1 #LyX 1.5.5svn 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
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 % link all cross references and URLs
27 \usepackage[colorlinks=true, bookmarks, bookmarksnumbered,
28 bookmarksopen, bookmarksopenlevel=1,
29 linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue,
30 pdfpagelayout=OneColumn, pdfnewwindow=true,
31 pdfstartview=XYZ, plainpages=false, pdfpagelabels,
32 pdfauthor={LyX Team}, pdftex,
33 pdftitle={LyX's Math Manual},
34 pdfsubject={LyX-documentation about math},
35 pdfkeywords={LyX, Mathed}]{hyperref}
37 \else % if dvi or ps is produced
39 % link all cross references and URLs in DVI output
40 \usepackage[ps2pdf, colorlinks=true,
41 linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue]{hyperref}
43 \fi % end if pdflatex is used
45 % Folgendes Problem lösen:
46 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
47 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
48 % die Kapitelnummer geschrieben.
49 % Als Lösung wird mehr Platz zwischen Nummer und
50 % Überschrift eingefügt.
51 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
52 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
54 % To be able to enter the character ° and · directly in LyX,
56 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
57 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
59 % increase link area for cross-references and autoname them,
61 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
62 %\renewcommand{\sectionautorefname}{sec.\negthinspace}
63 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
64 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
66 \settowidth{\abc}{\space}
67 \renewcommand{\equationautorefname}{\hspace{-\abc}}
69 % don't load packages twice
70 % see first footnote in sec. 9.3
71 \@ifundefined{textcolor}{\usepackage{color}}{}
73 % the pages of the TOC are numbered roman
74 % and a PDF-bookmark for the TOC is added
76 \let\myTOC\tableofcontents
77 \renewcommand{\tableofcontents}{%
79 \pdfbookmark[1]{Contents}{}
82 \pagenumbering{arabic}}
84 % insert additional vertical space of 1.5 mm between footnotes,
87 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
89 % provides caption formatting
90 \setkomafont{captionlabel}{\bfseries}
96 \usepackage[samesize]{cancel}
98 % enables calculation of values,
101 % for multiple table row and column cells
102 \usepackage{multirow}
103 \usepackage{multicol}
105 % needed for diagrams
108 % needed in sec. 19.4
109 \usepackage{remreset}
111 % center multirows (e.g. in sec. 13.3)
112 \renewcommand{\multirowsetup}{\centering}
114 % define a color, used in sec.9.3
115 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
117 % declare operators (see sec. 10.4 and sec. 15.2)
118 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
119 \DeclareMathOperator{\sgn}{sgn}
121 \newcommand{\spce}{\textvisiblespace}
123 % example definitions for sec. 20.1
124 \newcommand{\gr}{\Longrightarrow}
125 \newcommand{\us}[1]{\underline{#1}}
126 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
127 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
128 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
130 % example macro from sec. 19.4
131 %\def\tagform@#1{\maketag@@@{|#1|}}
133 % macro from sec. 10.2
134 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
135 \def\mathclap {\mathpalette \mathclapinternal}
136 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
138 % redefine the greyed out note
139 \renewenvironment{lyxgreyedout}
140 {\textcolor{blue}\bgroup}{\egroup}
142 % check for package eurosym
143 % used for the Euro symbol
145 \IfFileExists{eurosym.sty}
146 {\usepackage[gennarrow]{eurosym}
147 \setboolean{eurosym}{true}}
148 {\setboolean{eurosym}{false}}
150 % needed in sec. 22.4
151 % check for package braket
153 \IfFileExists{braket.sty}
155 \setboolean{braket}{true}}
156 {\setboolean{braket}{false}}
158 % needed in sec. 22.10
159 % check for package upgreek
161 \IfFileExists{upgreek.sty}
162 {\usepackage{upgreek}
163 \setboolean{upgreek}{true}}
164 {\setboolean{upgreek}{false}}
166 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
171 \font_typewriter default
172 \font_default_family default
186 \paperorientation portrait
189 \paragraph_separation skip
191 \quotes_language english
194 \paperpagestyle plain
198 \tracking_changes false
199 \output_changes false
207 LyX's detailed Math manual
215 \begin_layout Standard
217 If you have comments or error corrections, please send them to the LyX Documenta
224 \begin_layout Standard
228 href{mailto:lyx-docs@lists.lyx.org?subject=LyX's Math manual}{
233 lyx-docs@lists.lyx.org
237 \begin_layout Standard
250 \begin_inset Note Note
253 \begin_layout Standard
268 \begin_layout Standard
269 \begin_inset LatexCommand tableofcontents
276 \begin_layout Standard
277 \begin_inset Note Note
280 \begin_layout Standard
281 To export this document to PDF, PS, or DVI the LaTeX-packages
294 If they are not installed you can export the document anyway but the sections
295 where the packages are required won't appear in the output.
298 \begin_layout Standard
299 The latest PDF-version of this document can be found here:
303 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
311 \begin_layout Standard
317 \begin_layout Section
319 \begin_inset LatexCommand label
320 name "sec:Introduction"
327 \begin_layout Standard
328 This document explains LyX's math features and is furthermore a collection
329 of LaTeX-commands used for mathematical characters and constructs.
330 The explanations are designed for the usage of commands.
331 It is therefore required that you have read the section
333 Mathematical\InsetSpace ~
339 \begin_layout Standard
340 Most of the characters and many constructs explained in this manual are
341 also accessible via the menu
345 \SpecialChar \menuseparator
361 But everybody who has to write lots of formulas will notice that it is
362 much faster to use commands instead of the math toolbar.
363 Therefore this manual is focused on commands but also mentions the correspondin
364 g toolbar buttons when available.
367 \begin_layout Standard
368 If not specially mentioned the commands are only available within formulas.
369 To be able to use all commands explained in this document, the option
373 must be used in the document settings (menu
375 Document\SpecialChar \menuseparator
376 Settings\SpecialChar \menuseparator
384 \begin_layout Standard
387 Use AMS math package automatically
393 \begin_layout Standard
402 -math when math constructs are found that are supported by LyX.
410 \begin_layout Standard
411 This document doesn't list all
415 \begin_layout Standard
428 \begin_layout Standard
433 \begin_layout Standard
442 -math commands is in the file
446 \begin_layout Standard
450 href{ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps}{
463 \begin_layout Standard
470 , which is part of every LaTeX standard installation.
475 for lucidity reasons.
478 \begin_layout Section
480 \begin_inset LatexCommand label
481 name "sec:General-Instructions"
488 \begin_layout Standard
489 To create an inline formula
490 \begin_inset LatexCommand index
491 name "Formula ! inline"
495 that is embedded into a text line, press
499 or the toolbar button
500 \begin_inset Graphics
501 filename ../images/math-mode.png
508 To create a display style formula
509 \begin_inset LatexCommand index
510 name "Formula ! display style"
514 that will appear bigger and in an own paragraph, press
521 \begin_layout Standard
522 To change a display style formula to an inline formula, set the cursor into
523 the formula and press
529 Edit\SpecialChar \menuseparator
530 Math\SpecialChar \menuseparator
534 The same way is used to change an inline formula to a display style formula.
537 \begin_layout Standard
538 To display parts of an inline formula in the size of a display style formula,
544 \begin_inset LatexCommand index
545 name "Commands ! D ! \\textbackslash displaystyle"
552 Then a new blue box appears in which the desired formula part is inserted.
555 \begin_layout Standard
556 Only inline formulas are allowed inside tables.
559 \begin_layout Standard
564 can be turned on in the menu
566 View\SpecialChar \menuseparator
570 When you click there on
571 \begin_inset Quotes eld
575 \begin_inset Quotes erd
578 the toolbar will be shown permanently at the bottom; this state is visualized
583 menu with a checkmark.
584 When you click in this state again on
585 \begin_inset Quotes eld
589 \begin_inset Quotes erd
600 is only shown when the cursor is within a formula; this state is visualized
601 by the renaming of the menu entry from
602 \begin_inset Quotes eld
606 \begin_inset Quotes erd
610 \begin_inset Quotes eld
615 \begin_inset Quotes erd
621 \begin_layout Standard
623 \begin_inset LatexCommand index
628 is invoked by pressing the toolbar button
629 \begin_inset Graphics
630 filename ../images/ert-insert.png
637 Insert\SpecialChar \menuseparator
642 \begin_layout Standard
653 \begin_layout Standard
667 \begin_inset Note Note
670 \begin_layout Standard
671 In LyX there are three
672 \begin_inset Quotes eld
676 \begin_inset Quotes erd
679 that appear in the output with sub- and superscript letters: TeX, LaTeX,
683 \begin_layout Standard
684 To avoid that these names are recognized as proper names, TeX-braces are
685 set around one of the letters of the name.
693 \begin_layout Standard
694 To change the LaTeX-preamble
695 \begin_inset LatexCommand index
696 name "L@\\LaTeX-preamble"
702 Document\SpecialChar \menuseparator
703 Settings\SpecialChar \menuseparator
708 \begin_layout Standard
719 \begin_layout Standard
735 \begin_layout Standard
736 To edit matrices, case differentiations, and multiline formulas subsequently,
739 Edit\SpecialChar \menuseparator
744 Edit\SpecialChar \menuseparator
745 Rows\InsetSpace \thinspace{}
746 &\InsetSpace \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 Standard
767 For multiline formulas the command
774 \begin_inset LatexCommand ref
775 reference "sub:Text-in-multiline"
789 \begin_inset LatexCommand index
790 name "Text ! in formulas"
795 \begin_inset LatexCommand index
796 name "Mathematical text"
801 This mode is invoked with the the shortcut
806 or by the insertion of the command
811 \begin_inset LatexCommand index
812 name "Commands ! T ! \\textbackslash text"
819 The text appears black in LyX and can therefore be distinguished from the
820 other formula parts that appear blue.
821 In the output mathematical text is set upright, in contrary to other formula
825 \begin_layout Subsection*
829 \begin_layout Standard
830 Most of the LaTeX-commands for math constructs have the following scheme:
833 \begin_layout Standard
849 \begin_layout Standard
850 A command starts always with a backslash
851 \begin_inset Quotes gld
861 \begin_inset Quotes grd
865 To omit optional arguments, also omit the associated brackets.
866 The braces around the required arguments are named in this document as
868 \begin_inset LatexCommand index
869 name "T@\\TeX-braces"
874 If you add in a formula a left brace to a command name, LyX creates automatical
876 In all other cases TeX-braces are created in formulas with the command
884 TeX-braces appear red in LyX, in contrary to normal braces that appear
886 In TeX-mode no command is needed to get TeX-braces.
887 TeX-braces don't appear in the output.
890 \begin_layout Standard
891 When commands without arguments, like commands for symbols are entered in
892 TeX-mode, a space character must
896 be behind the command to end it.
897 This space doesn't appear in the output.
898 When the space should appear in the output, the space must be followed
899 by a protected space in normal text.
902 \begin_layout Standard
903 A protected space is inserted with
910 \begin_layout Subsection*
916 \begin_layout Itemize
921 \begin_layout Standard
922 This visible space character can be created with the command
929 \begin_inset LatexCommand index
930 name "Commands ! T ! \\textbackslash textvisiblespace"
934 , inserted in TeX-mode.
943 \begin_layout Standard
953 denotes a space character to be input.
956 \begin_layout Itemize
958 \begin_inset Formula $\to$
961 denotes the usage of the corresponding arrow key on the keyboard.
964 \begin_layout Subsection*
968 \begin_layout Standard
970 \begin_inset Float table
976 \begin_layout Standard
980 \begin_layout Standard
981 \begin_inset LatexCommand label
982 name "tab:Used-units"
994 \begin_layout Standard
997 <lyxtabular version="3" rows="13" columns="2">
999 <column alignment="center" valignment="top" leftline="true" width="0">
1000 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
1001 <row topline="true" bottomline="true">
1002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1005 \begin_layout Standard
1011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1014 \begin_layout Standard
1021 <row topline="true">
1022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1025 \begin_layout Standard
1031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1034 \begin_layout Standard
1041 <row topline="true">
1042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1045 \begin_layout Standard
1051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1054 \begin_layout Standard
1061 <row topline="true">
1062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1065 \begin_layout Standard
1071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1074 \begin_layout Standard
1075 Inch (1\InsetSpace \thinspace{}
1076 in = 2,54\InsetSpace \thinspace{}
1083 <row topline="true">
1084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1087 \begin_layout Standard
1093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1096 \begin_layout Standard
1097 Point (72.27\InsetSpace \thinspace{}
1098 pt = 1\InsetSpace \thinspace{}
1105 <row topline="true">
1106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1109 \begin_layout Standard
1115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1118 \begin_layout Standard
1119 Pica (1\InsetSpace \thinspace{}
1120 pc = 12\InsetSpace \thinspace{}
1127 <row topline="true">
1128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1131 \begin_layout Standard
1137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1140 \begin_layout Standard
1141 scaled point (65536\InsetSpace \thinspace{}
1142 sp = 1\InsetSpace \thinspace{}
1149 <row topline="true">
1150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1153 \begin_layout Standard
1159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1162 \begin_layout Standard
1163 big point (72\InsetSpace \thinspace{}
1164 bp = 1\InsetSpace \thinspace{}
1171 <row topline="true">
1172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1175 \begin_layout Standard
1181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1184 \begin_layout Standard
1185 Didot (1\InsetSpace \thinspace{}
1187 \begin_inset Formula $\approx$
1190 0.376\InsetSpace \thinspace{}
1197 <row topline="true">
1198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1201 \begin_layout Standard
1207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1210 \begin_layout Standard
1211 Cicero (1\InsetSpace \thinspace{}
1212 cc = 12\InsetSpace \thinspace{}
1219 <row topline="true">
1220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1223 \begin_layout Standard
1229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1232 \begin_layout Standard
1236 \begin_inset Quotes eld
1242 \begin_inset Quotes erd
1251 <row topline="true">
1252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1255 \begin_layout Standard
1261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1264 \begin_layout Standard
1266 \begin_inset Quotes eld
1274 \begin_inset Quotes erd
1283 <row topline="true" bottomline="true">
1284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1287 \begin_layout Standard
1293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1296 \begin_layout Standard
1297 math unit (1\InsetSpace \thinspace{}
1299 \begin_inset Formula $\nicefrac{1}{18}$
1302 \InsetSpace \thinspace{}
1304 \begin_inset Note Note
1307 \begin_layout Standard
1314 is explained in sec.\InsetSpace \thinspace{}
1316 \begin_inset LatexCommand ref
1317 reference "sub:Self-defined-Fractions"
1344 \begin_layout Standard
1350 \begin_layout Section
1354 \begin_layout Subsection
1356 \begin_inset LatexCommand index
1362 \begin_inset LatexCommand index
1368 \begin_inset LatexCommand index
1369 name "Superscripts|see{Exponents}"
1374 \begin_inset LatexCommand index
1375 name "Subscripts|see{Indices}"
1382 \begin_layout Standard
1383 Indices are created with an underscore
1384 \begin_inset Quotes eld
1388 \begin_inset Quotes erd
1391 or via the math toolbar button
1392 \begin_inset Graphics
1393 filename ../images/math-subscript.png
1398 , exponents with a caret
1399 \begin_inset Quotes eld
1403 \begin_inset Quotes erd
1406 or via the math toolbar button
1407 \begin_inset Graphics
1408 filename ../images/math-superscript.png
1416 \begin_layout Standard
1418 \begin_inset Tabular
1419 <lyxtabular version="3" rows="4" columns="2">
1421 <column alignment="center" valignment="top" leftline="true" width="0pt">
1422 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
1423 <row topline="true" bottomline="true">
1424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1427 \begin_layout Standard
1433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1436 \begin_layout Standard
1438 \begin_inset Note Note
1441 \begin_layout Standard
1448 is only used as spacer.
1459 <row topline="true">
1460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1463 \begin_layout Standard
1469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1472 \begin_layout Standard
1473 \begin_inset Formula $B_{V}$
1482 <row topline="true" bottomline="true">
1483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1486 \begin_layout Standard
1492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1495 \begin_layout Standard
1496 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1505 <row topline="true" bottomline="true">
1506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1509 \begin_layout Standard
1514 \begin_layout Standard
1528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1531 \begin_layout Standard
1532 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1548 \begin_layout Standard
1549 As the caret is in some languages an accent, vowels will be accentuated
1550 in this case and not set as exponents
1554 \begin_layout Standard
1555 Depending on the used keyboard settings this can also happen for other character
1562 To get in this case exponents, press
1566 after the caret as in the last example.
1569 \begin_layout Subsection
1571 \begin_inset LatexCommand label
1572 name "sub:Fractions"
1577 \begin_inset LatexCommand index
1585 \begin_layout Standard
1586 Fractions are generated with the command
1593 \begin_inset LatexCommand index
1594 name "Commands ! F ! \\textbackslash frac"
1598 or via the math toolbar button
1599 \begin_inset Graphics
1600 filename ../images/math/frac.png
1606 The font size is adjusted automatically, depending on whether the fraction
1607 is in an inline or display style formula.
1608 With the math toolbar button
1609 \begin_inset Graphics
1610 filename ../images/math/frac-square.png
1615 you can select different fraction types.
1618 \begin_layout Standard
1624 \begin_inset LatexCommand index
1625 name "Commands ! D ! \\textbackslash dfrac"
1631 a fraction can be created that has in any case the size of a display style
1638 \begin_inset LatexCommand index
1639 name "Commands ! T ! \\textbackslash tfrac"
1645 the fraction appears always with the size of an inline formula.
1649 \begin_layout Standard
1650 A line with the fraction
1651 \begin_inset Formula $\frac{1}{2}$
1654 that was created with the command
1663 \begin_layout Standard
1664 A line with the fraction
1665 \begin_inset Formula $\dfrac{1}{2}$
1668 that was created with the command
1677 \begin_layout Standard
1679 \begin_inset Tabular
1680 <lyxtabular version="3" rows="4" columns="2">
1682 <column alignment="center" valignment="top" leftline="true" width="0pt">
1683 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
1684 <row topline="true" bottomline="true">
1685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1688 \begin_layout Standard
1694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1697 \begin_layout Standard
1699 \begin_inset Note Note
1702 \begin_layout Standard
1709 is only used as spacer.
1720 <row topline="true">
1721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1724 \begin_layout Standard
1731 \begin_layout Standard
1741 \begin_inset Formula $\downarrow$
1749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1752 \begin_layout Standard
1753 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1762 <row topline="true">
1763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1766 \begin_layout Standard
1773 \begin_layout Standard
1783 \begin_inset Formula $\downarrow$
1791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1794 \begin_layout Standard
1795 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1804 <row topline="true" bottomline="true">
1805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1808 \begin_layout Standard
1815 \begin_layout Standard
1828 \begin_layout Standard
1843 \begin_layout Standard
1853 \begin_inset Formula $\downarrow$
1857 \begin_inset Formula $\downarrow\downarrow$
1865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1868 \begin_layout Standard
1869 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1885 \begin_layout Standard
1886 \begin_inset VSpace bigskip
1891 For nested fractions the command
1898 \begin_inset LatexCommand index
1899 name "Commands ! C ! \\textbackslash cfrac"
1905 \begin_inset VSpace -3mm
1911 \begin_layout Standard
1912 \begin_inset Formula \begin{align*}
1913 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1914 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
1921 \begin_layout Standard
1922 The command for the example above is:
1925 \begin_layout Standard
1931 \begin_inset Formula $\to$
1941 \begin_inset Formula $\to$
1947 \begin_inset Formula $\to\to$
1955 \begin_layout Standard
1956 \begin_inset VSpace medskip
1962 \begin_layout Standard
1969 sets the fraction always in the size of a displayed formula, also when
1970 it is part of another fraction.
1977 has the following command scheme:
1980 \begin_layout Standard
1985 cfrac[numerator position]{numerator}{denominator}
1988 \begin_layout Standard
1989 The numerator position can be
2002 l or r aligns the numerator to the left or right, resp.\InsetSpace ~
2009 or no position is given, the numerator appears centered.
2010 These fractions demonstrate the different alignments:
2015 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2019 \begin_inset Formula $\cfrac{A}{B+C}$
2023 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2029 \begin_layout Standard
2030 \begin_inset VSpace medskip
2033 It is often advantageous to combine
2046 \begin_inset Formula \[
2047 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2054 \begin_layout Standard
2055 For inline fractions with a sloped fraction stroke you can use the command
2061 \begin_inset LatexCommand index
2062 name "Commands ! N ! \\textbackslash nicefrac"
2069 \begin_inset Formula $\nicefrac{5}{31}$
2075 \begin_layout Standard
2076 How to define own fractions where the fraction stroke can be changed, is
2078 \begin_inset LatexCommand ref
2079 reference "sub:Self-defined-Fractions"
2086 \begin_layout Subsection
2088 \begin_inset LatexCommand index
2096 \begin_layout Standard
2097 Square roots are created with
2104 \begin_inset LatexCommand index
2105 name "Commands ! S ! \\textbackslash sqrt"
2109 or the math toolbar button
2110 \begin_inset Graphics
2111 filename ../images/math/sqrt.png
2116 , all other roots with the command
2123 \begin_inset LatexCommand index
2124 name "Commands ! R ! \\textbackslash root"
2128 or with the math toolbar button
2129 \begin_inset Graphics
2130 filename ../images/math/root.png
2138 \begin_layout Standard
2140 \begin_inset Tabular
2141 <lyxtabular version="3" rows="3" columns="2">
2143 <column alignment="center" valignment="top" leftline="true" width="0pt">
2144 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2145 <row topline="true" bottomline="true">
2146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2149 \begin_layout Standard
2155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2158 \begin_layout Standard
2160 \begin_inset Note Note
2163 \begin_layout Standard
2170 is only used as spacer.
2181 <row topline="true" bottomline="true">
2182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2185 \begin_layout Standard
2192 \begin_layout Standard
2206 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
2209 \begin_layout Standard
2210 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2219 <row bottomline="true">
2220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2223 \begin_layout Standard
2230 \begin_layout Standard
2240 \begin_inset Formula $\downarrow$
2248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2251 \begin_layout Standard
2252 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2268 \begin_layout Standard
2269 A square root can also be created with
2275 when the root index field is left empty.
2278 \begin_layout Standard
2279 With certain indices the distance to the root is too small, like in this
2281 \begin_inset Formula $\sqrt[\beta]{B}$
2287 \begin_inset Formula $\beta$
2291 To avoid this, the commands
2298 \begin_inset LatexCommand index
2299 name "Commands ! L ! \\textbackslash leftroot"
2310 \begin_inset LatexCommand index
2311 name "Commands ! U ! \\textbackslash uproot"
2315 are used with the following scheme:
2318 \begin_layout Standard
2332 \begin_layout Standard
2333 Distance is the number of Big Points (unit bp;
2334 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2337 ), that the index should be moved to the left or top, resp..
2338 The commands are written to the index.
2339 This way the command
2348 \begin_inset Formula $\to$
2354 \begin_inset Formula $\to$
2363 \begin_layout Standard
2373 \begin_inset Formula $\to$
2380 produces a correct typeset formula:
2381 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2387 \begin_layout Subsection
2388 Binomial coefficients
2389 \begin_inset LatexCommand index
2390 name "Binomial coefficient s"
2397 \begin_layout Standard
2398 Binomial coefficients are inserted with the command
2405 \begin_inset LatexCommand index
2406 name "Commands ! B ! \\textbackslash binom"
2410 or with the submenu of the math toolbar button
2411 \begin_inset Graphics
2412 filename ../images/math/frac-square.png
2420 \begin_layout Standard
2422 \begin_inset Tabular
2423 <lyxtabular version="3" rows="3" columns="2">
2425 <column alignment="center" valignment="top" leftline="true" width="0pt">
2426 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2427 <row topline="true" bottomline="true">
2428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2431 \begin_layout Standard
2437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2440 \begin_layout Standard
2442 \begin_inset Note Note
2445 \begin_layout Standard
2452 is only used as spacer.
2463 <row topline="true">
2464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2467 \begin_layout Standard
2474 \begin_layout Standard
2484 \begin_inset Formula $\downarrow$
2492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2495 \begin_layout Standard
2496 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2505 <row topline="true" bottomline="true">
2506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2509 \begin_layout Standard
2513 \begin_inset Formula $\to$
2523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2526 \begin_layout Standard
2527 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2543 \begin_layout Standard
2544 Analog to fractions (
2561 \begin_inset LatexCommand index
2562 name "Commands ! D ! \\textbackslash dbinom"
2575 \begin_inset LatexCommand index
2576 name "Commands ! T ! \\textbackslash tbinom"
2580 with the following command scheme:
2583 \begin_layout Standard
2588 dbinom{numerator}{denominator}
2596 tbinom{numerator}{denominator}
2599 \begin_layout Subsection
2600 Case differentiations
2601 \begin_inset LatexCommand index
2602 name "Case differentiations "
2609 \begin_layout Standard
2611 \begin_inset Tabular
2612 <lyxtabular version="3" rows="3" columns="2">
2614 <column alignment="center" valignment="top" leftline="true" width="0pt">
2615 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2616 <row topline="true" bottomline="true">
2617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2620 \begin_layout Standard
2626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2629 \begin_layout Standard
2636 <row topline="true">
2637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2640 \begin_layout Standard
2647 \begin_layout Standard
2657 \begin_inset Formula $\to$
2661 \begin_inset LatexCommand index
2662 name "Commands ! C ! \\textbackslash cases"
2671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2674 \begin_layout Standard
2675 \begin_inset Formula $\begin{cases}
2685 <row topline="true" bottomline="true">
2686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2689 \begin_layout Standard
2696 \begin_layout Standard
2710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2713 \begin_layout Standard
2714 \begin_inset Formula $\begin{cases}
2715 A & \textrm{for }x>0\\
2716 B & \textrm{for }x=0\end{cases}$
2732 \begin_layout Standard
2739 or the usage of the math toolbar button
2740 \begin_inset Graphics
2741 filename ../images/math/cases.png
2746 you can create new lines with the shortcut
2750 or the table toolbar button
2751 \begin_inset Graphics
2752 filename ../images/tabular-feature_append-row.png
2760 \begin_layout Standard
2767 is also available via the menu
2769 Insert\SpecialChar \menuseparator
2770 Math\SpecialChar \menuseparator
2776 \begin_layout Subsection
2778 \begin_inset LatexCommand index
2786 \begin_layout Standard
2794 \begin_inset LatexCommand index
2795 name "Commands ! N ! \\textbackslash not"
2799 every character can be displayed canceled.
2800 The characters are quasi accentuated by a slash.
2803 \begin_layout Standard
2805 \begin_inset Tabular
2806 <lyxtabular version="3" rows="4" columns="2">
2808 <column alignment="center" valignment="top" leftline="true" width="0pt">
2809 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2810 <row topline="true" bottomline="true">
2811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2814 \begin_layout Standard
2820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2823 \begin_layout Standard
2830 <row topline="true">
2831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2834 \begin_layout Standard
2842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2845 \begin_layout Standard
2846 \begin_inset Formula $\not=$
2855 <row topline="true" bottomline="true">
2856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2859 \begin_layout Standard
2869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2872 \begin_layout Standard
2873 \begin_inset Formula $\not\le$
2882 <row topline="true" bottomline="true">
2883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2886 \begin_layout Standard
2896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2899 \begin_layout Standard
2900 \begin_inset Formula $\not\parallel$
2916 \begin_layout Standard
2917 The last example shows, that not all negations look good.
2918 Therefore there are for some negations special commands (see
2919 \begin_inset LatexCommand ref
2920 reference "sub:Mathematical-Symbols"
2925 \begin_inset LatexCommand ref
2926 reference "sec:Relations"
2933 \begin_layout Subsection
2935 \begin_inset LatexCommand label
2936 name "sub:Placeholders"
2941 \begin_inset LatexCommand index
2947 \begin_inset LatexCommand index
2948 name "Chemical characters ! Isotopes"
2953 \begin_inset LatexCommand index
2954 name "Isotopes|see{Chemical characters}"
2961 \begin_layout Standard
2962 When displaying e.\InsetSpace \thinspace{}
2968 \begin_layout Standard
2969 More about chemical symbols is written in
2970 \begin_inset LatexCommand ref
2971 reference "sub:Chemical-Symbols-and"
2980 the following problem occurs:
2983 \begin_layout Standard
2985 \begin_inset Tabular
2986 <lyxtabular version="3" rows="2" columns="2">
2988 <column alignment="center" valignment="top" width="0pt">
2989 <column alignment="center" valignment="top" width="0pt">
2991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2994 \begin_layout Standard
2995 Indices created with sub- and superscripts:
3000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3003 \begin_layout Standard
3004 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3017 \begin_layout Standard
3023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3026 \begin_layout Standard
3027 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3041 \begin_inset Note Note
3044 \begin_layout Standard
3051 is only used as spacer.
3059 \begin_layout Standard
3060 The shorter index is by default placed below or above the first character
3061 of the longer index.
3062 To avoid this there is the command
3069 \begin_inset LatexCommand index
3070 name "Commands ! P ! \\textbackslash phantom"
3074 or the math toolbar button\InsetSpace \thinspace{}
3079 \begin_layout Standard
3080 can be found in the submenu of the toolbar button
3081 \begin_inset Graphics
3082 filename ../images/math/space.png
3093 \begin_inset Graphics
3094 filename ../images/math/phantom.png
3099 that creates one or more phantom characters.
3106 a small blue box appears that is superposed with two red arrows.
3107 The arrows indicate that the complete width and height of the box content
3108 will be created as placeholder.
3109 Phantom characters are accordingly placeholders with the size of the characters.
3112 \begin_layout Standard
3114 \begin_inset Tabular
3115 <lyxtabular version="3" rows="4" columns="2">
3117 <column alignment="center" valignment="top" leftline="true" width="0">
3118 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
3119 <row topline="true" bottomline="true">
3120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3123 \begin_layout Standard
3129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3132 \begin_layout Standard
3134 \begin_inset Note Note
3137 \begin_layout Standard
3144 is only used as spacer.
3155 <row topline="true">
3156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3159 \begin_layout Standard
3164 \begin_layout Standard
3179 \begin_layout Standard
3189 \begin_inset Formula $\to$
3196 \begin_layout Standard
3210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3213 \begin_layout Standard
3214 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3223 <row topline="true" bottomline="true">
3224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3227 \begin_layout Standard
3232 \begin_layout Standard
3247 \begin_layout Standard
3257 \begin_inset Formula $\to$
3264 \begin_layout Standard
3278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3281 \begin_layout Standard
3282 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3291 <row topline="true" bottomline="true">
3292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3295 \begin_layout Standard
3302 \begin_layout Standard
3317 \begin_layout Standard
3327 \begin_inset Formula $\to$
3334 \begin_layout Standard
3348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3351 \begin_layout Standard
3352 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3368 \begin_layout Standard
3369 Furthermore there are the commands
3376 \begin_inset LatexCommand index
3377 name "Commands ! V ! \\textbackslash vphantom"
3381 (toolbar button \InsetSpace ~
3383 \begin_inset Graphics
3384 filename ../images/math/vphantom.png
3396 \begin_inset LatexCommand index
3397 name "Commands ! H ! \\textbackslash hphantom"
3401 (toolbar button \InsetSpace ~
3403 \begin_inset Graphics
3404 filename ../images/math/hphantom.png
3416 creates only space for the maximal height of the characters in the box
3417 but not for its width.
3424 creates only space for the width of the box content.
3425 Therefore the boxes of both commands have only one red arrow.
3428 \begin_layout Standard
3439 \begin_layout Standard
3454 space for the height of the integral sign,
3458 \begin_layout Standard
3465 creates an integral sign, see
3466 \begin_inset LatexCommand ref
3467 reference "sub:Big-Operators"
3476 because this is the larger character.
3477 An example application is in
3478 \begin_inset LatexCommand ref
3479 reference "sub:Multiline-Brackets"
3486 \begin_layout Subsection
3488 \begin_inset LatexCommand index
3494 \begin_inset LatexCommand index
3495 name "Formula ! underlined"
3502 \begin_layout Standard
3504 \begin_inset Tabular
3505 <lyxtabular version="3" rows="4" columns="2">
3507 <column alignment="center" valignment="top" leftline="true" width="0pt">
3508 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3509 <row topline="true" bottomline="true">
3510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3513 \begin_layout Standard
3519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3522 \begin_layout Standard
3524 \begin_inset Note Note
3527 \begin_layout Standard
3534 is only used as spacer.
3545 <row topline="true" bottomline="true">
3546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3549 \begin_layout Standard
3556 \begin_layout Standard
3566 \begin_inset LatexCommand index
3567 name "Commands ! O ! \\textbackslash overline"
3576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3579 \begin_layout Standard
3580 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3589 <row bottomline="true">
3590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3593 \begin_layout Standard
3600 \begin_layout Standard
3610 \begin_inset LatexCommand index
3611 name "Commands ! U ! \\textbackslash underline"
3620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3623 \begin_layout Standard
3624 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3633 <row topline="true" bottomline="true">
3634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3637 \begin_layout Standard
3644 \begin_layout Standard
3659 \begin_layout Standard
3673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3676 \begin_layout Standard
3677 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
3693 \begin_layout Standard
3694 In the last example it doesn't matter if first
3709 \begin_layout Standard
3710 To double underline e.\InsetSpace \thinspace{}
3721 \begin_layout Standard
3722 It is possible to place up to 6 lines above or below characters.
3725 \begin_layout Subsection
3727 \begin_inset LatexCommand index
3735 \begin_layout Standard
3736 There are different types of ellipses available.
3740 \begin_layout Standard
3741 In the math toolbar in the submenu of the button
3742 \begin_inset Graphics
3743 filename ../images/math/ldots.png
3753 For listings dots at the baseline are used (
3760 \begin_inset LatexCommand index
3761 name "Commands ! L ! \\textbackslash ldots"
3765 ), while for operations dots are needed that are on the same height as the
3773 \begin_inset LatexCommand index
3774 name "Commands ! C ! \\textbackslash cdots"
3779 When using the command
3786 \begin_inset LatexCommand index
3787 name "Commands ! D ! \\textbackslash dots"
3791 , LaTeX decides on the basis of the next character what type is used.
3794 \begin_layout Standard
3796 \begin_inset Tabular
3797 <lyxtabular version="3" rows="8" columns="2">
3799 <column alignment="center" valignment="top" leftline="true" width="0pt">
3800 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3801 <row topline="true" bottomline="true">
3802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3805 \begin_layout Standard
3811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3814 \begin_layout Standard
3821 <row topline="true">
3822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3825 \begin_layout Standard
3830 \begin_layout Standard
3845 \begin_layout Standard
3859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3862 \begin_layout Standard
3863 \begin_inset Formula $A_{1},\dots,A_{n}$
3872 <row topline="true">
3873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3876 \begin_layout Standard
3881 \begin_layout Standard
3896 \begin_layout Standard
3910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3913 \begin_layout Standard
3914 \begin_inset Formula $A_{1}+\dots+A_{n}$
3923 <row topline="true">
3924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3927 \begin_layout Standard
3932 \begin_layout Standard
3947 \begin_layout Standard
3961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3964 \begin_layout Standard
3965 \begin_inset Formula $A_{1},\ldots,A_{n}$
3974 <row topline="true" bottomline="true">
3975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3978 \begin_layout Standard
3983 \begin_layout Standard
3998 \begin_layout Standard
4012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4015 \begin_layout Standard
4016 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4025 <row topline="true">
4026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4029 \begin_layout Standard
4037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4040 \begin_layout Standard
4041 \begin_inset Formula $\vdots$
4050 <row topline="true" bottomline="true">
4051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4054 \begin_layout Standard
4062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4065 \begin_layout Standard
4066 \begin_inset Formula $\ddots$
4075 <row topline="true" bottomline="true">
4076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4079 \begin_layout Standard
4080 3×3\InsetSpace \thinspace{}
4081 matrix with the different dots
4086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4089 \begin_layout Standard
4090 \begin_inset Formula $\begin{array}{ccc}
4091 A_{11} & \cdots & A_{1m}\\
4092 \vdots & \ddots & \vdots\\
4093 A_{n1} & \cdots & A_{nm}\end{array}$
4109 \begin_layout Standard
4110 The ellipses available in menu
4112 Insert\SpecialChar \menuseparator
4113 Special\InsetSpace ~
4125 \begin_layout Standard
4126 \begin_inset VSpace medskip
4129 Specially for matrices there are ellipses that span over several columns.
4130 They are created with the command
4137 \begin_inset LatexCommand index
4138 name "Commands ! H ! \\textbackslash hdotsfor"
4142 , that has the following scheme:
4145 \begin_layout Standard
4150 hdotsfor[distance]{number of columns}
4153 \begin_layout Standard
4154 The number of columns specifies how many columns should be spanned.
4155 Distance is a factor for the distance between the dots.
4158 \begin_layout Standard
4159 In the following matrix the command
4165 was inserted in the first box of the second line, to get an ellipsis with
4166 a dot distance twice as long as with the command
4173 \begin_inset Formula \[
4174 \left(\begin{array}{cccc}
4177 q & w & e & r\end{array}\right)\]
4181 Note that the matrix fields that should be spanned must be empty, otherwise
4182 you get LaTeX-errors.
4185 \begin_layout Standard
4186 \begin_inset VSpace bigskip
4189 Furthermore you can fill with the command
4196 \begin_inset LatexCommand index
4197 name "Commands ! D ! \\textbackslash dotfill"
4201 the rest of a line with dots.
4202 The effect of these commands is the same like with
4209 \begin_inset LatexCommand ref
4210 reference "sub:Variable-Space"
4217 \begin_layout Standard
4218 For example the command
4226 \begin_layout Standard
4240 \begin_layout Standard
4241 \begin_inset Formula $A\dotfill B$
4247 \begin_layout Standard
4254 there is for a line the command
4261 \begin_inset LatexCommand index
4262 name "Commands ! H ! \\textbackslash hrulefill"
4269 \begin_layout Standard
4270 \begin_inset Formula $A\hrulefill B$
4276 \begin_layout Standard
4277 To use the commands for text, they have to be inserted in TeX-mode.
4280 \begin_layout Section
4282 \begin_inset LatexCommand label
4288 \begin_inset LatexCommand index
4296 \begin_layout Standard
4297 Matrices can be inserted via the math toolbar button
4298 \begin_inset Graphics
4299 filename ../images/dialog-show_mathmatrix.png
4306 Insert\SpecialChar \menuseparator
4307 Math\SpecialChar \menuseparator
4311 You will be asked for the number of matrix columns and rows, and the alignment.
4312 The vertical alignment is hereby only of importance for matrices in inline
4316 \begin_layout Standard
4317 The first matrix is top
4318 \begin_inset Formula $\begin{array}[t]{cccc}
4321 C & F & I & L\end{array}$
4325 \begin_inset Formula $\begin{array}{cccc}
4328 C & F & I & L\end{array}$
4331 , and the third bottom
4332 \begin_inset Formula $\begin{array}[b]{cccc}
4335 C & F & I & L\end{array}$
4341 \begin_layout Standard
4342 The horizontal alignment specifies how the column entries should be aligned.
4343 It is set by entering a letter for every column.
4348 denotes left aligned,
4357 To create for example a 4
4362 matrix where the first column is left aligned, the second and third are
4363 centered, and the last one is right aligned, one enters for the horizontal
4369 Normally are in a matrix all columns centered, therefore the default is
4370 for every column is a
4377 \begin_layout Standard
4378 Horizontal alignment:
4381 \begin_layout Standard
4387 \begin_inset Formula $\begin{array}{lll}
4390 C & F & 10000\end{array}$
4398 \begin_inset Formula $\begin{array}{ccc}
4401 C & F & 10000\end{array}$
4409 \begin_inset Formula $\begin{array}{rrr}
4412 C & F & 10000\end{array}$
4418 \begin_layout Standard
4419 To add or delete rows and columns subsequently, the math toolbar buttons
4421 \begin_inset Graphics
4422 filename ../images/tabular-feature_append-row.png
4428 \begin_inset Graphics
4429 filename ../images/tabular-feature_delete-row.png
4434 , etc.\InsetSpace \thinspace{}
4437 Edit\SpecialChar \menuseparator
4441 New rows can also be created with
4448 \begin_layout Standard
4449 \begin_inset VSpace bigskip
4452 Parentheses around a matrix can can either be created with the commands
4460 \begin_inset LatexCommand index
4461 name "Commands ! L ! \\textbackslash left"
4472 \begin_inset LatexCommand index
4473 name "Commands ! R ! \\textbackslash right"
4483 \begin_inset LatexCommand ref
4484 reference "sub:Automatic-Bracket-Size"
4488 , or by using the following commands:
4489 \begin_inset VSpace medskip
4495 \begin_layout Standard
4499 \begin_inset Tabular
4500 <lyxtabular version="3" rows="4" columns="2">
4502 <column alignment="center" valignment="top" leftline="true" width="0">
4503 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4504 <row topline="true" bottomline="true">
4505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4508 \begin_layout Standard
4514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4517 \begin_layout Standard
4519 \begin_inset Note Note
4522 \begin_layout Standard
4529 is only used as spacer.
4540 <row topline="true">
4541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4544 \begin_layout Standard
4551 \begin_layout Standard
4564 2\InsetSpace \thinspace{}
4570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4573 \begin_layout Standard
4574 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
4575 0 & \textrm{-}\mathrm{i}\\
4576 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
4585 <row topline="true">
4586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4589 \begin_layout Standard
4596 \begin_layout Standard
4609 2\InsetSpace \thinspace{}
4615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4618 \begin_layout Standard
4619 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
4620 0 & \textrm{-}\mathrm{i}\\
4621 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
4630 <row topline="true" bottomline="true">
4631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4634 \begin_layout Standard
4641 \begin_layout Standard
4654 2\InsetSpace \thinspace{}
4660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4663 \begin_layout Standard
4664 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
4665 0 & \textrm{-}\mathrm{i}\\
4666 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
4682 \begin_inset Tabular
4683 <lyxtabular version="3" rows="4" columns="2">
4685 <column alignment="center" valignment="top" leftline="true" width="0">
4686 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4687 <row topline="true" bottomline="true">
4688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4691 \begin_layout Standard
4697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4700 \begin_layout Standard
4707 <row topline="true">
4708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4711 \begin_layout Standard
4718 \begin_layout Standard
4731 2\InsetSpace \thinspace{}
4737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4740 \begin_layout Standard
4741 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
4742 0 & \textrm{-}\mathrm{i}\\
4743 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
4752 <row topline="true" bottomline="true">
4753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4756 \begin_layout Standard
4763 \begin_layout Standard
4776 2\InsetSpace \thinspace{}
4782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4785 \begin_layout Standard
4786 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
4787 0 & \textrm{-}\mathrm{i}\\
4788 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
4797 <row topline="true" bottomline="true">
4798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4801 \begin_layout Standard
4808 \begin_layout Standard
4821 2\InsetSpace \thinspace{}
4827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4830 \begin_layout Standard
4831 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
4832 0 & \textrm{-}\mathrm{i}\\
4833 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
4851 \begin_layout Standard
4852 \begin_inset VSpace medskip
4855 When e.\InsetSpace \thinspace{}
4863 is inserted, a blue box appears between two vertical lines where the matrix
4867 \begin_layout Standard
4868 \begin_inset VSpace bigskip
4871 As all multiline formulas are matrices, the length
4878 \begin_inset LatexCommand index
4879 name "Commands ! A ! \\textbackslash arraycolsep"
4883 that is described in
4884 \begin_inset LatexCommand ref
4885 reference "sub:Column-Separation"
4889 can also be used to change the column separation of matrices.
4892 \begin_layout Standard
4893 To change the row separation, the command
4900 \begin_inset LatexCommand index
4901 name "Commands ! A ! \\textbackslash arraystretch"
4906 It is used as follows:
4909 \begin_layout Standard
4916 arraystretch}{stretch factor}
4917 \begin_inset LatexCommand index
4918 name "Commands ! R ! \\textbackslash renewcommand"
4925 \begin_layout Standard
4932 assigns the stretch factor to the predefined command
4939 To double e.\InsetSpace \thinspace{}
4941 the row separation, use the factor 2.
4942 This is then used for all following matrices.
4943 To go back to the original separation, assign the factor 1 to
4952 \begin_layout Standard
4953 To set matrices into a text line, the command
4960 \begin_inset LatexCommand index
4961 name "Commands ! S ! \\textbackslash smallmatrix"
4966 When it is inserted a blue box with two dashed lines appears.
4967 In this box the matrix is inserted.
4970 \begin_layout Standard
4972 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
4973 C & D\end{smallmatrix}\right)$
4979 \begin_layout Section
4980 Brackets and Delimiters
4981 \begin_inset LatexCommand index
4987 \begin_inset LatexCommand index
4995 \begin_layout Subsection
4996 Vertical Brackets and Delimiters
4997 \begin_inset LatexCommand index
4998 name "Brackets ! vertical"
5005 \begin_layout Standard
5009 \begin_inset Tabular
5010 <lyxtabular version="3" rows="9" columns="2">
5012 <column alignment="center" valignment="top" leftline="true" width="0pt">
5013 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5014 <row topline="true" bottomline="true">
5015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5018 \begin_layout Standard
5024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5027 \begin_layout Standard
5034 <row topline="true">
5035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5038 \begin_layout Standard
5044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5047 \begin_layout Standard
5048 \begin_inset Formula $($
5057 <row topline="true">
5058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5061 \begin_layout Standard
5067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5070 \begin_layout Standard
5071 \begin_inset Formula $\{$
5080 <row topline="true">
5081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5084 \begin_layout Standard
5090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5093 \begin_layout Standard
5094 \begin_inset Formula $[$
5103 <row topline="true">
5104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5107 \begin_layout Standard
5115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5118 \begin_layout Standard
5119 \begin_inset Formula $\langle$
5128 <row topline="true">
5129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5132 \begin_layout Standard
5140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5143 \begin_layout Standard
5144 \begin_inset Formula $\lceil$
5153 <row topline="true">
5154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5157 \begin_layout Standard
5165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5168 \begin_layout Standard
5169 \begin_inset Formula $\lfloor$
5178 <row topline="true">
5179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5182 \begin_layout Standard
5188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5191 \begin_layout Standard
5192 \begin_inset Formula $/$
5201 <row topline="true" bottomline="true">
5202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5205 \begin_layout Standard
5211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5214 \begin_layout Standard
5215 \begin_inset Formula $|$
5231 \begin_inset Tabular
5232 <lyxtabular version="3" rows="9" columns="2">
5234 <column alignment="center" valignment="top" leftline="true" width="0pt">
5235 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5236 <row topline="true" bottomline="true">
5237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5240 \begin_layout Standard
5246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5249 \begin_layout Standard
5256 <row topline="true">
5257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5260 \begin_layout Standard
5266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5269 \begin_layout Standard
5270 \begin_inset Formula $)$
5279 <row topline="true">
5280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5283 \begin_layout Standard
5289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5292 \begin_layout Standard
5293 \begin_inset Formula $\}$
5302 <row topline="true">
5303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5306 \begin_layout Standard
5312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5315 \begin_layout Standard
5316 \begin_inset Formula $]$
5325 <row topline="true">
5326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5329 \begin_layout Standard
5337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5340 \begin_layout Standard
5341 \begin_inset Formula $\rangle$
5350 <row topline="true">
5351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5354 \begin_layout Standard
5362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5365 \begin_layout Standard
5366 \begin_inset Formula $\rceil$
5375 <row topline="true">
5376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5379 \begin_layout Standard
5387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5390 \begin_layout Standard
5391 \begin_inset Formula $\rfloor$
5400 <row topline="true">
5401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5404 \begin_layout Standard
5414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5417 \begin_layout Standard
5418 \begin_inset Formula $\backslash$
5427 <row topline="true" bottomline="true">
5428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5431 \begin_layout Standard
5439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5442 \begin_layout Standard
5443 \begin_inset Formula $\|$
5461 \begin_layout Standard
5464 \begin_inset Note Greyedout
5467 \begin_layout Standard
5472 In TeX-mode the command
5479 \begin_inset LatexCommand index
5480 name "Commands ! T ! \\textbackslash textbackslash"
5484 must be used for the backslash, because the command
5492 produces there a line break.
5500 \begin_layout Standard
5501 For all characters listed above the size can be adjusted with the commands
5502 described in the following two subsections.
5503 When using these commands, the characters < and > can directly be used
5504 instead of the commands
5519 \begin_layout Subsubsection
5521 \begin_inset LatexCommand label
5522 name "sub:Manual-Bracket-Size"
5527 \begin_inset LatexCommand index
5528 name "Bracket size ! manual"
5535 \begin_layout Standard
5536 The bracket size can be specified manually by the LaTeX-commands
5543 \begin_inset LatexCommand index
5544 name "Commands ! B ! \\textbackslash big"
5573 denotes the smallest and
5579 the largest bracket size.
5582 \begin_layout Standard
5583 These commands are used to emphasize levels of brackets:
5586 \begin_layout Standard
5588 \begin_inset Tabular
5589 <lyxtabular version="3" rows="2" columns="2">
5591 <column alignment="center" valignment="top" width="0pt">
5592 <column alignment="center" valignment="top" width="0pt">
5594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5597 \begin_layout Standard
5598 all brackets in the same size:
5603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5606 \begin_layout Standard
5607 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
5617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5620 \begin_layout Standard
5626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5629 \begin_layout Standard
5630 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
5644 \begin_inset Note Note
5647 \begin_layout Standard
5654 is only used as spacer.
5662 \begin_layout Standard
5663 For the second formula the command
5673 \begin_layout Standard
5687 \begin_layout Standard
5688 Here is an overview about all bracket sizes:
5691 \begin_layout Standard
5711 \begin_layout Standard
5728 \begin_layout Standard
5741 \begin_layout Standard
5757 \begin_layout Standard
5759 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
5765 \begin_layout Standard
5774 -commands there is the variant
5781 \begin_inset LatexCommand index
5782 name "Commands ! B ! \\textbackslash bigm"
5786 that adds a bit more space between the bracket and its content, and the
5800 \begin_inset LatexCommand index
5801 name "Commands ! B ! \\textbackslash bigl - \\textbackslash bigr"
5805 , that don't add additional space.
5810 at the end of the command
5816 is for a left bracket; for a right bracket this will be replaced by an
5822 A left or right bracket can each be an opening or closing bracket.
5825 \begin_layout Standard
5826 In the following table is a comparison of the variants:
5829 \begin_layout Standard
5831 \begin_inset Tabular
5832 <lyxtabular version="3" rows="5" columns="2">
5834 <column alignment="center" valignment="middle" leftline="true" width="0">
5835 <column alignment="center" valignment="middle" leftline="true" rightline="true" width="0">
5836 <row topline="true" bottomline="true">
5837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5840 \begin_layout Standard
5846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5849 \begin_layout Standard
5851 \begin_inset Note Note
5854 \begin_layout Standard
5861 is only used as spacer.
5872 <row topline="true">
5873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5876 \begin_layout Standard
5891 \begin_layout Standard
5909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5912 \begin_layout Standard
5913 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
5922 <row topline="true">
5923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5926 \begin_layout Standard
5941 \begin_layout Standard
5959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5962 \begin_layout Standard
5963 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
5972 <row topline="true" bottomline="true">
5973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5976 \begin_layout Standard
5991 \begin_layout Standard
6009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6012 \begin_layout Standard
6013 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6022 <row topline="true" bottomline="true">
6023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6026 \begin_layout Standard
6038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6041 \begin_layout Standard
6042 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6058 \begin_layout Subsubsection
6059 Automatic Bracket Size
6060 \begin_inset LatexCommand label
6061 name "sub:Automatic-Bracket-Size"
6066 \begin_inset LatexCommand index
6067 name "Bracket size ! automatic"
6074 \begin_layout Standard
6075 Brackets with variable size can be inserted with the commands
6082 \begin_inset LatexCommand index
6083 name "Commands ! L ! \\textbackslash left"
6094 \begin_inset LatexCommand index
6095 name "Commands ! R ! \\textbackslash right"
6099 or via the math toolbar button
6100 \begin_inset Graphics
6101 filename ../images/dialog-show_mathdelimiter.png
6119 the wanted bracket must be inserted.
6120 The bracket size will then automatically be calculated for the output.
6123 \begin_layout Standard
6125 normal bracket: The command
6135 \begin_layout Standard
6145 \begin_inset Formula $\downarrow$
6152 \begin_layout Standard
6164 \begin_inset Formula \[
6172 \begin_layout Standard
6174 multiline bracket: The command
6186 \begin_layout Standard
6196 \begin_inset Formula $\downarrow$
6203 \begin_layout Standard
6217 \begin_inset Formula \[
6218 \ln\left(\frac{A}{C}\right)\]
6225 \begin_layout Standard
6244 This has the advantage that you can see in LyX immediately the real bracket
6245 size and that the matching right bracket will be created too.
6248 for the last example would then be:
6262 \begin_layout Standard
6272 \begin_inset Formula $\downarrow$
6278 \begin_layout Standard
6279 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6280 For example the command
6290 \begin_layout Standard
6300 \begin_inset Formula $\downarrow$
6307 \begin_layout Standard
6323 \begin_inset Formula \[
6324 \left.\frac{A}{B}\right\} \]
6342 will be converted by LyX to brackets in the right size when the document
6343 is reloaded and an omitted bracket will appear as dashed line.
6346 \begin_layout Standard
6347 \begin_inset VSpace bigskip
6350 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6358 \begin_inset LatexCommand index
6359 name "Commands ! M ! \\textbackslash middle"
6363 is additionally available for all brackets and limits.
6364 With this command the height of the following character is adapted to the
6365 one of the surrounding brackets, what is e.\InsetSpace \thinspace{}
6367 needed for physical vectors:
6368 \begin_inset Formula \[
6369 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
6373 For physical vectors there is a special LaTeX-package, described in
6374 \begin_inset LatexCommand ref
6375 reference "sub:Physical-Vectors"
6382 \begin_layout Subsection
6384 \begin_inset LatexCommand index
6385 name "Brackets ! horizontal"
6392 \begin_layout Standard
6394 \begin_inset Tabular
6395 <lyxtabular version="3" rows="4" columns="2">
6397 <column alignment="center" valignment="top" leftline="true" width="0pt">
6398 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
6399 <row topline="true" bottomline="true">
6400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6403 \begin_layout Standard
6405 \begin_inset Note Note
6408 \begin_layout Standard
6415 is only used as spacer.
6425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6428 \begin_layout Standard
6435 <row topline="true">
6436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6439 \begin_layout Standard
6443 \begin_layout Standard
6458 \begin_layout Standard
6471 \begin_layout Standard
6484 \begin_layout Standard
6497 \begin_layout Standard
6505 \begin_inset LatexCommand index
6506 name "Commands ! O ! \\textbackslash overbrace"
6515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6518 \begin_layout Standard
6519 \begin_inset Formula $\overbrace{A+B}^{3}$
6528 <row topline="true" bottomline="true">
6529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6532 \begin_layout Standard
6536 \begin_layout Standard
6551 \begin_layout Standard
6564 \begin_layout Standard
6577 \begin_layout Standard
6585 \begin_inset LatexCommand index
6586 name "Commands ! U ! \\textbackslash underbrace"
6595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6598 \begin_layout Standard
6599 \begin_inset Formula $\underbrace{A+B}_{5}$
6608 <row topline="true" bottomline="true">
6609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6612 \begin_layout Standard
6619 \begin_layout Standard
6634 \begin_layout Standard
6647 \begin_layout Standard
6660 \begin_layout Standard
6673 \begin_layout Standard
6686 \begin_layout Standard
6699 \begin_layout Standard
6713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6716 \begin_layout Standard
6717 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6733 \begin_layout Standard
6734 In the last example it doesn't matter if
6746 is inserted at first.
6749 \begin_layout Standard
6750 \begin_inset VSpace bigskip
6753 When brackets are needed that overlap each other, multiline formulas, as
6755 \begin_inset LatexCommand ref
6756 reference "sec:Multiline-Formulas"
6761 \begin_inset Formula \begin{eqnarray*}
6762 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
6763 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
6767 In the first row the formula is inserted together with the first brace.
6768 It is hereby important that the space command
6772 \begin_layout Standard
6773 Space commands are explained in
6774 \begin_inset LatexCommand ref
6775 reference "sub:Predefined-Space"
6790 is inserted before the first
6791 \begin_inset Formula $d$
6794 , because the brace that ends behind the
6795 \begin_inset Formula $q$
6798 prevents that the following
6799 \begin_inset Quotes eld
6803 \begin_inset Quotes erd
6806 is surrounded by space.
6810 \begin_layout Standard
6811 because a bracket is not handled as character, see
6812 \begin_inset LatexCommand ref
6813 reference "sub:Binary-Operators"
6822 In the second row the second brace is inserted.
6823 As it should begin before the
6824 \begin_inset Formula $b$
6839 \begin_layout Standard
6847 \begin_inset LatexCommand ref
6848 reference "sub:Placeholders"
6857 This space is needed because the
6858 \begin_inset Quotes eld
6862 \begin_inset Quotes erd
6865 is also surrounded by space in the formula.
6866 The brace is placed under the command
6875 \begin_layout Standard
6876 It gets more complicated when brackets overlap each other, like in the following
6881 \begin_layout Standard
6893 \begin_inset Formula \begin{eqnarray*}
6894 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
6895 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
6903 \begin_layout Standard
6914 The first formula row is the same as the second row of the previous example,
6915 with the difference that the brace is above.
6916 The second row contains the formula together with the second brace.
6917 To avoid that there is space between the upper brace in the first row and
6918 the formula, the row spacing need to be reduced.
6919 This is not easily possible due to a bug in LyX
6923 \begin_layout Standard
6927 \begin_layout Standard
6931 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
6940 \begin_layout Standard
6953 As solution for the problem, the global formula row separation
6960 \begin_inset LatexCommand index
6961 name "Commands ! J ! \\textbackslash jot"
6965 must be changed to -6\InsetSpace \thinspace{}
6966 pt before the formula with the command
6981 is set back after the formula to the standard value of 3\InsetSpace \thinspace{}
6984 More about the row separation in formulas is explained in
6985 \begin_inset LatexCommand ref
6986 reference "sub:Line-Separation"
6993 \begin_layout Section
6995 \begin_inset LatexCommand index
7003 \begin_layout Standard
7004 Arrows can be inserted via the math toolbar button
7005 \begin_inset Graphics
7006 filename ../images/math/leftarrow.png
7011 or the commands listed in the following subsections.
7014 \begin_layout Subsection
7016 \begin_inset LatexCommand index
7017 name "Arrows ! horizontal"
7024 \begin_layout Standard
7028 \begin_inset Tabular
7029 <lyxtabular version="3" rows="8" columns="2">
7031 <column alignment="center" valignment="top" leftline="true" width="0pt">
7032 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7033 <row topline="true" bottomline="true">
7034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7037 \begin_layout Standard
7043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7046 \begin_layout Standard
7053 <row topline="true">
7054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7057 \begin_layout Standard
7065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7068 \begin_layout Standard
7069 \begin_inset Formula $\gets$
7078 <row topline="true">
7079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7082 \begin_layout Standard
7090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7093 \begin_layout Standard
7094 \begin_inset Formula $\Leftarrow$
7103 <row topline="true" bottomline="true">
7104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7107 \begin_layout Standard
7115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7118 \begin_layout Standard
7119 \begin_inset Formula $\longleftarrow$
7128 <row bottomline="true">
7129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7132 \begin_layout Standard
7140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7143 \begin_layout Standard
7144 \begin_inset Formula $\Longleftarrow$
7153 <row bottomline="true">
7154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7157 \begin_layout Standard
7165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7168 \begin_layout Standard
7169 \begin_inset Formula $\leftharpoonup$
7178 <row bottomline="true">
7179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7182 \begin_layout Standard
7190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7193 \begin_layout Standard
7194 \begin_inset Formula $\leftharpoondown$
7203 <row bottomline="true">
7204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7207 \begin_layout Standard
7215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7218 \begin_layout Standard
7219 \begin_inset Formula $\hookleftarrow$
7235 \begin_inset Tabular
7236 <lyxtabular version="3" rows="8" columns="2">
7238 <column alignment="center" valignment="top" leftline="true" width="0pt">
7239 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7240 <row topline="true" bottomline="true">
7241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7244 \begin_layout Standard
7250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7253 \begin_layout Standard
7260 <row topline="true">
7261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7264 \begin_layout Standard
7272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7275 \begin_layout Standard
7276 \begin_inset Formula $\to$
7285 <row topline="true">
7286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7289 \begin_layout Standard
7297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7300 \begin_layout Standard
7301 \begin_inset Formula $\Rightarrow$
7310 <row topline="true">
7311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7314 \begin_layout Standard
7322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7325 \begin_layout Standard
7326 \begin_inset Formula $\longrightarrow$
7335 <row topline="true">
7336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7339 \begin_layout Standard
7347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7350 \begin_layout Standard
7351 \begin_inset Formula $\Longrightarrow$
7360 <row topline="true">
7361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7364 \begin_layout Standard
7372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7375 \begin_layout Standard
7376 \begin_inset Formula $\rightharpoonup$
7385 <row topline="true" bottomline="true">
7386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7389 \begin_layout Standard
7397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7400 \begin_layout Standard
7401 \begin_inset Formula $\rightharpoondown$
7410 <row bottomline="true">
7411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7414 \begin_layout Standard
7422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7425 \begin_layout Standard
7426 \begin_inset Formula $\hookrightarrow$
7444 \begin_layout Standard
7448 \begin_inset Tabular
7449 <lyxtabular version="3" rows="6" columns="2">
7451 <column alignment="center" valignment="top" leftline="true" width="0pt">
7452 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7453 <row topline="true" bottomline="true">
7454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7457 \begin_layout Standard
7463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7466 \begin_layout Standard
7473 <row topline="true">
7474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7477 \begin_layout Standard
7485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7488 \begin_layout Standard
7489 \begin_inset Formula $\leftrightarrow$
7498 <row topline="true">
7499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7502 \begin_layout Standard
7510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7513 \begin_layout Standard
7514 \begin_inset Formula $\Leftrightarrow$
7523 <row topline="true">
7524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7527 \begin_layout Standard
7535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7538 \begin_layout Standard
7539 \begin_inset Formula $\longleftrightarrow$
7548 <row topline="true">
7549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7552 \begin_layout Standard
7560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7563 \begin_layout Standard
7564 \begin_inset Formula $\Longleftrightarrow$
7573 <row topline="true" bottomline="true">
7574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7577 \begin_layout Standard
7585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7588 \begin_layout Standard
7589 \begin_inset Formula $\rightleftharpoons$
7606 \begin_layout Standard
7618 \begin_inset Tabular
7619 <lyxtabular version="3" rows="5" columns="2">
7621 <column alignment="center" valignment="top" leftline="true" width="0pt">
7622 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7623 <row topline="true" bottomline="true">
7624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7627 \begin_layout Standard
7633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7636 \begin_layout Standard
7643 <row topline="true">
7644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7647 \begin_layout Standard
7655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7658 \begin_layout Standard
7659 \begin_inset Formula $\mapsto$
7668 <row topline="true">
7669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7672 \begin_layout Standard
7680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7683 \begin_layout Standard
7684 \begin_inset Formula $\longmapsto$
7693 <row topline="true">
7694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7697 \begin_layout Standard
7705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7708 \begin_layout Standard
7709 \begin_inset Formula $\leadsto$
7718 <row topline="true" bottomline="true">
7719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7722 \begin_layout Standard
7730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7733 \begin_layout Standard
7734 \begin_inset Formula $\dasharrow$
7752 \begin_layout Standard
7753 \begin_inset VSpace medskip
7756 Arrows used as accent like e.\InsetSpace \thinspace{}
7758 vector arrows are listed in
7759 \begin_inset LatexCommand ref
7760 reference "sec:Accents"
7767 \begin_layout Standard
7768 \begin_inset VSpace bigskip
7771 Furthermore there are the labeled arrows
7772 \begin_inset LatexCommand index
7773 name "Arrows ! labeled"
7784 \begin_inset LatexCommand index
7785 name "Commands ! X ! \\textbackslash xleftarrow"
7796 \begin_inset LatexCommand index
7797 name "Commands ! X ! \\textbackslash xrightarrow\\vspace{4mm}"
7802 When inserting one of these commands in a formula, an arrow with two blue
7803 boxes appear where the label can be inserted.
7804 The length of the arrow adapts to the label width.
7807 \begin_layout Standard
7809 \begin_inset Tabular
7810 <lyxtabular version="3" rows="3" columns="2">
7812 <column alignment="center" valignment="top" leftline="true" width="0pt">
7813 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7814 <row topline="true" bottomline="true">
7815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7818 \begin_layout Standard
7824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7827 \begin_layout Standard
7829 \begin_inset Note Note
7832 \begin_layout Standard
7839 is only used as spacer.
7850 <row topline="true">
7851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7854 \begin_layout Standard
7861 \begin_layout Standard
7871 \begin_inset Formula $\downarrow$
7875 \begin_inset Formula $\to$
7883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7886 \begin_layout Standard
7887 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
7896 <row topline="true" bottomline="true">
7897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7900 \begin_layout Standard
7907 \begin_layout Standard
7917 \begin_inset Formula $\downarrow$
7921 \begin_inset Formula $\to$
7929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7932 \begin_layout Standard
7933 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
7949 \begin_layout Subsection
7950 Vertical and diagonal Arrows
7951 \begin_inset LatexCommand index
7952 name "Arrows ! diagonal"
7957 \begin_inset LatexCommand index
7958 name "Arrows ! vertical"
7965 \begin_layout Standard
7969 \begin_inset Tabular
7970 <lyxtabular version="3" rows="7" columns="2">
7972 <column alignment="center" valignment="top" leftline="true" width="0pt">
7973 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7974 <row topline="true" bottomline="true">
7975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7978 \begin_layout Standard
7984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7987 \begin_layout Standard
7994 <row topline="true">
7995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7998 \begin_layout Standard
8006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8009 \begin_layout Standard
8010 \begin_inset Formula $\uparrow$
8019 <row topline="true">
8020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8023 \begin_layout Standard
8031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8034 \begin_layout Standard
8035 \begin_inset Formula $\Uparrow$
8044 <row topline="true">
8045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8048 \begin_layout Standard
8056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8059 \begin_layout Standard
8060 \begin_inset Formula $\updownarrow$
8069 <row topline="true">
8070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8073 \begin_layout Standard
8081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8084 \begin_layout Standard
8085 \begin_inset Formula $\Updownarrow$
8094 <row topline="true" bottomline="true">
8095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8098 \begin_layout Standard
8106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8109 \begin_layout Standard
8110 \begin_inset Formula $\Downarrow$
8119 <row bottomline="true">
8120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8123 \begin_layout Standard
8131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8134 \begin_layout Standard
8135 \begin_inset Formula $\downarrow$
8151 \begin_inset Tabular
8152 <lyxtabular version="3" rows="5" columns="2">
8154 <column alignment="center" valignment="top" leftline="true" width="0pt">
8155 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8156 <row topline="true" bottomline="true">
8157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8160 \begin_layout Standard
8166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8169 \begin_layout Standard
8176 <row topline="true">
8177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8180 \begin_layout Standard
8188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8191 \begin_layout Standard
8192 \begin_inset Formula $\nearrow$
8201 <row topline="true">
8202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8205 \begin_layout Standard
8213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8216 \begin_layout Standard
8217 \begin_inset Formula $\searrow$
8226 <row topline="true" bottomline="true">
8227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8230 \begin_layout Standard
8238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8241 \begin_layout Standard
8242 \begin_inset Formula $\swarrow$
8251 <row bottomline="true">
8252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8255 \begin_layout Standard
8263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8266 \begin_layout Standard
8267 \begin_inset Formula $\nwarrow$
8285 \begin_layout Standard
8286 \begin_inset VSpace medskip
8289 Vertical arrows can be used also as delimiter together with the commands
8291 \begin_inset LatexCommand ref
8292 reference "sub:Manual-Bracket-Size"
8297 \begin_inset LatexCommand ref
8298 reference "sub:Automatic-Bracket-Size"
8305 \begin_layout Standard
8311 \begin_layout Section
8313 \begin_inset LatexCommand label
8319 \begin_inset LatexCommand index
8327 \begin_layout Standard
8328 Accents can be inserted via the math toolbar button
8329 \begin_inset Graphics
8330 filename ../images/math/hat.png
8335 or the commands listed in the following subsections.
8338 \begin_layout Subsection
8339 Accents for one Character
8343 \begin_layout Standard
8356 \begin_layout Standard
8358 \begin_inset LatexCommand ref
8359 reference "sub:Accents-in-Text"
8372 \begin_layout Standard
8380 \begin_inset Note Note
8383 \begin_layout Standard
8386 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
8389 \begin_layout Standard
8392 texorpdfstring is in section
8393 \begin_inset LatexCommand ref
8394 reference "sub:Formulas-in-Section"
8404 \begin_inset LatexCommand label
8405 name "sub:Accents-for-one"
8410 \begin_inset LatexCommand index
8411 name "Accents ! for one character"
8418 \begin_layout Standard
8422 \begin_inset Tabular
8423 <lyxtabular version="3" rows="8" columns="2">
8425 <column alignment="center" valignment="top" leftline="true" width="0pt">
8426 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8427 <row topline="true" bottomline="true">
8428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8431 \begin_layout Standard
8437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8440 \begin_layout Standard
8442 \begin_inset Note Note
8445 \begin_layout Standard
8452 is only used as spacer.
8463 <row topline="true" bottomline="true">
8464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8467 \begin_layout Standard
8474 \begin_layout Standard
8488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8491 \begin_layout Standard
8492 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8501 <row bottomline="true">
8502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8505 \begin_layout Standard
8512 \begin_layout Standard
8526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8529 \begin_layout Standard
8530 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8539 <row bottomline="true">
8540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8543 \begin_layout Standard
8550 \begin_layout Standard
8564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8567 \begin_layout Standard
8568 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8577 <row bottomline="true">
8578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8581 \begin_layout Standard
8589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8592 \begin_layout Standard
8593 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
8602 <row bottomline="true">
8603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8606 \begin_layout Standard
8613 \begin_layout Standard
8623 \begin_inset LatexCommand index
8633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8636 \begin_layout Standard
8637 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
8646 <row bottomline="true">
8647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8650 \begin_layout Standard
8657 \begin_layout Standard
8671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8674 \begin_layout Standard
8675 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
8684 <row bottomline="true">
8685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8688 \begin_layout Standard
8695 \begin_layout Standard
8709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8712 \begin_layout Standard
8713 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
8729 \begin_inset Tabular
8730 <lyxtabular version="3" rows="7" columns="2">
8732 <column alignment="center" valignment="top" leftline="true" width="0pt">
8733 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8734 <row topline="true" bottomline="true">
8735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8738 \begin_layout Standard
8744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8747 \begin_layout Standard
8754 <row topline="true" bottomline="true">
8755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8758 \begin_layout Standard
8765 \begin_layout Standard
8779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8782 \begin_layout Standard
8783 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
8792 <row bottomline="true">
8793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8796 \begin_layout Standard
8803 \begin_layout Standard
8817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8820 \begin_layout Standard
8821 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
8830 <row bottomline="true">
8831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8834 \begin_layout Standard
8841 \begin_layout Standard
8855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8858 \begin_layout Standard
8859 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
8868 <row bottomline="true">
8869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8872 \begin_layout Standard
8879 \begin_layout Standard
8893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8896 \begin_layout Standard
8897 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
8906 <row bottomline="true">
8907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8910 \begin_layout Standard
8917 \begin_layout Standard
8931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8934 \begin_layout Standard
8935 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
8944 <row bottomline="true">
8945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8948 \begin_layout Standard
8955 \begin_layout Standard
8969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8972 \begin_layout Standard
8973 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
8991 \begin_layout Standard
8992 \begin_inset VSpace bigskip
8996 \begin_inset LatexCommand index
9001 in formulas, a quotation mark is inserted before the vowel.
9002 These two characters are then treated by LaTeX as
9006 character when the formula part with the umlaut is marked as German.
9014 \begin_inset Quotes eld
9018 \begin_inset Quotes erd
9021 umlauts are created as demonstrated in the following example:
9024 \begin_layout Standard
9025 \begin_inset VSpace -2mm
9031 \begin_layout Standard
9033 \begin_inset Tabular
9034 <lyxtabular version="3" rows="3" columns="2">
9036 <column alignment="center" valignment="top" leftline="true" width="0">
9037 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
9038 <row topline="true" bottomline="true">
9039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9042 \begin_layout Standard
9048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9051 \begin_layout Standard
9053 \begin_inset Note Note
9056 \begin_layout Standard
9063 is only used as spacer.
9074 <row topline="true">
9075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9078 \begin_layout Standard
9081 \begin_inset Quotes grd
9089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9092 \begin_layout Standard
9095 \begin_inset Formula $"i$
9104 <row topline="true" bottomline="true">
9105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9108 \begin_layout Standard
9115 \begin_layout Standard
9129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9132 \begin_layout Standard
9133 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9149 \begin_layout Standard
9150 Another advantage to
9156 is that umlauts can directly be converted to mathematical text because
9157 the accent commands above are
9163 in mathematical text
9166 To convert an accented character to mathematical text, only the character
9167 under the accent may be converted.
9168 This applies also for all other conversions, e.\InsetSpace \thinspace{}
9173 \begin_layout Standard
9174 In mathematical text, umlauts and other accented characters can directly
9178 \begin_layout Subsection
9179 Accents for Operators
9180 \begin_inset LatexCommand index
9181 name "Accents ! for operators"
9188 \begin_layout Standard
9196 \begin_inset LatexCommand index
9197 name "Commands ! O ! \\textbackslash overset"
9208 \begin_inset LatexCommand index
9209 name "Commands ! U ! \\textbackslash underset"
9213 characters can be placed above or below an operator, respectively, to accent
9222 \begin_inset LatexCommand index
9223 name "Commands ! S ! \\textbackslash sideset"
9227 characters can be set before and behind an operator.
9228 The command scheme is:
9231 \begin_layout Standard
9247 \begin_layout Standard
9254 must always be before the operator that should be accented.
9255 You can accent with several characters and even with other operators and
9263 for example only characters behind an operator, write nothing between the
9264 first braces but don't omit the braces.
9267 \begin_layout Standard
9268 For example the command
9273 \begin_inset Formula $\to$
9283 \begin_inset Formula $\to$
9292 \begin_layout Standard
9308 \begin_inset Formula \[
9309 \sideset{}{'}\sum_{k=1}^{n}\]
9316 \begin_layout Standard
9325 \begin_layout Standard
9340 \begin_layout Standard
9352 \begin_inset Formula $\uparrow$
9360 \begin_inset Formula \[
9361 \overset{a}{\maltese}\]
9365 As seen in the last example, with
9377 also symbols and characters can be accented; with
9383 this is not possible.
9386 \begin_layout Subsection
9387 Accents for several Characters
9388 \begin_inset LatexCommand label
9389 name "sub:Accents-for-several"
9394 \begin_inset LatexCommand index
9395 name "Accents ! for several characters"
9402 \begin_layout Standard
9406 \begin_inset Tabular
9407 <lyxtabular version="3" rows="5" columns="2">
9409 <column alignment="center" valignment="top" leftline="true" width="0pt">
9410 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9411 <row topline="true" bottomline="true">
9412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9415 \begin_layout Standard
9421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9424 \begin_layout Standard
9426 \begin_inset Note Note
9429 \begin_layout Standard
9436 is only used as spacer.
9447 <row topline="true" bottomline="true">
9448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9451 \begin_layout Standard
9458 \begin_layout Standard
9472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9475 \begin_layout Standard
9476 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9485 <row bottomline="true">
9486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9489 \begin_layout Standard
9496 \begin_layout Standard
9510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9513 \begin_layout Standard
9514 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9523 <row bottomline="true">
9524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9527 \begin_layout Standard
9534 \begin_layout Standard
9548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9551 \begin_layout Standard
9552 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9561 <row bottomline="true">
9562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9565 \begin_layout Standard
9572 \begin_layout Standard
9586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9589 \begin_layout Standard
9590 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9606 \begin_inset Tabular
9607 <lyxtabular version="3" rows="5" columns="2">
9609 <column alignment="center" valignment="top" leftline="true" width="0pt">
9610 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9611 <row topline="true" bottomline="true">
9612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9615 \begin_layout Standard
9621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9624 \begin_layout Standard
9631 <row topline="true" bottomline="true">
9632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9635 \begin_layout Standard
9642 \begin_layout Standard
9656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9659 \begin_layout Standard
9660 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9669 <row bottomline="true">
9670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9673 \begin_layout Standard
9680 \begin_layout Standard
9694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9697 \begin_layout Standard
9698 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9707 <row bottomline="true">
9708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9711 \begin_layout Standard
9718 \begin_layout Standard
9732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9735 \begin_layout Standard
9736 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9745 <row bottomline="true">
9746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9749 \begin_layout Standard
9756 \begin_layout Standard
9770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9773 \begin_layout Standard
9774 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
9792 \begin_layout Standard
9793 \begin_inset VSpace medskip
9796 With these commands as many characters as you like can be accented.
9809 will only be set in the output with a length of three characters, as shown
9810 in the following example:
9811 \begin_inset Formula \[
9812 \widetilde{A+B=C-D}\]
9819 \begin_layout Standard
9827 \begin_inset LatexCommand index
9828 name "Commands ! O ! \\textbackslash overset"
9839 \begin_inset LatexCommand index
9840 name "Commands ! U ! \\textbackslash underset"
9844 described in the previous subsection it is also possible to accent several
9854 \begin_layout Standard
9864 \begin_inset Formula $\downarrow$
9870 \begin_inset Formula \[
9871 \underset{***}{A=B}\]
9878 \begin_layout Section
9880 \begin_inset LatexCommand label
9886 \begin_inset LatexCommand index
9887 name "Space ! horizontal"
9894 \begin_layout Subsection
9896 \begin_inset LatexCommand label
9897 name "sub:Predefined-Space"
9902 \begin_inset LatexCommand index
9903 name "Space ! horizontal ! predefined"
9910 \begin_layout Standard
9911 Sometimes it is necessary to insert horizontal space to a formula.
9912 This is done by inserting a protected space (shortcut
9918 \begin_inset Quotes eld
9928 \begin_layout Standard
9941 \begin_inset Quotes erd
9944 appears and by pressing
9948 several times one can select one of eight different space sizes.
9949 The spaces can also be inserted using the math toolbar button
9950 \begin_inset Graphics
9951 filename ../images/math/space.png
9956 or special commands.
9957 Independent from the inserted command, one can select the size again by
9965 \begin_layout Standard
9968 \begin_inset VSpace -5mm
9972 \begin_inset Tabular
9973 <lyxtabular version="3" rows="3" columns="7">
9975 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
9976 <column alignment="center" valignment="top" leftline="true" width="0">
9977 <column alignment="center" valignment="top" leftline="true" width="0">
9978 <column alignment="center" valignment="top" leftline="true" width="0">
9979 <column alignment="center" valignment="top" leftline="true" width="0">
9980 <column alignment="center" valignment="top" leftline="true" width="0">
9981 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
9982 <row topline="true">
9983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9986 \begin_layout Standard
9992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9995 \begin_layout Standard
10003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10006 \begin_layout Standard
10014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10017 \begin_layout Standard
10025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10028 \begin_layout Standard
10036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10039 \begin_layout Standard
10047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10050 \begin_layout Standard
10059 <row topline="true">
10060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10063 \begin_layout Standard
10068 keystrokes after inserting the protected space
10073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10076 \begin_layout Standard
10082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10085 \begin_layout Standard
10091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10094 \begin_layout Standard
10100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10103 \begin_layout Standard
10109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10112 \begin_layout Standard
10118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10121 \begin_layout Standard
10128 <row topline="true" bottomline="true">
10129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10132 \begin_layout Standard
10138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10141 \begin_layout Standard
10142 \begin_inset Formula $A\, B$
10150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10153 \begin_layout Standard
10154 \begin_inset Formula $A\: B$
10162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10165 \begin_layout Standard
10166 \begin_inset Formula $A\; B$
10174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10177 \begin_layout Standard
10178 \begin_inset Formula $A\quad B$
10186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10189 \begin_layout Standard
10190 \begin_inset Formula $A\qquad B$
10198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10201 \begin_layout Standard
10202 \begin_inset Formula $A\! B$
10218 \begin_layout Standard
10219 The last size seem to produce no space.
10220 It is displayed red in LyX contrary to the other sizes, because it is a
10222 There are two more negative spaces:
10225 \begin_layout Standard
10227 \begin_inset Tabular
10228 <lyxtabular version="3" rows="3" columns="3">
10230 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
10231 <column alignment="center" valignment="top" leftline="true" width="0pt">
10232 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
10233 <row topline="true" bottomline="true">
10234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10237 \begin_layout Standard
10243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10246 \begin_layout Standard
10254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10257 \begin_layout Standard
10266 <row bottomline="true">
10267 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10270 \begin_layout Standard
10275 keystrokes after inserting the protected space
10280 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10283 \begin_layout Standard
10289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10292 \begin_layout Standard
10299 <row bottomline="true">
10300 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10303 \begin_layout Standard
10309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10312 \begin_layout Standard
10313 \begin_inset Formula $A\negmedspace B$
10321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10324 \begin_layout Standard
10325 \begin_inset Formula $A\negthickspace B$
10341 \begin_layout Standard
10342 Negative spaces can lead to characters overlapping each other.
10343 Thus they can be used to enforce ligatures, what is e.\InsetSpace \thinspace{}
10345 useful for summation
10349 \begin_layout Standard
10351 \begin_inset Tabular
10352 <lyxtabular version="3" rows="3" columns="2">
10354 <column alignment="center" valignment="top" leftline="true" width="0">
10355 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10356 <row topline="true" bottomline="true">
10357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10360 \begin_layout Standard
10366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10369 \begin_layout Standard
10371 \begin_inset Note Note
10374 \begin_layout Standard
10381 is only used as spacer.
10392 <row topline="true">
10393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10396 \begin_layout Standard
10405 \begin_layout Standard
10419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10422 \begin_layout Standard
10423 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10432 <row topline="true" bottomline="true">
10433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10436 \begin_layout Standard
10447 \begin_layout Standard
10461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10464 \begin_layout Standard
10465 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10481 \begin_layout Standard
10482 Relations like for example equal signs, are always surrounded by space.
10483 To suppress this, the equal sign is placed into a TeX-brace.
10484 The following example demonstrates this:
10487 \begin_layout Standard
10489 \begin_inset Tabular
10490 <lyxtabular version="3" rows="2" 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" leftline="true" usebox="none">
10498 \begin_layout Standard
10504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10507 \begin_layout Standard
10508 \begin_inset Formula $A=B$
10518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10521 \begin_layout Standard
10522 \begin_inset Note Note
10525 \begin_layout Standard
10532 is only used as spacer.
10538 \begin_inset Formula $\raisebox{5mm}{}$
10541 equation without space
10546 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" usebox="none">
10549 \begin_layout Standard
10550 \begin_inset Formula $A{=}B$
10566 \begin_layout Standard
10568 The command for the last formula is:
10573 \begin_inset Formula $\to$
10579 \begin_layout Standard
10580 \begin_inset VSpace bigskip
10583 Spaces are needed for physical units, because the space between the value
10584 and the unit is the smallest one and not a normal space.
10585 For units in text, the smallest space is inserted via the menu
10587 Insert\SpecialChar \menuseparator
10588 Formatting\SpecialChar \menuseparator
10599 \begin_layout Standard
10600 An example to visualize the difference:
10603 \begin_layout Standard
10604 \begin_inset Tabular
10605 <lyxtabular version="3" rows="2" columns="2">
10607 <column alignment="left" valignment="top" width="0">
10608 <column alignment="left" valignment="top" width="0">
10610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10613 \begin_layout Standard
10615 \begin_inset Formula $\cdot$
10623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10626 \begin_layout Standard
10627 space between value and unit
10634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10637 \begin_layout Standard
10638 24\InsetSpace \thinspace{}
10640 \begin_inset Formula $\cdot$
10648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10651 \begin_layout Standard
10652 smallest space between value and unit
10665 \begin_layout Subsection
10670 \begin_layout Standard
10683 \begin_layout Standard
10684 for vertical space in formulas see
10685 \begin_inset LatexCommand ref
10686 reference "sub:Line-Separation"
10699 \begin_layout Standard
10707 \begin_inset Note Note
10710 \begin_layout Standard
10713 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
10716 \begin_layout Standard
10719 texorpdfstring is in section
10720 \begin_inset LatexCommand ref
10721 reference "sub:Formulas-in-Section"
10731 \begin_inset LatexCommand label
10732 name "sub:Variable-Space"
10737 \begin_inset LatexCommand index
10738 name "Space ! horizontal ! variable"
10745 \begin_layout Standard
10746 Space with a defined length can be inserted in LyX with the command
10755 \begin_inset LatexCommand index
10756 name "Commands ! H ! \\textbackslash hspace"
10761 For the length all units listed in
10762 \begin_inset LatexCommand ref
10763 reference "tab:Used-units"
10767 are allowed, except of the unit
10768 \begin_inset Quotes eld
10772 \begin_inset Quotes erd
10776 The length may also be negative.
10777 To insert so many space that the formula uses all available space, the
10785 \begin_inset LatexCommand index
10786 name "Commands ! H ! \\textbackslash hfill"
10793 \begin_layout Standard
10794 \begin_inset VSpace -1mm
10800 \begin_layout Standard
10802 \begin_inset Tabular
10803 <lyxtabular version="3" rows="4" columns="2">
10805 <column alignment="center" valignment="top" leftline="true" width="0">
10806 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10807 <row topline="true" bottomline="true">
10808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10811 \begin_layout Standard
10817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10820 \begin_layout Standard
10827 <row topline="true">
10828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10831 \begin_layout Standard
10835 \begin_inset Formula $\to$
10845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10848 \begin_layout Standard
10849 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
10858 <row topline="true" bottomline="true">
10859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10862 \begin_layout Standard
10866 \begin_inset Formula $\to$
10876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10879 \begin_layout Standard
10880 \begin_inset Formula $A\hspace{-1mm}A\not=A$
10889 <row topline="true" bottomline="true">
10890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10893 \begin_layout Standard
10900 \begin_layout Standard
10914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10917 \begin_layout Standard
10918 \begin_inset Formula $A=A\hfill B=B$
10934 \begin_layout Standard
10935 In the last example the available space is given by the longest column entry
10937 In an inline formula the space depends on the length of the line in which
10945 Thus, when the line uses the full width, no space will be created.
10952 has only an effect on displayed formulas when the formula style
10957 (Formula styles are explained in
10958 \begin_inset LatexCommand ref
10959 reference "sec:Formula-Styles"
10966 \begin_layout Standard
10979 can also be inserted in TeX-mode to use them for text:
10982 \begin_layout Standard
10983 This is a line with
10987 \begin_layout Standard
10996 2\InsetSpace \thinspace{}
11000 \begin_layout Standard
11001 This is a line with
11006 \begin_layout Standard
11007 In the last example
11013 was inserted via the menu
11015 Insert\SpecialChar \menuseparator
11016 Formatting\SpecialChar \menuseparator
11017 Horizontal\InsetSpace ~
11020 , what is not possible in formulas.
11021 This has the advantage that one can directly see in LyX that this is a
11025 \begin_layout Standard
11026 When the commands are at the begin of a text line but not at the beginning
11027 of a paragraph, they will be ignored by LaTeX.
11028 To avoid that, the command
11041 To get the same with
11047 , a line break and an empty placeholder
11053 \begin_layout Standard
11054 for placeholders see
11055 \begin_inset LatexCommand ref
11056 reference "sub:Placeholders"
11067 is inserted in TeX-mode with the command
11083 \begin_layout Subsection
11084 Space besides inline Formulas
11085 \begin_inset LatexCommand index
11086 name "Space ! besides inline formulas"
11093 \begin_layout Standard
11094 The space that surrounds inline formulas can be adjusted with the length
11100 \begin_inset LatexCommand index
11101 name "Commands ! M ! \\textbackslash mathsurround"
11108 The value of a length is set with the command
11113 \begin_inset LatexCommand index
11114 name "Commands ! S ! \\textbackslash setlength"
11120 that has the following scheme:
11123 \begin_layout Standard
11128 setlength{length name}{value}
11131 \begin_layout Standard
11138 to the value 5\InsetSpace \thinspace{}
11142 \begin_layout Standard
11152 \begin_layout Standard
11153 is inserted in TeX-mode.
11154 5\InsetSpace \thinspace{}
11155 mm space will now be set around all inline formulas:
11159 \begin_layout Standard
11173 \begin_layout Standard
11174 This is a line with an inline formula
11175 \begin_inset Formula $A=B$
11178 with 5\InsetSpace \thinspace{}
11179 mm surrounding space.
11183 \begin_layout Standard
11197 \begin_layout Standard
11198 To return to the predefined value,
11204 is set to the value 0\InsetSpace \thinspace{}
11208 \begin_layout Section
11210 \begin_inset LatexCommand index
11216 \begin_inset LatexCommand index
11217 name "Frames | see {Boxes}"
11224 \begin_layout Standard
11225 Boxes for text are described in chapter
11231 Embedded\InsetSpace ~
11237 \begin_layout Subsection
11239 \begin_inset LatexCommand label
11240 name "sub:Boxes-with-Frame"
11245 \begin_inset LatexCommand index
11246 name "Boxes ! with frame"
11253 \begin_layout Standard
11254 It is possible to frame formulas or parts of it with the commands
11261 \begin_inset LatexCommand index
11262 name "Commands ! F ! \\textbackslash fbox"
11273 \begin_inset LatexCommand index
11274 name "Commands ! B ! \\textbackslash boxed"
11281 \begin_layout Standard
11282 When one of these commands is inserted to a formula, a blue box appears
11283 within a frame to enter formula parts.
11290 an additional formula has to be created by
11298 \begin_layout Standard
11299 Due to a bug in LyX it is not possible to create a new formula with
11307 \begin_layout Standard
11311 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11320 \begin_layout Standard
11332 , because the box content will otherwise be treated as mathematical text.
11339 is used, a new formula is automatically created inside the frame.
11342 \begin_layout Standard
11349 is not suitable to frame displayed formulas, because the formula will always
11350 be set in the size of the text.
11357 is in contrary not suitable to frame inline formulas, because the formula
11358 will always be set in the size of a displayed formula.
11361 \begin_layout Standard
11368 there is the command
11375 \begin_inset LatexCommand index
11376 name "Commands ! F ! \\textbackslash framebox"
11380 where additionally the frame width and the alignment can be specified.
11387 is used in the following scheme:
11390 \begin_layout Standard
11395 framebox[frame width][position]{box content}
11398 \begin_layout Standard
11399 The position can either be
11416 right aligns the formula in the box.
11417 When no position is given, the formula will be centered.
11420 also no position can be given.
11421 In this case the frame width is adjusted to the box content like for
11430 \begin_layout Standard
11437 is inserted, a box appears containing three blue boxes.
11438 The first two boxes are surrounded by brackets and denote the two optional
11440 The third box is for formula parts like for
11449 \begin_layout Standard
11451 \begin_inset Note Note
11454 \begin_layout Standard
11455 The table has been set into a minipage to make the footnote appearing.
11456 Otherwise the footnote text would not be displayed.
11462 \begin_inset Box Frameless
11471 height_special "totalheight"
11474 \begin_layout Standard
11476 \begin_inset Tabular
11477 <lyxtabular version="3" rows="5" columns="2">
11479 <column alignment="center" valignment="top" leftline="true" width="0">
11480 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
11481 <row topline="true" bottomline="true">
11482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11485 \begin_layout Standard
11490 \begin_layout Standard
11491 Due to a bug in LyX it is not possible to create a new formula with
11499 \begin_layout Standard
11503 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11512 \begin_layout Standard
11529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11532 \begin_layout Standard
11534 \begin_inset Note Note
11537 \begin_layout Standard
11544 is only used as spacer.
11555 <row topline="true">
11556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11559 \begin_layout Standard
11566 \begin_layout Standard
11585 \begin_layout Standard
11599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11602 \begin_layout Standard
11603 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
11613 <row topline="true">
11614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11617 \begin_layout Standard
11624 \begin_layout Standard
11639 \begin_layout Standard
11653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11656 \begin_layout Standard
11657 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
11666 <row topline="true">
11667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11670 \begin_layout Standard
11677 \begin_layout Standard
11691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11694 \begin_layout Standard
11695 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
11704 <row topline="true" bottomline="true">
11705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11708 \begin_layout Standard
11715 \begin_layout Standard
11725 \begin_inset Formula $\to$
11729 \begin_inset Formula $\to$
11742 \begin_layout Standard
11752 \begin_inset Formula $\downarrow$
11760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11763 \begin_layout Standard
11764 \begin_inset Formula $\raisebox{6mm}{}$
11768 \begin_inset Formula $\framebox[20mm]{$\frac{A}{B}$}$
11772 \begin_inset Formula $\raisebox{-4mm}{}$
11793 \begin_layout Standard
11794 The frame thickness can also be adjusted.
11795 To do this the following commands have to be inserted in TeX-mode before
11799 \begin_layout Standard
11809 \begin_inset Quotes eld
11813 \begin_inset Quotes erd
11827 \begin_inset Quotes eld
11831 \begin_inset Quotes erd
11837 \begin_layout Standard
11838 \begin_inset Quotes eld
11842 \begin_inset Quotes erd
11845 specifies the minimal distance between the frame and the first character
11847 An example for this is the following framed formula:
11851 \begin_layout Standard
11863 \begin_inset Formula \[
11868 Before this formula the commands
11871 \begin_layout Standard
11893 \begin_layout Standard
11894 were inserted in TeX-mode.
11895 The given values are used for all following boxes.
11898 \begin_layout Standard
11899 To return to the standard frame size, the command
11902 \begin_layout Standard
11927 \begin_layout Standard
11941 \begin_layout Standard
11942 is inserted in TeX-mode before the next formula.
11945 \begin_layout Subsection
11946 Boxes without Frame
11947 \begin_inset LatexCommand label
11948 name "sub:Boxes-without-Frame"
11953 \begin_inset LatexCommand index
11954 name "Boxes ! without frame"
11961 \begin_layout Standard
11962 For boxes without a frame there are the following box commands:
11969 \begin_inset LatexCommand index
11970 name "Commands ! M ! \\textbackslash mbox"
11981 \begin_inset LatexCommand index
11982 name "Commands ! M ! \\textbackslash makebox"
11993 \begin_inset LatexCommand index
11994 name "Commands ! R ! \\textbackslash raisebox"
12001 \begin_layout Standard
12008 a box can be super- or subscripted.
12009 But in contrary to normal super- and subscripting, the characters in the
12010 box keep their font size.
12017 is used in the following scheme:
12020 \begin_layout Standard
12025 raisebox{height}{box content}
12028 \begin_layout Standard
12029 When the box should contain a formula, an extra formula is needed like for
12039 \begin_layout Standard
12041 \begin_inset Tabular
12042 <lyxtabular version="3" rows="4" columns="2">
12044 <column alignment="center" valignment="top" leftline="true" width="0">
12045 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12046 <row topline="true" bottomline="true">
12047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12050 \begin_layout Standard
12056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12059 \begin_layout Standard
12066 <row topline="true">
12067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12070 \begin_layout Standard
12074 \begin_inset Formula $\to$
12080 \begin_inset Formula $\to$
12088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12091 \begin_layout Standard
12092 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12101 <row topline="true" bottomline="true">
12102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12105 \begin_layout Standard
12109 \begin_inset Formula $\to$
12115 \begin_inset Formula $\to$
12123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12126 \begin_layout Standard
12127 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12136 <row topline="true" bottomline="true">
12137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12140 \begin_layout Standard
12144 \begin_inset Formula $\to$
12159 \begin_layout Standard
12173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12176 \begin_layout Standard
12180 \begin_layout Standard
12204 \begin_layout Standard
12205 The last formula can currently only be created using TeX-mode because LyX
12206 inserts a box instead of the needed extra formula.
12210 \begin_layout Standard
12215 \begin_layout Standard
12219 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12228 \begin_layout Standard
12243 \begin_layout Standard
12268 , with the difference that there is no frame.
12271 \begin_layout Subsection
12273 \begin_inset LatexCommand label
12274 name "sub:Colored-Boxes"
12279 \begin_inset LatexCommand index
12280 name "Boxes ! colored"
12287 \begin_layout Standard
12288 To be able to use all commands explained in this section, the LaTeX-package
12297 \begin_layout Standard
12302 is part of every LaTeX standard installation.
12308 \begin_inset LatexCommand index
12309 name "Packages ! color"
12313 has to be loaded in the LaTeX-preamble with the line
12317 \begin_layout Standard
12318 When text is colored somewhere in the document with a predefined color,
12319 LyX loads the LaTeX-package
12324 Thus it is possible that the package is loaded twice, but this doesn't
12331 \begin_inset Note Note
12334 \begin_layout Standard
12335 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12344 \begin_layout Standard
12352 \begin_layout Standard
12353 \begin_inset VSpace medskip
12356 To color boxes, the command
12363 \begin_inset LatexCommand index
12364 name "Commands ! C ! \\textbackslash colorbox"
12368 is used in the following scheme:
12371 \begin_layout Standard
12376 colorbox{color}{box content}
12379 \begin_layout Standard
12380 The box content can also be a box and a
12386 can also be part of another box (see the 2nd and 3rd example).
12387 When the box should contain a formula, an extra formula has to be created,
12398 \begin_layout Standard
12399 This also applies for the command
12410 \begin_layout Standard
12414 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12423 \begin_layout Standard
12438 \begin_layout Standard
12439 One of the following predefined colors can be chosen:
12442 \begin_layout Standard
12476 \begin_layout Standard
12478 \begin_inset Tabular
12479 <lyxtabular version="3" rows="4" columns="2">
12481 <column alignment="center" valignment="top" leftline="true" width="0">
12482 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12483 <row topline="true" bottomline="true">
12484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12487 \begin_layout Standard
12493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12496 \begin_layout Standard
12498 \begin_inset Note Note
12501 \begin_layout Standard
12508 is only used as spacer.
12519 <row topline="true">
12520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12523 \begin_layout Standard
12527 \begin_inset Formula $\to$
12537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12540 \begin_layout Standard
12541 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12550 <row topline="true">
12551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12554 \begin_layout Standard
12558 \begin_inset Formula $\to$
12569 \begin_layout Standard
12583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12586 \begin_layout Standard
12587 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
12596 <row topline="true" bottomline="true">
12597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12600 \begin_layout Standard
12607 \begin_layout Standard
12619 \begin_inset Formula $\to$
12629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12632 \begin_layout Standard
12633 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
12649 \begin_layout Standard
12656 only colors the box but not the characters in the box.
12657 To color all characters, the whole formula is highlighted and the wanted
12658 color is chosen in the
12664 The dialog can be called with the toolbar button
12665 \begin_inset Graphics
12666 filename ../images/dialog-show_character.png
12673 Edit\SpecialChar \menuseparator
12675 Style\SpecialChar \menuseparator
12679 The formula number has then the same color as the formula.
12680 When the formula number should get another color than the formula characters,
12681 the color must be changed within the formula.
12684 \begin_layout Standard
12688 \begin_layout Standard
12691 \begin_inset Formula \begin{equation}
12692 \int A=B\label{eq:red}\end{equation}
12699 \begin_inset Formula \begin{equation}
12700 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
12707 \begin_layout Standard
12709 \begin_inset LatexCommand eqref
12714 is completely colored red.
12717 \begin_inset LatexCommand eqref
12718 reference "eq:redgreen"
12722 was first completely colored green to set the color for the formula number.
12723 Subsequently the formula characters were colored red.
12726 \begin_layout Standard
12727 \begin_inset VSpace bigskip
12730 To color the frame different than the rest of the box, the command
12737 \begin_inset LatexCommand index
12738 name "Commands ! F ! \\textbackslash fcolorbox"
12742 is used in the following scheme:
12745 \begin_layout Standard
12750 fcolorbox{frame color}{color}{box content}
12753 \begin_layout Standard
12760 is an extension of the command
12767 The frame width is set, like for
12790 \begin_layout Standard
12802 \begin_inset Formula \[
12803 \fcolorbox{cyan}{magenta}{A=B}\]
12811 \begin_layout Standard
12825 \begin_layout Standard
12826 This formula was created with the command
12833 \begin_inset Formula $\to$
12839 \begin_inset Formula $\to$
12849 \begin_layout Standard
12850 \begin_inset VSpace bigskip
12853 To use other colors than the predefined ones, they have to be defined first.
12856 \begin_layout Standard
12857 One can for example define the color
12858 \begin_inset Quotes eld
12866 \begin_inset Quotes erd
12869 with the LaTeX-preamble line:
12872 \begin_layout Standard
12877 definecolor{darkgreen}{cmyk}{0.5,
12892 \begin_inset LatexCommand index
12893 name "Commands ! D ! \\textbackslash definecolor"
12900 \begin_layout Standard
12905 is the color space that denotes the colors
12922 The four comma separated numbers are the portion factor for the corresponding
12923 colors of the color space.
12924 The factors can be in the range of 0\InsetSpace \thinspace{}
12925 -\InsetSpace \thinspace{}
12931 also the color space
12935 can be used for definitions.
12952 , so that there are in this case three portion factors for the corresponding
12954 Furthermore there is the color space
12958 with one portion factor for the gray value.
12961 \begin_layout Standard
12962 As example a framed box with the new defined color
12966 where the characters have been colored
12971 \begin_inset Formula \begin{equation}
12972 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
12979 \begin_layout Standard
12980 Self-defined colors can also be used for text with the help of the command
12988 \begin_inset LatexCommand index
12989 name "Text ! colored"
12996 \begin_layout Standard
13000 \begin_layout Standard
13004 textcolor{darkgreen}{
13010 \begin_inset Quotes eld
13014 \begin_inset Quotes erd
13021 \begin_layout Standard
13031 \begin_layout Standard
13039 \begin_inset LatexCommand index
13040 name "Commands ! T ! \\textbackslash textcolor"
13044 is used in the scheme
13048 textcolor{color}{characters to color}
13053 \begin_layout Subsection
13055 \begin_inset LatexCommand label
13056 name "sub:Paragraph-Boxes"
13061 \begin_inset LatexCommand index
13062 name "Boxes ! as paragraph"
13069 \begin_layout Standard
13070 A box that can contain several lines and paragraphs, a so called paragraph
13071 box (parbox), can be created with the menu
13073 Insert\SpecialChar \menuseparator
13076 or the toolbar button
13077 \begin_inset Graphics
13078 filename ../images/box-insert.png
13086 \begin_layout Standard
13087 The following example shows a framed parbox in a line:
13090 \begin_layout Standard
13091 \begin_inset VSpace medskip
13095 \begin_inset Box Boxed
13104 height_special "totalheight"
13107 \begin_layout Standard
13108 This is a paragraph box.
13109 It is exactly 5\InsetSpace \thinspace{}
13110 cm long and can also contain formulas:
13111 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13122 \begin_layout Standard
13123 \begin_inset VSpace medskip
13129 \begin_layout Standard
13130 Such a box is created by right-clicking on the gray box inset.
13131 A dialog pops up showing the box properties.
13144 : 5\InsetSpace \thinspace{}
13147 Vertical Box Alignment
13152 \begin_layout Standard
13153 \begin_inset VSpace medskip
13156 In LaTeX a parbox is created with the command
13163 \begin_inset LatexCommand index
13164 name "Commands ! P ! \\textbackslash parbox"
13168 that has the following scheme:
13171 \begin_layout Standard
13176 parbox[position]{width}{box content}
13179 \begin_layout Standard
13193 for bottom means that the box is aligned within the surrounding text with
13199 for top this is done with the first line.
13200 When no position is given, the box will be vertically centered, see section
13207 Embedded\InsetSpace ~
13210 manual for examples.
13213 \begin_layout Standard
13214 \begin_inset VSpace bigskip
13217 To frame formulas completely, including the formula number, the formula
13218 must be set into a parbox.
13219 To do this, the command
13233 is inserted in TeX-mode before the formula.
13239 \begin_inset LatexCommand index
13240 name "Commands ! L ! \\textbackslash linewidth"
13246 is hereby the line width set for the document.
13247 Because the frame is outside the parbox, 2\InsetSpace \thinspace{}
13248 times the frame separation and
13249 the frame thickness must be subtracted from the line width.
13250 As this is not automatically done by LyX due to a bug
13254 \begin_layout Standard
13258 \begin_layout Standard
13262 href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
13271 \begin_layout Standard
13283 , TeX-mode has to be used.
13284 To be able to multiply and subtract in arguments, the LaTeX-package
13292 \begin_layout Standard
13297 is part of every LaTeX standard installation.
13303 \begin_inset LatexCommand index
13304 name "Packages ! calc"
13308 must be loaded in the LaTeX-preamble with the line
13311 \begin_layout Standard
13319 \begin_layout Standard
13320 Behind the formula both boxes are closed by entering
13325 Here is an example:
13329 \begin_layout Standard
13343 \begin_layout Standard
13347 \begin_layout Standard
13365 \begin_inset Formula \begin{equation}
13366 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
13374 \begin_layout Standard
13385 \begin_layout Standard
13399 \begin_layout Standard
13400 \begin_inset VSpace medskip
13403 As a parbox is used as argument of
13409 , there is in this case no difference between
13424 \begin_layout Standard
13425 \begin_inset VSpace bigskip
13428 Paragraph boxes are very useful to comment formulas directly.
13435 is used in combination with the command
13449 \begin_inset LatexCommand ref
13450 reference "sub:User-defined-Numbering"
13457 \begin_layout Standard
13458 An example of a formula commented with
13467 \begin_layout Standard
13471 \begin_layout Standard
13484 This is a description.
13485 It is distinctly separated from the formula and multiline.
13489 \begin_layout Standard
13501 \begin_layout Standard
13502 Such a formula must be inserted completely in TeX-mode because LyX does
13503 not yet support the command
13510 The formula is created with the following command sequence:
13513 \begin_layout Standard
13526 is inserted in TeX-mode.
13530 \begin_layout Standard
13531 When the formula style
13543 can also be replaced by
13550 (formula styles see
13551 \begin_inset LatexCommand ref
13552 reference "sec:Formula-Styles"
13561 Then the description follows as normal text, and finally
13567 is inserted in TeX-mode.
13580 hereby create a displayed formula.
13583 \begin_layout Standard
13590 can be seen in this example that was
13591 \begin_inset Quotes eld
13595 \begin_inset Quotes erd
13598 using the mathematical textmode:
13599 \begin_inset Formula \[
13600 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
13607 \begin_layout Section
13609 \begin_inset LatexCommand index
13617 \begin_layout Subsection
13619 \begin_inset LatexCommand label
13620 name "sub:Big-Operators"
13625 \begin_inset LatexCommand index
13626 name "Operators ! big"
13631 \begin_inset LatexCommand index
13637 \begin_inset LatexCommand index
13645 \begin_layout Standard
13646 To be able to use all integral operators listed here, the option
13648 Use esint package automatically
13650 must be set in the document settings under
13658 \begin_layout Standard
13662 \begin_inset Tabular
13663 <lyxtabular version="3" rows="11" columns="2">
13665 <column alignment="center" valignment="top" leftline="true" width="0pt">
13666 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13667 <row topline="true" bottomline="true">
13668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13671 \begin_layout Standard
13677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13680 \begin_layout Standard
13687 <row topline="true">
13688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13691 \begin_layout Standard
13695 \begin_inset LatexCommand index
13696 name "Commands ! S ! \\textbackslash sum"
13705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13708 \begin_layout Standard
13709 \begin_inset Formula $\sum$
13718 <row topline="true">
13719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13722 \begin_layout Standard
13726 \begin_inset LatexCommand index
13727 name "Commands ! I ! \\textbackslash int"
13736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13739 \begin_layout Standard
13740 \begin_inset Formula $\int$
13749 <row topline="true">
13750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13753 \begin_layout Standard
13761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13764 \begin_layout Standard
13765 \begin_inset Formula $\intop$
13774 <row topline="true">
13775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13778 \begin_layout Standard
13786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13789 \begin_layout Standard
13790 \begin_inset Formula $\oint$
13799 <row topline="true">
13800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13803 \begin_layout Standard
13811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13814 \begin_layout Standard
13815 \begin_inset Formula $\ointop$
13824 <row topline="true">
13825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13828 \begin_layout Standard
13836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13839 \begin_layout Standard
13840 \begin_inset Formula $\ointctrclockwise$
13849 <row topline="true">
13850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13853 \begin_layout Standard
13861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13864 \begin_layout Standard
13865 \begin_inset Formula $\ointclockwise$
13874 <row topline="true">
13875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13878 \begin_layout Standard
13886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13889 \begin_layout Standard
13890 \begin_inset Formula $\sqint$
13899 <row topline="true">
13900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13903 \begin_layout Standard
13911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13914 \begin_layout Standard
13915 \begin_inset Formula $\bigcap$
13924 <row topline="true" bottomline="true">
13925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13928 \begin_layout Standard
13936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13939 \begin_layout Standard
13940 \begin_inset Formula $\bigcup$
13956 \begin_inset Tabular
13957 <lyxtabular version="3" rows="10" columns="2">
13959 <column alignment="center" valignment="top" leftline="true" width="0pt">
13960 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13961 <row topline="true" bottomline="true">
13962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13965 \begin_layout Standard
13971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13974 \begin_layout Standard
13981 <row topline="true">
13982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13985 \begin_layout Standard
13989 \begin_inset LatexCommand index
13990 name "Commands ! P ! \\textbackslash prod"
13999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14002 \begin_layout Standard
14003 \begin_inset Formula $\prod$
14012 <row topline="true">
14013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14016 \begin_layout Standard
14024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14027 \begin_layout Standard
14028 \begin_inset Formula $\coprod$
14037 <row topline="true">
14038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14041 \begin_layout Standard
14049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14052 \begin_layout Standard
14053 \begin_inset Formula $\bigodot$
14062 <row topline="true">
14063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14066 \begin_layout Standard
14074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14077 \begin_layout Standard
14078 \begin_inset Formula $\bigotimes$
14087 <row topline="true">
14088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14091 \begin_layout Standard
14099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14102 \begin_layout Standard
14103 \begin_inset Formula $\bigoplus$
14112 <row topline="true">
14113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14116 \begin_layout Standard
14124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14127 \begin_layout Standard
14128 \begin_inset Formula $\bigwedge$
14137 <row topline="true">
14138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14141 \begin_layout Standard
14149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14152 \begin_layout Standard
14153 \begin_inset Formula $\bigvee$
14162 <row topline="true">
14163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14166 \begin_layout Standard
14174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14177 \begin_layout Standard
14178 \begin_inset Formula $\bigsqcup$
14187 <row topline="true" bottomline="true">
14188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14191 \begin_layout Standard
14199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14202 \begin_layout Standard
14203 \begin_inset Formula $\biguplus$
14221 \begin_layout Standard
14222 All big operators can also be inserted via the math toolbar button
14223 \begin_inset Graphics
14224 filename ../images/math/intop.png
14232 \begin_layout Standard
14233 The operators are called big because they are bigger than the sometimes
14234 equal looking binary operators.
14235 All big operators can have limits as described in the next subsection.
14238 \begin_layout Standard
14263 , resp.\InsetSpace ~
14264 in the style the operator limits are displayed, see
14265 \begin_inset LatexCommand ref
14266 reference "sub:Operator-Limits"
14274 \begin_layout Subsubsection*
14275 Advices for Integrals
14278 \begin_layout Standard
14283 in an integral is an operator, that therefore has to be set upright.
14284 This is done by highlighting the
14288 and using the keyboard shortcut
14297 \begin_layout Standard
14303 \begin_inset LatexCommand ref
14304 reference "sub:Font-Styles"
14314 Finally the smallest space is inserted before the
14318 , as this is usual for operators.
14322 \begin_layout Standard
14324 \begin_inset Formula $\int A(x)dx$
14333 \begin_layout Standard
14343 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14349 \begin_layout Standard
14350 For multiple integrals there are the following commands:
14351 \begin_inset VSpace medskip
14357 \begin_layout Standard
14361 \begin_inset Tabular
14362 <lyxtabular version="3" rows="4" columns="2">
14364 <column alignment="center" valignment="top" leftline="true" width="0">
14365 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14366 <row topline="true" bottomline="true">
14367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14370 \begin_layout Standard
14376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14379 \begin_layout Standard
14381 \begin_inset Note Note
14384 \begin_layout Standard
14391 is only used as spacer.
14402 <row topline="true">
14403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14406 \begin_layout Standard
14414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14417 \begin_layout Standard
14418 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
14427 <row topline="true">
14428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14431 \begin_layout Standard
14439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14442 \begin_layout Standard
14443 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
14452 <row topline="true" bottomline="true">
14453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14456 \begin_layout Standard
14464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14467 \begin_layout Standard
14468 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
14484 \begin_inset Tabular
14485 <lyxtabular version="3" rows="4" columns="2">
14487 <column alignment="center" valignment="top" leftline="true" width="0">
14488 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14489 <row topline="true" bottomline="true">
14490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14493 \begin_layout Standard
14499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14502 \begin_layout Standard
14509 <row topline="true">
14510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14513 \begin_layout Standard
14521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14524 \begin_layout Standard
14525 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
14534 <row topline="true">
14535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14538 \begin_layout Standard
14546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14549 \begin_layout Standard
14550 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
14559 <row topline="true" bottomline="true">
14560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14563 \begin_layout Standard
14571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14574 \begin_layout Standard
14575 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
14593 \begin_layout Subsection
14595 \begin_inset LatexCommand label
14596 name "sub:Operator-Limits"
14601 \begin_inset LatexCommand index
14602 name "Operators ! Limits"
14609 \begin_layout Standard
14610 Limits are created by super- and subscripts:
14613 \begin_layout Standard
14615 \begin_inset Tabular
14616 <lyxtabular version="3" rows="2" columns="2">
14618 <column alignment="center" valignment="top" leftline="true" width="0pt">
14619 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
14620 <row topline="true" bottomline="true">
14621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14624 \begin_layout Standard
14630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14633 \begin_layout Standard
14635 \begin_inset Note Note
14638 \begin_layout Standard
14645 is only used as spacer.
14656 <row topline="true" bottomline="true">
14657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14660 \begin_layout Standard
14669 \begin_layout Standard
14679 \begin_inset Formula $\to$
14683 \begin_inset Formula $\to$
14691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14694 \begin_layout Standard
14695 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
14711 \begin_layout Standard
14712 Limits of inline formulas are set right beside the operator.
14713 Limits in displayed formulas are set above or below the operator, except
14714 of integral limits.
14717 \begin_layout Standard
14718 To force that the limits are set beside the operator, the cursor is set
14719 directly behind the operator and the limits type is changed with the menu
14722 Edit\SpecialChar \menuseparator
14723 Math\SpecialChar \menuseparator
14741 \begin_layout Standard
14742 The default limits type is this:
14743 \begin_inset Formula \[
14744 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
14748 This is how it looks when the limits type was changed to
14755 \begin_inset Formula \[
14756 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
14760 For integrals, except of
14772 , the limits are by default set beside the operator.
14773 But for multiple integrals the limits are often set below the operator.
14774 In the following example the limits type was therefore set to
14778 and so set below the integrals:
14779 \begin_inset Formula \begin{equation}
14780 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
14787 \begin_layout Standard
14788 \begin_inset VSpace medskip
14791 To specify conditions for limits, the commands
14798 \begin_inset LatexCommand index
14799 name "Commands ! S ! \\textbackslash subarray"
14810 \begin_inset LatexCommand index
14811 name "Commands ! S ! \\textbackslash substack"
14816 To create for example this expression
14817 \begin_inset Formula \begin{equation}
14818 \sum_{\begin{subarray}{c}
14820 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
14827 \begin_layout Standard
14828 the following has to be done:
14842 \begin_layout Standard
14854 One is now in a blue box under the summation operator and insert there
14863 \begin_layout Standard
14875 The blue box is now within a purple box and now several lines can be written
14877 A new line is created by inserting a line break (
14886 0<k<1000 Ctrl-Return
14890 is typed in, a new box appears below for the new line.
14893 \begin_layout Standard
14894 The alignment of the lines can be changed to left aligned with the
14904 Edit\SpecialChar \menuseparator
14908 To get right alignment,
14916 \begin_layout Standard
14927 is inserted at the beginning of the line.
14930 \begin_layout Standard
14943 with the difference that the lines are always centered.
14946 \begin_layout Standard
14947 \begin_inset VSpace bigskip
14951 \begin_inset LatexCommand eqref
14952 reference "eq:substack"
14956 there can be too much space beside an operator, because the characters
14957 following the operator are set beside the limits.
14960 \begin_layout Standard
14961 To avoid this, the following macro can be used in the LaTeX-preamble:
14964 \begin_layout Standard
14993 mathclapinternal #1#2{
14997 mathsurround =0pt #1{#2}$}}
15000 \begin_layout Standard
15001 This defines the command
15008 \begin_inset LatexCommand index
15009 name "Commands ! M ! \\textbackslash mathclap"
15013 that sets the width of the limit to 0\InsetSpace \thinspace{}
15015 The command scheme is
15018 \begin_layout Standard
15026 \begin_layout Standard
15027 where the limit can consist of several conditions.
15030 \begin_layout Standard
15032 \begin_inset LatexCommand eqref
15033 reference "eq:substack"
15037 , one uses the command
15040 \begin_layout Standard
15053 \begin_layout Standard
15062 0<k<1000 Ctrl-Enter
15065 \begin_layout Standard
15066 to create the lower limit.
15067 The summand is now directly behind the summation operator:
15068 \begin_inset Formula \[
15069 \sum_{\mathclap{\substack{0<k<1000\\
15070 \\k\,\in\,\mathbb{N}}
15078 \begin_layout Standard
15079 \begin_inset VSpace bigskip
15082 How to use one limit for several operators is described in
15083 \begin_inset LatexCommand ref
15084 reference "sub:Self-defined-Operators"
15091 \begin_layout Subsection
15093 \begin_inset LatexCommand label
15094 name "sub:Binary-Operators"
15099 \begin_inset LatexCommand index
15100 name "Operators ! binary"
15107 \begin_layout Standard
15108 Binary operators are surrounded by space when there is a character before
15110 \begin_inset VSpace medskip
15116 \begin_layout Standard
15120 \begin_inset Tabular
15121 <lyxtabular version="3" rows="13" columns="2">
15123 <column alignment="center" valignment="top" leftline="true" width="0pt">
15124 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15125 <row topline="true" bottomline="true">
15126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15129 \begin_layout Standard
15131 \begin_inset Note Note
15134 \begin_layout Standard
15141 is only used as spacer.
15151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15154 \begin_layout Standard
15161 <row topline="true">
15162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15165 \begin_layout Standard
15171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15174 \begin_layout Standard
15175 \begin_inset Formula $+$
15184 <row topline="true">
15185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15188 \begin_layout Standard
15194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15197 \begin_layout Standard
15198 \begin_inset Formula $-$
15207 <row topline="true">
15208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15211 \begin_layout Standard
15219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15222 \begin_layout Standard
15223 \begin_inset Formula $\pm$
15232 <row topline="true">
15233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15236 \begin_layout Standard
15244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15247 \begin_layout Standard
15248 \begin_inset Formula $\mp$
15257 <row topline="true">
15258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15261 \begin_layout Standard
15269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15272 \begin_layout Standard
15273 \begin_inset Formula $\cdot$
15282 <row topline="true">
15283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15286 \begin_layout Standard
15294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15297 \begin_layout Standard
15298 \begin_inset Formula $\times$
15307 <row topline="true">
15308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15311 \begin_layout Standard
15319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15322 \begin_layout Standard
15323 \begin_inset Formula $\div$
15332 <row topline="true">
15333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15336 \begin_layout Standard
15340 \begin_layout Standard
15353 \begin_layout Standard
15365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15368 \begin_layout Standard
15369 \begin_inset Formula $*$
15378 <row topline="true">
15379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15382 \begin_layout Standard
15390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15393 \begin_layout Standard
15394 \begin_inset Formula $\star$
15403 <row topline="true">
15404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15407 \begin_layout Standard
15415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15418 \begin_layout Standard
15419 \begin_inset Formula $\circ$
15428 <row topline="true">
15429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15432 \begin_layout Standard
15440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15443 \begin_layout Standard
15444 \begin_inset Formula $\diamond$
15453 <row topline="true" bottomline="true">
15454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15457 \begin_layout Standard
15465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15468 \begin_layout Standard
15469 \begin_inset Formula $\bullet$
15485 \begin_inset Tabular
15486 <lyxtabular version="3" rows="13" columns="2">
15488 <column alignment="center" valignment="top" leftline="true" width="0pt">
15489 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15490 <row topline="true" bottomline="true">
15491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15494 \begin_layout Standard
15500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15503 \begin_layout Standard
15510 <row topline="true">
15511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15514 \begin_layout Standard
15522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15525 \begin_layout Standard
15526 \begin_inset Formula $\nabla$
15535 <row topline="true">
15536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15539 \begin_layout Standard
15547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15550 \begin_layout Standard
15551 \begin_inset Formula $\bigtriangledown$
15560 <row topline="true">
15561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15564 \begin_layout Standard
15572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15575 \begin_layout Standard
15576 \begin_inset Formula $\bigtriangleup$
15585 <row topline="true">
15586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15589 \begin_layout Standard
15597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15600 \begin_layout Standard
15601 \begin_inset Formula $\Box$
15610 <row topline="true">
15611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15614 \begin_layout Standard
15622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15625 \begin_layout Standard
15626 \begin_inset Formula $\cap$
15635 <row topline="true">
15636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15639 \begin_layout Standard
15647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15650 \begin_layout Standard
15651 \begin_inset Formula $\cup$
15660 <row topline="true">
15661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15664 \begin_layout Standard
15672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15675 \begin_layout Standard
15676 \begin_inset Formula $\dagger$
15685 <row topline="true">
15686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15689 \begin_layout Standard
15697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15700 \begin_layout Standard
15701 \begin_inset Formula $\ddagger$
15710 <row topline="true">
15711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15714 \begin_layout Standard
15722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15725 \begin_layout Standard
15726 \begin_inset Formula $\wr$
15735 <row topline="true">
15736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15739 \begin_layout Standard
15747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15750 \begin_layout Standard
15751 \begin_inset Formula $\bigcirc$
15760 <row topline="true">
15761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15764 \begin_layout Standard
15772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15775 \begin_layout Standard
15776 \begin_inset Formula $\wedge$
15785 <row topline="true" bottomline="true">
15786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15789 \begin_layout Standard
15797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15800 \begin_layout Standard
15801 \begin_inset Formula $\vee$
15817 \begin_inset Tabular
15818 <lyxtabular version="3" rows="13" columns="2">
15820 <column alignment="center" valignment="top" leftline="true" width="0pt">
15821 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15822 <row topline="true" bottomline="true">
15823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15826 \begin_layout Standard
15832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15835 \begin_layout Standard
15842 <row topline="true">
15843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15846 \begin_layout Standard
15854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15857 \begin_layout Standard
15858 \begin_inset Formula $\oplus$
15867 <row topline="true">
15868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15871 \begin_layout Standard
15879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15882 \begin_layout Standard
15883 \begin_inset Formula $\ominus$
15892 <row topline="true">
15893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15896 \begin_layout Standard
15904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15907 \begin_layout Standard
15908 \begin_inset Formula $\otimes$
15917 <row topline="true">
15918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15921 \begin_layout Standard
15929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15932 \begin_layout Standard
15933 \begin_inset Formula $\oslash$
15942 <row topline="true">
15943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15946 \begin_layout Standard
15954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15957 \begin_layout Standard
15958 \begin_inset Formula $\odot$
15967 <row topline="true">
15968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15971 \begin_layout Standard
15979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15982 \begin_layout Standard
15983 \begin_inset Formula $\amalg$
15992 <row topline="true">
15993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15996 \begin_layout Standard
16004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16007 \begin_layout Standard
16008 \begin_inset Formula $\uplus$
16017 <row topline="true">
16018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16021 \begin_layout Standard
16029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16032 \begin_layout Standard
16033 \begin_inset Formula $\setminus$
16042 <row topline="true">
16043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16046 \begin_layout Standard
16054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16057 \begin_layout Standard
16058 \begin_inset Formula $\sqcap$
16067 <row topline="true">
16068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16071 \begin_layout Standard
16079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16082 \begin_layout Standard
16083 \begin_inset Formula $\sqcup$
16092 <row topline="true">
16093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16096 \begin_layout Standard
16104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16107 \begin_layout Standard
16108 \begin_inset Formula $\triangleleft$
16117 <row topline="true" bottomline="true">
16118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16121 \begin_layout Standard
16129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16132 \begin_layout Standard
16133 \begin_inset Formula $\triangleright$
16151 \begin_layout Standard
16152 All binary operators can also be inserted via the math toolbar button
16153 \begin_inset Graphics
16154 filename ../images/math/pm.png
16162 \begin_layout Standard
16163 To typeset the Laplace operator also
16180 \begin_inset Formula $\nabla^{2}$
16183 ) can be used instead of
16192 \begin_layout Standard
16199 Insert\SpecialChar \menuseparator
16211 \begin_layout Subsection
16212 Self-defined Operators
16213 \begin_inset LatexCommand label
16214 name "sub:Self-defined-Operators"
16219 \begin_inset LatexCommand index
16220 name "Operators ! self-defined"
16227 \begin_layout Standard
16228 With the help of the command
16232 DeclareMathOperator
16235 \begin_inset LatexCommand index
16236 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
16240 custom operators can be defined in the LaTeX-preamble.
16241 Its command scheme is:
16244 \begin_layout Standard
16249 DeclareMathOperator{new command}{display}
16252 \begin_layout Standard
16253 Display can be characters or symbols that define how the operator looks
16255 To define a big operator a * is set behind the command.
16256 All self-defined big operators can have limits as described in
16257 \begin_inset LatexCommand ref
16258 reference "sub:Operator-Limits"
16265 \begin_layout Standard
16266 For example the LaTeX-preamble line
16269 \begin_layout Standard
16274 DeclareMathOperator*{
16281 \begin_layout Standard
16282 defines the command
16288 , that inserts a big operator consisting of the lozenge symbol from
16289 \begin_inset LatexCommand ref
16290 reference "sub:Miscellaneous-Symbols"
16295 \begin_inset Formula \[
16296 \Lozenge_{n=1}^{\infty}\]
16300 The command for this formula is:
16311 \begin_inset Formula $\to$
16317 \begin_layout Standard
16318 \begin_inset VSpace bigskip
16321 When self-defined operators are not used several times in the document,
16322 they can also be defined with the commands
16329 \begin_inset LatexCommand index
16330 name "Commands ! M ! \\textbackslash mathop"
16341 \begin_inset LatexCommand index
16342 name "Commands ! M ! \\textbackslash mathbin"
16346 , which have the following scheme:
16349 \begin_layout Standard
16363 \begin_layout Standard
16370 defines big operators,
16379 \begin_layout Standard
16386 can e.\InsetSpace \thinspace{}
16388 be used to use one limit for several operators:
16391 \begin_layout Standard
16392 \begin_inset Formula \[
16393 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
16400 \begin_layout Standard
16401 The command for the formula above is:
16419 \begin_layout Standard
16431 \begin_inset Formula $\to$
16440 \begin_layout Standard
16454 \begin_layout Section
16456 \begin_inset LatexCommand index
16464 \begin_layout Subsection
16466 \begin_inset LatexCommand label
16467 name "sub:Font-Styles"
16472 \begin_inset LatexCommand index
16473 name "Font ! style"
16480 \begin_layout Standard
16481 Latin letters in formulas can be set in one of the following font styles:
16482 \begin_inset VSpace -2mm
16488 \begin_layout Standard
16490 \begin_inset Tabular
16491 <lyxtabular version="3" rows="6" columns="3">
16493 <column alignment="center" valignment="top" leftline="true" width="0">
16494 <column alignment="center" valignment="top" leftline="true" width="0">
16495 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16496 <row topline="true" bottomline="true">
16497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16500 \begin_layout Standard
16506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16509 \begin_layout Standard
16515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16518 \begin_layout Standard
16525 <row topline="true">
16526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16529 \begin_layout Standard
16538 \begin_layout Standard
16554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16557 \begin_layout Standard
16558 \begin_inset Formula $\mathbb{ABC}$
16566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16569 \begin_layout Standard
16576 <row topline="true">
16577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16580 \begin_layout Standard
16589 \begin_layout Standard
16605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16608 \begin_layout Standard
16609 \begin_inset Formula $\mathbf{AbC}$
16617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16620 \begin_layout Standard
16627 <row topline="true">
16628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16631 \begin_layout Standard
16640 \begin_layout Standard
16656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16659 \begin_layout Standard
16660 \begin_inset Formula $\boldsymbol{AbC}$
16668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16671 \begin_layout Standard
16678 <row topline="true">
16679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16682 \begin_layout Standard
16691 \begin_layout Standard
16707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16710 \begin_layout Standard
16711 \begin_inset Formula $\mathcal{ABC}$
16719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16722 \begin_layout Standard
16729 <row topline="true" bottomline="true">
16730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16733 \begin_layout Standard
16742 \begin_layout Standard
16758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16761 \begin_layout Standard
16762 \begin_inset Formula $\mathfrak{AbC}$
16770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16773 \begin_layout Standard
16787 \begin_layout Standard
16789 \begin_inset Tabular
16790 <lyxtabular version="3" rows="5" columns="3">
16792 <column alignment="center" valignment="top" leftline="true" width="0">
16793 <column alignment="center" valignment="top" leftline="true" width="0">
16794 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16795 <row topline="true" bottomline="true">
16796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16799 \begin_layout Standard
16805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16808 \begin_layout Standard
16814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16817 \begin_layout Standard
16824 <row topline="true">
16825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16828 \begin_layout Standard
16837 \begin_layout Standard
16853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16856 \begin_layout Standard
16857 \begin_inset Formula $\mathit{AbC}$
16865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16868 \begin_layout Standard
16875 <row topline="true">
16876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16879 \begin_layout Standard
16888 \begin_layout Standard
16904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16907 \begin_layout Standard
16908 \begin_inset Formula $\mathrm{AbC}$
16916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16919 \begin_layout Standard
16926 <row topline="true">
16927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16930 \begin_layout Standard
16939 \begin_layout Standard
16955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16958 \begin_layout Standard
16959 \begin_inset Formula $\mathsf{AbC}$
16967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16970 \begin_layout Standard
16977 <row topline="true" bottomline="true">
16978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16981 \begin_layout Standard
16990 \begin_layout Standard
17006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17009 \begin_layout Standard
17010 \begin_inset Formula $\mathtt{AbC}$
17018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17021 \begin_layout Standard
17035 \begin_layout Standard
17036 \begin_inset Note Greyedout
17039 \begin_layout Standard
17056 can only be used for big letters.
17064 \begin_layout Standard
17065 Predefined is the style
17074 \begin_layout Standard
17075 The style commands work also for letters in mathematical constructs:
17076 \begin_inset Formula \[
17077 \mathfrak{A=\frac{b}{C}}\]
17084 \begin_layout Standard
17085 Characters in mathematical text don't appear in a math font style but in
17086 the text font style
17093 That their style can't be set correctly via the text style dialog is a
17098 \begin_layout Standard
17103 \begin_layout Standard
17107 href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
17116 \begin_layout Standard
17131 \begin_layout Standard
17132 Instead of the style commands the dialog
17134 Edit\SpecialChar \menuseparator
17135 Math\SpecialChar \menuseparator
17138 or the toolbar button
17139 \begin_inset Graphics
17140 filename ../images/math/font.png
17148 \begin_layout Subsection
17150 \begin_inset LatexCommand label
17151 name "sub:Bold-Formulas"
17156 \begin_inset LatexCommand index
17157 name "Formula ! bold"
17164 \begin_layout Standard
17165 To make a complete formula bold, the command
17171 from the previous subsection cannot be used, because it doesn't work for
17172 small Greek letters.
17173 Furthermore it prints Latin letters always upright, like in the following
17177 \begin_layout Standard
17178 \begin_inset Formula \[
17179 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
17186 \begin_layout Standard
17187 To display the formula correctly, the command
17194 \begin_inset Formula \[
17195 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
17199 It is also possible to set the formula in a
17201 boldmath environment
17204 This environment is created by inserting the command
17209 \begin_inset LatexCommand index
17210 name "Commands ! B ! \\textbackslash boldmath"
17217 To end the environment, the command
17222 \begin_inset LatexCommand index
17223 name "Commands ! U ! \\textbackslash unboldmath"
17229 is inserted in TeX-mode.
17233 \begin_layout Standard
17243 \begin_inset Formula \[
17244 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
17252 \begin_layout Standard
17264 \begin_layout Subsection
17266 \begin_inset LatexCommand label
17267 name "sub:Font-Sizes"
17272 \begin_inset LatexCommand index
17280 \begin_layout Standard
17281 For characters in formulas there are, analog to characters in text, the
17282 following size commands:
17285 \begin_layout Standard
17349 \begin_layout Standard
17350 The size produced by the commands depends on the document font size, that
17351 corresponds with the command
17358 The other commands produce smaller or larger sizes than
17365 The font size can however not exceed a certain value.
17366 Is for example the document font size 12\InsetSpace \thinspace{}
17373 switches to the same size as
17383 \begin_layout Standard
17384 A size command is inserted in TeX-mode before the formula and sets the size
17385 for all following formula and text characters.
17386 To switch back to the initial size, the command
17392 is inserted behind the formula in TeX-mode.
17395 \begin_layout Standard
17396 Within a formula the size can only be changed for symbols or letters in
17398 To do this, the size command is inserted in mathematical text.
17399 All following characters until the end of the mathematical text or until
17400 another size command will have the selected size.
17402 \begin_inset VSpace -2mm
17408 \begin_layout Standard
17412 \begin_layout Standard
17422 \begin_inset Formula \[
17423 A=\frac{B}{c}\cdot\maltese\]
17428 \begin_inset Formula \[
17429 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
17437 \begin_layout Standard
17449 \begin_layout Standard
17450 \begin_inset VSpace medskip
17453 Before both formulas the command
17460 The command for the second formula is:
17470 \begin_layout Standard
17485 \begin_layout Standard
17500 \begin_layout Standard
17515 \begin_layout Standard
17525 \begin_inset Formula $\to$
17529 \begin_inset Formula $\to$
17538 \begin_layout Standard
17557 \begin_layout Standard
17572 \begin_layout Standard
17587 \begin_layout Standard
17599 \begin_layout Standard
17600 If a symbol cannot be displayed in different sizes, it will always be displayed
17601 in the default size.
17604 \begin_layout Section
17606 \begin_inset LatexCommand index
17607 name "Greek letters"
17614 \begin_layout Standard
17615 All Greek letters can also be inserted via the toolbar button
17616 \begin_inset Graphics
17617 filename ../images/math/alpha.png
17625 \begin_layout Subsection
17627 \begin_inset LatexCommand label
17628 name "sub:Small-Letters"
17633 \begin_inset LatexCommand index
17634 name "Greek letters ! small"
17641 \begin_layout Standard
17645 \begin_inset Tabular
17646 <lyxtabular version="3" rows="11" columns="2">
17648 <column alignment="center" valignment="top" leftline="true" width="0pt">
17649 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17650 <row topline="true" bottomline="true">
17651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17654 \begin_layout Standard
17660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17663 \begin_layout Standard
17670 <row topline="true">
17671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17674 \begin_layout Standard
17682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17685 \begin_layout Standard
17686 \begin_inset Formula $\alpha$
17695 <row topline="true">
17696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17699 \begin_layout Standard
17707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17710 \begin_layout Standard
17711 \begin_inset Formula $\beta$
17720 <row topline="true">
17721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17724 \begin_layout Standard
17732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17735 \begin_layout Standard
17736 \begin_inset Formula $\gamma$
17745 <row topline="true">
17746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17749 \begin_layout Standard
17757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17760 \begin_layout Standard
17761 \begin_inset Formula $\delta$
17770 <row topline="true">
17771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17774 \begin_layout Standard
17782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17785 \begin_layout Standard
17786 \begin_inset Formula $\epsilon$
17795 <row topline="true">
17796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17799 \begin_layout Standard
17807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17810 \begin_layout Standard
17811 \begin_inset Formula $\varepsilon$
17820 <row topline="true">
17821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17824 \begin_layout Standard
17832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17835 \begin_layout Standard
17836 \begin_inset Formula $\zeta$
17845 <row topline="true">
17846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17849 \begin_layout Standard
17857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17860 \begin_layout Standard
17861 \begin_inset Formula $\eta$
17870 <row topline="true">
17871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17874 \begin_layout Standard
17882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17885 \begin_layout Standard
17886 \begin_inset Formula $\theta$
17895 <row topline="true" bottomline="true">
17896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17899 \begin_layout Standard
17907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17910 \begin_layout Standard
17911 \begin_inset Formula $\vartheta$
17927 \begin_inset Tabular
17928 <lyxtabular version="3" rows="12" columns="2">
17930 <column alignment="center" valignment="top" leftline="true" width="0pt">
17931 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17932 <row topline="true" bottomline="true">
17933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17936 \begin_layout Standard
17942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17945 \begin_layout Standard
17952 <row topline="true">
17953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17956 \begin_layout Standard
17964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17967 \begin_layout Standard
17968 \begin_inset Formula $\iota$
17977 <row topline="true">
17978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17981 \begin_layout Standard
17989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17992 \begin_layout Standard
17993 \begin_inset Formula $\kappa$
18002 <row topline="true">
18003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18006 \begin_layout Standard
18014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18017 \begin_layout Standard
18018 \begin_inset Formula $\varkappa$
18027 <row topline="true">
18028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18031 \begin_layout Standard
18039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18042 \begin_layout Standard
18043 \begin_inset Formula $\lambda$
18052 <row topline="true">
18053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18056 \begin_layout Standard
18064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18067 \begin_layout Standard
18068 \begin_inset Formula $\mu$
18077 <row topline="true">
18078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18081 \begin_layout Standard
18089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18092 \begin_layout Standard
18093 \begin_inset Formula $\nu$
18102 <row topline="true">
18103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18106 \begin_layout Standard
18114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18117 \begin_layout Standard
18118 \begin_inset Formula $\xi$
18127 <row topline="true">
18128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18131 \begin_layout Standard
18137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18140 \begin_layout Standard
18141 \begin_inset Formula $o$
18150 <row topline="true">
18151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18154 \begin_layout Standard
18162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18165 \begin_layout Standard
18166 \begin_inset Formula $\pi$
18175 <row topline="true">
18176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18179 \begin_layout Standard
18187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18190 \begin_layout Standard
18191 \begin_inset Formula $\varpi$
18200 <row topline="true" bottomline="true">
18201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18204 \begin_layout Standard
18212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18215 \begin_layout Standard
18216 \begin_inset Formula $\rho$
18232 \begin_inset Tabular
18233 <lyxtabular version="3" rows="11" columns="2">
18235 <column alignment="center" valignment="top" leftline="true" width="0pt">
18236 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18237 <row topline="true" bottomline="true">
18238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18241 \begin_layout Standard
18247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18250 \begin_layout Standard
18257 <row topline="true">
18258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18261 \begin_layout Standard
18269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18272 \begin_layout Standard
18273 \begin_inset Formula $\varrho$
18282 <row topline="true">
18283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18286 \begin_layout Standard
18294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18297 \begin_layout Standard
18298 \begin_inset Formula $\sigma$
18307 <row topline="true">
18308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18311 \begin_layout Standard
18319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18322 \begin_layout Standard
18323 \begin_inset Formula $\varsigma$
18332 <row topline="true">
18333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18336 \begin_layout Standard
18344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18347 \begin_layout Standard
18348 \begin_inset Formula $\tau$
18357 <row topline="true">
18358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18361 \begin_layout Standard
18369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18372 \begin_layout Standard
18373 \begin_inset Formula $\upsilon$
18382 <row topline="true">
18383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18386 \begin_layout Standard
18394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18397 \begin_layout Standard
18398 \begin_inset Formula $\phi$
18407 <row topline="true">
18408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18411 \begin_layout Standard
18419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18422 \begin_layout Standard
18423 \begin_inset Formula $\varphi$
18432 <row topline="true">
18433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18436 \begin_layout Standard
18444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18447 \begin_layout Standard
18448 \begin_inset Formula $\chi$
18457 <row topline="true">
18458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18461 \begin_layout Standard
18469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18472 \begin_layout Standard
18473 \begin_inset Formula $\psi$
18482 <row topline="true" bottomline="true">
18483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18486 \begin_layout Standard
18494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18497 \begin_layout Standard
18498 \begin_inset Formula $\omega$
18516 \begin_layout Standard
18517 \begin_inset VSpace medskip
18523 \begin_layout Standard
18524 How to create upright Greek letters is explained in
18525 \begin_inset LatexCommand ref
18526 reference "sub:Upright-small-Greek"
18533 \begin_layout Subsection
18535 \begin_inset LatexCommand index
18536 name "Greek letters ! big"
18543 \begin_layout Standard
18547 \begin_inset Tabular
18548 <lyxtabular version="3" rows="7" columns="2">
18550 <column alignment="center" valignment="top" leftline="true" width="0pt">
18551 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18552 <row topline="true" bottomline="true">
18553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18556 \begin_layout Standard
18562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18565 \begin_layout Standard
18572 <row topline="true">
18573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18576 \begin_layout Standard
18584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18587 \begin_layout Standard
18588 \begin_inset Formula $\Gamma$
18597 <row topline="true">
18598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18601 \begin_layout Standard
18609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18612 \begin_layout Standard
18613 \begin_inset Formula $\Delta$
18622 <row topline="true">
18623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18626 \begin_layout Standard
18634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18637 \begin_layout Standard
18638 \begin_inset Formula $\Theta$
18647 <row topline="true">
18648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18651 \begin_layout Standard
18659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18662 \begin_layout Standard
18663 \begin_inset Formula $\Lambda$
18672 <row topline="true">
18673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18676 \begin_layout Standard
18684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18687 \begin_layout Standard
18688 \begin_inset Formula $\Xi$
18697 <row topline="true" bottomline="true">
18698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18701 \begin_layout Standard
18709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18712 \begin_layout Standard
18713 \begin_inset Formula $\Pi$
18729 \begin_inset Tabular
18730 <lyxtabular version="3" rows="6" columns="2">
18732 <column alignment="center" valignment="top" leftline="true" width="0pt">
18733 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18734 <row topline="true" bottomline="true">
18735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18738 \begin_layout Standard
18744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18747 \begin_layout Standard
18754 <row topline="true">
18755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18758 \begin_layout Standard
18766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18769 \begin_layout Standard
18770 \begin_inset Formula $\Sigma$
18779 <row topline="true">
18780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18783 \begin_layout Standard
18791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18794 \begin_layout Standard
18795 \begin_inset Formula $\Upsilon$
18804 <row topline="true">
18805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18808 \begin_layout Standard
18816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18819 \begin_layout Standard
18820 \begin_inset Formula $\Phi$
18829 <row topline="true">
18830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18833 \begin_layout Standard
18841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18844 \begin_layout Standard
18845 \begin_inset Formula $\Psi$
18854 <row topline="true" bottomline="true">
18855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18858 \begin_layout Standard
18866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18869 \begin_layout Standard
18870 \begin_inset Formula $\Omega$
18888 \begin_layout Standard
18889 \begin_inset VSpace medskip
18892 That the big Greek letters appear upright is caused by a design bug when
18894 To get correct italic big letters, begin every command with
18899 For example the command
18906 \begin_inset Formula $\varGamma$
18912 \begin_layout Subsection
18914 \begin_inset LatexCommand index
18915 name "Greek letters ! bold"
18922 \begin_layout Standard
18923 Greek letters cannot be set with different font styles like Latin letters.
18924 They can only be made bold with the command
18931 \begin_inset LatexCommand index
18932 name "Commands ! B ! \\textbackslash boldsymbol"
18939 \begin_layout Standard
18941 \begin_inset Tabular
18942 <lyxtabular version="3" rows="3" columns="2">
18944 <column alignment="center" valignment="top" leftline="true" width="0">
18945 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
18946 <row topline="true" bottomline="true">
18947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18950 \begin_layout Standard
18956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18959 \begin_layout Standard
18966 <row topline="true">
18967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18970 \begin_layout Standard
18982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18985 \begin_layout Standard
18986 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
18995 <row topline="true" bottomline="true">
18996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18999 \begin_layout Standard
19011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19014 \begin_layout Standard
19015 \begin_inset Formula $\theta\boldsymbol{\theta}$
19031 \begin_layout Section
19036 \begin_layout Standard
19049 \begin_layout Standard
19050 A list with all symbols of most of the LaTeX-packages can be found in
19051 \begin_inset LatexCommand cite
19065 \begin_layout Standard
19073 \begin_inset Note Note
19076 \begin_layout Standard
19079 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
19082 \begin_layout Standard
19085 texorpdfstring is in section
19086 \begin_inset LatexCommand ref
19087 reference "sub:Formulas-in-Section"
19097 \begin_inset LatexCommand index
19105 \begin_layout Standard
19106 Many of the symbols listed in this section can also be inserted via the
19108 \begin_inset Graphics
19109 filename ../images/math/nabla.png
19115 \begin_inset Graphics
19116 filename ../images/math/digamma.png
19124 \begin_layout Subsection
19125 Mathematical Symbols
19126 \begin_inset LatexCommand label
19127 name "sub:Mathematical-Symbols"
19132 \begin_inset LatexCommand index
19133 name "Symbols ! mathematical"
19140 \begin_layout Standard
19144 \begin_inset Tabular
19145 <lyxtabular version="3" rows="10" columns="2">
19147 <column alignment="center" valignment="top" leftline="true" width="0pt">
19148 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19149 <row topline="true" bottomline="true">
19150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19153 \begin_layout Standard
19159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19162 \begin_layout Standard
19169 <row topline="true">
19170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19173 \begin_layout Standard
19181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19184 \begin_layout Standard
19185 \begin_inset Formula $\neg$
19194 <row topline="true">
19195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19198 \begin_layout Standard
19206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19209 \begin_layout Standard
19210 \begin_inset Formula $\Im$
19219 <row topline="true">
19220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19223 \begin_layout Standard
19231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19234 \begin_layout Standard
19235 \begin_inset Formula $\Re$
19244 <row topline="true">
19245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19248 \begin_layout Standard
19256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19259 \begin_layout Standard
19260 \begin_inset Formula $\aleph$
19269 <row topline="true">
19270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19273 \begin_layout Standard
19281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19284 \begin_layout Standard
19285 \begin_inset Formula $\partial$
19294 <row topline="true">
19295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19298 \begin_layout Standard
19306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19309 \begin_layout Standard
19310 \begin_inset Formula $\infty$
19319 <row topline="true" bottomline="true">
19320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19323 \begin_layout Standard
19331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19334 \begin_layout Standard
19335 \begin_inset Formula $\wp$
19344 <row bottomline="true">
19345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19348 \begin_layout Standard
19356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19359 \begin_layout Standard
19360 \begin_inset Formula $\imath$
19369 <row bottomline="true">
19370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19373 \begin_layout Standard
19381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19384 \begin_layout Standard
19385 \begin_inset Formula $\jmath$
19401 \begin_inset Tabular
19402 <lyxtabular version="3" rows="10" columns="2">
19404 <column alignment="center" valignment="top" leftline="true" width="0pt">
19405 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19406 <row topline="true" bottomline="true">
19407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19410 \begin_layout Standard
19416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19419 \begin_layout Standard
19421 \begin_inset Note Note
19424 \begin_layout Standard
19431 is only used as spacer.
19442 <row topline="true">
19443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19446 \begin_layout Standard
19454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19457 \begin_layout Standard
19458 \begin_inset Formula $\forall$
19467 <row topline="true">
19468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19471 \begin_layout Standard
19479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19482 \begin_layout Standard
19483 \begin_inset Formula $\exists$
19492 <row topline="true">
19493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19496 \begin_layout Standard
19504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19507 \begin_layout Standard
19508 \begin_inset Formula $\nexists$
19517 <row topline="true">
19518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19521 \begin_layout Standard
19529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19532 \begin_layout Standard
19533 \begin_inset Formula $\emptyset$
19542 <row topline="true">
19543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19546 \begin_layout Standard
19554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19557 \begin_layout Standard
19558 \begin_inset Formula $\varnothing$
19567 <row topline="true">
19568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19571 \begin_layout Standard
19579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19582 \begin_layout Standard
19583 \begin_inset Formula $\dag$
19592 <row topline="true" bottomline="true">
19593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19596 \begin_layout Standard
19604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19607 \begin_layout Standard
19608 \begin_inset Formula $\ddag$
19617 <row bottomline="true">
19618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19621 \begin_layout Standard
19629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19632 \begin_layout Standard
19636 \begin_layout Standard
19646 \begin_inset Formula $\complement$
19653 \begin_layout Standard
19666 <row bottomline="true">
19667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19670 \begin_layout Standard
19678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19681 \begin_layout Standard
19682 \begin_inset Formula $\Bbbk$
19698 \begin_inset Tabular
19699 <lyxtabular version="3" rows="10" columns="2">
19701 <column alignment="center" valignment="top" leftline="true" width="0pt">
19702 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19703 <row topline="true" bottomline="true">
19704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19707 \begin_layout Standard
19713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19716 \begin_layout Standard
19723 <row topline="true">
19724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19727 \begin_layout Standard
19735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19738 \begin_layout Standard
19739 \begin_inset Formula $\prime$
19748 <row topline="true">
19749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19752 \begin_layout Standard
19760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19763 \begin_layout Standard
19764 \begin_inset Formula $\backprime$
19773 <row topline="true">
19774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19777 \begin_layout Standard
19785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19788 \begin_layout Standard
19789 \begin_inset Formula $\mho$
19798 <row topline="true">
19799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19802 \begin_layout Standard
19810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19813 \begin_layout Standard
19814 \begin_inset Formula $\triangle$
19823 <row topline="true">
19824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19827 \begin_layout Standard
19835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19838 \begin_layout Standard
19839 \begin_inset Formula $\angle$
19848 <row topline="true">
19849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19852 \begin_layout Standard
19860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19863 \begin_layout Standard
19864 \begin_inset Formula $\measuredangle$
19873 <row topline="true" bottomline="true">
19874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19877 \begin_layout Standard
19885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19888 \begin_layout Standard
19889 \begin_inset Formula $\sphericalangle$
19898 <row bottomline="true">
19899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19902 \begin_layout Standard
19910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19913 \begin_layout Standard
19914 \begin_inset Formula $\top$
19923 <row bottomline="true">
19924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19927 \begin_layout Standard
19935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19938 \begin_layout Standard
19939 \begin_inset Formula $\bot$
19957 \begin_layout Standard
19963 \begin_layout Subsection
19964 Miscellaneous Symbols
19965 \begin_inset LatexCommand label
19966 name "sub:Miscellaneous-Symbols"
19971 \begin_inset LatexCommand index
19972 name "Symbols ! miscellaneous"
19979 \begin_layout Standard
19982 \begin_inset Tabular
19983 <lyxtabular version="3" rows="10" columns="2">
19985 <column alignment="center" valignment="top" leftline="true" width="0pt">
19986 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19987 <row topline="true" bottomline="true">
19988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19991 \begin_layout Standard
19997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20000 \begin_layout Standard
20007 <row topline="true">
20008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20011 \begin_layout Standard
20019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20022 \begin_layout Standard
20023 \begin_inset Formula $\flat$
20032 <row topline="true">
20033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20036 \begin_layout Standard
20044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20047 \begin_layout Standard
20048 \begin_inset Formula $\natural$
20057 <row topline="true">
20058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20061 \begin_layout Standard
20069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20072 \begin_layout Standard
20073 \begin_inset Formula $\sharp$
20082 <row topline="true" bottomline="true">
20083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20086 \begin_layout Standard
20094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20097 \begin_layout Standard
20098 \begin_inset Formula $\surd$
20107 <row bottomline="true">
20108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20111 \begin_layout Standard
20119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20122 \begin_layout Standard
20123 \begin_inset Formula $\checkmark$
20132 <row bottomline="true">
20133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20136 \begin_layout Standard
20144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20147 \begin_layout Standard
20148 \begin_inset Formula $\yen$
20157 <row bottomline="true">
20158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20161 \begin_layout Standard
20169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20172 \begin_layout Standard
20173 \begin_inset Formula $\pounds$
20182 <row bottomline="true">
20183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20186 \begin_layout Standard
20192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20195 \begin_layout Standard
20196 \begin_inset Formula $\$$
20205 <row bottomline="true">
20206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20209 \begin_layout Standard
20215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20218 \begin_layout Standard
20219 \begin_inset Formula $§$
20233 \begin_inset Tabular
20234 <lyxtabular version="3" rows="10" columns="2">
20236 <column alignment="center" valignment="top" leftline="true" width="0">
20237 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
20238 <row topline="true" bottomline="true">
20239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20242 \begin_layout Standard
20248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20251 \begin_layout Standard
20258 <row topline="true">
20259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20262 \begin_layout Standard
20270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20273 \begin_layout Standard
20274 \begin_inset Formula $\hbar$
20283 <row topline="true">
20284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20287 \begin_layout Standard
20295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20298 \begin_layout Standard
20299 \begin_inset Formula $\hslash$
20308 <row topline="true">
20309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20312 \begin_layout Standard
20320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20323 \begin_layout Standard
20324 \begin_inset Formula $\clubsuit$
20333 <row topline="true">
20334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20337 \begin_layout Standard
20345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20348 \begin_layout Standard
20349 \begin_inset Formula $\spadesuit$
20358 <row topline="true">
20359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20362 \begin_layout Standard
20370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20373 \begin_layout Standard
20374 \begin_inset Formula $\bigstar$
20383 <row topline="true">
20384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20387 \begin_layout Standard
20395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20398 \begin_layout Standard
20399 \begin_inset Formula $\blacklozenge$
20408 <row topline="true">
20409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20412 \begin_layout Standard
20420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20423 \begin_layout Standard
20424 \begin_inset Formula $\blacktriangle$
20433 <row topline="true">
20434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20437 \begin_layout Standard
20445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20448 \begin_layout Standard
20449 \begin_inset Formula $\blacktriangledown$
20458 <row topline="true" bottomline="true">
20459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20462 \begin_layout Standard
20470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20473 \begin_layout Standard
20474 \begin_inset Formula $\bullet$
20488 \begin_inset Tabular
20489 <lyxtabular version="3" rows="10" columns="2">
20491 <column alignment="center" valignment="top" leftline="true" width="0pt">
20492 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20493 <row topline="true" bottomline="true">
20494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20497 \begin_layout Standard
20503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20506 \begin_layout Standard
20513 <row topline="true">
20514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20517 \begin_layout Standard
20525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20528 \begin_layout Standard
20529 \begin_inset Formula $\diamondsuit$
20538 <row topline="true">
20539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20542 \begin_layout Standard
20550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20553 \begin_layout Standard
20554 \begin_inset Formula $\Diamond$
20563 <row topline="true">
20564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20567 \begin_layout Standard
20575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20578 \begin_layout Standard
20579 \begin_inset Formula $\heartsuit$
20588 <row topline="true" bottomline="true">
20589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20592 \begin_layout Standard
20600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20603 \begin_layout Standard
20604 \begin_inset Formula $\P$
20613 <row bottomline="true">
20614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20617 \begin_layout Standard
20625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20628 \begin_layout Standard
20629 \begin_inset Formula $\copyright$
20638 <row bottomline="true">
20639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20642 \begin_layout Standard
20650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20653 \begin_layout Standard
20654 \begin_inset Formula $\circledR$
20663 <row bottomline="true">
20664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20667 \begin_layout Standard
20675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20678 \begin_layout Standard
20679 \begin_inset Formula $\maltese$
20688 <row bottomline="true">
20689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20692 \begin_layout Standard
20700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20703 \begin_layout Standard
20704 \begin_inset Formula $\diagup$
20713 <row bottomline="true">
20714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20717 \begin_layout Standard
20725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20728 \begin_layout Standard
20729 \begin_inset Formula $\diagdown$
20745 \begin_layout Standard
20746 \begin_inset VSpace medskip
20749 More symbols are listed in
20750 \begin_inset LatexCommand ref
20751 reference "sub:Miscellaneous-Special-Characters"
20758 \begin_layout Standard
20759 Some symbols can be displayed in different sizes, see
20760 \begin_inset LatexCommand ref
20761 reference "sub:Font-Sizes"
20768 \begin_layout Subsection
20770 \begin_inset LatexCommand index
20771 name "Symbols ! Euro-symbol"
20776 \begin_inset LatexCommand index
20777 name "\\textcent@\\officialeuro"
20784 \begin_layout Standard
20785 To use the Euro symbol in formulas, the LaTeX-package
20790 \begin_inset LatexCommand index
20791 name "Packages ! eurosym"
20795 must be installed and loaded with the LaTeX-preamble line
20798 \begin_layout Standard
20803 usepackage[gennarrow]{eurosym}
20806 \begin_layout Standard
20807 The Euro symbol can now be inserted with the command
20814 \begin_inset LatexCommand index
20815 name "Commands ! E ! \\textbackslash euro"
20822 \begin_layout Standard
20823 The Euro symbol can directly be inserted with the € key in mathematical
20824 text, without having
20839 can also be inserted in TeX-mode.
20840 The official currency symbol can then be inserted with the command
20847 \begin_inset LatexCommand index
20848 name "Commands ! O ! \\textbackslash officialeuro"
20852 , that is only available in TeX-mode.
20855 \begin_layout Standard
20859 \begin_layout Standard
20869 \begin_inset Note Note
20872 \begin_layout Standard
20873 The following table will only be displayed when the LaTeX-package
20885 \begin_layout Standard
20886 An overview about the different Euro symbols:
20889 \begin_layout Standard
20891 \begin_inset Tabular
20892 <lyxtabular version="3" rows="4" columns="3">
20894 <column alignment="center" valignment="top" leftline="true" width="0pt">
20895 <column alignment="center" valignment="top" leftline="true" width="0pt">
20896 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20897 <row topline="true" bottomline="true">
20898 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
20901 \begin_layout Standard
20907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20910 \begin_layout Standard
20916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20919 \begin_layout Standard
20926 <row topline="true">
20927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20930 \begin_layout Standard
20936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20939 \begin_layout Standard
20947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20950 \begin_layout Standard
20951 \begin_inset Formula $\euro$
20960 <row topline="true">
20961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20964 \begin_layout Standard
20970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20973 \begin_layout Standard
20979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20982 \begin_layout Standard
20983 \begin_inset Formula $\mbox{€}$
20992 <row topline="true" bottomline="true">
20993 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20996 \begin_layout Standard
21002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21005 \begin_layout Standard
21013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21016 \begin_layout Standard
21020 \begin_layout Standard
21042 \begin_layout Standard
21046 \begin_layout Standard
21056 \begin_inset Note Note
21059 \begin_layout Standard
21060 The following will be displayed when the LaTeX-package
21072 \begin_layout Standard
21073 You need to install the LaTeX-package
21077 to see the rest of this subsection in the output.
21080 \begin_layout Standard
21084 \begin_layout Standard
21096 \begin_layout Section
21098 \begin_inset LatexCommand label
21099 name "sec:Relations"
21104 \begin_inset LatexCommand index
21110 \begin_inset LatexCommand index
21111 name "Comparisons|see{Relations}"
21118 \begin_layout Standard
21119 All relations can also be inserted via the toolbar button
21120 \begin_inset Graphics
21121 filename ../images/math/leq.png
21129 \begin_layout Standard
21133 \begin_inset Tabular
21134 <lyxtabular version="3" rows="17" columns="2">
21136 <column alignment="center" valignment="top" leftline="true" width="0pt">
21137 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21138 <row topline="true" bottomline="true">
21139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21142 \begin_layout Standard
21148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21151 \begin_layout Standard
21158 <row topline="true">
21159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21162 \begin_layout Standard
21168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21171 \begin_layout Standard
21172 \begin_inset Formula $<$
21181 <row topline="true">
21182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21185 \begin_layout Standard
21193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21196 \begin_layout Standard
21197 \begin_inset Formula $\le$
21206 <row topline="true">
21207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21210 \begin_layout Standard
21218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21221 \begin_layout Standard
21222 \begin_inset Formula $\ll$
21231 <row topline="true">
21232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21235 \begin_layout Standard
21243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21246 \begin_layout Standard
21247 \begin_inset Formula $\prec$
21256 <row topline="true">
21257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21260 \begin_layout Standard
21268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21271 \begin_layout Standard
21272 \begin_inset Formula $\preceq$
21281 <row topline="true">
21282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21285 \begin_layout Standard
21293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21296 \begin_layout Standard
21297 \begin_inset Formula $\subset$
21306 <row topline="true">
21307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21310 \begin_layout Standard
21318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21321 \begin_layout Standard
21322 \begin_inset Formula $\subseteq$
21331 <row topline="true">
21332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21335 \begin_layout Standard
21343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21346 \begin_layout Standard
21347 \begin_inset Formula $\sqsubseteq$
21356 <row topline="true">
21357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21360 \begin_layout Standard
21368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21371 \begin_layout Standard
21372 \begin_inset Formula $\in$
21381 <row topline="true">
21382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21385 \begin_layout Standard
21393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21396 \begin_layout Standard
21397 \begin_inset Formula $\vdash$
21406 <row topline="true">
21407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21410 \begin_layout Standard
21418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21421 \begin_layout Standard
21422 \begin_inset Formula $\smile$
21431 <row topline="true">
21432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21435 \begin_layout Standard
21443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21446 \begin_layout Standard
21447 \begin_inset Formula $\lhd$
21456 <row topline="true">
21457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21460 \begin_layout Standard
21468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21471 \begin_layout Standard
21472 \begin_inset Formula $\unlhd$
21481 <row topline="true">
21482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21485 \begin_layout Standard
21493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21496 \begin_layout Standard
21497 \begin_inset Formula $\gtrless$
21506 <row topline="true">
21507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21510 \begin_layout Standard
21518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21521 \begin_layout Standard
21522 \begin_inset Formula $\mid$
21531 <row topline="true" bottomline="true">
21532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21535 \begin_layout Standard
21543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21546 \begin_layout Standard
21547 \begin_inset Formula $\nmid$
21563 \begin_inset Tabular
21564 <lyxtabular version="3" rows="17" columns="2">
21566 <column alignment="center" valignment="top" leftline="true" width="0pt">
21567 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21568 <row topline="true" bottomline="true">
21569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21572 \begin_layout Standard
21578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21581 \begin_layout Standard
21588 <row topline="true">
21589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21592 \begin_layout Standard
21598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21601 \begin_layout Standard
21602 \begin_inset Formula $=$
21611 <row topline="true">
21612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21615 \begin_layout Standard
21623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21626 \begin_layout Standard
21627 \begin_inset Formula $\not=$
21636 <row topline="true">
21637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21640 \begin_layout Standard
21648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21651 \begin_layout Standard
21652 \begin_inset Formula $\equiv$
21661 <row topline="true">
21662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21665 \begin_layout Standard
21673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21676 \begin_layout Standard
21677 \begin_inset Formula $\sim$
21686 <row topline="true">
21687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21690 \begin_layout Standard
21698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21701 \begin_layout Standard
21702 \begin_inset Formula $\simeq$
21711 <row topline="true">
21712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21715 \begin_layout Standard
21723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21726 \begin_layout Standard
21727 \begin_inset Formula $\approx$
21736 <row topline="true">
21737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21740 \begin_layout Standard
21748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21751 \begin_layout Standard
21752 \begin_inset Formula $\cong$
21761 <row topline="true">
21762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21765 \begin_layout Standard
21773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21776 \begin_layout Standard
21777 \begin_inset Formula $\bowtie$
21786 <row topline="true">
21787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21790 \begin_layout Standard
21798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21801 \begin_layout Standard
21802 \begin_inset Formula $\notin$
21811 <row topline="true">
21812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21815 \begin_layout Standard
21823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21826 \begin_layout Standard
21827 \begin_inset Formula $\perp$
21836 <row topline="true">
21837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21840 \begin_layout Standard
21848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21851 \begin_layout Standard
21852 \begin_inset Formula $\propto$
21861 <row topline="true">
21862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21865 \begin_layout Standard
21873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21876 \begin_layout Standard
21877 \begin_inset Formula $\asymp$
21886 <row topline="true">
21887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21890 \begin_layout Standard
21898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21901 \begin_layout Standard
21902 \begin_inset Formula $\doteq$
21911 <row topline="true">
21912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21915 \begin_layout Standard
21923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21926 \begin_layout Standard
21927 \begin_inset Formula $\circeq$
21936 <row topline="true">
21937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21940 \begin_layout Standard
21948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21951 \begin_layout Standard
21952 \begin_inset Formula $\models$
21961 <row topline="true" bottomline="true">
21962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21965 \begin_layout Standard
21973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21976 \begin_layout Standard
21977 \begin_inset Formula $\widehat{=}$
21993 \begin_inset Tabular
21994 <lyxtabular version="3" rows="17" columns="2">
21996 <column alignment="center" valignment="top" leftline="true" width="0pt">
21997 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21998 <row topline="true" bottomline="true">
21999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22002 \begin_layout Standard
22008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22011 \begin_layout Standard
22018 <row topline="true">
22019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22022 \begin_layout Standard
22028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22031 \begin_layout Standard
22032 \begin_inset Formula $>$
22041 <row topline="true">
22042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22045 \begin_layout Standard
22053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22056 \begin_layout Standard
22057 \begin_inset Formula $\ge$
22066 <row topline="true">
22067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22070 \begin_layout Standard
22078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22081 \begin_layout Standard
22082 \begin_inset Formula $\gg$
22091 <row topline="true">
22092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22095 \begin_layout Standard
22103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22106 \begin_layout Standard
22107 \begin_inset Formula $\succ$
22116 <row topline="true">
22117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22120 \begin_layout Standard
22128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22131 \begin_layout Standard
22132 \begin_inset Formula $\succeq$
22141 <row topline="true">
22142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22145 \begin_layout Standard
22153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22156 \begin_layout Standard
22157 \begin_inset Formula $\supset$
22166 <row topline="true">
22167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22170 \begin_layout Standard
22178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22181 \begin_layout Standard
22182 \begin_inset Formula $\supseteq$
22191 <row topline="true">
22192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22195 \begin_layout Standard
22203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22206 \begin_layout Standard
22207 \begin_inset Formula $\sqsupseteq$
22216 <row topline="true">
22217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22220 \begin_layout Standard
22228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22231 \begin_layout Standard
22232 \begin_inset Formula $\ni$
22241 <row topline="true">
22242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22245 \begin_layout Standard
22253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22256 \begin_layout Standard
22257 \begin_inset Formula $\dashv$
22266 <row topline="true">
22267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22270 \begin_layout Standard
22278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22281 \begin_layout Standard
22282 \begin_inset Formula $\frown$
22291 <row topline="true">
22292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22295 \begin_layout Standard
22303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22306 \begin_layout Standard
22307 \begin_inset Formula $\rhd$
22316 <row topline="true">
22317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22320 \begin_layout Standard
22328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22331 \begin_layout Standard
22332 \begin_inset Formula $\unrhd$
22341 <row topline="true">
22342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22345 \begin_layout Standard
22353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22356 \begin_layout Standard
22357 \begin_inset Formula $\lessgtr$
22366 <row topline="true">
22367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22370 \begin_layout Standard
22378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22381 \begin_layout Standard
22382 \begin_inset Formula $\parallel$
22391 <row topline="true" bottomline="true">
22392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22395 \begin_layout Standard
22403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22406 \begin_layout Standard
22407 \begin_inset Formula $\nparallel$
22425 \begin_layout Standard
22426 \begin_inset VSpace medskip
22441 are bigger than the equal looking operators
22456 \begin_layout Standard
22457 Relations are, in contrary to symbols, always surrounded by space.
22460 \begin_layout Standard
22461 Relations with labels can be created with the command
22468 \begin_inset LatexCommand index
22469 name "Commands ! S ! \\textbackslash stackrel"
22476 \begin_layout Standard
22478 \begin_inset Tabular
22479 <lyxtabular version="3" rows="2" columns="2">
22481 <column alignment="center" valignment="top" leftline="true" width="0">
22482 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
22483 <row topline="true" bottomline="true">
22484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22487 \begin_layout Standard
22493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22496 \begin_layout Standard
22498 \begin_inset Note Note
22501 \begin_layout Standard
22508 is only used as spacer.
22519 <row topline="true" bottomline="true">
22520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22523 \begin_layout Standard
22530 \begin_layout Standard
22547 \begin_layout Standard
22557 \begin_inset Formula $\downarrow$
22566 \begin_layout Standard
22579 \begin_layout Standard
22593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22596 \begin_layout Standard
22597 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
22613 \begin_layout Section
22617 \begin_layout Subsection
22618 Predefined Functions
22619 \begin_inset LatexCommand label
22620 name "sub:Predefined-Functions"
22625 \begin_inset LatexCommand index
22626 name "Functions ! predefined"
22633 \begin_layout Standard
22634 In general, variables are set
22638 in mathematical expressions, but not function names, because
22639 \begin_inset Formula $sin$
22642 could be misunderstood as
22643 \begin_inset Formula $s\cdot i\cdot n$
22647 Therefore there are predefined functions, that are additionally a bit separated
22649 They are inserted as commands starting with a backslash before their name.
22652 \begin_layout Standard
22654 \begin_inset Tabular
22655 <lyxtabular version="3" rows="2" columns="4">
22657 <column alignment="center" valignment="top" leftline="true" width="0pt">
22658 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22659 <column alignment="center" valignment="top" leftline="true" width="0pt">
22660 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22661 <row topline="true" bottomline="true">
22662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22665 \begin_layout Standard
22671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22674 \begin_layout Standard
22680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22683 \begin_layout Standard
22689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22692 \begin_layout Standard
22699 <row topline="true" bottomline="true">
22700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22703 \begin_layout Standard
22709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22712 \begin_layout Standard
22713 \begin_inset Formula $Asin(x)+B$
22721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22724 \begin_layout Standard
22732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22735 \begin_layout Standard
22736 \begin_inset Formula $A\sin(x)+B$
22753 \begin_layout Standard
22765 \begin_layout Standard
22766 The following functions are predefined:
22769 \begin_layout Standard
22770 \begin_inset VSpace -2mm
22776 \begin_layout Standard
22778 \begin_inset Tabular
22779 <lyxtabular version="3" rows="9" columns="4">
22781 <column alignment="center" valignment="top" leftline="true" width="0pt">
22782 <column alignment="center" valignment="top" leftline="true" width="0pt">
22783 <column alignment="center" valignment="top" leftline="true" width="0pt">
22784 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22785 <row topline="true" bottomline="true">
22786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22789 \begin_layout Standard
22795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22798 \begin_layout Standard
22804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22807 \begin_layout Standard
22813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22816 \begin_layout Standard
22823 <row topline="true">
22824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22827 \begin_layout Standard
22835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22838 \begin_layout Standard
22846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22849 \begin_layout Standard
22857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22860 \begin_layout Standard
22869 <row topline="true">
22870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22873 \begin_layout Standard
22881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22884 \begin_layout Standard
22892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22895 \begin_layout Standard
22903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22906 \begin_layout Standard
22915 <row topline="true">
22916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22919 \begin_layout Standard
22927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22930 \begin_layout Standard
22938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22941 \begin_layout Standard
22949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22952 \begin_layout Standard
22961 <row topline="true">
22962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22965 \begin_layout Standard
22973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22976 \begin_layout Standard
22984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22987 \begin_layout Standard
22995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22998 \begin_layout Standard
23007 <row topline="true">
23008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23011 \begin_layout Standard
23019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23022 \begin_layout Standard
23030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23033 \begin_layout Standard
23041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23044 \begin_layout Standard
23053 <row topline="true">
23054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23057 \begin_layout Standard
23065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23068 \begin_layout Standard
23076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23079 \begin_layout Standard
23087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23090 \begin_layout Standard
23099 <row topline="true">
23100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23103 \begin_layout Standard
23111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23114 \begin_layout Standard
23122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23125 \begin_layout Standard
23133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23136 \begin_layout Standard
23145 <row topline="true" bottomline="true">
23146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23149 \begin_layout Standard
23157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23160 \begin_layout Standard
23168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23171 \begin_layout Standard
23179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23182 \begin_layout Standard
23198 \begin_layout Standard
23199 They can also be inserted with the math toolbar button
23200 \begin_inset Graphics
23201 filename ../images/math/functions.png
23209 \begin_layout Subsection
23210 Self-defined Functions
23211 \begin_inset LatexCommand index
23212 name "Functions ! self-defined"
23219 \begin_layout Standard
23220 To use a function that is not predefined, like for example the sign function
23221 sgn(x), there are two possibilities:
23224 \begin_layout Itemize
23225 Define the function by inserting the following line to the LaTeX-preamble
23229 \begin_layout Standard
23234 DeclareMathOperator
23237 \begin_inset LatexCommand ref
23238 reference "sub:Self-defined-Operators"
23250 \begin_inset VSpace -3mm
23259 DeclareMathOperator{
23264 \begin_inset LatexCommand index
23265 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
23272 \begin_inset VSpace -2mm
23277 Now the new defined function can be called with the command
23286 \begin_layout Itemize
23287 Write the the formula as usual, mark the formula name, in our example the
23292 , and change it to mathematical text.
23293 At last a space is inserted between prefactor and function.
23296 \begin_layout Standard
23297 The result is the same with both methods as with a predefined function
23301 \begin_layout Standard
23302 In LyX self-defined functions are displayed red, predefined ones black.
23310 \begin_layout Standard
23312 \begin_inset Tabular
23313 <lyxtabular version="3" rows="3" columns="2">
23315 <column alignment="center" valignment="top" leftline="true" width="0pt">
23316 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
23317 <row topline="true" bottomline="true">
23318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23321 \begin_layout Standard
23327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23330 \begin_layout Standard
23337 <row topline="true" bottomline="true">
23338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23341 \begin_layout Standard
23349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23352 \begin_layout Standard
23353 \begin_inset Formula $A\sgn(x)+B$
23362 <row topline="true" bottomline="true">
23363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23366 \begin_layout Standard
23370 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
23378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23381 \begin_layout Standard
23382 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
23398 \begin_layout Standard
23399 The first method is more suitable when the self-defined function should
23400 be used several times.
23403 \begin_layout Subsection
23405 \begin_inset LatexCommand index
23413 \begin_layout Standard
23414 For limits there are defined besides
23421 \begin_inset LatexCommand index
23422 name "Commands ! L ! \\textbackslash lim"
23438 furthermore the following functions:
23441 \begin_layout Standard
23443 \begin_inset Tabular
23444 <lyxtabular version="3" rows="5" columns="2">
23446 <column alignment="center" valignment="top" leftline="true" width="0">
23447 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
23448 <row topline="true" bottomline="true">
23449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23452 \begin_layout Standard
23458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23461 \begin_layout Standard
23463 \begin_inset Note Note
23466 \begin_layout Standard
23473 is only used as spacer.
23484 <row topline="true">
23485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23488 \begin_layout Standard
23496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23499 \begin_layout Standard
23500 \begin_inset Formula $\varliminf$
23510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23513 \begin_layout Standard
23521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23524 \begin_layout Standard
23525 \begin_inset Formula $\varlimsup$
23535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23538 \begin_layout Standard
23546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23549 \begin_layout Standard
23550 \begin_inset Formula $\varprojlim$
23559 <row bottomline="true">
23560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23563 \begin_layout Standard
23571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23574 \begin_layout Standard
23575 \begin_inset Formula $\varinjlim$
23579 \begin_inset Formula $\raisebox{-2.5mm}{}$
23595 \begin_layout Standard
23596 \begin_inset VSpace medskip
23599 The limit is created by inserting a subscript.
23600 It is set right beside the function in an inline formula:
23603 \begin_layout Standard
23605 \begin_inset Tabular
23606 <lyxtabular version="3" rows="2" columns="2">
23608 <column alignment="center" valignment="top" width="0pt">
23609 <column alignment="center" valignment="top" width="0pt">
23611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23614 \begin_layout Standard
23620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23623 \begin_layout Standard
23627 \begin_layout Standard
23637 \begin_inset Note Note
23640 \begin_layout Standard
23653 are used here as spacer.
23665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23668 \begin_layout Standard
23677 \begin_layout Standard
23690 \begin_layout Standard
23704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23707 \begin_layout Standard
23708 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
23724 \begin_layout Standard
23725 In a displayed formula the limit is set below the formula, as usual:
23726 \begin_inset Formula \[
23734 \begin_layout Subsection
23736 \begin_inset LatexCommand index
23737 name "Functions ! modulo-"
23744 \begin_layout Standard
23745 The modulo-function is special, because it exists in four variants.
23748 \begin_layout Standard
23749 The variants in a displayed formula:
23750 \begin_inset Formula \begin{align*}
23751 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
23752 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
23753 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
23754 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
23755 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
23762 \begin_layout Standard
23763 In an inline formula less space is set before the function names for all
23767 \begin_layout Section
23769 \begin_inset LatexCommand index
23770 name "Special characters"
23777 \begin_layout Subsection
23778 Special Characters in Mathematical Text
23781 \begin_layout Standard
23782 The following commands can only be used in mathematical text or in TeX-mode:
23785 \begin_layout Standard
23789 \begin_inset Tabular
23790 <lyxtabular version="3" rows="8" columns="2">
23792 <column alignment="block" valignment="top" leftline="true" width="0">
23793 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
23794 <row topline="true" bottomline="true">
23795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23798 \begin_layout Standard
23804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23807 \begin_layout Standard
23814 <row topline="true">
23815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23818 \begin_layout Standard
23826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23829 \begin_layout Standard
23830 \begin_inset Formula $\textrm{\oe}$
23839 <row topline="true">
23840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23843 \begin_layout Standard
23851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23854 \begin_layout Standard
23855 \begin_inset Formula $\textrm{\OE}$
23864 <row topline="true">
23865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23868 \begin_layout Standard
23876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23879 \begin_layout Standard
23880 \begin_inset Formula $\textrm{\ae}$
23889 <row topline="true">
23890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23893 \begin_layout Standard
23901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23904 \begin_layout Standard
23905 \begin_inset Formula $\textrm{\AE}$
23914 <row topline="true">
23915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23918 \begin_layout Standard
23926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23929 \begin_layout Standard
23930 \begin_inset Formula $\textrm{\aa}$
23939 <row topline="true" bottomline="true">
23940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23943 \begin_layout Standard
23947 \begin_inset LatexCommand index
23948 name "\\@\\textrm{\\AA}"
23957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23960 \begin_layout Standard
23961 \begin_inset Formula $\textrm{\AA}$
23970 <row bottomline="true">
23971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23974 \begin_layout Standard
23982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23985 \begin_layout Standard
23986 \begin_inset Formula $\textrm{\i}$
24002 \begin_inset Tabular
24003 <lyxtabular version="3" rows="8" columns="2">
24005 <column alignment="block" valignment="top" leftline="true" width="0">
24006 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24007 <row topline="true" bottomline="true">
24008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24011 \begin_layout Standard
24013 \begin_inset Note Note
24016 \begin_layout Standard
24023 is used for separation, because otherwise the output will be ¡ and ¿ respective
24034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24037 \begin_layout Standard
24044 <row topline="true">
24045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24048 \begin_layout Standard
24056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24059 \begin_layout Standard
24060 \begin_inset Formula $\textrm{\o}$
24069 <row topline="true">
24070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24073 \begin_layout Standard
24081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24084 \begin_layout Standard
24085 \begin_inset Formula $\textrm{\O}$
24094 <row topline="true">
24095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24098 \begin_layout Standard
24106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24109 \begin_layout Standard
24110 \begin_inset Formula $\textrm{\l}$
24119 <row topline="true">
24120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24123 \begin_layout Standard
24131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24134 \begin_layout Standard
24135 \begin_inset Formula $\textrm{\L}$
24144 <row topline="true" bottomline="true">
24145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24148 \begin_layout Standard
24153 \begin_layout Standard
24166 \begin_layout Standard
24180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24183 \begin_layout Standard
24184 \begin_inset Formula $\textrm{!`}$
24193 <row bottomline="true">
24194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24197 \begin_layout Standard
24202 \begin_layout Standard
24215 \begin_layout Standard
24229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24232 \begin_layout Standard
24233 \begin_inset Formula $\textrm{?`}$
24242 <row bottomline="true">
24243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24246 \begin_layout Standard
24254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24257 \begin_layout Standard
24258 \begin_inset Formula $\textrm{\j}$
24276 \begin_layout Standard
24278 \begin_inset Formula $\textrm{\textrm{Å}}$
24282 \begin_inset Formula $\textrm{\textrm{Ø}}$
24285 can also be inserted via the math toolbar button
24286 \begin_inset Graphics
24287 filename ../images/math/digamma.png
24295 \begin_layout Standard
24296 An exception are the commands
24302 \begin_layout Standard
24319 \begin_layout Standard
24330 , because they can be inserted in LyX directly to text.
24333 \begin_layout Subsection
24335 \begin_inset LatexCommand label
24336 name "sub:Accents-in-Text"
24341 \begin_inset LatexCommand index
24342 name "Accents ! in text"
24349 \begin_layout Standard
24350 With the following commands all letters can be accented.
24351 The commands must be inserted in TeX-mode.
24354 \begin_layout Standard
24358 \begin_inset Tabular
24359 <lyxtabular version="3" rows="8" columns="2">
24361 <column alignment="block" valignment="top" leftline="true" width="0">
24362 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
24363 <row topline="true" bottomline="true">
24364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24367 \begin_layout Standard
24373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24376 \begin_layout Standard
24383 <row topline="true">
24384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24387 \begin_layout Standard
24391 \begin_inset Quotes grd
24399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24402 \begin_layout Standard
24406 \begin_layout Standard
24421 <row topline="true">
24422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24425 \begin_layout Standard
24433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24436 \begin_layout Standard
24440 \begin_layout Standard
24455 <row topline="true">
24456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24459 \begin_layout Standard
24466 \begin_layout Standard
24480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24483 \begin_layout Standard
24487 \begin_layout Standard
24502 <row topline="true">
24503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24506 \begin_layout Standard
24514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24517 \begin_layout Standard
24521 \begin_layout Standard
24536 <row topline="true">
24537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24540 \begin_layout Standard
24547 \begin_layout Standard
24561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24564 \begin_layout Standard
24568 \begin_layout Standard
24583 <row topline="true" bottomline="true">
24584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24587 \begin_layout Standard
24594 \begin_layout Standard
24608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24611 \begin_layout Standard
24615 \begin_layout Standard
24630 <row bottomline="true">
24631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24634 \begin_layout Standard
24641 \begin_layout Standard
24655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24658 \begin_layout Standard
24662 \begin_layout Standard
24684 \begin_inset Tabular
24685 <lyxtabular version="3" rows="8" columns="2">
24687 <column alignment="block" valignment="top" leftline="true" width="0">
24688 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24689 <row topline="true" bottomline="true">
24690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24693 \begin_layout Standard
24699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24702 \begin_layout Standard
24709 <row topline="true">
24710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24713 \begin_layout Standard
24720 \begin_layout Standard
24734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24737 \begin_layout Standard
24741 \begin_layout Standard
24756 <row topline="true">
24757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24760 \begin_layout Standard
24768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24771 \begin_layout Standard
24775 \begin_layout Standard
24790 <row topline="true">
24791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24794 \begin_layout Standard
24798 \begin_inset LatexCommand index
24808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24811 \begin_layout Standard
24815 \begin_layout Standard
24830 <row topline="true">
24831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24834 \begin_layout Standard
24842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24845 \begin_layout Standard
24849 \begin_layout Standard
24864 <row topline="true" bottomline="true">
24865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24868 \begin_layout Standard
24875 \begin_layout Standard
24889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24892 \begin_layout Standard
24896 \begin_layout Standard
24911 <row bottomline="true">
24912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24915 \begin_layout Standard
24922 \begin_layout Standard
24936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24939 \begin_layout Standard
24943 \begin_layout Standard
24958 <row bottomline="true">
24959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24962 \begin_layout Standard
24969 \begin_layout Standard
24983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24986 \begin_layout Standard
24990 \begin_layout Standard
25014 \begin_layout Standard
25015 \begin_inset VSpace medskip
25024 also two different characters can be accented.
25033 \begin_layout Standard
25048 \begin_layout Standard
25060 \begin_layout Standard
25073 can in combination with vowels directly be inserted with the keyboard without
25075 The same applies for the tilde
25079 \begin_layout Standard
25080 This only applies for keyboards where the tilde is defined as accent.
25089 in combination with
25104 \begin_layout Standard
25147 , and accents inserted directly with the keyboard are also available in
25149 For the other accents there are special math commands to be used in formulas,
25151 \begin_inset LatexCommand ref
25152 reference "sub:Accents-for-one"
25159 \begin_layout Standard
25160 \begin_inset VSpace bigskip
25163 Furthermore, with the command
25170 \begin_inset LatexCommand index
25171 name "Commands ! T ! \\textbackslash textcircled"
25175 all numbers and letters can be set into a circle, quasi accented with a
25176 circle, similar to the the copyright symbol.
25179 \begin_layout Standard
25181 \begin_inset Tabular
25182 <lyxtabular version="3" rows="3" columns="2">
25184 <column alignment="center" valignment="top" leftline="true" width="0">
25185 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25186 <row topline="true" bottomline="true">
25187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25190 \begin_layout Standard
25196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25199 \begin_layout Standard
25201 \begin_inset Note Note
25204 \begin_layout Standard
25211 is only used as spacer.
25222 <row topline="true">
25223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25226 \begin_layout Standard
25234 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25237 \begin_layout Standard
25241 \begin_layout Standard
25256 <row topline="true" bottomline="true">
25257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25260 \begin_layout Standard
25271 raisebox{-1.5pt}{W}}
25276 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25279 \begin_layout Standard
25280 \begin_inset Formula $\raisebox{4.5mm}{}$
25287 \begin_layout Standard
25305 \begin_inset Formula $\raisebox{-2mm}{}$
25321 \begin_layout Standard
25322 One has to take care that the character fits in the circle.
25333 \begin_layout Standard
25335 \begin_inset LatexCommand ref
25336 reference "sub:Font-Sizes"
25345 specifies thereby the size of the circle.
25356 \begin_layout Standard
25358 \begin_inset LatexCommand ref
25359 reference "sub:Boxes-without-Frame"
25368 the character can be centered.
25371 \begin_layout Subsection
25373 \begin_inset LatexCommand index
25374 name "Minuscule numbers"
25381 \begin_layout Standard
25382 Minuscule numbers are created with the command
25389 \begin_inset LatexCommand index
25390 name "Commands ! O ! \\textbackslash oldstylenums"
25395 The command can be used in formulas and in TeX-mode.
25396 The command scheme is:
25399 \begin_layout Standard
25404 oldstylenums{number}
25407 \begin_layout Standard
25412 oldstylenums{0123456789
25415 \begin_inset Formula $\oldstylenums{0123456789}$
25421 \begin_layout Subsection
25422 Miscellaneous Special Characters
25423 \begin_inset LatexCommand label
25424 name "sub:Miscellaneous-Special-Characters"
25429 \begin_inset LatexCommand index
25430 name "Special characters ! miscellaneous"
25437 \begin_layout Standard
25438 The following characters can only be inserted to formulas by using commands:
25441 \begin_layout Standard
25443 \begin_inset Tabular
25444 <lyxtabular version="3" rows="4" columns="2">
25446 <column alignment="center" valignment="top" leftline="true" width="0">
25447 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25448 <row topline="true" bottomline="true">
25449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25452 \begin_layout Standard
25458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25461 \begin_layout Standard
25468 <row topline="true">
25469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25472 \begin_layout Standard
25479 \begin_layout Standard
25493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25496 \begin_layout Standard
25497 \begin_inset Formula $\mathcircumflex$
25506 <row topline="true">
25507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25510 \begin_layout Standard
25518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25521 \begin_layout Standard
25522 \begin_inset Formula $\_$
25531 <row topline="true" bottomline="true">
25532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25535 \begin_layout Standard
25540 \begin_layout Standard
25552 \begin_inset LatexCommand index
25562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25565 \begin_layout Standard
25566 \begin_inset Formula $^{\circ}$
25582 \begin_layout Standard
25583 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
25584 contains the following line
25588 \begin_layout Standard
25589 More about this is described in
25590 \begin_inset LatexCommand ref
25591 reference "sub:Text-Characters-in"
25603 \begin_layout Standard
25608 DeclareInputtext{176}{
25618 f\SpecialChar \textcompwordmark{}
25622 \begin_layout Standard
25623 \begin_inset VSpace bigskip
25627 \begin_inset LatexCommand index
25632 is designed as accent, thus is looks alone a bit misplaced: ~
25635 addresses (URLs) sometimes a single tilde is needed.
25636 In this case the relation sign
25644 \begin_layout Standard
25646 \begin_inset LatexCommand ref
25647 reference "sec:Relations"
25658 is used in a formula.
25659 As a formula cannot be created in an URL-box (menu
25661 Insert\SpecialChar \menuseparator
25664 ), the URL is inserted as normal text with the font style '
25669 Should the URL be a hyperlink in the DVI- or PDF-output, the command
25679 \begin_layout Standard
25686 can only be used together with the LaTeX-package
25691 \begin_inset LatexCommand index
25692 name "Packages ! hyperref"
25703 is written in the section
25709 Embedded\InsetSpace ~
25718 \begin_inset LatexCommand index
25719 name "Commands ! H ! \\textbackslash href"
25726 \begin_layout Standard
25727 As example an URL with a tilde:
25730 \begin_layout Standard
25733 http://www.lyx.org/
25734 \begin_inset Formula $\sim$
25740 \begin_layout Standard
25751 \begin_layout Standard
25755 href{http://www.lyx.org/~mustermann}{
25760 http://www.lyx.org/
25761 \begin_inset Formula $\sim$
25768 \begin_layout Standard
25778 \begin_layout Section
25780 \begin_inset LatexCommand label
25781 name "sec:Formula-Styles"
25786 \begin_inset LatexCommand index
25787 name "Formula ! styles"
25794 \begin_layout Itemize
25795 There are two different alignment styles:
25799 \begin_layout Description
25800 Centered is the predefined standard
25803 \begin_layout Description
25804 Indented for this the option
25808 must be inserted in the menu
25810 Document\SpecialChar \menuseparator
25815 Document\InsetSpace ~
25819 \begin_layout Standard
25824 is used, the indentation can be adjusted with the length
25831 \begin_inset LatexCommand index
25832 name "Commands ! M ! \\textbackslash mathindent"
25837 Should the distance be 15\InsetSpace \thinspace{}
25838 mm, the following command line is inserted in
25842 \begin_layout Standard
25852 \begin_layout Standard
25853 When no length is specified, the predefined value of 30\InsetSpace \thinspace{}
25858 \begin_layout Itemize
25859 And two different numbering styles:
25863 \begin_layout Description
25864 Right is the predefined standard
25867 \begin_layout Description
25868 Left for this the option
25872 must be inserted in the menu
25874 Document\SpecialChar \menuseparator
25879 Document\InsetSpace ~
25884 \begin_layout Standard
25893 can also be used together.
25894 In this case both options are inserted, separated by a comma.
25897 \begin_layout Standard
25898 The chosen styles are used for all displayed formulas of the document.
25899 When both, centered and indented formulas should be created in a document,
25905 The indented formulas are then set in a flalign environment, see
25906 \begin_inset LatexCommand ref
25907 reference "sub:Flalign-Environment"
25914 \begin_layout Section
25916 \begin_inset LatexCommand label
25917 name "sec:Multiline-Formulas"
25922 \begin_inset LatexCommand index
25923 name "Formula ! multiline"
25930 \begin_layout Subsection
25934 \begin_layout Standard
25935 In LyX multiline formulas are created by pressing
25946 that is described in
25947 \begin_inset LatexCommand ref
25948 reference "sub:Standard-align-Environment"
25955 \begin_layout Standard
25956 There are other multiline formula environments that can be created via the
25959 Insert\SpecialChar \menuseparator
25963 These environments are described in the following sections.
25966 \begin_layout Standard
25967 In all multiline formula environments a new line is created by pressing
25973 To add or delete lines, the math toolbar buttons
25974 \begin_inset Graphics
25975 filename ../images/tabular-feature_append-row.png
25981 \begin_inset Graphics
25982 filename ../images/tabular-feature_delete-row.png
25987 , respectively, or the menu
25989 Edit\SpecialChar \menuseparator
25995 \begin_layout Subsubsection
25997 \begin_inset LatexCommand label
25998 name "sub:Line-Separation"
26003 \begin_inset LatexCommand index
26004 name "Formula ! multiline ! Line separation"
26011 \begin_layout Standard
26012 There is sometimes not enough space in multiline formulas between the lines:
26013 \begin_inset Formula \begin{eqnarray*}
26014 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}\\
26015 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*}
26022 \begin_layout Standard
26023 In LaTeX additional line space is specified as optional argument of the
26025 This is not yet possible in LyX
26029 \begin_layout Standard
26034 \begin_layout Standard
26038 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
26047 \begin_layout Standard
26059 , therefore the whole formula must be inserted in TeX-mode.
26060 To add in our example space, the command
26068 is inserted at the end of the first line.
26073 \begin_layout Standard
26080 \begin_layout Standard
26082 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26085 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26092 \begin_layout Standard
26096 left(B^{2}+x_{0}^{2}
26104 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26109 \begin_layout Standard
26121 \begin_layout Standard
26122 \begin_inset VSpace bigskip
26125 To set the the line separation for all lines in a formula, the length
26132 \begin_inset LatexCommand index
26133 name "Commands ! J ! \\textbackslash jot"
26139 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26149 is the value 3\InsetSpace \thinspace{}
26151 To create 3\InsetSpace \thinspace{}
26152 mm additional line separation as in the previous example, the
26156 \begin_layout Standard
26166 \begin_layout Standard
26167 is inserted in TeX-mode before the formula.
26168 This requires that the LaTeX-package
26176 \begin_layout Standard
26181 is part of every LaTeX standard installation.
26187 \begin_inset LatexCommand index
26188 name "Packages ! calc"
26192 was loaded in LaTeX-preamble with the line
26195 \begin_layout Standard
26203 \begin_layout Standard
26208 \begin_layout Standard
26220 \begin_inset Formula \begin{eqnarray*}
26221 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}\\
26222 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*}
26229 \begin_layout Standard
26233 \begin_layout Standard
26244 To get back to the predefined distance,
26250 is set to the value 3\InsetSpace \thinspace{}
26254 \begin_layout Subsubsection
26256 \begin_inset LatexCommand label
26257 name "sub:Column-Separation"
26262 \begin_inset LatexCommand index
26263 name "Formula ! multiline ! Column separation"
26270 \begin_layout Standard
26271 Multiline formulas form a matrix.
26272 A formula in the eqnarray environment is for example a matrix with three
26274 By changing the column separation in this environment, the space beside
26275 the relation sign can be changed.
26278 \begin_layout Standard
26279 The column separation is specified with the length
26286 \begin_inset LatexCommand index
26287 name "Commands ! A ! \\textbackslash arraycolsep"
26293 column separation = 2\InsetSpace \thinspace{}
26305 \begin_layout Standard
26315 \begin_layout Standard
26316 inserted in TeX-mode, sets for all following formulas a column separation
26317 of 2\InsetSpace \thinspace{}
26319 To get back to the predefined distance,
26325 is set to 5\InsetSpace \thinspace{}
26329 \begin_layout Standard
26330 A formula with 2\InsetSpace \thinspace{}
26331 cm column separation:
26335 \begin_layout Standard
26347 \begin_inset Formula \begin{eqnarray*}
26349 C & \ne & A\end{eqnarray*}
26353 A formula with the predefined column separation for matrices of 10\InsetSpace \thinspace{}
26358 \begin_layout Standard
26370 \begin_inset Formula \begin{eqnarray*}
26372 C & \ne & A\end{eqnarray*}
26379 \begin_layout Subsubsection
26381 \begin_inset LatexCommand index
26382 name "Formula ! long"
26389 \begin_layout Standard
26390 Long formulas can be typeset using these methods:
26393 \begin_layout Itemize
26394 When one side of the equation is much shorther than the line width, this
26395 one is chosen for the left side and the right side is typeset over two
26400 \begin_layout Standard
26410 \begin_inset Formula \begin{eqnarray}
26411 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 \\
26412 & & -\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:kurzlang}\end{eqnarray}
26420 \begin_layout Standard
26431 The minus sign at the beginning of the second line does normally not appear
26432 as operator because it is the first character of the line.
26433 Thus it would not be surrounded by space and could not be distinguished
26434 from the fraction bar.
26435 To avoid this, space was inserted behind the minus sign with the command
26446 \begin_layout Standard
26454 \begin_inset LatexCommand ref
26455 reference "sub:Variable-Space"
26465 \begin_inset LatexCommand index
26466 name "Commands ! H ! \\textbackslash hspace"
26473 \begin_layout Itemize
26474 When both sides of the equation are too long, the command
26481 \begin_inset LatexCommand index
26482 name "Commands ! L ! \\textbackslash lefteqn"
26487 It is inserted to the first column of the first line and effects that all
26488 further insertions overwrite the following columns:
26492 \begin_layout Standard
26502 \begin_inset Formula \begin{eqnarray}
26503 \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 \\
26504 & & -\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 \\
26505 & & =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}
26513 \begin_layout Standard
26524 After the insertion of
26530 , the cursor is in a purple box that is a bit shifted to the left from the
26532 In this the formula is inserted.
26536 \begin_layout Standard
26547 The content of the further lines is inserted to the second or another formula
26549 The greater the column number where it was inserted, the larger the indentation.
26553 \begin_layout Standard
26565 \begin_inset Note Greyedout
26568 \begin_layout Standard
26569 Note the following when using
26578 \begin_layout Itemize
26579 The formula doesn't use the full page width.
26580 When e.\InsetSpace \thinspace{}
26583 \begin_inset Formula $-B^{2}$
26586 is added to the first line in the above example, it would have been outside
26588 To better use the width, negative space can be inserted at the beginning
26592 \begin_layout Itemize
26593 Due to a bug in LyX the cursor cannot be set with the mouse into the first
26598 \begin_layout Standard
26602 \begin_layout Standard
26606 href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
26615 \begin_layout Standard
26627 One can only set the cursor at the beginning of the line and move it with
26636 \begin_layout Itemize
26637 Other methods to set long formulas are offered by the environments described
26639 \begin_inset LatexCommand ref
26640 reference "sub:Multline-Environment"
26645 \begin_inset LatexCommand ref
26646 reference "sub:Multiline-Formula-Parts"
26653 \begin_layout Subsubsection
26655 \begin_inset LatexCommand label
26656 name "sub:Multiline-Brackets"
26661 \begin_inset LatexCommand index
26662 name "Brackets ! for multiline expressions"
26669 \begin_layout Standard
26670 For brackets spanning multiple lines the following problem occurs:
26671 \begin_inset Formula \begin{eqnarray*}
26672 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26673 & & \left.\cdots+B-D\right]\end{eqnarray*}
26680 \begin_layout Standard
26681 The closing bracket is smaller than the opening bracket because brackets
26682 with variable size may not span multiple lines.
26685 \begin_layout Standard
26686 To set the bracket size for the second line correctly, the first line is
26694 \begin_inset LatexCommand index
26695 name "Commands ! R ! \\textbackslash right"
26699 and the second line with
26707 \begin_layout Standard
26721 \begin_inset LatexCommand ref
26722 reference "sub:Automatic-Bracket-Size"
26734 \begin_inset LatexCommand index
26735 name "Commands ! L ! \\textbackslash left"
26757 \begin_layout Standard
26776 \begin_layout Standard
26795 \begin_layout Standard
26807 \begin_inset Formula $\downarrow$
26813 \begin_inset LatexCommand index
26814 name "Commands ! V ! \\textbackslash vphantom"
26818 is inserted, because the multiplication operator with its limits is the
26819 largest symbol in the first line and this should be the size for the bracket
26820 in the second line.
26823 \begin_layout Standard
26824 The result is this:
26825 \begin_inset Formula \begin{eqnarray*}
26826 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26827 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
26834 \begin_layout Subsection
26838 \begin_layout Standard
26839 Align environments can be used for every kind of multiline formulas.
26840 They are specially useful to set several formulas side by side.
26843 \begin_layout Standard
26844 Align environments consist of columns.
26845 The odd columns are right aligned, the even ones left aligned.
26846 Every line in an Align environment can be numbered.
26849 \begin_layout Standard
26850 Align environments are created via the menu
26852 Insert\SpecialChar \menuseparator
26858 Edit\SpecialChar \menuseparator
26859 Math\SpecialChar \menuseparator
26860 Change Formula Type
26862 already existing formulas can be converted to Align environments.
26865 \begin_layout Standard
26866 To add or delete columns, the math toolbar buttons
26867 \begin_inset Graphics
26868 filename ../images/tabular-feature_append-column.png
26874 \begin_inset Graphics
26875 filename ../images/tabular-feature_delete-column.png
26880 , respectively, or the menu
26882 Edit\SpecialChar \menuseparator
26888 \begin_layout Subsubsection
26889 Standard align Environment
26890 \begin_inset LatexCommand label
26891 name "sub:Standard-align-Environment"
26896 \begin_inset LatexCommand index
26897 name "Formula ! multiline ! align environment"
26904 \begin_layout Standard
26905 This Align environment is created by presssing
26909 in a formula or by the menu
26911 Insert\SpecialChar \menuseparator
26912 Math\SpecialChar \menuseparator
26913 AMS align Environment
26918 \begin_layout Standard
26919 An example for two formulas set side by side, that are created with a four
26920 column align environment:
26921 \begin_inset Formula \begin{align*}
26922 A & =\sin(B) & C & =D\\
26923 C & \ne A & B & \ne D\end{align*}
26927 As it can be seen, the formulas in this environment are placed so as if
26936 \begin_layout Standard
26944 \begin_inset LatexCommand ref
26945 reference "sub:Variable-Space"
26956 before the first and after every even column.
26957 When the formula style
26963 \begin_layout Standard
26965 \begin_inset LatexCommand ref
26966 reference "sec:Formula-Styles"
26977 is used, the formula is set without the
26983 before the first column.
26986 \begin_layout Subsubsection
26987 Alignat Environment
26988 \begin_inset LatexCommand index
26989 name "Formula ! multiline ! alignat environment"
26996 \begin_layout Standard
26997 The alignat environment has no predefined column separation.
26998 It can be inserted manually with the spaces that are described
26999 \begin_inset LatexCommand ref
27000 reference "sub:Space"
27007 \begin_layout Standard
27008 The above example in the alignat environment where 1\InsetSpace \thinspace{}
27009 cm space was inserted
27010 at the beginning of the second formula:
27011 \begin_inset Formula \begin{alignat*}{2}
27012 A & =\sin(B) & \hspace{1cm}C & =D\\
27013 C & \ne A & B & \ne D\end{alignat*}
27017 Because the column separation can be set separately for every column, this
27018 environment is especially suitable to set three and more formulas side
27022 \begin_layout Subsubsection
27023 Flalign Environment
27024 \begin_inset LatexCommand label
27025 name "sub:Flalign-Environment"
27030 \begin_inset LatexCommand index
27031 name "Formula ! multiline ! flalign environment"
27038 \begin_layout Standard
27039 In this environment the first two columns are always set as much as possible
27040 to the left and the last two ones to the right.
27042 \begin_inset Formula \begin{flalign*}
27043 A & =1 & B & =2 & C & =3\\
27044 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
27051 \begin_layout Standard
27052 By creating a flalign environment with an odd number of columns where an
27053 empty TeX-brace is inserted to the last column, several formulas in a document
27054 can be set to the left, although the formula style
27059 As example the indented formula
27060 \begin_inset LatexCommand eqref
27061 reference "eq:VolInt"
27066 \begin_inset Formula \begin{flalign}
27067 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
27071 The first two columns contain the formula.
27072 To indent it as with the formula style
27076 , 30\InsetSpace \thinspace{}
27077 pt space was inserted at the beginning of the first column.
27080 \begin_layout Subsection
27081 Eqnarray Environment
27082 \begin_inset LatexCommand index
27083 name "Formula ! multiline ! eqnarray environment"
27090 \begin_layout Standard
27091 When this environment has been created, three blue boxes appear.
27092 The content of the first box is right aligned, the content of the last
27094 The content of the middle box appears centered and a bit smaller, because
27095 it is designed to insert there only relation characters.
27096 \begin_inset Formula \begin{eqnarray*}
27097 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27099 A & = & A\end{eqnarray*}
27106 \begin_layout Subsection
27108 \begin_inset LatexCommand index
27109 name "Formula ! multiline ! gather environment"
27116 \begin_layout Standard
27117 This environment consists of only one centered column.
27118 Every line can be numbered.
27119 \begin_inset Formula \begin{gather}
27121 X=\textrm{-}1\end{gather}
27128 \begin_layout Subsection
27129 Multline Environment
27130 \begin_inset LatexCommand label
27131 name "sub:Multline-Environment"
27136 \begin_inset LatexCommand index
27137 name "Formula ! multiline ! multline environment"
27144 \begin_layout Standard
27145 The multline environment consists, like the gather environment, of only
27147 But the first line is left aligned, the last one right aligned.
27148 All other lines are centered.
27149 Therefore this environment is suitable for long formulas.
27151 \begin_inset LatexCommand eqref
27152 reference "eq:lefteqn"
27156 in the multline environment:
27157 \begin_inset Formula \begin{multline}
27158 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}\\
27159 -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}\\
27160 =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}
27167 \begin_layout Standard
27168 In the output only the last (first) line of a multline environment appears
27169 numbered when the document numbering is right (left).
27173 \begin_layout Standard
27174 numbering styles see
27175 \begin_inset LatexCommand ref
27176 reference "sec:Formula-Styles"
27185 This is also the case when there is a formula number displayed after every
27190 \begin_layout Standard
27195 \begin_layout Standard
27199 href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
27208 \begin_layout Standard
27223 \begin_layout Standard
27229 \begin_inset LatexCommand index
27230 name "Commands ! S ! \\textbackslash shoveright"
27241 \begin_inset LatexCommand index
27242 name "Commands ! S ! \\textbackslash shoveleft"
27248 a centered line can be right or left aligned, respectively.
27249 The commands are used as follows:
27252 \begin_layout Standard
27257 shoveright{line content}
27263 shoveleft{line content}
27266 \begin_layout Standard
27267 \begin_inset VSpace medskip
27275 \begin_inset LatexCommand index
27276 name "Commands ! M ! \\textbackslash multlinegap"
27282 specifies the distance of the first line from the left page margin.
27283 Predefined is the length 0\InsetSpace \thinspace{}
27287 \begin_layout Standard
27288 As example the above formula where the command
27291 \begin_layout Standard
27301 \begin_layout Standard
27302 was inserted in TeX-mode before:
27306 \begin_layout Standard
27318 \begin_inset Formula \begin{multline}
27319 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}\\
27320 \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}}\\
27321 =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}
27329 \begin_layout Standard
27340 The second line was left aligned using
27349 \begin_layout Subsection
27350 Multiline Formula Parts
27351 \begin_inset LatexCommand label
27352 name "sub:Multiline-Formula-Parts"
27357 \begin_inset LatexCommand index
27358 name "Formula ! multiline ! formula parts"
27365 \begin_layout Standard
27366 To display only parts of a formula with multiple lines, one of the following
27367 environments are used:
27384 They can be inserted via the menu
27386 Insert\SpecialChar \menuseparator
27389 or by using the commands described in this section.
27392 \begin_layout Standard
27393 The first three have the same properties as the corresponding multiline
27394 formula environments, but it is possible to set further formula parts beside
27397 \begin_inset Formula \[
27398 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
27399 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
27400 \right\} \textrm{Uncertainty relations}\]
27407 \begin_layout Standard
27408 To get this formula, a displayed formula is created where the command
27413 \begin_inset LatexCommand index
27414 name "Commands ! A ! \\textbackslash aligned"
27421 A purple box appears around the blue formula box where now columns and
27422 lines can be added.
27423 Outside the multiline environment other formula parts can be set, like
27427 \begin_layout Standard
27428 The aligned environment is also suitable for long formulas whose lines are
27429 horizontally aligned.
27430 Using aligned in a displayed formula has the advantage that the formula
27431 number is vertically centered behind the lines.
27433 \begin_inset LatexCommand eqref
27434 reference "eq:kurzlang"
27438 in the aligned environment:
27439 \begin_inset Formula \begin{equation}
27440 \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}|}\\
27441 & -\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}
27449 \begin_layout Standard
27450 To use the environments
27469 \begin_inset LatexCommand index
27470 name "Commands ! A ! \\textbackslash alignedat"
27481 \begin_inset LatexCommand index
27482 name "Commands ! G ! \\textbackslash gathered"
27493 \begin_inset LatexCommand index
27494 name "Commands ! S ! \\textbackslash split"
27498 are inserted, respectively.
27499 The split environment has the same properties as the aligned environment
27500 but it can only have two columns.
27503 \begin_layout Subsection
27504 Text in multiline Formulas
27505 \begin_inset LatexCommand label
27506 name "sub:Text-in-multiline"
27511 \begin_inset LatexCommand index
27512 name "Text ! in formulas"
27517 \begin_inset LatexCommand index
27518 name "Formula ! multiline ! text"
27525 \begin_layout Standard
27526 In the Align environments, and the multline and gather environment, text
27527 can be inserted that will appear in a separate line and doesn't affect
27528 the column alignment.
27529 To do this, the command
27534 \begin_inset LatexCommand index
27535 name "Commands ! I ! \\textbackslash intertext"
27541 is used in the following scheme:
27544 \begin_layout Standard
27552 \begin_layout Standard
27553 The text should not be longer than a line because it cannot be hyphenated.
27554 As LyX doesn't yet support
27560 directly, the text is written as mathematical text.
27567 must hereby be at the beginning of a line and appears in the output above
27569 An example where the text was inserted at the beginning of the second line:
27570 \begin_inset Formula \begin{align}
27571 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
27572 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
27579 \begin_layout Section
27581 \begin_inset LatexCommand index
27582 name "Formula numbering"
27587 \begin_inset LatexCommand index
27588 name "Formula ! numbering|see{Formula numbering}"
27595 \begin_layout Subsection
27599 \begin_layout Standard
27600 Numbered formulas can be created with the menu
27602 Insert\SpecialChar \menuseparator
27603 Math\SpecialChar \menuseparator
27604 Numbered\InsetSpace ~
27609 Ctrl-Alt\InsetSpace ~
27613 Existing formulas can be numbered with the menu
27615 Edit\SpecialChar \menuseparator
27616 Math\SpecialChar \menuseparator
27617 Toggle\InsetSpace ~
27626 The formula number is displayed in LyX behind the formula as number sign
27628 The number sign is replaced in the output by the formula number.
27631 \begin_layout Standard
27632 When numbering is turned on in multiline formulas, all lines will be numbered.
27633 But the numbering can be controlled with the menu
27635 Edit\SpecialChar \menuseparator
27636 Math\SpecialChar \menuseparator
27637 Toggle\InsetSpace ~
27638 Numbering\InsetSpace ~
27650 \begin_layout Standard
27651 Except of inline formulas, all formulas can be numbered with two different
27653 \begin_inset LatexCommand ref
27654 reference "sec:Formula-Styles"
27661 \begin_layout Subsection
27663 \begin_inset LatexCommand label
27664 name "sub:Cross-References"
27669 \begin_inset LatexCommand index
27670 name "Cross-references ! to formulas"
27677 \begin_layout Standard
27678 All labeled formulas can be cross-referenced.
27679 A label is added by the menu
27681 Insert\SpecialChar \menuseparator
27684 or the toolbar button
27685 \begin_inset Graphics
27686 filename ../images/label-insert.png
27692 The cursor must hereby be inside a displayed formula.
27693 A dialog pops up displaying the prefix
27698 The label is inserted there behind the prefix.
27699 The predefined prefix means
27700 \begin_inset Quotes eld
27704 \begin_inset Quotes erd
27707 and makes it easier to find labels in large documents because it marks
27708 it as formula label to divide it from e.\InsetSpace \thinspace{}
27711 To change a label, the menu
27713 Insert\SpecialChar \menuseparator
27719 \begin_layout Standard
27720 The name of the label is displayed in LyX within two parentheses behind
27722 A formula with a label is always numbered.
27723 When a label is deleted, the numbering is turned off, and vice versa.
27726 \begin_layout Standard
27727 Cross-references are inserted via the menu
27729 Insert\SpecialChar \menuseparator
27732 or with the toolbar button
27733 \begin_inset Graphics
27734 filename ../images/dialog-show-new-inset_ref.png
27740 A formula cross-reference appears in the output as formula number.
27741 When in the cross-reference dialog window the format
27745 is chosen, the cross-reference appears in the output as formula number
27748 By right-clicking on a cross-reference in LyX, one jumps
27749 to the formula that is referenced.
27752 \begin_layout Standard
27753 Here are as examples cross-references to formulas of the following subsections:
27754 \begin_inset Note Note
27757 \begin_layout Standard
27758 Note the different cross-reference types.
27766 \begin_layout Standard
27768 \begin_inset LatexCommand eqref
27774 \begin_inset LatexCommand eqref
27781 \begin_inset LatexCommand ref
27786 ) big Latin letters are used for the numbering in contrary to (
27787 \begin_inset LatexCommand ref
27795 \begin_layout Standard
27796 \begin_inset VSpace medskip
27799 When the argument of
27807 \begin_layout Standard
27815 \begin_inset LatexCommand ref
27816 reference "sub:User-defined-Numbering"
27827 contains a box like in
27828 \begin_inset LatexCommand ref
27829 reference "sub:Paragraph-Boxes"
27833 , the formula cannot be referenced.
27836 \begin_layout Subsection
27838 \begin_inset LatexCommand index
27839 name "Formula numbering ! subnumbering"
27846 \begin_layout Standard
27847 With the help of the commands
27851 begin{subequations}
27859 formulas can be subnumbered.
27860 Both commands are inserted in TeX-mode.
27863 \begin_layout Standard
27865 \begin_inset Formula \begin{equation}
27866 A=C-B\label{eq:a}\end{equation}
27874 \begin_layout Standard
27878 addtocounter{equation}{-1}
27887 \begin_layout Standard
27891 begin{subequations}
27897 \begin_inset VSpace -5mm
27901 \begin_inset Formula \begin{equation}
27902 B=C-A\label{eq:b}\end{equation}
27907 \begin_inset Formula \begin{equation}
27908 C=A+B\label{eq:c}\end{equation}
27915 \begin_layout Standard
27919 \begin_layout Standard
27931 \begin_layout Standard
27932 To create the example, the following is done:
27935 \begin_layout Enumerate
27936 first formula is inserted
27939 \begin_layout Enumerate
27944 addtocounter{equation}{-1}
27946 begin{subequations}
27947 \begin_inset LatexCommand index
27948 name "Commands ! A ! \\textbackslash addtocounter"
27956 is inserted after the first formula
27959 \begin_layout Enumerate
27960 second formula is inserted
27963 \begin_layout Enumerate
27964 third formula is inserted
27967 \begin_layout Enumerate
27974 is inserted after the third formula
27977 \begin_layout Standard
27978 Every formula between the commands
27990 is subnumbered as a, b,
27994 \begin_layout Standard
28003 c, \SpecialChar \ldots{}
28004 For multiline formulas every line will be subnumbered.
28005 All subnumbered formulas are treated as
28010 But as every numbered formula increases the counter
28014 by one, the command
28020 is needed to decrease it.
28021 Otherwise the formulas
28022 \begin_inset LatexCommand eqref
28028 \begin_inset LatexCommand eqref
28034 \begin_inset LatexCommand eqref
28039 would be numbered as
28040 \begin_inset LatexCommand eqref
28046 \begin_inset LatexCommand eqref
28052 \begin_inset LatexCommand eqref
28060 \begin_layout Standard
28061 By inserting the commands in TeX-mode, a space is created between the first
28063 To revert this -5\InsetSpace \thinspace{}
28064 mm vertical space is inserted after the command
28068 begin{subequations}
28071 When the formula style
28077 \begin_layout Standard
28079 \begin_inset LatexCommand ref
28080 reference "sec:Formula-Styles"
28091 is used, -7\InsetSpace \thinspace{}
28092 mm space is inserted instead.
28095 \begin_layout Standard
28096 Here is an example for a multiline formula where the numbering was turned
28097 off for the second line:
28101 \begin_layout Standard
28105 begin{subequations}
28111 \begin_inset Formula \begin{eqnarray}
28112 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
28113 & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
28114 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
28122 \begin_layout Standard
28134 \begin_layout Subsection
28135 User-defined Numbering
28136 \begin_inset LatexCommand label
28137 name "sub:User-defined-Numbering"
28142 \begin_inset LatexCommand index
28143 name "Formula numbering ! user-defined"
28150 \begin_layout Standard
28151 \begin_inset LatexCommand index
28152 name "Formula numbering ! self-defined delimiters"
28156 With the standard numbering parentheses are set around the formula number.
28157 To replace the parentheses for example by vertical bars, the following
28158 line is added to the LaTeX-preamble:
28161 \begin_layout Standard
28173 \begin_inset Note Note
28176 \begin_layout Standard
28177 This macro is already declared in the LaTeX-preamble for testing.
28178 To activate it, remove the percent sign at the beginning.
28186 \begin_layout Standard
28187 To use other characters, the vertical bars besides the
28191 are replaced by one ore more characters.
28192 To get only the formula number the vertical bars are omitted.
28195 \begin_layout Standard
28196 \begin_inset VSpace bigskip
28199 When there should be an expression of your choice instead of the consecutive
28200 formula number in parentheses behind the formula, the command
28207 \begin_inset LatexCommand index
28208 name "Commands ! T ! \\textbackslash tag"
28213 \begin_inset Formula \begin{equation}
28214 A+B=C\tag{something}\label{eq:tag}\end{equation}
28218 In this example the command
28226 \begin_layout Standard
28237 was inserted to the formula.
28240 \begin_layout Standard
28249 \begin_layout Standard
28260 is inserted instead, the star prevents the parentheses around the expression:
28261 \begin_inset Formula \[
28262 A+B=C\tag*{something}\]
28269 \begin_layout Standard
28270 \begin_inset VSpace bigskip
28273 To restart the formula numbering with new document parts or sections, the
28274 following command is used:
28277 \begin_layout Standard
28282 @addtoreset{equation}{part}
28285 \begin_inset LatexCommand index
28286 name "Commands ! \"@\" ! \\textbackslash \"@\"addtoreset"
28298 @addtoreset{equation}{section}
28301 \begin_layout Standard
28302 To be able to use these commands in TeX-mode, the
28303 \begin_inset Quotes eld
28307 \begin_inset Quotes erd
28310 character has to be made
28311 \begin_inset Quotes eld
28315 \begin_inset Quotes erd
28318 for LaTeX using the command
28332 So the command sequence in TeX-mode is:
28335 \begin_layout Standard
28344 @addtoreset{equation}{section}
28351 \begin_layout Standard
28352 In the LaTeX-preamble
28364 can be omitted as they are automatically internally inserted by LyX.
28367 \begin_layout Standard
28382 \begin_layout Standard
28387 is part of the LaTeX-package
28392 \begin_inset LatexCommand index
28393 name "Packages ! carlisle"
28397 that is part of every LaTeX standard installation.
28403 \begin_inset LatexCommand index
28404 name "Packages ! remreset"
28408 has to be loaded in the LaTeX-preamble with the line
28411 \begin_layout Standard
28416 usepackage{remreset}
28419 \begin_layout Standard
28427 \begin_inset LatexCommand index
28428 name "Commands ! \"@\" ! \\textbackslash \"@\"removefromreset"
28432 can be used with the same scheme as
28441 \begin_layout Standard
28442 \begin_inset VSpace bigskip
28445 Sometimes formulas should be numbered in the following form:
28448 \begin_layout Standard
28451 (section number.formula number)
28454 \begin_layout Standard
28455 The formula number should start with every section with
28456 \begin_inset Quotes eld
28460 \begin_inset Quotes erd
28466 \begin_layout Standard
28467 For this case there is the command
28474 \begin_inset LatexCommand index
28475 name "Commands ! N ! \\textbackslash numberwithin"
28479 , which is used with the following scheme:
28482 \begin_layout Standard
28487 numberwithin{counter}{sectioning}
28490 \begin_layout Standard
28491 Counter denotes what kind of numbering is affected, sectioning denotes what
28492 number is before the dot.
28495 \begin_layout Standard
28496 Thus in our case the following LaTeX-preamble or ERT line is used:
28499 \begin_layout Standard
28504 numberwithin{equation}{section}
28507 \begin_layout Standard
28508 This is the result:
28512 \begin_layout Standard
28516 numberwithin{equation}{section}
28522 \begin_inset Formula \begin{equation}
28523 A+B=C\end{equation}
28530 \begin_layout Standard
28531 To number e.\InsetSpace \thinspace{}
28533 tables so that the number of the part is the sectioning,
28539 numberwithin{table}{part}
28544 \begin_layout Standard
28545 To go back to the standard numbering or to prevent this kind of numbering
28546 when it is defined by the document class, the following command is inserted
28547 as ERT or to the LaTeX-preamble:
28550 \begin_layout Standard
28560 \begin_inset LatexCommand index
28561 name "Commands ! A ! \\textbackslash arabic"
28571 \begin_layout Standard
28603 \begin_layout Standard
28610 uses internally the command
28616 , described above, that also needs to be reverted.
28620 \begin_layout Standard
28627 \begin_layout Standard
28631 @removefromreset{equation}{section}
28634 \begin_layout Standard
28646 \begin_layout Subsection
28647 Numbering with Roman Numbers and Letters
28648 \begin_inset LatexCommand label
28649 name "sub:Numbering-with-Roman"
28654 \begin_inset LatexCommand index
28655 name "Formula numbering ! with letters"
28660 \begin_inset LatexCommand index
28661 name "Formula numbering ! with Roman numbers"
28668 \begin_layout Standard
28669 Formulas can also be numbered with Roman numbers and Latin letters.
28670 To number for example with small Roman numbers, the command
28673 \begin_layout Standard
28685 \begin_layout Standard
28686 is inserted before the formula in TeX-mode.
28694 \begin_inset LatexCommand index
28695 name "Commands ! R ! \\textbackslash renewcommand"
28699 redefines the predefined command
28715 \begin_layout Standard
28722 has the same scheme like the command
28728 that is described in
28729 \begin_inset LatexCommand ref
28730 reference "sec:User-defined-commands"
28744 is the formula counter.
28751 is used as prefix for a counter, the value of the counter is output as
28753 When a formula is numbered, LaTeX sets internally the command
28759 behind the formula.
28765 \begin_inset LatexCommand index
28766 name "Commands ! R ! \\textbackslash roman"
28772 outputs the counter as small Roman number.
28775 \begin_layout Standard
28776 All formulas behind the command
28786 are now numbered Roman.
28787 To switch to numbering with big Roman numbers, the command is inserted
28801 \begin_inset LatexCommand index
28802 name "Commands ! R ! \\textbackslash roman@\\textbackslash Roman"
28808 \begin_inset Quotes eld
28812 \begin_inset Quotes erd
28815 with small Latin letters there is the command
28822 \begin_inset LatexCommand index
28823 name "Commands ! A ! \\textbackslash alph"
28827 , for big ones there is the command
28834 \begin_inset LatexCommand index
28835 name "Commands ! A ! \\textbackslash alph@\\textbackslash Alph"
28842 \begin_layout Standard
28843 \begin_inset Note Greyedout
28846 \begin_layout Standard
28851 Only maximal 26 formulas can be numbered with Latin letters in one document.
28859 \begin_layout Standard
28863 \begin_layout Standard
28879 \begin_layout Standard
28880 \begin_inset Formula \begin{equation}
28881 A=\textrm{small roman}\label{eq:rom}\end{equation}
28889 \begin_layout Standard
28903 \begin_inset Formula \begin{equation}
28904 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
28912 \begin_layout Standard
28926 \begin_inset Formula \begin{equation}
28927 C=\textrm{small Latin}\label{eq:lat}\end{equation}
28935 \begin_layout Standard
28949 \begin_inset Formula \begin{equation}
28950 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
28957 \begin_layout Standard
28958 To switch back to the default numbering, insert the command:
28961 \begin_layout Standard
28971 \begin_inset LatexCommand index
28972 name "Commands ! A ! \\textbackslash arabic"
28979 \begin_layout Standard
28983 \begin_layout Standard
28997 \begin_inset Formula \begin{equation}
28998 E=\textrm{Arabic}\label{eq:arab}\end{equation}
29005 \begin_layout Standard
29006 \begin_inset VSpace medskip
29009 As you see, formulas are numbered serially independent from the numbering
29011 When then numbering should start with
29012 \begin_inset Quotes eld
29016 \begin_inset Quotes erd
29019 when the style is changed, new equation counters have to be defined.
29020 A description about this can be found in the file
29024 \begin_layout Standard
29028 href{Formula-numbering.lyx}{
29033 Formula-numbering.lyx
29037 \begin_layout Standard
29047 \begin_layout Section
29048 User-defined commands
29049 \begin_inset LatexCommand label
29050 name "sec:User-defined-commands"
29055 \begin_inset LatexCommand index
29056 name "User-defined commands"
29063 \begin_layout Standard
29064 Many LaTeX-commands are too long to be used frequently.
29065 But it is possible to define with the command
29072 \begin_inset LatexCommand index
29073 name "Commands ! N ! \\textbackslash newcommand"
29077 new shorter commands.
29080 \begin_layout Standard
29081 The command scheme of
29090 \begin_layout Standard
29095 newcommand{new command name}[number of arguments][optional
29105 \begin_layout Standard
29120 \begin_layout Standard
29127 {command definition}
29130 \begin_layout Standard
29131 \begin_inset Note Greyedout
29134 \begin_layout Standard
29139 Assure that the name of the new command is not already used in your document
29140 or by LaTeX-packages that you use.
29141 When you for example define the command
29153 , you get an error message because
29159 is already defined as command for
29160 \begin_inset Quotes eld
29164 \begin_inset Formula $\le$
29168 \begin_inset Quotes erd
29179 \begin_layout Standard
29180 \begin_inset Note Greyedout
29183 \begin_layout Standard
29188 The names of user-defined commands may only consist of Latin letters.
29196 \begin_layout Standard
29197 The number of arguments is an integer in the range 0\InsetSpace \thinspace{}
29198 -\InsetSpace \thinspace{}
29199 9 and specifies how
29200 many arguments the new command should have.
29201 With the optional value a value for an optional argument can be predefined.
29202 When this is done, the
29210 rgument of the new command is automatically an optional one.
29213 \begin_layout Standard
29214 Here are some examples:
29217 \begin_layout Itemize
29218 To define the command
29230 , the LaTeX-preamble line is:
29234 \begin_layout Standard
29256 \begin_layout Itemize
29257 To define the command
29269 , the argument (that should be underlined) must be taken into account.
29270 For this the preamble line is:
29274 \begin_layout Standard
29299 \begin_layout Standard
29318 acts as argument placeholder, the
29322 behind it denotes that it is the placeholder for the first argument.
29325 \begin_layout Itemize
29332 one can e.\InsetSpace \thinspace{}
29344 \begin_layout Standard
29363 framebox#1#2{$#3$}}
29369 \begin_layout Standard
29384 The two Dollar signs creates the extra formula needed for
29391 \begin_inset LatexCommand ref
29392 reference "sub:Boxes-with-Frame"
29399 \begin_layout Itemize
29400 To create a new command for
29406 where the color for the box needn't to be specified, the argument for the
29407 color is defined optional:
29411 \begin_layout Standard
29430 fcolorbox{#2}{#1}{$#3$}}
29436 \begin_layout Standard
29447 When the color is not specified when using
29453 , the predefined color
29460 \begin_layout Standard
29461 A test of the new defined commands:
29464 \begin_layout Standard
29466 \begin_inset Tabular
29467 <lyxtabular version="3" rows="6" columns="2">
29469 <column alignment="center" valignment="top" leftline="true" width="0">
29470 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
29471 <row topline="true" bottomline="true">
29472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29475 \begin_layout Standard
29481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29484 \begin_layout Standard
29486 \begin_inset Note Note
29489 \begin_layout Standard
29496 is only used as spacer.
29507 <row topline="true">
29508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29511 \begin_layout Standard
29518 \begin_layout Standard
29532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29535 \begin_layout Standard
29536 \begin_inset Formula $A\gr B$
29545 <row topline="true">
29546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29549 \begin_layout Standard
29557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29560 \begin_layout Standard
29561 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
29570 <row topline="true">
29571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29574 \begin_layout Standard
29578 \begin_inset Formula $\to$
29584 \begin_inset Formula $\to$
29595 \begin_layout Standard
29609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29612 \begin_layout Standard
29613 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
29622 <row topline="true">
29623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29626 \begin_layout Standard
29630 \begin_inset Formula $\to$
29641 \begin_layout Standard
29655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29658 \begin_layout Standard
29659 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
29668 <row topline="true" bottomline="true">
29669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29672 \begin_layout Standard
29678 \begin_inset Formula $\to$
29689 \begin_layout Standard
29703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29706 \begin_layout Standard
29707 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
29723 \begin_layout Section
29725 \begin_inset LatexCommand index
29733 \begin_layout Standard
29734 To create diagrams, the LaTeX-package
29740 \begin_layout Standard
29745 is part of every LaTeX standard installation.
29753 \begin_inset LatexCommand index
29754 name "Packages ! amscd"
29759 It is loaded in the LaTeX-preamble with the line
29762 \begin_layout Standard
29770 \begin_layout Standard
29771 Diagrams visualize relations and look like this:
29772 \begin_inset Formula \[
29773 \begin{CD}A@>>>B@>>>C\\
29775 F@<<<E@<<<D\end{CD}\]
29782 \begin_layout Standard
29783 To get them, the command
29788 \begin_inset LatexCommand index
29789 name "Commands ! C ! \\textbackslash CD"
29795 is inserted to a formula.
29796 A blue box appears with two dashed lines where further commands can be
29802 a new line is created.
29803 Horizontal relations are inserted in odd, vertical in even formula lines.
29806 \begin_layout Standard
29807 To create the relations there are the following commands:
29810 \begin_layout Itemize
29815 creates a left arrow,
29826 \begin_layout Itemize
29831 creates an up arrow,
29839 a vertical equal sign
29842 \begin_layout Itemize
29848 is a placeholder for non-existent relations
29851 \begin_layout Standard
29852 All arrows can be labeled as follows:
29855 \begin_layout Itemize
29856 Is text inserted between the first and second < or >, resp., it is placed
29858 When it is inserted between the second and third one, it appears under
29862 \begin_layout Itemize
29863 When text for vertical arrows is inserted between the first and second A
29864 or V, resp., it is placed left beside the arrow.
29865 When it is inserted between the second and third one, it appears right
29867 If the text contains an A or V, these letters must be set into a TeX-brace.
29870 \begin_layout Standard
29871 As example a diagram with all possible relations:
29874 \begin_layout Standard
29875 \begin_inset Formula \[
29876 \begin{CD}A@>j>>B@>>k>C@=F\\
29878 D@<<j<E@>k>>F@=C\end{CD}\]
29885 \begin_layout Standard
29886 The command for this is:
29896 \begin_layout Standard
29905 A@>j>>B@>>k>C@=F Ctrl-Enter
29911 \begin_layout Standard
29926 \begin_layout Standard
29939 \begin_layout Standard
29951 \begin_inset Formula $\to$
29962 \begin_layout Standard
29977 \begin_layout Standard
29990 \begin_layout Standard
30000 \begin_layout Standard
30006 \begin_layout Section
30011 \begin_layout Standard
30024 \begin_layout Standard
30025 Other useful math tips can be found in
30026 \begin_inset LatexCommand cite
30040 \begin_layout Standard
30048 \begin_inset Note Note
30051 \begin_layout Standard
30054 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
30057 \begin_layout Standard
30060 texorpdfstring is in section
30061 \begin_inset LatexCommand ref
30062 reference "sub:Formulas-in-Section"
30072 \begin_inset LatexCommand index
30078 \begin_inset LatexCommand index
30079 name "Ions|see{Chemical characters}"
30086 \begin_layout Subsection
30087 Chemical Symbols and Equations
30088 \begin_inset LatexCommand label
30089 name "sub:Chemical-Symbols-and"
30094 \begin_inset LatexCommand index
30095 name "Chemical characters ! Symbols"
30100 \begin_inset LatexCommand index
30101 name "Chemical equations"
30106 \begin_inset LatexCommand index
30107 name "Symbols ! chemical"
30114 \begin_layout Standard
30115 An example text from chemistry:
30118 \begin_layout Quote
30120 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30123 -ion reacts with two
30124 \begin_inset Formula $\mathrm{Na^{+}}$
30127 -ions to sodium sulfate
30128 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30132 The chemical equation for this is:
30133 \begin_inset Formula \[
30134 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
30141 \begin_layout Standard
30142 This chemical equation can directly be created as formula.
30143 To avoid that the symbols appear italic, everything is highlighted and
30144 changed by the shortcut
30149 to the upright font style.
30153 \begin_layout Standard
30159 \begin_inset LatexCommand ref
30160 reference "sub:Font-Styles"
30172 \begin_layout Subsection
30174 \begin_inset LatexCommand index
30175 name "Numbers ! negative"
30182 \begin_layout Standard
30183 Negative numbers often look ugly in formulas because the minus sign before
30184 the number is set with the same length as the minus operator sign.
30185 When writing the negative number in normal text, the minus sign appears
30189 \begin_layout Standard
30190 Thus, the problem disappears when converting the minus sign to mathematical
30194 \begin_layout Standard
30195 An example to visualize the problem:
30198 \begin_layout Standard
30200 \begin_inset Tabular
30201 <lyxtabular version="3" rows="3" columns="2">
30203 <column alignment="right" valignment="top" leftline="true" width="0">
30204 <column alignment="left" valignment="top" rightline="true" width="0">
30205 <row topline="true">
30206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30209 \begin_layout Standard
30215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30218 \begin_layout Standard
30225 <row topline="true" bottomline="true">
30226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30229 \begin_layout Standard
30235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30238 \begin_layout Standard
30239 \begin_inset Formula $x=-2$
30248 <row topline="true" bottomline="true">
30249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30252 \begin_layout Standard
30258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30261 \begin_layout Standard
30262 \begin_inset Formula $x=\textrm{-}2$
30278 \begin_layout Subsection
30279 Comma as Decimal Separator
30280 \begin_inset LatexCommand index
30288 \begin_layout Standard
30289 In LaTeX a comma inside a formula is used, according to the English convention,
30290 as number group separator.
30291 So there will be space added behind all commas in formulas.
30294 \begin_layout Standard
30295 To avoid this, the comma is highlighted and changed to mathematical text
30304 \begin_layout Standard
30305 To use all formula commas in the document as decimal separator, the file
30314 \begin_layout Standard
30319 is part of the LaTeX-package
30324 \begin_inset LatexCommand index
30325 name "Packages ! was\\vspace{4mm}"
30335 \begin_inset LatexCommand index
30336 name "Packages ! icomma"
30340 is loaded with the LaTeX-preamble line
30343 \begin_layout Standard
30351 \begin_layout Subsection
30353 \begin_inset LatexCommand label
30354 name "sub:Physical-Vectors"
30359 \begin_inset LatexCommand index
30360 name "Vectors ! physical"
30367 \begin_layout Standard
30368 Predefined vectors are offered by the LaTeX-package
30376 \begin_layout Standard
30381 should be part of every LaTeX standard installation.
30387 \begin_inset LatexCommand index
30388 name "Packages ! braket"
30392 that is loaded with the LaTeX-preamble line
30395 \begin_layout Standard
30403 \begin_layout Standard
30407 \begin_layout Standard
30417 \begin_inset Note Note
30420 \begin_layout Standard
30421 The following table will only be displayed when the LaTeX-package
30430 The following commands are defined:
30433 \begin_layout Standard
30435 \begin_inset Tabular
30436 <lyxtabular version="3" rows="4" columns="2">
30438 <column alignment="center" valignment="top" leftline="true" width="0">
30439 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30440 <row topline="true" bottomline="true">
30441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30444 \begin_layout Standard
30450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30453 \begin_layout Standard
30460 <row topline="true">
30461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30464 \begin_layout Standard
30474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30477 \begin_layout Standard
30478 \begin_inset Formula $\Bra{\psi}$
30487 <row topline="true">
30488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30491 \begin_layout Standard
30501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30504 \begin_layout Standard
30505 \begin_inset Formula $\Ket{\psi}$
30514 <row topline="true" bottomline="true">
30515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30518 \begin_layout Standard
30530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30533 \begin_layout Standard
30534 \begin_inset Formula $\Braket{\psi|\phi}$
30550 \begin_layout Standard
30557 assures that all vertical bars are set in the size of the surrounding brackets:
30558 \begin_inset Formula \[
30559 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
30567 \begin_layout Standard
30577 \begin_inset Note Note
30580 \begin_layout Standard
30581 The following will be displayed when the LaTeX-package
30593 \begin_layout Standard
30594 You need to install the LaTeX-package
30598 to see the rest of this subsection in the output.
30601 \begin_layout Standard
30605 \begin_layout Standard
30617 \begin_layout Standard
30624 can also be achieved using the command
30630 , that is described in
30631 \begin_inset LatexCommand ref
30632 reference "sub:Automatic-Bracket-Size"
30639 \begin_layout Subsection
30640 Self-defined Fractions
30641 \begin_inset LatexCommand label
30642 name "sub:Self-defined-Fractions"
30647 \begin_inset LatexCommand index
30648 name "Fractions ! self-defined"
30655 \begin_layout Standard
30656 To define custom commands for fractions, the command
30663 \begin_inset LatexCommand index
30664 name "Commands ! G ! \\textbackslash genfrac"
30668 is used in the following scheme:
30671 \begin_layout Standard
30684 bracket}{fraction bar thickness}{style}
30690 \begin_layout Standard
30705 \begin_layout Standard
30712 {numerator}{denominator}
30715 \begin_layout Standard
30716 The style is a number in the range of 0\InsetSpace \thinspace{}
30717 -\InsetSpace \thinspace{}
30721 \begin_layout Standard
30723 \begin_inset Tabular
30724 <lyxtabular version="3" rows="5" columns="2">
30726 <column alignment="center" valignment="top" leftline="true" width="0">
30727 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30728 <row topline="true" bottomline="true">
30729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30732 \begin_layout Standard
30738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30741 \begin_layout Standard
30748 <row topline="true">
30749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30752 \begin_layout Standard
30758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30761 \begin_layout Standard
30762 display style formula
30768 <row topline="true">
30769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30772 \begin_layout Standard
30778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30781 \begin_layout Standard
30788 <row topline="true">
30789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30792 \begin_layout Standard
30798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30801 \begin_layout Standard
30808 <row topline="true" bottomline="true">
30809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30812 \begin_layout Standard
30818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30821 \begin_layout Standard
30835 \begin_layout Standard
30836 When no style is given, the size is adjusted to the surrounding environment
30837 like for the command
30846 \begin_layout Standard
30847 When no fraction bar thickness is given, the predefined value of 0.4\InsetSpace \thinspace{}
30852 \begin_layout Standard
30853 \begin_inset VSpace medskip
30856 For example, the commands
30869 \begin_inset LatexCommand ref
30870 reference "sub:Fractions"
30874 are defined with the commands
30877 \begin_layout Standard
30886 genfrac{}{}{}{0}{#1}{#2}}
30889 \begin_layout Standard
30893 \begin_layout Standard
30902 genfrac{(}{)}{0pt}{1}{#1}{#2}}
30905 \begin_layout Standard
30906 \begin_inset VSpace medskip
30909 To define a fraction where the fraction bar thickness can be given as optional
30910 argument, the following line is inserted to the LaTeX-preamble:
30913 \begin_layout Standard
30922 genfrac{}{}{#1}{}{#2}{#3}}
30925 \begin_layout Standard
30927 \begin_inset Formula \begin{align*}
30928 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
30929 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
30933 As one can see, the distance of the numerator and the denominator to the
30934 fraction bar is round about three times the bar thickness.
30937 \begin_layout Subsection
30939 \begin_inset LatexCommand label
30940 name "sub:Canceled-Formulas"
30945 \begin_inset LatexCommand index
30946 name "Formula ! canceled"
30953 \begin_layout Standard
30954 To cancel formulas or formula parts, the LaTeX-package
30962 \begin_layout Standard
30967 is part of every LaTeX standard installation.
30973 \begin_inset LatexCommand index
30974 name "Packages ! cancel"
30978 has to be loaded with the LaTeX-preamble line
30981 \begin_layout Standard
30986 usepackage[samesize]{cancel}
30989 \begin_layout Standard
30990 There are four ways to cancel formulas:
30993 \begin_layout Standard
30995 \begin_inset Tabular
30996 <lyxtabular version="3" rows="5" columns="2">
30998 <column alignment="center" valignment="top" leftline="true" width="0">
30999 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
31000 <row topline="true" bottomline="true">
31001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31004 \begin_layout Standard
31010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31013 \begin_layout Standard
31015 \begin_inset Note Note
31018 \begin_layout Standard
31031 are used here as spacer.
31042 <row topline="true">
31043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31046 \begin_layout Standard
31055 \begin_layout Standard
31069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31072 \begin_layout Standard
31073 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
31082 <row topline="true">
31083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31086 \begin_layout Standard
31095 \begin_layout Standard
31109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31112 \begin_layout Standard
31113 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
31122 <row topline="true" bottomline="true">
31123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31126 \begin_layout Standard
31135 \begin_layout Standard
31149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31152 \begin_layout Standard
31153 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
31162 <row topline="true" bottomline="true">
31163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31166 \begin_layout Standard
31170 \begin_inset Formula $\to$
31181 \begin_layout Standard
31195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31198 \begin_layout Standard
31199 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
31215 \begin_layout Standard
31222 is especially suitable to visualize the reduction of fractions within formulas:
31223 \begin_inset Formula \[
31224 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
31231 \begin_layout Subsection
31232 Formulas in Section Headings
31233 \begin_inset LatexCommand label
31234 name "sub:Formulas-in-Section"
31239 \begin_inset LatexCommand index
31240 name "Formula ! in section headings"
31247 \begin_layout Standard
31248 When formulas are used in section headings, the following has to be taken
31252 \begin_layout Standard
31253 \begin_inset Note Greyedout
31256 \begin_layout Standard
31257 When the LaTeX-package
31262 \begin_inset LatexCommand index
31263 name "Packages ! hyperref"
31267 is used, PDF-bookmarks are automatically created for every section heading
31268 in the table of contents.
31269 If a section heading contains formulas, they are incorrectly displayed
31270 in the bookmark text, because formulas in bookmarks infringe the PDF convention
31279 \begin_layout Standard
31280 Both problems can be solved by inserting at the end of the section heading
31281 a short title with the menu
31283 Insert\SpecialChar \menuseparator
31288 Short titles are used as alternative for multiline section headings to
31289 keep the table of contents clearly arranged.
31290 Only the short title appears in the table of contents and therefore also
31291 in the PDF-bookmark.
31294 \begin_layout Standard
31295 When formulas should be used in the table of contents but
31299 is used, one can use the following command in TeX-mode:
31302 \begin_layout Standard
31307 texorpdfstring{part}{alternative}
31308 \begin_inset LatexCommand index
31309 name "Commands ! T ! \\textbackslash texorpdfstring"
31316 \begin_layout Standard
31317 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
31318 This can be characters, formulas, footnotes, but also cross-references.
31319 The alternative is used instead of the part for the bookmark.
31322 \begin_layout Standard
31323 Here are two example headings:
31324 \begin_inset VSpace -3mm
31331 \begin_layout Standard
31343 \begin_layout Subsubsection
31344 Heading without formula in table of contents
31345 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31349 \begin_inset OptArg
31352 \begin_layout Standard
31353 Heading without formula in table of contents
31361 \begin_layout Subsubsection
31362 Heading with formula in table of contents
31366 \begin_layout Standard
31376 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31383 \begin_layout Standard
31393 \begin_layout Standard
31397 \begin_layout Standard
31406 In the first heading a short title was used, in the second one
31415 \begin_layout Standard
31416 To get the same formatting as for the other headings, the complete heading
31419 boldmath environment
31425 \begin_layout Standard
31427 \begin_inset LatexCommand ref
31428 reference "sub:Bold-Formulas"
31440 \begin_layout Subsection
31441 Formulas in multi-column Text
31442 \begin_inset LatexCommand index
31443 name "Formula ! in multi-column text"
31450 \begin_layout Standard
31451 Formulas in multi-column text are often too wide to fit into a column and
31452 thus need to be set over the whole page width.
31453 This is done by using the LaTeX-package
31461 \begin_layout Standard
31466 is part of every LaTeX standard installation.
31472 \begin_inset LatexCommand index
31473 name "Packages ! multicol"
31477 , that is loaded with the LaTeX-preamble line
31480 \begin_layout Standard
31485 usepackage{multicol}
31488 \begin_layout Standard
31489 \begin_inset Note Greyedout
31492 \begin_layout Standard
31493 Note herby that the setting
31495 Two-column\InsetSpace ~
31500 Document\SpecialChar \menuseparator
31523 \begin_layout Standard
31524 Before the multi-column text the command
31527 \begin_layout Standard
31532 begin{multicols}{column number}
31535 \begin_layout Standard
31536 is written in TeX-mode.
31537 The column number is a number in the range of 2\InsetSpace \thinspace{}
31538 -\InsetSpace \thinspace{}
31540 Before the formula the multi-column text is ended by inserting the command
31543 \begin_layout Standard
31551 \begin_layout Standard
31555 \begin_layout Standard
31556 Due to the command some space is automatically added before the formula.
31557 To revert this, -6\InsetSpace \thinspace{}
31558 mm vertical space is inserted before the formula.
31559 When the formula style
31565 \begin_layout Standard
31567 \begin_inset LatexCommand ref
31568 reference "sec:Formula-Styles"
31579 is used, -9\InsetSpace \thinspace{}
31580 mm space is inserted instead.
31583 \begin_layout Standard
31584 As example a multi-column text with a displayed formula:
31587 \begin_layout Standard
31591 \begin_layout Standard
31595 begin{multicols}{2}
31600 Das Spektrum wird fouriertransformiert.
31601 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
31602 , Lösungsmittel) zu trennen.
31603 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
31604 nun das Aussehen des Ausgangssignals.
31605 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
31606 über alle Phasen integrieren muss.
31608 \begin_inset Formula $S$
31611 unser normiertes Ausgangssignal and
31612 \begin_inset Formula $P$
31615 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
31619 \begin_layout Standard
31629 \begin_inset VSpace -6mm
31633 \begin_inset Formula \begin{equation}
31634 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
31642 \begin_layout Standard
31646 begin{multicols}{2}
31652 \begin_inset Formula $S_{0}$
31655 das Signal ohne Gradient ist and the Normierungsbedingung
31656 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
31660 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
31662 \begin_inset Formula $\nicefrac{\pi}{2}$
31665 \InsetSpace \thinspace{}
31666 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
31667 das Signal zusätzlich abschwächt.
31668 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
31670 \begin_inset Formula $T_{2}$
31676 \begin_layout Standard
31680 \begin_layout Standard
31692 \begin_layout Subsection
31693 Formulas with Description of Variables
31694 \begin_inset LatexCommand index
31695 name "Formula ! with description of variables"
31702 \begin_layout Standard
31703 To describe variables within a formula, like in formula
31704 \begin_inset LatexCommand eqref
31705 reference "eq:within"
31714 \begin_inset Formula $n$
31718 matrix is used with left aligned columns for the
31719 \begin_inset Formula $n$
31726 \begin_layout Standard
31728 \begin_inset LatexCommand ref
31729 reference "sec:Matrices"
31738 To set the description in a smaller size, before the matrix e.\InsetSpace \thinspace{}
31751 \begin_layout Standard
31753 \begin_inset LatexCommand ref
31754 reference "sub:Font-Sizes"
31766 \begin_layout Standard
31767 When the formula style
31773 \begin_layout Standard
31775 \begin_inset LatexCommand ref
31776 reference "sec:Formula-Styles"
31797 \begin_layout Standard
31804 only works in formulas with the style
31809 \begin_inset LatexCommand ref
31810 reference "sub:Variable-Space"
31819 is inserted before and after the matrix to have the same separation of
31820 the matrix from the equation and the side margin.
31823 \begin_layout Standard
31824 When the formula style
31828 is used, the method described in
31829 \begin_inset LatexCommand ref
31830 reference "sub:Flalign-Environment"
31834 is used to indent formulas.
31836 \begin_inset LatexCommand eqref
31837 reference "eq:within"
31841 consists of five columns whereas in the first two columns contain the equation,
31842 the third the matrix, and the last one an empty TeX-brace.
31843 \begin_inset Formula \begin{flalign}
31844 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
31845 \rho & \textrm{density}\\
31846 V & \textrm{volume}\\
31847 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
31854 \begin_layout Subsection
31855 Upright small Greek Letters
31856 \begin_inset LatexCommand label
31857 name "sub:Upright-small-Greek"
31862 \begin_inset LatexCommand index
31863 name "Greek letters ! upright"
31870 \begin_layout Standard
31871 Most of the math fonts only provide italic small Greek letters.
31872 But for symbols of elementary particles like pions and neutrinos, upright
31873 Greek letters are needed.
31882 \begin_layout Standard
31887 is part of the LaTeX-package
31892 \begin_inset LatexCommand index
31893 name "Packages ! was\\vspace{4mm}"
31903 \begin_inset LatexCommand index
31904 name "Packages ! upgreek"
31908 that is loaded with the LaTeX-preamble line
31911 \begin_layout Standard
31916 usepackage{upgreek}
31919 \begin_layout Standard
31925 \begin_layout Standard
31935 \begin_inset Note Note
31938 \begin_layout Standard
31939 The following table will only be displayed when the LaTeX-package
31948 They are created when the command for a small Greek letters is started
31954 For example the command
31961 \begin_inset Formula $\uptau$
31967 \begin_layout Standard
31968 With these commands reactions of elementary particles can be typeset:
31969 \begin_inset Formula \[
31970 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
31977 \begin_layout Standard
31978 The upright letters are more bold and wider than the italic ones.
31979 They should therefore not be used for units like
31980 \begin_inset Quotes eld
31984 \begin_inset Quotes erd
31990 \begin_layout Standard
31994 \begin_layout Standard
32004 \begin_inset Note Note
32007 \begin_layout Standard
32008 The following will be displayed when the LaTeX-package
32020 \begin_layout Standard
32021 You need to install the LaTeX-package
32025 to see the rest of this subsection in the output.
32028 \begin_layout Standard
32032 \begin_layout Standard
32044 \begin_layout Subsection
32045 Text Characters in Formulas
32046 \begin_inset LatexCommand label
32047 name "sub:Text-Characters-in"
32052 \begin_inset LatexCommand index
32053 name "Text ! in formulas"
32060 \begin_layout Standard
32061 In some cases you might want to insert text characters directly into formulas.
32062 When for example the centered dot · is often used in formulas like
32063 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
32066 , one would have to insert the command
32076 \begin_layout Standard
32078 \begin_inset LatexCommand ref
32079 reference "sub:Binary-Operators"
32088 all the time, because this character is defined in all encodings as text
32090 But the encoding can be changed by this LaTeX-preamble line:
32093 \begin_layout Standard
32098 Declare Inputtext{183}{
32108 f\SpecialChar \textcompwordmark{}
32112 \begin_layout Standard
32113 The character encoding (menu
32115 Document\SpecialChar \menuseparator
32116 Settings\SpecialChar \menuseparator
32119 ) specifies what character appears when a keyboard key is pressed.
32120 When the key for the character '·' is pressed, internally the command
32127 But this command is not available in a formula so that you would get LaTeX-erro
32129 With the changed encoding the right command is chosen automatically, depending
32130 on if the character was inserted into a formula or not.
32133 \begin_layout Standard
32134 The encoding of several characters is saved in definition files.
32135 Fore example the encoding
32139 is defined in the file
32143 that is in the installation folder of LaTeX.
32144 Encodings should only be changed via the LaTeX-preamble and not in the
32146 Otherwise own documents could not be edited by other LyX users working
32147 on other computers.
32150 \begin_layout Standard
32151 \begin_inset VSpace medskip
32154 Besides the centered dot, in this document the degree sign ° is defined
32155 with the following LaTeX-preamble line so that it can directly be inserted
32159 \begin_layout Standard
32164 DeclareInputtext{176}{
32174 f\SpecialChar \textcompwordmark{}
32178 \begin_layout Standard
32184 \begin_layout Section
32186 Typographic Advises
32187 \begin_inset LatexCommand index
32188 name "Typographic Advises"
32195 \begin_layout Standard
32196 This section is a summary of the most important typographic rules, listed
32201 \begin_layout Standard
32202 This collection was partly taken from the German semi-official dictionary
32204 \begin_inset Quotes eld
32208 \begin_inset Quotes erd
32212 \begin_inset LatexCommand cite
32217 that lists some of the ISO rules.
32225 \begin_layout Itemize
32234 \begin_layout Standard
32235 done with font styles, see
32236 \begin_inset LatexCommand ref
32237 reference "sub:Font-Styles"
32246 : 30\InsetSpace \thinspace{}
32249 Between the value and the unit is the smallest space, see
32250 \begin_inset LatexCommand ref
32251 reference "sub:Predefined-Space"
32258 \begin_layout Itemize
32259 Percent and perthousand signs are set like physical units:
32261 1,2\InsetSpace \thinspace{}
32266 \begin_layout Standard
32279 \begin_layout Itemize
32280 The degree sign follows directly on the value: 15°, but not when it is used
32281 in units: 15\InsetSpace \thinspace{}
32285 \begin_layout Itemize
32286 In numbers with more than four digits the smallest space is inserted before
32287 every third digit to group them:
32296 18\InsetSpace \thinspace{}
32297 473\InsetSpace \thinspace{}
32301 \begin_layout Itemize
32302 For dimensionings like 120×90×40\InsetSpace \thinspace{}
32303 cm the multiplication sign
32304 \begin_inset Quotes eld
32308 \begin_inset Quotes erd
32312 It is available with the LaTeX-command
32318 , but can also directly be inserted with some keyboard definitions.
32321 \begin_layout Itemize
32322 Functions with names consisting of several letters are set upright to avoid
32324 \begin_inset LatexCommand ref
32325 reference "sub:Predefined-Functions"
32332 \begin_layout Itemize
32333 Indices consisting of several letters, are set upright:
32334 \begin_inset Formula $E_{\mathrm{kin}}$
32339 Components of matrices are set italic:
32340 \begin_inset Formula $\hat{H}_{kl}$
32346 \begin_layout Itemize
32347 The differentiation/integration operator 'd', the Euler's number 'e', and
32348 the imaginary unit 'i' should be set upright, to avoid mixing them up with
32352 \begin_layout Standard
32358 \begin_layout Section
32360 \begin_inset LatexCommand index
32368 \begin_layout Standard
32369 Some characters and symbols can be created with several commands.
32370 Here is a list of the synonym commands:
32373 \begin_layout Standard
32374 \begin_inset VSpace bigskip
32380 \begin_inset Tabular
32381 <lyxtabular version="3" rows="12" columns="2">
32383 <column alignment="center" valignment="top" leftline="true" width="0pt">
32384 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
32385 <row topline="true" bottomline="true">
32386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32389 \begin_layout Standard
32395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32398 \begin_layout Standard
32400 \begin_inset Note Note
32403 \begin_layout Standard
32410 is only used as spacer.
32421 <row topline="true">
32422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32425 \begin_layout Standard
32433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32436 \begin_layout Standard
32440 \begin_layout Standard
32453 \begin_layout Standard
32466 <row topline="true">
32467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32470 \begin_layout Standard
32478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32481 \begin_layout Standard
32490 <row topline="true">
32491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32494 \begin_layout Standard
32502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32505 \begin_layout Standard
32514 <row topline="true">
32515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32518 \begin_layout Standard
32526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32529 \begin_layout Standard
32536 <row topline="true">
32537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32540 \begin_layout Standard
32548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32551 \begin_layout Standard
32558 <row topline="true">
32559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32562 \begin_layout Standard
32570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32573 \begin_layout Standard
32582 <row topline="true">
32583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32586 \begin_layout Standard
32594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32597 \begin_layout Standard
32606 <row topline="true">
32607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32610 \begin_layout Standard
32618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32621 \begin_layout Standard
32630 <row topline="true">
32631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32634 \begin_layout Standard
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32645 \begin_layout Standard
32654 <row topline="true">
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32669 \begin_layout Standard
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32760 \begin_layout Standard
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32771 \begin_layout Standard
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32784 \begin_layout Standard
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32876 \begin_layout Standard
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32887 \begin_layout Standard
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32900 \begin_layout Standard
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32935 \begin_layout Standard
32944 <row topline="true">
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32948 \begin_layout Standard
32956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32959 \begin_layout Standard
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32972 \begin_layout Standard
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33001 \begin_layout Standard
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33020 The LaTeX Companion
33023 Addison Wesley, 2004
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33036 \begin_layout Standard
33040 href{ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf}{
33049 \begin_layout Standard
33056 of LaTeX's math abilities
33059 \begin_layout Bibliography
33060 \begin_inset LatexCommand bibitem
33065 LaTeX tips and tricks-
33069 \begin_layout Standard
33073 href{http://tug.org/TeXnik/}{
33082 \begin_layout Standard
33092 \begin_layout Bibliography
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33102 \begin_layout Standard
33106 href{ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf}{
33115 \begin_layout Standard
33126 \begin_layout Standard
33138 \begin_layout Bibliography
33139 \begin_inset LatexCommand bibitem
33148 \begin_layout Standard
33152 href{ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}{
33161 \begin_layout Standard
33168 of all symbols available with LaTeX-packages
33171 \begin_layout Bibliography
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33181 \begin_layout Standard
33185 href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{
33194 \begin_layout Standard
33201 of the LaTeX-package
33206 \begin_inset LatexCommand index
33207 name "Packages ! hyperref"
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33215 \begin_inset LatexCommand bibitem
33224 \begin_layout Standard
33228 href{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}{
33237 \begin_layout Standard
33251 \begin_inset LatexCommand ref
33252 reference "sub:Operator-Limits"
33257 \begin_inset LatexCommand index
33258 name "Commands ! M ! \\textbackslash mathclap"
33265 \begin_layout Bibliography
33266 \begin_inset LatexCommand bibitem
33277 Auflage, Duden 2001
33280 \begin_layout Subsubsection*
33281 \begin_inset LatexCommand printindex