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.
11441 \begin_layout Standard
11442 Due to a bug in LyX the cursor has to be placed left beside blue the boxes
11447 \begin_layout Standard
11451 href{http://bugzilla.lyx.org/show_bug.cgi?id=2461}{
11460 \begin_layout Standard
11472 The first two boxes are surrounded by brackets and denote the two optional
11474 The third box is for formula parts like for
11483 \begin_layout Standard
11485 \begin_inset Note Note
11488 \begin_layout Standard
11489 The table has been set into a minipage to make the footnote appearing.
11490 Otherwise the footnote text would not be displayed.
11496 \begin_inset Box Frameless
11505 height_special "totalheight"
11508 \begin_layout Standard
11510 \begin_inset Tabular
11511 <lyxtabular version="3" rows="5" columns="2">
11513 <column alignment="center" valignment="top" leftline="true" width="0">
11514 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
11515 <row topline="true" bottomline="true">
11516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11519 \begin_layout Standard
11524 \begin_layout Standard
11525 Due to a bug in LyX it is not possible to create a new formula with
11533 \begin_layout Standard
11537 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11546 \begin_layout Standard
11563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11566 \begin_layout Standard
11568 \begin_inset Note Note
11571 \begin_layout Standard
11578 is only used as spacer.
11589 <row topline="true">
11590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11593 \begin_layout Standard
11600 \begin_layout Standard
11619 \begin_layout Standard
11633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11636 \begin_layout Standard
11637 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
11647 <row topline="true">
11648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11651 \begin_layout Standard
11658 \begin_layout Standard
11673 \begin_layout Standard
11687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11690 \begin_layout Standard
11691 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
11700 <row topline="true">
11701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11704 \begin_layout Standard
11711 \begin_layout Standard
11725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11728 \begin_layout Standard
11729 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
11738 <row topline="true" bottomline="true">
11739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11742 \begin_layout Standard
11749 \begin_layout Standard
11759 \begin_inset Formula $\to$
11763 \begin_inset Formula $\to$
11776 \begin_layout Standard
11786 \begin_inset Formula $\downarrow$
11794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11797 \begin_layout Standard
11798 \begin_inset Formula $\raisebox{6mm}{}$
11802 \begin_inset Formula $\framebox[20mm]{$\frac{A}{B}$}$
11806 \begin_inset Formula $\raisebox{-4mm}{}$
11827 \begin_layout Standard
11828 The frame thickness can also be adjusted.
11829 To do this the following commands have to be inserted in TeX-mode before
11833 \begin_layout Standard
11843 \begin_inset Quotes eld
11847 \begin_inset Quotes erd
11861 \begin_inset Quotes eld
11865 \begin_inset Quotes erd
11871 \begin_layout Standard
11872 \begin_inset Quotes eld
11876 \begin_inset Quotes erd
11879 specifies the minimal distance between the frame and the first character
11881 An example for this is the following framed formula:
11885 \begin_layout Standard
11897 \begin_inset Formula \[
11902 Before this formula the commands
11905 \begin_layout Standard
11927 \begin_layout Standard
11928 were inserted in TeX-mode.
11929 The given values are used for all following boxes.
11932 \begin_layout Standard
11933 To return to the standard frame size, the command
11936 \begin_layout Standard
11961 \begin_layout Standard
11975 \begin_layout Standard
11976 is inserted in TeX-mode before the next formula.
11979 \begin_layout Subsection
11980 Boxes without Frame
11981 \begin_inset LatexCommand label
11982 name "sub:Boxes-without-Frame"
11987 \begin_inset LatexCommand index
11988 name "Boxes ! without frame"
11995 \begin_layout Standard
11996 For boxes without a frame there are the following box commands:
12003 \begin_inset LatexCommand index
12004 name "Commands ! M ! \\textbackslash mbox"
12015 \begin_inset LatexCommand index
12016 name "Commands ! M ! \\textbackslash makebox"
12027 \begin_inset LatexCommand index
12028 name "Commands ! R ! \\textbackslash raisebox"
12035 \begin_layout Standard
12042 a box can be super- or subscripted.
12043 But in contrary to normal super- and subscripting, the characters in the
12044 box keep their font size.
12051 is used in the following scheme:
12054 \begin_layout Standard
12059 raisebox{height}{box content}
12062 \begin_layout Standard
12063 When the box should contain a formula, an extra formula is needed like for
12073 \begin_layout Standard
12075 \begin_inset Tabular
12076 <lyxtabular version="3" rows="4" columns="2">
12078 <column alignment="center" valignment="top" leftline="true" width="0">
12079 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12080 <row topline="true" bottomline="true">
12081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12084 \begin_layout Standard
12090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12093 \begin_layout Standard
12100 <row topline="true">
12101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12104 \begin_layout Standard
12108 \begin_inset Formula $\to$
12114 \begin_inset Formula $\to$
12122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12125 \begin_layout Standard
12126 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12135 <row topline="true" bottomline="true">
12136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12139 \begin_layout Standard
12143 \begin_inset Formula $\to$
12149 \begin_inset Formula $\to$
12157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12160 \begin_layout Standard
12161 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12170 <row topline="true" bottomline="true">
12171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12174 \begin_layout Standard
12178 \begin_inset Formula $\to$
12193 \begin_layout Standard
12207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12210 \begin_layout Standard
12214 \begin_layout Standard
12238 \begin_layout Standard
12239 The last formula can currently only be created using TeX-mode because LyX
12240 inserts a box instead of the needed extra formula.
12244 \begin_layout Standard
12249 \begin_layout Standard
12253 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12262 \begin_layout Standard
12277 \begin_layout Standard
12302 , with the difference that there is no frame.
12305 \begin_layout Subsection
12307 \begin_inset LatexCommand label
12308 name "sub:Colored-Boxes"
12313 \begin_inset LatexCommand index
12314 name "Boxes ! colored"
12321 \begin_layout Standard
12322 To be able to use all commands explained in this section, the LaTeX-package
12331 \begin_layout Standard
12336 is part of every LaTeX standard installation.
12342 \begin_inset LatexCommand index
12343 name "Packages ! color"
12347 has to be loaded in the LaTeX-preamble with the line
12351 \begin_layout Standard
12352 When text is colored somewhere in the document with a predefined color,
12353 LyX loads the LaTeX-package
12358 Thus it is possible that the package is loaded twice, but this doesn't
12365 \begin_inset Note Note
12368 \begin_layout Standard
12369 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12378 \begin_layout Standard
12386 \begin_layout Standard
12387 \begin_inset VSpace medskip
12390 To color boxes, the command
12397 \begin_inset LatexCommand index
12398 name "Commands ! C ! \\textbackslash colorbox"
12402 is used in the following scheme:
12405 \begin_layout Standard
12410 colorbox{color}{box content}
12413 \begin_layout Standard
12414 The box content can also be a box and a
12420 can also be part of another box (see the 2nd and 3rd example).
12421 When the box should contain a formula, an extra formula has to be created,
12432 \begin_layout Standard
12433 This also applies for the command
12444 \begin_layout Standard
12448 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12457 \begin_layout Standard
12472 \begin_layout Standard
12473 One of the following predefined colors can be chosen:
12476 \begin_layout Standard
12510 \begin_layout Standard
12512 \begin_inset Tabular
12513 <lyxtabular version="3" rows="4" columns="2">
12515 <column alignment="center" valignment="top" leftline="true" width="0">
12516 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12517 <row topline="true" bottomline="true">
12518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12521 \begin_layout Standard
12527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12530 \begin_layout Standard
12532 \begin_inset Note Note
12535 \begin_layout Standard
12542 is only used as spacer.
12553 <row topline="true">
12554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12557 \begin_layout Standard
12561 \begin_inset Formula $\to$
12571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12574 \begin_layout Standard
12575 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12584 <row topline="true">
12585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12588 \begin_layout Standard
12592 \begin_inset Formula $\to$
12603 \begin_layout Standard
12617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12620 \begin_layout Standard
12621 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
12630 <row topline="true" bottomline="true">
12631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12634 \begin_layout Standard
12641 \begin_layout Standard
12653 \begin_inset Formula $\to$
12663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12666 \begin_layout Standard
12667 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
12683 \begin_layout Standard
12690 only colors the box but not the characters in the box.
12691 To color all characters, the whole formula is highlighted and the wanted
12692 color is chosen in the
12698 The dialog can be called with the toolbar button
12699 \begin_inset Graphics
12700 filename ../images/dialog-show_character.png
12707 Edit\SpecialChar \menuseparator
12709 Style\SpecialChar \menuseparator
12713 The formula number has then the same color as the formula.
12714 When the formula number should get another color than the formula characters,
12715 the color must be changed within the formula.
12718 \begin_layout Standard
12722 \begin_layout Standard
12725 \begin_inset Formula \begin{equation}
12726 \int A=B\label{eq:red}\end{equation}
12733 \begin_inset Formula \begin{equation}
12734 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
12741 \begin_layout Standard
12743 \begin_inset LatexCommand eqref
12748 is completely colored red.
12751 \begin_inset LatexCommand eqref
12752 reference "eq:redgreen"
12756 was first completely colored green to set the color for the formula number.
12757 Subsequently the formula characters were colored red.
12760 \begin_layout Standard
12761 \begin_inset VSpace bigskip
12764 To color the frame different than the rest of the box, the command
12771 \begin_inset LatexCommand index
12772 name "Commands ! F ! \\textbackslash fcolorbox"
12776 is used in the following scheme:
12779 \begin_layout Standard
12784 fcolorbox{frame color}{color}{box content}
12787 \begin_layout Standard
12794 is an extension of the command
12801 The frame width is set, like for
12824 \begin_layout Standard
12836 \begin_inset Formula \[
12837 \fcolorbox{cyan}{magenta}{A=B}\]
12845 \begin_layout Standard
12859 \begin_layout Standard
12860 This formula was created with the command
12867 \begin_inset Formula $\to$
12873 \begin_inset Formula $\to$
12883 \begin_layout Standard
12884 \begin_inset VSpace bigskip
12887 To use other colors than the predefined ones, they have to be defined first.
12890 \begin_layout Standard
12891 One can for example define the color
12892 \begin_inset Quotes eld
12900 \begin_inset Quotes erd
12903 with the LaTeX-preamble line:
12906 \begin_layout Standard
12911 definecolor{darkgreen}{cmyk}{0.5,
12926 \begin_inset LatexCommand index
12927 name "Commands ! D ! \\textbackslash definecolor"
12934 \begin_layout Standard
12939 is the color space that denotes the colors
12956 The four comma separated numbers are the portion factor for the corresponding
12957 colors of the color space.
12958 The factors can be in the range of 0\InsetSpace \thinspace{}
12959 -\InsetSpace \thinspace{}
12965 also the color space
12969 can be used for definitions.
12986 , so that there are in this case three portion factors for the corresponding
12988 Furthermore there is the color space
12992 with one portion factor for the gray value.
12995 \begin_layout Standard
12996 As example a framed box with the new defined color
13000 where the characters have been colored
13005 \begin_inset Formula \begin{equation}
13006 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13013 \begin_layout Standard
13014 Self-defined colors can also be used for text with the help of the command
13022 \begin_inset LatexCommand index
13023 name "Text ! colored"
13030 \begin_layout Standard
13034 \begin_layout Standard
13038 textcolor{darkgreen}{
13044 \begin_inset Quotes eld
13048 \begin_inset Quotes erd
13055 \begin_layout Standard
13065 \begin_layout Standard
13073 \begin_inset LatexCommand index
13074 name "Commands ! T ! \\textbackslash textcolor"
13078 is used in the scheme
13082 textcolor{color}{characters to color}
13087 \begin_layout Subsection
13089 \begin_inset LatexCommand label
13090 name "sub:Paragraph-Boxes"
13095 \begin_inset LatexCommand index
13096 name "Boxes ! as paragraph"
13103 \begin_layout Standard
13104 A box that can contain several lines and paragraphs, a so called paragraph
13105 box (parbox), can be created with the menu
13107 Insert\SpecialChar \menuseparator
13110 or the toolbar button
13111 \begin_inset Graphics
13112 filename ../images/box-insert.png
13120 \begin_layout Standard
13121 The following example shows a framed parbox in a line:
13124 \begin_layout Standard
13125 \begin_inset VSpace medskip
13129 \begin_inset Box Boxed
13138 height_special "totalheight"
13141 \begin_layout Standard
13142 This is a paragraph box.
13143 It is exactly 5\InsetSpace \thinspace{}
13144 cm long and can also contain formulas:
13145 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13156 \begin_layout Standard
13157 \begin_inset VSpace medskip
13163 \begin_layout Standard
13164 Such a box is created by right-clicking on the gray box inset.
13165 A dialog pops up showing the box properties.
13178 : 5\InsetSpace \thinspace{}
13181 Vertical Box Alignment
13186 \begin_layout Standard
13187 \begin_inset VSpace medskip
13190 In LaTeX a parbox is created with the command
13197 \begin_inset LatexCommand index
13198 name "Commands ! P ! \\textbackslash parbox"
13202 that has the following scheme:
13205 \begin_layout Standard
13210 parbox[position]{width}{box content}
13213 \begin_layout Standard
13227 for bottom means that the box is aligned within the surrounding text with
13233 for top this is done with the first line.
13234 When no position is given, the box will be vertically centered, see section
13241 Embedded\InsetSpace ~
13244 manual for examples.
13247 \begin_layout Standard
13248 \begin_inset VSpace bigskip
13251 To frame formulas completely, including the formula number, the formula
13252 must be set into a parbox.
13253 To do this, the command
13267 is inserted in TeX-mode before the formula.
13273 \begin_inset LatexCommand index
13274 name "Commands ! L ! \\textbackslash linewidth"
13280 is hereby the line width set for the document.
13281 Because the frame is outside the parbox, 2\InsetSpace \thinspace{}
13282 times the frame separation and
13283 the frame thickness must be subtracted from the line width.
13284 As this is not automatically done by LyX due to a bug
13288 \begin_layout Standard
13292 \begin_layout Standard
13296 href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
13305 \begin_layout Standard
13317 , TeX-mode has to be used.
13318 To be able to multiply and subtract in arguments, the LaTeX-package
13326 \begin_layout Standard
13331 is part of every LaTeX standard installation.
13337 \begin_inset LatexCommand index
13338 name "Packages ! calc"
13342 must be loaded in the LaTeX-preamble with the line
13345 \begin_layout Standard
13353 \begin_layout Standard
13354 Behind the formula both boxes are closed by entering
13359 Here is an example:
13363 \begin_layout Standard
13377 \begin_layout Standard
13381 \begin_layout Standard
13399 \begin_inset Formula \begin{equation}
13400 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
13408 \begin_layout Standard
13419 \begin_layout Standard
13433 \begin_layout Standard
13434 \begin_inset VSpace medskip
13437 As a parbox is used as argument of
13443 , there is in this case no difference between
13458 \begin_layout Standard
13459 \begin_inset VSpace bigskip
13462 Paragraph boxes are very useful to comment formulas directly.
13469 is used in combination with the command
13483 \begin_inset LatexCommand ref
13484 reference "sub:User-defined-Numbering"
13491 \begin_layout Standard
13492 An example of a formula commented with
13501 \begin_layout Standard
13505 \begin_layout Standard
13518 This is a description.
13519 It is distinctly separated from the formula and multiline.
13523 \begin_layout Standard
13535 \begin_layout Standard
13536 Such a formula must be inserted completely in TeX-mode because LyX does
13537 not yet support the command
13544 The formula is created with the following command sequence:
13547 \begin_layout Standard
13560 is inserted in TeX-mode.
13564 \begin_layout Standard
13565 When the formula style
13577 can also be replaced by
13584 (formula styles see
13585 \begin_inset LatexCommand ref
13586 reference "sec:Formula-Styles"
13595 Then the description follows as normal text, and finally
13601 is inserted in TeX-mode.
13614 hereby create a displayed formula.
13617 \begin_layout Standard
13624 can be seen in this example that was
13625 \begin_inset Quotes eld
13629 \begin_inset Quotes erd
13632 using the mathematical textmode:
13633 \begin_inset Formula \[
13634 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
13641 \begin_layout Section
13643 \begin_inset LatexCommand index
13651 \begin_layout Subsection
13653 \begin_inset LatexCommand label
13654 name "sub:Big-Operators"
13659 \begin_inset LatexCommand index
13660 name "Operators ! big"
13665 \begin_inset LatexCommand index
13671 \begin_inset LatexCommand index
13679 \begin_layout Standard
13680 To be able to use all integral operators listed here, the option
13682 Use esint package automatically
13684 must be set in the document settings under
13692 \begin_layout Standard
13696 \begin_inset Tabular
13697 <lyxtabular version="3" rows="11" columns="2">
13699 <column alignment="center" valignment="top" leftline="true" width="0pt">
13700 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13701 <row topline="true" bottomline="true">
13702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13705 \begin_layout Standard
13711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13714 \begin_layout Standard
13721 <row topline="true">
13722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13725 \begin_layout Standard
13729 \begin_inset LatexCommand index
13730 name "Commands ! S ! \\textbackslash sum"
13739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13742 \begin_layout Standard
13743 \begin_inset Formula $\sum$
13752 <row topline="true">
13753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13756 \begin_layout Standard
13760 \begin_inset LatexCommand index
13761 name "Commands ! I ! \\textbackslash int"
13770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13773 \begin_layout Standard
13774 \begin_inset Formula $\int$
13783 <row topline="true">
13784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13787 \begin_layout Standard
13795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13798 \begin_layout Standard
13799 \begin_inset Formula $\intop$
13808 <row topline="true">
13809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13812 \begin_layout Standard
13820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13823 \begin_layout Standard
13824 \begin_inset Formula $\oint$
13833 <row topline="true">
13834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13837 \begin_layout Standard
13845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13848 \begin_layout Standard
13849 \begin_inset Formula $\ointop$
13858 <row topline="true">
13859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13862 \begin_layout Standard
13870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13873 \begin_layout Standard
13874 \begin_inset Formula $\ointctrclockwise$
13883 <row topline="true">
13884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13887 \begin_layout Standard
13895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13898 \begin_layout Standard
13899 \begin_inset Formula $\ointclockwise$
13908 <row topline="true">
13909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13912 \begin_layout Standard
13920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13923 \begin_layout Standard
13924 \begin_inset Formula $\sqint$
13933 <row topline="true">
13934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13937 \begin_layout Standard
13945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13948 \begin_layout Standard
13949 \begin_inset Formula $\bigcap$
13958 <row topline="true" bottomline="true">
13959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13962 \begin_layout Standard
13970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13973 \begin_layout Standard
13974 \begin_inset Formula $\bigcup$
13990 \begin_inset Tabular
13991 <lyxtabular version="3" rows="10" columns="2">
13993 <column alignment="center" valignment="top" leftline="true" width="0pt">
13994 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13995 <row topline="true" bottomline="true">
13996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13999 \begin_layout Standard
14005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14008 \begin_layout Standard
14015 <row topline="true">
14016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14019 \begin_layout Standard
14023 \begin_inset LatexCommand index
14024 name "Commands ! P ! \\textbackslash prod"
14033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14036 \begin_layout Standard
14037 \begin_inset Formula $\prod$
14046 <row topline="true">
14047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14050 \begin_layout Standard
14058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14061 \begin_layout Standard
14062 \begin_inset Formula $\coprod$
14071 <row topline="true">
14072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14075 \begin_layout Standard
14083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14086 \begin_layout Standard
14087 \begin_inset Formula $\bigodot$
14096 <row topline="true">
14097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14100 \begin_layout Standard
14108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14111 \begin_layout Standard
14112 \begin_inset Formula $\bigotimes$
14121 <row topline="true">
14122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14125 \begin_layout Standard
14133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14136 \begin_layout Standard
14137 \begin_inset Formula $\bigoplus$
14146 <row topline="true">
14147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14150 \begin_layout Standard
14158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14161 \begin_layout Standard
14162 \begin_inset Formula $\bigwedge$
14171 <row topline="true">
14172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14175 \begin_layout Standard
14183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14186 \begin_layout Standard
14187 \begin_inset Formula $\bigvee$
14196 <row topline="true">
14197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14200 \begin_layout Standard
14208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14211 \begin_layout Standard
14212 \begin_inset Formula $\bigsqcup$
14221 <row topline="true" bottomline="true">
14222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14225 \begin_layout Standard
14233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14236 \begin_layout Standard
14237 \begin_inset Formula $\biguplus$
14255 \begin_layout Standard
14256 All big operators can also be inserted via the math toolbar button
14257 \begin_inset Graphics
14258 filename ../images/math/intop.png
14266 \begin_layout Standard
14267 The operators are called big because they are bigger than the sometimes
14268 equal looking binary operators.
14269 All big operators can have limits as described in the next subsection.
14272 \begin_layout Standard
14297 , resp.\InsetSpace ~
14298 in the style the operator limits are displayed, see
14299 \begin_inset LatexCommand ref
14300 reference "sub:Operator-Limits"
14308 \begin_layout Subsubsection*
14309 Advices for Integrals
14312 \begin_layout Standard
14317 in an integral is an operator, that therefore has to be set upright.
14318 This is done by highlighting the
14322 and using the keyboard shortcut
14331 \begin_layout Standard
14337 \begin_inset LatexCommand ref
14338 reference "sub:Font-Styles"
14348 Finally the smallest space is inserted before the
14352 , as this is usual for operators.
14356 \begin_layout Standard
14358 \begin_inset Formula $\int A(x)dx$
14367 \begin_layout Standard
14377 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14383 \begin_layout Standard
14384 For multiple integrals there are the following commands:
14385 \begin_inset VSpace medskip
14391 \begin_layout Standard
14395 \begin_inset Tabular
14396 <lyxtabular version="3" rows="4" columns="2">
14398 <column alignment="center" valignment="top" leftline="true" width="0">
14399 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14400 <row topline="true" bottomline="true">
14401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14404 \begin_layout Standard
14410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14413 \begin_layout Standard
14415 \begin_inset Note Note
14418 \begin_layout Standard
14425 is only used as spacer.
14436 <row topline="true">
14437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14440 \begin_layout Standard
14448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14451 \begin_layout Standard
14452 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
14461 <row topline="true">
14462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14465 \begin_layout Standard
14473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14476 \begin_layout Standard
14477 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
14486 <row topline="true" bottomline="true">
14487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14490 \begin_layout Standard
14498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14501 \begin_layout Standard
14502 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
14518 \begin_inset Tabular
14519 <lyxtabular version="3" rows="4" columns="2">
14521 <column alignment="center" valignment="top" leftline="true" width="0">
14522 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14523 <row topline="true" bottomline="true">
14524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14527 \begin_layout Standard
14533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14536 \begin_layout Standard
14543 <row topline="true">
14544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14547 \begin_layout Standard
14555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14558 \begin_layout Standard
14559 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
14568 <row topline="true">
14569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14572 \begin_layout Standard
14580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14583 \begin_layout Standard
14584 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
14593 <row topline="true" bottomline="true">
14594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14597 \begin_layout Standard
14605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14608 \begin_layout Standard
14609 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
14627 \begin_layout Subsection
14629 \begin_inset LatexCommand label
14630 name "sub:Operator-Limits"
14635 \begin_inset LatexCommand index
14636 name "Operators ! Limits"
14643 \begin_layout Standard
14644 Limits are created by super- and subscripts:
14647 \begin_layout Standard
14649 \begin_inset Tabular
14650 <lyxtabular version="3" rows="2" columns="2">
14652 <column alignment="center" valignment="top" leftline="true" width="0pt">
14653 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
14654 <row topline="true" bottomline="true">
14655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14658 \begin_layout Standard
14664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14667 \begin_layout Standard
14669 \begin_inset Note Note
14672 \begin_layout Standard
14679 is only used as spacer.
14690 <row topline="true" bottomline="true">
14691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14694 \begin_layout Standard
14703 \begin_layout Standard
14713 \begin_inset Formula $\to$
14717 \begin_inset Formula $\to$
14725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14728 \begin_layout Standard
14729 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
14745 \begin_layout Standard
14746 Limits of inline formulas are set right beside the operator.
14747 Limits in displayed formulas are set above or below the operator, except
14748 of integral limits.
14751 \begin_layout Standard
14752 To force that the limits are set beside the operator, the cursor is set
14753 directly behind the operator and the limits type is changed with the menu
14756 Edit\SpecialChar \menuseparator
14757 Math\SpecialChar \menuseparator
14775 \begin_layout Standard
14776 The default limits type is this:
14777 \begin_inset Formula \[
14778 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
14782 This is how it looks when the limits type was changed to
14789 \begin_inset Formula \[
14790 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
14794 For integrals, except of
14806 , the limits are by default set beside the operator.
14807 But for multiple integrals the limits are often set below the operator.
14808 In the following example the limits type was therefore set to
14812 and so set below the integrals:
14813 \begin_inset Formula \begin{equation}
14814 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
14821 \begin_layout Standard
14822 \begin_inset VSpace medskip
14825 To specify conditions for limits, the commands
14832 \begin_inset LatexCommand index
14833 name "Commands ! S ! \\textbackslash subarray"
14844 \begin_inset LatexCommand index
14845 name "Commands ! S ! \\textbackslash substack"
14850 To create for example this expression
14851 \begin_inset Formula \begin{equation}
14852 \sum_{\begin{subarray}{c}
14854 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
14861 \begin_layout Standard
14862 the following has to be done:
14876 \begin_layout Standard
14888 One is now in a blue box under the summation operator and insert there
14897 \begin_layout Standard
14909 The blue box is now within a purple box and now several lines can be written
14911 A new line is created by inserting a line break (
14920 0<k<1000 Ctrl-Return
14924 is typed in, a new box appears below for the new line.
14927 \begin_layout Standard
14928 The alignment of the lines can be changed to left aligned with the
14938 Edit\SpecialChar \menuseparator
14942 To get right alignment,
14950 \begin_layout Standard
14961 is inserted at the beginning of the line.
14964 \begin_layout Standard
14977 with the difference that the lines are always centered.
14980 \begin_layout Standard
14981 \begin_inset VSpace bigskip
14985 \begin_inset LatexCommand eqref
14986 reference "eq:substack"
14990 there can be too much space beside an operator, because the characters
14991 following the operator are set beside the limits.
14994 \begin_layout Standard
14995 To avoid this, the following macro can be used in the LaTeX-preamble:
14998 \begin_layout Standard
15027 mathclapinternal #1#2{
15031 mathsurround =0pt #1{#2}$}}
15034 \begin_layout Standard
15035 This defines the command
15042 \begin_inset LatexCommand index
15043 name "Commands ! M ! \\textbackslash mathclap"
15047 that sets the width of the limit to 0\InsetSpace \thinspace{}
15049 The command scheme is
15052 \begin_layout Standard
15060 \begin_layout Standard
15061 where the limit can consist of several conditions.
15064 \begin_layout Standard
15066 \begin_inset LatexCommand eqref
15067 reference "eq:substack"
15071 , one uses the command
15074 \begin_layout Standard
15087 \begin_layout Standard
15096 0<k<1000 Ctrl-Enter
15099 \begin_layout Standard
15100 to create the lower limit.
15101 The summand is now directly behind the summation operator:
15102 \begin_inset Formula \[
15103 \sum_{\mathclap{\substack{0<k<1000\\
15104 \\k\,\in\,\mathbb{N}}
15112 \begin_layout Standard
15113 \begin_inset VSpace bigskip
15116 How to use one limit for several operators is described in
15117 \begin_inset LatexCommand ref
15118 reference "sub:Self-defined-Operators"
15125 \begin_layout Subsection
15127 \begin_inset LatexCommand label
15128 name "sub:Binary-Operators"
15133 \begin_inset LatexCommand index
15134 name "Operators ! binary"
15141 \begin_layout Standard
15142 Binary operators are surrounded by space when there is a character before
15144 \begin_inset VSpace medskip
15150 \begin_layout Standard
15154 \begin_inset Tabular
15155 <lyxtabular version="3" rows="13" columns="2">
15157 <column alignment="center" valignment="top" leftline="true" width="0pt">
15158 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15159 <row topline="true" bottomline="true">
15160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15163 \begin_layout Standard
15165 \begin_inset Note Note
15168 \begin_layout Standard
15175 is only used as spacer.
15185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15188 \begin_layout Standard
15195 <row topline="true">
15196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15199 \begin_layout Standard
15205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15208 \begin_layout Standard
15209 \begin_inset Formula $+$
15218 <row topline="true">
15219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15222 \begin_layout Standard
15228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15231 \begin_layout Standard
15232 \begin_inset Formula $-$
15241 <row topline="true">
15242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15245 \begin_layout Standard
15253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15256 \begin_layout Standard
15257 \begin_inset Formula $\pm$
15266 <row topline="true">
15267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15270 \begin_layout Standard
15278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15281 \begin_layout Standard
15282 \begin_inset Formula $\mp$
15291 <row topline="true">
15292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15295 \begin_layout Standard
15303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15306 \begin_layout Standard
15307 \begin_inset Formula $\cdot$
15316 <row topline="true">
15317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15320 \begin_layout Standard
15328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15331 \begin_layout Standard
15332 \begin_inset Formula $\times$
15341 <row topline="true">
15342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15345 \begin_layout Standard
15353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15356 \begin_layout Standard
15357 \begin_inset Formula $\div$
15366 <row topline="true">
15367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15370 \begin_layout Standard
15374 \begin_layout Standard
15387 \begin_layout Standard
15399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15402 \begin_layout Standard
15403 \begin_inset Formula $*$
15412 <row topline="true">
15413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15416 \begin_layout Standard
15424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15427 \begin_layout Standard
15428 \begin_inset Formula $\star$
15437 <row topline="true">
15438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15441 \begin_layout Standard
15449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15452 \begin_layout Standard
15453 \begin_inset Formula $\circ$
15462 <row topline="true">
15463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15466 \begin_layout Standard
15474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15477 \begin_layout Standard
15478 \begin_inset Formula $\diamond$
15487 <row topline="true" bottomline="true">
15488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15491 \begin_layout Standard
15499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15502 \begin_layout Standard
15503 \begin_inset Formula $\bullet$
15519 \begin_inset Tabular
15520 <lyxtabular version="3" rows="13" columns="2">
15522 <column alignment="center" valignment="top" leftline="true" width="0pt">
15523 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15524 <row topline="true" bottomline="true">
15525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15528 \begin_layout Standard
15534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15537 \begin_layout Standard
15544 <row topline="true">
15545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15548 \begin_layout Standard
15556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15559 \begin_layout Standard
15560 \begin_inset Formula $\nabla$
15569 <row topline="true">
15570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15573 \begin_layout Standard
15581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15584 \begin_layout Standard
15585 \begin_inset Formula $\bigtriangledown$
15594 <row topline="true">
15595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15598 \begin_layout Standard
15606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15609 \begin_layout Standard
15610 \begin_inset Formula $\bigtriangleup$
15619 <row topline="true">
15620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15623 \begin_layout Standard
15631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15634 \begin_layout Standard
15635 \begin_inset Formula $\Box$
15644 <row topline="true">
15645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15648 \begin_layout Standard
15656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15659 \begin_layout Standard
15660 \begin_inset Formula $\cap$
15669 <row topline="true">
15670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15673 \begin_layout Standard
15681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15684 \begin_layout Standard
15685 \begin_inset Formula $\cup$
15694 <row topline="true">
15695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15698 \begin_layout Standard
15706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15709 \begin_layout Standard
15710 \begin_inset Formula $\dagger$
15719 <row topline="true">
15720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15723 \begin_layout Standard
15731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15734 \begin_layout Standard
15735 \begin_inset Formula $\ddagger$
15744 <row topline="true">
15745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15748 \begin_layout Standard
15756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15759 \begin_layout Standard
15760 \begin_inset Formula $\wr$
15769 <row topline="true">
15770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15773 \begin_layout Standard
15781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15784 \begin_layout Standard
15785 \begin_inset Formula $\bigcirc$
15794 <row topline="true">
15795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15798 \begin_layout Standard
15806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15809 \begin_layout Standard
15810 \begin_inset Formula $\wedge$
15819 <row topline="true" bottomline="true">
15820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15823 \begin_layout Standard
15831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15834 \begin_layout Standard
15835 \begin_inset Formula $\vee$
15851 \begin_inset Tabular
15852 <lyxtabular version="3" rows="13" columns="2">
15854 <column alignment="center" valignment="top" leftline="true" width="0pt">
15855 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15856 <row topline="true" bottomline="true">
15857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15860 \begin_layout Standard
15866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15869 \begin_layout Standard
15876 <row topline="true">
15877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15880 \begin_layout Standard
15888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15891 \begin_layout Standard
15892 \begin_inset Formula $\oplus$
15901 <row topline="true">
15902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15905 \begin_layout Standard
15913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15916 \begin_layout Standard
15917 \begin_inset Formula $\ominus$
15926 <row topline="true">
15927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15930 \begin_layout Standard
15938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15941 \begin_layout Standard
15942 \begin_inset Formula $\otimes$
15951 <row topline="true">
15952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15955 \begin_layout Standard
15963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15966 \begin_layout Standard
15967 \begin_inset Formula $\oslash$
15976 <row topline="true">
15977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15980 \begin_layout Standard
15988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15991 \begin_layout Standard
15992 \begin_inset Formula $\odot$
16001 <row topline="true">
16002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16005 \begin_layout Standard
16013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16016 \begin_layout Standard
16017 \begin_inset Formula $\amalg$
16026 <row topline="true">
16027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16030 \begin_layout Standard
16038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16041 \begin_layout Standard
16042 \begin_inset Formula $\uplus$
16051 <row topline="true">
16052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16055 \begin_layout Standard
16063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16066 \begin_layout Standard
16067 \begin_inset Formula $\setminus$
16076 <row topline="true">
16077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16080 \begin_layout Standard
16088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16091 \begin_layout Standard
16092 \begin_inset Formula $\sqcap$
16101 <row topline="true">
16102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16105 \begin_layout Standard
16113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16116 \begin_layout Standard
16117 \begin_inset Formula $\sqcup$
16126 <row topline="true">
16127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16130 \begin_layout Standard
16138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16141 \begin_layout Standard
16142 \begin_inset Formula $\triangleleft$
16151 <row topline="true" bottomline="true">
16152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16155 \begin_layout Standard
16163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16166 \begin_layout Standard
16167 \begin_inset Formula $\triangleright$
16185 \begin_layout Standard
16186 All binary operators can also be inserted via the math toolbar button
16187 \begin_inset Graphics
16188 filename ../images/math/pm.png
16196 \begin_layout Standard
16197 To typeset the Laplace operator also
16214 \begin_inset Formula $\nabla^{2}$
16217 ) can be used instead of
16226 \begin_layout Standard
16233 Insert\SpecialChar \menuseparator
16245 \begin_layout Subsection
16246 Self-defined Operators
16247 \begin_inset LatexCommand label
16248 name "sub:Self-defined-Operators"
16253 \begin_inset LatexCommand index
16254 name "Operators ! self-defined"
16261 \begin_layout Standard
16262 With the help of the command
16266 DeclareMathOperator
16269 \begin_inset LatexCommand index
16270 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
16274 custom operators can be defined in the LaTeX-preamble.
16275 Its command scheme is:
16278 \begin_layout Standard
16283 DeclareMathOperator{new command}{display}
16286 \begin_layout Standard
16287 Display can be characters or symbols that define how the operator looks
16289 To define a big operator a * is set behind the command.
16290 All self-defined big operators can have limits as described in
16291 \begin_inset LatexCommand ref
16292 reference "sub:Operator-Limits"
16299 \begin_layout Standard
16300 For example the LaTeX-preamble line
16303 \begin_layout Standard
16308 DeclareMathOperator*{
16315 \begin_layout Standard
16316 defines the command
16322 , that inserts a big operator consisting of the lozenge symbol from
16323 \begin_inset LatexCommand ref
16324 reference "sub:Miscellaneous-Symbols"
16329 \begin_inset Formula \[
16330 \Lozenge_{n=1}^{\infty}\]
16334 The command for this formula is:
16345 \begin_inset Formula $\to$
16351 \begin_layout Standard
16352 \begin_inset VSpace bigskip
16355 When self-defined operators are not used several times in the document,
16356 they can also be defined with the commands
16363 \begin_inset LatexCommand index
16364 name "Commands ! M ! \\textbackslash mathop"
16375 \begin_inset LatexCommand index
16376 name "Commands ! M ! \\textbackslash mathbin"
16380 , which have the following scheme:
16383 \begin_layout Standard
16397 \begin_layout Standard
16404 defines big operators,
16413 \begin_layout Standard
16420 can e.\InsetSpace \thinspace{}
16422 be used to use one limit for several operators:
16425 \begin_layout Standard
16426 \begin_inset Formula \[
16427 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
16434 \begin_layout Standard
16435 The command for the formula above is:
16453 \begin_layout Standard
16465 \begin_inset Formula $\to$
16474 \begin_layout Standard
16488 \begin_layout Section
16490 \begin_inset LatexCommand index
16498 \begin_layout Subsection
16500 \begin_inset LatexCommand label
16501 name "sub:Font-Styles"
16506 \begin_inset LatexCommand index
16507 name "Font ! style"
16514 \begin_layout Standard
16515 Latin letters in formulas can be set in one of the following font styles:
16516 \begin_inset VSpace -2mm
16522 \begin_layout Standard
16524 \begin_inset Tabular
16525 <lyxtabular version="3" rows="6" columns="3">
16527 <column alignment="center" valignment="top" leftline="true" width="0">
16528 <column alignment="center" valignment="top" leftline="true" width="0">
16529 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16530 <row topline="true" bottomline="true">
16531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16534 \begin_layout Standard
16540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16543 \begin_layout Standard
16549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16552 \begin_layout Standard
16559 <row topline="true">
16560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16563 \begin_layout Standard
16572 \begin_layout Standard
16588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16591 \begin_layout Standard
16592 \begin_inset Formula $\mathbb{ABC}$
16600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16603 \begin_layout Standard
16610 <row topline="true">
16611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16614 \begin_layout Standard
16623 \begin_layout Standard
16639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16642 \begin_layout Standard
16643 \begin_inset Formula $\mathbf{AbC}$
16651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16654 \begin_layout Standard
16661 <row topline="true">
16662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16665 \begin_layout Standard
16674 \begin_layout Standard
16690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16693 \begin_layout Standard
16694 \begin_inset Formula $\boldsymbol{AbC}$
16702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16705 \begin_layout Standard
16712 <row topline="true">
16713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16716 \begin_layout Standard
16725 \begin_layout Standard
16741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16744 \begin_layout Standard
16745 \begin_inset Formula $\mathcal{ABC}$
16753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16756 \begin_layout Standard
16763 <row topline="true" bottomline="true">
16764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16767 \begin_layout Standard
16776 \begin_layout Standard
16792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16795 \begin_layout Standard
16796 \begin_inset Formula $\mathfrak{AbC}$
16804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16807 \begin_layout Standard
16821 \begin_layout Standard
16823 \begin_inset Tabular
16824 <lyxtabular version="3" rows="5" columns="3">
16826 <column alignment="center" valignment="top" leftline="true" width="0">
16827 <column alignment="center" valignment="top" leftline="true" width="0">
16828 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16829 <row topline="true" bottomline="true">
16830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16833 \begin_layout Standard
16839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16842 \begin_layout Standard
16848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16851 \begin_layout Standard
16858 <row topline="true">
16859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16862 \begin_layout Standard
16871 \begin_layout Standard
16887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16890 \begin_layout Standard
16891 \begin_inset Formula $\mathit{AbC}$
16899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16902 \begin_layout Standard
16909 <row topline="true">
16910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16913 \begin_layout Standard
16922 \begin_layout Standard
16938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16941 \begin_layout Standard
16942 \begin_inset Formula $\mathrm{AbC}$
16950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16953 \begin_layout Standard
16960 <row topline="true">
16961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16964 \begin_layout Standard
16973 \begin_layout Standard
16989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16992 \begin_layout Standard
16993 \begin_inset Formula $\mathsf{AbC}$
17001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17004 \begin_layout Standard
17011 <row topline="true" bottomline="true">
17012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17015 \begin_layout Standard
17024 \begin_layout Standard
17040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17043 \begin_layout Standard
17044 \begin_inset Formula $\mathtt{AbC}$
17052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17055 \begin_layout Standard
17069 \begin_layout Standard
17070 \begin_inset Note Greyedout
17073 \begin_layout Standard
17090 can only be used for big letters.
17098 \begin_layout Standard
17099 Predefined is the style
17108 \begin_layout Standard
17109 The style commands work also for letters in mathematical constructs:
17110 \begin_inset Formula \[
17111 \mathfrak{A=\frac{b}{C}}\]
17118 \begin_layout Standard
17119 Characters in mathematical text don't appear in a math font style but in
17120 the text font style
17127 That their style can't be set correctly via the text style dialog is a
17132 \begin_layout Standard
17137 \begin_layout Standard
17141 href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
17150 \begin_layout Standard
17165 \begin_layout Standard
17166 Instead of the style commands the dialog
17168 Edit\SpecialChar \menuseparator
17169 Math\SpecialChar \menuseparator
17172 or the toolbar button
17173 \begin_inset Graphics
17174 filename ../images/math/font.png
17182 \begin_layout Subsection
17184 \begin_inset LatexCommand label
17185 name "sub:Bold-Formulas"
17190 \begin_inset LatexCommand index
17191 name "Formula ! bold"
17198 \begin_layout Standard
17199 To make a complete formula bold, the command
17205 from the previous subsection cannot be used, because it doesn't work for
17206 small Greek letters.
17207 Furthermore it prints Latin letters always upright, like in the following
17211 \begin_layout Standard
17212 \begin_inset Formula \[
17213 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
17220 \begin_layout Standard
17221 To display the formula correctly, the command
17228 \begin_inset Formula \[
17229 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
17233 It is also possible to set the formula in a
17235 boldmath environment
17238 This environment is created by inserting the command
17243 \begin_inset LatexCommand index
17244 name "Commands ! B ! \\textbackslash boldmath"
17251 To end the environment, the command
17256 \begin_inset LatexCommand index
17257 name "Commands ! U ! \\textbackslash unboldmath"
17263 is inserted in TeX-mode.
17267 \begin_layout Standard
17277 \begin_inset Formula \[
17278 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
17286 \begin_layout Standard
17298 \begin_layout Subsection
17300 \begin_inset LatexCommand label
17301 name "sub:Font-Sizes"
17306 \begin_inset LatexCommand index
17314 \begin_layout Standard
17315 For characters in formulas there are, analog to characters in text, the
17316 following size commands:
17319 \begin_layout Standard
17383 \begin_layout Standard
17384 The size produced by the commands depends on the document font size, that
17385 corresponds with the command
17392 The other commands produce smaller or larger sizes than
17399 The font size can however not exceed a certain value.
17400 Is for example the document font size 12\InsetSpace \thinspace{}
17407 switches to the same size as
17417 \begin_layout Standard
17418 A size command is inserted in TeX-mode before the formula and sets the size
17419 for all following formula and text characters.
17420 To switch back to the initial size, the command
17426 is inserted behind the formula in TeX-mode.
17429 \begin_layout Standard
17430 Within a formula the size can only be changed for symbols or letters in
17432 To do this, the size command is inserted in mathematical text.
17433 All following characters until the end of the mathematical text or until
17434 another size command will have the selected size.
17436 \begin_inset VSpace -2mm
17442 \begin_layout Standard
17446 \begin_layout Standard
17456 \begin_inset Formula \[
17457 A=\frac{B}{c}\cdot\maltese\]
17462 \begin_inset Formula \[
17463 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
17471 \begin_layout Standard
17483 \begin_layout Standard
17484 \begin_inset VSpace medskip
17487 Before both formulas the command
17494 The command for the second formula is:
17504 \begin_layout Standard
17519 \begin_layout Standard
17534 \begin_layout Standard
17549 \begin_layout Standard
17559 \begin_inset Formula $\to$
17563 \begin_inset Formula $\to$
17572 \begin_layout Standard
17591 \begin_layout Standard
17606 \begin_layout Standard
17621 \begin_layout Standard
17633 \begin_layout Standard
17634 If a symbol cannot be displayed in different sizes, it will always be displayed
17635 in the default size.
17638 \begin_layout Section
17640 \begin_inset LatexCommand index
17641 name "Greek letters"
17648 \begin_layout Standard
17649 All Greek letters can also be inserted via the toolbar button
17650 \begin_inset Graphics
17651 filename ../images/math/alpha.png
17659 \begin_layout Subsection
17661 \begin_inset LatexCommand label
17662 name "sub:Small-Letters"
17667 \begin_inset LatexCommand index
17668 name "Greek letters ! small"
17675 \begin_layout Standard
17679 \begin_inset Tabular
17680 <lyxtabular version="3" rows="11" columns="2">
17682 <column alignment="center" valignment="top" leftline="true" width="0pt">
17683 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17684 <row topline="true" bottomline="true">
17685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17688 \begin_layout Standard
17694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17697 \begin_layout Standard
17704 <row topline="true">
17705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17708 \begin_layout Standard
17716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17719 \begin_layout Standard
17720 \begin_inset Formula $\alpha$
17729 <row topline="true">
17730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17733 \begin_layout Standard
17741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17744 \begin_layout Standard
17745 \begin_inset Formula $\beta$
17754 <row topline="true">
17755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17758 \begin_layout Standard
17766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17769 \begin_layout Standard
17770 \begin_inset Formula $\gamma$
17779 <row topline="true">
17780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17783 \begin_layout Standard
17791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17794 \begin_layout Standard
17795 \begin_inset Formula $\delta$
17804 <row topline="true">
17805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17808 \begin_layout Standard
17816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17819 \begin_layout Standard
17820 \begin_inset Formula $\epsilon$
17829 <row topline="true">
17830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17833 \begin_layout Standard
17841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17844 \begin_layout Standard
17845 \begin_inset Formula $\varepsilon$
17854 <row topline="true">
17855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17858 \begin_layout Standard
17866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17869 \begin_layout Standard
17870 \begin_inset Formula $\zeta$
17879 <row topline="true">
17880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17883 \begin_layout Standard
17891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17894 \begin_layout Standard
17895 \begin_inset Formula $\eta$
17904 <row topline="true">
17905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17908 \begin_layout Standard
17916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17919 \begin_layout Standard
17920 \begin_inset Formula $\theta$
17929 <row topline="true" bottomline="true">
17930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17933 \begin_layout Standard
17941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17944 \begin_layout Standard
17945 \begin_inset Formula $\vartheta$
17961 \begin_inset Tabular
17962 <lyxtabular version="3" rows="12" columns="2">
17964 <column alignment="center" valignment="top" leftline="true" width="0pt">
17965 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17966 <row topline="true" bottomline="true">
17967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17970 \begin_layout Standard
17976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17979 \begin_layout Standard
17986 <row topline="true">
17987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17990 \begin_layout Standard
17998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18001 \begin_layout Standard
18002 \begin_inset Formula $\iota$
18011 <row topline="true">
18012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18015 \begin_layout Standard
18023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18026 \begin_layout Standard
18027 \begin_inset Formula $\kappa$
18036 <row topline="true">
18037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18040 \begin_layout Standard
18048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18051 \begin_layout Standard
18052 \begin_inset Formula $\varkappa$
18061 <row topline="true">
18062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18065 \begin_layout Standard
18073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18076 \begin_layout Standard
18077 \begin_inset Formula $\lambda$
18086 <row topline="true">
18087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18090 \begin_layout Standard
18098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18101 \begin_layout Standard
18102 \begin_inset Formula $\mu$
18111 <row topline="true">
18112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18115 \begin_layout Standard
18123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18126 \begin_layout Standard
18127 \begin_inset Formula $\nu$
18136 <row topline="true">
18137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18140 \begin_layout Standard
18148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18151 \begin_layout Standard
18152 \begin_inset Formula $\xi$
18161 <row topline="true">
18162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18165 \begin_layout Standard
18171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18174 \begin_layout Standard
18175 \begin_inset Formula $o$
18184 <row topline="true">
18185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18188 \begin_layout Standard
18196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18199 \begin_layout Standard
18200 \begin_inset Formula $\pi$
18209 <row topline="true">
18210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18213 \begin_layout Standard
18221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18224 \begin_layout Standard
18225 \begin_inset Formula $\varpi$
18234 <row topline="true" bottomline="true">
18235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18238 \begin_layout Standard
18246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18249 \begin_layout Standard
18250 \begin_inset Formula $\rho$
18266 \begin_inset Tabular
18267 <lyxtabular version="3" rows="11" columns="2">
18269 <column alignment="center" valignment="top" leftline="true" width="0pt">
18270 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18271 <row topline="true" bottomline="true">
18272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18275 \begin_layout Standard
18281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18284 \begin_layout Standard
18291 <row topline="true">
18292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18295 \begin_layout Standard
18303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18306 \begin_layout Standard
18307 \begin_inset Formula $\varrho$
18316 <row topline="true">
18317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18320 \begin_layout Standard
18328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18331 \begin_layout Standard
18332 \begin_inset Formula $\sigma$
18341 <row topline="true">
18342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18345 \begin_layout Standard
18353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18356 \begin_layout Standard
18357 \begin_inset Formula $\varsigma$
18366 <row topline="true">
18367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18370 \begin_layout Standard
18378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18381 \begin_layout Standard
18382 \begin_inset Formula $\tau$
18391 <row topline="true">
18392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18395 \begin_layout Standard
18403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18406 \begin_layout Standard
18407 \begin_inset Formula $\upsilon$
18416 <row topline="true">
18417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18420 \begin_layout Standard
18428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18431 \begin_layout Standard
18432 \begin_inset Formula $\phi$
18441 <row topline="true">
18442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18445 \begin_layout Standard
18453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18456 \begin_layout Standard
18457 \begin_inset Formula $\varphi$
18466 <row topline="true">
18467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18470 \begin_layout Standard
18478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18481 \begin_layout Standard
18482 \begin_inset Formula $\chi$
18491 <row topline="true">
18492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18495 \begin_layout Standard
18503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18506 \begin_layout Standard
18507 \begin_inset Formula $\psi$
18516 <row topline="true" bottomline="true">
18517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18520 \begin_layout Standard
18528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18531 \begin_layout Standard
18532 \begin_inset Formula $\omega$
18550 \begin_layout Standard
18551 \begin_inset VSpace medskip
18557 \begin_layout Standard
18558 How to create upright Greek letters is explained in
18559 \begin_inset LatexCommand ref
18560 reference "sub:Upright-small-Greek"
18567 \begin_layout Subsection
18569 \begin_inset LatexCommand index
18570 name "Greek letters ! big"
18577 \begin_layout Standard
18581 \begin_inset Tabular
18582 <lyxtabular version="3" rows="7" columns="2">
18584 <column alignment="center" valignment="top" leftline="true" width="0pt">
18585 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18586 <row topline="true" bottomline="true">
18587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18590 \begin_layout Standard
18596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18599 \begin_layout Standard
18606 <row topline="true">
18607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18610 \begin_layout Standard
18618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18621 \begin_layout Standard
18622 \begin_inset Formula $\Gamma$
18631 <row topline="true">
18632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18635 \begin_layout Standard
18643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18646 \begin_layout Standard
18647 \begin_inset Formula $\Delta$
18656 <row topline="true">
18657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18660 \begin_layout Standard
18668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18671 \begin_layout Standard
18672 \begin_inset Formula $\Theta$
18681 <row topline="true">
18682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18685 \begin_layout Standard
18693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18696 \begin_layout Standard
18697 \begin_inset Formula $\Lambda$
18706 <row topline="true">
18707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18710 \begin_layout Standard
18718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18721 \begin_layout Standard
18722 \begin_inset Formula $\Xi$
18731 <row topline="true" bottomline="true">
18732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18735 \begin_layout Standard
18743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18746 \begin_layout Standard
18747 \begin_inset Formula $\Pi$
18763 \begin_inset Tabular
18764 <lyxtabular version="3" rows="6" columns="2">
18766 <column alignment="center" valignment="top" leftline="true" width="0pt">
18767 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18768 <row topline="true" bottomline="true">
18769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18772 \begin_layout Standard
18778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18781 \begin_layout Standard
18788 <row topline="true">
18789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18792 \begin_layout Standard
18800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18803 \begin_layout Standard
18804 \begin_inset Formula $\Sigma$
18813 <row topline="true">
18814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18817 \begin_layout Standard
18825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18828 \begin_layout Standard
18829 \begin_inset Formula $\Upsilon$
18838 <row topline="true">
18839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18842 \begin_layout Standard
18850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18853 \begin_layout Standard
18854 \begin_inset Formula $\Phi$
18863 <row topline="true">
18864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18867 \begin_layout Standard
18875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18878 \begin_layout Standard
18879 \begin_inset Formula $\Psi$
18888 <row topline="true" bottomline="true">
18889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18892 \begin_layout Standard
18900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18903 \begin_layout Standard
18904 \begin_inset Formula $\Omega$
18922 \begin_layout Standard
18923 \begin_inset VSpace medskip
18926 That the big Greek letters appear upright is caused by a design bug when
18928 To get correct italic big letters, begin every command with
18933 For example the command
18940 \begin_inset Formula $\varGamma$
18946 \begin_layout Subsection
18948 \begin_inset LatexCommand index
18949 name "Greek letters ! bold"
18956 \begin_layout Standard
18957 Greek letters cannot be set with different font styles like Latin letters.
18958 They can only be made bold with the command
18965 \begin_inset LatexCommand index
18966 name "Commands ! B ! \\textbackslash boldsymbol"
18973 \begin_layout Standard
18975 \begin_inset Tabular
18976 <lyxtabular version="3" rows="3" columns="2">
18978 <column alignment="center" valignment="top" leftline="true" width="0">
18979 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
18980 <row topline="true" bottomline="true">
18981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18984 \begin_layout Standard
18990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18993 \begin_layout Standard
19000 <row topline="true">
19001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19004 \begin_layout Standard
19016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19019 \begin_layout Standard
19020 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
19029 <row topline="true" bottomline="true">
19030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19033 \begin_layout Standard
19045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19048 \begin_layout Standard
19049 \begin_inset Formula $\theta\boldsymbol{\theta}$
19065 \begin_layout Section
19070 \begin_layout Standard
19083 \begin_layout Standard
19084 A list with all symbols of most of the LaTeX-packages can be found in
19085 \begin_inset LatexCommand cite
19099 \begin_layout Standard
19107 \begin_inset Note Note
19110 \begin_layout Standard
19113 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
19116 \begin_layout Standard
19119 texorpdfstring is in section
19120 \begin_inset LatexCommand ref
19121 reference "sub:Formulas-in-Section"
19131 \begin_inset LatexCommand index
19139 \begin_layout Standard
19140 Many of the symbols listed in this section can also be inserted via the
19142 \begin_inset Graphics
19143 filename ../images/math/nabla.png
19149 \begin_inset Graphics
19150 filename ../images/math/digamma.png
19158 \begin_layout Subsection
19159 Mathematical Symbols
19160 \begin_inset LatexCommand label
19161 name "sub:Mathematical-Symbols"
19166 \begin_inset LatexCommand index
19167 name "Symbols ! mathematical"
19174 \begin_layout Standard
19178 \begin_inset Tabular
19179 <lyxtabular version="3" rows="10" columns="2">
19181 <column alignment="center" valignment="top" leftline="true" width="0pt">
19182 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19183 <row topline="true" bottomline="true">
19184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19187 \begin_layout Standard
19193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19196 \begin_layout Standard
19203 <row topline="true">
19204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19207 \begin_layout Standard
19215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19218 \begin_layout Standard
19219 \begin_inset Formula $\neg$
19228 <row topline="true">
19229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19232 \begin_layout Standard
19240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19243 \begin_layout Standard
19244 \begin_inset Formula $\Im$
19253 <row topline="true">
19254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19257 \begin_layout Standard
19265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19268 \begin_layout Standard
19269 \begin_inset Formula $\Re$
19278 <row topline="true">
19279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19282 \begin_layout Standard
19290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19293 \begin_layout Standard
19294 \begin_inset Formula $\aleph$
19303 <row topline="true">
19304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19307 \begin_layout Standard
19315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19318 \begin_layout Standard
19319 \begin_inset Formula $\partial$
19328 <row topline="true">
19329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19332 \begin_layout Standard
19340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19343 \begin_layout Standard
19344 \begin_inset Formula $\infty$
19353 <row topline="true" bottomline="true">
19354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19357 \begin_layout Standard
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19368 \begin_layout Standard
19369 \begin_inset Formula $\wp$
19378 <row bottomline="true">
19379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19382 \begin_layout Standard
19390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19393 \begin_layout Standard
19394 \begin_inset Formula $\imath$
19403 <row bottomline="true">
19404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19407 \begin_layout Standard
19415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19418 \begin_layout Standard
19419 \begin_inset Formula $\jmath$
19435 \begin_inset Tabular
19436 <lyxtabular version="3" rows="10" columns="2">
19438 <column alignment="center" valignment="top" leftline="true" width="0pt">
19439 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19440 <row topline="true" bottomline="true">
19441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19444 \begin_layout Standard
19450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19453 \begin_layout Standard
19455 \begin_inset Note Note
19458 \begin_layout Standard
19465 is only used as spacer.
19476 <row topline="true">
19477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19480 \begin_layout Standard
19488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19491 \begin_layout Standard
19492 \begin_inset Formula $\forall$
19501 <row topline="true">
19502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19505 \begin_layout Standard
19513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19516 \begin_layout Standard
19517 \begin_inset Formula $\exists$
19526 <row topline="true">
19527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19530 \begin_layout Standard
19538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19541 \begin_layout Standard
19542 \begin_inset Formula $\nexists$
19551 <row topline="true">
19552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19555 \begin_layout Standard
19563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19566 \begin_layout Standard
19567 \begin_inset Formula $\emptyset$
19576 <row topline="true">
19577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19580 \begin_layout Standard
19588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19591 \begin_layout Standard
19592 \begin_inset Formula $\varnothing$
19601 <row topline="true">
19602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19605 \begin_layout Standard
19613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19616 \begin_layout Standard
19617 \begin_inset Formula $\dag$
19626 <row topline="true" bottomline="true">
19627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19630 \begin_layout Standard
19638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19641 \begin_layout Standard
19642 \begin_inset Formula $\ddag$
19651 <row bottomline="true">
19652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19655 \begin_layout Standard
19663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19666 \begin_layout Standard
19670 \begin_layout Standard
19680 \begin_inset Formula $\complement$
19687 \begin_layout Standard
19700 <row bottomline="true">
19701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19704 \begin_layout Standard
19712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19715 \begin_layout Standard
19716 \begin_inset Formula $\Bbbk$
19732 \begin_inset Tabular
19733 <lyxtabular version="3" rows="10" columns="2">
19735 <column alignment="center" valignment="top" leftline="true" width="0pt">
19736 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19737 <row topline="true" bottomline="true">
19738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19741 \begin_layout Standard
19747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19750 \begin_layout Standard
19757 <row topline="true">
19758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19761 \begin_layout Standard
19769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19772 \begin_layout Standard
19773 \begin_inset Formula $\prime$
19782 <row topline="true">
19783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19786 \begin_layout Standard
19794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19797 \begin_layout Standard
19798 \begin_inset Formula $\backprime$
19807 <row topline="true">
19808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19811 \begin_layout Standard
19819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19822 \begin_layout Standard
19823 \begin_inset Formula $\mho$
19832 <row topline="true">
19833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19836 \begin_layout Standard
19844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19847 \begin_layout Standard
19848 \begin_inset Formula $\triangle$
19857 <row topline="true">
19858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19861 \begin_layout Standard
19869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19872 \begin_layout Standard
19873 \begin_inset Formula $\angle$
19882 <row topline="true">
19883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19886 \begin_layout Standard
19894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19897 \begin_layout Standard
19898 \begin_inset Formula $\measuredangle$
19907 <row topline="true" bottomline="true">
19908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19911 \begin_layout Standard
19919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19922 \begin_layout Standard
19923 \begin_inset Formula $\sphericalangle$
19932 <row bottomline="true">
19933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19936 \begin_layout Standard
19944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19947 \begin_layout Standard
19948 \begin_inset Formula $\top$
19957 <row bottomline="true">
19958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19961 \begin_layout Standard
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19972 \begin_layout Standard
19973 \begin_inset Formula $\bot$
19991 \begin_layout Standard
19997 \begin_layout Subsection
19998 Miscellaneous Symbols
19999 \begin_inset LatexCommand label
20000 name "sub:Miscellaneous-Symbols"
20005 \begin_inset LatexCommand index
20006 name "Symbols ! miscellaneous"
20013 \begin_layout Standard
20016 \begin_inset Tabular
20017 <lyxtabular version="3" rows="10" columns="2">
20019 <column alignment="center" valignment="top" leftline="true" width="0pt">
20020 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20021 <row topline="true" bottomline="true">
20022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20025 \begin_layout Standard
20031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20034 \begin_layout Standard
20041 <row topline="true">
20042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20045 \begin_layout Standard
20053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20056 \begin_layout Standard
20057 \begin_inset Formula $\flat$
20066 <row topline="true">
20067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20070 \begin_layout Standard
20078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20081 \begin_layout Standard
20082 \begin_inset Formula $\natural$
20091 <row topline="true">
20092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20095 \begin_layout Standard
20103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20106 \begin_layout Standard
20107 \begin_inset Formula $\sharp$
20116 <row topline="true" bottomline="true">
20117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20120 \begin_layout Standard
20128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20131 \begin_layout Standard
20132 \begin_inset Formula $\surd$
20141 <row bottomline="true">
20142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20145 \begin_layout Standard
20153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20156 \begin_layout Standard
20157 \begin_inset Formula $\checkmark$
20166 <row bottomline="true">
20167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20170 \begin_layout Standard
20178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20181 \begin_layout Standard
20182 \begin_inset Formula $\yen$
20191 <row bottomline="true">
20192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20195 \begin_layout Standard
20203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20206 \begin_layout Standard
20207 \begin_inset Formula $\pounds$
20216 <row bottomline="true">
20217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20220 \begin_layout Standard
20226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20229 \begin_layout Standard
20230 \begin_inset Formula $\$$
20239 <row bottomline="true">
20240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20243 \begin_layout Standard
20249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20252 \begin_layout Standard
20253 \begin_inset Formula $§$
20267 \begin_inset Tabular
20268 <lyxtabular version="3" rows="10" columns="2">
20270 <column alignment="center" valignment="top" leftline="true" width="0">
20271 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
20272 <row topline="true" bottomline="true">
20273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20276 \begin_layout Standard
20282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20285 \begin_layout Standard
20292 <row topline="true">
20293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20296 \begin_layout Standard
20304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20307 \begin_layout Standard
20308 \begin_inset Formula $\hbar$
20317 <row topline="true">
20318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20321 \begin_layout Standard
20329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20332 \begin_layout Standard
20333 \begin_inset Formula $\hslash$
20342 <row topline="true">
20343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20346 \begin_layout Standard
20354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20357 \begin_layout Standard
20358 \begin_inset Formula $\clubsuit$
20367 <row topline="true">
20368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20371 \begin_layout Standard
20379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20382 \begin_layout Standard
20383 \begin_inset Formula $\spadesuit$
20392 <row topline="true">
20393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20396 \begin_layout Standard
20404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20407 \begin_layout Standard
20408 \begin_inset Formula $\bigstar$
20417 <row topline="true">
20418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20421 \begin_layout Standard
20429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20432 \begin_layout Standard
20433 \begin_inset Formula $\blacklozenge$
20442 <row topline="true">
20443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20446 \begin_layout Standard
20454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20457 \begin_layout Standard
20458 \begin_inset Formula $\blacktriangle$
20467 <row topline="true">
20468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20471 \begin_layout Standard
20479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20482 \begin_layout Standard
20483 \begin_inset Formula $\blacktriangledown$
20492 <row topline="true" bottomline="true">
20493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20496 \begin_layout Standard
20504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20507 \begin_layout Standard
20508 \begin_inset Formula $\bullet$
20522 \begin_inset Tabular
20523 <lyxtabular version="3" rows="10" columns="2">
20525 <column alignment="center" valignment="top" leftline="true" width="0pt">
20526 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20527 <row topline="true" bottomline="true">
20528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20531 \begin_layout Standard
20537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20540 \begin_layout Standard
20547 <row topline="true">
20548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20551 \begin_layout Standard
20559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20562 \begin_layout Standard
20563 \begin_inset Formula $\diamondsuit$
20572 <row topline="true">
20573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20576 \begin_layout Standard
20584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20587 \begin_layout Standard
20588 \begin_inset Formula $\Diamond$
20597 <row topline="true">
20598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20601 \begin_layout Standard
20609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20612 \begin_layout Standard
20613 \begin_inset Formula $\heartsuit$
20622 <row topline="true" bottomline="true">
20623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20626 \begin_layout Standard
20634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20637 \begin_layout Standard
20638 \begin_inset Formula $\P$
20647 <row bottomline="true">
20648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20651 \begin_layout Standard
20659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20662 \begin_layout Standard
20663 \begin_inset Formula $\copyright$
20672 <row bottomline="true">
20673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20676 \begin_layout Standard
20684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20687 \begin_layout Standard
20688 \begin_inset Formula $\circledR$
20697 <row bottomline="true">
20698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20701 \begin_layout Standard
20709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20712 \begin_layout Standard
20713 \begin_inset Formula $\maltese$
20722 <row bottomline="true">
20723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20726 \begin_layout Standard
20734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20737 \begin_layout Standard
20738 \begin_inset Formula $\diagup$
20747 <row bottomline="true">
20748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20751 \begin_layout Standard
20759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20762 \begin_layout Standard
20763 \begin_inset Formula $\diagdown$
20779 \begin_layout Standard
20780 \begin_inset VSpace medskip
20783 More symbols are listed in
20784 \begin_inset LatexCommand ref
20785 reference "sub:Miscellaneous-Special-Characters"
20792 \begin_layout Standard
20793 Some symbols can be displayed in different sizes, see
20794 \begin_inset LatexCommand ref
20795 reference "sub:Font-Sizes"
20802 \begin_layout Subsection
20804 \begin_inset LatexCommand index
20805 name "Symbols ! Euro-symbol"
20810 \begin_inset LatexCommand index
20811 name "\\textcent@\\officialeuro"
20818 \begin_layout Standard
20819 To use the Euro symbol in formulas, the LaTeX-package
20824 \begin_inset LatexCommand index
20825 name "Packages ! eurosym"
20829 must be installed and loaded with the LaTeX-preamble line
20832 \begin_layout Standard
20837 usepackage[gennarrow]{eurosym}
20840 \begin_layout Standard
20841 The Euro symbol can now be inserted with the command
20848 \begin_inset LatexCommand index
20849 name "Commands ! E ! \\textbackslash euro"
20856 \begin_layout Standard
20857 The Euro symbol can directly be inserted with the € key in mathematical
20858 text, without having
20873 can also be inserted in TeX-mode.
20874 The official currency symbol can then be inserted with the command
20881 \begin_inset LatexCommand index
20882 name "Commands ! O ! \\textbackslash officialeuro"
20886 , that is only available in TeX-mode.
20889 \begin_layout Standard
20893 \begin_layout Standard
20903 \begin_inset Note Note
20906 \begin_layout Standard
20907 The following table will only be displayed when the LaTeX-package
20919 \begin_layout Standard
20920 An overview about the different Euro symbols:
20923 \begin_layout Standard
20925 \begin_inset Tabular
20926 <lyxtabular version="3" rows="4" columns="3">
20928 <column alignment="center" valignment="top" leftline="true" width="0pt">
20929 <column alignment="center" valignment="top" leftline="true" width="0pt">
20930 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20931 <row topline="true" bottomline="true">
20932 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
20935 \begin_layout Standard
20941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20944 \begin_layout Standard
20950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20953 \begin_layout Standard
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
20981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20984 \begin_layout Standard
20985 \begin_inset Formula $\euro$
20994 <row topline="true">
20995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20998 \begin_layout Standard
21004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21007 \begin_layout Standard
21013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21016 \begin_layout Standard
21017 \begin_inset Formula $\mbox{€}$
21026 <row topline="true" bottomline="true">
21027 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21030 \begin_layout Standard
21036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21039 \begin_layout Standard
21047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21050 \begin_layout Standard
21054 \begin_layout Standard
21076 \begin_layout Standard
21080 \begin_layout Standard
21090 \begin_inset Note Note
21093 \begin_layout Standard
21094 The following will be displayed when the LaTeX-package
21106 \begin_layout Standard
21107 You need to install the LaTeX-package
21111 to see the rest of this subsection in the output.
21114 \begin_layout Standard
21118 \begin_layout Standard
21130 \begin_layout Section
21132 \begin_inset LatexCommand label
21133 name "sec:Relations"
21138 \begin_inset LatexCommand index
21144 \begin_inset LatexCommand index
21145 name "Comparisons|see{Relations}"
21152 \begin_layout Standard
21153 All relations can also be inserted via the toolbar button
21154 \begin_inset Graphics
21155 filename ../images/math/leq.png
21163 \begin_layout Standard
21167 \begin_inset Tabular
21168 <lyxtabular version="3" rows="17" columns="2">
21170 <column alignment="center" valignment="top" leftline="true" width="0pt">
21171 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21172 <row topline="true" bottomline="true">
21173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21176 \begin_layout Standard
21182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21185 \begin_layout Standard
21192 <row topline="true">
21193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21196 \begin_layout Standard
21202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21205 \begin_layout Standard
21206 \begin_inset Formula $<$
21215 <row topline="true">
21216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21219 \begin_layout Standard
21227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21230 \begin_layout Standard
21231 \begin_inset Formula $\le$
21240 <row topline="true">
21241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21244 \begin_layout Standard
21252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21255 \begin_layout Standard
21256 \begin_inset Formula $\ll$
21265 <row topline="true">
21266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21269 \begin_layout Standard
21277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21280 \begin_layout Standard
21281 \begin_inset Formula $\prec$
21290 <row topline="true">
21291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21294 \begin_layout Standard
21302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21305 \begin_layout Standard
21306 \begin_inset Formula $\preceq$
21315 <row topline="true">
21316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21319 \begin_layout Standard
21327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21330 \begin_layout Standard
21331 \begin_inset Formula $\subset$
21340 <row topline="true">
21341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21344 \begin_layout Standard
21352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21355 \begin_layout Standard
21356 \begin_inset Formula $\subseteq$
21365 <row topline="true">
21366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21369 \begin_layout Standard
21377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21380 \begin_layout Standard
21381 \begin_inset Formula $\sqsubseteq$
21390 <row topline="true">
21391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21394 \begin_layout Standard
21402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21405 \begin_layout Standard
21406 \begin_inset Formula $\in$
21415 <row topline="true">
21416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21419 \begin_layout Standard
21427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21430 \begin_layout Standard
21431 \begin_inset Formula $\vdash$
21440 <row topline="true">
21441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21444 \begin_layout Standard
21452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21455 \begin_layout Standard
21456 \begin_inset Formula $\smile$
21465 <row topline="true">
21466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21469 \begin_layout Standard
21477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21480 \begin_layout Standard
21481 \begin_inset Formula $\lhd$
21490 <row topline="true">
21491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21494 \begin_layout Standard
21502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21505 \begin_layout Standard
21506 \begin_inset Formula $\unlhd$
21515 <row topline="true">
21516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21519 \begin_layout Standard
21527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21530 \begin_layout Standard
21531 \begin_inset Formula $\gtrless$
21540 <row topline="true">
21541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21544 \begin_layout Standard
21552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21555 \begin_layout Standard
21556 \begin_inset Formula $\mid$
21565 <row topline="true" bottomline="true">
21566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21569 \begin_layout Standard
21577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21580 \begin_layout Standard
21581 \begin_inset Formula $\nmid$
21597 \begin_inset Tabular
21598 <lyxtabular version="3" rows="17" columns="2">
21600 <column alignment="center" valignment="top" leftline="true" width="0pt">
21601 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21602 <row topline="true" bottomline="true">
21603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21606 \begin_layout Standard
21612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21615 \begin_layout Standard
21622 <row topline="true">
21623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21626 \begin_layout Standard
21632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21635 \begin_layout Standard
21636 \begin_inset Formula $=$
21645 <row topline="true">
21646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21649 \begin_layout Standard
21657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21660 \begin_layout Standard
21661 \begin_inset Formula $\not=$
21670 <row topline="true">
21671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21674 \begin_layout Standard
21682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21685 \begin_layout Standard
21686 \begin_inset Formula $\equiv$
21695 <row topline="true">
21696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21699 \begin_layout Standard
21707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21710 \begin_layout Standard
21711 \begin_inset Formula $\sim$
21720 <row topline="true">
21721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21724 \begin_layout Standard
21732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21735 \begin_layout Standard
21736 \begin_inset Formula $\simeq$
21745 <row topline="true">
21746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21749 \begin_layout Standard
21757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21760 \begin_layout Standard
21761 \begin_inset Formula $\approx$
21770 <row topline="true">
21771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21774 \begin_layout Standard
21782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21785 \begin_layout Standard
21786 \begin_inset Formula $\cong$
21795 <row topline="true">
21796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21799 \begin_layout Standard
21807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21810 \begin_layout Standard
21811 \begin_inset Formula $\bowtie$
21820 <row topline="true">
21821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21824 \begin_layout Standard
21832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21835 \begin_layout Standard
21836 \begin_inset Formula $\notin$
21845 <row topline="true">
21846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21849 \begin_layout Standard
21857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21860 \begin_layout Standard
21861 \begin_inset Formula $\perp$
21870 <row topline="true">
21871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21874 \begin_layout Standard
21882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21885 \begin_layout Standard
21886 \begin_inset Formula $\propto$
21895 <row topline="true">
21896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21899 \begin_layout Standard
21907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21910 \begin_layout Standard
21911 \begin_inset Formula $\asymp$
21920 <row topline="true">
21921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21924 \begin_layout Standard
21932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21935 \begin_layout Standard
21936 \begin_inset Formula $\doteq$
21945 <row topline="true">
21946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21949 \begin_layout Standard
21957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21960 \begin_layout Standard
21961 \begin_inset Formula $\circeq$
21970 <row topline="true">
21971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21974 \begin_layout Standard
21982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21985 \begin_layout Standard
21986 \begin_inset Formula $\models$
21995 <row topline="true" bottomline="true">
21996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21999 \begin_layout Standard
22007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22010 \begin_layout Standard
22011 \begin_inset Formula $\widehat{=}$
22027 \begin_inset Tabular
22028 <lyxtabular version="3" rows="17" columns="2">
22030 <column alignment="center" valignment="top" leftline="true" width="0pt">
22031 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22032 <row topline="true" bottomline="true">
22033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22036 \begin_layout Standard
22042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22045 \begin_layout Standard
22052 <row topline="true">
22053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22056 \begin_layout Standard
22062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22065 \begin_layout Standard
22066 \begin_inset Formula $>$
22075 <row topline="true">
22076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22079 \begin_layout Standard
22087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22090 \begin_layout Standard
22091 \begin_inset Formula $\ge$
22100 <row topline="true">
22101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22104 \begin_layout Standard
22112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22115 \begin_layout Standard
22116 \begin_inset Formula $\gg$
22125 <row topline="true">
22126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22129 \begin_layout Standard
22137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22140 \begin_layout Standard
22141 \begin_inset Formula $\succ$
22150 <row topline="true">
22151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22154 \begin_layout Standard
22162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22165 \begin_layout Standard
22166 \begin_inset Formula $\succeq$
22175 <row topline="true">
22176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22179 \begin_layout Standard
22187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22190 \begin_layout Standard
22191 \begin_inset Formula $\supset$
22200 <row topline="true">
22201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22204 \begin_layout Standard
22212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22215 \begin_layout Standard
22216 \begin_inset Formula $\supseteq$
22225 <row topline="true">
22226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22229 \begin_layout Standard
22237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22240 \begin_layout Standard
22241 \begin_inset Formula $\sqsupseteq$
22250 <row topline="true">
22251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22254 \begin_layout Standard
22262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22265 \begin_layout Standard
22266 \begin_inset Formula $\ni$
22275 <row topline="true">
22276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22279 \begin_layout Standard
22287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22290 \begin_layout Standard
22291 \begin_inset Formula $\dashv$
22300 <row topline="true">
22301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22304 \begin_layout Standard
22312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22315 \begin_layout Standard
22316 \begin_inset Formula $\frown$
22325 <row topline="true">
22326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22329 \begin_layout Standard
22337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22340 \begin_layout Standard
22341 \begin_inset Formula $\rhd$
22350 <row topline="true">
22351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22354 \begin_layout Standard
22362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22365 \begin_layout Standard
22366 \begin_inset Formula $\unrhd$
22375 <row topline="true">
22376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22379 \begin_layout Standard
22387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22390 \begin_layout Standard
22391 \begin_inset Formula $\lessgtr$
22400 <row topline="true">
22401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22404 \begin_layout Standard
22412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22415 \begin_layout Standard
22416 \begin_inset Formula $\parallel$
22425 <row topline="true" bottomline="true">
22426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22429 \begin_layout Standard
22437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22440 \begin_layout Standard
22441 \begin_inset Formula $\nparallel$
22459 \begin_layout Standard
22460 \begin_inset VSpace medskip
22475 are bigger than the equal looking operators
22490 \begin_layout Standard
22491 Relations are, in contrary to symbols, always surrounded by space.
22494 \begin_layout Standard
22495 Relations with labels can be created with the command
22502 \begin_inset LatexCommand index
22503 name "Commands ! S ! \\textbackslash stackrel"
22510 \begin_layout Standard
22512 \begin_inset Tabular
22513 <lyxtabular version="3" rows="2" columns="2">
22515 <column alignment="center" valignment="top" leftline="true" width="0">
22516 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
22517 <row topline="true" bottomline="true">
22518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22521 \begin_layout Standard
22527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22530 \begin_layout Standard
22532 \begin_inset Note Note
22535 \begin_layout Standard
22542 is only used as spacer.
22553 <row topline="true" bottomline="true">
22554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22557 \begin_layout Standard
22564 \begin_layout Standard
22581 \begin_layout Standard
22591 \begin_inset Formula $\downarrow$
22600 \begin_layout Standard
22613 \begin_layout Standard
22627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22630 \begin_layout Standard
22631 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
22647 \begin_layout Section
22651 \begin_layout Subsection
22652 Predefined Functions
22653 \begin_inset LatexCommand label
22654 name "sub:Predefined-Functions"
22659 \begin_inset LatexCommand index
22660 name "Functions ! predefined"
22667 \begin_layout Standard
22668 In general, variables are set
22672 in mathematical expressions, but not function names, because
22673 \begin_inset Formula $sin$
22676 could be misunderstood as
22677 \begin_inset Formula $s\cdot i\cdot n$
22681 Therefore there are predefined functions, that are additionally a bit separated
22683 They are inserted as commands starting with a backslash before their name.
22686 \begin_layout Standard
22688 \begin_inset Tabular
22689 <lyxtabular version="3" rows="2" columns="4">
22691 <column alignment="center" valignment="top" leftline="true" width="0pt">
22692 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22693 <column alignment="center" valignment="top" leftline="true" width="0pt">
22694 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22695 <row topline="true" bottomline="true">
22696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22699 \begin_layout Standard
22705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22708 \begin_layout Standard
22714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22717 \begin_layout Standard
22723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22726 \begin_layout Standard
22733 <row topline="true" bottomline="true">
22734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22737 \begin_layout Standard
22743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22746 \begin_layout Standard
22747 \begin_inset Formula $Asin(x)+B$
22755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22758 \begin_layout Standard
22766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22769 \begin_layout Standard
22770 \begin_inset Formula $A\sin(x)+B$
22787 \begin_layout Standard
22799 \begin_layout Standard
22800 The following functions are predefined:
22803 \begin_layout Standard
22804 \begin_inset VSpace -2mm
22810 \begin_layout Standard
22812 \begin_inset Tabular
22813 <lyxtabular version="3" rows="9" columns="4">
22815 <column alignment="center" valignment="top" leftline="true" width="0pt">
22816 <column alignment="center" valignment="top" leftline="true" width="0pt">
22817 <column alignment="center" valignment="top" leftline="true" width="0pt">
22818 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22819 <row topline="true" bottomline="true">
22820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22823 \begin_layout Standard
22829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22832 \begin_layout Standard
22838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22841 \begin_layout Standard
22847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22850 \begin_layout Standard
22857 <row topline="true">
22858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22861 \begin_layout Standard
22869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22872 \begin_layout Standard
22880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22883 \begin_layout Standard
22891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22894 \begin_layout Standard
22903 <row topline="true">
22904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22907 \begin_layout Standard
22915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22918 \begin_layout Standard
22926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22929 \begin_layout Standard
22937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22940 \begin_layout Standard
22949 <row topline="true">
22950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22953 \begin_layout Standard
22961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22964 \begin_layout Standard
22972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22975 \begin_layout Standard
22983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22986 \begin_layout Standard
22995 <row topline="true">
22996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22999 \begin_layout Standard
23007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23010 \begin_layout Standard
23018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23021 \begin_layout Standard
23029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23032 \begin_layout Standard
23041 <row topline="true">
23042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23045 \begin_layout Standard
23053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23056 \begin_layout Standard
23064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23067 \begin_layout Standard
23075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23078 \begin_layout Standard
23087 <row topline="true">
23088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23091 \begin_layout Standard
23099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23102 \begin_layout Standard
23110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23113 \begin_layout Standard
23121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23124 \begin_layout Standard
23133 <row topline="true">
23134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23137 \begin_layout Standard
23145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23148 \begin_layout Standard
23156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23159 \begin_layout Standard
23167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23170 \begin_layout Standard
23179 <row topline="true" bottomline="true">
23180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23183 \begin_layout Standard
23191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23194 \begin_layout Standard
23202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23205 \begin_layout Standard
23213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23216 \begin_layout Standard
23232 \begin_layout Standard
23233 They can also be inserted with the math toolbar button
23234 \begin_inset Graphics
23235 filename ../images/math/functions.png
23243 \begin_layout Subsection
23244 Self-defined Functions
23245 \begin_inset LatexCommand index
23246 name "Functions ! self-defined"
23253 \begin_layout Standard
23254 To use a function that is not predefined, like for example the sign function
23255 sgn(x), there are two possibilities:
23258 \begin_layout Itemize
23259 Define the function by inserting the following line to the LaTeX-preamble
23263 \begin_layout Standard
23268 DeclareMathOperator
23271 \begin_inset LatexCommand ref
23272 reference "sub:Self-defined-Operators"
23284 \begin_inset VSpace -3mm
23293 DeclareMathOperator{
23298 \begin_inset LatexCommand index
23299 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
23306 \begin_inset VSpace -2mm
23311 Now the new defined function can be called with the command
23320 \begin_layout Itemize
23321 Write the the formula as usual, mark the formula name, in our example the
23326 , and change it to mathematical text.
23327 At last a space is inserted between prefactor and function.
23330 \begin_layout Standard
23331 The result is the same with both methods as with a predefined function
23335 \begin_layout Standard
23336 In LyX self-defined functions are displayed red, predefined ones black.
23344 \begin_layout Standard
23346 \begin_inset Tabular
23347 <lyxtabular version="3" rows="3" columns="2">
23349 <column alignment="center" valignment="top" leftline="true" width="0pt">
23350 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
23351 <row topline="true" bottomline="true">
23352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23355 \begin_layout Standard
23361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23364 \begin_layout Standard
23371 <row topline="true" bottomline="true">
23372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23375 \begin_layout Standard
23383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23386 \begin_layout Standard
23387 \begin_inset Formula $A\sgn(x)+B$
23396 <row topline="true" bottomline="true">
23397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23400 \begin_layout Standard
23404 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
23412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23415 \begin_layout Standard
23416 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
23432 \begin_layout Standard
23433 The first method is more suitable when the self-defined function should
23434 be used several times.
23437 \begin_layout Subsection
23439 \begin_inset LatexCommand index
23447 \begin_layout Standard
23448 For limits there are defined besides
23455 \begin_inset LatexCommand index
23456 name "Commands ! L ! \\textbackslash lim"
23472 furthermore the following functions:
23475 \begin_layout Standard
23477 \begin_inset Tabular
23478 <lyxtabular version="3" rows="5" columns="2">
23480 <column alignment="center" valignment="top" leftline="true" width="0">
23481 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
23482 <row topline="true" bottomline="true">
23483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23486 \begin_layout Standard
23492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23495 \begin_layout Standard
23497 \begin_inset Note Note
23500 \begin_layout Standard
23507 is only used as spacer.
23518 <row topline="true">
23519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23522 \begin_layout Standard
23530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23533 \begin_layout Standard
23534 \begin_inset Formula $\varliminf$
23544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23547 \begin_layout Standard
23555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23558 \begin_layout Standard
23559 \begin_inset Formula $\varlimsup$
23569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23572 \begin_layout Standard
23580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23583 \begin_layout Standard
23584 \begin_inset Formula $\varprojlim$
23593 <row bottomline="true">
23594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23597 \begin_layout Standard
23605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23608 \begin_layout Standard
23609 \begin_inset Formula $\varinjlim$
23613 \begin_inset Formula $\raisebox{-2.5mm}{}$
23629 \begin_layout Standard
23630 \begin_inset VSpace medskip
23633 The limit is created by inserting a subscript.
23634 It is set right beside the function in an inline formula:
23637 \begin_layout Standard
23639 \begin_inset Tabular
23640 <lyxtabular version="3" rows="2" columns="2">
23642 <column alignment="center" valignment="top" width="0pt">
23643 <column alignment="center" valignment="top" width="0pt">
23645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23648 \begin_layout Standard
23654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23657 \begin_layout Standard
23661 \begin_layout Standard
23671 \begin_inset Note Note
23674 \begin_layout Standard
23687 are used here as spacer.
23699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23702 \begin_layout Standard
23711 \begin_layout Standard
23724 \begin_layout Standard
23738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23741 \begin_layout Standard
23742 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
23758 \begin_layout Standard
23759 In a displayed formula the limit is set below the formula, as usual:
23760 \begin_inset Formula \[
23768 \begin_layout Subsection
23770 \begin_inset LatexCommand index
23771 name "Functions ! modulo-"
23778 \begin_layout Standard
23779 The modulo-function is special, because it exists in four variants.
23782 \begin_layout Standard
23783 The variants in a displayed formula:
23784 \begin_inset Formula \begin{align*}
23785 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
23786 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
23787 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
23788 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
23789 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
23796 \begin_layout Standard
23797 In an inline formula less space is set before the function names for all
23801 \begin_layout Section
23803 \begin_inset LatexCommand index
23804 name "Special characters"
23811 \begin_layout Subsection
23812 Special Characters in Mathematical Text
23815 \begin_layout Standard
23816 The following commands can only be used in mathematical text or in TeX-mode:
23819 \begin_layout Standard
23823 \begin_inset Tabular
23824 <lyxtabular version="3" rows="8" columns="2">
23826 <column alignment="block" valignment="top" leftline="true" width="0">
23827 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
23828 <row topline="true" bottomline="true">
23829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23832 \begin_layout Standard
23838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23841 \begin_layout Standard
23848 <row topline="true">
23849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23852 \begin_layout Standard
23860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23863 \begin_layout Standard
23864 \begin_inset Formula $\textrm{\oe}$
23873 <row topline="true">
23874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23877 \begin_layout Standard
23885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23888 \begin_layout Standard
23889 \begin_inset Formula $\textrm{\OE}$
23898 <row topline="true">
23899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23902 \begin_layout Standard
23910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23913 \begin_layout Standard
23914 \begin_inset Formula $\textrm{\ae}$
23923 <row topline="true">
23924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23927 \begin_layout Standard
23935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23938 \begin_layout Standard
23939 \begin_inset Formula $\textrm{\AE}$
23948 <row topline="true">
23949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23952 \begin_layout Standard
23960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23963 \begin_layout Standard
23964 \begin_inset Formula $\textrm{\aa}$
23973 <row topline="true" bottomline="true">
23974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23977 \begin_layout Standard
23981 \begin_inset LatexCommand index
23982 name "\\@\\textrm{\\AA}"
23991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23994 \begin_layout Standard
23995 \begin_inset Formula $\textrm{\AA}$
24004 <row bottomline="true">
24005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24008 \begin_layout Standard
24016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24019 \begin_layout Standard
24020 \begin_inset Formula $\textrm{\i}$
24036 \begin_inset Tabular
24037 <lyxtabular version="3" rows="8" columns="2">
24039 <column alignment="block" valignment="top" leftline="true" width="0">
24040 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24041 <row topline="true" bottomline="true">
24042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24045 \begin_layout Standard
24047 \begin_inset Note Note
24050 \begin_layout Standard
24057 is used for separation, because otherwise the output will be ¡ and ¿ respective
24068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24071 \begin_layout Standard
24078 <row topline="true">
24079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24082 \begin_layout Standard
24090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24093 \begin_layout Standard
24094 \begin_inset Formula $\textrm{\o}$
24103 <row topline="true">
24104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24107 \begin_layout Standard
24115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24118 \begin_layout Standard
24119 \begin_inset Formula $\textrm{\O}$
24128 <row topline="true">
24129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24132 \begin_layout Standard
24140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24143 \begin_layout Standard
24144 \begin_inset Formula $\textrm{\l}$
24153 <row topline="true">
24154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24157 \begin_layout Standard
24165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24168 \begin_layout Standard
24169 \begin_inset Formula $\textrm{\L}$
24178 <row topline="true" bottomline="true">
24179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24182 \begin_layout Standard
24187 \begin_layout Standard
24200 \begin_layout Standard
24214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24217 \begin_layout Standard
24218 \begin_inset Formula $\textrm{!`}$
24227 <row bottomline="true">
24228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24231 \begin_layout Standard
24236 \begin_layout Standard
24249 \begin_layout Standard
24263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24266 \begin_layout Standard
24267 \begin_inset Formula $\textrm{?`}$
24276 <row bottomline="true">
24277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24280 \begin_layout Standard
24288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24291 \begin_layout Standard
24292 \begin_inset Formula $\textrm{\j}$
24310 \begin_layout Standard
24312 \begin_inset Formula $\textrm{\textrm{Å}}$
24316 \begin_inset Formula $\textrm{\textrm{Ø}}$
24319 can also be inserted via the math toolbar button
24320 \begin_inset Graphics
24321 filename ../images/math/digamma.png
24329 \begin_layout Standard
24330 An exception are the commands
24336 \begin_layout Standard
24353 \begin_layout Standard
24364 , because they can be inserted in LyX directly to text.
24367 \begin_layout Subsection
24369 \begin_inset LatexCommand label
24370 name "sub:Accents-in-Text"
24375 \begin_inset LatexCommand index
24376 name "Accents ! in text"
24383 \begin_layout Standard
24384 With the following commands all letters can be accented.
24385 The commands must be inserted in TeX-mode.
24388 \begin_layout Standard
24392 \begin_inset Tabular
24393 <lyxtabular version="3" rows="8" columns="2">
24395 <column alignment="block" valignment="top" leftline="true" width="0">
24396 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
24397 <row topline="true" bottomline="true">
24398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24401 \begin_layout Standard
24407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24410 \begin_layout Standard
24417 <row topline="true">
24418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24421 \begin_layout Standard
24425 \begin_inset Quotes grd
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
24467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24470 \begin_layout Standard
24474 \begin_layout Standard
24489 <row topline="true">
24490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24493 \begin_layout Standard
24500 \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
24548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24551 \begin_layout Standard
24555 \begin_layout Standard
24570 <row topline="true">
24571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24574 \begin_layout Standard
24581 \begin_layout Standard
24595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24598 \begin_layout Standard
24602 \begin_layout Standard
24617 <row topline="true" bottomline="true">
24618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24621 \begin_layout Standard
24628 \begin_layout Standard
24642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24645 \begin_layout Standard
24649 \begin_layout Standard
24664 <row bottomline="true">
24665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24668 \begin_layout Standard
24675 \begin_layout Standard
24689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24692 \begin_layout Standard
24696 \begin_layout Standard
24718 \begin_inset Tabular
24719 <lyxtabular version="3" rows="8" columns="2">
24721 <column alignment="block" valignment="top" leftline="true" width="0">
24722 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24723 <row topline="true" bottomline="true">
24724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24727 \begin_layout Standard
24733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24736 \begin_layout Standard
24743 <row topline="true">
24744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24747 \begin_layout Standard
24754 \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
24802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24805 \begin_layout Standard
24809 \begin_layout Standard
24824 <row topline="true">
24825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24828 \begin_layout Standard
24832 \begin_inset LatexCommand index
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">
24865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24868 \begin_layout Standard
24876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24879 \begin_layout Standard
24883 \begin_layout Standard
24898 <row topline="true" bottomline="true">
24899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24902 \begin_layout Standard
24909 \begin_layout Standard
24923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24926 \begin_layout Standard
24930 \begin_layout Standard
24945 <row bottomline="true">
24946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24949 \begin_layout Standard
24956 \begin_layout Standard
24970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24973 \begin_layout Standard
24977 \begin_layout Standard
24992 <row bottomline="true">
24993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24996 \begin_layout Standard
25003 \begin_layout Standard
25017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25020 \begin_layout Standard
25024 \begin_layout Standard
25048 \begin_layout Standard
25049 \begin_inset VSpace medskip
25058 also two different characters can be accented.
25067 \begin_layout Standard
25082 \begin_layout Standard
25094 \begin_layout Standard
25107 can in combination with vowels directly be inserted with the keyboard without
25109 The same applies for the tilde
25113 \begin_layout Standard
25114 This only applies for keyboards where the tilde is defined as accent.
25123 in combination with
25138 \begin_layout Standard
25181 , and accents inserted directly with the keyboard are also available in
25183 For the other accents there are special math commands to be used in formulas,
25185 \begin_inset LatexCommand ref
25186 reference "sub:Accents-for-one"
25193 \begin_layout Standard
25194 \begin_inset VSpace bigskip
25197 Furthermore, with the command
25204 \begin_inset LatexCommand index
25205 name "Commands ! T ! \\textbackslash textcircled"
25209 all numbers and letters can be set into a circle, quasi accented with a
25210 circle, similar to the the copyright symbol.
25213 \begin_layout Standard
25215 \begin_inset Tabular
25216 <lyxtabular version="3" rows="3" columns="2">
25218 <column alignment="center" valignment="top" leftline="true" width="0">
25219 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25220 <row topline="true" bottomline="true">
25221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25224 \begin_layout Standard
25230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25233 \begin_layout Standard
25235 \begin_inset Note Note
25238 \begin_layout Standard
25245 is only used as spacer.
25256 <row topline="true">
25257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25260 \begin_layout Standard
25268 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25271 \begin_layout Standard
25275 \begin_layout Standard
25290 <row topline="true" bottomline="true">
25291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25294 \begin_layout Standard
25305 raisebox{-1.5pt}{W}}
25310 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25313 \begin_layout Standard
25314 \begin_inset Formula $\raisebox{4.5mm}{}$
25321 \begin_layout Standard
25339 \begin_inset Formula $\raisebox{-2mm}{}$
25355 \begin_layout Standard
25356 One has to take care that the character fits in the circle.
25367 \begin_layout Standard
25369 \begin_inset LatexCommand ref
25370 reference "sub:Font-Sizes"
25379 specifies thereby the size of the circle.
25390 \begin_layout Standard
25392 \begin_inset LatexCommand ref
25393 reference "sub:Boxes-without-Frame"
25402 the character can be centered.
25405 \begin_layout Subsection
25407 \begin_inset LatexCommand index
25408 name "Minuscule numbers"
25415 \begin_layout Standard
25416 Minuscule numbers are created with the command
25423 \begin_inset LatexCommand index
25424 name "Commands ! O ! \\textbackslash oldstylenums"
25429 The command can be used in formulas and in TeX-mode.
25430 The command scheme is:
25433 \begin_layout Standard
25438 oldstylenums{number}
25441 \begin_layout Standard
25446 oldstylenums{0123456789
25449 \begin_inset Formula $\oldstylenums{0123456789}$
25455 \begin_layout Subsection
25456 Miscellaneous Special Characters
25457 \begin_inset LatexCommand label
25458 name "sub:Miscellaneous-Special-Characters"
25463 \begin_inset LatexCommand index
25464 name "Special characters ! miscellaneous"
25471 \begin_layout Standard
25472 The following characters can only be inserted to formulas by using commands:
25475 \begin_layout Standard
25477 \begin_inset Tabular
25478 <lyxtabular version="3" rows="4" columns="2">
25480 <column alignment="center" valignment="top" leftline="true" width="0">
25481 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25482 <row topline="true" bottomline="true">
25483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25486 \begin_layout Standard
25492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25495 \begin_layout Standard
25502 <row topline="true">
25503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25506 \begin_layout Standard
25513 \begin_layout Standard
25527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25530 \begin_layout Standard
25531 \begin_inset Formula $\mathcircumflex$
25540 <row topline="true">
25541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25544 \begin_layout Standard
25552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25555 \begin_layout Standard
25556 \begin_inset Formula $\_$
25565 <row topline="true" bottomline="true">
25566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25569 \begin_layout Standard
25574 \begin_layout Standard
25586 \begin_inset LatexCommand index
25596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25599 \begin_layout Standard
25600 \begin_inset Formula $^{\circ}$
25616 \begin_layout Standard
25617 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
25618 contains the following line
25622 \begin_layout Standard
25623 More about this is described in
25624 \begin_inset LatexCommand ref
25625 reference "sub:Text-Characters-in"
25637 \begin_layout Standard
25642 DeclareInputtext{176}{
25652 f\SpecialChar \textcompwordmark{}
25656 \begin_layout Standard
25657 \begin_inset VSpace bigskip
25661 \begin_inset LatexCommand index
25666 is designed as accent, thus is looks alone a bit misplaced: ~
25669 addresses (URLs) sometimes a single tilde is needed.
25670 In this case the relation sign
25678 \begin_layout Standard
25680 \begin_inset LatexCommand ref
25681 reference "sec:Relations"
25692 is used in a formula.
25693 As a formula cannot be created in an URL-box (menu
25695 Insert\SpecialChar \menuseparator
25698 ), the URL is inserted as normal text with the font style '
25703 Should the URL be a hyperlink in the DVI- or PDF-output, the command
25713 \begin_layout Standard
25720 can only be used together with the LaTeX-package
25725 \begin_inset LatexCommand index
25726 name "Packages ! hyperref"
25737 is written in the section
25743 Embedded\InsetSpace ~
25752 \begin_inset LatexCommand index
25753 name "Commands ! H ! \\textbackslash href"
25760 \begin_layout Standard
25761 As example an URL with a tilde:
25764 \begin_layout Standard
25767 http://www.lyx.org/
25768 \begin_inset Formula $\sim$
25774 \begin_layout Standard
25785 \begin_layout Standard
25789 href{http://www.lyx.org/~mustermann}{
25794 http://www.lyx.org/
25795 \begin_inset Formula $\sim$
25802 \begin_layout Standard
25812 \begin_layout Section
25814 \begin_inset LatexCommand label
25815 name "sec:Formula-Styles"
25820 \begin_inset LatexCommand index
25821 name "Formula ! styles"
25828 \begin_layout Itemize
25829 There are two different alignment styles:
25833 \begin_layout Description
25834 Centered is the predefined standard
25837 \begin_layout Description
25838 Indented for this the option
25842 must be inserted in the menu
25844 Document\SpecialChar \menuseparator
25849 Document\InsetSpace ~
25853 \begin_layout Standard
25858 is used, the indentation can be adjusted with the length
25865 \begin_inset LatexCommand index
25866 name "Commands ! M ! \\textbackslash mathindent"
25871 Should the distance be 15\InsetSpace \thinspace{}
25872 mm, the following command line is inserted in
25876 \begin_layout Standard
25886 \begin_layout Standard
25887 When no length is specified, the predefined value of 30\InsetSpace \thinspace{}
25892 \begin_layout Itemize
25893 And two different numbering styles:
25897 \begin_layout Description
25898 Right is the predefined standard
25901 \begin_layout Description
25902 Left for this the option
25906 must be inserted in the menu
25908 Document\SpecialChar \menuseparator
25913 Document\InsetSpace ~
25918 \begin_layout Standard
25927 can also be used together.
25928 In this case both options are inserted, separated by a comma.
25931 \begin_layout Standard
25932 The chosen styles are used for all displayed formulas of the document.
25933 When both, centered and indented formulas should be created in a document,
25939 The indented formulas are then set in a flalign environment, see
25940 \begin_inset LatexCommand ref
25941 reference "sub:Flalign-Environment"
25948 \begin_layout Section
25950 \begin_inset LatexCommand label
25951 name "sec:Multiline-Formulas"
25956 \begin_inset LatexCommand index
25957 name "Formula ! multiline"
25964 \begin_layout Subsection
25968 \begin_layout Standard
25969 In LyX multiline formulas are created by pressing
25980 that is described in
25981 \begin_inset LatexCommand ref
25982 reference "sub:Standard-align-Environment"
25989 \begin_layout Standard
25990 There are other multiline formula environments that can be created via the
25993 Insert\SpecialChar \menuseparator
25997 These environments are described in the following sections.
26000 \begin_layout Standard
26001 In all multiline formula environments a new line is created by pressing
26007 To add or delete lines, the math toolbar buttons
26008 \begin_inset Graphics
26009 filename ../images/tabular-feature_append-row.png
26015 \begin_inset Graphics
26016 filename ../images/tabular-feature_delete-row.png
26021 , respectively, or the menu
26023 Edit\SpecialChar \menuseparator
26029 \begin_layout Subsubsection
26031 \begin_inset LatexCommand label
26032 name "sub:Line-Separation"
26037 \begin_inset LatexCommand index
26038 name "Formula ! multiline ! Line separation"
26045 \begin_layout Standard
26046 There is sometimes not enough space in multiline formulas between the lines:
26047 \begin_inset Formula \begin{eqnarray*}
26048 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}\\
26049 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*}
26056 \begin_layout Standard
26057 In LaTeX additional line space is specified as optional argument of the
26059 This is not yet possible in LyX
26063 \begin_layout Standard
26068 \begin_layout Standard
26072 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
26081 \begin_layout Standard
26093 , therefore the whole formula must be inserted in TeX-mode.
26094 To add in our example space, the command
26102 is inserted at the end of the first line.
26107 \begin_layout Standard
26114 \begin_layout Standard
26116 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26119 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26126 \begin_layout Standard
26130 left(B^{2}+x_{0}^{2}
26138 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26143 \begin_layout Standard
26155 \begin_layout Standard
26156 \begin_inset VSpace bigskip
26159 To set the the line separation for all lines in a formula, the length
26166 \begin_inset LatexCommand index
26167 name "Commands ! J ! \\textbackslash jot"
26173 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26183 is the value 3\InsetSpace \thinspace{}
26185 To create 3\InsetSpace \thinspace{}
26186 mm additional line separation as in the previous example, the
26190 \begin_layout Standard
26200 \begin_layout Standard
26201 is inserted in TeX-mode before the formula.
26202 This requires that the LaTeX-package
26210 \begin_layout Standard
26215 is part of every LaTeX standard installation.
26221 \begin_inset LatexCommand index
26222 name "Packages ! calc"
26226 was loaded in LaTeX-preamble with the line
26229 \begin_layout Standard
26237 \begin_layout Standard
26242 \begin_layout Standard
26254 \begin_inset Formula \begin{eqnarray*}
26255 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}\\
26256 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*}
26263 \begin_layout Standard
26267 \begin_layout Standard
26278 To get back to the predefined distance,
26284 is set to the value 3\InsetSpace \thinspace{}
26288 \begin_layout Subsubsection
26290 \begin_inset LatexCommand label
26291 name "sub:Column-Separation"
26296 \begin_inset LatexCommand index
26297 name "Formula ! multiline ! Column separation"
26304 \begin_layout Standard
26305 Multiline formulas form a matrix.
26306 A formula in the eqnarray environment is for example a matrix with three
26308 By changing the column separation in this environment, the space beside
26309 the relation sign can be changed.
26312 \begin_layout Standard
26313 The column separation is specified with the length
26320 \begin_inset LatexCommand index
26321 name "Commands ! A ! \\textbackslash arraycolsep"
26327 column separation = 2\InsetSpace \thinspace{}
26339 \begin_layout Standard
26349 \begin_layout Standard
26350 inserted in TeX-mode, sets for all following formulas a column separation
26351 of 2\InsetSpace \thinspace{}
26353 To get back to the predefined distance,
26359 is set to 5\InsetSpace \thinspace{}
26363 \begin_layout Standard
26364 A formula with 2\InsetSpace \thinspace{}
26365 cm column separation:
26369 \begin_layout Standard
26381 \begin_inset Formula \begin{eqnarray*}
26383 C & \ne & A\end{eqnarray*}
26387 A formula with the predefined column separation for matrices of 10\InsetSpace \thinspace{}
26392 \begin_layout Standard
26404 \begin_inset Formula \begin{eqnarray*}
26406 C & \ne & A\end{eqnarray*}
26413 \begin_layout Subsubsection
26415 \begin_inset LatexCommand index
26416 name "Formula ! long"
26423 \begin_layout Standard
26424 Long formulas can be typeset using these methods:
26427 \begin_layout Itemize
26428 When one side of the equation is much shorther than the line width, this
26429 one is chosen for the left side and the right side is typeset over two
26434 \begin_layout Standard
26444 \begin_inset Formula \begin{eqnarray}
26445 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 \\
26446 & & -\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}
26454 \begin_layout Standard
26465 The minus sign at the beginning of the second line does normally not appear
26466 as operator because it is the first character of the line.
26467 Thus it would not be surrounded by space and could not be distinguished
26468 from the fraction bar.
26469 To avoid this, space was inserted behind the minus sign with the command
26480 \begin_layout Standard
26488 \begin_inset LatexCommand ref
26489 reference "sub:Variable-Space"
26499 \begin_inset LatexCommand index
26500 name "Commands ! H ! \\textbackslash hspace"
26507 \begin_layout Itemize
26508 When both sides of the equation are too long, the command
26515 \begin_inset LatexCommand index
26516 name "Commands ! L ! \\textbackslash lefteqn"
26521 It is inserted to the first column of the first line and effects that all
26522 further insertions overwrite the following columns:
26526 \begin_layout Standard
26536 \begin_inset Formula \begin{eqnarray}
26537 \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 \\
26538 & & -\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 \\
26539 & & =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}
26547 \begin_layout Standard
26558 After the insertion of
26564 , the cursor is in a purple box that is a bit shifted to the left from the
26566 In this the formula is inserted.
26570 \begin_layout Standard
26581 The content of the further lines is inserted to the second or another formula
26583 The greater the column number where it was inserted, the larger the indentation.
26587 \begin_layout Standard
26599 \begin_inset Note Greyedout
26602 \begin_layout Standard
26603 Note the following when using
26612 \begin_layout Itemize
26613 The formula doesn't use the full page width.
26614 When e.\InsetSpace \thinspace{}
26617 \begin_inset Formula $-B^{2}$
26620 is added to the first line in the above example, it would have been outside
26622 To better use the width, negative space can be inserted at the beginning
26626 \begin_layout Itemize
26627 Due to a bug in LyX the cursor cannot be set with the mouse into the first
26632 \begin_layout Standard
26636 \begin_layout Standard
26640 href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
26649 \begin_layout Standard
26661 One can only set the cursor at the beginning of the line and move it with
26670 \begin_layout Itemize
26671 Other methods to set long formulas are offered by the environments described
26673 \begin_inset LatexCommand ref
26674 reference "sub:Multline-Environment"
26679 \begin_inset LatexCommand ref
26680 reference "sub:Multiline-Formula-Parts"
26687 \begin_layout Subsubsection
26689 \begin_inset LatexCommand label
26690 name "sub:Multiline-Brackets"
26695 \begin_inset LatexCommand index
26696 name "Brackets ! for multiline expressions"
26703 \begin_layout Standard
26704 For brackets spanning multiple lines the following problem occurs:
26705 \begin_inset Formula \begin{eqnarray*}
26706 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26707 & & \left.\cdots+B-D\right]\end{eqnarray*}
26714 \begin_layout Standard
26715 The closing bracket is smaller than the opening bracket because brackets
26716 with variable size may not span multiple lines.
26719 \begin_layout Standard
26720 To set the bracket size for the second line correctly, the first line is
26728 \begin_inset LatexCommand index
26729 name "Commands ! R ! \\textbackslash right"
26733 and the second line with
26741 \begin_layout Standard
26755 \begin_inset LatexCommand ref
26756 reference "sub:Automatic-Bracket-Size"
26768 \begin_inset LatexCommand index
26769 name "Commands ! L ! \\textbackslash left"
26791 \begin_layout Standard
26810 \begin_layout Standard
26829 \begin_layout Standard
26841 \begin_inset Formula $\downarrow$
26847 \begin_inset LatexCommand index
26848 name "Commands ! V ! \\textbackslash vphantom"
26852 is inserted, because the multiplication operator with its limits is the
26853 largest symbol in the first line and this should be the size for the bracket
26854 in the second line.
26857 \begin_layout Standard
26858 The result is this:
26859 \begin_inset Formula \begin{eqnarray*}
26860 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26861 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
26868 \begin_layout Subsection
26872 \begin_layout Standard
26873 Align environments can be used for every kind of multiline formulas.
26874 They are specially useful to set several formulas side by side.
26877 \begin_layout Standard
26878 Align environments consist of columns.
26879 The odd columns are right aligned, the even ones left aligned.
26880 Every line in an Align environment can be numbered.
26883 \begin_layout Standard
26884 Align environments are created via the menu
26886 Insert\SpecialChar \menuseparator
26892 Edit\SpecialChar \menuseparator
26893 Math\SpecialChar \menuseparator
26894 Change Formula Type
26896 already existing formulas can be converted to Align environments.
26899 \begin_layout Standard
26900 To add or delete columns, the math toolbar buttons
26901 \begin_inset Graphics
26902 filename ../images/tabular-feature_append-column.png
26908 \begin_inset Graphics
26909 filename ../images/tabular-feature_delete-column.png
26914 , respectively, or the menu
26916 Edit\SpecialChar \menuseparator
26922 \begin_layout Subsubsection
26923 Standard align Environment
26924 \begin_inset LatexCommand label
26925 name "sub:Standard-align-Environment"
26930 \begin_inset LatexCommand index
26931 name "Formula ! multiline ! align environment"
26938 \begin_layout Standard
26939 This Align environment is created by presssing
26943 in a formula or by the menu
26945 Insert\SpecialChar \menuseparator
26946 Math\SpecialChar \menuseparator
26947 AMS align Environment
26952 \begin_layout Standard
26953 An example for two formulas set side by side, that are created with a four
26954 column align environment:
26955 \begin_inset Formula \begin{align*}
26956 A & =\sin(B) & C & =D\\
26957 C & \ne A & B & \ne D\end{align*}
26961 As it can be seen, the formulas in this environment are placed so as if
26970 \begin_layout Standard
26978 \begin_inset LatexCommand ref
26979 reference "sub:Variable-Space"
26990 before the first and after every even column.
26991 When the formula style
26997 \begin_layout Standard
26999 \begin_inset LatexCommand ref
27000 reference "sec:Formula-Styles"
27011 is used, the formula is set without the
27017 before the first column.
27020 \begin_layout Subsubsection
27021 Alignat Environment
27022 \begin_inset LatexCommand index
27023 name "Formula ! multiline ! alignat environment"
27030 \begin_layout Standard
27031 The alignat environment has no predefined column separation.
27032 It can be inserted manually with the spaces that are described
27033 \begin_inset LatexCommand ref
27034 reference "sub:Space"
27041 \begin_layout Standard
27042 The above example in the alignat environment where 1\InsetSpace \thinspace{}
27043 cm space was inserted
27044 at the beginning of the second formula:
27045 \begin_inset Formula \begin{alignat*}{2}
27046 A & =\sin(B) & \hspace{1cm}C & =D\\
27047 C & \ne A & B & \ne D\end{alignat*}
27051 Because the column separation can be set separately for every column, this
27052 environment is especially suitable to set three and more formulas side
27056 \begin_layout Subsubsection
27057 Flalign Environment
27058 \begin_inset LatexCommand label
27059 name "sub:Flalign-Environment"
27064 \begin_inset LatexCommand index
27065 name "Formula ! multiline ! flalign environment"
27072 \begin_layout Standard
27073 In this environment the first two columns are always set as much as possible
27074 to the left and the last two ones to the right.
27076 \begin_inset Formula \begin{flalign*}
27077 A & =1 & B & =2 & C & =3\\
27078 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
27085 \begin_layout Standard
27086 By creating a flalign environment with an odd number of columns where an
27087 empty TeX-brace is inserted to the last column, several formulas in a document
27088 can be set to the left, although the formula style
27093 As example the indented formula
27094 \begin_inset LatexCommand eqref
27095 reference "eq:VolInt"
27100 \begin_inset Formula \begin{flalign}
27101 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
27105 The first two columns contain the formula.
27106 To indent it as with the formula style
27110 , 30\InsetSpace \thinspace{}
27111 pt space was inserted at the beginning of the first column.
27114 \begin_layout Subsection
27115 Eqnarray Environment
27116 \begin_inset LatexCommand index
27117 name "Formula ! multiline ! eqnarray environment"
27124 \begin_layout Standard
27125 When this environment has been created, three blue boxes appear.
27126 The content of the first box is right aligned, the content of the last
27128 The content of the middle box appears centered and a bit smaller, because
27129 it is designed to insert there only relation characters.
27130 \begin_inset Formula \begin{eqnarray*}
27131 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27133 A & = & A\end{eqnarray*}
27140 \begin_layout Subsection
27142 \begin_inset LatexCommand index
27143 name "Formula ! multiline ! gather environment"
27150 \begin_layout Standard
27151 This environment consists of only one centered column.
27152 Every line can be numbered.
27153 \begin_inset Formula \begin{gather}
27155 X=\textrm{-}1\end{gather}
27162 \begin_layout Subsection
27163 Multline Environment
27164 \begin_inset LatexCommand label
27165 name "sub:Multline-Environment"
27170 \begin_inset LatexCommand index
27171 name "Formula ! multiline ! multline environment"
27178 \begin_layout Standard
27179 The multline environment consists, like the gather environment, of only
27181 But the first line is left aligned, the last one right aligned.
27182 All other lines are centered.
27183 Therefore this environment is suitable for long formulas.
27185 \begin_inset LatexCommand eqref
27186 reference "eq:lefteqn"
27190 in the multline environment:
27191 \begin_inset Formula \begin{multline}
27192 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}\\
27193 -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}\\
27194 =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}
27201 \begin_layout Standard
27202 In the output only the last (first) line of a multline environment appears
27203 numbered when the document numbering is right (left).
27207 \begin_layout Standard
27208 numbering styles see
27209 \begin_inset LatexCommand ref
27210 reference "sec:Formula-Styles"
27219 This is also the case when there is a formula number displayed after every
27224 \begin_layout Standard
27229 \begin_layout Standard
27233 href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
27242 \begin_layout Standard
27257 \begin_layout Standard
27263 \begin_inset LatexCommand index
27264 name "Commands ! S ! \\textbackslash shoveright"
27275 \begin_inset LatexCommand index
27276 name "Commands ! S ! \\textbackslash shoveleft"
27282 a centered line can be right or left aligned, respectively.
27283 The commands are used as follows:
27286 \begin_layout Standard
27291 shoveright{line content}
27297 shoveleft{line content}
27300 \begin_layout Standard
27301 \begin_inset VSpace medskip
27309 \begin_inset LatexCommand index
27310 name "Commands ! M ! \\textbackslash multlinegap"
27316 specifies the distance of the first line from the left page margin.
27317 Predefined is the length 0\InsetSpace \thinspace{}
27321 \begin_layout Standard
27322 As example the above formula where the command
27325 \begin_layout Standard
27335 \begin_layout Standard
27336 was inserted in TeX-mode before:
27340 \begin_layout Standard
27352 \begin_inset Formula \begin{multline}
27353 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}\\
27354 \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}}\\
27355 =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}
27363 \begin_layout Standard
27374 The second line was left aligned using
27383 \begin_layout Subsection
27384 Multiline Formula Parts
27385 \begin_inset LatexCommand label
27386 name "sub:Multiline-Formula-Parts"
27391 \begin_inset LatexCommand index
27392 name "Formula ! multiline ! formula parts"
27399 \begin_layout Standard
27400 To display only parts of a formula with multiple lines, one of the following
27401 environments are used:
27418 They can be inserted via the menu
27420 Insert\SpecialChar \menuseparator
27423 or by using the commands described in this section.
27426 \begin_layout Standard
27427 The first three have the same properties as the corresponding multiline
27428 formula environments, but it is possible to set further formula parts beside
27431 \begin_inset Formula \[
27432 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
27433 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
27434 \right\} \textrm{Uncertainty relations}\]
27441 \begin_layout Standard
27442 To get this formula, a displayed formula is created where the command
27447 \begin_inset LatexCommand index
27448 name "Commands ! A ! \\textbackslash aligned"
27455 A purple box appears around the blue formula box where now columns and
27456 lines can be added.
27457 Outside the multiline environment other formula parts can be set, like
27461 \begin_layout Standard
27462 The aligned environment is also suitable for long formulas whose lines are
27463 horizontally aligned.
27464 Using aligned in a displayed formula has the advantage that the formula
27465 number is vertically centered behind the lines.
27467 \begin_inset LatexCommand eqref
27468 reference "eq:kurzlang"
27472 in the aligned environment:
27473 \begin_inset Formula \begin{equation}
27474 \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}|}\\
27475 & -\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}
27483 \begin_layout Standard
27484 To use the environments
27503 \begin_inset LatexCommand index
27504 name "Commands ! A ! \\textbackslash alignedat"
27515 \begin_inset LatexCommand index
27516 name "Commands ! G ! \\textbackslash gathered"
27527 \begin_inset LatexCommand index
27528 name "Commands ! S ! \\textbackslash split"
27532 are inserted, respectively.
27533 The split environment has the same properties as the aligned environment
27534 but it can only have two columns.
27537 \begin_layout Subsection
27538 Text in multiline Formulas
27539 \begin_inset LatexCommand label
27540 name "sub:Text-in-multiline"
27545 \begin_inset LatexCommand index
27546 name "Text ! in formulas"
27551 \begin_inset LatexCommand index
27552 name "Formula ! multiline ! text"
27559 \begin_layout Standard
27560 In the Align environments, and the multline and gather environment, text
27561 can be inserted that will appear in a separate line and doesn't affect
27562 the column alignment.
27563 To do this, the command
27568 \begin_inset LatexCommand index
27569 name "Commands ! I ! \\textbackslash intertext"
27575 is used in the following scheme:
27578 \begin_layout Standard
27586 \begin_layout Standard
27587 The text should not be longer than a line because it cannot be hyphenated.
27588 As LyX doesn't yet support
27594 directly, the text is written as mathematical text.
27601 must hereby be at the beginning of a line and appears in the output above
27603 An example where the text was inserted at the beginning of the second line:
27604 \begin_inset Formula \begin{align}
27605 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
27606 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
27613 \begin_layout Section
27615 \begin_inset LatexCommand index
27616 name "Formula numbering"
27621 \begin_inset LatexCommand index
27622 name "Formula ! numbering|see{Formula numbering}"
27629 \begin_layout Subsection
27633 \begin_layout Standard
27634 Numbered formulas can be created with the menu
27636 Insert\SpecialChar \menuseparator
27637 Math\SpecialChar \menuseparator
27638 Numbered\InsetSpace ~
27643 Ctrl-Alt\InsetSpace ~
27647 Existing formulas can be numbered with the menu
27649 Edit\SpecialChar \menuseparator
27650 Math\SpecialChar \menuseparator
27651 Toggle\InsetSpace ~
27660 The formula number is displayed in LyX behind the formula as number sign
27662 The number sign is replaced in the output by the formula number.
27665 \begin_layout Standard
27666 When numbering is turned on in multiline formulas, all lines will be numbered.
27667 But the numbering can be controlled with the menu
27669 Edit\SpecialChar \menuseparator
27670 Math\SpecialChar \menuseparator
27671 Toggle\InsetSpace ~
27672 Numbering\InsetSpace ~
27684 \begin_layout Standard
27685 Except of inline formulas, all formulas can be numbered with two different
27687 \begin_inset LatexCommand ref
27688 reference "sec:Formula-Styles"
27695 \begin_layout Subsection
27697 \begin_inset LatexCommand label
27698 name "sub:Cross-References"
27703 \begin_inset LatexCommand index
27704 name "Cross-references ! to formulas"
27711 \begin_layout Standard
27712 All labeled formulas can be cross-referenced.
27713 A label is added by the menu
27715 Insert\SpecialChar \menuseparator
27718 or the toolbar button
27719 \begin_inset Graphics
27720 filename ../images/label-insert.png
27726 The cursor must hereby be inside a displayed formula.
27727 A dialog pops up displaying the prefix
27732 The label is inserted there behind the prefix.
27733 The predefined prefix means
27734 \begin_inset Quotes eld
27738 \begin_inset Quotes erd
27741 and makes it easier to find labels in large documents because it marks
27742 it as formula label to divide it from e.\InsetSpace \thinspace{}
27745 To change a label, the menu
27747 Insert\SpecialChar \menuseparator
27753 \begin_layout Standard
27754 The name of the label is displayed in LyX within two parentheses behind
27756 A formula with a label is always numbered.
27757 The label is deleted when the numbering is turned off.
27758 This is at the moment the only way to delete a label, see
27762 \begin_layout Standard
27766 href{http://bugzilla.lyx.org/show_bug.cgi?id=2556}{
27775 \begin_layout Standard
27785 \begin_layout Standard
27786 Cross-references are inserted via the menu
27788 Insert\SpecialChar \menuseparator
27791 or with the toolbar button
27792 \begin_inset Graphics
27793 filename ../images/dialog-show-new-inset_ref.png
27799 A formula cross-reference appears in the output as formula number.
27800 When in the cross-reference dialog window the format
27804 is chosen, the cross-reference appears in the output as formula number
27807 By right-clicking on a cross-reference in LyX, one jumps
27808 to the formula that is referenced.
27811 \begin_layout Standard
27812 Here are as examples cross-references to formulas of the following subsections:
27813 \begin_inset Note Note
27816 \begin_layout Standard
27817 Note the different cross-reference types.
27825 \begin_layout Standard
27827 \begin_inset LatexCommand eqref
27833 \begin_inset LatexCommand eqref
27840 \begin_inset LatexCommand ref
27845 ) big Latin letters are used for the numbering in contrary to (
27846 \begin_inset LatexCommand ref
27854 \begin_layout Standard
27855 \begin_inset VSpace medskip
27858 When the argument of
27866 \begin_layout Standard
27874 \begin_inset LatexCommand ref
27875 reference "sub:User-defined-Numbering"
27886 contains a box like in
27887 \begin_inset LatexCommand ref
27888 reference "sub:Paragraph-Boxes"
27892 , the formula cannot be referenced.
27895 \begin_layout Subsection
27897 \begin_inset LatexCommand index
27898 name "Formula numbering ! subnumbering"
27905 \begin_layout Standard
27906 With the help of the commands
27910 begin{subequations}
27918 formulas can be subnumbered.
27919 Both commands are inserted in TeX-mode.
27922 \begin_layout Standard
27924 \begin_inset Formula \begin{equation}
27925 A=C-B\label{eq:a}\end{equation}
27933 \begin_layout Standard
27937 addtocounter{equation}{-1}
27946 \begin_layout Standard
27950 begin{subequations}
27956 \begin_inset VSpace -5mm
27960 \begin_inset Formula \begin{equation}
27961 B=C-A\label{eq:b}\end{equation}
27966 \begin_inset Formula \begin{equation}
27967 C=A+B\label{eq:c}\end{equation}
27974 \begin_layout Standard
27978 \begin_layout Standard
27990 \begin_layout Standard
27991 To create the example, the following is done:
27994 \begin_layout Enumerate
27995 first formula is inserted
27998 \begin_layout Enumerate
28003 addtocounter{equation}{-1}
28005 begin{subequations}
28006 \begin_inset LatexCommand index
28007 name "Commands ! A ! \\textbackslash addtocounter"
28015 is inserted after the first formula
28018 \begin_layout Enumerate
28019 second formula is inserted
28022 \begin_layout Enumerate
28023 third formula is inserted
28026 \begin_layout Enumerate
28033 is inserted after the third formula
28036 \begin_layout Standard
28037 Every formula between the commands
28049 is subnumbered as a, b,
28053 \begin_layout Standard
28062 c, \SpecialChar \ldots{}
28063 For multiline formulas every line will be subnumbered.
28064 All subnumbered formulas are treated as
28069 But as every numbered formula increases the counter
28073 by one, the command
28079 is needed to decrease it.
28080 Otherwise the formulas
28081 \begin_inset LatexCommand eqref
28087 \begin_inset LatexCommand eqref
28093 \begin_inset LatexCommand eqref
28098 would be numbered as
28099 \begin_inset LatexCommand eqref
28105 \begin_inset LatexCommand eqref
28111 \begin_inset LatexCommand eqref
28119 \begin_layout Standard
28120 By inserting the commands in TeX-mode, a space is created between the first
28122 To revert this -5\InsetSpace \thinspace{}
28123 mm vertical space is inserted after the command
28127 begin{subequations}
28130 When the formula style
28136 \begin_layout Standard
28138 \begin_inset LatexCommand ref
28139 reference "sec:Formula-Styles"
28150 is used, -7\InsetSpace \thinspace{}
28151 mm space is inserted instead.
28154 \begin_layout Standard
28155 Here is an example for a multiline formula where the numbering was turned
28156 off for the second line:
28160 \begin_layout Standard
28164 begin{subequations}
28170 \begin_inset Formula \begin{eqnarray}
28171 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
28172 & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
28173 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
28181 \begin_layout Standard
28193 \begin_layout Subsection
28194 User-defined Numbering
28195 \begin_inset LatexCommand label
28196 name "sub:User-defined-Numbering"
28201 \begin_inset LatexCommand index
28202 name "Formula numbering ! user-defined"
28209 \begin_layout Standard
28210 \begin_inset LatexCommand index
28211 name "Formula numbering ! self-defined delimiters"
28215 With the standard numbering parentheses are set around the formula number.
28216 To replace the parentheses for example by vertical bars, the following
28217 line is added to the LaTeX-preamble:
28220 \begin_layout Standard
28232 \begin_inset Note Note
28235 \begin_layout Standard
28236 This macro is already declared in the LaTeX-preamble for testing.
28237 To activate it, remove the percent sign at the beginning.
28245 \begin_layout Standard
28246 To use other characters, the vertical bars besides the
28250 are replaced by one ore more characters.
28251 To get only the formula number the vertical bars are omitted.
28254 \begin_layout Standard
28255 \begin_inset VSpace bigskip
28258 When there should be an expression of your choice instead of the consecutive
28259 formula number in parentheses behind the formula, the command
28266 \begin_inset LatexCommand index
28267 name "Commands ! T ! \\textbackslash tag"
28272 \begin_inset Formula \begin{equation}
28273 A+B=C\tag{something}\label{eq:tag}\end{equation}
28277 In this example the command
28285 \begin_layout Standard
28296 was inserted to the formula.
28299 \begin_layout Standard
28308 \begin_layout Standard
28319 is inserted instead, the star prevents the parentheses around the expression:
28320 \begin_inset Formula \[
28321 A+B=C\tag*{something}\]
28328 \begin_layout Standard
28329 \begin_inset VSpace bigskip
28332 To restart the formula numbering with new document parts or sections, the
28333 following command is used:
28336 \begin_layout Standard
28341 @addtoreset{equation}{part}
28344 \begin_inset LatexCommand index
28345 name "Commands ! \"@\" ! \\textbackslash \"@\"addtoreset"
28357 @addtoreset{equation}{section}
28360 \begin_layout Standard
28361 To be able to use these commands in TeX-mode, the
28362 \begin_inset Quotes eld
28366 \begin_inset Quotes erd
28369 character has to be made
28370 \begin_inset Quotes eld
28374 \begin_inset Quotes erd
28377 for LaTeX using the command
28391 So the command sequence in TeX-mode is:
28394 \begin_layout Standard
28403 @addtoreset{equation}{section}
28410 \begin_layout Standard
28411 In the LaTeX-preamble
28423 can be omitted as they are automatically internally inserted by LyX.
28426 \begin_layout Standard
28441 \begin_layout Standard
28446 is part of the LaTeX-package
28451 \begin_inset LatexCommand index
28452 name "Packages ! carlisle"
28456 that is part of every LaTeX standard installation.
28462 \begin_inset LatexCommand index
28463 name "Packages ! remreset"
28467 has to be loaded in the LaTeX-preamble with the line
28470 \begin_layout Standard
28475 usepackage{remreset}
28478 \begin_layout Standard
28486 \begin_inset LatexCommand index
28487 name "Commands ! \"@\" ! \\textbackslash \"@\"removefromreset"
28491 can be used with the same scheme as
28500 \begin_layout Standard
28501 \begin_inset VSpace bigskip
28504 Sometimes formulas should be numbered in the following form:
28507 \begin_layout Standard
28510 (section number.formula number)
28513 \begin_layout Standard
28514 The formula number should start with every section with
28515 \begin_inset Quotes eld
28519 \begin_inset Quotes erd
28525 \begin_layout Standard
28526 For this case there is the command
28533 \begin_inset LatexCommand index
28534 name "Commands ! N ! \\textbackslash numberwithin"
28538 , which is used with the following scheme:
28541 \begin_layout Standard
28546 numberwithin{counter}{sectioning}
28549 \begin_layout Standard
28550 Counter denotes what kind of numbering is affected, sectioning denotes what
28551 number is before the dot.
28554 \begin_layout Standard
28555 Thus in our case the following LaTeX-preamble or ERT line is used:
28558 \begin_layout Standard
28563 numberwithin{equation}{section}
28566 \begin_layout Standard
28567 This is the result:
28571 \begin_layout Standard
28575 numberwithin{equation}{section}
28581 \begin_inset Formula \begin{equation}
28582 A+B=C\end{equation}
28589 \begin_layout Standard
28590 To number e.\InsetSpace \thinspace{}
28592 tables so that the number of the part is the sectioning,
28598 numberwithin{table}{part}
28603 \begin_layout Standard
28604 To go back to the standard numbering or to prevent this kind of numbering
28605 when it is defined by the document class, the following command is inserted
28606 as ERT or to the LaTeX-preamble:
28609 \begin_layout Standard
28619 \begin_inset LatexCommand index
28620 name "Commands ! A ! \\textbackslash arabic"
28630 \begin_layout Standard
28662 \begin_layout Standard
28669 uses internally the command
28675 , described above, that also needs to be reverted.
28679 \begin_layout Standard
28686 \begin_layout Standard
28690 @removefromreset{equation}{section}
28693 \begin_layout Standard
28705 \begin_layout Subsection
28706 Numbering with Roman Numbers and Letters
28707 \begin_inset LatexCommand label
28708 name "sub:Numbering-with-Roman"
28713 \begin_inset LatexCommand index
28714 name "Formula numbering ! with letters"
28719 \begin_inset LatexCommand index
28720 name "Formula numbering ! with Roman numbers"
28727 \begin_layout Standard
28728 Formulas can also be numbered with Roman numbers and Latin letters.
28729 To number for example with small Roman numbers, the command
28732 \begin_layout Standard
28744 \begin_layout Standard
28745 is inserted before the formula in TeX-mode.
28753 \begin_inset LatexCommand index
28754 name "Commands ! R ! \\textbackslash renewcommand"
28758 redefines the predefined command
28774 \begin_layout Standard
28781 has the same scheme like the command
28787 that is described in
28788 \begin_inset LatexCommand ref
28789 reference "sec:User-defined-commands"
28803 is the formula counter.
28810 is used as prefix for a counter, the value of the counter is output as
28812 When a formula is numbered, LaTeX sets internally the command
28818 behind the formula.
28824 \begin_inset LatexCommand index
28825 name "Commands ! R ! \\textbackslash roman"
28831 outputs the counter as small Roman number.
28834 \begin_layout Standard
28835 All formulas behind the command
28845 are now numbered Roman.
28846 To switch to numbering with big Roman numbers, the command is inserted
28860 \begin_inset LatexCommand index
28861 name "Commands ! R ! \\textbackslash roman@\\textbackslash Roman"
28867 \begin_inset Quotes eld
28871 \begin_inset Quotes erd
28874 with small Latin letters there is the command
28881 \begin_inset LatexCommand index
28882 name "Commands ! A ! \\textbackslash alph"
28886 , for big ones there is the command
28893 \begin_inset LatexCommand index
28894 name "Commands ! A ! \\textbackslash alph@\\textbackslash Alph"
28901 \begin_layout Standard
28902 \begin_inset Note Greyedout
28905 \begin_layout Standard
28910 Only maximal 26 formulas can be numbered with Latin letters in one document.
28918 \begin_layout Standard
28922 \begin_layout Standard
28938 \begin_layout Standard
28939 \begin_inset Formula \begin{equation}
28940 A=\textrm{small roman}\label{eq:rom}\end{equation}
28948 \begin_layout Standard
28962 \begin_inset Formula \begin{equation}
28963 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
28971 \begin_layout Standard
28985 \begin_inset Formula \begin{equation}
28986 C=\textrm{small Latin}\label{eq:lat}\end{equation}
28994 \begin_layout Standard
29008 \begin_inset Formula \begin{equation}
29009 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
29016 \begin_layout Standard
29017 To switch back to the default numbering, insert the command:
29020 \begin_layout Standard
29030 \begin_inset LatexCommand index
29031 name "Commands ! A ! \\textbackslash arabic"
29038 \begin_layout Standard
29042 \begin_layout Standard
29056 \begin_inset Formula \begin{equation}
29057 E=\textrm{Arabic}\label{eq:arab}\end{equation}
29064 \begin_layout Standard
29065 \begin_inset VSpace medskip
29068 As you see, formulas are numbered serially independent from the numbering
29070 When then numbering should start with
29071 \begin_inset Quotes eld
29075 \begin_inset Quotes erd
29078 when the style is changed, new equation counters have to be defined.
29079 A description about this can be found in the file
29083 \begin_layout Standard
29087 href{Formula-numbering.lyx}{
29092 Formula-numbering.lyx
29096 \begin_layout Standard
29106 \begin_layout Section
29107 User-defined commands
29108 \begin_inset LatexCommand label
29109 name "sec:User-defined-commands"
29114 \begin_inset LatexCommand index
29115 name "User-defined commands"
29122 \begin_layout Standard
29123 Many LaTeX-commands are too long to be used frequently.
29124 But it is possible to define with the command
29131 \begin_inset LatexCommand index
29132 name "Commands ! N ! \\textbackslash newcommand"
29136 new shorter commands.
29139 \begin_layout Standard
29140 The command scheme of
29149 \begin_layout Standard
29154 newcommand{new command name}[number of arguments][optional
29164 \begin_layout Standard
29179 \begin_layout Standard
29186 {command definition}
29189 \begin_layout Standard
29190 \begin_inset Note Greyedout
29193 \begin_layout Standard
29198 Assure that the name of the new command is not already used in your document
29199 or by LaTeX-packages that you use.
29200 When you for example define the command
29212 , you get an error message because
29218 is already defined as command for
29219 \begin_inset Quotes eld
29223 \begin_inset Formula $\le$
29227 \begin_inset Quotes erd
29238 \begin_layout Standard
29239 \begin_inset Note Greyedout
29242 \begin_layout Standard
29247 The names of user-defined commands may only consist of Latin letters.
29255 \begin_layout Standard
29256 The number of arguments is an integer in the range 0\InsetSpace \thinspace{}
29257 -\InsetSpace \thinspace{}
29258 9 and specifies how
29259 many arguments the new command should have.
29260 With the optional value a value for an optional argument can be predefined.
29261 When this is done, the
29269 rgument of the new command is automatically an optional one.
29272 \begin_layout Standard
29273 Here are some examples:
29276 \begin_layout Itemize
29277 To define the command
29289 , the LaTeX-preamble line is:
29293 \begin_layout Standard
29315 \begin_layout Itemize
29316 To define the command
29328 , the argument (that should be underlined) must be taken into account.
29329 For this the preamble line is:
29333 \begin_layout Standard
29358 \begin_layout Standard
29377 acts as argument placeholder, the
29381 behind it denotes that it is the placeholder for the first argument.
29384 \begin_layout Itemize
29391 one can e.\InsetSpace \thinspace{}
29403 \begin_layout Standard
29422 framebox#1#2{$#3$}}
29428 \begin_layout Standard
29443 The two Dollar signs creates the extra formula needed for
29450 \begin_inset LatexCommand ref
29451 reference "sub:Boxes-with-Frame"
29458 \begin_layout Itemize
29459 To create a new command for
29465 where the color for the box needn't to be specified, the argument for the
29466 color is defined optional:
29470 \begin_layout Standard
29489 fcolorbox{#2}{#1}{$#3$}}
29495 \begin_layout Standard
29506 When the color is not specified when using
29512 , the predefined color
29519 \begin_layout Standard
29520 A test of the new defined commands:
29523 \begin_layout Standard
29525 \begin_inset Tabular
29526 <lyxtabular version="3" rows="6" columns="2">
29528 <column alignment="center" valignment="top" leftline="true" width="0">
29529 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
29530 <row topline="true" bottomline="true">
29531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29534 \begin_layout Standard
29540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29543 \begin_layout Standard
29545 \begin_inset Note Note
29548 \begin_layout Standard
29555 is only used as spacer.
29566 <row topline="true">
29567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29570 \begin_layout Standard
29577 \begin_layout Standard
29591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29594 \begin_layout Standard
29595 \begin_inset Formula $A\gr B$
29604 <row topline="true">
29605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29608 \begin_layout Standard
29616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29619 \begin_layout Standard
29620 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
29629 <row topline="true">
29630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29633 \begin_layout Standard
29637 \begin_inset Formula $\to$
29643 \begin_inset Formula $\to$
29654 \begin_layout Standard
29668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29671 \begin_layout Standard
29672 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
29681 <row topline="true">
29682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29685 \begin_layout Standard
29689 \begin_inset Formula $\to$
29700 \begin_layout Standard
29714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29717 \begin_layout Standard
29718 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
29727 <row topline="true" bottomline="true">
29728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29731 \begin_layout Standard
29737 \begin_inset Formula $\to$
29748 \begin_layout Standard
29762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29765 \begin_layout Standard
29766 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
29782 \begin_layout Section
29784 \begin_inset LatexCommand index
29792 \begin_layout Standard
29793 To create diagrams, the LaTeX-package
29799 \begin_layout Standard
29804 is part of every LaTeX standard installation.
29812 \begin_inset LatexCommand index
29813 name "Packages ! amscd"
29818 It is loaded in the LaTeX-preamble with the line
29821 \begin_layout Standard
29829 \begin_layout Standard
29830 Diagrams visualize relations and look like this:
29831 \begin_inset Formula \[
29832 \begin{CD}A@>>>B@>>>C\\
29834 F@<<<E@<<<D\end{CD}\]
29841 \begin_layout Standard
29842 To get them, the command
29847 \begin_inset LatexCommand index
29848 name "Commands ! C ! \\textbackslash CD"
29854 is inserted to a formula.
29855 A blue box appears with two dashed lines where further commands can be
29861 a new line is created.
29862 Horizontal relations are inserted in odd, vertical in even formula lines.
29865 \begin_layout Standard
29866 To create the relations there are the following commands:
29869 \begin_layout Itemize
29874 creates a left arrow,
29885 \begin_layout Itemize
29890 creates an up arrow,
29898 a vertical equal sign
29901 \begin_layout Itemize
29907 is a placeholder for non-existent relations
29910 \begin_layout Standard
29911 All arrows can be labeled as follows:
29914 \begin_layout Itemize
29915 Is text inserted between the first and second < or >, resp., it is placed
29917 When it is inserted between the second and third one, it appears under
29921 \begin_layout Itemize
29922 When text for vertical arrows is inserted between the first and second A
29923 or V, resp., it is placed left beside the arrow.
29924 When it is inserted between the second and third one, it appears right
29926 If the text contains an A or V, these letters must be set into a TeX-brace.
29929 \begin_layout Standard
29930 As example a diagram with all possible relations:
29933 \begin_layout Standard
29934 \begin_inset Formula \[
29935 \begin{CD}A@>j>>B@>>k>C@=F\\
29937 D@<<j<E@>k>>F@=C\end{CD}\]
29944 \begin_layout Standard
29945 The command for this is:
29955 \begin_layout Standard
29964 A@>j>>B@>>k>C@=F Ctrl-Enter
29970 \begin_layout Standard
29985 \begin_layout Standard
29998 \begin_layout Standard
30010 \begin_inset Formula $\to$
30021 \begin_layout Standard
30036 \begin_layout Standard
30049 \begin_layout Standard
30059 \begin_layout Standard
30065 \begin_layout Section
30070 \begin_layout Standard
30083 \begin_layout Standard
30084 Other useful math tips can be found in
30085 \begin_inset LatexCommand cite
30099 \begin_layout Standard
30107 \begin_inset Note Note
30110 \begin_layout Standard
30113 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
30116 \begin_layout Standard
30119 texorpdfstring is in section
30120 \begin_inset LatexCommand ref
30121 reference "sub:Formulas-in-Section"
30131 \begin_inset LatexCommand index
30137 \begin_inset LatexCommand index
30138 name "Ions|see{Chemical characters}"
30145 \begin_layout Subsection
30146 Chemical Symbols and Equations
30147 \begin_inset LatexCommand label
30148 name "sub:Chemical-Symbols-and"
30153 \begin_inset LatexCommand index
30154 name "Chemical characters ! Symbols"
30159 \begin_inset LatexCommand index
30160 name "Chemical equations"
30165 \begin_inset LatexCommand index
30166 name "Symbols ! chemical"
30173 \begin_layout Standard
30174 An example text from chemistry:
30177 \begin_layout Quote
30179 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30182 -ion reacts with two
30183 \begin_inset Formula $\mathrm{Na^{+}}$
30186 -ions to sodium sulfate
30187 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30191 The chemical equation for this is:
30192 \begin_inset Formula \[
30193 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
30200 \begin_layout Standard
30201 This chemical equation can directly be created as formula.
30202 To avoid that the symbols appear italic, everything is highlighted and
30203 changed by the shortcut
30208 to the upright font style.
30212 \begin_layout Standard
30218 \begin_inset LatexCommand ref
30219 reference "sub:Font-Styles"
30231 \begin_layout Subsection
30233 \begin_inset LatexCommand index
30234 name "Numbers ! negative"
30241 \begin_layout Standard
30242 Negative numbers often look ugly in formulas because the minus sign before
30243 the number is set with the same length as the minus operator sign.
30244 When writing the negative number in normal text, the minus sign appears
30248 \begin_layout Standard
30249 Thus, the problem disappears when converting the minus sign to mathematical
30253 \begin_layout Standard
30254 An example to visualize the problem:
30257 \begin_layout Standard
30259 \begin_inset Tabular
30260 <lyxtabular version="3" rows="3" columns="2">
30262 <column alignment="right" valignment="top" leftline="true" width="0">
30263 <column alignment="left" valignment="top" rightline="true" width="0">
30264 <row topline="true">
30265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30268 \begin_layout Standard
30274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30277 \begin_layout Standard
30284 <row topline="true" bottomline="true">
30285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30288 \begin_layout Standard
30294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30297 \begin_layout Standard
30298 \begin_inset Formula $x=-2$
30307 <row topline="true" bottomline="true">
30308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30311 \begin_layout Standard
30317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30320 \begin_layout Standard
30321 \begin_inset Formula $x=\textrm{-}2$
30337 \begin_layout Subsection
30338 Comma as Decimal Separator
30339 \begin_inset LatexCommand index
30347 \begin_layout Standard
30348 In LaTeX a comma inside a formula is used, according to the English convention,
30349 as number group separator.
30350 So there will be space added behind all commas in formulas.
30353 \begin_layout Standard
30354 To avoid this, the comma is highlighted and changed to mathematical text
30363 \begin_layout Standard
30364 To use all formula commas in the document as decimal separator, the file
30373 \begin_layout Standard
30378 is part of the LaTeX-package
30383 \begin_inset LatexCommand index
30384 name "Packages ! was\\vspace{4mm}"
30394 \begin_inset LatexCommand index
30395 name "Packages ! icomma"
30399 is loaded with the LaTeX-preamble line
30402 \begin_layout Standard
30410 \begin_layout Subsection
30412 \begin_inset LatexCommand label
30413 name "sub:Physical-Vectors"
30418 \begin_inset LatexCommand index
30419 name "Vectors ! physical"
30426 \begin_layout Standard
30427 Predefined vectors are offered by the LaTeX-package
30435 \begin_layout Standard
30440 should be part of every LaTeX standard installation.
30446 \begin_inset LatexCommand index
30447 name "Packages ! braket"
30451 that is loaded with the LaTeX-preamble line
30454 \begin_layout Standard
30462 \begin_layout Standard
30466 \begin_layout Standard
30476 \begin_inset Note Note
30479 \begin_layout Standard
30480 The following table will only be displayed when the LaTeX-package
30489 The following commands are defined:
30492 \begin_layout Standard
30494 \begin_inset Tabular
30495 <lyxtabular version="3" rows="4" columns="2">
30497 <column alignment="center" valignment="top" leftline="true" width="0">
30498 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30499 <row topline="true" bottomline="true">
30500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30503 \begin_layout Standard
30509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30512 \begin_layout Standard
30519 <row topline="true">
30520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30523 \begin_layout Standard
30533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30536 \begin_layout Standard
30537 \begin_inset Formula $\Bra{\psi}$
30546 <row topline="true">
30547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30550 \begin_layout Standard
30560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30563 \begin_layout Standard
30564 \begin_inset Formula $\Ket{\psi}$
30573 <row topline="true" bottomline="true">
30574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30577 \begin_layout Standard
30589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30592 \begin_layout Standard
30593 \begin_inset Formula $\Braket{\psi|\phi}$
30609 \begin_layout Standard
30616 assures that all vertical bars are set in the size of the surrounding brackets:
30617 \begin_inset Formula \[
30618 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
30626 \begin_layout Standard
30636 \begin_inset Note Note
30639 \begin_layout Standard
30640 The following will be displayed when the LaTeX-package
30652 \begin_layout Standard
30653 You need to install the LaTeX-package
30657 to see the rest of this subsection in the output.
30660 \begin_layout Standard
30664 \begin_layout Standard
30676 \begin_layout Standard
30683 can also be achieved using the command
30689 , that is described in
30690 \begin_inset LatexCommand ref
30691 reference "sub:Automatic-Bracket-Size"
30698 \begin_layout Subsection
30699 Self-defined Fractions
30700 \begin_inset LatexCommand label
30701 name "sub:Self-defined-Fractions"
30706 \begin_inset LatexCommand index
30707 name "Fractions ! self-defined"
30714 \begin_layout Standard
30715 To define custom commands for fractions, the command
30722 \begin_inset LatexCommand index
30723 name "Commands ! G ! \\textbackslash genfrac"
30727 is used in the following scheme:
30730 \begin_layout Standard
30743 bracket}{fraction bar thickness}{style}
30749 \begin_layout Standard
30764 \begin_layout Standard
30771 {numerator}{denominator}
30774 \begin_layout Standard
30775 The style is a number in the range of 0\InsetSpace \thinspace{}
30776 -\InsetSpace \thinspace{}
30780 \begin_layout Standard
30782 \begin_inset Tabular
30783 <lyxtabular version="3" rows="5" columns="2">
30785 <column alignment="center" valignment="top" leftline="true" width="0">
30786 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30787 <row topline="true" bottomline="true">
30788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30791 \begin_layout Standard
30797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30800 \begin_layout Standard
30807 <row topline="true">
30808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30811 \begin_layout Standard
30817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30820 \begin_layout Standard
30821 display style formula
30827 <row topline="true">
30828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30831 \begin_layout Standard
30837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30840 \begin_layout Standard
30847 <row topline="true">
30848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30851 \begin_layout Standard
30857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30860 \begin_layout Standard
30867 <row topline="true" bottomline="true">
30868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30871 \begin_layout Standard
30877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30880 \begin_layout Standard
30894 \begin_layout Standard
30895 When no style is given, the size is adjusted to the surrounding environment
30896 like for the command
30905 \begin_layout Standard
30906 When no fraction bar thickness is given, the predefined value of 0.4\InsetSpace \thinspace{}
30911 \begin_layout Standard
30912 \begin_inset VSpace medskip
30915 For example, the commands
30928 \begin_inset LatexCommand ref
30929 reference "sub:Fractions"
30933 are defined with the commands
30936 \begin_layout Standard
30945 genfrac{}{}{}{0}{#1}{#2}}
30948 \begin_layout Standard
30952 \begin_layout Standard
30961 genfrac{(}{)}{0pt}{1}{#1}{#2}}
30964 \begin_layout Standard
30965 \begin_inset VSpace medskip
30968 To define a fraction where the fraction bar thickness can be given as optional
30969 argument, the following line is inserted to the LaTeX-preamble:
30972 \begin_layout Standard
30981 genfrac{}{}{#1}{}{#2}{#3}}
30984 \begin_layout Standard
30986 \begin_inset Formula \begin{align*}
30987 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
30988 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
30992 As one can see, the distance of the numerator and the denominator to the
30993 fraction bar is round about three times the bar thickness.
30996 \begin_layout Subsection
30998 \begin_inset LatexCommand label
30999 name "sub:Canceled-Formulas"
31004 \begin_inset LatexCommand index
31005 name "Formula ! canceled"
31012 \begin_layout Standard
31013 To cancel formulas or formula parts, the LaTeX-package
31021 \begin_layout Standard
31026 is part of every LaTeX standard installation.
31032 \begin_inset LatexCommand index
31033 name "Packages ! cancel"
31037 has to be loaded with the LaTeX-preamble line
31040 \begin_layout Standard
31045 usepackage[samesize]{cancel}
31048 \begin_layout Standard
31049 There are four ways to cancel formulas:
31052 \begin_layout Standard
31054 \begin_inset Tabular
31055 <lyxtabular version="3" rows="5" columns="2">
31057 <column alignment="center" valignment="top" leftline="true" width="0">
31058 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
31059 <row topline="true" bottomline="true">
31060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31063 \begin_layout Standard
31069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31072 \begin_layout Standard
31074 \begin_inset Note Note
31077 \begin_layout Standard
31090 are used here as spacer.
31101 <row topline="true">
31102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31105 \begin_layout Standard
31114 \begin_layout Standard
31128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31131 \begin_layout Standard
31132 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
31141 <row topline="true">
31142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31145 \begin_layout Standard
31154 \begin_layout Standard
31168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31171 \begin_layout Standard
31172 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
31181 <row topline="true" bottomline="true">
31182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31185 \begin_layout Standard
31194 \begin_layout Standard
31208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31211 \begin_layout Standard
31212 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
31221 <row topline="true" bottomline="true">
31222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31225 \begin_layout Standard
31229 \begin_inset Formula $\to$
31240 \begin_layout Standard
31254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31257 \begin_layout Standard
31258 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
31274 \begin_layout Standard
31281 is especially suitable to visualize the reduction of fractions within formulas:
31282 \begin_inset Formula \[
31283 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
31290 \begin_layout Subsection
31291 Formulas in Section Headings
31292 \begin_inset LatexCommand label
31293 name "sub:Formulas-in-Section"
31298 \begin_inset LatexCommand index
31299 name "Formula ! in section headings"
31306 \begin_layout Standard
31307 When formulas are used in section headings, the following has to be taken
31311 \begin_layout Standard
31312 \begin_inset Note Greyedout
31315 \begin_layout Standard
31316 When the LaTeX-package
31321 \begin_inset LatexCommand index
31322 name "Packages ! hyperref"
31326 is used, PDF-bookmarks are automatically created for every section heading
31327 in the table of contents.
31328 If a section heading contains formulas, they are incorrectly displayed
31329 in the bookmark text, because formulas in bookmarks infringe the PDF convention
31338 \begin_layout Standard
31339 Both problems can be solved by inserting at the end of the section heading
31340 a short title with the menu
31342 Insert\SpecialChar \menuseparator
31347 Short titles are used as alternative for multiline section headings to
31348 keep the table of contents clearly arranged.
31349 Only the short title appears in the table of contents and therefore also
31350 in the PDF-bookmark.
31353 \begin_layout Standard
31354 When formulas should be used in the table of contents but
31358 is used, one can use the following command in TeX-mode:
31361 \begin_layout Standard
31366 texorpdfstring{part}{alternative}
31367 \begin_inset LatexCommand index
31368 name "Commands ! T ! \\textbackslash texorpdfstring"
31375 \begin_layout Standard
31376 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
31377 This can be characters, formulas, footnotes, but also cross-references.
31378 The alternative is used instead of the part for the bookmark.
31381 \begin_layout Standard
31382 Here are two example headings:
31383 \begin_inset VSpace -3mm
31390 \begin_layout Standard
31402 \begin_layout Subsubsection
31403 Heading without formula in table of contents
31404 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31408 \begin_inset OptArg
31411 \begin_layout Standard
31412 Heading without formula in table of contents
31420 \begin_layout Subsubsection
31421 Heading with formula in table of contents
31425 \begin_layout Standard
31435 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31442 \begin_layout Standard
31452 \begin_layout Standard
31456 \begin_layout Standard
31465 In the first heading a short title was used, in the second one
31474 \begin_layout Standard
31475 To get the same formatting as for the other headings, the complete heading
31478 boldmath environment
31484 \begin_layout Standard
31486 \begin_inset LatexCommand ref
31487 reference "sub:Bold-Formulas"
31499 \begin_layout Subsection
31500 Formulas in multi-column Text
31501 \begin_inset LatexCommand index
31502 name "Formula ! in multi-column text"
31509 \begin_layout Standard
31510 Formulas in multi-column text are often too wide to fit into a column and
31511 thus need to be set over the whole page width.
31512 This is done by using the LaTeX-package
31520 \begin_layout Standard
31525 is part of every LaTeX standard installation.
31531 \begin_inset LatexCommand index
31532 name "Packages ! multicol"
31536 , that is loaded with the LaTeX-preamble line
31539 \begin_layout Standard
31544 usepackage{multicol}
31547 \begin_layout Standard
31548 \begin_inset Note Greyedout
31551 \begin_layout Standard
31552 Note herby that the setting
31554 Two-column\InsetSpace ~
31559 Document\SpecialChar \menuseparator
31582 \begin_layout Standard
31583 Before the multi-column text the command
31586 \begin_layout Standard
31591 begin{multicols}{column number}
31594 \begin_layout Standard
31595 is written in TeX-mode.
31596 The column number is a number in the range of 2\InsetSpace \thinspace{}
31597 -\InsetSpace \thinspace{}
31599 Before the formula the multi-column text is ended by inserting the command
31602 \begin_layout Standard
31610 \begin_layout Standard
31614 \begin_layout Standard
31615 Due to the command some space is automatically added before the formula.
31616 To revert this, -6\InsetSpace \thinspace{}
31617 mm vertical space is inserted before the formula.
31618 When the formula style
31624 \begin_layout Standard
31626 \begin_inset LatexCommand ref
31627 reference "sec:Formula-Styles"
31638 is used, -9\InsetSpace \thinspace{}
31639 mm space is inserted instead.
31642 \begin_layout Standard
31643 As example a multi-column text with a displayed formula:
31646 \begin_layout Standard
31650 \begin_layout Standard
31654 begin{multicols}{2}
31659 Das Spektrum wird fouriertransformiert.
31660 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
31661 , Lösungsmittel) zu trennen.
31662 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
31663 nun das Aussehen des Ausgangssignals.
31664 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
31665 über alle Phasen integrieren muss.
31667 \begin_inset Formula $S$
31670 unser normiertes Ausgangssignal and
31671 \begin_inset Formula $P$
31674 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
31678 \begin_layout Standard
31688 \begin_inset VSpace -6mm
31692 \begin_inset Formula \begin{equation}
31693 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
31701 \begin_layout Standard
31705 begin{multicols}{2}
31711 \begin_inset Formula $S_{0}$
31714 das Signal ohne Gradient ist and the Normierungsbedingung
31715 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
31719 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
31721 \begin_inset Formula $\nicefrac{\pi}{2}$
31724 \InsetSpace \thinspace{}
31725 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
31726 das Signal zusätzlich abschwächt.
31727 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
31729 \begin_inset Formula $T_{2}$
31735 \begin_layout Standard
31739 \begin_layout Standard
31751 \begin_layout Subsection
31752 Formulas with Description of Variables
31753 \begin_inset LatexCommand index
31754 name "Formula ! with description of variables"
31761 \begin_layout Standard
31762 To describe variables within a formula, like in formula
31763 \begin_inset LatexCommand eqref
31764 reference "eq:within"
31773 \begin_inset Formula $n$
31777 matrix is used with left aligned columns for the
31778 \begin_inset Formula $n$
31785 \begin_layout Standard
31787 \begin_inset LatexCommand ref
31788 reference "sec:Matrices"
31797 To set the description in a smaller size, before the matrix e.\InsetSpace \thinspace{}
31810 \begin_layout Standard
31812 \begin_inset LatexCommand ref
31813 reference "sub:Font-Sizes"
31825 \begin_layout Standard
31826 When the formula style
31832 \begin_layout Standard
31834 \begin_inset LatexCommand ref
31835 reference "sec:Formula-Styles"
31856 \begin_layout Standard
31863 only works in formulas with the style
31868 \begin_inset LatexCommand ref
31869 reference "sub:Variable-Space"
31878 is inserted before and after the matrix to have the same separation of
31879 the matrix from the equation and the side margin.
31882 \begin_layout Standard
31883 When the formula style
31887 is used, the method described in
31888 \begin_inset LatexCommand ref
31889 reference "sub:Flalign-Environment"
31893 is used to indent formulas.
31895 \begin_inset LatexCommand eqref
31896 reference "eq:within"
31900 consists of five columns whereas in the first two columns contain the equation,
31901 the third the matrix, and the last one an empty TeX-brace.
31902 \begin_inset Formula \begin{flalign}
31903 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
31904 \rho & \textrm{density}\\
31905 V & \textrm{volume}\\
31906 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
31913 \begin_layout Subsection
31914 Upright small Greek Letters
31915 \begin_inset LatexCommand label
31916 name "sub:Upright-small-Greek"
31921 \begin_inset LatexCommand index
31922 name "Greek letters ! upright"
31929 \begin_layout Standard
31930 Most of the math fonts only provide italic small Greek letters.
31931 But for symbols of elementary particles like pions and neutrinos, upright
31932 Greek letters are needed.
31941 \begin_layout Standard
31946 is part of the LaTeX-package
31951 \begin_inset LatexCommand index
31952 name "Packages ! was\\vspace{4mm}"
31962 \begin_inset LatexCommand index
31963 name "Packages ! upgreek"
31967 that is loaded with the LaTeX-preamble line
31970 \begin_layout Standard
31975 usepackage{upgreek}
31978 \begin_layout Standard
31984 \begin_layout Standard
31994 \begin_inset Note Note
31997 \begin_layout Standard
31998 The following table will only be displayed when the LaTeX-package
32007 They are created when the command for a small Greek letters is started
32013 For example the command
32020 \begin_inset Formula $\uptau$
32026 \begin_layout Standard
32027 With these commands reactions of elementary particles can be typeset:
32028 \begin_inset Formula \[
32029 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
32036 \begin_layout Standard
32037 The upright letters are more bold and wider than the italic ones.
32038 They should therefore not be used for units like
32039 \begin_inset Quotes eld
32043 \begin_inset Quotes erd
32049 \begin_layout Standard
32053 \begin_layout Standard
32063 \begin_inset Note Note
32066 \begin_layout Standard
32067 The following will be displayed when the LaTeX-package
32079 \begin_layout Standard
32080 You need to install the LaTeX-package
32084 to see the rest of this subsection in the output.
32087 \begin_layout Standard
32091 \begin_layout Standard
32103 \begin_layout Subsection
32104 Text Characters in Formulas
32105 \begin_inset LatexCommand label
32106 name "sub:Text-Characters-in"
32111 \begin_inset LatexCommand index
32112 name "Text ! in formulas"
32119 \begin_layout Standard
32120 In some cases you might want to insert text characters directly into formulas.
32121 When for example the centered dot · is often used in formulas like
32122 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
32125 , one would have to insert the command
32135 \begin_layout Standard
32137 \begin_inset LatexCommand ref
32138 reference "sub:Binary-Operators"
32147 all the time, because this character is defined in all encodings as text
32149 But the encoding can be changed by this LaTeX-preamble line:
32152 \begin_layout Standard
32157 Declare Inputtext{183}{
32167 f\SpecialChar \textcompwordmark{}
32171 \begin_layout Standard
32172 The character encoding (menu
32174 Document\SpecialChar \menuseparator
32175 Settings\SpecialChar \menuseparator
32178 ) specifies what character appears when a keyboard key is pressed.
32179 When the key for the character '·' is pressed, internally the command
32186 But this command is not available in a formula so that you would get LaTeX-erro
32188 With the changed encoding the right command is chosen automatically, depending
32189 on if the character was inserted into a formula or not.
32192 \begin_layout Standard
32193 The encoding of several characters is saved in definition files.
32194 Fore example the encoding
32198 is defined in the file
32202 that is in the installation folder of LaTeX.
32203 Encodings should only be changed via the LaTeX-preamble and not in the
32205 Otherwise own documents could not be edited by other LyX users working
32206 on other computers.
32209 \begin_layout Standard
32210 \begin_inset VSpace medskip
32213 Besides the centered dot, in this document the degree sign ° is defined
32214 with the following LaTeX-preamble line so that it can directly be inserted
32218 \begin_layout Standard
32223 DeclareInputtext{176}{
32233 f\SpecialChar \textcompwordmark{}
32237 \begin_layout Standard
32243 \begin_layout Section
32245 Typographic Advises
32246 \begin_inset LatexCommand index
32247 name "Typographic Advises"
32254 \begin_layout Standard
32255 This section is a summary of the most important typographic rules, listed
32260 \begin_layout Standard
32261 This collection was partly taken from the German semi-official dictionary
32263 \begin_inset Quotes eld
32267 \begin_inset Quotes erd
32271 \begin_inset LatexCommand cite
32276 that lists some of the ISO rules.
32284 \begin_layout Itemize
32293 \begin_layout Standard
32294 done with font styles, see
32295 \begin_inset LatexCommand ref
32296 reference "sub:Font-Styles"
32305 : 30\InsetSpace \thinspace{}
32308 Between the value and the unit is the smallest space, see
32309 \begin_inset LatexCommand ref
32310 reference "sub:Predefined-Space"
32317 \begin_layout Itemize
32318 Percent and perthousand signs are set like physical units:
32320 1,2\InsetSpace \thinspace{}
32325 \begin_layout Standard
32338 \begin_layout Itemize
32339 The degree sign follows directly on the value: 15°, but not when it is used
32340 in units: 15\InsetSpace \thinspace{}
32344 \begin_layout Itemize
32345 In numbers with more than four digits the smallest space is inserted before
32346 every third digit to group them:
32355 18\InsetSpace \thinspace{}
32356 473\InsetSpace \thinspace{}
32360 \begin_layout Itemize
32361 For dimensionings like 120×90×40\InsetSpace \thinspace{}
32362 cm the multiplication sign
32363 \begin_inset Quotes eld
32367 \begin_inset Quotes erd
32371 It is available with the LaTeX-command
32377 , but can also directly be inserted with some keyboard definitions.
32380 \begin_layout Itemize
32381 Functions with names consisting of several letters are set upright to avoid
32383 \begin_inset LatexCommand ref
32384 reference "sub:Predefined-Functions"
32391 \begin_layout Itemize
32392 Indices consisting of several letters, are set upright:
32393 \begin_inset Formula $E_{\mathrm{kin}}$
32398 Components of matrices are set italic:
32399 \begin_inset Formula $\hat{H}_{kl}$
32405 \begin_layout Itemize
32406 The differentiation/integration operator 'd', the Euler's number 'e', and
32407 the imaginary unit 'i' should be set upright, to avoid mixing them up with
32411 \begin_layout Standard
32417 \begin_layout Section
32419 \begin_inset LatexCommand index
32427 \begin_layout Standard
32428 Some characters and symbols can be created with several commands.
32429 Here is a list of the synonym commands:
32432 \begin_layout Standard
32433 \begin_inset VSpace bigskip
32439 \begin_inset Tabular
32440 <lyxtabular version="3" rows="12" columns="2">
32442 <column alignment="center" valignment="top" leftline="true" width="0pt">
32443 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
32444 <row topline="true" bottomline="true">
32445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32448 \begin_layout Standard
32454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32457 \begin_layout Standard
32459 \begin_inset Note Note
32462 \begin_layout Standard
32469 is only used as spacer.
32480 <row topline="true">
32481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32484 \begin_layout Standard
32492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32495 \begin_layout Standard
32499 \begin_layout Standard
32512 \begin_layout Standard
32525 <row topline="true">
32526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32529 \begin_layout Standard
32537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32540 \begin_layout Standard
32549 <row topline="true">
32550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32553 \begin_layout Standard
32561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32564 \begin_layout Standard
32573 <row topline="true">
32574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32577 \begin_layout Standard
32585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32588 \begin_layout Standard
32595 <row topline="true">
32596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32599 \begin_layout Standard
32607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32610 \begin_layout Standard
32617 <row topline="true">
32618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32621 \begin_layout Standard
32629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32632 \begin_layout Standard
32641 <row topline="true">
32642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32645 \begin_layout Standard
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33018 \begin_layout Standard
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33079 The LaTeX Companion
33082 Addison Wesley, 2004
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33099 href{ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf}{
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33115 of LaTeX's math abilities
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33124 LaTeX tips and tricks-
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33132 href{http://tug.org/TeXnik/}{
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33185 \begin_layout Standard
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33211 href{ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}{
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33227 of all symbols available with LaTeX-packages
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33244 href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{
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33260 of the LaTeX-package
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33287 href{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}{
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33311 reference "sub:Operator-Limits"
33316 \begin_inset LatexCommand index
33317 name "Commands ! M ! \\textbackslash mathclap"
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33336 Auflage, Duden 2001
33339 \begin_layout Subsubsection*
33340 \begin_inset LatexCommand printindex