904 \begin_layout Plain Layout
26924 \begin_inset space \hfill{}
26930 \begin_layout Standard
26931 \begin_inset VSpace medskip
26940 also two different characters can be accented.
26949 \begin_layout Plain Layout
26964 \begin_layout Plain Layout
26976 \begin_layout Standard
26989 can in combination with vowels directly be inserted with the keyboard without
26991 The same applies for the tilde
26995 \begin_layout Plain Layout
26996 This only applies for keyboards where the tilde is defined as accent.
27005 in combination with
27020 \begin_layout Standard
27063 and accents that are inserted directly with the keyboard are also available
27064 in mathematical text.
27065 For the other accents there are special math commands to be used in formulas,
27067 \begin_inset CommandInset ref
27069 reference "sub:Accents-for-one"
27076 \begin_layout Standard
27077 \begin_inset VSpace bigskip
27080 Furthermore, with the command
27090 \begin_layout Plain Layout
27098 all numbers and letters can be set into a circle, quasi accented with a
27099 circle, similar to the copyright symbol.
27102 \begin_layout Standard
27104 \begin_inset Tabular
27105 <lyxtabular version="3" rows="3" columns="2">
27107 <column alignment="center" valignment="top" width="0">
27108 <column alignment="center" valignment="top" width="0">
27110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27113 \begin_layout Plain Layout
27119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27122 \begin_layout Plain Layout
27124 \begin_inset Note Note
27127 \begin_layout Plain Layout
27134 is only used as spacer.
27146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27149 \begin_layout Plain Layout
27157 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27160 \begin_layout Plain Layout
27164 \begin_layout Plain Layout
27180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27183 \begin_layout Plain Layout
27194 raisebox{-1.5pt}{W}}
27199 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27202 \begin_layout Plain Layout
27203 \begin_inset Formula $\raisebox{4.5mm}{}$
27210 \begin_layout Plain Layout
27228 \begin_inset Formula $\raisebox{-2mm}{}$
27244 \begin_layout Standard
27245 One has to take care that the character fits in the circle.
27256 \begin_layout Plain Layout
27258 \begin_inset CommandInset ref
27260 reference "sub:Font-Sizes"
27269 specifies thereby the size of the circle.
27280 \begin_layout Plain Layout
27282 \begin_inset CommandInset ref
27284 reference "sub:Boxes-without-Frame"
27293 the character can be centered.
27296 \begin_layout Subsection
27301 \begin_layout Plain Layout
27310 \begin_layout Standard
27311 Minuscule numbers are created with the command
27321 \begin_layout Plain Layout
27330 The command can be used in formulas and in TeX-mode.
27331 The command scheme is:
27334 \begin_layout Standard
27339 oldstylenums{number}
27342 \begin_layout Standard
27347 oldstylenums{0123456789
27350 \begin_inset Formula $\oldstylenums{0123456789}$
27356 \begin_layout Subsection
27357 Miscellaneous special Characters
27358 \begin_inset CommandInset label
27360 name "sub:Miscellaneous-special-Characters"
27368 \begin_layout Plain Layout
27369 Special characters ! miscellaneous
27377 \begin_layout Standard
27378 The following characters can only be inserted to formulas by using commands:
27381 \begin_layout Standard
27383 \begin_inset Tabular
27384 <lyxtabular version="3" rows="4" columns="2">
27386 <column alignment="center" valignment="top" width="0">
27387 <column alignment="center" valignment="top" width="0">
27389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27392 \begin_layout Plain Layout
27398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27401 \begin_layout Plain Layout
27409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27412 \begin_layout Plain Layout
27419 \begin_layout Plain Layout
27433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27436 \begin_layout Plain Layout
27437 \begin_inset Formula $\mathcircumflex$
27447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27450 \begin_layout Plain Layout
27458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27461 \begin_layout Plain Layout
27462 \begin_inset Formula $\_$
27472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27475 \begin_layout Plain Layout
27480 \begin_layout Plain Layout
27495 \begin_layout Plain Layout
27508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27511 \begin_layout Plain Layout
27512 \begin_inset Formula $^{\circ}$
27528 \begin_layout Standard
27529 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27530 contains the following line
27534 \begin_layout Plain Layout
27535 More about this is described in
27536 \begin_inset CommandInset ref
27538 reference "sub:Text-Characters-in"
27550 \begin_layout Standard
27555 DeclareInputtext{176}{
27568 \begin_layout Section
27570 \begin_inset CommandInset label
27572 name "sec:Formula-Styles"
27580 \begin_layout Plain Layout
27589 \begin_layout Itemize
27590 There are two different alignment styles:
27594 \begin_layout Description
27595 Centered is the predefined standard
27598 \begin_layout Description
27599 Indented for this the option
27603 must be inserted in the menu
27605 Document\SpecialChar \menuseparator
27611 \begin_inset space ~
27617 \begin_layout Standard
27622 is used, the indentation can be adjusted with the length
27632 \begin_layout Plain Layout
27641 Should the distance be 15
27642 \begin_inset space \thinspace{}
27645 mm, the following command line is inserted in the LaTeX-preamble
27648 \begin_layout Standard
27658 \begin_layout Standard
27659 When no length is specified, the predefined value of 30
27660 \begin_inset space \thinspace{}
27667 \begin_layout Itemize
27668 And two different numbering styles:
27672 \begin_layout Description
27673 Right is the predefined standard
27676 \begin_layout Description
27677 Left for this the option
27681 must be inserted in the menu
27683 Document\SpecialChar \menuseparator
27689 \begin_inset space ~
27696 \begin_layout Standard
27705 can also be used together.
27706 In this case both options are inserted, separated by a comma.
27709 \begin_layout Standard
27710 The chosen styles are used for all displayed formulas of the document.
27711 When both, centered and indented formulas should be created in a document,
27717 The indented formulas are then set in a flalign environment, see
27718 \begin_inset CommandInset ref
27720 reference "sub:Flalign-Environment"
27727 \begin_layout Section
27729 \begin_inset CommandInset label
27731 name "sec:Multiline-Formulas"
27739 \begin_layout Plain Layout
27740 Formula ! multiline
27748 \begin_layout Subsection
27752 \begin_layout Standard
27753 In LyX multiline formulas are created by pressing
27758 arg "newline-insert newline"
27764 This creates either an
27766 eqnarray environment
27768 that is described in
27769 \begin_inset CommandInset ref
27771 reference "sub:Eqnarray-Environment"
27775 or, when the option
27777 Use AMS math package
27779 in the document settings is selected, an
27783 that is described in
27784 \begin_inset CommandInset ref
27786 reference "sub:Standard-align-Environment"
27793 \begin_layout Standard
27794 There are other multiline formula environments that can be created via the
27797 Insert\SpecialChar \menuseparator
27801 These environments are described in the following sections.
27804 \begin_layout Standard
27805 In all multiline formula environments a new line is created by pressing
27809 arg "newline-insert newline"
27813 To add or delete lines, the math toolbar buttons
27814 \begin_inset Graphics
27815 filename ../images/tabular-feature_append-row.png
27821 \begin_inset Graphics
27822 filename ../images/tabular-feature_delete-row.png
27827 , respectively, or the menu
27829 Edit\SpecialChar \menuseparator
27835 \begin_layout Subsubsection
27837 \begin_inset CommandInset label
27839 name "sub:Line-Separation"
27847 \begin_layout Plain Layout
27848 Formula ! multiline ! Line separation
27856 \begin_layout Standard
27857 There is sometimes not enough space in multiline formulas between the lines:
27858 \begin_inset Formula \begin{eqnarray*}
27859 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}\\
27860 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*}
27867 \begin_layout Standard
27868 In LaTeX additional line space is specified as optional argument of the
27870 This is not yet possible in LyX
27874 \begin_layout Plain Layout
27876 \begin_inset CommandInset href
27878 name "LyX-bug #1505"
27879 target "http://www.lyx.org/trac/ticket/1505"
27888 , therefore the whole formula must be inserted in TeX-mode.
27889 To add in our example space, the command
27897 is inserted at the end of the first line.
27902 \begin_layout Plain Layout
27909 \begin_layout Plain Layout
27911 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27914 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27921 \begin_layout Plain Layout
27925 left(B^{2}+x_{0}^{2}
27933 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27938 \begin_layout Plain Layout
27950 \begin_layout Standard
27951 \begin_inset VSpace bigskip
27954 To set the line separation for all lines in a formula, the length
27964 \begin_layout Plain Layout
27974 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27985 \begin_inset space \thinspace{}
27990 \begin_inset space \thinspace{}
27993 mm additional line separation as in the previous example, the command
27996 \begin_layout Standard
28006 \begin_layout Standard
28007 is inserted in TeX-mode before the formula.
28008 This requires that the LaTeX-package
28016 \begin_layout Plain Layout
28021 is part of every LaTeX standard installation.
28030 \begin_layout Plain Layout
28036 was loaded in LaTeX-preamble with the line
28039 \begin_layout Standard
28047 \begin_layout Standard
28052 \begin_layout Plain Layout
28064 \begin_inset Formula \begin{eqnarray*}
28065 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}\\
28066 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*}
28073 \begin_layout Standard
28077 \begin_layout Plain Layout
28088 To get back to the predefined distance,
28094 is set to the value 3
28095 \begin_inset space \thinspace{}
28101 \begin_layout Subsubsection
28103 \begin_inset CommandInset label
28105 name "sub:Column-Separation"
28113 \begin_layout Plain Layout
28114 Formula ! multiline ! Column separation
28122 \begin_layout Standard
28123 Multiline formulas form a matrix.
28124 A formula in the eqnarray environment is for example a matrix with three
28126 By changing the column separation in this environment, the space beside
28127 the relation sign can be changed.
28130 \begin_layout Standard
28131 The column separation is specified with the length
28141 \begin_layout Plain Layout
28150 \begin_inset Newline newline
28153 column separation = 2
28154 \begin_inset space \thinspace{}
28164 \begin_inset Newline newline
28170 \begin_layout Standard
28180 \begin_layout Standard
28181 inserted in TeX-mode, sets for all following formulas a column separation
28183 \begin_inset space \thinspace{}
28187 To get back to the predefined distance,
28194 \begin_inset space \thinspace{}
28200 \begin_layout Standard
28202 \begin_inset space \thinspace{}
28205 cm column separation:
28209 \begin_layout Plain Layout
28221 \begin_inset Formula \begin{eqnarray*}
28223 C & \ne & A\end{eqnarray*}
28227 A formula with the predefined column separation for matrices of 10
28228 \begin_inset space \thinspace{}
28235 \begin_layout Plain Layout
28247 \begin_inset Formula \begin{eqnarray*}
28249 C & \ne & A\end{eqnarray*}
28256 \begin_layout Subsubsection
28261 \begin_layout Plain Layout
28270 \begin_layout Standard
28271 Long formulas can be typeset using these methods:
28274 \begin_layout Itemize
28275 When one side of the equation is much shorther than the line width, this
28276 one is chosen for the left side and the right side is typeset over two
28278 \begin_inset Formula \begin{eqnarray}
28279 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 \\
28280 & & -\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}
28284 The minus sign at the beginning of the second line does normally not appear
28285 as operator because it is the first character of the line.
28286 Thus it would not be surrounded by space and could not be distinguished
28287 from the fraction bar.
28289 \begin_inset space \thinspace{}
28292 pt space was inserted behind the minus sign with the command
28302 \begin_layout Plain Layout
28310 \begin_inset CommandInset ref
28312 reference "sub:Variable-Space"
28325 \begin_layout Plain Layout
28336 \begin_layout Itemize
28337 When both sides of the equation are too long, the command
28347 \begin_layout Plain Layout
28356 It is inserted to the first column of the first line and effects that all
28357 further insertions overwrite the following columns:
28358 \begin_inset Formula \begin{eqnarray}
28359 \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 \\
28360 & & -\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 \\
28361 & & =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}
28365 After the insertion of
28371 , the cursor is in a purple box that is a bit shifted to the left from the
28373 In this the formula is inserted.
28374 \begin_inset Newline newline
28377 The content of the further lines is inserted to the second or another formula
28379 The greater the column number where it was inserted, the larger the indentation.
28380 \begin_inset VSpace medskip
28384 \begin_inset Newline newline
28388 \begin_inset Note Greyedout
28391 \begin_layout Plain Layout
28392 Note the following when using
28401 \begin_layout Itemize
28402 The formula doesn't use the full page width.
28404 \begin_inset space \thinspace{}
28408 \begin_inset space \space{}
28412 \begin_inset Formula $-B^{2}$
28415 is added to the first line in the above example, it would have been outside
28417 To better use the width, negative space can be inserted at the beginning
28421 \begin_layout Itemize
28422 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28427 \begin_layout Plain Layout
28428 \begin_inset CommandInset href
28430 name "LyX-bug #1429"
28431 target "http://www.lyx.org/trac/ticket/1429"
28440 One can only set the cursor at the beginning of the line and move it with
28449 \begin_layout Itemize
28450 Other methods to set long formulas are offered by the environments described
28452 \begin_inset CommandInset ref
28454 reference "sub:Multline-Environment"
28459 \begin_inset CommandInset ref
28461 reference "sub:Multiline-Formula-Parts"
28468 \begin_layout Subsubsection
28470 \begin_inset CommandInset label
28472 name "sub:Multiline-Brackets"
28480 \begin_layout Plain Layout
28481 Brackets ! for multiline expressions
28489 \begin_layout Standard
28490 For brackets spanning multiple lines the following problem occurs:
28491 \begin_inset Formula \begin{eqnarray*}
28492 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28493 & & \left.\cdots+B-D\right]\end{eqnarray*}
28500 \begin_layout Standard
28501 The closing bracket is smaller than the opening bracket because brackets
28502 with variable size may not span multiple lines.
28505 \begin_layout Standard
28506 To set the bracket size for the second line correctly, the first line is
28517 \begin_layout Plain Layout
28525 and the second line with
28533 \begin_layout Plain Layout
28547 \begin_inset CommandInset ref
28549 reference "sub:Automatic-Bracket-Size"
28564 \begin_layout Plain Layout
28590 \begin_layout Plain Layout
28609 \begin_layout Plain Layout
28628 \begin_layout Plain Layout
28640 \begin_inset Formula $\downarrow$
28649 \begin_layout Plain Layout
28657 is inserted, because the multiplication operator with its limits is the
28658 largest symbol in the first line and this should be the size for the bracket
28659 in the second line.
28662 \begin_layout Standard
28663 The result is this:
28664 \begin_inset Formula \begin{eqnarray*}
28665 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28666 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28673 \begin_layout Subsection
28677 \begin_layout Standard
28678 Align environments can be used for every kind of multiline formulas.
28679 They are specially useful to set several formulas side by side.
28682 \begin_layout Standard
28683 Align environments consist of columns.
28684 The odd columns are right aligned, the even ones left aligned.
28685 Every line in an Align environment can be numbered.
28688 \begin_layout Standard
28689 Align environments are created via the menu
28691 Insert\SpecialChar \menuseparator
28697 Edit\SpecialChar \menuseparator
28698 Math\SpecialChar \menuseparator
28699 Change Formula Type
28701 already existing formulas can be converted to Align environments.
28704 \begin_layout Standard
28705 To add or delete columns, the math toolbar buttons
28706 \begin_inset Graphics
28707 filename ../images/tabular-feature_append-column.png
28713 \begin_inset Graphics
28714 filename ../images/tabular-feature_delete-column.png
28719 , respectively, or the menu
28721 Edit\SpecialChar \menuseparator
28727 \begin_layout Subsubsection
28728 Standard align Environment
28729 \begin_inset CommandInset label
28731 name "sub:Standard-align-Environment"
28739 \begin_layout Plain Layout
28740 Formula ! multiline ! align environment
28748 \begin_layout Standard
28749 This Align environment is created by presssing
28752 arg "newline-insert newline"
28755 in a formula or by the menu
28757 Insert\SpecialChar \menuseparator
28758 Math\SpecialChar \menuseparator
28759 AMS align Environment
28764 \begin_layout Standard
28765 An example for two formulas set side by side, that are created with a four
28766 column align environment:
28767 \begin_inset Formula \begin{align*}
28768 A & =\sin(B) & C & =D\\
28769 C & \ne A & B & \ne D\end{align*}
28773 As it can be seen, the formulas in this environment are placed so as if
28782 \begin_layout Plain Layout
28790 \begin_inset CommandInset ref
28792 reference "sub:Variable-Space"
28803 before the first and after every even column.
28804 When the formula style
28810 \begin_layout Plain Layout
28812 \begin_inset CommandInset ref
28814 reference "sec:Formula-Styles"
28825 is used, the formula is set without the
28831 before the first column.
28834 \begin_layout Subsubsection
28835 Alignat Environment
28839 \begin_layout Plain Layout
28840 Formula ! multiline ! alignat environment
28848 \begin_layout Standard
28849 The alignat environment has no predefined column separation.
28850 It can be inserted manually with the spaces that are described
28851 \begin_inset CommandInset ref
28853 reference "sub:Space"
28860 \begin_layout Standard
28861 The above example in the alignat environment where 1
28862 \begin_inset space \thinspace{}
28865 cm space was inserted at the beginning of the second formula:
28866 \begin_inset Formula \begin{alignat*}{2}
28867 A & =\sin(B) & \hspace{1cm}C & =D\\
28868 C & \ne A & B & \ne D\end{alignat*}
28872 Because the column separation can be set separately for every column, this
28873 environment is especially suitable to set three and more formulas side
28877 \begin_layout Subsubsection
28878 Flalign Environment
28879 \begin_inset CommandInset label
28881 name "sub:Flalign-Environment"
28889 \begin_layout Plain Layout
28890 Formula ! multiline ! flalign environment
28898 \begin_layout Standard
28899 In this environment the first two columns are always set as much as possible
28900 to the left and the last two ones to the right.
28902 \begin_inset Formula \begin{flalign*}
28903 A & =1 & B & =2 & C & =3\\
28904 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28911 \begin_layout Standard
28912 By creating a flalign environment with an odd number of columns where an
28913 empty TeX-brace is inserted to the last column, several formulas in a document
28914 can be set to the left, although the formula style
28919 As example the indented formula
28920 \begin_inset CommandInset ref
28922 reference "eq:VolInt"
28927 \begin_inset Formula \begin{flalign}
28928 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28932 The first two columns contain the formula.
28933 To indent it as with the formula style
28938 \begin_inset space \thinspace{}
28941 pt space was inserted at the beginning of the first column.
28944 \begin_layout Subsection
28945 Eqnarray Environment
28946 \begin_inset CommandInset label
28948 name "sub:Eqnarray-Environment"
28956 \begin_layout Plain Layout
28957 Formula ! multiline ! eqnarray environment
28965 \begin_layout Standard
28966 When this environment has been created, three blue boxes appear.
28967 The content of the first box is right aligned, the content of the last
28969 The content of the middle box appears centered and a bit smaller, because
28970 it is designed to insert there only relation characters.
28971 \begin_inset Formula \begin{eqnarray*}
28972 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28974 A & = & A\end{eqnarray*}
28981 \begin_layout Subsection
28986 \begin_layout Plain Layout
28987 Formula ! multiline ! gather environment
28995 \begin_layout Standard
28996 This environment consists of only one centered column.
28997 Every line can be numbered.
28998 \begin_inset Formula \begin{gather}
29000 X=\textrm{-}1\end{gather}
29007 \begin_layout Subsection
29008 Multline Environment
29009 \begin_inset CommandInset label
29011 name "sub:Multline-Environment"
29019 \begin_layout Plain Layout
29020 Formula ! multiline ! multline environment
29028 \begin_layout Standard
29029 The multline environment consists, like the gather environment, of only
29031 But the first line is left aligned, the last one right aligned.
29032 All other lines are centered.
29033 Therefore this environment is suitable for long formulas.
29035 \begin_inset CommandInset ref
29037 reference "eq:lefteqn"
29041 in the multline environment:
29042 \begin_inset Formula \begin{multline}
29043 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}\\
29044 -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}\\
29045 =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}
29052 \begin_layout Standard
29053 In the output only the last (first) line of a multline environment appears
29054 numbered when the document numbering is right (left).
29058 \begin_layout Plain Layout
29059 numbering styles see
29060 \begin_inset CommandInset ref
29062 reference "sec:Formula-Styles"
29074 \begin_layout Standard
29085 \begin_layout Plain Layout
29103 \begin_layout Plain Layout
29111 a centered line can be right or left aligned, respectively.
29112 The commands are used as follows:
29115 \begin_layout Standard
29120 shoveright{line content}
29126 shoveleft{line content}
29129 \begin_layout Standard
29130 \begin_inset VSpace medskip
29143 \begin_layout Plain Layout
29151 specifies the distance of the first line from the left page margin.
29152 Predefined is the length 0
29153 \begin_inset space \thinspace{}
29159 \begin_layout Standard
29160 As example the above formula where the command
29163 \begin_layout Standard
29173 \begin_layout Standard
29174 was inserted in TeX-mode before:
29178 \begin_layout Plain Layout
29190 \begin_inset Formula \begin{multline}
29191 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}\\
29192 \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}}\\
29193 =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}
29201 \begin_layout Plain Layout
29212 The second line was left aligned using
29221 \begin_layout Subsection
29222 Multiline Formula Parts
29223 \begin_inset CommandInset label
29225 name "sub:Multiline-Formula-Parts"
29233 \begin_layout Plain Layout
29234 Formula ! multiline ! formula parts
29242 \begin_layout Standard
29243 To display only parts of a formula with multiple lines, one of the following
29244 environments are used:
29261 They can be inserted via the menu
29263 Insert\SpecialChar \menuseparator
29266 or by using the commands described in this section.
29269 \begin_layout Standard
29270 The first three have the same properties as the corresponding multiline
29271 formula environments, but it is possible to set further formula parts beside
29274 \begin_inset Formula \[
29275 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29276 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29277 \right\} \textrm{Uncertainty relations}\]
29284 \begin_layout Standard
29285 To get this formula, a displayed formula is created where the command
29295 \begin_layout Plain Layout
29304 A purple box appears around the blue formula box where now columns and
29305 lines can be added.
29306 Outside the multiline environment other formula parts can be set, like
29310 \begin_layout Standard
29311 The aligned environment is also suitable for long formulas whose lines are
29312 horizontally aligned.
29313 Using aligned in a displayed formula has the advantage that the formula
29314 number is vertically centered behind the lines.
29316 \begin_inset CommandInset ref
29318 reference "eq:shortlong"
29322 in the aligned environment:
29323 \begin_inset Formula \begin{equation}
29324 \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}|}\\
29325 & -\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}
29333 \begin_layout Standard
29334 To use the environments
29356 \begin_layout Plain Layout
29374 \begin_layout Plain Layout
29392 \begin_layout Plain Layout
29400 are inserted, respectively.
29401 The split environment has the same properties as the aligned environment
29402 but it can only have two columns.
29405 \begin_layout Subsection
29406 Text in multiline Formulas
29407 \begin_inset CommandInset label
29409 name "sub:Text-in-multiline"
29417 \begin_layout Plain Layout
29427 \begin_layout Plain Layout
29428 Formula ! multiline ! text
29436 \begin_layout Standard
29437 In the Align environments, and the multline and gather environment, text
29438 can be inserted that will appear in a separate line and doesn't affect
29439 the column alignment.
29440 To do this, the command
29450 \begin_layout Plain Layout
29458 is used in the following scheme:
29461 \begin_layout Standard
29469 \begin_layout Standard
29470 The text should not be longer than a line because it cannot be hyphenated.
29471 As LyX doesn't yet support
29477 directly, the text is written as mathematical text.
29484 must hereby be at the beginning of a line and appears in the output above
29486 An example where the text was inserted at the beginning of the second line:
29487 \begin_inset Formula \begin{align}
29488 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29489 \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}
29496 \begin_layout Section
29501 \begin_layout Plain Layout
29511 \begin_layout Plain Layout
29512 Formula ! numbering|see
29516 \begin_layout Plain Layout
29527 \begin_layout Plain Layout
29542 \begin_layout Subsection
29546 \begin_layout Standard
29547 Numbered formulas can be created with the menu
29549 Insert\SpecialChar \menuseparator
29550 Math\SpecialChar \menuseparator
29552 \begin_inset space ~
29560 \begin_inset space ~
29566 Existing formulas can be numbered with the menu
29568 Edit\SpecialChar \menuseparator
29569 Math\SpecialChar \menuseparator
29571 \begin_inset space ~
29579 arg "math-number-toggle"
29583 The formula number is displayed in LyX behind the formula as number sign
29585 The number sign is replaced in the output by the formula number.
29588 \begin_layout Standard
29589 When numbering is turned on in multiline formulas, all lines will be numbered.
29590 But the numbering can be controlled with the menu
29592 Edit\SpecialChar \menuseparator
29593 Math\SpecialChar \menuseparator
29595 \begin_inset space ~
29599 \begin_inset space ~
29603 \begin_inset space ~
29611 arg "math-number-line-toggle"
29617 \begin_layout Standard
29618 Except for inline formulas, all formulas can be numbered with two different
29620 \begin_inset CommandInset ref
29622 reference "sec:Formula-Styles"
29629 \begin_layout Subsection
29634 \begin_layout Plain Layout
29635 Cross-references ! to formulas
29643 \begin_layout Standard
29644 All labeled formulas can be cross-referenced.
29645 A label is added by the menu
29647 Insert\SpecialChar \menuseparator
29650 or the toolbar button
29651 \begin_inset Graphics
29652 filename ../images/label-insert.png
29658 The cursor must hereby be inside a displayed formula.
29659 A dialog pops up displaying the prefix
29664 The label is inserted there behind the prefix.
29665 The predefined prefix means
29666 \begin_inset Quotes eld
29670 \begin_inset Quotes erd
29673 and makes it easier to find labels in large documents because it marks
29674 it as formula label to divide it from e.
29675 \begin_inset space \thinspace{}
29679 \begin_inset space \space{}
29683 To change a label, the menu
29685 Insert\SpecialChar \menuseparator
29691 \begin_layout Standard
29692 The name of the label is displayed in LyX within two parentheses behind
29694 A formula with a label is always numbered.
29697 \begin_layout Standard
29698 Cross-references are inserted via the menu
29700 Insert\SpecialChar \menuseparator
29703 or with the toolbar button
29704 \begin_inset Graphics
29705 filename ../images/dialog-show-new-inset_ref.png
29711 A formula cross-reference appears in the output as formula number.
29712 When in the cross-reference dialog window the format
29716 is chosen, the cross-reference appears in the output as formula number
29718 \begin_inset Newline newline
29721 By right-clicking on a cross-reference in LyX, one jumps to the formula
29722 that is referenced.
29725 \begin_layout Standard
29726 Here are as examples cross-references to formulas of the following subsections:
29727 \begin_inset Note Note
29730 \begin_layout Plain Layout
29731 Note the different cross-reference types.
29739 \begin_layout Standard
29741 \begin_inset CommandInset ref
29748 \begin_inset CommandInset ref
29756 \begin_inset CommandInset ref
29762 ) big Latin letters are used for the numbering in contrary to (
29763 \begin_inset CommandInset ref
29772 \begin_layout Standard
29773 \begin_inset VSpace medskip
29776 When the argument of
29784 \begin_layout Plain Layout
29792 \begin_inset CommandInset ref
29794 reference "sub:User-defined-Numbering"
29805 contains a box like in
29806 \begin_inset CommandInset ref
29808 reference "sub:Paragraph-Boxes"
29812 , the formula cannot be referenced.
29815 \begin_layout Subsection
29820 \begin_layout Plain Layout
29821 Formula numbering ! subnumbering
29829 \begin_layout Standard
29830 With the help of the commands
29834 begin{subequations}
29842 formulas can be subnumbered.
29843 Both commands are inserted in TeX-mode.
29846 \begin_layout Standard
29848 \begin_inset Formula \begin{equation}
29849 A=C-B\label{eq:a}\end{equation}
29857 \begin_layout Plain Layout
29861 addtocounter{equation}{-1}
29870 \begin_layout Plain Layout
29874 begin{subequations}
29880 \begin_inset VSpace -5mm
29884 \begin_inset Formula \begin{equation}
29885 B=C-A\label{eq:b}\end{equation}
29890 \begin_inset Formula \begin{equation}
29891 C=A+B\label{eq:c}\end{equation}
29898 \begin_layout Standard
29902 \begin_layout Plain Layout
29914 \begin_layout Standard
29915 To create the example, the following is done:
29918 \begin_layout Enumerate
29919 first formula is inserted
29922 \begin_layout Enumerate
29927 addtocounter{equation}{-1}
29929 begin{subequations}
29933 \begin_layout Plain Layout
29942 \begin_inset Newline newline
29947 is inserted after the first formula
29950 \begin_layout Enumerate
29951 second formula is inserted
29954 \begin_layout Enumerate
29955 third formula is inserted
29958 \begin_layout Enumerate
29965 is inserted after the third formula
29968 \begin_layout Standard
29969 Every formula between the commands
29981 is subnumbered as a, b,
29982 \begin_inset Newline linebreak
29985 c, \SpecialChar \ldots{}
29986 For multiline formulas every line will be subnumbered.
29987 All subnumbered formulas are treated as
29992 But as every numbered formula increases the counter
29996 by one, the command
30002 is needed to decrease it.
30003 Otherwise the formulas
30004 \begin_inset CommandInset ref
30011 \begin_inset CommandInset ref
30018 \begin_inset CommandInset ref
30024 would be numbered as
30025 \begin_inset CommandInset ref
30032 \begin_inset CommandInset ref
30039 \begin_inset CommandInset ref
30048 \begin_layout Standard
30049 By inserting the commands in TeX-mode, a space is created between the first
30052 \begin_inset space \thinspace{}
30055 mm vertical space is inserted after the command
30059 begin{subequations}
30062 When the formula style
30068 \begin_layout Plain Layout
30070 \begin_inset CommandInset ref
30072 reference "sec:Formula-Styles"
30084 \begin_inset space \thinspace{}
30087 mm space is inserted instead.
30090 \begin_layout Standard
30091 Here is an example for a multiline formula where the numbering was turned
30092 off for the second line:
30096 \begin_layout Plain Layout
30100 begin{subequations}
30106 \begin_inset Formula \begin{eqnarray}
30107 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30108 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30109 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
30117 \begin_layout Plain Layout
30129 \begin_layout Subsection
30130 User-defined Numbering
30131 \begin_inset CommandInset label
30133 name "sub:User-defined-Numbering"
30141 \begin_layout Plain Layout
30142 Formula numbering ! user-defined
30150 \begin_layout Standard
30154 \begin_layout Plain Layout
30155 Formula numbering ! self-defined delimiters
30160 With the standard numbering parentheses are set around the formula number.
30161 To replace the parentheses for example by vertical bars, the following
30162 line is added to the LaTeX-preamble:
30165 \begin_layout Standard
30177 \begin_inset Note Note
30180 \begin_layout Plain Layout
30181 This macro is already declared in the LaTeX-preamble for testing.
30182 To activate it, remove the percent sign at the beginning.
30190 \begin_layout Standard
30191 To use other characters, the vertical bars besides the
30195 are replaced by one ore more characters.
30196 To get only the formula number the vertical bars are omitted.
30199 \begin_layout Standard
30200 \begin_inset VSpace bigskip
30203 When there should be an expression of your choice instead of the consecutive
30204 formula number in parentheses behind the formula, the command
30214 \begin_layout Plain Layout
30223 \begin_inset Formula \begin{equation}
30224 A+B=C\tag{something}\label{eq:tag}\end{equation}
30228 In this example the command
30236 \begin_layout Plain Layout
30247 was inserted to the formula.
30250 \begin_layout Standard
30259 \begin_layout Plain Layout
30270 is inserted instead, the star prevents the parentheses around the expression:
30271 \begin_inset Formula \[
30272 A+B=C\tag*{something}\]
30279 \begin_layout Standard
30280 \begin_inset VSpace bigskip
30283 To restart the formula numbering with new document parts or sections, the
30284 following command is used:
30287 \begin_layout Standard
30292 @addtoreset{equation}{part}
30298 \begin_layout Plain Layout
30303 \begin_layout Plain Layout
30314 \begin_layout Plain Layout
30327 \begin_layout Plain Layout
30338 \begin_layout Plain Layout
30351 \begin_inset Newline newline
30355 \begin_inset Newline newline
30362 @addtoreset{equation}{section}
30365 \begin_layout Standard
30366 To be able to use these commands in TeX-mode, the
30367 \begin_inset Quotes eld
30371 \begin_inset Quotes erd
30374 character has to be made
30375 \begin_inset Quotes eld
30379 \begin_inset Quotes erd
30382 for LaTeX using the command
30396 So the command sequence in TeX-mode is:
30399 \begin_layout Standard
30405 \begin_inset Newline newline
30410 @addtoreset{equation}{section}
30411 \begin_inset Newline newline
30419 \begin_layout Standard
30420 In the LaTeX-preamble
30432 can be omitted as they are automatically internally inserted by LyX.
30435 \begin_layout Standard
30450 \begin_layout Plain Layout
30455 is part of the LaTeX-package
30463 \begin_layout Plain Layout
30464 Packages ! carlisle
30469 that is part of every LaTeX standard installation.
30478 \begin_layout Plain Layout
30479 Packages ! remreset
30484 has to be loaded in the LaTeX-preamble with the line
30487 \begin_layout Standard
30492 usepackage{remreset}
30495 \begin_layout Standard
30506 \begin_layout Plain Layout
30511 \begin_layout Plain Layout
30522 \begin_layout Plain Layout
30535 \begin_layout Plain Layout
30546 \begin_layout Plain Layout
30558 can be used with the same scheme as
30567 \begin_layout Standard
30568 \begin_inset VSpace bigskip
30571 Sometimes formulas should be numbered in the following form:
30574 \begin_layout Standard
30577 (section number.formula number)
30580 \begin_layout Standard
30581 The formula number should start with every section with
30582 \begin_inset Quotes eld
30586 \begin_inset Quotes erd
30592 \begin_layout Standard
30593 For this case there is the command
30603 \begin_layout Plain Layout
30611 , which is used with the following scheme:
30614 \begin_layout Standard
30619 numberwithin{counter}{sectioning}
30622 \begin_layout Standard
30623 Counter denotes what kind of numbering is affected, sectioning denotes what
30624 number is before the dot.
30627 \begin_layout Standard
30628 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30631 \begin_layout Standard
30636 numberwithin{equation}{section}
30639 \begin_layout Standard
30640 This is the result:
30644 \begin_layout Plain Layout
30648 numberwithin{equation}{section}
30654 \begin_inset Formula \begin{equation}
30655 A+B=C\end{equation}
30662 \begin_layout Standard
30664 \begin_inset space \thinspace{}
30668 \begin_inset space \space{}
30671 tables so that the number of the part is the sectioning,
30672 \begin_inset Newline newline
30679 numberwithin{table}{part}
30684 \begin_layout Standard
30685 To go back to the standard numbering or to prevent this kind of numbering
30686 when it is defined by the document class, the following command is inserted
30687 as TeX-Code or to the LaTeX-preamble:
30690 \begin_layout Standard
30703 \begin_layout Plain Layout
30717 \begin_layout Plain Layout
30733 \begin_inset Newline newline
30741 \begin_inset Newline newline
30753 \begin_layout Standard
30760 uses internally the command
30766 , described above, that also needs to be reverted.
30770 \begin_layout Plain Layout
30777 \begin_layout Plain Layout
30781 @removefromreset{equation}{section}
30784 \begin_layout Plain Layout
30796 \begin_layout Subsection
30797 Numbering with Roman Numbers and Letters
30801 \begin_layout Plain Layout
30802 Formula numbering ! with letters
30811 \begin_layout Plain Layout
30812 Formula numbering ! with Roman numbers
30820 \begin_layout Standard
30821 Formulas can also be numbered with Roman numbers and Latin letters.
30822 To number for example with small Roman numbers, the command
30825 \begin_layout Standard
30837 \begin_layout Standard
30838 is inserted before the formula in TeX-mode.
30849 \begin_layout Plain Layout
30857 redefines the predefined command
30873 \begin_layout Plain Layout
30880 has the same scheme like the command
30886 that is described in
30887 \begin_inset CommandInset ref
30889 reference "sub:The-Command-newcommand"
30902 is the formula counter.
30909 is used as prefix for a counter, the value of the counter is output as
30911 When a formula is numbered, LaTeX sets internally the command
30917 behind the formula.
30926 \begin_layout Plain Layout
30936 outputs the counter as small Roman number.
30939 \begin_layout Standard
30940 All formulas behind the command
30950 are now numbered Roman.
30951 To switch to numbering with big Roman numbers, the command is inserted
30968 \begin_layout Plain Layout
30980 \begin_inset Quotes eld
30984 \begin_inset Quotes erd
30987 with small Latin letters there is the command
30997 \begin_layout Plain Layout
31005 , for big ones there is the command
31015 \begin_layout Plain Layout
31028 \begin_layout Standard
31029 \begin_inset Note Greyedout
31032 \begin_layout Plain Layout
31037 Only maximal 26 formulas can be numbered with Latin letters in one document.
31045 \begin_layout Standard
31049 \begin_layout Plain Layout
31065 \begin_layout Standard
31066 \begin_inset Formula \begin{equation}
31067 A=\textrm{small roman}\end{equation}
31075 \begin_layout Plain Layout
31089 \begin_inset Formula \begin{equation}
31090 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
31098 \begin_layout Plain Layout
31112 \begin_inset Formula \begin{equation}
31113 C=\textrm{small Latin}\end{equation}
31121 \begin_layout Plain Layout
31135 \begin_inset Formula \begin{equation}
31136 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31143 \begin_layout Standard
31144 To switch back to the default numbering, insert the command:
31147 \begin_layout Standard
31160 \begin_layout Plain Layout
31171 \begin_layout Standard
31175 \begin_layout Plain Layout
31189 \begin_inset Formula \begin{equation}
31190 E=\textrm{Arabic}\end{equation}
31197 \begin_layout Standard
31198 \begin_inset VSpace medskip
31201 As you see, formulas are numbered serially independent from the numbering
31203 When then numbering should start with
31204 \begin_inset Quotes eld
31208 \begin_inset Quotes erd
31211 when the style is changed, new equation counters have to be defined.
31212 A description about this can be found in the file
31213 \begin_inset CommandInset href
31215 name "Formula-numbering.lyx"
31216 target "run:Formula-numbering.lyx"
31223 \begin_layout Section
31224 Chemical Symbols and Equations
31225 \begin_inset CommandInset label
31227 name "sub:Chemical-Symbols-and"
31235 \begin_layout Plain Layout
31236 Chemical characters ! Symbols
31245 \begin_layout Plain Layout
31255 \begin_layout Plain Layout
31264 \begin_layout Standard
31265 An example text from chemistry:
31268 \begin_layout Quote
31270 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31273 -ion reacts with two
31274 \begin_inset Formula $\mathrm{Na^{+}}$
31277 -ions to sodium sulfate
31278 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31282 The chemical equation for this is:
31283 \begin_inset Formula \begin{equation}
31284 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31291 \begin_layout Standard
31292 This chemical equation can directly be created as formula.
31293 To avoid that the symbols appear italic, everything is highlighted and
31294 changed by the shortcut
31300 to the upright font style.
31304 \begin_layout Plain Layout
31310 \begin_inset CommandInset ref
31312 reference "sub:Font-Styles"
31324 \begin_layout Standard
31325 A more convenient way to typeset chemical formulas is to use the command
31336 \begin_layout Plain Layout
31344 that is available when the LaTeX-package
31352 \begin_layout Plain Layout
31365 to a formula a new blue box appears where chemical formulas can be inserted
31366 in an intuitive way.
31369 \begin_layout Standard
31371 \begin_inset Tabular
31372 <lyxtabular version="3" rows="9" columns="2">
31374 <column alignment="center" valignment="top" width="0">
31375 <column alignment="center" valignment="top" width="0">
31377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31380 \begin_layout Plain Layout
31386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31389 \begin_layout Plain Layout
31391 \begin_inset Note Note
31394 \begin_layout Plain Layout
31401 is only used as spacer.
31413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31416 \begin_layout Plain Layout
31423 \begin_layout Plain Layout
31437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31440 \begin_layout Plain Layout
31441 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31454 \begin_layout Plain Layout
31461 \begin_layout Plain Layout
31475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31478 \begin_layout Plain Layout
31479 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31492 \begin_layout Plain Layout
31499 \begin_layout Plain Layout
31513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31516 \begin_layout Plain Layout
31517 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31530 \begin_layout Plain Layout
31537 \begin_layout Plain Layout
31551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31554 \begin_layout Plain Layout
31555 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31568 \begin_layout Plain Layout
31575 \begin_layout Plain Layout
31590 \begin_layout Plain Layout
31605 \begin_layout Plain Layout
31619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31622 \begin_layout Plain Layout
31623 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31636 \begin_layout Plain Layout
31643 \begin_layout Plain Layout
31653 \begin_inset Formula $\downarrow$
31657 \begin_inset Formula $\to$
31665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31668 \begin_layout Plain Layout
31669 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31682 \begin_layout Plain Layout
31689 \begin_layout Plain Layout
31702 \begin_layout Plain Layout
31715 \begin_layout Plain Layout
31728 \begin_layout Plain Layout
31741 \begin_layout Plain Layout
31755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31758 \begin_layout Plain Layout
31759 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31772 \begin_layout Plain Layout
31779 \begin_layout Plain Layout
31792 \begin_layout Plain Layout
31805 \begin_layout Plain Layout
31818 \begin_layout Plain Layout
31835 \begin_layout Plain Layout
31849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31852 \begin_layout Plain Layout
31853 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
31869 \begin_layout Standard
31870 \begin_inset Note Greyedout
31873 \begin_layout Plain Layout
31878 Inserting a formula to a
31884 box will lead to LaTeX errors.
31885 In this case TeX code has to be used like for
31899 \begin_layout Plain Layout
31920 \begin_layout Standard
31927 the command for equation
31928 \begin_inset space ~
31932 \begin_inset CommandInset ref
31934 reference "eq:chem-reaction"
31939 \begin_inset Newline newline
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
32015 \begin_layout Plain Layout
32027 \begin_layout Standard
32028 To create multiline chemical equations first a multiline formula is created
32030 \begin_inset CommandInset ref
32032 reference "sec:Multiline-Formulas"
32037 Afterwards the command
32043 is used in every small blue box of the formula.
32045 \begin_inset CommandInset ref
32047 reference "eq:TEOS-reaction-1"
32052 \begin_inset CommandInset ref
32054 reference "eq:TEOS-reaction-2"
32058 are an example of a multi-stage chemical reaction where every equation
32059 has its own number.
32060 \begin_inset Formula \begin{eqnarray}
32061 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32062 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}\end{eqnarray}
32069 \begin_layout Standard
32080 package provides the command
32090 \begin_layout Plain Layout
32098 that has to be used for special cases.
32099 For more information about
32105 and more examples have a look at the documentation of
32110 \begin_inset CommandInset citation
32119 \begin_layout Standard
32120 \begin_inset Newpage newpage
32126 \begin_layout Section
32130 \begin_layout Standard
32131 LyX supports two types of commutative diagrams:
32139 that are explained in the following.
32142 \begin_layout Subsection
32147 \begin_layout Plain Layout
32156 \begin_layout Standard
32157 Diagrams of this type visualize relations by vertical and horizontal lines
32159 \begin_inset Formula \[
32160 \begin{CD}A@>>>B@>>>C\\
32162 F@<<<E@<<<D\end{CD}\]
32169 \begin_layout Standard
32170 To get them, the command
32178 \begin_layout Plain Layout
32188 is inserted to a formula.
32189 A blue box appears with two dashed lines where further commands can be
32194 arg "newline-insert newline"
32197 a new line is created.
32198 Horizontal relations are inserted in odd, vertical in even formula lines.
32201 \begin_layout Standard
32202 To create the relations there are the following commands:
32205 \begin_layout Itemize
32210 creates a left arrow,
32221 \begin_layout Itemize
32226 creates an up arrow,
32234 a vertical equal sign
32237 \begin_layout Itemize
32243 is a placeholder for non-existent relations
32246 \begin_layout Standard
32247 All arrows can be labeled as follows:
32250 \begin_layout Itemize
32251 Is text inserted between the first and second < or >, resp., it is placed
32253 When it is inserted between the second and third one, it appears under
32257 \begin_layout Itemize
32258 When text for vertical arrows is inserted between the first and second A
32259 or V, resp., it is placed left beside the arrow.
32260 When it is inserted between the second and third one, it appears right
32262 If the text contains an A or V, these letters must be set into a TeX-brace.
32265 \begin_layout Standard
32266 As example a diagram with all possible relations:
32269 \begin_layout Standard
32270 \begin_inset Formula \[
32271 \begin{CD}A@>j>>B@>>k>C@=F\\
32273 D@<<j<E@>k>>F@=C\end{CD}\]
32280 \begin_layout Standard
32281 The command for this is:
32282 \begin_inset Newline newline
32293 \begin_layout Plain Layout
32302 A@>j>>B@>>k>C@=F Ctrl+Return
32303 \begin_inset Newline newline
32310 \begin_layout Plain Layout
32325 \begin_layout Plain Layout
32338 \begin_layout Plain Layout
32350 \begin_inset Formula $\to$
32356 \begin_inset Newline newline
32363 \begin_layout Plain Layout
32378 \begin_layout Plain Layout
32391 \begin_layout Plain Layout
32401 \begin_layout Subsection
32406 \begin_layout Plain Layout
32407 Diagrams ! xymatrix
32415 \begin_layout Standard
32416 To be able to use xymatrices, the LaTeX-package
32421 A xymatrix is created by inserting the command
32428 Then you are able to add new matrix columns and rows like for normal matrices,
32430 \begin_inset CommandInset ref
32432 reference "sec:Matrices"
32439 \begin_layout Standard
32440 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32442 All possibilities to create commutative diagrams and decorations are explained
32447 that you find in the menu
32449 Help\SpecialChar \menuseparator
32451 \begin_inset space ~
32454 Manuals\SpecialChar \menuseparator
32456 \begin_inset space ~
32464 \begin_layout Section
32465 User-defined Commands
32469 \begin_layout Plain Layout
32470 User-defined commands
32478 \begin_layout Standard
32479 \begin_inset Note Greyedout
32482 \begin_layout Plain Layout
32487 The names of user-defined commands and macros may only consist of Latin
32496 \begin_layout Subsection
32500 \begin_inset CommandInset label
32502 name "sub:The-Command-newcommand"
32510 \begin_layout Plain Layout
32511 User-defined commands !
32522 \begin_layout Plain Layout
32533 \begin_layout Standard
32534 Many LaTeX-commands are too long to be used frequently.
32535 But it is possible to define with the command
32541 new shorter commands.
32544 \begin_layout Standard
32545 The command scheme of
32554 \begin_layout Standard
32559 newcommand{new command name}[number of arguments][optional
32564 \begin_inset Newline newline
32571 \begin_layout Plain Layout
32586 \begin_layout Plain Layout
32593 {command definition}
32596 \begin_layout Standard
32597 \begin_inset Note Greyedout
32600 \begin_layout Plain Layout
32605 Assure that the name of the new command is not already used in your document
32606 or by LaTeX-packages that you use.
32607 When you for example define the command
32619 , you get an error message because
32625 is already defined as command for
32626 \begin_inset Quotes eld
32630 \begin_inset Formula $\le$
32634 \begin_inset Quotes erd
32645 \begin_layout Standard
32646 The number of arguments is an integer in the range 0
32647 \begin_inset space \thinspace{}
32651 \begin_inset space \thinspace{}
32654 9 and specifies how many arguments the new command should have.
32655 With the optional value a value for an optional argument can be predefined.
32656 When this is done, the
32664 rgument of the new command is automatically an optional one.
32667 \begin_layout Standard
32668 Here are some examples:
32671 \begin_layout Itemize
32672 To define the command
32684 , the LaTeX-preamble line is:
32685 \begin_inset VSpace medskip
32689 \begin_inset Newline newline
32703 \begin_layout Itemize
32704 To define the command
32716 , the argument (that should be underlined) must be taken into account.
32717 For this the preamble line is:
32718 \begin_inset VSpace medskip
32722 \begin_inset Newline newline
32736 \begin_inset VSpace medskip
32740 \begin_inset Newline newline
32747 acts as argument placeholder, the
32751 behind it denotes that it is the placeholder for the first argument.
32754 \begin_layout Itemize
32762 \begin_inset space \thinspace{}
32766 \begin_inset space \space{}
32776 \begin_inset VSpace medskip
32780 \begin_inset Newline newline
32791 framebox#1#2{$#3$}}
32794 \begin_inset VSpace medskip
32798 \begin_inset Newline newline
32801 The two Dollar signs creates the extra formula needed for
32808 \begin_inset CommandInset ref
32810 reference "sub:Boxes-with-Frame"
32817 \begin_layout Itemize
32818 To create a new command for
32824 where the color for the box needn't to be specified, the argument for the
32825 color is defined optional:
32826 \begin_inset VSpace medskip
32830 \begin_inset Newline newline
32841 fcolorbox{#2}{#1}{$#3$}}
32844 \begin_inset VSpace medskip
32848 \begin_inset Newline newline
32851 When the color is not specified when using
32857 , the predefined color
32864 \begin_layout Standard
32865 A test of the new defined commands:
32868 \begin_layout Standard
32870 \begin_inset Tabular
32871 <lyxtabular version="3" rows="6" columns="2">
32873 <column alignment="center" valignment="top" width="0">
32874 <column alignment="center" valignment="top" width="0">
32876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32879 \begin_layout Plain Layout
32885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32888 \begin_layout Plain Layout
32890 \begin_inset Note Note
32893 \begin_layout Plain Layout
32900 is only used as spacer.
32912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32915 \begin_layout Plain Layout
32922 \begin_layout Plain Layout
32936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32939 \begin_layout Plain Layout
32940 \begin_inset Formula $A\gr B$
32950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32953 \begin_layout Plain Layout
32961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32964 \begin_layout Plain Layout
32965 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32978 \begin_layout Plain Layout
32982 \begin_inset Formula $\to$
32988 \begin_inset Formula $\to$
32999 \begin_layout Plain Layout
33013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33016 \begin_layout Plain Layout
33017 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33030 \begin_layout Plain Layout
33034 \begin_inset Formula $\to$
33045 \begin_layout Plain Layout
33059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33062 \begin_layout Plain Layout
33063 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33076 \begin_layout Plain Layout
33082 \begin_inset Formula $\to$
33093 \begin_layout Plain Layout
33107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33110 \begin_layout Plain Layout
33111 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33127 \begin_layout Subsection
33132 \begin_layout Plain Layout
33133 User-defined commands! Math macros
33142 \begin_layout Plain Layout
33151 \begin_layout Standard
33152 User-defined commands are especially convenient for complex expressions.
33153 When you are for example dealing in a document with quadratic equations,
33154 the same solution type occurs several times.
33155 The general form of a quadratic equation is
33156 \begin_inset Formula \[
33157 0=\lambda^{2}+p\lambda+q\]
33161 The general form of the solution is
33162 \begin_inset Formula \[
33163 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33170 \begin_layout Standard
33171 To define a command for the solution formula where only the three parameters
33173 \begin_inset Formula $\lambda$
33177 \begin_inset Formula $p$
33181 \begin_inset Formula $q$
33184 need to be specified and the index of
33185 \begin_inset Formula $\lambda$
33188 can be given optionally, the LaTeX-preamble line is
33189 \begin_inset Newline newline
33205 \begin_inset Newline newline
33212 \begin_layout Plain Layout
33227 \begin_layout Plain Layout
33238 frac{#3^{2}}{4}-#4}}
33241 \begin_layout Standard
33242 To create with this the solution formula, the command
33243 \begin_inset Newline newline
33253 \begin_inset Formula $\to$
33259 \begin_inset Formula $\to$
33266 is inserted to a formula
33271 \begin_layout Standard
33272 The definition of the new command is unintuitive because one has to know
33273 the schemes of all used LaTeX commands, e.
33274 \begin_inset space \thinspace{}
33278 \begin_inset space \space{}
33281 that a fraction is inserted in LaTeX as
33285 frac{numerator}{denominator}
33288 Furthermore one can easily forget a brace in the definition and cannot
33289 see in LyX what the new command is doing.
33290 To avoid these problems LyX offers the possibility to use math macros instead
33300 \begin_layout Standard
33301 A math macro is created by using the menu
33303 Insert\SpecialChar \menuseparator
33304 Math\SpecialChar \menuseparator
33307 or the toolbar button
33308 \begin_inset Graphics
33309 filename ../images/math-macro_newmacroname_newcommand.png
33315 The math macro toolbar appears together with the following box where the
33317 \begin_inset Newline newline
33321 \begin_inset space \hspace*{\fill}
33325 \begin_inset Graphics
33326 filename clipart/macrobox.png
33331 \begin_inset space \hspace*{\fill}
33335 \begin_inset Newline newline
33339 \begin_inset FormulaMacro
33340 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33345 newmacroname is the default name of the macro that should be changed to
33346 something sensible.
33347 The wanted formula is inserted in the first blue box.
33348 An argument placeholder is inserted with the command
33355 \begin_inset space \thinspace{}
33359 \begin_inset space \space{}
33368 or by using the macro toolbar button
33369 \begin_inset Graphics
33370 filename ../images/math-macro-add-param.png
33376 Argument placeholders are displayed red.
33377 Maximum 9 arguments are possible.
33378 Optional arguments are created with the toolbar button
33379 \begin_inset Graphics
33380 filename ../images/math-macro-add-optional-param.png
33386 The first non-optional argument can be transformed to an optional one with
33388 \begin_inset Graphics
33389 filename ../images/math-macro-make-optional.png
33395 In the second blue box the appearance of the macro in LyX can be defined.
33396 Normally you want to see it as it is defined, so the box is kept empty.
33397 But when you have created a macro that needs lot of space on the screen,
33398 you can insert in the box for example
33399 \begin_inset Newline newline
33429 \begin_inset Newline newline
33434 For the macro only the arguments with the macro name in front of them will
33435 then be displayed in LyX, leading to a better overview.
33436 The formula appears in the output as defined in the first box.
33437 \begin_inset Newline newline
33440 The appearance of macros in formulas can furthermore be changed for single
33441 macros by setting the cursor in the macro and using the menu
33443 View\SpecialChar \menuseparator
33445 \begin_inset space ~
33449 \begin_inset space ~
33457 \begin_layout Standard
33458 To use a macro, the macro name is inserted as command to a formula, in our
33466 Our macro looks in LyX like this:
33467 \begin_inset Newline newline
33471 \begin_inset space \hspace*{\fill}
33475 \begin_inset Graphics
33476 filename clipart/macrouse.png
33481 \begin_inset space \hspace*{\fill}
33485 \begin_inset Newline newline
33488 Here is our macro example with the arguments
33489 \begin_inset Formula $x$
33493 \begin_inset Formula $\ln(x)$
33497 \begin_inset Formula $B$
33503 \begin_layout Standard
33504 \begin_inset Formula \[
33512 \begin_layout Standard
33513 LyX offers in the menu
33515 Tools\SpecialChar \menuseparator
33516 Preferences\SpecialChar \menuseparator
33517 Editing\SpecialChar \menuseparator
33520 different styles to edit macros.
33521 To find the style that suits you the most, choose a style and set the cursor
33522 in a macro formula to see the difference.
33525 \begin_layout Standard
33526 A math macro is transformed internally to a
33532 command when exporting the document.
33539 command is not placed in the LaTeX-preamble, therefore macros can only
33540 be used in formulas that are in the document below the macro definition
33544 \begin_layout Standard
33545 Math macros can also be directly be created from a
33552 When writing for example the command
33555 \begin_inset Newline newline
33564 xleftarrow[#2]{#1}}
33565 \begin_inset Newline newline
33570 in LyX as normal text, highlighting it completely and using then the shortcut
33575 , the command will be transformed to a math macro.
33576 Using this method you need to be careful that the
33582 command is typed correctly, otherwise you get a faulty macro leading to
33586 \begin_layout Standard
33587 Math macros currently yet have the problem that further formulas in macro
33588 definitions are handled wrongly.
33589 Therefore the example
33596 \begin_inset CommandInset ref
33598 reference "sub:The-Command-newcommand"
33602 cannot be created as macro.
33605 \begin_layout Standard
33606 When the cursor is in a macro definition box, you will see the macro toolbar
33610 \begin_layout Standard
33611 \begin_inset VSpace defskip
33617 \begin_layout Standard
33618 \begin_inset Graphics
33619 filename clipart/MacroToolbar.png
33627 \begin_layout Plain Layout
33636 \begin_layout Standard
33637 \begin_inset VSpace defskip
33643 \begin_layout Standard
33644 The macro toolbar contains from left to right the following buttons:
33647 \begin_layout Standard
33648 \begin_inset VSpace defskip
33654 \begin_layout Standard
33655 \begin_inset Tabular
33656 <lyxtabular version="3" rows="9" columns="2">
33657 <features islongtable="true">
33658 <column alignment="left" valignment="top" width="0">
33659 <column alignment="left" valignment="top" width="85col%">
33660 <row interlinespace="2.5mm">
33661 <cell alignment="center" valignment="top" usebox="none">
33664 \begin_layout Plain Layout
33665 \begin_inset Graphics
33666 filename ../images/math-macro-remove-param.png
33667 BoundingBox 0bp 5bp 20bp 25bp
33668 rotateOrigin center
33677 <cell alignment="center" valignment="top" usebox="none">
33680 \begin_layout Plain Layout
33683 Edit\SpecialChar \menuseparator
33684 Math\SpecialChar \menuseparator
33686 \begin_inset space ~
33689 Definition\SpecialChar \menuseparator
33690 Remove Last Argument
33696 <row interlinespace="2.5mm">
33697 <cell alignment="center" valignment="top" usebox="none">
33700 \begin_layout Plain Layout
33701 \begin_inset Graphics
33702 filename ../images/math-macro-add-param.png
33703 BoundingBox 0bp 5bp 20bp 25bp
33704 rotateOrigin center
33713 <cell alignment="center" valignment="top" usebox="none">
33716 \begin_layout Plain Layout
33719 Edit\SpecialChar \menuseparator
33720 Math\SpecialChar \menuseparator
33722 \begin_inset space ~
33725 Definition\SpecialChar \menuseparator
33732 <row interlinespace="2.5mm">
33733 <cell alignment="center" valignment="top" usebox="none">
33736 \begin_layout Plain Layout
33737 \begin_inset Graphics
33738 filename ../images/math-macro-make-optional.png
33739 BoundingBox 0bp 5bp 20bp 25bp
33740 rotateOrigin center
33749 <cell alignment="center" valignment="top" usebox="none">
33752 \begin_layout Plain Layout
33755 Edit\SpecialChar \menuseparator
33756 Math\SpecialChar \menuseparator
33758 \begin_inset space ~
33761 Definition\SpecialChar \menuseparator
33762 Make First Non-Optional into
33763 \begin_inset Newline newline
33770 \begin_layout Plain Layout
33779 Edit\SpecialChar \menuseparator
33780 Math\SpecialChar \menuseparator
33782 \begin_inset space ~
33785 Definition\SpecialChar \menuseparator
33790 \begin_layout Plain Layout
33803 <row interlinespace="2.5mm">
33804 <cell alignment="center" valignment="top" usebox="none">
33807 \begin_layout Plain Layout
33808 \begin_inset Graphics
33809 filename ../images/math-macro-make-nonoptional.png
33810 BoundingBox 0bp 5bp 20bp 25bp
33811 rotateOrigin center
33820 <cell alignment="center" valignment="top" usebox="none">
33823 \begin_layout Plain Layout
33826 Edit\SpecialChar \menuseparator
33827 Math\SpecialChar \menuseparator
33829 \begin_inset space ~
33832 Definition\SpecialChar \menuseparator
33833 Make Last Optional into
33834 \begin_inset Newline newline
33841 \begin_layout Plain Layout
33850 Edit\SpecialChar \menuseparator
33851 Math\SpecialChar \menuseparator
33853 \begin_inset space ~
33856 Definition\SpecialChar \menuseparator
33861 \begin_layout Plain Layout
33868 Non-Optional Argument
33874 <row interlinespace="2.5mm">
33875 <cell alignment="center" valignment="top" usebox="none">
33878 \begin_layout Plain Layout
33879 \begin_inset Graphics
33880 filename ../images/math-macro-remove-optional-param.png
33881 BoundingBox 0bp 5bp 20bp 25bp
33882 rotateOrigin center
33891 <cell alignment="center" valignment="top" usebox="none">
33894 \begin_layout Plain Layout
33897 Edit\SpecialChar \menuseparator
33898 Math\SpecialChar \menuseparator
33900 \begin_inset space ~
33903 Definition\SpecialChar \menuseparator
33904 Remove Optional Argument
33910 <row interlinespace="2.5mm">
33911 <cell alignment="center" valignment="top" usebox="none">
33914 \begin_layout Plain Layout
33915 \begin_inset Graphics
33916 filename ../images/math-macro-add-optional-param.png
33917 BoundingBox 0bp 5bp 20bp 25bp
33918 rotateOrigin center
33927 <cell alignment="center" valignment="top" usebox="none">
33930 \begin_layout Plain Layout
33933 Edit\SpecialChar \menuseparator
33934 Math\SpecialChar \menuseparator
33936 \begin_inset space ~
33939 Definition\SpecialChar \menuseparator
33940 Insert Optional Argument
33946 <row interlinespace="2.5mm">
33947 <cell alignment="center" valignment="top" usebox="none">
33950 \begin_layout Plain Layout
33951 \begin_inset Graphics
33952 filename ../images/math-macro-remove-greedy-param.png
33953 BoundingBox 0bp 5bp 20bp 25bp
33954 rotateOrigin center
33963 <cell alignment="center" valignment="top" usebox="none">
33966 \begin_layout Plain Layout
33969 Edit\SpecialChar \menuseparator
33970 Math\SpecialChar \menuseparator
33972 \begin_inset space ~
33975 Definition\SpecialChar \menuseparator
33976 Remove Last Argument
33977 \begin_inset Newline newline
33984 \begin_layout Plain Layout
33993 Edit\SpecialChar \menuseparator
33994 Math\SpecialChar \menuseparator
33996 \begin_inset space ~
33999 Definition\SpecialChar \menuseparator
34004 \begin_layout Plain Layout
34011 Spitting Out To The Right
34017 <row interlinespace="2.5mm">
34018 <cell alignment="center" valignment="top" usebox="none">
34021 \begin_layout Plain Layout
34022 \begin_inset Graphics
34023 filename ../images/math-macro-append-greedy-param.png
34024 BoundingBox 0bp 5bp 20bp 25bp
34025 rotateOrigin center
34034 <cell alignment="center" valignment="top" usebox="none">
34037 \begin_layout Plain Layout
34040 Edit\SpecialChar \menuseparator
34041 Math\SpecialChar \menuseparator
34043 \begin_inset space ~
34046 Definition\SpecialChar \menuseparator
34048 \begin_inset Newline newline
34055 \begin_layout Plain Layout
34064 Edit\SpecialChar \menuseparator
34065 Math\SpecialChar \menuseparator
34067 \begin_inset space ~
34070 Definition\SpecialChar \menuseparator
34075 \begin_layout Plain Layout
34082 Eating From The Right
34088 <row interlinespace="2.5mm">
34089 <cell alignment="center" valignment="top" usebox="none">
34092 \begin_layout Plain Layout
34093 \begin_inset Graphics
34094 filename ../images/math-macro-add-greedy-optional-param.png
34095 BoundingBox 0bp 5bp 20bp 25bp
34096 rotateOrigin center
34105 <cell alignment="center" valignment="top" usebox="none">
34108 \begin_layout Plain Layout
34111 Edit\SpecialChar \menuseparator
34112 Math\SpecialChar \menuseparator
34114 \begin_inset space ~
34117 Definition\SpecialChar \menuseparator
34118 Append Optional Argument
34119 \begin_inset Newline newline
34126 \begin_layout Plain Layout
34135 Edit\SpecialChar \menuseparator
34136 Math\SpecialChar \menuseparator
34138 \begin_inset space ~
34141 Definition\SpecialChar \menuseparator
34146 \begin_layout Plain Layout
34153 Eating From The Right
34166 \begin_layout Standard
34167 \begin_inset Newpage newpage
34173 \begin_layout Section
34178 \begin_layout Plain Layout
34187 \begin_layout Subsection
34192 \begin_layout Plain Layout
34201 \begin_layout Standard
34202 Negative numbers often look ugly in formulas because the minus sign before
34203 the number is set with the same length as the minus operator sign.
34204 When writing the negative number in normal text, the minus sign appears
34208 \begin_layout Standard
34209 Thus, the problem disappears when converting the minus sign to mathematical
34213 \begin_layout Standard
34214 An example to visualize the problem:
34217 \begin_layout Standard
34219 \begin_inset Tabular
34220 <lyxtabular version="3" rows="3" columns="2">
34222 <column alignment="right" valignment="top" width="0">
34223 <column alignment="left" valignment="top" width="0">
34225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34228 \begin_layout Plain Layout
34234 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34237 \begin_layout Plain Layout
34245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34248 \begin_layout Plain Layout
34254 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34257 \begin_layout Plain Layout
34258 \begin_inset Formula $x=-2$
34268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34271 \begin_layout Plain Layout
34277 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34280 \begin_layout Plain Layout
34281 \begin_inset Formula $x=\textrm{-}2$
34297 \begin_layout Subsection
34298 Comma as decimal Separator
34302 \begin_layout Plain Layout
34311 \begin_layout Standard
34312 In LaTeX a comma inside a formula is used, according to the English convention,
34313 as number group separator.
34314 So there will be space added behind all commas in formulas.
34317 \begin_layout Standard
34318 To avoid this, the comma is highlighted and changed to mathematical text
34328 \begin_layout Standard
34329 To use all formula commas in the document as decimal separator, the file
34338 \begin_layout Plain Layout
34343 is part of the LaTeX-package
34351 \begin_layout Plain Layout
34356 \begin_layout Plain Layout
34379 \begin_layout Plain Layout
34385 is loaded with the LaTeX-preamble line
34388 \begin_layout Standard
34396 \begin_layout Subsection
34398 \begin_inset CommandInset label
34400 name "sub:Physical-Vectors"
34408 \begin_layout Plain Layout
34417 \begin_layout Standard
34418 Predefined vectors are offered by the LaTeX-package
34426 \begin_layout Plain Layout
34432 that is loaded with the LaTeX-preamble line
34435 \begin_layout Standard
34443 \begin_layout Standard
34447 \begin_layout Plain Layout
34457 \begin_inset Note Note
34460 \begin_layout Plain Layout
34461 The following table will only be displayed when the LaTeX-package
34473 \begin_layout Standard
34474 The following commands are defined:
34477 \begin_layout Standard
34479 \begin_inset Tabular
34480 <lyxtabular version="3" rows="4" columns="2">
34482 <column alignment="center" valignment="top" width="0">
34483 <column alignment="center" valignment="top" width="0">
34485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34488 \begin_layout Plain Layout
34494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34497 \begin_layout Plain Layout
34505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34508 \begin_layout Plain Layout
34518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34521 \begin_layout Plain Layout
34522 \begin_inset Formula $\Bra{\psi}$
34532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34535 \begin_layout Plain Layout
34545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34548 \begin_layout Plain Layout
34549 \begin_inset Formula $\Ket{\psi}$
34559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34562 \begin_layout Plain Layout
34574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34577 \begin_layout Plain Layout
34578 \begin_inset Formula $\Braket{\psi|\phi}$
34594 \begin_layout Standard
34601 assures that all vertical bars are set in the size of the surrounding brackets:
34602 \begin_inset Formula \[
34603 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34611 \begin_layout Plain Layout
34621 \begin_inset Note Note
34624 \begin_layout Plain Layout
34625 The following will be displayed when the LaTeX-package
34637 \begin_layout Standard
34638 You need to install the LaTeX-package
34642 to see the rest of this subsection in the output.
34645 \begin_layout Standard
34649 \begin_layout Plain Layout
34661 \begin_layout Standard
34668 can also be achieved using the command
34674 , that is described in
34675 \begin_inset CommandInset ref
34677 reference "sub:Automatic-Bracket-Size"
34684 \begin_layout Subsection
34685 Self-defined Fractions
34686 \begin_inset CommandInset label
34688 name "sub:Self-defined-Fractions"
34696 \begin_layout Plain Layout
34697 Fractions ! self-defined
34705 \begin_layout Standard
34706 To define custom commands for fractions, the command
34716 \begin_layout Plain Layout
34724 is used in the following scheme:
34727 \begin_layout Standard
34740 bracket}{fraction bar thickness}{style}
34741 \begin_inset Newline newline
34748 \begin_layout Plain Layout
34763 \begin_layout Plain Layout
34770 {numerator}{denominator}
34773 \begin_layout Standard
34774 The style is a number in the range of 0
34775 \begin_inset space \thinspace{}
34779 \begin_inset space \thinspace{}
34785 \begin_layout Standard
34787 \begin_inset Tabular
34788 <lyxtabular version="3" rows="5" columns="2">
34790 <column alignment="center" valignment="top" width="0">
34791 <column alignment="center" valignment="top" width="0">
34793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34796 \begin_layout Plain Layout
34802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34805 \begin_layout Plain Layout
34813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34816 \begin_layout Plain Layout
34822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34825 \begin_layout Plain Layout
34826 display style formula
34833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34836 \begin_layout Plain Layout
34842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34845 \begin_layout Plain Layout
34853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34856 \begin_layout Plain Layout
34862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34865 \begin_layout Plain Layout
34873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34876 \begin_layout Plain Layout
34882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34885 \begin_layout Plain Layout
34899 \begin_layout Standard
34900 When no style is given, the size is adjusted to the surrounding environment
34901 like for the command
34910 \begin_layout Standard
34911 When no fraction bar thickness is given, the predefined value of 0.4
34912 \begin_inset space \thinspace{}
34918 \begin_layout Standard
34919 \begin_inset VSpace medskip
34922 For example, the commands
34935 \begin_inset CommandInset ref
34937 reference "sub:Fractions"
34941 are defined with the commands
34944 \begin_layout Standard
34953 genfrac{}{}{}{0}{#1}{#2}}
34956 \begin_layout Standard
34960 \begin_layout Standard
34969 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34972 \begin_layout Standard
34973 \begin_inset VSpace medskip
34976 To define a fraction where the fraction bar thickness can be given as optional
34977 argument, the following line is inserted to the LaTeX-preamble:
34980 \begin_layout Standard
34989 genfrac{}{}{#1}{}{#2}{#3}}
34992 \begin_layout Standard
34994 \begin_inset Formula \begin{align*}
34995 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34996 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
35000 As one can see, the distance of the numerator and the denominator to the
35001 fraction bar is round about three times the bar thickness.
35004 \begin_layout Subsection
35009 \begin_layout Plain Layout
35018 \begin_layout Standard
35019 To cancel formulas or formula parts, the LaTeX-package
35027 \begin_layout Plain Layout
35033 has to be loaded with the LaTeX-preamble line
35036 \begin_layout Standard
35041 usepackage[samesize]{cancel}
35044 \begin_layout Standard
35048 \begin_layout Plain Layout
35058 \begin_inset Note Note
35061 \begin_layout Plain Layout
35062 The following table will only be displayed when the LaTeX-package
35074 \begin_layout Standard
35075 There are four ways to cancel formulas:
35078 \begin_layout Standard
35080 \begin_inset Tabular
35081 <lyxtabular version="3" rows="5" columns="2">
35083 <column alignment="center" valignment="top" width="0">
35084 <column alignment="center" valignment="top" width="0">
35086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35089 \begin_layout Plain Layout
35095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35098 \begin_layout Plain Layout
35100 \begin_inset Note Note
35103 \begin_layout Plain Layout
35110 are used here as spacer.
35122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35125 \begin_layout Plain Layout
35134 \begin_layout Plain Layout
35148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35151 \begin_layout Plain Layout
35152 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35165 \begin_layout Plain Layout
35174 \begin_layout Plain Layout
35188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35191 \begin_layout Plain Layout
35192 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35205 \begin_layout Plain Layout
35214 \begin_layout Plain Layout
35228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35231 \begin_layout Plain Layout
35232 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35245 \begin_layout Plain Layout
35249 \begin_inset Formula $\to$
35260 \begin_layout Plain Layout
35274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35277 \begin_layout Plain Layout
35278 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35294 \begin_layout Standard
35301 is especially suitable to visualize the reduction of fractions within formulas:
35302 \begin_inset Formula \[
35303 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35310 \begin_layout Standard
35314 \begin_layout Plain Layout
35324 \begin_inset Note Note
35327 \begin_layout Plain Layout
35328 The following will be displayed when the LaTeX-package
35340 \begin_layout Standard
35341 You need to install the LaTeX-package
35345 to see the rest of this subsection in the output.
35348 \begin_layout Standard
35352 \begin_layout Plain Layout
35364 \begin_layout Subsection
35365 Formulas in Section Headings
35366 \begin_inset CommandInset label
35368 name "sub:Formulas-in-Section"
35376 \begin_layout Plain Layout
35377 Formula ! in section headings
35385 \begin_layout Standard
35386 When formulas are used in section headings, the following has to be taken
35390 \begin_layout Standard
35391 \begin_inset Note Greyedout
35394 \begin_layout Plain Layout
35403 \begin_layout Plain Layout
35404 Packages ! hyperref
35409 support is enabled in the document settings dialog under
35412 \begin_inset space ~
35417 , PDF-bookmarks are created for every section heading in the table of contents.
35418 If a section heading contains formulas, they are incorrectly displayed
35419 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35428 \begin_layout Standard
35429 Both problems can be solved by inserting at the end of the section heading
35430 a short title with the menu
35432 Insert\SpecialChar \menuseparator
35434 \begin_inset space ~
35440 Short titles are used as alternative for multiline section headings to
35441 keep the table of contents clearly arranged.
35442 Only the short title appears in the table of contents and therefore also
35443 in the PDF-bookmark.
35446 \begin_layout Standard
35447 When formulas should be used in the table of contents but
35451 is used, one can use the following command in TeX-mode:
35454 \begin_layout Standard
35459 texorpdfstring{part}{alternative}
35463 \begin_layout Plain Layout
35474 \begin_layout Standard
35475 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35476 This can be characters, formulas, footnotes, but also cross-references.
35477 The alternative is used instead of the part for the bookmark.
35480 \begin_layout Standard
35481 Here are two example headings:
35482 \begin_inset VSpace -3mm
35489 \begin_layout Plain Layout
35501 \begin_layout Subsubsection
35502 Heading without formula in table of contents
35503 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35507 \begin_inset OptArg
35510 \begin_layout Plain Layout
35511 Heading without formula in table of contents
35519 \begin_layout Subsubsection
35520 Heading with formula in table of contents
35524 \begin_layout Plain Layout
35534 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35541 \begin_layout Plain Layout
35551 \begin_layout Standard
35555 \begin_layout Plain Layout
35564 In the first heading a short title was used, in the second one
35573 \begin_layout Standard
35574 To get the same formatting as for the other headings, the complete heading
35583 \begin_layout Plain Layout
35585 \begin_inset CommandInset ref
35587 reference "sub:Bold-Formulas"
35599 \begin_layout Subsection
35600 Formulas in multi-column Text
35604 \begin_layout Plain Layout
35605 Formula ! in multi-column text
35613 \begin_layout Standard
35614 Formulas in multi-column text are often too wide to fit into a column and
35615 thus need to be set over the whole page width.
35616 This is done by using the LaTeX-package
35624 \begin_layout Plain Layout
35629 is part of every LaTeX standard installation.
35638 \begin_layout Plain Layout
35639 Packages ! multicol
35644 , that is loaded with the LaTeX-preamble line
35647 \begin_layout Standard
35652 usepackage{multicol}
35655 \begin_layout Standard
35656 \begin_inset Note Greyedout
35659 \begin_layout Plain Layout
35660 Note herby that the setting
35663 \begin_inset space ~
35670 Document\SpecialChar \menuseparator
35676 \begin_inset space ~
35696 \begin_layout Standard
35697 Before the multi-column text the command
35700 \begin_layout Standard
35705 begin{multicols}{column number}
35708 \begin_layout Standard
35709 is written in TeX-mode.
35710 The column number is a number in the range of 2
35711 \begin_inset space \thinspace{}
35715 \begin_inset space \thinspace{}
35719 Before the formula the multi-column text is ended by inserting the command
35722 \begin_layout Standard
35730 \begin_layout Standard
35734 \begin_layout Standard
35735 Due to the command some space is automatically added before the formula.
35737 \begin_inset space \thinspace{}
35740 mm vertical space is inserted before the formula.
35741 When the formula style
35747 \begin_layout Plain Layout
35749 \begin_inset CommandInset ref
35751 reference "sec:Formula-Styles"
35763 \begin_inset space \thinspace{}
35766 mm space is inserted instead.
35769 \begin_layout Standard
35770 As example a multi-column text with a displayed formula:
35773 \begin_layout Standard
35779 \begin_layout Plain Layout
35783 begin{multicols}{2}
35788 Das Spektrum wird fouriertransformiert.
35789 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35790 , Lösungsmittel) zu trennen.
35791 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35792 nun das Aussehen des Ausgangssignals.
35793 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35794 über alle Phasen integrieren muss.
35796 \begin_inset Formula $S$
35799 unser normiertes Ausgangssignal und
35800 \begin_inset Formula $P$
35803 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35807 \begin_layout Plain Layout
35817 \begin_inset VSpace -6mm
35821 \begin_inset Formula \begin{equation}
35822 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35830 \begin_layout Plain Layout
35834 begin{multicols}{2}
35840 \begin_inset Formula $S_{0}$
35843 das Signal ohne Gradient ist und die Normierungsbedingung
35844 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35848 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35850 \begin_inset Formula $\nicefrac{\pi}{2}$
35854 \begin_inset space \thinspace{}
35857 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35858 das Signal zusätzlich abschwächt.
35859 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35861 \begin_inset Formula $T_{2}$
35867 \begin_layout Standard
35873 \begin_layout Plain Layout
35885 \begin_layout Subsection
35886 Formulas with Description of Variables
35890 \begin_layout Plain Layout
35891 Formula ! with description of variables
35899 \begin_layout Standard
35900 To describe variables within a formula, like in formula
35901 \begin_inset CommandInset ref
35903 reference "eq:within"
35912 \begin_inset Formula $n$
35916 \begin_inset space ~
35919 matrix is used with left aligned columns for the
35920 \begin_inset Formula $n$
35927 \begin_layout Plain Layout
35929 \begin_inset CommandInset ref
35931 reference "sec:Matrices"
35940 To set the description in a smaller size, before the matrix e.
35941 \begin_inset space \thinspace{}
35945 \begin_inset space \space{}
35958 \begin_layout Plain Layout
35960 \begin_inset CommandInset ref
35962 reference "sub:Font-Sizes"
35974 \begin_layout Standard
35975 When the formula style
35981 \begin_layout Plain Layout
35983 \begin_inset CommandInset ref
35985 reference "sec:Formula-Styles"
36006 \begin_layout Plain Layout
36013 only works in formulas with the style
36018 \begin_inset CommandInset ref
36020 reference "sub:Variable-Space"
36029 is inserted before and after the matrix to have the same separation of
36030 the matrix from the equation and the side margin.
36033 \begin_layout Standard
36034 When the formula style
36038 is used, the method described in
36039 \begin_inset CommandInset ref
36041 reference "sub:Flalign-Environment"
36045 is used to indent formulas.
36047 \begin_inset CommandInset ref
36049 reference "eq:within"
36053 consists of five columns whereas in the first two columns contain the equation,
36054 the third the matrix and the last one an empty TeX-brace.
36055 \begin_inset Formula \begin{flalign}
36056 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36057 \rho & \textrm{density}\\
36058 V & \textrm{volume}\\
36059 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
36066 \begin_layout Subsection
36067 Upright small Greek Letters
36068 \begin_inset CommandInset label
36070 name "sub:Upright-small-Greek"
36078 \begin_layout Plain Layout
36079 Greek letters ! upright
36087 \begin_layout Standard
36088 Most of the math fonts only provide italic small Greek letters.
36089 But for symbols of elementary particles like pions and neutrinos, upright
36090 Greek letters are needed.
36099 \begin_layout Plain Layout
36104 is part of the LaTeX-package
36112 \begin_layout Plain Layout
36117 \begin_layout Plain Layout
36140 \begin_layout Plain Layout
36146 that is loaded with the LaTeX-preamble line
36149 \begin_layout Standard
36154 usepackage{upgreek}
36157 \begin_layout Standard
36163 \begin_layout Plain Layout
36173 \begin_inset Note Note
36176 \begin_layout Plain Layout
36177 The following table will only be displayed when the LaTeX-package
36186 They are created when the command for a small Greek letters is started
36192 For example the command
36199 \begin_inset Formula $\uptau$
36205 \begin_layout Standard
36206 With these commands reactions of elementary particles can be typeset:
36207 \begin_inset Formula \[
36208 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36215 \begin_layout Standard
36216 The upright letters are more bold and wider than the italic ones.
36217 They should therefore not be used for units like
36218 \begin_inset Quotes eld
36222 \begin_inset Quotes erd
36228 \begin_layout Standard
36232 \begin_layout Plain Layout
36242 \begin_inset Note Note
36245 \begin_layout Plain Layout
36246 The following will be displayed when the LaTeX-package
36258 \begin_layout Standard
36259 You need to install the LaTeX-package
36263 to see the rest of this subsection in the output.
36266 \begin_layout Standard
36270 \begin_layout Plain Layout
36282 \begin_layout Subsection
36283 Text Characters in Formulas
36284 \begin_inset CommandInset label
36286 name "sub:Text-Characters-in"
36294 \begin_layout Plain Layout
36303 \begin_layout Standard
36304 In some cases you might want to insert text characters directly into formulas.
36305 When for example the centered dot · is often used in formulas like
36306 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36309 , one would have to insert the command
36319 \begin_layout Plain Layout
36321 \begin_inset CommandInset ref
36323 reference "sub:Binary-Operators"
36332 all the time, because this character is defined in all encodings as text
36334 But the encoding can be changed by this LaTeX-preamble line:
36337 \begin_layout Standard
36342 Declare Inputtext{183}{
36352 f\SpecialChar \textcompwordmark{}
36356 \begin_layout Standard
36357 The character encoding (menu
36359 Document\SpecialChar \menuseparator
36360 Settings\SpecialChar \menuseparator
36363 ) specifies what character appears when a keyboard key is pressed.
36364 When the key for the character '·' is pressed, internally the command
36371 But this command is not available in a formula so that you would get LaTeX-erro
36373 With the changed encoding the right command is chosen automatically, depending
36374 on if the character was inserted into a formula or not.
36377 \begin_layout Standard
36378 The encoding of several characters is saved in definition files.
36379 Fore example the encoding
36383 is defined in the file
36387 that is in the installation folder of LaTeX.
36388 Encodings should only be changed via the LaTeX-preamble and not in the
36390 Otherwise own documents could not be edited by other LyX users working
36391 on other computers.
36394 \begin_layout Standard
36395 \begin_inset VSpace medskip
36398 Besides the centered dot, in this document the degree sign ° is defined
36399 with the following LaTeX-preamble line so that it can directly be inserted
36403 \begin_layout Standard
36408 DeclareInputtext{176}{
36418 f\SpecialChar \textcompwordmark{}
36422 \begin_layout Standard
36423 \begin_inset Newpage newpage
36429 \begin_layout Section
36435 \begin_layout Plain Layout
36444 \begin_layout Standard
36445 This section is a summary of the most important typographic rules, listed
36450 \begin_layout Plain Layout
36451 This collection was partly taken from the German semi-official dictionary
36453 \begin_inset Quotes eld
36457 \begin_inset Quotes erd
36461 \begin_inset CommandInset citation
36467 that lists some of the ISO rules.
36468 More rules are listed in
36469 \begin_inset CommandInset citation
36483 \begin_layout Itemize
36492 \begin_layout Plain Layout
36493 done with font styles, see
36494 \begin_inset CommandInset ref
36496 reference "sub:Font-Styles"
36505 , no matter if they appear in italic text: 30
36506 \begin_inset space \thinspace{}
36510 \begin_inset Newline newline
36513 Between the value and the unit is the smallest space, see
36514 \begin_inset CommandInset ref
36516 reference "sub:Predefined-Space"
36521 \begin_inset Newline newline
36524 This convention is automatically fulfilled when the command
36531 When it is entered to a formula, two boxes appear.
36532 In the first one the value is inserted, in the second one the unit, and
36534 \begin_inset Formula $\unit[30]{km/h}$
36538 \begin_inset space \thinspace{}
36548 is not a real LaTeX command but the command
36554 , therefore you cannot use it in TeX code.
36557 \begin_layout Itemize
36558 Percent and perthousand signs are set like physical units:
36559 \begin_inset Newline newline
36563 \begin_inset space \thinspace{}
36569 \begin_layout Itemize
36570 The degree sign follows directly on the value: 15°, but not when it is used
36572 \begin_inset space \thinspace{}
36578 \begin_layout Itemize
36579 In numbers with more than four digits the smallest space is inserted before
36580 every third digit to group them:
36590 \begin_inset space \thinspace{}
36594 \begin_inset space \thinspace{}
36600 \begin_layout Itemize
36601 For dimensions like 120×90×40
36602 \begin_inset space \thinspace{}
36605 cm the multiplication sign
36606 \begin_inset Quotes eld
36610 \begin_inset Quotes erd
36614 It is available either via the command
36622 Insert\SpecialChar \menuseparator
36623 Special Character\SpecialChar \menuseparator
36629 \begin_layout Itemize
36630 Functions with names consisting of several letters are set upright to avoid
36632 \begin_inset CommandInset ref
36634 reference "sub:Predefined-Functions"
36641 \begin_layout Itemize
36642 Indices consisting of several letters, are set upright:
36643 \begin_inset Formula $E_{\mathrm{kin}}$
36647 \begin_inset Newline newline
36650 Components of matrices are set italic:
36651 \begin_inset Formula $\hat{H}_{kl}$
36657 \begin_layout Itemize
36658 The differentiation/integration operator 'd', the Euler's number 'e' and
36659 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36663 \begin_layout Itemize
36664 The character that denotes a
36668 transformation is inserted either by the command
36676 \begin_layout Plain Layout
36693 \begin_layout Plain Layout
36703 Insert\SpecialChar \menuseparator
36704 Special Character\SpecialChar \menuseparator
36705 Symbols\SpecialChar \menuseparator
36707 \begin_inset space ~
36713 \begin_inset Formula $\mathscr{F}$
36717 \begin_inset Newline newline
36720 To be able to use the command
36726 , the LaTeX package
36734 \begin_layout Plain Layout
36735 Packages ! mathrsfs
36740 needs to be loaded with the LaTeX-preamble line
36744 usepackage{mathrsfs}
36749 \begin_layout Standard
36750 \begin_inset Newpage newpage
36756 \begin_layout Section
36761 \begin_layout Plain Layout
36770 \begin_layout Standard
36771 Some characters and symbols can be created with several commands.
36772 Here is a list of the synonym commands:
36775 \begin_layout Standard
36776 \begin_inset VSpace bigskip
36780 \begin_inset space \hfill{}
36784 \begin_inset Tabular
36785 <lyxtabular version="3" rows="12" columns="2">
36787 <column alignment="center" valignment="top" width="0pt">
36788 <column alignment="center" valignment="top" width="0pt">
36790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36793 \begin_layout Plain Layout
36799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36802 \begin_layout Plain Layout
36804 \begin_inset Note Note
36807 \begin_layout Plain Layout
36814 is only used as spacer.
36826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36829 \begin_layout Plain Layout
36837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36840 \begin_layout Plain Layout
36844 \begin_layout Plain Layout
36857 \begin_layout Plain Layout
36871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36874 \begin_layout Plain Layout
36882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36885 \begin_layout Plain Layout
36895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36898 \begin_layout Plain Layout
36906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36909 \begin_layout Plain Layout
36919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36922 \begin_layout Plain Layout
36930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36933 \begin_layout Plain Layout
36941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36944 \begin_layout Plain Layout
36952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36955 \begin_layout Plain Layout
36963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36966 \begin_layout Plain Layout
36974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36977 \begin_layout Plain Layout
36987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36990 \begin_layout Plain Layout
36998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37001 \begin_layout Plain Layout
37011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37014 \begin_layout Plain Layout
37022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37025 \begin_layout Plain Layout
37035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37038 \begin_layout Plain Layout
37046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37049 \begin_layout Plain Layout
37059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37062 \begin_layout Plain Layout
37070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37073 \begin_layout Plain Layout
37081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37084 \begin_layout Plain Layout
37092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37095 \begin_layout Plain Layout
37107 \begin_inset space \hfill{}
37111 \begin_inset Tabular
37112 <lyxtabular version="3" rows="12" columns="2">
37114 <column alignment="center" valignment="top" width="0pt">
37115 <column alignment="center" valignment="top" width="0pt">
37117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37120 \begin_layout Plain Layout
37126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37129 \begin_layout Plain Layout
37137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37140 \begin_layout Plain Layout
37148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37151 \begin_layout Plain Layout
37163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37166 \begin_layout Plain Layout
37174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37177 \begin_layout Plain Layout
37187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37190 \begin_layout Plain Layout
37198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37201 \begin_layout Plain Layout
37211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37214 \begin_layout Plain Layout
37222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37225 \begin_layout Plain Layout
37233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37236 \begin_layout Plain Layout
37244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37247 \begin_layout Plain Layout
37255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37258 \begin_layout Plain Layout
37266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37269 \begin_layout Plain Layout
37279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37282 \begin_layout Plain Layout
37290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37293 \begin_layout Plain Layout
37303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37306 \begin_layout Plain Layout
37314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37317 \begin_layout Plain Layout
37327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37330 \begin_layout Plain Layout
37338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37341 \begin_layout Plain Layout
37351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37354 \begin_layout Plain Layout
37362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37365 \begin_layout Plain Layout
37375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37378 \begin_layout Plain Layout
37386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37389 \begin_layout Plain Layout
37403 \begin_inset space \hfill{}
37409 \begin_layout Standard
37410 \begin_inset Newpage newpage
37416 \begin_layout Bibliography
37417 \begin_inset CommandInset bibitem
37418 LatexCommand bibitem
37430 The LaTeX Companion
37433 Addison Wesley, 2004
37436 \begin_layout Bibliography
37437 \begin_inset CommandInset bibitem
37438 LatexCommand bibitem
37444 \begin_inset CommandInset href
37447 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37451 of LaTeX's math abilities
37454 \begin_layout Bibliography
37455 \begin_inset CommandInset bibitem
37456 LatexCommand bibitem
37462 \begin_inset CommandInset href
37465 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37473 \begin_layout Plain Layout
37485 \begin_layout Bibliography
37486 \begin_inset CommandInset bibitem
37487 LatexCommand bibitem
37493 \begin_inset CommandInset href
37496 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37500 of all symbols available with LaTeX-packages
37503 \begin_layout Bibliography
37504 \begin_inset CommandInset bibitem
37505 LatexCommand bibitem
37511 \begin_inset CommandInset href
37513 name "Documentation"
37514 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37518 of the LaTeX-package
37526 \begin_layout Plain Layout
37527 Packages ! hyperref
37535 \begin_layout Bibliography
37536 \begin_inset CommandInset bibitem
37537 LatexCommand bibitem
37543 \begin_inset CommandInset href
37545 name "Documentation"
37546 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37550 of the LaTeX-package
37558 \begin_layout Plain Layout
37567 \begin_layout Bibliography
37568 \begin_inset CommandInset bibitem
37569 LatexCommand bibitem
37575 \begin_inset CommandInset href
37578 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37589 \begin_inset CommandInset ref
37591 reference "sub:Operator-Limits"
37599 \begin_layout Plain Layout
37610 \begin_layout Bibliography
37611 \begin_inset CommandInset bibitem
37612 LatexCommand bibitem
37623 Auflage, Duden 2001
37626 \begin_layout Bibliography
37627 \begin_inset CommandInset bibitem
37628 LatexCommand bibitem
37634 \begin_inset CommandInset href
37637 target "http://physics.nist.gov/Document/checklist.pdf"
37641 for reviewing manuscripts
37644 \begin_layout Standard
37645 \begin_inset CommandInset index_print
37646 LatexCommand printindex