1 #LyX 1.5.4svn 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. 22.10
151 % check for package upgreek
153 \IfFileExists{upgreek.sty}
154 {\usepackage{upgreek}
155 \setboolean{upgreek}{true}}
156 {\setboolean{upgreek}{false}}
158 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
163 \font_typewriter default
164 \font_default_family default
178 \paperorientation portrait
181 \paragraph_separation skip
183 \quotes_language english
186 \paperpagestyle plain
190 \tracking_changes false
191 \output_changes false
199 LyX's detailed Math manual
207 \begin_layout Standard
209 If you have comments or error corrections, please send them to the LyX Documenta
216 \begin_layout Standard
220 href{mailto:lyx-docs@lists.lyx.org?subject=LyX's Math manual}{
225 lyx-docs@lists.lyx.org
229 \begin_layout Standard
242 \begin_inset Note Note
245 \begin_layout Standard
262 \begin_layout Standard
263 \begin_inset LatexCommand tableofcontents
270 \begin_layout Standard
271 \begin_inset Note Note
274 \begin_layout Standard
275 To export this document to PDF, PS, or DVI the LaTeX-packages
288 If they are not installed you can export the document anyway but the sections
289 where the packages are required won't appear in the output.
297 \begin_layout Standard
303 \begin_layout Section
305 \begin_inset LatexCommand label
306 name "sec:Introduction"
313 \begin_layout Standard
314 This document explains LyX's math features and is furthermore a collection
315 of LaTeX-commands used for mathematical characters and constructs.
316 The explanations are designed for the usage of commands.
317 It is therefore required that you have read the section
319 Mathematical\InsetSpace ~
325 \begin_layout Standard
326 Most of the characters and many constructs explained in this manual are
327 also accessible via the menu
331 \SpecialChar \menuseparator
347 But everybody who has to write lots of formulas will notice that it is
348 much faster to use commands instead of the math toolbar.
349 Therefore this manual is focused on commands but also mentions the correspondin
350 g toolbar buttons when available.
353 \begin_layout Standard
354 If not specially mentioned the commands are only available within formulas.
355 To be able to use all commands explained in this document, the option
359 must be used in the document settings (menu
361 Document\SpecialChar \menuseparator
362 Settings\SpecialChar \menuseparator
370 \begin_layout Standard
373 Use AMS math package automatically
379 \begin_layout Standard
388 -math when math constructs are found that are supported by LyX.
396 \begin_layout Standard
397 This document doesn't list all
401 \begin_layout Standard
414 \begin_layout Standard
419 \begin_layout Standard
428 -math commands is in the file
432 \begin_layout Standard
436 href{ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps}{
449 \begin_layout Standard
456 , which is part of every LaTeX standard installation.
461 for lucidity reasons.
464 \begin_layout Section
466 \begin_inset LatexCommand label
467 name "sec:General-Instructions"
474 \begin_layout Standard
475 To create an inline formula
476 \begin_inset LatexCommand index
477 name "Formula ! inline"
481 that is embedded into a text line, press
485 or the toolbar button
486 \begin_inset Graphics
487 filename ../images/math-mode.png
494 To create a display style formula
495 \begin_inset LatexCommand index
496 name "Formula ! display style"
500 that will appear bigger and in an own paragraph, press
507 \begin_layout Standard
508 To change a display style formula to an inline formula, set the cursor into
509 the formula and press
515 Edit\SpecialChar \menuseparator
516 Math\SpecialChar \menuseparator
520 The same way is used to change an inline formula to a display style formula.
523 \begin_layout Standard
524 To display parts of an inline formula in the size of a display style formula,
530 \begin_inset LatexCommand index
531 name "Commands ! D ! \\textbackslash displaystyle"
538 Then a new blue box appears in which the desired formula part is inserted.
541 \begin_layout Standard
542 Only inline formulas are allowed inside tables.
545 \begin_layout Standard
550 can be turned on in the menu
552 View\SpecialChar \menuseparator
556 When you click there on
557 \begin_inset Quotes eld
561 \begin_inset Quotes erd
564 the toolbar will be shown permanently at the bottom; this state is visualized
569 menu with a checkmark.
570 When you click in this state again on
571 \begin_inset Quotes eld
575 \begin_inset Quotes erd
586 is only shown when the cursor is within a formula; this state is visualized
587 by the renaming of the menu entry from
588 \begin_inset Quotes eld
592 \begin_inset Quotes erd
596 \begin_inset Quotes eld
601 \begin_inset Quotes erd
607 \begin_layout Standard
609 \begin_inset LatexCommand index
614 is invoked by pressing the toolbar button
615 \begin_inset Graphics
616 filename ../images/ert-insert.png
623 Insert\SpecialChar \menuseparator
628 \begin_layout Standard
639 \begin_layout Standard
653 \begin_inset Note Note
656 \begin_layout Standard
657 In LyX there are three
658 \begin_inset Quotes eld
662 \begin_inset Quotes erd
665 that appear in the output with sub- and superscript letters: TeX, LaTeX,
669 \begin_layout Standard
670 To avoid that these names are recognized as proper names, TeX-braces are
671 set around one of the letters of the name.
679 \begin_layout Standard
680 To change the LaTeX-preamble
681 \begin_inset LatexCommand index
682 name "L@\\LaTeX-preamble"
688 Document\SpecialChar \menuseparator
689 Settings\SpecialChar \menuseparator
694 \begin_layout Standard
705 \begin_layout Standard
721 \begin_layout Standard
722 To edit matrices, case differentiations, and multiline formulas subsequently,
725 Edit\SpecialChar \menuseparator
730 Edit\SpecialChar \menuseparator
731 Rows\InsetSpace \thinspace{}
732 &\InsetSpace \thinspace{}
740 When lines and columns are swapped via the menu, the column or line where
741 the cursor is in is exchanged with the column to the right or the line
743 Is the cursor in the last column or row, the exchange is done with the
744 column to the left or the line above.
747 \begin_layout Standard
748 To write text in formulas
752 \begin_layout Standard
753 For multiline formulas the command
760 \begin_inset LatexCommand ref
761 reference "sub:Text-in-multiline"
775 \begin_inset LatexCommand index
776 name "Text ! in formulas"
781 \begin_inset LatexCommand index
782 name "Mathematical text"
787 This mode is invoked with the the shortcut
792 or by the insertion of the command
797 \begin_inset LatexCommand index
798 name "Commands ! T ! \\textbackslash text"
805 The text appears black in LyX and can therefore be distinguished from the
806 other formula parts that appear blue.
807 In the output mathematical text is set upright, in contrary to other formula
811 \begin_layout Subsection*
815 \begin_layout Standard
816 Most of the LaTeX-commands for math constructs have the following scheme:
819 \begin_layout Standard
835 \begin_layout Standard
836 A command starts always with a backslash
837 \begin_inset Quotes gld
847 \begin_inset Quotes grd
851 To omit optional arguments, also omit the associated brackets.
852 The braces around the required arguments are named in this document as
854 \begin_inset LatexCommand index
855 name "T@\\TeX-braces"
860 If you add in a formula a left brace to a command name, LyX creates automatical
862 In all other cases TeX-braces are created in formulas with the command
870 TeX-braces appear red in LyX, in contrary to normal braces that appear
872 In TeX-mode no command is needed to get TeX-braces.
873 TeX-braces don't appear in the output.
876 \begin_layout Standard
877 When commands without arguments, like commands for symbols are entered in
878 TeX-mode, a space character must
882 be behind the command to end it.
883 This space doesn't appear in the output.
884 When the space should appear in the output, the space must be followed
885 by a protected space in normal text.
888 \begin_layout Standard
889 A protected space is inserted with
896 \begin_layout Subsection*
902 \begin_layout Itemize
907 \begin_layout Standard
908 This visible space character can be created with the command
915 \begin_inset LatexCommand index
916 name "Commands ! T ! \\textbackslash textvisiblespace"
920 , inserted in TeX-mode.
929 \begin_layout Standard
939 denotes a space character to be input.
942 \begin_layout Itemize
944 \begin_inset Formula $\to$
947 denotes the usage of the corresponding arrow key on the keyboard.
950 \begin_layout Subsection*
954 \begin_layout Standard
956 \begin_inset Float table
962 \begin_layout Standard
966 \begin_layout Standard
967 \begin_inset LatexCommand label
968 name "tab:Used-units"
980 \begin_layout Standard
983 <lyxtabular version="3" rows="13" columns="2">
985 <column alignment="center" valignment="top" leftline="true" width="0">
986 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
987 <row topline="true" bottomline="true">
988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
991 \begin_layout Standard
997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1000 \begin_layout Standard
1007 <row topline="true">
1008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1011 \begin_layout Standard
1017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1020 \begin_layout Standard
1027 <row topline="true">
1028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1031 \begin_layout Standard
1037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1040 \begin_layout Standard
1047 <row topline="true">
1048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1051 \begin_layout Standard
1057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1060 \begin_layout Standard
1061 Inch (1\InsetSpace \thinspace{}
1062 in = 2,54\InsetSpace \thinspace{}
1069 <row topline="true">
1070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1073 \begin_layout Standard
1079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1082 \begin_layout Standard
1083 Point (72.27\InsetSpace \thinspace{}
1084 pt = 1\InsetSpace \thinspace{}
1091 <row topline="true">
1092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1095 \begin_layout Standard
1101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1104 \begin_layout Standard
1105 Pica (1\InsetSpace \thinspace{}
1106 pc = 12\InsetSpace \thinspace{}
1113 <row topline="true">
1114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1117 \begin_layout Standard
1123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1126 \begin_layout Standard
1127 scaled point (65536\InsetSpace \thinspace{}
1128 sp = 1\InsetSpace \thinspace{}
1135 <row topline="true">
1136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1139 \begin_layout Standard
1145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1148 \begin_layout Standard
1149 big point (72\InsetSpace \thinspace{}
1150 bp = 1\InsetSpace \thinspace{}
1157 <row topline="true">
1158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1161 \begin_layout Standard
1167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1170 \begin_layout Standard
1171 Didot (1\InsetSpace \thinspace{}
1173 \begin_inset Formula $\approx$
1176 0.376\InsetSpace \thinspace{}
1183 <row topline="true">
1184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1187 \begin_layout Standard
1193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1196 \begin_layout Standard
1197 Cicero (1\InsetSpace \thinspace{}
1198 cc = 12\InsetSpace \thinspace{}
1205 <row topline="true">
1206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1209 \begin_layout Standard
1215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1218 \begin_layout Standard
1222 \begin_inset Quotes eld
1228 \begin_inset Quotes erd
1237 <row topline="true">
1238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1241 \begin_layout Standard
1247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1250 \begin_layout Standard
1252 \begin_inset Quotes eld
1260 \begin_inset Quotes erd
1269 <row topline="true" bottomline="true">
1270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1273 \begin_layout Standard
1279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1282 \begin_layout Standard
1283 math unit (1\InsetSpace \thinspace{}
1285 \begin_inset Formula $\nicefrac{1}{18}$
1288 \InsetSpace \thinspace{}
1290 \begin_inset Note Note
1293 \begin_layout Standard
1300 is explained in sec.\InsetSpace \thinspace{}
1302 \begin_inset LatexCommand ref
1303 reference "sub:Self-defined-Fractions"
1330 \begin_layout Standard
1336 \begin_layout Section
1340 \begin_layout Subsection
1342 \begin_inset LatexCommand index
1348 \begin_inset LatexCommand index
1354 \begin_inset LatexCommand index
1355 name "Superscripts|see{Exponents}"
1360 \begin_inset LatexCommand index
1361 name "Subscripts|see{Indices}"
1368 \begin_layout Standard
1369 Indices are created with an underscore
1370 \begin_inset Quotes eld
1374 \begin_inset Quotes erd
1377 or via the math toolbar button
1378 \begin_inset Graphics
1379 filename ../images/math-subscript.png
1384 , exponents with a caret
1385 \begin_inset Quotes eld
1389 \begin_inset Quotes erd
1392 or via the math toolbar button
1393 \begin_inset Graphics
1394 filename ../images/math-superscript.png
1402 \begin_layout Standard
1404 \begin_inset Tabular
1405 <lyxtabular version="3" rows="4" columns="2">
1407 <column alignment="center" valignment="top" leftline="true" width="0pt">
1408 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
1409 <row topline="true" bottomline="true">
1410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1413 \begin_layout Standard
1419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1422 \begin_layout Standard
1424 \begin_inset Note Note
1427 \begin_layout Standard
1434 is only used as spacer.
1445 <row topline="true">
1446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1449 \begin_layout Standard
1455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1458 \begin_layout Standard
1459 \begin_inset Formula $B_{V}$
1468 <row topline="true" bottomline="true">
1469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1472 \begin_layout Standard
1478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1481 \begin_layout Standard
1482 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1491 <row topline="true" bottomline="true">
1492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1495 \begin_layout Standard
1500 \begin_layout Standard
1514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1517 \begin_layout Standard
1518 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1534 \begin_layout Standard
1535 As the caret is in some languages an accent, vowels will be accentuated
1536 in this case and not set as exponents
1540 \begin_layout Standard
1541 Depending on the used keyboard settings this can also happen for other character
1548 To get in this case exponents, press
1552 after the caret as in the last example.
1555 \begin_layout Subsection
1557 \begin_inset LatexCommand label
1558 name "sub:Fractions"
1563 \begin_inset LatexCommand index
1571 \begin_layout Standard
1572 Fractions are generated with the command
1579 \begin_inset LatexCommand index
1580 name "Commands ! F ! \\textbackslash frac"
1584 or via the math toolbar button
1585 \begin_inset Graphics
1586 filename ../images/math/frac.png
1592 The font size is adjusted automatically, depending on whether the fraction
1593 is in an inline or display style formula.
1594 With the math toolbar button
1595 \begin_inset Graphics
1596 filename ../images/math/frac-square.png
1601 you can select different fraction types.
1604 \begin_layout Standard
1610 \begin_inset LatexCommand index
1611 name "Commands ! D ! \\textbackslash dfrac"
1617 a fraction can be created that has in any case the size of a display style
1624 \begin_inset LatexCommand index
1625 name "Commands ! T ! \\textbackslash tfrac"
1631 the fraction appears always with the size of an inline formula.
1635 \begin_layout Standard
1636 A line with the fraction
1637 \begin_inset Formula $\frac{1}{2}$
1640 that was created with the command
1649 \begin_layout Standard
1650 A line with the fraction
1651 \begin_inset Formula $\dfrac{1}{2}$
1654 that was created with the command
1663 \begin_layout Standard
1665 \begin_inset Tabular
1666 <lyxtabular version="3" rows="4" columns="2">
1668 <column alignment="center" valignment="top" leftline="true" width="0pt">
1669 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
1670 <row topline="true" bottomline="true">
1671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1674 \begin_layout Standard
1680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1683 \begin_layout Standard
1685 \begin_inset Note Note
1688 \begin_layout Standard
1695 is only used as spacer.
1706 <row topline="true">
1707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1710 \begin_layout Standard
1717 \begin_layout Standard
1727 \begin_inset Formula $\downarrow$
1735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1738 \begin_layout Standard
1739 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1748 <row topline="true">
1749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1752 \begin_layout Standard
1759 \begin_layout Standard
1769 \begin_inset Formula $\downarrow$
1777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1780 \begin_layout Standard
1781 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1790 <row topline="true" bottomline="true">
1791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1794 \begin_layout Standard
1801 \begin_layout Standard
1814 \begin_layout Standard
1829 \begin_layout Standard
1839 \begin_inset Formula $\downarrow$
1843 \begin_inset Formula $\downarrow\downarrow$
1851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1854 \begin_layout Standard
1855 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1871 \begin_layout Standard
1872 \begin_inset VSpace bigskip
1877 For nested fractions the command
1884 \begin_inset LatexCommand index
1885 name "Commands ! C ! \\textbackslash cfrac"
1891 \begin_inset VSpace -3mm
1897 \begin_layout Standard
1898 \begin_inset Formula \begin{align*}
1899 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1900 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
1907 \begin_layout Standard
1908 The command for the example above is:
1911 \begin_layout Standard
1917 \begin_inset Formula $\to$
1927 \begin_inset Formula $\to$
1933 \begin_inset Formula $\to\to$
1941 \begin_layout Standard
1942 \begin_inset VSpace medskip
1948 \begin_layout Standard
1955 sets the fraction always in the size of a displayed formula, also when
1956 it is part of another fraction.
1963 has the following command scheme:
1966 \begin_layout Standard
1971 cfrac[numerator position]{numerator}{denominator}
1974 \begin_layout Standard
1975 The numerator position can be
1988 l or r aligns the numerator to the left or right, resp.\InsetSpace ~
1995 or no position is given, the numerator appears centered.
1996 These fractions demonstrate the different alignments:
2001 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2005 \begin_inset Formula $\cfrac{A}{B+C}$
2009 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2015 \begin_layout Standard
2016 \begin_inset VSpace medskip
2019 It is often advantageous to combine
2032 \begin_inset Formula \[
2033 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2040 \begin_layout Standard
2041 For inline fractions with a sloped fraction stroke you can use the command
2047 \begin_inset LatexCommand index
2048 name "Commands ! N ! \\textbackslash nicefrac"
2055 \begin_inset Formula $\nicefrac{5}{31}$
2061 \begin_layout Standard
2062 How to define own fractions where the fraction stroke can be changed, is
2064 \begin_inset LatexCommand ref
2065 reference "sub:Self-defined-Fractions"
2072 \begin_layout Subsection
2074 \begin_inset LatexCommand index
2082 \begin_layout Standard
2083 Square roots are created with
2090 \begin_inset LatexCommand index
2091 name "Commands ! S ! \\textbackslash sqrt"
2095 or the math toolbar button
2096 \begin_inset Graphics
2097 filename ../images/math/sqrt.png
2102 , all other roots with the command
2109 \begin_inset LatexCommand index
2110 name "Commands ! R ! \\textbackslash root"
2114 or with the math toolbar button
2115 \begin_inset Graphics
2116 filename ../images/math/root.png
2124 \begin_layout Standard
2126 \begin_inset Tabular
2127 <lyxtabular version="3" rows="3" columns="2">
2129 <column alignment="center" valignment="top" leftline="true" width="0pt">
2130 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2131 <row topline="true" bottomline="true">
2132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2135 \begin_layout Standard
2141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2144 \begin_layout Standard
2146 \begin_inset Note Note
2149 \begin_layout Standard
2156 is only used as spacer.
2167 <row topline="true" bottomline="true">
2168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2171 \begin_layout Standard
2178 \begin_layout Standard
2192 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
2195 \begin_layout Standard
2196 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2205 <row bottomline="true">
2206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2209 \begin_layout Standard
2216 \begin_layout Standard
2226 \begin_inset Formula $\downarrow$
2234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2237 \begin_layout Standard
2238 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2254 \begin_layout Standard
2255 A square root can also be created with
2261 when the root index field is left empty.
2264 \begin_layout Standard
2265 With certain indices the distance to the root is too small, like in this
2267 \begin_inset Formula $\sqrt[\beta]{B}$
2273 \begin_inset Formula $\beta$
2277 To avoid this, the commands
2284 \begin_inset LatexCommand index
2285 name "Commands ! L ! \\textbackslash leftroot"
2296 \begin_inset LatexCommand index
2297 name "Commands ! U ! \\textbackslash uproot"
2301 are used with the following scheme:
2304 \begin_layout Standard
2318 \begin_layout Standard
2319 Distance is the number of Big Points (unit bp;
2320 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2323 ), that the index should be moved to the left or top, resp..
2324 The commands are written to the index.
2325 This way the command
2334 \begin_inset Formula $\to$
2340 \begin_inset Formula $\to$
2349 \begin_layout Standard
2359 \begin_inset Formula $\to$
2366 produces a correct typeset formula:
2367 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2373 \begin_layout Subsection
2374 Binomial coefficients
2375 \begin_inset LatexCommand index
2376 name "Binomial coefficient s"
2383 \begin_layout Standard
2384 Binomial coefficients are inserted with the command
2391 \begin_inset LatexCommand index
2392 name "Commands ! B ! \\textbackslash binom"
2396 or with the submenu of the math toolbar button
2397 \begin_inset Graphics
2398 filename ../images/math/frac-square.png
2406 \begin_layout Standard
2408 \begin_inset Tabular
2409 <lyxtabular version="3" rows="3" columns="2">
2411 <column alignment="center" valignment="top" leftline="true" width="0pt">
2412 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2413 <row topline="true" bottomline="true">
2414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2417 \begin_layout Standard
2423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2426 \begin_layout Standard
2428 \begin_inset Note Note
2431 \begin_layout Standard
2438 is only used as spacer.
2449 <row topline="true">
2450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2453 \begin_layout Standard
2460 \begin_layout Standard
2470 \begin_inset Formula $\downarrow$
2478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2481 \begin_layout Standard
2482 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2491 <row topline="true" bottomline="true">
2492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2495 \begin_layout Standard
2499 \begin_inset Formula $\to$
2509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2512 \begin_layout Standard
2513 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2529 \begin_layout Standard
2530 Analog to fractions (
2547 \begin_inset LatexCommand index
2548 name "Commands ! D ! \\textbackslash dbinom"
2561 \begin_inset LatexCommand index
2562 name "Commands ! T ! \\textbackslash tbinom"
2566 with the following command scheme:
2569 \begin_layout Standard
2574 dbinom{numerator}{denominator}
2582 tbinom{numerator}{denominator}
2585 \begin_layout Subsection
2586 Case differentiations
2587 \begin_inset LatexCommand index
2588 name "Case differentiations "
2595 \begin_layout Standard
2597 \begin_inset Tabular
2598 <lyxtabular version="3" rows="3" columns="2">
2600 <column alignment="center" valignment="top" leftline="true" width="0pt">
2601 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2602 <row topline="true" bottomline="true">
2603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2606 \begin_layout Standard
2612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2615 \begin_layout Standard
2622 <row topline="true">
2623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2626 \begin_layout Standard
2633 \begin_layout Standard
2643 \begin_inset Formula $\to$
2647 \begin_inset LatexCommand index
2648 name "Commands ! C ! \\textbackslash cases"
2657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2660 \begin_layout Standard
2661 \begin_inset Formula $\begin{cases}
2671 <row topline="true" bottomline="true">
2672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2675 \begin_layout Standard
2682 \begin_layout Standard
2696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2699 \begin_layout Standard
2700 \begin_inset Formula $\begin{cases}
2701 A & \textrm{für }x>0\\
2702 B & \textrm{für }x=0\end{cases}$
2718 \begin_layout Standard
2725 or the usage of the math toolbar button
2726 \begin_inset Graphics
2727 filename ../images/math/cases.png
2732 you can create new lines with the shortcut
2736 or the table toolbar button
2737 \begin_inset Graphics
2738 filename ../images/tabular-feature_append-row.png
2747 \begin_layout Standard
2748 Umlauts and accents in formulas, like in the table above, are explained
2750 \begin_inset LatexCommand ref
2751 reference "sub:Accents-for-one"
2763 \begin_layout Standard
2770 is also available via the menu
2772 Insert\SpecialChar \menuseparator
2773 Math\SpecialChar \menuseparator
2779 \begin_layout Subsection
2781 \begin_inset LatexCommand index
2789 \begin_layout Standard
2797 \begin_inset LatexCommand index
2798 name "Commands ! N ! \\textbackslash not"
2802 every character can be displayed canceled.
2803 The characters are quasi accentuated by a slash.
2806 \begin_layout Standard
2808 \begin_inset Tabular
2809 <lyxtabular version="3" rows="4" columns="2">
2811 <column alignment="center" valignment="top" leftline="true" width="0pt">
2812 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2813 <row topline="true" bottomline="true">
2814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2817 \begin_layout Standard
2823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2826 \begin_layout Standard
2833 <row topline="true">
2834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2837 \begin_layout Standard
2845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2848 \begin_layout Standard
2849 \begin_inset Formula $\not=$
2858 <row topline="true" bottomline="true">
2859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2862 \begin_layout Standard
2872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2875 \begin_layout Standard
2876 \begin_inset Formula $\not\le$
2885 <row topline="true" bottomline="true">
2886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2889 \begin_layout Standard
2899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2902 \begin_layout Standard
2903 \begin_inset Formula $\not\parallel$
2919 \begin_layout Standard
2920 The last example shows, that not all negations look good.
2921 Therefore there are for some negations special commands (see
2922 \begin_inset LatexCommand ref
2923 reference "sub:Mathematical-Symbols"
2931 \begin_layout Standard
2937 sectionautorefname}{
2947 \begin_inset LatexCommand ref
2948 reference "sec:Relations"
2956 \begin_layout Standard
2962 sectionautorefname}{sec.
2970 \begin_inset Note Note
2973 \begin_layout Standard
2980 -commands in TeX-mode are necessary that the cross-reference name
2981 \begin_inset Quotes eld
2985 \begin_inset Quotes erd
2988 don't appear twice, see sec.\InsetSpace \thinspace{}
2990 \begin_inset LatexCommand ref
2991 reference "sub:Verlinkte-Querverweise"
3003 \begin_layout Subsection
3005 \begin_inset LatexCommand label
3006 name "sub:Placeholders"
3011 \begin_inset LatexCommand index
3017 \begin_inset LatexCommand index
3018 name "Chemical characters ! Isotopes"
3023 \begin_inset LatexCommand index
3024 name "Isotopes|see{Chemical characters}"
3031 \begin_layout Standard
3032 When displaying e.\InsetSpace \thinspace{}
3038 \begin_layout Standard
3039 More about chemical symbols is written in
3040 \begin_inset LatexCommand ref
3041 reference "sub:Chemical-Symbols-and"
3050 the following problem occurs:
3053 \begin_layout Standard
3055 \begin_inset Tabular
3056 <lyxtabular version="3" rows="2" columns="2">
3058 <column alignment="center" valignment="top" width="0pt">
3059 <column alignment="center" valignment="top" width="0pt">
3061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3064 \begin_layout Standard
3065 Indices created with sub- and superscripts:
3070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3073 \begin_layout Standard
3074 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3087 \begin_layout Standard
3093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3096 \begin_layout Standard
3097 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3111 \begin_inset Note Note
3114 \begin_layout Standard
3121 is only used as spacer.
3129 \begin_layout Standard
3130 The shorter index is by default placed below or above the first character
3131 of the longer index.
3132 To avoid this there is the command
3139 \begin_inset LatexCommand index
3140 name "Commands ! P ! \\textbackslash phantom"
3144 or the math toolbar button \InsetSpace ~
3146 \begin_inset Graphics
3147 filename ../images/math/phantom.png
3152 that creates one or more phantom characters.
3159 a small blue box appears that is superposed with two red arrows.
3160 The arrows indicate that the complete width and height of the box content
3161 will be created as placeholder.
3162 Phantom characters are accordingly placeholders with the size of the characters.
3165 \begin_layout Standard
3167 \begin_inset Tabular
3168 <lyxtabular version="3" rows="4" columns="2">
3170 <column alignment="center" valignment="top" leftline="true" width="0">
3171 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
3172 <row topline="true" bottomline="true">
3173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3176 \begin_layout Standard
3182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3185 \begin_layout Standard
3187 \begin_inset Note Note
3190 \begin_layout Standard
3197 is only used as spacer.
3208 <row topline="true">
3209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3212 \begin_layout Standard
3217 \begin_layout Standard
3232 \begin_layout Standard
3242 \begin_inset Formula $\to$
3249 \begin_layout Standard
3263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3266 \begin_layout Standard
3267 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3276 <row topline="true" bottomline="true">
3277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3280 \begin_layout Standard
3285 \begin_layout Standard
3300 \begin_layout Standard
3310 \begin_inset Formula $\to$
3317 \begin_layout Standard
3331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3334 \begin_layout Standard
3335 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3344 <row topline="true" bottomline="true">
3345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3348 \begin_layout Standard
3355 \begin_layout Standard
3370 \begin_layout Standard
3380 \begin_inset Formula $\to$
3387 \begin_layout Standard
3401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3404 \begin_layout Standard
3405 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3421 \begin_layout Standard
3422 Furthermore there are the commands
3429 \begin_inset LatexCommand index
3430 name "Commands ! V ! \\textbackslash vphantom"
3434 (toolbar button \InsetSpace ~
3436 \begin_inset Graphics
3437 filename ../images/math/vphantom.png
3449 \begin_inset LatexCommand index
3450 name "Commands ! H ! \\textbackslash hphantom"
3454 (toolbar button \InsetSpace ~
3456 \begin_inset Graphics
3457 filename ../images/math/hphantom.png
3469 creates only space for the maximal height of the characters in the box
3470 but not for its width.
3477 creates only space for the width of the box content.
3478 Therefore the boxes of both commands have only one red arrow.
3481 \begin_layout Standard
3492 \begin_layout Standard
3507 space for the height of the integral sign,
3511 \begin_layout Standard
3518 creates an integral sign, see
3519 \begin_inset LatexCommand ref
3520 reference "sub:Big-Operators"
3529 because this is the larger character.
3530 An example application is in
3531 \begin_inset LatexCommand ref
3532 reference "sub:Multiline-Brackets"
3539 \begin_layout Subsection
3541 \begin_inset LatexCommand index
3547 \begin_inset LatexCommand index
3548 name "Formula ! underlined"
3555 \begin_layout Standard
3557 \begin_inset Tabular
3558 <lyxtabular version="3" rows="4" columns="2">
3560 <column alignment="center" valignment="top" leftline="true" width="0pt">
3561 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3562 <row topline="true" bottomline="true">
3563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3566 \begin_layout Standard
3572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3575 \begin_layout Standard
3577 \begin_inset Note Note
3580 \begin_layout Standard
3587 is only used as spacer.
3598 <row topline="true" bottomline="true">
3599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3602 \begin_layout Standard
3609 \begin_layout Standard
3619 \begin_inset LatexCommand index
3620 name "Commands ! O ! \\textbackslash overline"
3629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3632 \begin_layout Standard
3633 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3642 <row bottomline="true">
3643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3646 \begin_layout Standard
3653 \begin_layout Standard
3663 \begin_inset LatexCommand index
3664 name "Commands ! U ! \\textbackslash underline"
3673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3676 \begin_layout Standard
3677 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3686 <row topline="true" bottomline="true">
3687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3690 \begin_layout Standard
3697 \begin_layout Standard
3712 \begin_layout Standard
3726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3729 \begin_layout Standard
3730 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
3746 \begin_layout Standard
3747 In the last example it doesn't matter if first
3762 \begin_layout Standard
3763 To double underline e.\InsetSpace \thinspace{}
3774 \begin_layout Standard
3775 It is possible to place up to 6 lines above or below characters.
3778 \begin_layout Subsection
3780 \begin_inset LatexCommand index
3788 \begin_layout Standard
3789 There are different types of ellipses available.
3793 \begin_layout Standard
3794 In the math toolbar in the submenu of the button
3795 \begin_inset Graphics
3796 filename ../images/math/ldots.png
3806 For listings dots at the baseline are used (
3813 \begin_inset LatexCommand index
3814 name "Commands ! L ! \\textbackslash ldots"
3818 ), while for operations dots are needed that are on the same height as the
3826 \begin_inset LatexCommand index
3827 name "Commands ! C ! \\textbackslash cdots"
3832 When using the command
3839 \begin_inset LatexCommand index
3840 name "Commands ! D ! \\textbackslash dots"
3844 , LaTeX decides on the basis of the next character what type is used.
3847 \begin_layout Standard
3849 \begin_inset Tabular
3850 <lyxtabular version="3" rows="8" columns="2">
3852 <column alignment="center" valignment="top" leftline="true" width="0pt">
3853 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3854 <row topline="true" bottomline="true">
3855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3858 \begin_layout Standard
3864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3867 \begin_layout Standard
3874 <row topline="true">
3875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3878 \begin_layout Standard
3883 \begin_layout Standard
3898 \begin_layout Standard
3912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3915 \begin_layout Standard
3916 \begin_inset Formula $A_{1},\dots,A_{n}$
3925 <row topline="true">
3926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3929 \begin_layout Standard
3934 \begin_layout Standard
3949 \begin_layout Standard
3963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3966 \begin_layout Standard
3967 \begin_inset Formula $A_{1}+\dots+A_{n}$
3976 <row topline="true">
3977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3980 \begin_layout Standard
3985 \begin_layout Standard
4000 \begin_layout Standard
4014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4017 \begin_layout Standard
4018 \begin_inset Formula $A_{1},\ldots,A_{n}$
4027 <row topline="true" bottomline="true">
4028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4031 \begin_layout Standard
4036 \begin_layout Standard
4051 \begin_layout Standard
4065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4068 \begin_layout Standard
4069 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4078 <row topline="true">
4079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4082 \begin_layout Standard
4090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4093 \begin_layout Standard
4094 \begin_inset Formula $\vdots$
4103 <row topline="true" bottomline="true">
4104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4107 \begin_layout Standard
4115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4118 \begin_layout Standard
4119 \begin_inset Formula $\ddots$
4128 <row topline="true" bottomline="true">
4129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4132 \begin_layout Standard
4133 3×3\InsetSpace \thinspace{}
4134 matrix with the different dots
4139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4142 \begin_layout Standard
4143 \begin_inset Formula $\begin{array}{ccc}
4144 A_{11} & \cdots & A_{1m}\\
4145 \vdots & \ddots & \vdots\\
4146 A_{n1} & \cdots & A_{nm}\end{array}$
4162 \begin_layout Standard
4163 The ellipses available in menu
4165 Insert\SpecialChar \menuseparator
4166 Special\InsetSpace ~
4178 \begin_layout Standard
4179 \begin_inset VSpace medskip
4182 Specially for matrices there are ellipses that span over several columns.
4183 They are created with the command
4190 \begin_inset LatexCommand index
4191 name "Commands ! H ! \\textbackslash hdotsfor"
4195 , that has the following scheme:
4198 \begin_layout Standard
4203 hdotsfor[distance]{number of columns}
4206 \begin_layout Standard
4207 The number of columns specifies how many columns should be spanned.
4208 Distance is a factor for the distance between the dots.
4211 \begin_layout Standard
4212 In the following matrix the command
4218 was inserted in the first box of the second line, to get an ellipsis with
4219 a dot distance twice as long as with the command
4226 \begin_inset Formula \[
4227 \left(\begin{array}{cccc}
4230 q & w & e & r\end{array}\right)\]
4234 Note that the matrix fields that should be spanned must be empty, otherwise
4235 you get LaTeX-errors.
4238 \begin_layout Standard
4239 \begin_inset VSpace bigskip
4242 Furthermore you can fill with the command
4249 \begin_inset LatexCommand index
4250 name "Commands ! D ! \\textbackslash dotfill"
4254 the rest of a line with dots.
4255 The effect of these commands is the same like with
4262 \begin_inset LatexCommand ref
4263 reference "sub:Variable-Space"
4270 \begin_layout Standard
4271 For example the command
4279 \begin_layout Standard
4293 \begin_layout Standard
4294 \begin_inset Formula $A\dotfill B$
4300 \begin_layout Standard
4307 there is for a line the command
4314 \begin_inset LatexCommand index
4315 name "Commands ! H ! \\textbackslash hrulefill"
4322 \begin_layout Standard
4323 \begin_inset Formula $A\hrulefill B$
4329 \begin_layout Standard
4330 To use the commands for text, they have to be inserted in TeX-mode.
4333 \begin_layout Section
4335 \begin_inset LatexCommand label
4341 \begin_inset LatexCommand index
4349 \begin_layout Standard
4350 Matrices can be inserted via the math toolbar button
4351 \begin_inset Graphics
4352 filename ../images/dialog-show_mathmatrix.png
4359 Insert\SpecialChar \menuseparator
4360 Math\SpecialChar \menuseparator
4364 You will be asked for the number of matrix columns and rows, and the alignment.
4365 The vertical alignment is hereby only of importance for matrices in inline
4369 \begin_layout Standard
4370 The first matrix is top
4371 \begin_inset Formula $\begin{array}[t]{cccc}
4374 C & F & I & L\end{array}$
4378 \begin_inset Formula $\begin{array}{cccc}
4381 C & F & I & L\end{array}$
4384 , and the third bottom
4385 \begin_inset Formula $\begin{array}[b]{cccc}
4388 C & F & I & L\end{array}$
4394 \begin_layout Standard
4395 The horizontal alignment specifies how the column entries should be aligned.
4396 It is set by entering a letter for every column.
4401 denotes left aligned,
4410 To create for example a 4
4415 matrix where the first column is left aligned, the second and third are
4416 centered, and the last one is right aligned, one enters for the horizontal
4422 Normally are in a matrix all columns centered, therefore the default is
4423 for every column is a
4431 \begin_layout Standard
4443 \begin_layout Standard
4444 Horizontal alignment:
4447 \begin_layout Standard
4453 \begin_inset Formula $\begin{array}{lll}
4456 C & F & 10000\end{array}$
4464 \begin_inset Formula $\begin{array}{ccc}
4467 C & F & 10000\end{array}$
4475 \begin_inset Formula $\begin{array}{rrr}
4478 C & F & 10000\end{array}$
4484 \begin_layout Standard
4485 To add or delete rows and columns subsequently, the math toolbar buttons
4487 \begin_inset Graphics
4488 filename ../images/tabular-feature_append-row.png
4494 \begin_inset Graphics
4495 filename ../images/tabular-feature_delete-row.png
4500 , etc.\InsetSpace \thinspace{}
4503 Edit\SpecialChar \menuseparator
4507 New rows can also be created with
4514 \begin_layout Standard
4515 \begin_inset VSpace bigskip
4518 Parentheses around a matrix can can either be created with the commands
4526 \begin_inset LatexCommand index
4527 name "Commands ! L ! \\textbackslash left"
4538 \begin_inset LatexCommand index
4539 name "Commands ! R ! \\textbackslash right"
4549 \begin_inset LatexCommand ref
4550 reference "sub:Automatic-Bracket-Size"
4554 , or by using the following commands:
4555 \begin_inset VSpace medskip
4561 \begin_layout Standard
4565 \begin_inset Tabular
4566 <lyxtabular version="3" rows="4" columns="2">
4568 <column alignment="center" valignment="top" leftline="true" width="0">
4569 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4570 <row topline="true" bottomline="true">
4571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4574 \begin_layout Standard
4580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4583 \begin_layout Standard
4585 \begin_inset Note Note
4588 \begin_layout Standard
4595 is only used as spacer.
4606 <row topline="true">
4607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4610 \begin_layout Standard
4617 \begin_layout Standard
4630 2\InsetSpace \thinspace{}
4636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4639 \begin_layout Standard
4640 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
4641 0 & \textrm{-}\mathrm{i}\\
4642 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
4651 <row topline="true">
4652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4655 \begin_layout Standard
4662 \begin_layout Standard
4675 2\InsetSpace \thinspace{}
4681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4684 \begin_layout Standard
4685 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
4686 0 & \textrm{-}\mathrm{i}\\
4687 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
4696 <row topline="true" bottomline="true">
4697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4700 \begin_layout Standard
4707 \begin_layout Standard
4720 2\InsetSpace \thinspace{}
4726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4729 \begin_layout Standard
4730 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
4731 0 & \textrm{-}\mathrm{i}\\
4732 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
4748 \begin_inset Tabular
4749 <lyxtabular version="3" rows="4" columns="2">
4751 <column alignment="center" valignment="top" leftline="true" width="0">
4752 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4753 <row topline="true" bottomline="true">
4754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4757 \begin_layout Standard
4763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4766 \begin_layout Standard
4773 <row topline="true">
4774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4777 \begin_layout Standard
4784 \begin_layout Standard
4797 2\InsetSpace \thinspace{}
4803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4806 \begin_layout Standard
4807 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
4808 0 & \textrm{-}\mathrm{i}\\
4809 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
4818 <row topline="true" bottomline="true">
4819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4822 \begin_layout Standard
4829 \begin_layout Standard
4842 2\InsetSpace \thinspace{}
4848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4851 \begin_layout Standard
4852 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
4853 0 & \textrm{-}\mathrm{i}\\
4854 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
4863 <row topline="true" bottomline="true">
4864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4867 \begin_layout Standard
4874 \begin_layout Standard
4887 2\InsetSpace \thinspace{}
4893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4896 \begin_layout Standard
4897 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
4898 0 & \textrm{-}\mathrm{i}\\
4899 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
4917 \begin_layout Standard
4918 \begin_inset VSpace medskip
4921 When e.\InsetSpace \thinspace{}
4929 is inserted, a blue box appears between two vertical lines where the matrix
4933 \begin_layout Standard
4934 \begin_inset VSpace bigskip
4937 As all multiline formulas are matrices, the length
4944 \begin_inset LatexCommand index
4945 name "Commands ! A ! \\textbackslash arraycolsep"
4949 that is described in
4950 \begin_inset LatexCommand ref
4951 reference "sub:Column-Separation"
4955 can also be used to change the column separation of matrices.
4958 \begin_layout Standard
4959 To change the row separation, the command
4966 \begin_inset LatexCommand index
4967 name "Commands ! A ! \\textbackslash arraystretch"
4972 It is used as follows:
4975 \begin_layout Standard
4982 arraystretch}{stretch factor}
4983 \begin_inset LatexCommand index
4984 name "Commands ! R ! \\textbackslash renewcommand"
4991 \begin_layout Standard
4998 assigns the stretch factor to the predefined command
5005 To double e.\InsetSpace \thinspace{}
5007 the row separation, use the factor 2.
5008 This is then used for all following matrices.
5009 To go back to the original separation, assign the factor 1 to
5018 \begin_layout Standard
5019 To set matrices into a text line, the command
5026 \begin_inset LatexCommand index
5027 name "Commands ! S ! \\textbackslash smallmatrix"
5032 When it is inserted a blue box with two dashed lines appears.
5033 In this box the matrix is inserted.
5036 \begin_layout Standard
5038 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5039 C & D\end{smallmatrix}\right)$
5045 \begin_layout Section
5046 Brackets and Delimiters
5047 \begin_inset LatexCommand index
5053 \begin_inset LatexCommand index
5061 \begin_layout Subsection
5062 Vertical Brackets and Delimiters
5063 \begin_inset LatexCommand index
5064 name "Brackets ! vertical"
5071 \begin_layout Standard
5075 \begin_inset Tabular
5076 <lyxtabular version="3" rows="9" columns="2">
5078 <column alignment="center" valignment="top" leftline="true" width="0pt">
5079 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5080 <row topline="true" bottomline="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
5100 <row topline="true">
5101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5104 \begin_layout Standard
5110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5113 \begin_layout Standard
5114 \begin_inset Formula $($
5123 <row topline="true">
5124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5127 \begin_layout Standard
5133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5136 \begin_layout Standard
5137 \begin_inset Formula $\{$
5146 <row topline="true">
5147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5150 \begin_layout Standard
5156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5159 \begin_layout Standard
5160 \begin_inset Formula $[$
5169 <row topline="true">
5170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5173 \begin_layout Standard
5181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5184 \begin_layout Standard
5185 \begin_inset Formula $\langle$
5194 <row topline="true">
5195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5198 \begin_layout Standard
5206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5209 \begin_layout Standard
5210 \begin_inset Formula $\lceil$
5219 <row topline="true">
5220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5223 \begin_layout Standard
5231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5234 \begin_layout Standard
5235 \begin_inset Formula $\lfloor$
5244 <row topline="true">
5245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5248 \begin_layout Standard
5254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5257 \begin_layout Standard
5258 \begin_inset Formula $/$
5267 <row topline="true" bottomline="true">
5268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5271 \begin_layout Standard
5277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5280 \begin_layout Standard
5281 \begin_inset Formula $|$
5297 \begin_inset Tabular
5298 <lyxtabular version="3" rows="9" columns="2">
5300 <column alignment="center" valignment="top" leftline="true" width="0pt">
5301 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5302 <row topline="true" bottomline="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
5322 <row topline="true">
5323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5326 \begin_layout Standard
5332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5335 \begin_layout Standard
5336 \begin_inset Formula $)$
5345 <row topline="true">
5346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5349 \begin_layout Standard
5355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5358 \begin_layout Standard
5359 \begin_inset Formula $\}$
5368 <row topline="true">
5369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5372 \begin_layout Standard
5378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5381 \begin_layout Standard
5382 \begin_inset Formula $]$
5391 <row topline="true">
5392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5395 \begin_layout Standard
5403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5406 \begin_layout Standard
5407 \begin_inset Formula $\rangle$
5416 <row topline="true">
5417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5420 \begin_layout Standard
5428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5431 \begin_layout Standard
5432 \begin_inset Formula $\rceil$
5441 <row topline="true">
5442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5445 \begin_layout Standard
5453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5456 \begin_layout Standard
5457 \begin_inset Formula $\rfloor$
5466 <row topline="true">
5467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5470 \begin_layout Standard
5480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5483 \begin_layout Standard
5484 \begin_inset Formula $\backslash$
5493 <row topline="true" bottomline="true">
5494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5497 \begin_layout Standard
5505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5508 \begin_layout Standard
5509 \begin_inset Formula $\|$
5527 \begin_layout Standard
5530 \begin_inset Note Greyedout
5533 \begin_layout Standard
5538 In TeX-mode the command
5545 \begin_inset LatexCommand index
5546 name "Commands ! T ! \\textbackslash textbackslash"
5550 must be used for the backslash, because the command
5558 produces there a line break.
5566 \begin_layout Standard
5567 For all characters listed above the size can be adjusted with the commands
5568 described in the following two subsections.
5569 When using these commands, the characters < and > can directly be used
5570 instead of the commands
5585 \begin_layout Subsubsection
5587 \begin_inset LatexCommand label
5588 name "sub:Manual-Bracket-Size"
5593 \begin_inset LatexCommand index
5594 name "Bracket size ! manual"
5601 \begin_layout Standard
5602 The bracket size can be specified manually by the LaTeX-commands
5609 \begin_inset LatexCommand index
5610 name "Commands ! B ! \\textbackslash big"
5639 denotes the smallest and
5645 the largest bracket size.
5648 \begin_layout Standard
5649 These commands are used to emphasize levels of brackets:
5652 \begin_layout Standard
5654 \begin_inset Tabular
5655 <lyxtabular version="3" rows="2" columns="2">
5657 <column alignment="center" valignment="top" width="0pt">
5658 <column alignment="center" valignment="top" width="0pt">
5660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5663 \begin_layout Standard
5664 all brackets in the same size:
5669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5672 \begin_layout Standard
5673 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
5683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5686 \begin_layout Standard
5692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5695 \begin_layout Standard
5696 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
5710 \begin_inset Note Note
5713 \begin_layout Standard
5720 is only used as spacer.
5728 \begin_layout Standard
5729 For the second formula the command
5739 \begin_layout Standard
5753 \begin_layout Standard
5754 Here is an overview about all bracket sizes:
5757 \begin_layout Standard
5777 \begin_layout Standard
5794 \begin_layout Standard
5807 \begin_layout Standard
5823 \begin_layout Standard
5825 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
5831 \begin_layout Standard
5840 -commands there is the variant
5847 \begin_inset LatexCommand index
5848 name "Commands ! B ! \\textbackslash bigm"
5852 that adds a bit more space between the bracket and its content, and the
5866 \begin_inset LatexCommand index
5867 name "Commands ! B ! \\textbackslash bigl - \\textbackslash bigr"
5871 , that don't add additional space.
5876 at the end of the command
5882 is for a left bracket; for a right bracket this will be replaced by an
5888 A left or right bracket can each be an opening or closing bracket.
5891 \begin_layout Standard
5892 In the following table is a comparison of the variants:
5895 \begin_layout Standard
5897 \begin_inset Tabular
5898 <lyxtabular version="3" rows="5" columns="2">
5900 <column alignment="center" valignment="middle" leftline="true" width="0">
5901 <column alignment="center" valignment="middle" leftline="true" rightline="true" width="0">
5902 <row topline="true" bottomline="true">
5903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5906 \begin_layout Standard
5912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5915 \begin_layout Standard
5917 \begin_inset Note Note
5920 \begin_layout Standard
5927 is only used as spacer.
5938 <row topline="true">
5939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5942 \begin_layout Standard
5957 \begin_layout Standard
5975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5978 \begin_layout Standard
5979 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
5988 <row topline="true">
5989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5992 \begin_layout Standard
6007 \begin_layout Standard
6025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6028 \begin_layout Standard
6029 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6038 <row topline="true" bottomline="true">
6039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6042 \begin_layout Standard
6057 \begin_layout Standard
6075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6078 \begin_layout Standard
6079 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6088 <row topline="true" bottomline="true">
6089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6092 \begin_layout Standard
6104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6107 \begin_layout Standard
6108 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6124 \begin_layout Subsubsection
6125 Automatic Bracket Size
6126 \begin_inset LatexCommand label
6127 name "sub:Automatic-Bracket-Size"
6132 \begin_inset LatexCommand index
6133 name "Bracket size ! automatic"
6140 \begin_layout Standard
6141 Brackets with variable size can be inserted with the commands
6148 \begin_inset LatexCommand index
6149 name "Commands ! L ! \\textbackslash left"
6160 \begin_inset LatexCommand index
6161 name "Commands ! R ! \\textbackslash right"
6165 or via the math toolbar button
6166 \begin_inset Graphics
6167 filename ../images/dialog-show_mathdelimiter.png
6185 the wanted bracket must be inserted.
6186 The bracket size will then automatically be calculated for the output.
6189 \begin_layout Standard
6191 normal bracket: The command
6201 \begin_layout Standard
6211 \begin_inset Formula $\downarrow$
6218 \begin_layout Standard
6230 \begin_inset Formula \[
6238 \begin_layout Standard
6240 multiline bracket: The command
6252 \begin_layout Standard
6262 \begin_inset Formula $\downarrow$
6269 \begin_layout Standard
6283 \begin_inset Formula \[
6284 \ln\left(\frac{A}{C}\right)\]
6291 \begin_layout Standard
6310 This has the advantage that you can see in LyX immediately the real bracket
6311 size and that the matching right bracket will be created too.
6314 for the last example would then be:
6328 \begin_layout Standard
6338 \begin_inset Formula $\downarrow$
6344 \begin_layout Standard
6345 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6346 For example the command
6356 \begin_layout Standard
6366 \begin_inset Formula $\downarrow$
6373 \begin_layout Standard
6389 \begin_inset Formula \[
6390 \left.\frac{A}{B}\right\} \]
6408 will be converted by LyX to brackets in the right size when the document
6409 is reloaded and an omitted bracket will appear as dashed line.
6412 \begin_layout Standard
6413 \begin_inset VSpace bigskip
6416 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6424 \begin_inset LatexCommand index
6425 name "Commands ! M ! \\textbackslash middle"
6429 is additionally available for all brackets and limits.
6430 With this command the height of the following character is adapted to the
6431 one of the surrounding brackets, what is e.\InsetSpace \thinspace{}
6433 needed for physical vectors:
6434 \begin_inset Formula \[
6435 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
6439 For physical vectors there is a special LaTeX-package, described in
6440 \begin_inset LatexCommand ref
6441 reference "sub:Physical-Vectors"
6448 \begin_layout Subsection
6450 \begin_inset LatexCommand index
6451 name "Brackets ! horizontal"
6458 \begin_layout Standard
6460 \begin_inset Tabular
6461 <lyxtabular version="3" rows="4" columns="2">
6463 <column alignment="center" valignment="top" leftline="true" width="0pt">
6464 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
6465 <row topline="true" bottomline="true">
6466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6469 \begin_layout Standard
6471 \begin_inset Note Note
6474 \begin_layout Standard
6481 is only used as spacer.
6491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6494 \begin_layout Standard
6501 <row topline="true">
6502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6505 \begin_layout Standard
6509 \begin_layout Standard
6524 \begin_layout Standard
6537 \begin_layout Standard
6550 \begin_layout Standard
6563 \begin_layout Standard
6571 \begin_inset LatexCommand index
6572 name "Commands ! O ! \\textbackslash overbrace"
6581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6584 \begin_layout Standard
6585 \begin_inset Formula $\overbrace{A+B}^{3}$
6594 <row topline="true" bottomline="true">
6595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6598 \begin_layout Standard
6602 \begin_layout Standard
6617 \begin_layout Standard
6630 \begin_layout Standard
6643 \begin_layout Standard
6651 \begin_inset LatexCommand index
6652 name "Commands ! U ! \\textbackslash underbrace"
6661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6664 \begin_layout Standard
6665 \begin_inset Formula $\underbrace{A+B}_{5}$
6674 <row topline="true" bottomline="true">
6675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6678 \begin_layout Standard
6687 \begin_layout Standard
6700 \begin_layout Standard
6713 \begin_layout Standard
6726 \begin_layout Standard
6739 \begin_layout Standard
6752 \begin_layout Standard
6766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6769 \begin_layout Standard
6770 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6786 \begin_layout Standard
6787 In the last example it doesn't matter if
6799 is inserted at first.
6802 \begin_layout Standard
6803 \begin_inset VSpace bigskip
6806 When brackets are needed that overlap each other, multiline formulas, as
6808 \begin_inset LatexCommand ref
6809 reference "sec:Multiline-Formulas"
6814 \begin_inset Formula \begin{eqnarray*}
6815 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
6816 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
6820 In the first row the formula is inserted together with the first brace.
6821 It is hereby important that the space command
6825 \begin_layout Standard
6826 Space commands are explained in
6827 \begin_inset LatexCommand ref
6828 reference "sub:Predefined-Space"
6843 is inserted before the first
6844 \begin_inset Formula $d$
6847 , because the brace that ends behind the
6848 \begin_inset Formula $q$
6851 prevents that the following
6852 \begin_inset Quotes eld
6856 \begin_inset Quotes erd
6859 is surrounded by space.
6863 \begin_layout Standard
6864 because a bracket is not handled as character, see
6865 \begin_inset LatexCommand ref
6866 reference "sub:Binary-Operators"
6875 In the second row the second brace is inserted.
6876 As it should begin before the
6877 \begin_inset Formula $b$
6892 \begin_layout Standard
6900 \begin_inset LatexCommand ref
6901 reference "sub:Placeholders"
6910 This space is needed because the
6911 \begin_inset Quotes eld
6915 \begin_inset Quotes erd
6918 is also surrounded by space in the formula.
6919 The brace is placed under the command
6928 \begin_layout Standard
6929 It gets more complicated when brackets overlap each other, like in the following
6934 \begin_layout Standard
6946 \begin_inset Formula \begin{eqnarray*}
6947 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
6948 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
6956 \begin_layout Standard
6967 The first formula row is the same as the second row of the previous example,
6968 with the difference that the brace is above.
6969 The second row contains the formula together with the second brace.
6970 To avoid that there is space between the upper brace in the first row and
6971 the formula, the row spacing need to be reduced.
6972 This is not easily possible due to a bug in LyX
6976 \begin_layout Standard
6980 \begin_layout Standard
6984 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
6993 \begin_layout Standard
7006 As solution for the problem, the global formula row separation
7013 \begin_inset LatexCommand index
7014 name "Commands ! J ! \\textbackslash jot"
7018 must be changed to -6\InsetSpace \thinspace{}
7019 pt before the formula with the command
7034 is set back after the formula to the standard value of 3\InsetSpace \thinspace{}
7037 More about the row separation in formulas is explained in
7038 \begin_inset LatexCommand ref
7039 reference "sub:Line-Separation"
7046 \begin_layout Section
7048 \begin_inset LatexCommand index
7056 \begin_layout Standard
7057 Arrows can be inserted via the math toolbar button
7058 \begin_inset Graphics
7059 filename ../images/math/leftarrow.png
7064 or the commands listed in the following subsections.
7067 \begin_layout Subsection
7069 \begin_inset LatexCommand index
7070 name "Arrows ! horizontal"
7077 \begin_layout Standard
7081 \begin_inset Tabular
7082 <lyxtabular version="3" rows="8" columns="2">
7084 <column alignment="center" valignment="top" leftline="true" width="0pt">
7085 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7086 <row topline="true" bottomline="true">
7087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7090 \begin_layout Standard
7096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7099 \begin_layout Standard
7106 <row topline="true">
7107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7110 \begin_layout Standard
7118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7121 \begin_layout Standard
7122 \begin_inset Formula $\gets$
7131 <row topline="true">
7132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7135 \begin_layout Standard
7143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7146 \begin_layout Standard
7147 \begin_inset Formula $\Leftarrow$
7156 <row topline="true" bottomline="true">
7157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7160 \begin_layout Standard
7168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7171 \begin_layout Standard
7172 \begin_inset Formula $\longleftarrow$
7181 <row bottomline="true">
7182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7185 \begin_layout Standard
7193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7196 \begin_layout Standard
7197 \begin_inset Formula $\Longleftarrow$
7206 <row bottomline="true">
7207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7210 \begin_layout Standard
7218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7221 \begin_layout Standard
7222 \begin_inset Formula $\leftharpoonup$
7231 <row bottomline="true">
7232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7235 \begin_layout Standard
7243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7246 \begin_layout Standard
7247 \begin_inset Formula $\leftharpoondown$
7256 <row bottomline="true">
7257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7260 \begin_layout Standard
7268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7271 \begin_layout Standard
7272 \begin_inset Formula $\hookleftarrow$
7288 \begin_inset Tabular
7289 <lyxtabular version="3" rows="8" columns="2">
7291 <column alignment="center" valignment="top" leftline="true" width="0pt">
7292 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7293 <row topline="true" bottomline="true">
7294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7297 \begin_layout Standard
7303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7306 \begin_layout Standard
7313 <row topline="true">
7314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7317 \begin_layout Standard
7325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7328 \begin_layout Standard
7329 \begin_inset Formula $\to$
7338 <row topline="true">
7339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7342 \begin_layout Standard
7350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7353 \begin_layout Standard
7354 \begin_inset Formula $\Rightarrow$
7363 <row topline="true">
7364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7367 \begin_layout Standard
7375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7378 \begin_layout Standard
7379 \begin_inset Formula $\longrightarrow$
7388 <row topline="true">
7389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7392 \begin_layout Standard
7400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7403 \begin_layout Standard
7404 \begin_inset Formula $\Longrightarrow$
7413 <row topline="true">
7414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7417 \begin_layout Standard
7425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7428 \begin_layout Standard
7429 \begin_inset Formula $\rightharpoonup$
7438 <row topline="true" bottomline="true">
7439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7442 \begin_layout Standard
7450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7453 \begin_layout Standard
7454 \begin_inset Formula $\rightharpoondown$
7463 <row bottomline="true">
7464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7467 \begin_layout Standard
7475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7478 \begin_layout Standard
7479 \begin_inset Formula $\hookrightarrow$
7497 \begin_layout Standard
7501 \begin_inset Tabular
7502 <lyxtabular version="3" rows="6" columns="2">
7504 <column alignment="center" valignment="top" leftline="true" width="0pt">
7505 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7506 <row topline="true" bottomline="true">
7507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7510 \begin_layout Standard
7516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7519 \begin_layout Standard
7526 <row topline="true">
7527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7530 \begin_layout Standard
7538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7541 \begin_layout Standard
7542 \begin_inset Formula $\leftrightarrow$
7551 <row topline="true">
7552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7555 \begin_layout Standard
7563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7566 \begin_layout Standard
7567 \begin_inset Formula $\Leftrightarrow$
7576 <row topline="true">
7577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7580 \begin_layout Standard
7588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7591 \begin_layout Standard
7592 \begin_inset Formula $\longleftrightarrow$
7601 <row topline="true">
7602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7605 \begin_layout Standard
7613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7616 \begin_layout Standard
7617 \begin_inset Formula $\Longleftrightarrow$
7626 <row topline="true" bottomline="true">
7627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7630 \begin_layout Standard
7638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7641 \begin_layout Standard
7642 \begin_inset Formula $\rightleftharpoons$
7659 \begin_layout Standard
7671 \begin_inset Tabular
7672 <lyxtabular version="3" rows="5" columns="2">
7674 <column alignment="center" valignment="top" leftline="true" width="0pt">
7675 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7676 <row topline="true" bottomline="true">
7677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7680 \begin_layout Standard
7686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7689 \begin_layout Standard
7696 <row topline="true">
7697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7700 \begin_layout Standard
7708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7711 \begin_layout Standard
7712 \begin_inset Formula $\mapsto$
7721 <row topline="true">
7722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7725 \begin_layout Standard
7733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7736 \begin_layout Standard
7737 \begin_inset Formula $\longmapsto$
7746 <row topline="true">
7747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7750 \begin_layout Standard
7758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7761 \begin_layout Standard
7762 \begin_inset Formula $\leadsto$
7771 <row topline="true" bottomline="true">
7772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7775 \begin_layout Standard
7783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7786 \begin_layout Standard
7787 \begin_inset Formula $\dasharrow$
7805 \begin_layout Standard
7806 \begin_inset VSpace medskip
7809 Arrows used as accent like e.\InsetSpace \thinspace{}
7811 vector arrows are listed in
7812 \begin_inset LatexCommand ref
7813 reference "sec:Accents"
7820 \begin_layout Standard
7821 \begin_inset VSpace bigskip
7824 Furthermore there are the labeled arrows
7825 \begin_inset LatexCommand index
7826 name "Arrows ! labeled"
7837 \begin_inset LatexCommand index
7838 name "Commands ! X ! \\textbackslash xleftarrow"
7849 \begin_inset LatexCommand index
7850 name "Commands ! X ! \\textbackslash xrightarrow\\vspace{4mm}"
7855 When inserting one of these commands in a formula, an arrow with two blue
7856 boxes appear where the label can be inserted.
7857 The length of the arrow adapts to the label width.
7860 \begin_layout Standard
7862 \begin_inset Tabular
7863 <lyxtabular version="3" rows="3" columns="2">
7865 <column alignment="center" valignment="top" leftline="true" width="0pt">
7866 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7867 <row topline="true" bottomline="true">
7868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7871 \begin_layout Standard
7877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7880 \begin_layout Standard
7882 \begin_inset Note Note
7885 \begin_layout Standard
7892 is only used as spacer.
7903 <row topline="true">
7904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7907 \begin_layout Standard
7914 \begin_layout Standard
7924 \begin_inset Formula $\downarrow$
7928 \begin_inset Formula $\to$
7936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7939 \begin_layout Standard
7940 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
7949 <row topline="true" bottomline="true">
7950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7953 \begin_layout Standard
7960 \begin_layout Standard
7970 \begin_inset Formula $\downarrow$
7974 \begin_inset Formula $\to$
7982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7985 \begin_layout Standard
7986 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8002 \begin_layout Subsection
8003 Vertical and diagonal Arrows
8004 \begin_inset LatexCommand index
8005 name "Arrows ! diagonal"
8010 \begin_inset LatexCommand index
8011 name "Arrows ! vertical"
8018 \begin_layout Standard
8022 \begin_inset Tabular
8023 <lyxtabular version="3" rows="7" columns="2">
8025 <column alignment="center" valignment="top" leftline="true" width="0pt">
8026 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8027 <row topline="true" bottomline="true">
8028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8031 \begin_layout Standard
8037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8040 \begin_layout Standard
8047 <row topline="true">
8048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8051 \begin_layout Standard
8059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8062 \begin_layout Standard
8063 \begin_inset Formula $\uparrow$
8072 <row topline="true">
8073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8076 \begin_layout Standard
8084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8087 \begin_layout Standard
8088 \begin_inset Formula $\Uparrow$
8097 <row topline="true">
8098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8101 \begin_layout Standard
8109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8112 \begin_layout Standard
8113 \begin_inset Formula $\updownarrow$
8122 <row topline="true">
8123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8126 \begin_layout Standard
8134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8137 \begin_layout Standard
8138 \begin_inset Formula $\Updownarrow$
8147 <row topline="true" bottomline="true">
8148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8151 \begin_layout Standard
8159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8162 \begin_layout Standard
8163 \begin_inset Formula $\Downarrow$
8172 <row bottomline="true">
8173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8176 \begin_layout Standard
8184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8187 \begin_layout Standard
8188 \begin_inset Formula $\downarrow$
8204 \begin_inset Tabular
8205 <lyxtabular version="3" rows="5" columns="2">
8207 <column alignment="center" valignment="top" leftline="true" width="0pt">
8208 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8209 <row topline="true" bottomline="true">
8210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8213 \begin_layout Standard
8219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8222 \begin_layout Standard
8229 <row topline="true">
8230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8233 \begin_layout Standard
8241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8244 \begin_layout Standard
8245 \begin_inset Formula $\nearrow$
8254 <row topline="true">
8255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8258 \begin_layout Standard
8266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8269 \begin_layout Standard
8270 \begin_inset Formula $\searrow$
8279 <row topline="true" bottomline="true">
8280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8283 \begin_layout Standard
8291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8294 \begin_layout Standard
8295 \begin_inset Formula $\swarrow$
8304 <row bottomline="true">
8305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8308 \begin_layout Standard
8316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8319 \begin_layout Standard
8320 \begin_inset Formula $\nwarrow$
8338 \begin_layout Standard
8339 \begin_inset VSpace medskip
8342 Vertical arrows can be used also as delimiter together with the commands
8344 \begin_inset LatexCommand ref
8345 reference "sub:Manual-Bracket-Size"
8350 \begin_inset LatexCommand ref
8351 reference "sub:Automatic-Bracket-Size"
8358 \begin_layout Standard
8364 \begin_layout Section
8366 \begin_inset LatexCommand label
8372 \begin_inset LatexCommand index
8380 \begin_layout Standard
8381 Accents can be inserted via the math toolbar button
8382 \begin_inset Graphics
8383 filename ../images/math/hat.png
8388 or the commands listed in the following subsections.
8391 \begin_layout Subsection
8392 Accents for one Character
8396 \begin_layout Standard
8409 \begin_layout Standard
8411 \begin_inset LatexCommand ref
8412 reference "sub:Accents-in-Text"
8425 \begin_layout Standard
8433 \begin_inset Note Note
8436 \begin_layout Standard
8439 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
8442 \begin_layout Standard
8445 texorpdfstring is in section
8446 \begin_inset LatexCommand ref
8447 reference "sub:Formulas-in-Section"
8457 \begin_inset LatexCommand label
8458 name "sub:Accents-for-one"
8463 \begin_inset LatexCommand index
8464 name "Accents ! for one character"
8471 \begin_layout Standard
8475 \begin_inset Tabular
8476 <lyxtabular version="3" rows="8" columns="2">
8478 <column alignment="center" valignment="top" leftline="true" width="0pt">
8479 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8480 <row topline="true" bottomline="true">
8481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8484 \begin_layout Standard
8490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8493 \begin_layout Standard
8495 \begin_inset Note Note
8498 \begin_layout Standard
8505 is only used as spacer.
8516 <row topline="true" bottomline="true">
8517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8520 \begin_layout Standard
8527 \begin_layout Standard
8541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8544 \begin_layout Standard
8545 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8554 <row bottomline="true">
8555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8558 \begin_layout Standard
8565 \begin_layout Standard
8579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8582 \begin_layout Standard
8583 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8592 <row bottomline="true">
8593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8596 \begin_layout Standard
8603 \begin_layout Standard
8617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8620 \begin_layout Standard
8621 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8630 <row bottomline="true">
8631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8634 \begin_layout Standard
8642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8645 \begin_layout Standard
8646 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
8655 <row bottomline="true">
8656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8659 \begin_layout Standard
8666 \begin_layout Standard
8676 \begin_inset LatexCommand index
8686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8689 \begin_layout Standard
8690 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
8699 <row bottomline="true">
8700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8703 \begin_layout Standard
8710 \begin_layout Standard
8724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8727 \begin_layout Standard
8728 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
8737 <row bottomline="true">
8738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8741 \begin_layout Standard
8748 \begin_layout Standard
8762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8765 \begin_layout Standard
8766 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
8782 \begin_inset Tabular
8783 <lyxtabular version="3" rows="7" columns="2">
8785 <column alignment="center" valignment="top" leftline="true" width="0pt">
8786 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8787 <row topline="true" bottomline="true">
8788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8791 \begin_layout Standard
8797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8800 \begin_layout Standard
8807 <row topline="true" bottomline="true">
8808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8811 \begin_layout Standard
8818 \begin_layout Standard
8832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8835 \begin_layout Standard
8836 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
8845 <row bottomline="true">
8846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8849 \begin_layout Standard
8856 \begin_layout Standard
8870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8873 \begin_layout Standard
8874 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
8883 <row bottomline="true">
8884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8887 \begin_layout Standard
8894 \begin_layout Standard
8908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8911 \begin_layout Standard
8912 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
8921 <row bottomline="true">
8922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8925 \begin_layout Standard
8932 \begin_layout Standard
8946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8949 \begin_layout Standard
8950 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
8959 <row bottomline="true">
8960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8963 \begin_layout Standard
8970 \begin_layout Standard
8984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8987 \begin_layout Standard
8988 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
8997 <row bottomline="true">
8998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9001 \begin_layout Standard
9008 \begin_layout Standard
9022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9025 \begin_layout Standard
9026 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9044 \begin_layout Standard
9045 \begin_inset VSpace bigskip
9049 \begin_inset LatexCommand index
9054 in formulas, a quotation mark is inserted before the vowel.
9055 These two characters are then treated by LaTeX as
9059 character when the formula part with the umlaut is marked as German.
9067 \begin_inset Quotes eld
9071 \begin_inset Quotes erd
9074 umlauts are created as demonstrated in the following example:
9077 \begin_layout Standard
9078 \begin_inset VSpace -2mm
9084 \begin_layout Standard
9086 \begin_inset Tabular
9087 <lyxtabular version="3" rows="3" columns="2">
9089 <column alignment="center" valignment="top" leftline="true" width="0">
9090 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
9091 <row topline="true" bottomline="true">
9092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9095 \begin_layout Standard
9101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9104 \begin_layout Standard
9106 \begin_inset Note Note
9109 \begin_layout Standard
9116 is only used as spacer.
9127 <row topline="true">
9128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9131 \begin_layout Standard
9134 \begin_inset Quotes grd
9142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9145 \begin_layout Standard
9148 \begin_inset Formula $"i$
9157 <row topline="true" bottomline="true">
9158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9161 \begin_layout Standard
9168 \begin_layout Standard
9182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9185 \begin_layout Standard
9186 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9202 \begin_layout Standard
9203 Another advantage to
9209 is that umlauts can directly be converted to mathematical text because
9210 the accent commands above are
9216 in mathematical text
9219 To convert an accented character to mathematical text, only the character
9220 under the accent may be converted.
9221 This applies also for all other conversions, e.\InsetSpace \thinspace{}
9226 \begin_layout Standard
9227 In mathematical text, umlauts and other accented characters can directly
9231 \begin_layout Subsection
9232 Accents for Operators
9233 \begin_inset LatexCommand index
9234 name "Accents ! for operators"
9241 \begin_layout Standard
9249 \begin_inset LatexCommand index
9250 name "Commands ! O ! \\textbackslash overset"
9261 \begin_inset LatexCommand index
9262 name "Commands ! U ! \\textbackslash underset"
9266 characters can be placed above or below an operator, respectively, to accent
9275 \begin_inset LatexCommand index
9276 name "Commands ! S ! \\textbackslash sideset"
9280 characters can be set before and behind an operator.
9281 The command scheme is:
9284 \begin_layout Standard
9300 \begin_layout Standard
9307 must always be before the operator that should be accented.
9308 You can accent with several characters and even with other operators and
9316 for example only characters behind an operator, write nothing between the
9317 first braces but don't omit the braces.
9320 \begin_layout Standard
9321 For example the command
9326 \begin_inset Formula $\to$
9336 \begin_inset Formula $\to$
9345 \begin_layout Standard
9361 \begin_inset Formula \[
9362 \sideset{}{'}\sum_{k=1}^{n}\]
9369 \begin_layout Standard
9378 \begin_layout Standard
9393 \begin_layout Standard
9405 \begin_inset Formula $\uparrow$
9413 \begin_inset Formula \[
9414 \overset{a}{\maltese}\]
9418 As seen in the last example, with
9430 also symbols and characters can be accented; with
9436 this is not possible.
9439 \begin_layout Subsection
9440 Accents for several Characters
9441 \begin_inset LatexCommand label
9442 name "sub:Accents-for-several"
9447 \begin_inset LatexCommand index
9448 name "Accents ! for several characters"
9455 \begin_layout Standard
9459 \begin_inset Tabular
9460 <lyxtabular version="3" rows="5" columns="2">
9462 <column alignment="center" valignment="top" leftline="true" width="0pt">
9463 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9464 <row topline="true" bottomline="true">
9465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9468 \begin_layout Standard
9474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9477 \begin_layout Standard
9479 \begin_inset Note Note
9482 \begin_layout Standard
9489 is only used as spacer.
9500 <row topline="true" bottomline="true">
9501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9504 \begin_layout Standard
9511 \begin_layout Standard
9525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9528 \begin_layout Standard
9529 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9538 <row bottomline="true">
9539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9542 \begin_layout Standard
9549 \begin_layout Standard
9563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9566 \begin_layout Standard
9567 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9576 <row bottomline="true">
9577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9580 \begin_layout Standard
9587 \begin_layout Standard
9601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9604 \begin_layout Standard
9605 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9614 <row bottomline="true">
9615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9618 \begin_layout Standard
9625 \begin_layout Standard
9639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9642 \begin_layout Standard
9643 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9659 \begin_inset Tabular
9660 <lyxtabular version="3" rows="5" columns="2">
9662 <column alignment="center" valignment="top" leftline="true" width="0pt">
9663 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9664 <row topline="true" bottomline="true">
9665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9668 \begin_layout Standard
9674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9677 \begin_layout Standard
9684 <row topline="true" bottomline="true">
9685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9688 \begin_layout Standard
9695 \begin_layout Standard
9709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9712 \begin_layout Standard
9713 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9722 <row bottomline="true">
9723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9726 \begin_layout Standard
9733 \begin_layout Standard
9747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9750 \begin_layout Standard
9751 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9760 <row bottomline="true">
9761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9764 \begin_layout Standard
9771 \begin_layout Standard
9785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9788 \begin_layout Standard
9789 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9798 <row bottomline="true">
9799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9802 \begin_layout Standard
9809 \begin_layout Standard
9823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9826 \begin_layout Standard
9827 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
9845 \begin_layout Standard
9846 \begin_inset VSpace medskip
9849 With these commands as many characters as you like can be accented.
9862 will only be set in the output with a length of three characters, as shown
9863 in the following example:
9864 \begin_inset Formula \[
9865 \widetilde{A+B=C-D}\]
9872 \begin_layout Standard
9880 \begin_inset LatexCommand index
9881 name "Commands ! O ! \\textbackslash overset"
9892 \begin_inset LatexCommand index
9893 name "Commands ! U ! \\textbackslash underset"
9897 described in the previous subsection it is also possible to accent several
9907 \begin_layout Standard
9917 \begin_inset Formula $\downarrow$
9923 \begin_inset Formula \[
9924 \underset{***}{A=B}\]
9931 \begin_layout Section
9933 \begin_inset LatexCommand label
9939 \begin_inset LatexCommand index
9940 name "Space ! horizontal"
9947 \begin_layout Subsection
9949 \begin_inset LatexCommand label
9950 name "sub:Predefined-Space"
9955 \begin_inset LatexCommand index
9956 name "Space ! horizontal ! predefined"
9963 \begin_layout Standard
9964 Sometimes it is necessary to insert horizontal space to a formula.
9965 This is done by inserting a protected space (shortcut
9971 \begin_inset Quotes eld
9981 \begin_layout Standard
9994 \begin_inset Quotes erd
9997 appears and by pressing
10001 several times one can select one of eight different space sizes.
10002 The spaces can also be inserted using the math toolbar button
10003 \begin_inset Graphics
10004 filename ../images/math/space.png
10009 or special commands.
10010 Independent from the inserted command, one can select the size again by
10018 \begin_layout Standard
10021 \begin_inset VSpace -5mm
10025 \begin_inset Tabular
10026 <lyxtabular version="3" rows="3" columns="7">
10028 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
10029 <column alignment="center" valignment="top" leftline="true" width="0">
10030 <column alignment="center" valignment="top" leftline="true" width="0">
10031 <column alignment="center" valignment="top" leftline="true" width="0">
10032 <column alignment="center" valignment="top" leftline="true" width="0">
10033 <column alignment="center" valignment="top" leftline="true" width="0">
10034 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10035 <row topline="true">
10036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10039 \begin_layout Standard
10045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10048 \begin_layout Standard
10056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10059 \begin_layout Standard
10067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10070 \begin_layout Standard
10078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10081 \begin_layout Standard
10089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10092 \begin_layout Standard
10100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10103 \begin_layout Standard
10112 <row topline="true">
10113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10116 \begin_layout Standard
10121 keystrokes after inserting the protected space
10126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10129 \begin_layout Standard
10135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10138 \begin_layout Standard
10144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10147 \begin_layout Standard
10153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10156 \begin_layout Standard
10162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10165 \begin_layout Standard
10171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10174 \begin_layout Standard
10181 <row topline="true" bottomline="true">
10182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10185 \begin_layout Standard
10191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10194 \begin_layout Standard
10195 \begin_inset Formula $A\, B$
10203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10206 \begin_layout Standard
10207 \begin_inset Formula $A\: B$
10215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10218 \begin_layout Standard
10219 \begin_inset Formula $A\; B$
10227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10230 \begin_layout Standard
10231 \begin_inset Formula $A\quad B$
10239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10242 \begin_layout Standard
10243 \begin_inset Formula $A\qquad B$
10251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10254 \begin_layout Standard
10255 \begin_inset Formula $A\! B$
10271 \begin_layout Standard
10272 The last size seem to produce no space.
10273 It is displayed red in LyX contrary to the other sizes, because it is a
10275 There are two more negative spaces:
10278 \begin_layout Standard
10280 \begin_inset Tabular
10281 <lyxtabular version="3" rows="3" columns="3">
10283 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
10284 <column alignment="center" valignment="top" leftline="true" width="0pt">
10285 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
10286 <row topline="true" bottomline="true">
10287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10290 \begin_layout Standard
10296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10299 \begin_layout Standard
10307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10310 \begin_layout Standard
10319 <row bottomline="true">
10320 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10323 \begin_layout Standard
10328 keystrokes after inserting the protected space
10333 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10336 \begin_layout Standard
10342 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10345 \begin_layout Standard
10352 <row bottomline="true">
10353 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10356 \begin_layout Standard
10362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10365 \begin_layout Standard
10366 \begin_inset Formula $A\negmedspace B$
10374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10377 \begin_layout Standard
10378 \begin_inset Formula $A\negthickspace B$
10394 \begin_layout Standard
10395 Negative spaces can lead to characters overlapping each other.
10396 Thus they can be used to enforce ligatures, what is e.\InsetSpace \thinspace{}
10398 useful for summation
10402 \begin_layout Standard
10404 \begin_inset Tabular
10405 <lyxtabular version="3" rows="3" columns="2">
10407 <column alignment="center" valignment="top" leftline="true" width="0">
10408 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10409 <row topline="true" bottomline="true">
10410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10413 \begin_layout Standard
10419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10422 \begin_layout Standard
10424 \begin_inset Note Note
10427 \begin_layout Standard
10434 is only used as spacer.
10445 <row topline="true">
10446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10449 \begin_layout Standard
10458 \begin_layout Standard
10472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10475 \begin_layout Standard
10476 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10485 <row topline="true" bottomline="true">
10486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10489 \begin_layout Standard
10500 \begin_layout Standard
10514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10517 \begin_layout Standard
10518 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10534 \begin_layout Standard
10535 Relations like for example equal signs, are always surrounded by space.
10536 To suppress this, the equal sign is placed into a TeX-brace.
10537 The following example demonstrates this:
10540 \begin_layout Standard
10542 \begin_inset Tabular
10543 <lyxtabular version="3" rows="2" columns="2">
10545 <column alignment="center" valignment="top" width="0pt">
10546 <column alignment="center" valignment="top" width="0pt">
10548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10551 \begin_layout Standard
10557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10560 \begin_layout Standard
10561 \begin_inset Formula $A=B$
10571 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10574 \begin_layout Standard
10575 \begin_inset Note Note
10578 \begin_layout Standard
10585 is only used as spacer.
10591 \begin_inset Formula $\raisebox{5mm}{}$
10594 equation without space
10599 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" usebox="none">
10602 \begin_layout Standard
10603 \begin_inset Formula $A{=}B$
10619 \begin_layout Standard
10621 The command for the last formula is:
10626 \begin_inset Formula $\to$
10632 \begin_layout Standard
10633 \begin_inset VSpace bigskip
10636 Spaces are needed for physical units, because the space between the value
10637 and the unit is the smallest one and not a normal space.
10638 For units in text, the smallest space is inserted via the menu
10640 Insert\SpecialChar \menuseparator
10641 Formatting\SpecialChar \menuseparator
10652 \begin_layout Standard
10653 An example to visualize the difference:
10656 \begin_layout Standard
10657 \begin_inset Tabular
10658 <lyxtabular version="3" rows="2" columns="2">
10660 <column alignment="left" valignment="top" width="0">
10661 <column alignment="left" valignment="top" width="0">
10663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10666 \begin_layout Standard
10668 \begin_inset Formula $\cdot$
10676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10679 \begin_layout Standard
10680 space between value and unit
10687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10690 \begin_layout Standard
10691 24\InsetSpace \thinspace{}
10693 \begin_inset Formula $\cdot$
10701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10704 \begin_layout Standard
10705 smallest space between value and unit
10718 \begin_layout Subsection
10723 \begin_layout Standard
10736 \begin_layout Standard
10737 for vertical space in formulas see
10738 \begin_inset LatexCommand ref
10739 reference "sub:Line-Separation"
10752 \begin_layout Standard
10760 \begin_inset Note Note
10763 \begin_layout Standard
10766 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
10769 \begin_layout Standard
10772 texorpdfstring is in section
10773 \begin_inset LatexCommand ref
10774 reference "sub:Formulas-in-Section"
10784 \begin_inset LatexCommand label
10785 name "sub:Variable-Space"
10790 \begin_inset LatexCommand index
10791 name "Space ! horizontal ! variable"
10798 \begin_layout Standard
10799 Space with a defined length can be inserted in LyX with the command
10808 \begin_inset LatexCommand index
10809 name "Commands ! H ! \\textbackslash hspace"
10814 For the length all units listed in
10815 \begin_inset LatexCommand ref
10816 reference "tab:Used-units"
10820 are allowed, except of the unit
10821 \begin_inset Quotes eld
10825 \begin_inset Quotes erd
10829 The length may also be negative.
10830 To insert so many space that the formula uses all available space, the
10838 \begin_inset LatexCommand index
10839 name "Commands ! H ! \\textbackslash hfill"
10846 \begin_layout Standard
10847 \begin_inset VSpace -1mm
10853 \begin_layout Standard
10855 \begin_inset Tabular
10856 <lyxtabular version="3" rows="4" columns="2">
10858 <column alignment="center" valignment="top" leftline="true" width="0">
10859 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10860 <row topline="true" bottomline="true">
10861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10864 \begin_layout Standard
10870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10873 \begin_layout Standard
10880 <row topline="true">
10881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10884 \begin_layout Standard
10888 \begin_inset Formula $\to$
10898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10901 \begin_layout Standard
10902 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
10911 <row topline="true" bottomline="true">
10912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10915 \begin_layout Standard
10919 \begin_inset Formula $\to$
10929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10932 \begin_layout Standard
10933 \begin_inset Formula $A\hspace{-1mm}A\not=A$
10942 <row topline="true" bottomline="true">
10943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10946 \begin_layout Standard
10953 \begin_layout Standard
10967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10970 \begin_layout Standard
10971 \begin_inset Formula $A=A\hfill B=B$
10987 \begin_layout Standard
10988 In the last example the available space is given by the longest column entry
10990 In an inline formula the space depends on the length of the line in which
10998 Thus, when the line uses the full width, no space will be created.
11005 has only an effect on displayed formulas when the formula style
11010 (Formula styles are explained in
11011 \begin_inset LatexCommand ref
11012 reference "sec:Formula-Styles"
11019 \begin_layout Standard
11032 can also be inserted in TeX-mode to use them for text:
11035 \begin_layout Standard
11036 This is a line with
11040 \begin_layout Standard
11049 2\InsetSpace \thinspace{}
11053 \begin_layout Standard
11054 This is a line with
11059 \begin_layout Standard
11060 In the last example
11066 was inserted via the menu
11068 Insert\SpecialChar \menuseparator
11069 Formatting\SpecialChar \menuseparator
11070 Horizontal\InsetSpace ~
11073 , what is not possible in formulas.
11074 This has the advantage that one can directly see in LyX that this is a
11078 \begin_layout Standard
11079 When the commands are at the begin of a text line but not at the beginning
11080 of a paragraph, they will be ignored by LaTeX.
11081 To avoid that, the command
11094 To get the same with
11100 , a line break and an empty placeholder
11106 \begin_layout Standard
11107 for placeholders see
11108 \begin_inset LatexCommand ref
11109 reference "sub:Placeholders"
11120 is inserted in TeX-mode with the command
11136 \begin_layout Subsection
11137 Space besides inline Formulas
11138 \begin_inset LatexCommand index
11139 name "Space ! besides inline formulas"
11146 \begin_layout Standard
11147 The space that surrounds inline formulas can be adjusted with the length
11153 \begin_inset LatexCommand index
11154 name "Commands ! M ! \\textbackslash mathsurround"
11161 The value of a length is set with the command
11166 \begin_inset LatexCommand index
11167 name "Commands ! S ! \\textbackslash setlength"
11173 that has the following scheme:
11176 \begin_layout Standard
11181 setlength{length name}{value}
11184 \begin_layout Standard
11191 to the value 5\InsetSpace \thinspace{}
11195 \begin_layout Standard
11205 \begin_layout Standard
11206 is inserted in TeX-mode.
11207 5\InsetSpace \thinspace{}
11208 mm space will now be set around all inline formulas:
11212 \begin_layout Standard
11226 \begin_layout Standard
11227 This is a line with an inline formula
11228 \begin_inset Formula $A=B$
11231 with 5\InsetSpace \thinspace{}
11232 mm surrounding space.
11236 \begin_layout Standard
11250 \begin_layout Standard
11251 To return to the predefined value,
11257 is set to the value 0\InsetSpace \thinspace{}
11261 \begin_layout Section
11263 \begin_inset LatexCommand index
11269 \begin_inset LatexCommand index
11270 name "Frames | see {Boxes}"
11277 \begin_layout Standard
11278 Boxes for text are described in chapter
11284 Embedded\InsetSpace ~
11290 \begin_layout Subsection
11292 \begin_inset LatexCommand label
11293 name "sub:Boxes-with-Frame"
11298 \begin_inset LatexCommand index
11299 name "Boxes ! with frame"
11306 \begin_layout Standard
11307 It is possible to frame formulas or parts of it with the commands
11314 \begin_inset LatexCommand index
11315 name "Commands ! F ! \\textbackslash fbox"
11326 \begin_inset LatexCommand index
11327 name "Commands ! B ! \\textbackslash boxed"
11334 \begin_layout Standard
11335 When one of these commands is inserted to a formula, a blue box appears
11336 within a frame to enter formula parts.
11343 an additional formula has to be created by
11351 \begin_layout Standard
11352 Due to a bug in LyX it is not possible to create a new formula with
11360 \begin_layout Standard
11364 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11373 \begin_layout Standard
11385 , because the box content will otherwise be treated as mathematical text.
11392 is used, a new formula is automatically created inside the frame.
11395 \begin_layout Standard
11402 is not suitable to frame displayed formulas, because the formula will always
11403 be set in the size of the text.
11410 is in contrary not suitable to frame inline formulas, because the formula
11411 will always be set in the size of a displayed formula.
11414 \begin_layout Standard
11421 there is the command
11428 \begin_inset LatexCommand index
11429 name "Commands ! F ! \\textbackslash framebox"
11433 where additionally the frame width and the alignment can be specified.
11440 is used in the following scheme:
11443 \begin_layout Standard
11448 framebox[frame width][position]{box content}
11451 \begin_layout Standard
11452 The position can either be
11469 right aligns the formula in the box.
11470 When no position is given, the formula will be centered.
11473 also no position can be given.
11474 In this case the frame width is adjusted to the box content like for
11483 \begin_layout Standard
11490 is inserted, a box appears containing three blue boxes.
11494 \begin_layout Standard
11495 Due to a bug in LyX the cursor has to be placed left beside blue the boxes
11500 \begin_layout Standard
11504 href{http://bugzilla.lyx.org/show_bug.cgi?id=2461}{
11513 \begin_layout Standard
11525 The first two boxes are surrounded by brackets and denote the two optional
11527 The third box is for formula parts like for
11536 \begin_layout Standard
11538 \begin_inset Note Note
11541 \begin_layout Standard
11542 The table has been set into a minipage to make the footnote appearing.
11543 Otherwise the footnote text would not be displayed.
11549 \begin_inset Box Frameless
11558 height_special "totalheight"
11561 \begin_layout Standard
11563 \begin_inset Tabular
11564 <lyxtabular version="3" rows="5" columns="2">
11566 <column alignment="center" valignment="top" leftline="true" width="0">
11567 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
11568 <row topline="true" bottomline="true">
11569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11572 \begin_layout Standard
11577 \begin_layout Standard
11578 Due to a bug in LyX it is not possible to create a new formula with
11586 \begin_layout Standard
11590 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11599 \begin_layout Standard
11616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11619 \begin_layout Standard
11621 \begin_inset Note Note
11624 \begin_layout Standard
11631 is only used as spacer.
11642 <row topline="true">
11643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11646 \begin_layout Standard
11653 \begin_layout Standard
11672 \begin_layout Standard
11686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11689 \begin_layout Standard
11690 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
11700 <row topline="true">
11701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11704 \begin_layout Standard
11711 \begin_layout Standard
11726 \begin_layout Standard
11740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11743 \begin_layout Standard
11744 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
11753 <row topline="true">
11754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11757 \begin_layout Standard
11764 \begin_layout Standard
11778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11781 \begin_layout Standard
11782 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
11791 <row topline="true" bottomline="true">
11792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11795 \begin_layout Standard
11802 \begin_layout Standard
11812 \begin_inset Formula $\to$
11816 \begin_inset Formula $\to$
11829 \begin_layout Standard
11839 \begin_inset Formula $\downarrow$
11847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11850 \begin_layout Standard
11851 \begin_inset Formula $\raisebox{6mm}{}$
11855 \begin_inset Formula $\framebox[20mm]{$\frac{A}{B}$}$
11859 \begin_inset Formula $\raisebox{-4mm}{}$
11880 \begin_layout Standard
11881 The frame thickness can also be adjusted.
11882 To do this the following commands have to be inserted in TeX-mode before
11886 \begin_layout Standard
11896 \begin_inset Quotes eld
11900 \begin_inset Quotes erd
11914 \begin_inset Quotes eld
11918 \begin_inset Quotes erd
11924 \begin_layout Standard
11925 \begin_inset Quotes eld
11929 \begin_inset Quotes erd
11932 specifies the minimal distance between the frame and the first character
11934 An example for this is the following framed formula:
11938 \begin_layout Standard
11950 \begin_inset Formula \[
11955 Before this formula the commands
11958 \begin_layout Standard
11980 \begin_layout Standard
11981 were inserted in TeX-mode.
11982 The given values are used for all following boxes.
11985 \begin_layout Standard
11986 To return to the standard frame size, the command
11989 \begin_layout Standard
12014 \begin_layout Standard
12028 \begin_layout Standard
12029 is inserted in TeX-mode before the next formula.
12032 \begin_layout Subsection
12033 Boxes without Frame
12034 \begin_inset LatexCommand label
12035 name "sub:Boxes-without-Frame"
12040 \begin_inset LatexCommand index
12041 name "Boxes ! without frame"
12048 \begin_layout Standard
12049 For boxes without a frame there are the following box commands:
12056 \begin_inset LatexCommand index
12057 name "Commands ! M ! \\textbackslash mbox"
12068 \begin_inset LatexCommand index
12069 name "Commands ! M ! \\textbackslash makebox"
12080 \begin_inset LatexCommand index
12081 name "Commands ! R ! \\textbackslash raisebox"
12088 \begin_layout Standard
12095 a box can be super- or subscripted.
12096 But in contrary to normal super- and subscripting, the characters in the
12097 box keep their font size.
12104 is used in the following scheme:
12107 \begin_layout Standard
12112 raisebox{height}{box content}
12115 \begin_layout Standard
12116 When the box should contain a formula, an extra formula is needed like for
12126 \begin_layout Standard
12128 \begin_inset Tabular
12129 <lyxtabular version="3" rows="4" columns="2">
12131 <column alignment="center" valignment="top" leftline="true" width="0">
12132 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12133 <row topline="true" bottomline="true">
12134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12137 \begin_layout Standard
12143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12146 \begin_layout Standard
12153 <row topline="true">
12154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12157 \begin_layout Standard
12161 \begin_inset Formula $\to$
12167 \begin_inset Formula $\to$
12175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12178 \begin_layout Standard
12179 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12188 <row topline="true" bottomline="true">
12189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12192 \begin_layout Standard
12196 \begin_inset Formula $\to$
12202 \begin_inset Formula $\to$
12210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12213 \begin_layout Standard
12214 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12223 <row topline="true" bottomline="true">
12224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12227 \begin_layout Standard
12231 \begin_inset Formula $\to$
12246 \begin_layout Standard
12260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12263 \begin_layout Standard
12267 \begin_layout Standard
12291 \begin_layout Standard
12292 The last formula can currently only be created using TeX-mode because LyX
12293 inserts a box instead of the needed extra formula.
12297 \begin_layout Standard
12302 \begin_layout Standard
12306 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12315 \begin_layout Standard
12330 \begin_layout Standard
12355 , with the difference that there is no frame.
12358 \begin_layout Subsection
12360 \begin_inset LatexCommand label
12361 name "sub:Colored-Boxes"
12366 \begin_inset LatexCommand index
12367 name "Boxes ! colored"
12374 \begin_layout Standard
12375 To be able to use all commands explained in this section, the LaTeX-package
12384 \begin_layout Standard
12389 is part of every LaTeX standard installation.
12395 \begin_inset LatexCommand index
12396 name "Packages ! color"
12400 has to be loaded in the LaTeX-preamble with the line
12404 \begin_layout Standard
12405 When text is colored somewhere in the document with a predefined color,
12406 LyX loads the LaTeX-package
12411 Thus it is possible that the package is loaded twice, but this doesn't
12418 \begin_inset Note Note
12421 \begin_layout Standard
12422 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12431 \begin_layout Standard
12439 \begin_layout Standard
12440 \begin_inset VSpace medskip
12443 To color boxes, the command
12450 \begin_inset LatexCommand index
12451 name "Commands ! C ! \\textbackslash colorbox"
12455 is used in the following scheme:
12458 \begin_layout Standard
12463 colorbox{color}{box content}
12466 \begin_layout Standard
12467 The box content can also be a box and a
12473 can also be part of another box (see the 2nd and 3rd example).
12474 When the box should contain a formula, an extra formula has to be created,
12485 \begin_layout Standard
12486 This also applies for the command
12497 \begin_layout Standard
12501 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12510 \begin_layout Standard
12525 \begin_layout Standard
12526 One of the following predefined colors can be chosen:
12529 \begin_layout Standard
12563 \begin_layout Standard
12565 \begin_inset Tabular
12566 <lyxtabular version="3" rows="4" columns="2">
12568 <column alignment="center" valignment="top" leftline="true" width="0">
12569 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12570 <row topline="true" bottomline="true">
12571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12574 \begin_layout Standard
12580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12583 \begin_layout Standard
12585 \begin_inset Note Note
12588 \begin_layout Standard
12595 is only used as spacer.
12606 <row topline="true">
12607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12610 \begin_layout Standard
12614 \begin_inset Formula $\to$
12624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12627 \begin_layout Standard
12628 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12637 <row topline="true">
12638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12641 \begin_layout Standard
12645 \begin_inset Formula $\to$
12656 \begin_layout Standard
12670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12673 \begin_layout Standard
12674 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
12683 <row topline="true" bottomline="true">
12684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12687 \begin_layout Standard
12694 \begin_layout Standard
12706 \begin_inset Formula $\to$
12716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12719 \begin_layout Standard
12720 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
12736 \begin_layout Standard
12743 only colors the box but not the characters in the box.
12744 To color all characters, the whole formula is highlighted and the wanted
12745 color is chosen in the
12751 The dialog can be called with the toolbar button
12752 \begin_inset Graphics
12753 filename ../images/dialog-show_character.png
12760 Edit\SpecialChar \menuseparator
12762 Style\SpecialChar \menuseparator
12766 The formula number has then the same color as the formula.
12767 When the formula number should get another color than the formula characters,
12768 the color must be changed within the formula.
12771 \begin_layout Standard
12775 \begin_layout Standard
12778 \begin_inset Formula \begin{equation}
12779 \int A=B\label{eq:red}\end{equation}
12786 \begin_inset Formula \begin{equation}
12787 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
12794 \begin_layout Standard
12796 \begin_inset LatexCommand eqref
12801 is completely colored red.
12804 \begin_inset LatexCommand eqref
12805 reference "eq:redgreen"
12809 was first completely colored green to set the color for the formula number.
12810 Subsequently the formula characters were colored red.
12813 \begin_layout Standard
12814 \begin_inset VSpace bigskip
12817 To color the frame different than the rest of the box, the command
12824 \begin_inset LatexCommand index
12825 name "Commands ! F ! \\textbackslash fcolorbox"
12829 is used in the following scheme:
12832 \begin_layout Standard
12837 fcolorbox{frame color}{color}{box content}
12840 \begin_layout Standard
12847 is an extension of the command
12854 The frame width is set, like for
12877 \begin_layout Standard
12889 \begin_inset Formula \[
12890 \fcolorbox{cyan}{magenta}{A=B}\]
12898 \begin_layout Standard
12912 \begin_layout Standard
12913 This formula was created with the command
12920 \begin_inset Formula $\to$
12926 \begin_inset Formula $\to$
12936 \begin_layout Standard
12937 \begin_inset VSpace bigskip
12940 To use other colors than the predefined ones, they have to be defined first.
12943 \begin_layout Standard
12944 One can for example define the color
12945 \begin_inset Quotes eld
12953 \begin_inset Quotes erd
12956 with the LaTeX-preamble line:
12959 \begin_layout Standard
12964 definecolor{darkgreen}{cmyk}{0.5,
12979 \begin_inset LatexCommand index
12980 name "Commands ! D ! \\textbackslash definecolor"
12987 \begin_layout Standard
12992 is the color space that denotes the colors
13009 The four comma separated numbers are the portion factor for the corresponding
13010 colors of the color space.
13011 The factors can be in the range of 0\InsetSpace \thinspace{}
13012 -\InsetSpace \thinspace{}
13018 also the color space
13022 can be used for definitions.
13039 , so that there are in this case three portion factors for the corresponding
13041 Furthermore there is the color space
13045 with one portion factor for the gray value.
13048 \begin_layout Standard
13049 As example a framed box with the new defined color
13053 where the characters have been colored
13058 \begin_inset Formula \begin{equation}
13059 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13066 \begin_layout Standard
13067 Self-defined colors can also be be used for text with the help of the command
13075 \begin_inset LatexCommand index
13076 name "Text ! colored"
13083 \begin_layout Standard
13087 \begin_layout Standard
13091 textcolor{darkgreen}{
13097 \begin_inset Quotes eld
13101 \begin_inset Quotes erd
13108 \begin_layout Standard
13118 \begin_layout Standard
13126 \begin_inset LatexCommand index
13127 name "Commands ! T ! \\textbackslash textcolor"
13131 is used in the scheme
13135 textcolor{color}{characters to color}
13140 \begin_layout Subsection
13142 \begin_inset LatexCommand label
13143 name "sub:Paragraph-Boxes"
13148 \begin_inset LatexCommand index
13149 name "Boxes ! as paragraph"
13156 \begin_layout Standard
13157 A box that can contain several lines and paragraphs, a so called paragraph
13158 box (parbox), can be created with the menu
13160 Insert\SpecialChar \menuseparator
13163 or the toolbar button
13164 \begin_inset Graphics
13165 filename ../images/box-insert.png
13173 \begin_layout Standard
13174 The following example shows a framed parbox in a line:
13177 \begin_layout Standard
13178 \begin_inset VSpace medskip
13182 \begin_inset Box Boxed
13191 height_special "totalheight"
13194 \begin_layout Standard
13195 This is a paragraph box.
13196 It is exactly 5\InsetSpace \thinspace{}
13197 cm long and can also contain formulas:
13198 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13209 \begin_layout Standard
13210 \begin_inset VSpace medskip
13216 \begin_layout Standard
13217 Such a box is created by right-clicking on the gray box inset.
13218 A dialog pops up showing the box properties.
13231 : 5\InsetSpace \thinspace{}
13234 Vertical Box Alignment
13239 \begin_layout Standard
13240 \begin_inset VSpace medskip
13243 In LaTeX a parbox is created with the command
13250 \begin_inset LatexCommand index
13251 name "Commands ! P ! \\textbackslash parbox"
13255 that has the following scheme:
13258 \begin_layout Standard
13263 parbox[position]{width}{box content}
13266 \begin_layout Standard
13280 for bottom means that the box is aligned within the surrounding text with
13286 for top this is done with the first line.
13287 When no position is given, the box will be vertically centered, see section
13294 Embedded\InsetSpace ~
13297 manual for examples.
13300 \begin_layout Standard
13301 \begin_inset VSpace bigskip
13304 To frame formulas completely, including the formula number, the formula
13305 must be set into a parbox.
13306 To do this, the command
13320 is inserted in TeX-mode before the formula.
13326 \begin_inset LatexCommand index
13327 name "Commands ! L ! \\textbackslash linewidth"
13333 is hereby the line width set for the document.
13334 Because the frame is outside the parbox, 2\InsetSpace \thinspace{}
13335 times the frame separation and
13336 the frame thickness must be subtracted from the line width.
13337 As this is not automatically done by LyX due to a bug
13341 \begin_layout Standard
13345 \begin_layout Standard
13349 href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
13358 \begin_layout Standard
13370 , TeX-mode has to be used.
13371 To be able to multiply and subtract in arguments, the LaTeX-package
13379 \begin_layout Standard
13384 is part of every LaTeX standard installation.
13390 \begin_inset LatexCommand index
13391 name "Packages ! calc"
13395 must be loaded in the LaTeX-preamble with the line
13398 \begin_layout Standard
13406 \begin_layout Standard
13407 Behind the formula both boxes are closed by entering
13412 Here is an example:
13416 \begin_layout Standard
13430 \begin_layout Standard
13434 \begin_layout Standard
13452 \begin_inset Formula \begin{equation}
13453 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
13461 \begin_layout Standard
13472 \begin_layout Standard
13486 \begin_layout Standard
13487 \begin_inset VSpace medskip
13490 As a parbox is used as argument of
13496 , there is in this case no difference between
13511 \begin_layout Standard
13512 \begin_inset VSpace bigskip
13515 Paragraph boxes are very useful to comment formulas directly.
13522 is used in combination with the command
13536 \begin_inset LatexCommand ref
13537 reference "sub:User-defined-Numbering"
13544 \begin_layout Standard
13545 An example of a formula commented with
13554 \begin_layout Standard
13558 \begin_layout Standard
13571 This is a description.
13572 It is distinctly separated from the formula and multiline.
13576 \begin_layout Standard
13588 \begin_layout Standard
13589 Such a formula must be inserted completely in TeX-mode because LyX does
13590 not yet support the command
13597 The formula is created with the following command sequence:
13600 \begin_layout Standard
13613 is inserted in TeX-mode.
13617 \begin_layout Standard
13618 When the formula style
13630 can also be replaced by
13637 (formula styles see
13638 \begin_inset LatexCommand ref
13639 reference "sec:Formula-Styles"
13648 Then the description follows as normal text, and finally
13654 is inserted in TeX-mode.
13667 hereby create a displayed formula.
13670 \begin_layout Standard
13677 can be seen in this example that was
13678 \begin_inset Quotes eld
13682 \begin_inset Quotes erd
13685 using the mathematical textmode:
13686 \begin_inset Formula \[
13687 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
13694 \begin_layout Section
13696 \begin_inset LatexCommand index
13704 \begin_layout Subsection
13706 \begin_inset LatexCommand label
13707 name "sub:Big-Operators"
13712 \begin_inset LatexCommand index
13713 name "Operators ! big"
13718 \begin_inset LatexCommand index
13724 \begin_inset LatexCommand index
13732 \begin_layout Standard
13733 To be able to use all integral operators listed here, the option
13735 Use esint package automatically
13737 must be set in the document settings under
13745 \begin_layout Standard
13749 \begin_inset Tabular
13750 <lyxtabular version="3" rows="11" columns="2">
13752 <column alignment="center" valignment="top" leftline="true" width="0pt">
13753 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13754 <row topline="true" bottomline="true">
13755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13758 \begin_layout Standard
13764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13767 \begin_layout Standard
13774 <row topline="true">
13775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13778 \begin_layout Standard
13782 \begin_inset LatexCommand index
13783 name "Commands ! S ! \\textbackslash sum"
13792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13795 \begin_layout Standard
13796 \begin_inset Formula $\sum$
13805 <row topline="true">
13806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13809 \begin_layout Standard
13813 \begin_inset LatexCommand index
13814 name "Commands ! I ! \\textbackslash int"
13823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13826 \begin_layout Standard
13827 \begin_inset Formula $\int$
13836 <row topline="true">
13837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13840 \begin_layout Standard
13848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13851 \begin_layout Standard
13852 \begin_inset Formula $\intop$
13861 <row topline="true">
13862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13865 \begin_layout Standard
13873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13876 \begin_layout Standard
13877 \begin_inset Formula $\oint$
13886 <row topline="true">
13887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13890 \begin_layout Standard
13898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13901 \begin_layout Standard
13902 \begin_inset Formula $\ointop$
13911 <row topline="true">
13912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13915 \begin_layout Standard
13923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13926 \begin_layout Standard
13927 \begin_inset Formula $\ointctrclockwise$
13936 <row topline="true">
13937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13940 \begin_layout Standard
13948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13951 \begin_layout Standard
13952 \begin_inset Formula $\ointclockwise$
13961 <row topline="true">
13962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13965 \begin_layout Standard
13973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13976 \begin_layout Standard
13977 \begin_inset Formula $\sqint$
13986 <row topline="true">
13987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13990 \begin_layout Standard
13998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14001 \begin_layout Standard
14002 \begin_inset Formula $\bigcap$
14011 <row topline="true" bottomline="true">
14012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14015 \begin_layout Standard
14023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14026 \begin_layout Standard
14027 \begin_inset Formula $\bigcup$
14043 \begin_inset Tabular
14044 <lyxtabular version="3" rows="10" columns="2">
14046 <column alignment="center" valignment="top" leftline="true" width="0pt">
14047 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
14048 <row topline="true" bottomline="true">
14049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14052 \begin_layout Standard
14058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14061 \begin_layout Standard
14068 <row topline="true">
14069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14072 \begin_layout Standard
14076 \begin_inset LatexCommand index
14077 name "Commands ! P ! \\textbackslash prod"
14086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14089 \begin_layout Standard
14090 \begin_inset Formula $\prod$
14099 <row topline="true">
14100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14103 \begin_layout Standard
14111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14114 \begin_layout Standard
14115 \begin_inset Formula $\coprod$
14124 <row topline="true">
14125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14128 \begin_layout Standard
14136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14139 \begin_layout Standard
14140 \begin_inset Formula $\bigodot$
14149 <row topline="true">
14150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14153 \begin_layout Standard
14161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14164 \begin_layout Standard
14165 \begin_inset Formula $\bigotimes$
14174 <row topline="true">
14175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14178 \begin_layout Standard
14186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14189 \begin_layout Standard
14190 \begin_inset Formula $\bigoplus$
14199 <row topline="true">
14200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14203 \begin_layout Standard
14211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14214 \begin_layout Standard
14215 \begin_inset Formula $\bigwedge$
14224 <row topline="true">
14225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14228 \begin_layout Standard
14236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14239 \begin_layout Standard
14240 \begin_inset Formula $\bigvee$
14249 <row topline="true">
14250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14253 \begin_layout Standard
14261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14264 \begin_layout Standard
14265 \begin_inset Formula $\bigsqcup$
14274 <row topline="true" bottomline="true">
14275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14278 \begin_layout Standard
14286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14289 \begin_layout Standard
14290 \begin_inset Formula $\biguplus$
14308 \begin_layout Standard
14309 All big operators can also be inserted via the math toolbar button
14310 \begin_inset Graphics
14311 filename ../images/math/intop.png
14319 \begin_layout Standard
14320 The operators are called big because they are bigger than the sometimes
14321 equal looking binary operators.
14322 All big operators can have limits as described in the next subsection.
14325 \begin_layout Standard
14350 , resp.\InsetSpace ~
14351 in the style the operator limits are displayed, see
14352 \begin_inset LatexCommand ref
14353 reference "sub:Operator-Limits"
14361 \begin_layout Subsubsection*
14362 Advices for Integrals
14365 \begin_layout Standard
14370 in an integral is an operator, that therefore has to be set upright.
14371 This is done by highlighting the
14375 and using the keyboard shortcut
14384 \begin_layout Standard
14390 \begin_inset LatexCommand ref
14391 reference "sub:Font-Styles"
14401 Finally the smallest space is inserted before the
14405 , as this is usual for operators.
14409 \begin_layout Standard
14411 \begin_inset Formula $\int A(x)dx$
14420 \begin_layout Standard
14430 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14436 \begin_layout Standard
14437 For multiple integrals there are the following commands:
14438 \begin_inset VSpace medskip
14444 \begin_layout Standard
14448 \begin_inset Tabular
14449 <lyxtabular version="3" rows="4" columns="2">
14451 <column alignment="center" valignment="top" leftline="true" width="0">
14452 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14453 <row topline="true" bottomline="true">
14454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14457 \begin_layout Standard
14463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14466 \begin_layout Standard
14468 \begin_inset Note Note
14471 \begin_layout Standard
14478 is only used as spacer.
14489 <row topline="true">
14490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14493 \begin_layout Standard
14501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14504 \begin_layout Standard
14505 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
14514 <row topline="true">
14515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14518 \begin_layout Standard
14526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14529 \begin_layout Standard
14530 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
14539 <row topline="true" bottomline="true">
14540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14543 \begin_layout Standard
14551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14554 \begin_layout Standard
14555 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
14571 \begin_inset Tabular
14572 <lyxtabular version="3" rows="4" columns="2">
14574 <column alignment="center" valignment="top" leftline="true" width="0">
14575 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14576 <row topline="true" bottomline="true">
14577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14580 \begin_layout Standard
14586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14589 \begin_layout Standard
14596 <row topline="true">
14597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14600 \begin_layout Standard
14608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14611 \begin_layout Standard
14612 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
14621 <row topline="true">
14622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14625 \begin_layout Standard
14633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14636 \begin_layout Standard
14637 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
14646 <row topline="true" bottomline="true">
14647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14650 \begin_layout Standard
14658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14661 \begin_layout Standard
14662 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
14680 \begin_layout Subsection
14682 \begin_inset LatexCommand label
14683 name "sub:Operator-Limits"
14688 \begin_inset LatexCommand index
14689 name "Operators ! Limits"
14696 \begin_layout Standard
14697 Limits are created by super- and subscripts:
14700 \begin_layout Standard
14702 \begin_inset Tabular
14703 <lyxtabular version="3" rows="2" columns="2">
14705 <column alignment="center" valignment="top" leftline="true" width="0pt">
14706 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
14707 <row topline="true" bottomline="true">
14708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14711 \begin_layout Standard
14717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14720 \begin_layout Standard
14722 \begin_inset Note Note
14725 \begin_layout Standard
14732 is only used as spacer.
14743 <row topline="true" bottomline="true">
14744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14747 \begin_layout Standard
14756 \begin_layout Standard
14766 \begin_inset Formula $\to$
14770 \begin_inset Formula $\to$
14778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14781 \begin_layout Standard
14782 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
14798 \begin_layout Standard
14799 Limits of inline formulas are set right beside the operator.
14800 Limits in displayed formulas are set above or below the operator, except
14801 of integral limits.
14804 \begin_layout Standard
14805 To force that the limits are set beside the operator, the cursor is set
14806 directly behind the operator and the limits type is changed with the menu
14809 Edit\SpecialChar \menuseparator
14810 Math\SpecialChar \menuseparator
14828 \begin_layout Standard
14829 The default limits type is this:
14830 \begin_inset Formula \[
14831 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
14835 This is how it looks when the limits type was changed to
14842 \begin_inset Formula \[
14843 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
14847 For integrals, except of
14859 , the limits are by default set beside the operator.
14860 But for multiple integrals the limits are often set below the operator.
14861 In the following example the limits type was therefore set to
14865 and so set below the integrals:
14866 \begin_inset Formula \begin{equation}
14867 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
14874 \begin_layout Standard
14875 \begin_inset VSpace medskip
14878 To specify conditions for limits, the commands
14885 \begin_inset LatexCommand index
14886 name "Commands ! S ! \\textbackslash subarray"
14897 \begin_inset LatexCommand index
14898 name "Commands ! S ! \\textbackslash substack"
14903 To create for example this expression
14904 \begin_inset Formula \begin{equation}
14905 \sum_{\begin{subarray}{c}
14907 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
14914 \begin_layout Standard
14915 the following has to be done:
14929 \begin_layout Standard
14941 One is now in a blue box under the summation operator and insert there
14950 \begin_layout Standard
14962 The blue box is now within a purple box and now several lines can be written
14964 A new line is created by inserting a line break (
14973 0<k<1000 Ctrl-Return
14977 is typed in, a new box appears below for the new line.
14980 \begin_layout Standard
14981 The alignment of the lines can be changed to left aligned with the
14991 Edit\SpecialChar \menuseparator
14995 To get right alignment,
15003 \begin_layout Standard
15014 is inserted at the beginning of the line.
15017 \begin_layout Standard
15030 with the difference that the lines are always centered.
15033 \begin_layout Standard
15034 \begin_inset VSpace bigskip
15038 \begin_inset LatexCommand eqref
15039 reference "eq:substack"
15043 there can be too much space beside an operator, because the characters
15044 following the operator are set beside the limits.
15047 \begin_layout Standard
15048 To avoid this, the following macro can be used in the LaTeX-preamble:
15051 \begin_layout Standard
15080 mathclapinternal #1#2{
15084 mathsurround =0pt #1{#2}$}}
15087 \begin_layout Standard
15088 This defines the command
15095 \begin_inset LatexCommand index
15096 name "Commands ! M ! \\textbackslash mathclap"
15100 that sets the width of the limit to 0\InsetSpace \thinspace{}
15102 The command scheme is
15105 \begin_layout Standard
15113 \begin_layout Standard
15114 where the limit can consist of several conditions.
15117 \begin_layout Standard
15119 \begin_inset LatexCommand eqref
15120 reference "eq:substack"
15124 , one uses the command
15127 \begin_layout Standard
15140 \begin_layout Standard
15149 0<k<1000 Ctrl-Enter
15152 \begin_layout Standard
15153 to create the lower limit.
15154 The summand is now directly behind the summation operator:
15155 \begin_inset Formula \[
15156 \sum_{\mathclap{\substack{0<k<1000\\
15157 \\k\,\in\,\mathbb{N}}
15165 \begin_layout Standard
15166 \begin_inset VSpace bigskip
15169 How to use one limit for several operators is described in
15170 \begin_inset LatexCommand ref
15171 reference "sub:Self-defined-Operators"
15178 \begin_layout Subsection
15180 \begin_inset LatexCommand label
15181 name "sub:Binary-Operators"
15186 \begin_inset LatexCommand index
15187 name "Operators ! binary"
15194 \begin_layout Standard
15195 Binary operators are surrounded by space when there is a character before
15197 \begin_inset VSpace medskip
15203 \begin_layout Standard
15207 \begin_inset Tabular
15208 <lyxtabular version="3" rows="13" columns="2">
15210 <column alignment="center" valignment="top" leftline="true" width="0pt">
15211 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15212 <row topline="true" bottomline="true">
15213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15216 \begin_layout Standard
15218 \begin_inset Note Note
15221 \begin_layout Standard
15228 is only used as spacer.
15238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15241 \begin_layout Standard
15248 <row topline="true">
15249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15252 \begin_layout Standard
15258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15261 \begin_layout Standard
15262 \begin_inset Formula $+$
15271 <row topline="true">
15272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15275 \begin_layout Standard
15281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15284 \begin_layout Standard
15285 \begin_inset Formula $-$
15294 <row topline="true">
15295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15298 \begin_layout Standard
15306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15309 \begin_layout Standard
15310 \begin_inset Formula $\pm$
15319 <row topline="true">
15320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15323 \begin_layout Standard
15331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15334 \begin_layout Standard
15335 \begin_inset Formula $\mp$
15344 <row topline="true">
15345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15348 \begin_layout Standard
15356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15359 \begin_layout Standard
15360 \begin_inset Formula $\cdot$
15369 <row topline="true">
15370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15373 \begin_layout Standard
15381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15384 \begin_layout Standard
15385 \begin_inset Formula $\times$
15394 <row topline="true">
15395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15398 \begin_layout Standard
15406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15409 \begin_layout Standard
15410 \begin_inset Formula $\div$
15419 <row topline="true">
15420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15423 \begin_layout Standard
15427 \begin_layout Standard
15440 \begin_layout Standard
15452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15455 \begin_layout Standard
15456 \begin_inset Formula $*$
15465 <row topline="true">
15466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15469 \begin_layout Standard
15477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15480 \begin_layout Standard
15481 \begin_inset Formula $\star$
15490 <row topline="true">
15491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15494 \begin_layout Standard
15502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15505 \begin_layout Standard
15506 \begin_inset Formula $\circ$
15515 <row topline="true">
15516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15519 \begin_layout Standard
15527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15530 \begin_layout Standard
15531 \begin_inset Formula $\diamond$
15540 <row topline="true" bottomline="true">
15541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15544 \begin_layout Standard
15552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15555 \begin_layout Standard
15556 \begin_inset Formula $\bullet$
15572 \begin_inset Tabular
15573 <lyxtabular version="3" rows="13" columns="2">
15575 <column alignment="center" valignment="top" leftline="true" width="0pt">
15576 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15577 <row topline="true" bottomline="true">
15578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15581 \begin_layout Standard
15587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15590 \begin_layout Standard
15597 <row topline="true">
15598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15601 \begin_layout Standard
15609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15612 \begin_layout Standard
15613 \begin_inset Formula $\nabla$
15622 <row topline="true">
15623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15626 \begin_layout Standard
15634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15637 \begin_layout Standard
15638 \begin_inset Formula $\bigtriangledown$
15647 <row topline="true">
15648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15651 \begin_layout Standard
15659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15662 \begin_layout Standard
15663 \begin_inset Formula $\bigtriangleup$
15672 <row topline="true">
15673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15676 \begin_layout Standard
15684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15687 \begin_layout Standard
15688 \begin_inset Formula $\Box$
15697 <row topline="true">
15698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15701 \begin_layout Standard
15709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15712 \begin_layout Standard
15713 \begin_inset Formula $\cap$
15722 <row topline="true">
15723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15726 \begin_layout Standard
15734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15737 \begin_layout Standard
15738 \begin_inset Formula $\cup$
15747 <row topline="true">
15748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15751 \begin_layout Standard
15759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15762 \begin_layout Standard
15763 \begin_inset Formula $\dagger$
15772 <row topline="true">
15773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15776 \begin_layout Standard
15784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15787 \begin_layout Standard
15788 \begin_inset Formula $\ddagger$
15797 <row topline="true">
15798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15801 \begin_layout Standard
15809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15812 \begin_layout Standard
15813 \begin_inset Formula $\wr$
15822 <row topline="true">
15823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15826 \begin_layout Standard
15834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15837 \begin_layout Standard
15838 \begin_inset Formula $\bigcirc$
15847 <row topline="true">
15848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15851 \begin_layout Standard
15859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15862 \begin_layout Standard
15863 \begin_inset Formula $\wedge$
15872 <row topline="true" bottomline="true">
15873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15876 \begin_layout Standard
15884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15887 \begin_layout Standard
15888 \begin_inset Formula $\vee$
15904 \begin_inset Tabular
15905 <lyxtabular version="3" rows="13" columns="2">
15907 <column alignment="center" valignment="top" leftline="true" width="0pt">
15908 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15909 <row topline="true" bottomline="true">
15910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15913 \begin_layout Standard
15919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15922 \begin_layout Standard
15929 <row topline="true">
15930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15933 \begin_layout Standard
15941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15944 \begin_layout Standard
15945 \begin_inset Formula $\oplus$
15954 <row topline="true">
15955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15958 \begin_layout Standard
15966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15969 \begin_layout Standard
15970 \begin_inset Formula $\ominus$
15979 <row topline="true">
15980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15983 \begin_layout Standard
15991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15994 \begin_layout Standard
15995 \begin_inset Formula $\otimes$
16004 <row topline="true">
16005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16008 \begin_layout Standard
16016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16019 \begin_layout Standard
16020 \begin_inset Formula $\oslash$
16029 <row topline="true">
16030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16033 \begin_layout Standard
16041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16044 \begin_layout Standard
16045 \begin_inset Formula $\odot$
16054 <row topline="true">
16055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16058 \begin_layout Standard
16066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16069 \begin_layout Standard
16070 \begin_inset Formula $\amalg$
16079 <row topline="true">
16080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16083 \begin_layout Standard
16091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16094 \begin_layout Standard
16095 \begin_inset Formula $\uplus$
16104 <row topline="true">
16105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16108 \begin_layout Standard
16116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16119 \begin_layout Standard
16120 \begin_inset Formula $\setminus$
16129 <row topline="true">
16130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16133 \begin_layout Standard
16141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16144 \begin_layout Standard
16145 \begin_inset Formula $\sqcap$
16154 <row topline="true">
16155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16158 \begin_layout Standard
16166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16169 \begin_layout Standard
16170 \begin_inset Formula $\sqcup$
16179 <row topline="true">
16180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16183 \begin_layout Standard
16191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16194 \begin_layout Standard
16195 \begin_inset Formula $\triangleleft$
16204 <row topline="true" bottomline="true">
16205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16208 \begin_layout Standard
16216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16219 \begin_layout Standard
16220 \begin_inset Formula $\triangleright$
16238 \begin_layout Standard
16239 All binary operators can also be inserted via the math toolbar button
16240 \begin_inset Graphics
16241 filename ../images/math/pm.png
16249 \begin_layout Standard
16250 To typeset the Laplace operator also
16267 \begin_inset Formula $\nabla^{2}$
16270 ) can be used instead of
16279 \begin_layout Standard
16286 Insert\SpecialChar \menuseparator
16298 \begin_layout Subsection
16299 Self-defined Operators
16300 \begin_inset LatexCommand label
16301 name "sub:Self-defined-Operators"
16306 \begin_inset LatexCommand index
16307 name "Operators ! self-defined"
16314 \begin_layout Standard
16315 With the help of the command
16319 DeclareMathOperator
16322 \begin_inset LatexCommand index
16323 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
16327 custom operators can be defined in the LaTeX-preamble.
16328 Its command scheme is:
16331 \begin_layout Standard
16336 DeclareMathOperator{new command}{display}
16339 \begin_layout Standard
16340 Display can be characters or symbols that define how the operator looks
16342 To define a big operator a * is set behind the command.
16343 All self-defined big operators can have limits as described in
16344 \begin_inset LatexCommand ref
16345 reference "sub:Operator-Limits"
16352 \begin_layout Standard
16353 For example the LaTeX-preamble line
16356 \begin_layout Standard
16361 DeclareMathOperator*{
16368 \begin_layout Standard
16369 defines the command
16375 , that inserts a big operator consisting of the lozenge symbol from
16376 \begin_inset LatexCommand ref
16377 reference "sub:Miscellaneous-Symbols"
16382 \begin_inset Formula \[
16383 \Lozenge_{n=1}^{\infty}\]
16387 The command for this formula is:
16398 \begin_inset Formula $\to$
16404 \begin_layout Standard
16405 \begin_inset VSpace bigskip
16408 When self-defined operators are not used several times in the document,
16409 they can also be defined with the commands
16416 \begin_inset LatexCommand index
16417 name "Commands ! M ! \\textbackslash mathop"
16428 \begin_inset LatexCommand index
16429 name "Commands ! M ! \\textbackslash mathbin"
16433 , which have the following scheme:
16436 \begin_layout Standard
16450 \begin_layout Standard
16457 defines big operators,
16466 \begin_layout Standard
16473 can e.\InsetSpace \thinspace{}
16475 be used to use one limit for several operators:
16478 \begin_layout Standard
16479 \begin_inset Formula \[
16480 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
16487 \begin_layout Standard
16488 The command for the formula above is:
16506 \begin_layout Standard
16518 \begin_inset Formula $\to$
16527 \begin_layout Standard
16541 \begin_layout Section
16543 \begin_inset LatexCommand index
16551 \begin_layout Subsection
16553 \begin_inset LatexCommand label
16554 name "sub:Font-Styles"
16559 \begin_inset LatexCommand index
16560 name "Font ! style"
16567 \begin_layout Standard
16568 Latin letters in formulas can be set in one of the following font styles:
16569 \begin_inset VSpace -2mm
16575 \begin_layout Standard
16577 \begin_inset Tabular
16578 <lyxtabular version="3" rows="6" columns="3">
16580 <column alignment="center" valignment="top" leftline="true" width="0">
16581 <column alignment="center" valignment="top" leftline="true" width="0">
16582 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16583 <row topline="true" bottomline="true">
16584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16587 \begin_layout Standard
16593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16596 \begin_layout Standard
16602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16605 \begin_layout Standard
16612 <row topline="true">
16613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16616 \begin_layout Standard
16625 \begin_layout Standard
16641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16644 \begin_layout Standard
16645 \begin_inset Formula $\mathbb{ABC}$
16653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16656 \begin_layout Standard
16663 <row topline="true">
16664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16667 \begin_layout Standard
16676 \begin_layout Standard
16692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16695 \begin_layout Standard
16696 \begin_inset Formula $\mathbf{AbC}$
16704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16707 \begin_layout Standard
16714 <row topline="true">
16715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16718 \begin_layout Standard
16727 \begin_layout Standard
16743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16746 \begin_layout Standard
16747 \begin_inset Formula $\boldsymbol{AbC}$
16755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16758 \begin_layout Standard
16765 <row topline="true">
16766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16769 \begin_layout Standard
16778 \begin_layout Standard
16794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16797 \begin_layout Standard
16798 \begin_inset Formula $\mathcal{ABC}$
16806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16809 \begin_layout Standard
16816 <row topline="true" bottomline="true">
16817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16820 \begin_layout Standard
16829 \begin_layout Standard
16845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16848 \begin_layout Standard
16849 \begin_inset Formula $\mathfrak{AbC}$
16857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16860 \begin_layout Standard
16874 \begin_layout Standard
16876 \begin_inset Tabular
16877 <lyxtabular version="3" rows="5" columns="3">
16879 <column alignment="center" valignment="top" leftline="true" width="0">
16880 <column alignment="center" valignment="top" leftline="true" width="0">
16881 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16882 <row topline="true" bottomline="true">
16883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16886 \begin_layout Standard
16892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16895 \begin_layout Standard
16901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16904 \begin_layout Standard
16911 <row topline="true">
16912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16915 \begin_layout Standard
16924 \begin_layout Standard
16940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16943 \begin_layout Standard
16944 \begin_inset Formula $\mathit{AbC}$
16952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16955 \begin_layout Standard
16962 <row topline="true">
16963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16966 \begin_layout Standard
16975 \begin_layout Standard
16991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16994 \begin_layout Standard
16995 \begin_inset Formula $\mathrm{AbC}$
17003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17006 \begin_layout Standard
17013 <row topline="true">
17014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17017 \begin_layout Standard
17026 \begin_layout Standard
17042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17045 \begin_layout Standard
17046 \begin_inset Formula $\mathsf{AbC}$
17054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17057 \begin_layout Standard
17064 <row topline="true" bottomline="true">
17065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17068 \begin_layout Standard
17077 \begin_layout Standard
17093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17096 \begin_layout Standard
17097 \begin_inset Formula $\mathtt{AbC}$
17105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17108 \begin_layout Standard
17122 \begin_layout Standard
17123 \begin_inset Note Greyedout
17126 \begin_layout Standard
17143 can only be used for big letters.
17151 \begin_layout Standard
17152 Predefined is the style
17161 \begin_layout Standard
17162 The style commands work also for letters in mathematical constructs:
17163 \begin_inset Formula \[
17164 \mathfrak{A=\frac{b}{C}}\]
17171 \begin_layout Standard
17172 Characters in mathematical text don't appear in a math font style but in
17173 the text font style
17180 That their style can't be set correctly via the text style dialog is a
17185 \begin_layout Standard
17190 \begin_layout Standard
17194 href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
17203 \begin_layout Standard
17218 \begin_layout Standard
17219 Instead of the style commands the dialog
17221 Edit\SpecialChar \menuseparator
17222 Math\SpecialChar \menuseparator
17225 or the toolbar button
17226 \begin_inset Graphics
17227 filename ../images/math/font.png
17235 \begin_layout Subsection
17237 \begin_inset LatexCommand label
17238 name "sub:Bold-Formulas"
17243 \begin_inset LatexCommand index
17244 name "Formula ! bold"
17251 \begin_layout Standard
17252 To make a complete formula bold, the command
17258 from the previous subsection cannot be used, because it doesn't work for
17259 small Greek letters.
17260 Furthermore it prints Latin letters always upright, like in the following
17264 \begin_layout Standard
17265 \begin_inset Formula \[
17266 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
17273 \begin_layout Standard
17274 To display the formula correctly, the command
17281 \begin_inset Formula \[
17282 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
17286 It is also possible to set the formula in a
17288 boldmath environment
17291 This environment is created by inserting the command
17296 \begin_inset LatexCommand index
17297 name "Commands ! B ! \\textbackslash boldmath"
17304 To end the environment, the command
17309 \begin_inset LatexCommand index
17310 name "Commands ! U ! \\textbackslash unboldmath"
17316 is inserted in TeX-mode.
17320 \begin_layout Standard
17330 \begin_inset Formula \[
17331 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
17339 \begin_layout Standard
17351 \begin_layout Subsection
17353 \begin_inset LatexCommand label
17354 name "sub:Font-Sizes"
17359 \begin_inset LatexCommand index
17367 \begin_layout Standard
17368 For characters in formulas there are, analog to characters in text, the
17369 following size commands:
17372 \begin_layout Standard
17436 \begin_layout Standard
17437 The size produced by the commands depends on the document font size, that
17438 corresponds with the command
17445 The other commands produce smaller or larger sizes than
17452 The font size can however not exceed a certain value.
17453 Is for example the document font size 12\InsetSpace \thinspace{}
17460 switches to the same size as
17470 \begin_layout Standard
17471 A size command is inserted in TeX-mode before the formula and sets the size
17472 for all following formula and text characters.
17473 To switch back to the initial size, the command
17479 is inserted behind the formula in TeX-mode.
17482 \begin_layout Standard
17483 Within a formula the size can only be changed for symbols or letters in
17485 To do this, the size command is inserted in mathematical text.
17486 All following characters until the end of the mathematical text or until
17487 another size command will have the selected size.
17489 \begin_inset VSpace -2mm
17495 \begin_layout Standard
17499 \begin_layout Standard
17509 \begin_inset Formula \[
17510 A=\frac{B}{c}\cdot\maltese\]
17515 \begin_inset Formula \[
17516 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
17524 \begin_layout Standard
17536 \begin_layout Standard
17537 \begin_inset VSpace medskip
17540 Before both formulas the command
17547 The command for the second formula is:
17557 \begin_layout Standard
17572 \begin_layout Standard
17587 \begin_layout Standard
17602 \begin_layout Standard
17612 \begin_inset Formula $\to$
17616 \begin_inset Formula $\to$
17625 \begin_layout Standard
17644 \begin_layout Standard
17659 \begin_layout Standard
17674 \begin_layout Standard
17686 \begin_layout Standard
17687 If a symbol cannot be displayed in different sizes, it will always be displayed
17688 in the default size.
17691 \begin_layout Section
17693 \begin_inset LatexCommand index
17694 name "Greek letters"
17701 \begin_layout Standard
17702 All Greek letters can also be inserted via the toolbar button
17703 \begin_inset Graphics
17704 filename ../images/math/alpha.png
17712 \begin_layout Subsection
17714 \begin_inset LatexCommand label
17715 name "sub:Small-Letters"
17720 \begin_inset LatexCommand index
17721 name "Greek letters ! small"
17728 \begin_layout Standard
17732 \begin_inset Tabular
17733 <lyxtabular version="3" rows="11" columns="2">
17735 <column alignment="center" valignment="top" leftline="true" width="0pt">
17736 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17737 <row topline="true" bottomline="true">
17738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17741 \begin_layout Standard
17747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17750 \begin_layout Standard
17757 <row topline="true">
17758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17761 \begin_layout Standard
17769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17772 \begin_layout Standard
17773 \begin_inset Formula $\alpha$
17782 <row topline="true">
17783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17786 \begin_layout Standard
17794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17797 \begin_layout Standard
17798 \begin_inset Formula $\beta$
17807 <row topline="true">
17808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17811 \begin_layout Standard
17819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17822 \begin_layout Standard
17823 \begin_inset Formula $\gamma$
17832 <row topline="true">
17833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17836 \begin_layout Standard
17844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17847 \begin_layout Standard
17848 \begin_inset Formula $\delta$
17857 <row topline="true">
17858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17861 \begin_layout Standard
17869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17872 \begin_layout Standard
17873 \begin_inset Formula $\epsilon$
17882 <row topline="true">
17883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17886 \begin_layout Standard
17894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17897 \begin_layout Standard
17898 \begin_inset Formula $\varepsilon$
17907 <row topline="true">
17908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17911 \begin_layout Standard
17919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17922 \begin_layout Standard
17923 \begin_inset Formula $\zeta$
17932 <row topline="true">
17933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17936 \begin_layout Standard
17944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17947 \begin_layout Standard
17948 \begin_inset Formula $\eta$
17957 <row topline="true">
17958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17961 \begin_layout Standard
17969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17972 \begin_layout Standard
17973 \begin_inset Formula $\theta$
17982 <row topline="true" bottomline="true">
17983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17986 \begin_layout Standard
17994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17997 \begin_layout Standard
17998 \begin_inset Formula $\vartheta$
18014 \begin_inset Tabular
18015 <lyxtabular version="3" rows="12" columns="2">
18017 <column alignment="center" valignment="top" leftline="true" width="0pt">
18018 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18019 <row topline="true" bottomline="true">
18020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18023 \begin_layout Standard
18029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18032 \begin_layout Standard
18039 <row topline="true">
18040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18043 \begin_layout Standard
18051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18054 \begin_layout Standard
18055 \begin_inset Formula $\iota$
18064 <row topline="true">
18065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18068 \begin_layout Standard
18076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18079 \begin_layout Standard
18080 \begin_inset Formula $\kappa$
18089 <row topline="true">
18090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18093 \begin_layout Standard
18101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18104 \begin_layout Standard
18105 \begin_inset Formula $\varkappa$
18114 <row topline="true">
18115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18118 \begin_layout Standard
18126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18129 \begin_layout Standard
18130 \begin_inset Formula $\lambda$
18139 <row topline="true">
18140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18143 \begin_layout Standard
18151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18154 \begin_layout Standard
18155 \begin_inset Formula $\mu$
18164 <row topline="true">
18165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18168 \begin_layout Standard
18176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18179 \begin_layout Standard
18180 \begin_inset Formula $\nu$
18189 <row topline="true">
18190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18193 \begin_layout Standard
18201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18204 \begin_layout Standard
18205 \begin_inset Formula $\xi$
18214 <row topline="true">
18215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18218 \begin_layout Standard
18224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18227 \begin_layout Standard
18228 \begin_inset Formula $o$
18237 <row topline="true">
18238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18241 \begin_layout Standard
18249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18252 \begin_layout Standard
18253 \begin_inset Formula $\pi$
18262 <row topline="true">
18263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18266 \begin_layout Standard
18274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18277 \begin_layout Standard
18278 \begin_inset Formula $\varpi$
18287 <row topline="true" bottomline="true">
18288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18291 \begin_layout Standard
18299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18302 \begin_layout Standard
18303 \begin_inset Formula $\rho$
18319 \begin_inset Tabular
18320 <lyxtabular version="3" rows="11" columns="2">
18322 <column alignment="center" valignment="top" leftline="true" width="0pt">
18323 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18324 <row topline="true" bottomline="true">
18325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18328 \begin_layout Standard
18334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18337 \begin_layout Standard
18344 <row topline="true">
18345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18348 \begin_layout Standard
18356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18359 \begin_layout Standard
18360 \begin_inset Formula $\varrho$
18369 <row topline="true">
18370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18373 \begin_layout Standard
18381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18384 \begin_layout Standard
18385 \begin_inset Formula $\sigma$
18394 <row topline="true">
18395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18398 \begin_layout Standard
18406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18409 \begin_layout Standard
18410 \begin_inset Formula $\varsigma$
18419 <row topline="true">
18420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18423 \begin_layout Standard
18431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18434 \begin_layout Standard
18435 \begin_inset Formula $\tau$
18444 <row topline="true">
18445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18448 \begin_layout Standard
18456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18459 \begin_layout Standard
18460 \begin_inset Formula $\upsilon$
18469 <row topline="true">
18470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18473 \begin_layout Standard
18481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18484 \begin_layout Standard
18485 \begin_inset Formula $\phi$
18494 <row topline="true">
18495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18498 \begin_layout Standard
18506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18509 \begin_layout Standard
18510 \begin_inset Formula $\varphi$
18519 <row topline="true">
18520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18523 \begin_layout Standard
18531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18534 \begin_layout Standard
18535 \begin_inset Formula $\chi$
18544 <row topline="true">
18545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18548 \begin_layout Standard
18556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18559 \begin_layout Standard
18560 \begin_inset Formula $\psi$
18569 <row topline="true" bottomline="true">
18570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18573 \begin_layout Standard
18581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18584 \begin_layout Standard
18585 \begin_inset Formula $\omega$
18603 \begin_layout Standard
18604 \begin_inset VSpace medskip
18610 \begin_layout Standard
18611 How to create upright Greek letters is explained in
18612 \begin_inset LatexCommand ref
18613 reference "sub:Upright-small-Greek"
18620 \begin_layout Subsection
18622 \begin_inset LatexCommand index
18623 name "Greek letters ! big"
18630 \begin_layout Standard
18634 \begin_inset Tabular
18635 <lyxtabular version="3" rows="7" columns="2">
18637 <column alignment="center" valignment="top" leftline="true" width="0pt">
18638 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18639 <row topline="true" bottomline="true">
18640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18643 \begin_layout Standard
18649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18652 \begin_layout Standard
18659 <row topline="true">
18660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18663 \begin_layout Standard
18671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18674 \begin_layout Standard
18675 \begin_inset Formula $\Gamma$
18684 <row topline="true">
18685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18688 \begin_layout Standard
18696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18699 \begin_layout Standard
18700 \begin_inset Formula $\Delta$
18709 <row topline="true">
18710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18713 \begin_layout Standard
18721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18724 \begin_layout Standard
18725 \begin_inset Formula $\Theta$
18734 <row topline="true">
18735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18738 \begin_layout Standard
18746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18749 \begin_layout Standard
18750 \begin_inset Formula $\Lambda$
18759 <row topline="true">
18760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18763 \begin_layout Standard
18771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18774 \begin_layout Standard
18775 \begin_inset Formula $\Xi$
18784 <row topline="true" bottomline="true">
18785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18788 \begin_layout Standard
18796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18799 \begin_layout Standard
18800 \begin_inset Formula $\Pi$
18816 \begin_inset Tabular
18817 <lyxtabular version="3" rows="6" columns="2">
18819 <column alignment="center" valignment="top" leftline="true" width="0pt">
18820 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18821 <row topline="true" bottomline="true">
18822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18825 \begin_layout Standard
18831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18834 \begin_layout Standard
18841 <row topline="true">
18842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18845 \begin_layout Standard
18853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18856 \begin_layout Standard
18857 \begin_inset Formula $\Sigma$
18866 <row topline="true">
18867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18870 \begin_layout Standard
18878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18881 \begin_layout Standard
18882 \begin_inset Formula $\Upsilon$
18891 <row topline="true">
18892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18895 \begin_layout Standard
18903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18906 \begin_layout Standard
18907 \begin_inset Formula $\Phi$
18916 <row topline="true">
18917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18920 \begin_layout Standard
18928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18931 \begin_layout Standard
18932 \begin_inset Formula $\Psi$
18941 <row topline="true" bottomline="true">
18942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18945 \begin_layout Standard
18953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18956 \begin_layout Standard
18957 \begin_inset Formula $\Omega$
18975 \begin_layout Standard
18976 \begin_inset VSpace medskip
18979 That the big Greek letters appear upright is caused by a design bug when
18981 To get correct italic big letters, begin every command with
18986 For example the command
18993 \begin_inset Formula $\varGamma$
18999 \begin_layout Subsection
19001 \begin_inset LatexCommand index
19002 name "Greek letters ! bold"
19009 \begin_layout Standard
19010 Greek letters cannot be set with different font styles like Latin letters.
19011 They can only be made bold with the command
19018 \begin_inset LatexCommand index
19019 name "Commands ! B ! \\textbackslash boldsymbol"
19026 \begin_layout Standard
19028 \begin_inset Tabular
19029 <lyxtabular version="3" rows="3" columns="2">
19031 <column alignment="center" valignment="top" leftline="true" width="0">
19032 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
19033 <row topline="true" bottomline="true">
19034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19037 \begin_layout Standard
19043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19046 \begin_layout Standard
19053 <row topline="true">
19054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19057 \begin_layout Standard
19069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19072 \begin_layout Standard
19073 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
19082 <row topline="true" bottomline="true">
19083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19086 \begin_layout Standard
19098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19101 \begin_layout Standard
19102 \begin_inset Formula $\theta\boldsymbol{\theta}$
19118 \begin_layout Section
19123 \begin_layout Standard
19136 \begin_layout Standard
19137 A list with all symbols of most of the LaTeX-packages can be found in
19138 \begin_inset LatexCommand cite
19152 \begin_layout Standard
19160 \begin_inset Note Note
19163 \begin_layout Standard
19166 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
19169 \begin_layout Standard
19172 texorpdfstring is in section
19173 \begin_inset LatexCommand ref
19174 reference "sub:Formulas-in-Section"
19184 \begin_inset LatexCommand index
19192 \begin_layout Standard
19193 Many of the symbols listed in this section can also be inserted via the
19195 \begin_inset Graphics
19196 filename ../images/math/nabla.png
19202 \begin_inset Graphics
19203 filename ../images/math/digamma.png
19211 \begin_layout Subsection
19212 Mathematical Symbols
19213 \begin_inset LatexCommand label
19214 name "sub:Mathematical-Symbols"
19219 \begin_inset LatexCommand index
19220 name "Symbols ! mathematical"
19227 \begin_layout Standard
19231 \begin_inset Tabular
19232 <lyxtabular version="3" rows="10" columns="2">
19234 <column alignment="center" valignment="top" leftline="true" width="0pt">
19235 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19236 <row topline="true" bottomline="true">
19237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19240 \begin_layout Standard
19246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19249 \begin_layout Standard
19256 <row topline="true">
19257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19260 \begin_layout Standard
19268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19271 \begin_layout Standard
19272 \begin_inset Formula $\neg$
19281 <row topline="true">
19282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19285 \begin_layout Standard
19293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19296 \begin_layout Standard
19297 \begin_inset Formula $\Im$
19306 <row topline="true">
19307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19310 \begin_layout Standard
19318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19321 \begin_layout Standard
19322 \begin_inset Formula $\Re$
19331 <row topline="true">
19332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19335 \begin_layout Standard
19343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19346 \begin_layout Standard
19347 \begin_inset Formula $\aleph$
19356 <row topline="true">
19357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19360 \begin_layout Standard
19368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19371 \begin_layout Standard
19372 \begin_inset Formula $\partial$
19381 <row topline="true">
19382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19385 \begin_layout Standard
19393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19396 \begin_layout Standard
19397 \begin_inset Formula $\infty$
19406 <row topline="true" bottomline="true">
19407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19410 \begin_layout Standard
19418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19421 \begin_layout Standard
19422 \begin_inset Formula $\wp$
19431 <row bottomline="true">
19432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19435 \begin_layout Standard
19443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19446 \begin_layout Standard
19447 \begin_inset Formula $\imath$
19456 <row bottomline="true">
19457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19460 \begin_layout Standard
19468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19471 \begin_layout Standard
19472 \begin_inset Formula $\jmath$
19488 \begin_inset Tabular
19489 <lyxtabular version="3" rows="10" columns="2">
19491 <column alignment="center" valignment="top" leftline="true" width="0pt">
19492 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19493 <row topline="true" bottomline="true">
19494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19497 \begin_layout Standard
19503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19506 \begin_layout Standard
19508 \begin_inset Note Note
19511 \begin_layout Standard
19518 is only used as spacer.
19529 <row topline="true">
19530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19533 \begin_layout Standard
19541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19544 \begin_layout Standard
19545 \begin_inset Formula $\forall$
19554 <row topline="true">
19555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19558 \begin_layout Standard
19566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19569 \begin_layout Standard
19570 \begin_inset Formula $\exists$
19579 <row topline="true">
19580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19583 \begin_layout Standard
19591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19594 \begin_layout Standard
19595 \begin_inset Formula $\nexists$
19604 <row topline="true">
19605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19608 \begin_layout Standard
19616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19619 \begin_layout Standard
19620 \begin_inset Formula $\emptyset$
19629 <row topline="true">
19630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19633 \begin_layout Standard
19641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19644 \begin_layout Standard
19645 \begin_inset Formula $\varnothing$
19654 <row topline="true">
19655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19658 \begin_layout Standard
19666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19669 \begin_layout Standard
19670 \begin_inset Formula $\dag$
19679 <row topline="true" bottomline="true">
19680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19683 \begin_layout Standard
19691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19694 \begin_layout Standard
19695 \begin_inset Formula $\ddag$
19704 <row bottomline="true">
19705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19708 \begin_layout Standard
19716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19719 \begin_layout Standard
19723 \begin_layout Standard
19733 \begin_inset Formula $\complement$
19740 \begin_layout Standard
19753 <row bottomline="true">
19754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19757 \begin_layout Standard
19765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19768 \begin_layout Standard
19769 \begin_inset Formula $\Bbbk$
19785 \begin_inset Tabular
19786 <lyxtabular version="3" rows="10" columns="2">
19788 <column alignment="center" valignment="top" leftline="true" width="0pt">
19789 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19790 <row topline="true" bottomline="true">
19791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19794 \begin_layout Standard
19800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19803 \begin_layout Standard
19810 <row topline="true">
19811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19814 \begin_layout Standard
19822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19825 \begin_layout Standard
19826 \begin_inset Formula $\prime$
19835 <row topline="true">
19836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19839 \begin_layout Standard
19847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19850 \begin_layout Standard
19851 \begin_inset Formula $\backprime$
19860 <row topline="true">
19861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19864 \begin_layout Standard
19872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19875 \begin_layout Standard
19876 \begin_inset Formula $\mho$
19885 <row topline="true">
19886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19889 \begin_layout Standard
19897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19900 \begin_layout Standard
19901 \begin_inset Formula $\triangle$
19910 <row topline="true">
19911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19914 \begin_layout Standard
19922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19925 \begin_layout Standard
19926 \begin_inset Formula $\angle$
19935 <row topline="true">
19936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19939 \begin_layout Standard
19947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19950 \begin_layout Standard
19951 \begin_inset Formula $\measuredangle$
19960 <row topline="true" bottomline="true">
19961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19964 \begin_layout Standard
19972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19975 \begin_layout Standard
19976 \begin_inset Formula $\sphericalangle$
19985 <row bottomline="true">
19986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19989 \begin_layout Standard
19997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20000 \begin_layout Standard
20001 \begin_inset Formula $\top$
20010 <row bottomline="true">
20011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20014 \begin_layout Standard
20022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20025 \begin_layout Standard
20026 \begin_inset Formula $\bot$
20044 \begin_layout Standard
20050 \begin_layout Subsection
20051 Miscellaneous Symbols
20052 \begin_inset LatexCommand label
20053 name "sub:Miscellaneous-Symbols"
20058 \begin_inset LatexCommand index
20059 name "Symbols ! miscellaneous"
20066 \begin_layout Standard
20067 \begin_inset Tabular
20068 <lyxtabular version="3" rows="10" columns="2">
20070 <column alignment="center" valignment="top" leftline="true" width="0pt">
20071 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20072 <row topline="true" bottomline="true">
20073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20076 \begin_layout Standard
20082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20085 \begin_layout Standard
20092 <row topline="true">
20093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20096 \begin_layout Standard
20104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20107 \begin_layout Standard
20108 \begin_inset Formula $\flat$
20117 <row topline="true">
20118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20121 \begin_layout Standard
20129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20132 \begin_layout Standard
20133 \begin_inset Formula $\natural$
20142 <row topline="true">
20143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20146 \begin_layout Standard
20154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20157 \begin_layout Standard
20158 \begin_inset Formula $\sharp$
20167 <row topline="true" bottomline="true">
20168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20171 \begin_layout Standard
20179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20182 \begin_layout Standard
20183 \begin_inset Formula $\surd$
20192 <row bottomline="true">
20193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20196 \begin_layout Standard
20204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20207 \begin_layout Standard
20208 \begin_inset Formula $\checkmark$
20217 <row bottomline="true">
20218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20221 \begin_layout Standard
20229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20232 \begin_layout Standard
20233 \begin_inset Formula $\yen$
20242 <row bottomline="true">
20243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20246 \begin_layout Standard
20254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20257 \begin_layout Standard
20258 \begin_inset Formula $\pounds$
20267 <row bottomline="true">
20268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20271 \begin_layout Standard
20277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20280 \begin_layout Standard
20281 \begin_inset Formula $\$$
20290 <row bottomline="true">
20291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20294 \begin_layout Standard
20300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20303 \begin_layout Standard
20304 \begin_inset Formula $§$
20318 \begin_inset Tabular
20319 <lyxtabular version="3" rows="10" columns="2">
20321 <column alignment="center" valignment="top" leftline="true" width="0">
20322 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
20323 <row topline="true" bottomline="true">
20324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20327 \begin_layout Standard
20333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20336 \begin_layout Standard
20343 <row topline="true">
20344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20347 \begin_layout Standard
20355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20358 \begin_layout Standard
20359 \begin_inset Formula $\hbar$
20368 <row topline="true">
20369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20372 \begin_layout Standard
20380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20383 \begin_layout Standard
20384 \begin_inset Formula $\hslash$
20393 <row topline="true">
20394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20397 \begin_layout Standard
20405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20408 \begin_layout Standard
20409 \begin_inset Formula $\clubsuit$
20418 <row topline="true">
20419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20422 \begin_layout Standard
20430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20433 \begin_layout Standard
20434 \begin_inset Formula $\spadesuit$
20443 <row topline="true">
20444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20447 \begin_layout Standard
20455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20458 \begin_layout Standard
20459 \begin_inset Formula $\bigstar$
20468 <row topline="true">
20469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20472 \begin_layout Standard
20480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20483 \begin_layout Standard
20484 \begin_inset Formula $\blacklozenge$
20493 <row topline="true">
20494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20497 \begin_layout Standard
20505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20508 \begin_layout Standard
20509 \begin_inset Formula $\blacktriangle$
20518 <row topline="true">
20519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20522 \begin_layout Standard
20530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20533 \begin_layout Standard
20534 \begin_inset Formula $\blacktriangledown$
20543 <row topline="true" bottomline="true">
20544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20547 \begin_layout Standard
20555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20558 \begin_layout Standard
20559 \begin_inset Formula $\bullet$
20573 \begin_inset Tabular
20574 <lyxtabular version="3" rows="10" columns="2">
20576 <column alignment="center" valignment="top" leftline="true" width="0pt">
20577 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20578 <row topline="true" bottomline="true">
20579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20582 \begin_layout Standard
20588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20591 \begin_layout Standard
20598 <row topline="true">
20599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20602 \begin_layout Standard
20610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20613 \begin_layout Standard
20614 \begin_inset Formula $\diamondsuit$
20623 <row topline="true">
20624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20627 \begin_layout Standard
20635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20638 \begin_layout Standard
20639 \begin_inset Formula $\Diamond$
20648 <row topline="true">
20649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20652 \begin_layout Standard
20660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20663 \begin_layout Standard
20664 \begin_inset Formula $\heartsuit$
20673 <row topline="true" bottomline="true">
20674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20677 \begin_layout Standard
20685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20688 \begin_layout Standard
20689 \begin_inset Formula $\P$
20698 <row bottomline="true">
20699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20702 \begin_layout Standard
20710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20713 \begin_layout Standard
20714 \begin_inset Formula $\copyright$
20723 <row bottomline="true">
20724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20727 \begin_layout Standard
20735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20738 \begin_layout Standard
20739 \begin_inset Formula $\circledR$
20748 <row bottomline="true">
20749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20752 \begin_layout Standard
20760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20763 \begin_layout Standard
20764 \begin_inset Formula $\maltese$
20773 <row bottomline="true">
20774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20777 \begin_layout Standard
20785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20788 \begin_layout Standard
20789 \begin_inset Formula $\diagup$
20798 <row bottomline="true">
20799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20802 \begin_layout Standard
20810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20813 \begin_layout Standard
20814 \begin_inset Formula $\diagdown$
20830 \begin_layout Standard
20831 \begin_inset VSpace medskip
20834 More symbols are listed in
20835 \begin_inset LatexCommand ref
20836 reference "sub:Miscellaneous-Special-Characters"
20843 \begin_layout Standard
20844 Some symbols can be displayed in different sizes, see
20845 \begin_inset LatexCommand ref
20846 reference "sub:Font-Sizes"
20853 \begin_layout Subsection
20855 \begin_inset LatexCommand index
20856 name "Symbols ! Euro-symbol"
20861 \begin_inset LatexCommand index
20862 name "\\textcent@\\officialeuro"
20869 \begin_layout Standard
20870 To use the Euro symbol in formulas, the LaTeX-package
20875 \begin_inset LatexCommand index
20876 name "Packages ! eurosym"
20880 must be installed and loaded with the LaTeX-preamble line
20883 \begin_layout Standard
20888 usepackage[gennarrow]{eurosym}
20891 \begin_layout Standard
20892 The Euro symbol can now be inserted with the command
20899 \begin_inset LatexCommand index
20900 name "Commands ! E ! \\textbackslash euro"
20907 \begin_layout Standard
20908 The Euro symbol can directly be inserted with the € key in mathematical
20909 text, without having
20924 can also be inserted in TeX-mode.
20925 The official currency symbol can then be inserted with the command
20932 \begin_inset LatexCommand index
20933 name "Commands ! O ! \\textbackslash officialeuro"
20937 , that is only available in TeX-mode.
20940 \begin_layout Standard
20944 \begin_layout Standard
20954 \begin_inset Note Note
20957 \begin_layout Standard
20958 The following table will only be displayed when the LaTeX-package
20970 \begin_layout Standard
20971 An overview about the different Euro symbols:
20974 \begin_layout Standard
20976 \begin_inset Tabular
20977 <lyxtabular version="3" rows="4" columns="3">
20979 <column alignment="center" valignment="top" leftline="true" width="0pt">
20980 <column alignment="center" valignment="top" leftline="true" width="0pt">
20981 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20982 <row topline="true" bottomline="true">
20983 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
20986 \begin_layout Standard
20992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20995 \begin_layout Standard
21001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21004 \begin_layout Standard
21011 <row topline="true">
21012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21015 \begin_layout Standard
21021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21024 \begin_layout Standard
21032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21035 \begin_layout Standard
21036 \begin_inset Formula $\euro$
21045 <row topline="true">
21046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21049 \begin_layout Standard
21055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21058 \begin_layout Standard
21064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21067 \begin_layout Standard
21068 \begin_inset Formula $\mbox{€}$
21077 <row topline="true" bottomline="true">
21078 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21081 \begin_layout Standard
21087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21090 \begin_layout Standard
21098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21101 \begin_layout Standard
21105 \begin_layout Standard
21127 \begin_layout Standard
21131 \begin_layout Standard
21141 \begin_inset Note Note
21144 \begin_layout Standard
21145 The following will be displayed when the LaTeX-package
21157 \begin_layout Standard
21158 You need to install the package
21162 to see the rest of this subsection in the output.
21165 \begin_layout Standard
21169 \begin_layout Standard
21181 \begin_layout Section
21183 \begin_inset LatexCommand label
21184 name "sec:Relations"
21189 \begin_inset LatexCommand index
21195 \begin_inset LatexCommand index
21196 name "Comparisons|see{Relations}"
21203 \begin_layout Standard
21204 All relations can also be inserted via the toolbar button
21205 \begin_inset Graphics
21206 filename ../images/math/leq.png
21214 \begin_layout Standard
21218 \begin_inset Tabular
21219 <lyxtabular version="3" rows="17" columns="2">
21221 <column alignment="center" valignment="top" leftline="true" width="0pt">
21222 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21223 <row topline="true" bottomline="true">
21224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21227 \begin_layout Standard
21233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21236 \begin_layout Standard
21243 <row topline="true">
21244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21247 \begin_layout Standard
21253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21256 \begin_layout Standard
21257 \begin_inset Formula $<$
21266 <row topline="true">
21267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21270 \begin_layout Standard
21278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21281 \begin_layout Standard
21282 \begin_inset Formula $\le$
21291 <row topline="true">
21292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21295 \begin_layout Standard
21303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21306 \begin_layout Standard
21307 \begin_inset Formula $\ll$
21316 <row topline="true">
21317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21320 \begin_layout Standard
21328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21331 \begin_layout Standard
21332 \begin_inset Formula $\prec$
21341 <row topline="true">
21342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21345 \begin_layout Standard
21353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21356 \begin_layout Standard
21357 \begin_inset Formula $\preceq$
21366 <row topline="true">
21367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21370 \begin_layout Standard
21378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21381 \begin_layout Standard
21382 \begin_inset Formula $\subset$
21391 <row topline="true">
21392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21395 \begin_layout Standard
21403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21406 \begin_layout Standard
21407 \begin_inset Formula $\subseteq$
21416 <row topline="true">
21417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21420 \begin_layout Standard
21428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21431 \begin_layout Standard
21432 \begin_inset Formula $\sqsubseteq$
21441 <row topline="true">
21442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21445 \begin_layout Standard
21453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21456 \begin_layout Standard
21457 \begin_inset Formula $\in$
21466 <row topline="true">
21467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21470 \begin_layout Standard
21478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21481 \begin_layout Standard
21482 \begin_inset Formula $\vdash$
21491 <row topline="true">
21492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21495 \begin_layout Standard
21503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21506 \begin_layout Standard
21507 \begin_inset Formula $\smile$
21516 <row topline="true">
21517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21520 \begin_layout Standard
21528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21531 \begin_layout Standard
21532 \begin_inset Formula $\lhd$
21541 <row topline="true">
21542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21545 \begin_layout Standard
21553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21556 \begin_layout Standard
21557 \begin_inset Formula $\unlhd$
21566 <row topline="true">
21567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21570 \begin_layout Standard
21578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21581 \begin_layout Standard
21582 \begin_inset Formula $\gtrless$
21591 <row topline="true">
21592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21595 \begin_layout Standard
21603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21606 \begin_layout Standard
21607 \begin_inset Formula $\mid$
21616 <row topline="true" bottomline="true">
21617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21620 \begin_layout Standard
21628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21631 \begin_layout Standard
21632 \begin_inset Formula $\nmid$
21648 \begin_inset Tabular
21649 <lyxtabular version="3" rows="17" columns="2">
21651 <column alignment="center" valignment="top" leftline="true" width="0pt">
21652 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21653 <row topline="true" bottomline="true">
21654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21657 \begin_layout Standard
21663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21666 \begin_layout Standard
21673 <row topline="true">
21674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21677 \begin_layout Standard
21683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21686 \begin_layout Standard
21687 \begin_inset Formula $=$
21696 <row topline="true">
21697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21700 \begin_layout Standard
21708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21711 \begin_layout Standard
21712 \begin_inset Formula $\not=$
21721 <row topline="true">
21722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21725 \begin_layout Standard
21733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21736 \begin_layout Standard
21737 \begin_inset Formula $\equiv$
21746 <row topline="true">
21747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21750 \begin_layout Standard
21758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21761 \begin_layout Standard
21762 \begin_inset Formula $\sim$
21771 <row topline="true">
21772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21775 \begin_layout Standard
21783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21786 \begin_layout Standard
21787 \begin_inset Formula $\simeq$
21796 <row topline="true">
21797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21800 \begin_layout Standard
21808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21811 \begin_layout Standard
21812 \begin_inset Formula $\approx$
21821 <row topline="true">
21822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21825 \begin_layout Standard
21833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21836 \begin_layout Standard
21837 \begin_inset Formula $\cong$
21846 <row topline="true">
21847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21850 \begin_layout Standard
21858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21861 \begin_layout Standard
21862 \begin_inset Formula $\bowtie$
21871 <row topline="true">
21872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21875 \begin_layout Standard
21883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21886 \begin_layout Standard
21887 \begin_inset Formula $\notin$
21896 <row topline="true">
21897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21900 \begin_layout Standard
21908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21911 \begin_layout Standard
21912 \begin_inset Formula $\perp$
21921 <row topline="true">
21922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21925 \begin_layout Standard
21933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21936 \begin_layout Standard
21937 \begin_inset Formula $\propto$
21946 <row topline="true">
21947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21950 \begin_layout Standard
21958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21961 \begin_layout Standard
21962 \begin_inset Formula $\asymp$
21971 <row topline="true">
21972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21975 \begin_layout Standard
21983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21986 \begin_layout Standard
21987 \begin_inset Formula $\doteq$
21996 <row topline="true">
21997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22000 \begin_layout Standard
22008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22011 \begin_layout Standard
22012 \begin_inset Formula $\circeq$
22021 <row topline="true">
22022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22025 \begin_layout Standard
22033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22036 \begin_layout Standard
22037 \begin_inset Formula $\models$
22046 <row topline="true" bottomline="true">
22047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22050 \begin_layout Standard
22058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22061 \begin_layout Standard
22062 \begin_inset Formula $\widehat{=}$
22078 \begin_inset Tabular
22079 <lyxtabular version="3" rows="17" columns="2">
22081 <column alignment="center" valignment="top" leftline="true" width="0pt">
22082 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22083 <row topline="true" bottomline="true">
22084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22087 \begin_layout Standard
22093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22096 \begin_layout Standard
22103 <row topline="true">
22104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22107 \begin_layout Standard
22113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22116 \begin_layout Standard
22117 \begin_inset Formula $>$
22126 <row topline="true">
22127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22130 \begin_layout Standard
22138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22141 \begin_layout Standard
22142 \begin_inset Formula $\ge$
22151 <row topline="true">
22152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22155 \begin_layout Standard
22163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22166 \begin_layout Standard
22167 \begin_inset Formula $\gg$
22176 <row topline="true">
22177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22180 \begin_layout Standard
22188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22191 \begin_layout Standard
22192 \begin_inset Formula $\succ$
22201 <row topline="true">
22202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22205 \begin_layout Standard
22213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22216 \begin_layout Standard
22217 \begin_inset Formula $\succeq$
22226 <row topline="true">
22227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22230 \begin_layout Standard
22238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22241 \begin_layout Standard
22242 \begin_inset Formula $\supset$
22251 <row topline="true">
22252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22255 \begin_layout Standard
22263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22266 \begin_layout Standard
22267 \begin_inset Formula $\supseteq$
22276 <row topline="true">
22277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22280 \begin_layout Standard
22288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22291 \begin_layout Standard
22292 \begin_inset Formula $\sqsupseteq$
22301 <row topline="true">
22302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22305 \begin_layout Standard
22313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22316 \begin_layout Standard
22317 \begin_inset Formula $\ni$
22326 <row topline="true">
22327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22330 \begin_layout Standard
22338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22341 \begin_layout Standard
22342 \begin_inset Formula $\dashv$
22351 <row topline="true">
22352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22355 \begin_layout Standard
22363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22366 \begin_layout Standard
22367 \begin_inset Formula $\frown$
22376 <row topline="true">
22377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22380 \begin_layout Standard
22388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22391 \begin_layout Standard
22392 \begin_inset Formula $\rhd$
22401 <row topline="true">
22402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22405 \begin_layout Standard
22413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22416 \begin_layout Standard
22417 \begin_inset Formula $\unrhd$
22426 <row topline="true">
22427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22430 \begin_layout Standard
22438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22441 \begin_layout Standard
22442 \begin_inset Formula $\lessgtr$
22451 <row topline="true">
22452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22455 \begin_layout Standard
22463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22466 \begin_layout Standard
22467 \begin_inset Formula $\parallel$
22476 <row topline="true" bottomline="true">
22477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22480 \begin_layout Standard
22488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22491 \begin_layout Standard
22492 \begin_inset Formula $\nparallel$
22510 \begin_layout Standard
22511 \begin_inset VSpace medskip
22526 are bigger than the equal looking operators
22541 \begin_layout Standard
22542 Relations are, in contrary to symbols, always surrounded by space.
22545 \begin_layout Standard
22546 Relations with labels can be created with the command
22553 \begin_inset LatexCommand index
22554 name "Commands ! S ! \\textbackslash stackrel"
22561 \begin_layout Standard
22563 \begin_inset Tabular
22564 <lyxtabular version="3" rows="2" columns="2">
22566 <column alignment="center" valignment="top" leftline="true" width="0">
22567 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
22568 <row topline="true" bottomline="true">
22569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22572 \begin_layout Standard
22578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22581 \begin_layout Standard
22583 \begin_inset Note Note
22586 \begin_layout Standard
22593 is only used as spacer.
22604 <row topline="true" bottomline="true">
22605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22608 \begin_layout Standard
22615 \begin_layout Standard
22632 \begin_layout Standard
22642 \begin_inset Formula $\downarrow$
22651 \begin_layout Standard
22664 \begin_layout Standard
22678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22681 \begin_layout Standard
22682 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
22698 \begin_layout Section
22702 \begin_layout Subsection
22703 Predefined Functions
22704 \begin_inset LatexCommand label
22705 name "sub:Predefined-Functions"
22710 \begin_inset LatexCommand index
22711 name "Functions ! predefined"
22718 \begin_layout Standard
22719 In general, variables are set
22723 in mathematical expressions, but not function names, because
22724 \begin_inset Formula $sin$
22727 could be misunderstood as
22728 \begin_inset Formula $s\cdot i\cdot n$
22732 Therefore there are predefined functions, that are additionally a bit separated
22734 They are inserted as commands starting with a backslash before their name.
22737 \begin_layout Standard
22739 \begin_inset Tabular
22740 <lyxtabular version="3" rows="2" columns="4">
22742 <column alignment="center" valignment="top" leftline="true" width="0pt">
22743 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22744 <column alignment="center" valignment="top" leftline="true" width="0pt">
22745 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22746 <row topline="true" bottomline="true">
22747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22750 \begin_layout Standard
22756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22759 \begin_layout Standard
22765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22768 \begin_layout Standard
22774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22777 \begin_layout Standard
22784 <row topline="true" bottomline="true">
22785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22788 \begin_layout Standard
22794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22797 \begin_layout Standard
22798 \begin_inset Formula $Asin(x)+B$
22806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22809 \begin_layout Standard
22817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22820 \begin_layout Standard
22821 \begin_inset Formula $A\sin(x)+B$
22838 \begin_layout Standard
22850 \begin_layout Standard
22851 The following functions are predefined:
22854 \begin_layout Standard
22855 \begin_inset VSpace -2mm
22861 \begin_layout Standard
22863 \begin_inset Tabular
22864 <lyxtabular version="3" rows="9" columns="4">
22866 <column alignment="center" valignment="top" leftline="true" width="0pt">
22867 <column alignment="center" valignment="top" leftline="true" width="0pt">
22868 <column alignment="center" valignment="top" leftline="true" width="0pt">
22869 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22870 <row topline="true" bottomline="true">
22871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22874 \begin_layout Standard
22880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22883 \begin_layout Standard
22889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22892 \begin_layout Standard
22898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22901 \begin_layout Standard
22908 <row topline="true">
22909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22912 \begin_layout Standard
22920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22923 \begin_layout Standard
22931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22934 \begin_layout Standard
22942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22945 \begin_layout Standard
22954 <row topline="true">
22955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22958 \begin_layout Standard
22966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22969 \begin_layout Standard
22977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22980 \begin_layout Standard
22988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22991 \begin_layout Standard
23000 <row topline="true">
23001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23004 \begin_layout Standard
23012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23015 \begin_layout Standard
23023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23026 \begin_layout Standard
23034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23037 \begin_layout Standard
23046 <row topline="true">
23047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23050 \begin_layout Standard
23058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23061 \begin_layout Standard
23069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23072 \begin_layout Standard
23080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23083 \begin_layout Standard
23092 <row topline="true">
23093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23096 \begin_layout Standard
23104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23107 \begin_layout Standard
23115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23118 \begin_layout Standard
23126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23129 \begin_layout Standard
23138 <row topline="true">
23139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23142 \begin_layout Standard
23150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23153 \begin_layout Standard
23161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23164 \begin_layout Standard
23172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23175 \begin_layout Standard
23184 <row topline="true">
23185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23188 \begin_layout Standard
23196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23199 \begin_layout Standard
23207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23210 \begin_layout Standard
23218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23221 \begin_layout Standard
23230 <row topline="true" bottomline="true">
23231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23234 \begin_layout Standard
23242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23245 \begin_layout Standard
23253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23256 \begin_layout Standard
23264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23267 \begin_layout Standard
23283 \begin_layout Standard
23284 They can also be inserted with the math toolbar button
23285 \begin_inset Graphics
23286 filename ../images/math/functions.png
23294 \begin_layout Subsection
23295 Self-defined Functions
23296 \begin_inset LatexCommand index
23297 name "Functions ! self-defined"
23304 \begin_layout Standard
23305 To use a function that is not predefined, like for example the sign function
23306 sgn(x), there are two possibilities:
23309 \begin_layout Itemize
23310 Define the function by inserting the following line to the LaTeX-preamble
23314 \begin_layout Standard
23319 DeclareMathOperator
23322 \begin_inset LatexCommand ref
23323 reference "sub:Self-defined-Operators"
23335 \begin_inset VSpace -3mm
23344 DeclareMathOperator{
23349 \begin_inset LatexCommand index
23350 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
23357 \begin_inset VSpace -2mm
23362 Now the new defined function can be called with the command
23371 \begin_layout Itemize
23372 Write the the formula as usual, mark the formula name, in our example the
23377 , and change it to mathematical text.
23378 At last a space is inserted between prefactor and function.
23381 \begin_layout Standard
23382 The result is the same with both methods as with a predefined function
23386 \begin_layout Standard
23387 In LyX self-defined functions are displayed red, predefined ones black.
23395 \begin_layout Standard
23397 \begin_inset Tabular
23398 <lyxtabular version="3" rows="3" columns="2">
23400 <column alignment="center" valignment="top" leftline="true" width="0pt">
23401 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
23402 <row topline="true" bottomline="true">
23403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23406 \begin_layout Standard
23412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23415 \begin_layout Standard
23422 <row topline="true" bottomline="true">
23423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23426 \begin_layout Standard
23434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23437 \begin_layout Standard
23438 \begin_inset Formula $A\sgn(x)+B$
23447 <row topline="true" bottomline="true">
23448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23451 \begin_layout Standard
23455 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
23463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23466 \begin_layout Standard
23467 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
23483 \begin_layout Standard
23484 The first method is more suitable when the self-defined function should
23485 be used several times.
23488 \begin_layout Subsection
23490 \begin_inset LatexCommand index
23498 \begin_layout Standard
23499 For limits there are defined besides
23506 \begin_inset LatexCommand index
23507 name "Commands ! L ! \\textbackslash lim"
23523 furthermore the following functions:
23526 \begin_layout Standard
23528 \begin_inset Tabular
23529 <lyxtabular version="3" rows="5" columns="2">
23531 <column alignment="center" valignment="top" leftline="true" width="0">
23532 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
23533 <row topline="true" bottomline="true">
23534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23537 \begin_layout Standard
23543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23546 \begin_layout Standard
23548 \begin_inset Note Note
23551 \begin_layout Standard
23558 is only used as spacer.
23569 <row topline="true">
23570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23573 \begin_layout Standard
23581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23584 \begin_layout Standard
23585 \begin_inset Formula $\varliminf$
23595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23598 \begin_layout Standard
23606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23609 \begin_layout Standard
23610 \begin_inset Formula $\varlimsup$
23620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23623 \begin_layout Standard
23631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23634 \begin_layout Standard
23635 \begin_inset Formula $\varprojlim$
23644 <row bottomline="true">
23645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23648 \begin_layout Standard
23656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23659 \begin_layout Standard
23660 \begin_inset Formula $\varinjlim$
23664 \begin_inset Formula $\raisebox{-2.5mm}{}$
23680 \begin_layout Standard
23681 \begin_inset VSpace medskip
23684 The limit is created by inserting a subscript.
23685 It is set right beside the function in an inline formula:
23688 \begin_layout Standard
23690 \begin_inset Tabular
23691 <lyxtabular version="3" rows="2" columns="2">
23693 <column alignment="center" valignment="top" width="0pt">
23694 <column alignment="center" valignment="top" width="0pt">
23696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23699 \begin_layout Standard
23705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23708 \begin_layout Standard
23712 \begin_layout Standard
23722 \begin_inset Note Note
23725 \begin_layout Standard
23738 are used here as spacer.
23750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23753 \begin_layout Standard
23762 \begin_layout Standard
23775 \begin_layout Standard
23789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23792 \begin_layout Standard
23793 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
23809 \begin_layout Standard
23810 In a displayed formula the limit is set below the formula, as usual:
23811 \begin_inset Formula \[
23819 \begin_layout Subsection
23821 \begin_inset LatexCommand index
23822 name "Functions ! modulo-"
23829 \begin_layout Standard
23830 The modulo-function is special, because it exists in four variants.
23833 \begin_layout Standard
23834 The variants in a displayed formula:
23835 \begin_inset Formula \begin{align*}
23836 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
23837 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
23838 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
23839 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
23840 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
23847 \begin_layout Standard
23848 In an inline formula less space is set before the function names for all
23852 \begin_layout Section
23854 \begin_inset LatexCommand index
23855 name "Special characters"
23862 \begin_layout Subsection
23863 Special Characters in Mathematical Text
23866 \begin_layout Standard
23867 The following commands can only be used in mathematical text or in TeX-mode:
23870 \begin_layout Standard
23874 \begin_inset Tabular
23875 <lyxtabular version="3" rows="8" columns="2">
23877 <column alignment="block" valignment="top" leftline="true" width="0">
23878 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
23879 <row topline="true" bottomline="true">
23880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23883 \begin_layout Standard
23889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23892 \begin_layout Standard
23899 <row topline="true">
23900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23903 \begin_layout Standard
23911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23914 \begin_layout Standard
23915 \begin_inset Formula $\textrm{\oe}$
23924 <row topline="true">
23925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23928 \begin_layout Standard
23936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23939 \begin_layout Standard
23940 \begin_inset Formula $\textrm{\OE}$
23949 <row topline="true">
23950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23953 \begin_layout Standard
23961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23964 \begin_layout Standard
23965 \begin_inset Formula $\textrm{\ae}$
23974 <row topline="true">
23975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23978 \begin_layout Standard
23986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23989 \begin_layout Standard
23990 \begin_inset Formula $\textrm{\AE}$
23999 <row topline="true">
24000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24003 \begin_layout Standard
24011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24014 \begin_layout Standard
24015 \begin_inset Formula $\textrm{\aa}$
24024 <row topline="true" bottomline="true">
24025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24028 \begin_layout Standard
24032 \begin_inset LatexCommand index
24033 name "\\@\\textrm{\\AA}"
24042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24045 \begin_layout Standard
24046 \begin_inset Formula $\textrm{\AA}$
24055 <row bottomline="true">
24056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24059 \begin_layout Standard
24067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24070 \begin_layout Standard
24071 \begin_inset Formula $\textrm{\i}$
24087 \begin_inset Tabular
24088 <lyxtabular version="3" rows="8" columns="2">
24090 <column alignment="block" valignment="top" leftline="true" width="0">
24091 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24092 <row topline="true" bottomline="true">
24093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24096 \begin_layout Standard
24098 \begin_inset Note Note
24101 \begin_layout Standard
24108 is used for separation, because otherwise the output will be ¡ and ¿ respective
24119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24122 \begin_layout Standard
24129 <row topline="true">
24130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24133 \begin_layout Standard
24141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24144 \begin_layout Standard
24145 \begin_inset Formula $\textrm{\o}$
24154 <row topline="true">
24155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24158 \begin_layout Standard
24166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24169 \begin_layout Standard
24170 \begin_inset Formula $\textrm{\O}$
24179 <row topline="true">
24180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24183 \begin_layout Standard
24191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24194 \begin_layout Standard
24195 \begin_inset Formula $\textrm{\l}$
24204 <row topline="true">
24205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24208 \begin_layout Standard
24216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24219 \begin_layout Standard
24220 \begin_inset Formula $\textrm{\L}$
24229 <row topline="true" bottomline="true">
24230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24233 \begin_layout Standard
24238 \begin_layout Standard
24251 \begin_layout Standard
24265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24268 \begin_layout Standard
24269 \begin_inset Formula $\textrm{!`}$
24278 <row bottomline="true">
24279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24282 \begin_layout Standard
24287 \begin_layout Standard
24300 \begin_layout Standard
24314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24317 \begin_layout Standard
24318 \begin_inset Formula $\textrm{?`}$
24327 <row bottomline="true">
24328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24331 \begin_layout Standard
24339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24342 \begin_layout Standard
24343 \begin_inset Formula $\textrm{\j}$
24361 \begin_layout Standard
24363 \begin_inset Formula $\textrm{\textrm{Å}}$
24367 \begin_inset Formula $\textrm{\textrm{Ø}}$
24370 can also be inserted via the math toolbar button
24371 \begin_inset Graphics
24372 filename ../images/math/digamma.png
24380 \begin_layout Standard
24381 An exception are the commands
24387 \begin_layout Standard
24404 \begin_layout Standard
24415 , because they can be inserted in LyX directly to text.
24418 \begin_layout Subsection
24420 \begin_inset LatexCommand label
24421 name "sub:Accents-in-Text"
24426 \begin_inset LatexCommand index
24427 name "Accents ! in text"
24434 \begin_layout Standard
24435 With the following commands all letters can be accented.
24436 The commands must be inserted in TeX-mode.
24439 \begin_layout Standard
24443 \begin_inset Tabular
24444 <lyxtabular version="3" rows="8" columns="2">
24446 <column alignment="block" valignment="top" leftline="true" width="0">
24447 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
24448 <row topline="true" bottomline="true">
24449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24452 \begin_layout Standard
24458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24461 \begin_layout Standard
24468 <row topline="true">
24469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24472 \begin_layout Standard
24476 \begin_inset Quotes grd
24484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24487 \begin_layout Standard
24491 \begin_layout Standard
24506 <row topline="true">
24507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24510 \begin_layout Standard
24518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24521 \begin_layout Standard
24525 \begin_layout Standard
24540 <row topline="true">
24541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24544 \begin_layout Standard
24551 \begin_layout Standard
24565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24568 \begin_layout Standard
24572 \begin_layout Standard
24587 <row topline="true">
24588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24591 \begin_layout Standard
24599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24602 \begin_layout Standard
24606 \begin_layout Standard
24621 <row topline="true">
24622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24625 \begin_layout Standard
24632 \begin_layout Standard
24646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24649 \begin_layout Standard
24653 \begin_layout Standard
24668 <row topline="true" bottomline="true">
24669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24672 \begin_layout Standard
24679 \begin_layout Standard
24693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24696 \begin_layout Standard
24700 \begin_layout Standard
24715 <row bottomline="true">
24716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24719 \begin_layout Standard
24726 \begin_layout Standard
24740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24743 \begin_layout Standard
24747 \begin_layout Standard
24769 \begin_inset Tabular
24770 <lyxtabular version="3" rows="8" columns="2">
24772 <column alignment="block" valignment="top" leftline="true" width="0">
24773 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24774 <row topline="true" bottomline="true">
24775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24778 \begin_layout Standard
24784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24787 \begin_layout Standard
24794 <row topline="true">
24795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24798 \begin_layout Standard
24805 \begin_layout Standard
24819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24822 \begin_layout Standard
24826 \begin_layout Standard
24841 <row topline="true">
24842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24845 \begin_layout Standard
24853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24856 \begin_layout Standard
24860 \begin_layout Standard
24875 <row topline="true">
24876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24879 \begin_layout Standard
24883 \begin_inset LatexCommand index
24893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24896 \begin_layout Standard
24900 \begin_layout Standard
24915 <row topline="true">
24916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24919 \begin_layout Standard
24927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24930 \begin_layout Standard
24934 \begin_layout Standard
24949 <row topline="true" bottomline="true">
24950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24953 \begin_layout Standard
24960 \begin_layout Standard
24974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24977 \begin_layout Standard
24981 \begin_layout Standard
24996 <row bottomline="true">
24997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25000 \begin_layout Standard
25007 \begin_layout Standard
25021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25024 \begin_layout Standard
25028 \begin_layout Standard
25043 <row bottomline="true">
25044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25047 \begin_layout Standard
25054 \begin_layout Standard
25068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25071 \begin_layout Standard
25075 \begin_layout Standard
25099 \begin_layout Standard
25100 \begin_inset VSpace medskip
25109 also two different characters can be accented.
25118 \begin_layout Standard
25133 \begin_layout Standard
25145 \begin_layout Standard
25158 can in combination with vowels directly be inserted with the keyboard without
25160 The same applies for the tilde
25164 \begin_layout Standard
25165 This only applies for keyboards where the tilde is defined as accent.
25174 in combination with
25189 \begin_layout Standard
25232 , and accents inserted directly with the keyboard are also available in
25234 For the other accents there are special math commands to be used in formulas,
25236 \begin_inset LatexCommand ref
25237 reference "sub:Accents-for-one"
25244 \begin_layout Standard
25245 \begin_inset VSpace bigskip
25248 Furthermore, with the command
25255 \begin_inset LatexCommand index
25256 name "Commands ! T ! \\textbackslash textcircled"
25260 all numbers and letters can be set into a circle, quasi accented with a
25261 circle, similar to the the copyright symbol.
25264 \begin_layout Standard
25266 \begin_inset Tabular
25267 <lyxtabular version="3" rows="3" columns="2">
25269 <column alignment="center" valignment="top" leftline="true" width="0">
25270 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25271 <row topline="true" bottomline="true">
25272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25275 \begin_layout Standard
25281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25284 \begin_layout Standard
25286 \begin_inset Note Note
25289 \begin_layout Standard
25296 is only used as spacer.
25307 <row topline="true">
25308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25311 \begin_layout Standard
25319 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25322 \begin_layout Standard
25326 \begin_layout Standard
25341 <row topline="true" bottomline="true">
25342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25345 \begin_layout Standard
25356 raisebox{-1.5pt}{W}}
25361 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25364 \begin_layout Standard
25365 \begin_inset Formula $\raisebox{4.5mm}{}$
25372 \begin_layout Standard
25390 \begin_inset Formula $\raisebox{-2mm}{}$
25406 \begin_layout Standard
25407 One has to take care that the character fits in the circle.
25418 \begin_layout Standard
25420 \begin_inset LatexCommand ref
25421 reference "sub:Font-Sizes"
25430 specifies thereby the size of the circle.
25441 \begin_layout Standard
25443 \begin_inset LatexCommand ref
25444 reference "sub:Boxes-without-Frame"
25453 the character can be centered.
25456 \begin_layout Subsection
25458 \begin_inset LatexCommand index
25459 name "Minuscule numbers"
25466 \begin_layout Standard
25467 Minuscule numbers are created with the command
25474 \begin_inset LatexCommand index
25475 name "Commands ! O ! \\textbackslash oldstylenums"
25480 The command can be used in formulas and in TeX-mode.
25481 The command scheme is:
25484 \begin_layout Standard
25489 oldstylenums{number}
25492 \begin_layout Standard
25497 oldstylenums{0123456789
25500 \begin_inset Formula $\oldstylenums{0123456789}$
25506 \begin_layout Subsection
25507 Miscellaneous Special Characters
25508 \begin_inset LatexCommand label
25509 name "sub:Miscellaneous-Special-Characters"
25514 \begin_inset LatexCommand index
25515 name "Special characters ! miscellaneous"
25522 \begin_layout Standard
25523 The following characters can only be inserted to formulas by using commands:
25526 \begin_layout Standard
25528 \begin_inset Tabular
25529 <lyxtabular version="3" rows="4" columns="2">
25531 <column alignment="center" valignment="top" leftline="true" width="0">
25532 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25533 <row topline="true" bottomline="true">
25534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25537 \begin_layout Standard
25543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25546 \begin_layout Standard
25553 <row topline="true">
25554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25557 \begin_layout Standard
25564 \begin_layout Standard
25578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25581 \begin_layout Standard
25582 \begin_inset Formula $\mathcircumflex$
25591 <row topline="true">
25592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25595 \begin_layout Standard
25603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25606 \begin_layout Standard
25607 \begin_inset Formula $\_$
25616 <row topline="true" bottomline="true">
25617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25620 \begin_layout Standard
25625 \begin_layout Standard
25637 \begin_inset LatexCommand index
25647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25650 \begin_layout Standard
25651 \begin_inset Formula $^{\circ}$
25667 \begin_layout Standard
25668 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
25669 contains the following line
25673 \begin_layout Standard
25674 More about this is described in
25675 \begin_inset LatexCommand ref
25676 reference "sub:Text-Characters-in"
25688 \begin_layout Standard
25693 DeclareInputtext{176}{
25703 f\SpecialChar \textcompwordmark{}
25707 \begin_layout Standard
25708 \begin_inset VSpace bigskip
25712 \begin_inset LatexCommand index
25717 is designed as accent, thus is looks alone a bit misplaced: ~
25720 addresses (URLs) sometimes a single tilde is needed.
25721 In this case the relation sign
25729 \begin_layout Standard
25731 \begin_inset LatexCommand ref
25732 reference "sec:Relations"
25743 is used in a formula.
25744 As a formula cannot be created in an URL-box (menu
25746 Insert\SpecialChar \menuseparator
25749 ), the URL is inserted as normal text with the font style '
25754 Should the URL be a hyperlink in the DVI- or PDF-output, the command
25764 \begin_layout Standard
25771 can only be used together with the LaTeX-package
25776 \begin_inset LatexCommand index
25777 name "Packages ! hyperref"
25788 is written in the section
25794 Embedded\InsetSpace ~
25803 \begin_inset LatexCommand index
25804 name "Commands ! H ! \\textbackslash href"
25811 \begin_layout Standard
25812 As example an URL with a tilde:
25815 \begin_layout Standard
25818 http://www.lyx.org/
25819 \begin_inset Formula $\sim$
25825 \begin_layout Standard
25836 \begin_layout Standard
25840 href{http://www.lyx.org/~mustermann}{
25845 http://www.lyx.org/
25846 \begin_inset Formula $\sim$
25853 \begin_layout Standard
25863 \begin_layout Section
25865 \begin_inset LatexCommand label
25866 name "sec:Formula-Styles"
25871 \begin_inset LatexCommand index
25872 name "Formula ! styles"
25879 \begin_layout Itemize
25880 There are two different alignment styles:
25884 \begin_layout Description
25885 Centered is the predefined standard
25888 \begin_layout Description
25889 Indented for this the option
25893 must be inserted in the menu
25895 Document\SpecialChar \menuseparator
25900 Document\InsetSpace ~
25904 \begin_layout Standard
25909 is used, the indentation can be adjusted with the length
25916 \begin_inset LatexCommand index
25917 name "Commands ! M ! \\textbackslash mathindent"
25922 Should the distance be 15\InsetSpace \thinspace{}
25923 mm, the following command line is inserted in
25927 \begin_layout Standard
25937 \begin_layout Standard
25938 When no length is specified, the predefined value of 30\InsetSpace \thinspace{}
25943 \begin_layout Itemize
25944 And two different numbering styles:
25948 \begin_layout Description
25949 Right is the predefined standard
25952 \begin_layout Description
25953 Left for this the option
25957 must be inserted in the menu
25959 Document\SpecialChar \menuseparator
25964 Document\InsetSpace ~
25969 \begin_layout Standard
25978 can also be used together.
25979 In this case both options are inserted, separated by a comma.
25982 \begin_layout Standard
25983 The chosen styles are used for all displayed formulas of the document.
25984 When both, centered and indented formulas should be created in a document,
25990 The indented formulas are then set in a flalign environment, see
25991 \begin_inset LatexCommand ref
25992 reference "sub:Flalign-Environment"
25999 \begin_layout Section
26001 \begin_inset LatexCommand label
26002 name "sec:Multiline-Formulas"
26007 \begin_inset LatexCommand index
26008 name "Formula ! multiline"
26015 \begin_layout Subsection
26019 \begin_layout Standard
26020 In LyX multiline formulas are created by pressing
26031 that is described in
26032 \begin_inset LatexCommand ref
26033 reference "sub:Standard-align-Environment"
26040 \begin_layout Standard
26041 There are other multiline formula environments that can be created via the
26044 Insert\SpecialChar \menuseparator
26048 These environments are described in the following sections.
26051 \begin_layout Standard
26052 In all multiline formula environments a new line is created by pressing
26058 To add or delete lines, the math toolbar buttons
26059 \begin_inset Graphics
26060 filename ../images/tabular-feature_append-row.png
26066 \begin_inset Graphics
26067 filename ../images/tabular-feature_delete-row.png
26072 , respectively, or the menu
26074 Edit\SpecialChar \menuseparator
26080 \begin_layout Subsubsection
26082 \begin_inset LatexCommand label
26083 name "sub:Line-Separation"
26088 \begin_inset LatexCommand index
26089 name "Formula ! multiline ! Line separation"
26096 \begin_layout Standard
26097 There is sometimes not enough space in multiline formulas between the lines:
26098 \begin_inset Formula \begin{eqnarray*}
26099 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}\\
26100 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*}
26107 \begin_layout Standard
26108 In LaTeX additional line space is specified as optional argument of the
26110 This is not yet possible in LyX
26114 \begin_layout Standard
26119 \begin_layout Standard
26123 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
26132 \begin_layout Standard
26144 , therefore the whole formula must be inserted in TeX-mode.
26145 To add in our example space, the command
26153 is inserted at the end of the first line.
26158 \begin_layout Standard
26165 \begin_layout Standard
26167 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26170 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26177 \begin_layout Standard
26181 left(B^{2}+x_{0}^{2}
26189 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26194 \begin_layout Standard
26206 \begin_layout Standard
26207 \begin_inset VSpace bigskip
26210 To set the the line separation for all lines in a formula, the length
26217 \begin_inset LatexCommand index
26218 name "Commands ! J ! \\textbackslash jot"
26224 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26234 is the value 3\InsetSpace \thinspace{}
26236 To create 3\InsetSpace \thinspace{}
26237 mm additional line separation as in the previous example, the
26241 \begin_layout Standard
26251 \begin_layout Standard
26252 is inserted in TeX-mode before the formula.
26253 This requires that the LaTeX-package
26261 \begin_layout Standard
26266 is part of every LaTeX standard installation.
26272 \begin_inset LatexCommand index
26273 name "Packages ! calc"
26277 was loaded in LaTeX-preamble with the line
26280 \begin_layout Standard
26288 \begin_layout Standard
26293 \begin_layout Standard
26305 \begin_inset Formula \begin{eqnarray*}
26306 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}\\
26307 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*}
26314 \begin_layout Standard
26318 \begin_layout Standard
26329 To get back to the predefined distance,
26335 is set to the value 3\InsetSpace \thinspace{}
26339 \begin_layout Subsubsection
26341 \begin_inset LatexCommand label
26342 name "sub:Column-Separation"
26347 \begin_inset LatexCommand index
26348 name "Formula ! multiline ! Column separation"
26355 \begin_layout Standard
26356 Multiline formulas form a matrix.
26357 A formula in the eqnarray environment is for example a matrix with three
26359 By changing the column separation in this environment, the space beside
26360 the relation sign can be changed.
26363 \begin_layout Standard
26364 The column separation is specified with the length
26371 \begin_inset LatexCommand index
26372 name "Commands ! A ! \\textbackslash arraycolsep"
26378 column separation = 2\InsetSpace \thinspace{}
26390 \begin_layout Standard
26400 \begin_layout Standard
26401 inserted in TeX-mode, sets for all following formulas a column separation
26402 of 2\InsetSpace \thinspace{}
26404 To get back to the predefined distance,
26410 is set to 5\InsetSpace \thinspace{}
26414 \begin_layout Standard
26415 A formula with 2\InsetSpace \thinspace{}
26416 cm column separation:
26420 \begin_layout Standard
26432 \begin_inset Formula \begin{eqnarray*}
26434 C & \ne & A\end{eqnarray*}
26438 A formula with the predefined column separation for matrices of 10\InsetSpace \thinspace{}
26443 \begin_layout Standard
26455 \begin_inset Formula \begin{eqnarray*}
26457 C & \ne & A\end{eqnarray*}
26464 \begin_layout Subsubsection
26466 \begin_inset LatexCommand index
26467 name "Formula ! long"
26474 \begin_layout Standard
26475 Long formulas can be typeset using these methods:
26478 \begin_layout Itemize
26479 When one side of the equation is much shorther than the line width, this
26480 one is chosen for the left side and the right side is typeset over two
26485 \begin_layout Standard
26495 \begin_inset Formula \begin{eqnarray}
26496 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 \\
26497 & & -\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}
26505 \begin_layout Standard
26516 The minus sign at the beginning of the second line does normally not appear
26517 as operator because it is the first character of the line.
26518 Thus it would not be surrounded by space and could not be distinguished
26519 from the fraction bar.
26520 To avoid this, space was inserted behind the minus sign with the command
26531 \begin_layout Standard
26539 \begin_inset LatexCommand ref
26540 reference "sub:Variable-Space"
26550 \begin_inset LatexCommand index
26551 name "Commands ! H ! \\textbackslash hspace"
26558 \begin_layout Itemize
26559 When both sides of the equation are too long, the command
26566 \begin_inset LatexCommand index
26567 name "Commands ! L ! \\textbackslash lefteqn"
26572 It is inserted to the first column of the first line and effects that all
26573 further insertions overwrite the following columns:
26577 \begin_layout Standard
26587 \begin_inset Formula \begin{eqnarray}
26588 \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 \\
26589 & & -\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 \\
26590 & & =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}
26598 \begin_layout Standard
26609 After the insertion of
26615 , the cursor is in a purple box that is a bit shifted to the left from the
26617 In this the formula is inserted.
26621 \begin_layout Standard
26632 The content of the further lines is inserted to the second or another formula
26634 The greater the column number where it was inserted, the larger the indentation.
26638 \begin_layout Standard
26650 \begin_inset Note Greyedout
26653 \begin_layout Standard
26654 Note the following when using
26663 \begin_layout Itemize
26664 The formula doesn't use the full page width.
26665 When e.\InsetSpace \thinspace{}
26668 \begin_inset Formula $-B^{2}$
26671 is added to the first line in the above example, it would have been outside
26673 To better use the width, negative space can be inserted at the beginning
26677 \begin_layout Itemize
26678 Due to a bug in LyX the cursor cannot be set with the mouse into the first
26683 \begin_layout Standard
26687 \begin_layout Standard
26691 href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
26700 \begin_layout Standard
26712 One can only set the cursor at the beginning of the line and move it with
26721 \begin_layout Itemize
26722 Other methods to set long formulas are offered by the environments described
26724 \begin_inset LatexCommand ref
26725 reference "sub:Multline-Environment"
26730 \begin_inset LatexCommand ref
26731 reference "sub:Multiline-Formula-Parts"
26738 \begin_layout Subsubsection
26740 \begin_inset LatexCommand label
26741 name "sub:Multiline-Brackets"
26746 \begin_inset LatexCommand index
26747 name "Brackets ! for multiline expressions"
26754 \begin_layout Standard
26755 For brackets spanning multiple lines the following problem occurs:
26756 \begin_inset Formula \begin{eqnarray*}
26757 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26758 & & \left.\cdots+B-D\right]\end{eqnarray*}
26765 \begin_layout Standard
26766 The closing bracket is smaller than the opening bracket because brackets
26767 with variable size may not span multiple lines.
26770 \begin_layout Standard
26771 To set the bracket size for the second line correctly, the first line is
26779 \begin_inset LatexCommand index
26780 name "Commands ! R ! \\textbackslash right"
26784 and the second line with
26792 \begin_layout Standard
26806 \begin_inset LatexCommand ref
26807 reference "sub:Automatic-Bracket-Size"
26819 \begin_inset LatexCommand index
26820 name "Commands ! L ! \\textbackslash left"
26842 \begin_layout Standard
26861 \begin_layout Standard
26880 \begin_layout Standard
26892 \begin_inset Formula $\downarrow$
26898 \begin_inset LatexCommand index
26899 name "Commands ! V ! \\textbackslash vphantom"
26903 is inserted, because the multiplication operator with its limits is the
26904 largest symbol in the first line and this should be the size for the bracket
26905 in the second line.
26908 \begin_layout Standard
26909 The result is this:
26910 \begin_inset Formula \begin{eqnarray*}
26911 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26912 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
26919 \begin_layout Subsection
26923 \begin_layout Standard
26924 Align environments can be used for every kind of multiline formulas.
26925 They are specially useful to set several formulas side by side.
26928 \begin_layout Standard
26929 Align environments consist of columns.
26930 The odd columns are right aligned, the even ones left aligned.
26931 Every line in an Align environment can be numbered.
26934 \begin_layout Standard
26935 Align environments are created via the menu
26937 Insert\SpecialChar \menuseparator
26943 Edit\SpecialChar \menuseparator
26944 Math\SpecialChar \menuseparator
26945 Change Formula Type
26947 already existing existing formulas can be converted to Align environments.
26950 \begin_layout Standard
26951 To add or delete columns, the math toolbar buttons
26952 \begin_inset Graphics
26953 filename ../images/tabular-feature_append-column.png
26959 \begin_inset Graphics
26960 filename ../images/tabular-feature_delete-column.png
26965 , respectively, or the menu
26967 Edit\SpecialChar \menuseparator
26973 \begin_layout Subsubsection
26974 Standard align Environment
26975 \begin_inset LatexCommand label
26976 name "sub:Standard-align-Environment"
26981 \begin_inset LatexCommand index
26982 name "Formula ! multiline ! align environment"
26989 \begin_layout Standard
26990 This Align environment is created by presssing
26994 in a formula or by the menu
26996 Insert\SpecialChar \menuseparator
26997 Math\SpecialChar \menuseparator
26998 AMS align Environment
27003 \begin_layout Standard
27004 An example for two formulas set side by side, that are created with a four
27005 column align environment:
27006 \begin_inset Formula \begin{align*}
27007 A & =\sin(B) & C & =D\\
27008 C & \ne A & B & \ne D\end{align*}
27012 As it can be seen, the formulas in this environment are placed so as if
27021 \begin_layout Standard
27029 \begin_inset LatexCommand ref
27030 reference "sub:Variable-Space"
27041 before the first and after every even column.
27042 When the formula style
27048 \begin_layout Standard
27050 \begin_inset LatexCommand ref
27051 reference "sec:Formula-Styles"
27062 is used, the formula is set without the
27068 before the first column.
27071 \begin_layout Subsubsection
27072 Alignat Environment
27073 \begin_inset LatexCommand index
27074 name "Formula ! multiline ! alignat environment"
27081 \begin_layout Standard
27082 The alignat environment has no predefined column separation.
27083 It can be inserted manually with the spaces that are described
27084 \begin_inset LatexCommand ref
27085 reference "sub:Space"
27092 \begin_layout Standard
27093 The above example in the alignat environment where 1\InsetSpace \thinspace{}
27094 cm space was inserted
27095 at the beginning of the second formula:
27096 \begin_inset Formula \begin{alignat*}{2}
27097 A & =\sin(B) & \hspace{1cm}C & =D\\
27098 C & \ne A & B & \ne D\end{alignat*}
27102 Because the column separation can be set separately for every column, this
27103 environment is especially suitable to set three and more formulas side
27107 \begin_layout Subsubsection
27108 Flalign Environment
27109 \begin_inset LatexCommand label
27110 name "sub:Flalign-Environment"
27115 \begin_inset LatexCommand index
27116 name "Formula ! multiline ! flalign environment"
27123 \begin_layout Standard
27124 In this environment the first two columns are always set as much as possible
27125 to the left and the last two ones to the right.
27127 \begin_inset Formula \begin{flalign*}
27128 A & =1 & B & =2 & C & =3\\
27129 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
27136 \begin_layout Standard
27137 By creating a flalign environment with an odd number of columns where an
27138 empty TeX-brace is inserted to the last column, several formulas in a document
27139 can be set to the left, although the formula style
27144 As example the indented formula
27145 \begin_inset LatexCommand eqref
27146 reference "eq:VolInt"
27151 \begin_inset Formula \begin{flalign}
27152 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
27156 The first two columns contain the formula.
27157 To indent it as with the formula style
27161 , 30\InsetSpace \thinspace{}
27162 pt space was inserted at the beginning of the first column.
27165 \begin_layout Subsection
27166 Eqnarray Environment
27167 \begin_inset LatexCommand index
27168 name "Formula ! multiline ! eqnarray environment"
27175 \begin_layout Standard
27176 When this environment has been created, three blue boxes appear.
27177 The content of the first box is right aligned, the content of the last
27179 The content of the middle box appears centered and a bit smaller, because
27180 it is designed to insert there only relation characters.
27181 \begin_inset Formula \begin{eqnarray*}
27182 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27184 A & = & A\end{eqnarray*}
27191 \begin_layout Subsection
27193 \begin_inset LatexCommand index
27194 name "Formula ! multiline ! gather environment"
27201 \begin_layout Standard
27202 This environment consists of only one centered column.
27203 Every line can be numbered.
27204 \begin_inset Formula \begin{gather}
27206 X=\textrm{-}1\end{gather}
27213 \begin_layout Subsection
27214 Multline Environment
27215 \begin_inset LatexCommand label
27216 name "sub:Multline-Environment"
27221 \begin_inset LatexCommand index
27222 name "Formula ! multiline ! multline environment"
27229 \begin_layout Standard
27230 The multline environment consists, like the gather environment, of only
27232 But the first line is left aligned, the last one right aligned.
27233 All other lines are centered.
27234 Therefore this environment is suitable for long formulas.
27236 \begin_inset LatexCommand eqref
27237 reference "eq:lefteqn"
27241 in the multline environment:
27242 \begin_inset Formula \begin{multline}
27243 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}\\
27244 -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}\\
27245 =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}
27252 \begin_layout Standard
27253 In the output only the the last (first) line of a multline environment appears
27254 numbered when the document numbering is right (left).
27258 \begin_layout Standard
27259 numbering styles see
27260 \begin_inset LatexCommand ref
27261 reference "sec:Formula-Styles"
27270 This is also the case when there is a formula number displayed after every
27275 \begin_layout Standard
27280 \begin_layout Standard
27284 href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
27293 \begin_layout Standard
27308 \begin_layout Standard
27314 \begin_inset LatexCommand index
27315 name "Commands ! S ! \\textbackslash shoveright"
27326 \begin_inset LatexCommand index
27327 name "Commands ! S ! \\textbackslash shoveleft"
27333 a centered line can be right or left aligned, respectively.
27334 The commands are used as follows:
27337 \begin_layout Standard
27342 shoveright{line content}
27348 shoveleft{line content}
27351 \begin_layout Standard
27352 \begin_inset VSpace medskip
27360 \begin_inset LatexCommand index
27361 name "Commands ! M ! \\textbackslash multlinegap"
27367 specifies the distance of the first line from the left page margin.
27368 Predefined is the length 0\InsetSpace \thinspace{}
27372 \begin_layout Standard
27373 As example the above formula where the command
27376 \begin_layout Standard
27386 \begin_layout Standard
27387 was inserted in TeX-mode before:
27391 \begin_layout Standard
27403 \begin_inset Formula \begin{multline}
27404 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}\\
27405 \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}}\\
27406 =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}
27414 \begin_layout Standard
27425 The second line was left aligned using
27434 \begin_layout Subsection
27435 Multiline Formula Parts
27436 \begin_inset LatexCommand label
27437 name "sub:Multiline-Formula-Parts"
27442 \begin_inset LatexCommand index
27443 name "Formula ! multiline ! formula parts"
27450 \begin_layout Standard
27451 To display only parts of a formula with multiple lines, one of the following
27452 environments are used:
27469 They can be inserted via the menu
27471 Insert\SpecialChar \menuseparator
27474 or by using the commands described in this section.
27477 \begin_layout Standard
27478 The first three have the same properties as the corresponding multiline
27479 formula environments, but it is possible to set further formula parts beside
27482 \begin_inset Formula \[
27483 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
27484 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
27485 \right\} \textrm{Uncertainty relations}\]
27492 \begin_layout Standard
27493 To get this formula, a displayed formula is created where the command
27498 \begin_inset LatexCommand index
27499 name "Commands ! A ! \\textbackslash aligned"
27506 A purple box appears around the blue formula box where now columns and
27507 lines can be added.
27508 Outside the multiline environment other formula parts can be set, like
27512 \begin_layout Standard
27513 The aligned environment is also suitable for long formulas whose lines are
27514 horizontally aligned.
27515 Using aligned in a displayed formula has the advantage that the formula
27516 number is vertically centered behind the lines.
27518 \begin_inset LatexCommand eqref
27519 reference "eq:kurzlang"
27523 in the aligned environment:
27524 \begin_inset Formula \begin{equation}
27525 \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}|}\\
27526 & -\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}
27534 \begin_layout Standard
27535 To use the environments
27554 \begin_inset LatexCommand index
27555 name "Commands ! A ! \\textbackslash alignedat"
27566 \begin_inset LatexCommand index
27567 name "Commands ! G ! \\textbackslash gathered"
27578 \begin_inset LatexCommand index
27579 name "Commands ! S ! \\textbackslash split"
27583 are inserted, respectively.
27584 The split environment has the same properties as the aligned environment
27585 but it can only have two columns.
27588 \begin_layout Subsection
27589 Text in multiline Formulas
27590 \begin_inset LatexCommand label
27591 name "sub:Text-in-multiline"
27596 \begin_inset LatexCommand index
27597 name "Text ! in formulas"
27602 \begin_inset LatexCommand index
27603 name "Formula ! multiline ! text"
27610 \begin_layout Standard
27611 In the Align environments, and the multline and gather environment, text
27612 can be inserted that will appear in a separate line and doesn't affect
27613 the column alignment.
27614 To do this, the command
27619 \begin_inset LatexCommand index
27620 name "Commands ! I ! \\textbackslash intertext"
27626 is used in the following scheme:
27629 \begin_layout Standard
27637 \begin_layout Standard
27638 The text should not be longer than a line because it cannot be hyphenated.
27639 As LyX doesn't yet support
27645 directly, the text is written as mathematical text.
27652 must hereby be at the beginning of a line and appears in the output above
27654 An example where the text was inserted at the beginning of the second line:
27655 \begin_inset Formula \begin{align}
27656 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
27657 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
27664 \begin_layout Section
27666 \begin_inset LatexCommand index
27667 name "Formula numbering"
27672 \begin_inset LatexCommand index
27673 name "Formula ! numbering|see{Formula numbering}"
27680 \begin_layout Subsection
27684 \begin_layout Standard
27685 Numbered formulas can be created with the menu
27687 Insert\SpecialChar \menuseparator
27688 Math\SpecialChar \menuseparator
27689 Numbered\InsetSpace ~
27694 Ctrl-Alt\InsetSpace ~
27698 Existing formulas can be numbered with the menu
27700 Edit\SpecialChar \menuseparator
27701 Math\SpecialChar \menuseparator
27702 Toggle\InsetSpace ~
27711 The formula number is displayed in LyX behind the formula as number sign
27713 The number sign is replaced in the output by the formula number.
27716 \begin_layout Standard
27717 When numbering is turned on in multiline formulas, all lines will be numbered.
27718 But the numbering can be controlled with the menu
27720 Edit\SpecialChar \menuseparator
27721 Math\SpecialChar \menuseparator
27722 Toggle\InsetSpace ~
27723 Numbering\InsetSpace ~
27735 \begin_layout Standard
27736 Except of inline formulas, all formulas can be numbered with two different
27738 \begin_inset LatexCommand ref
27739 reference "sec:Formula-Styles"
27746 \begin_layout Subsection
27748 \begin_inset LatexCommand label
27749 name "sub:Cross-References"
27754 \begin_inset LatexCommand index
27755 name "Cross-references ! to formulas"
27762 \begin_layout Standard
27763 All labeled formulas can be cross-referenced.
27764 A label is added by the menu
27766 Insert\SpecialChar \menuseparator
27769 or the toolbar button
27770 \begin_inset Graphics
27771 filename ../images/label-insert.png
27777 The cursor must hereby be inside a displayed formula.
27778 A dialog pops up displaying the prefix
27783 The label is inserted there behind the prefix.
27784 The predefined prefix means
27785 \begin_inset Quotes eld
27789 \begin_inset Quotes erd
27792 and makes it easier to find labels in large documents because it marks
27793 it as formula label to divide it from e.\InsetSpace \thinspace{}
27796 To change a label, the menu
27798 Insert\SpecialChar \menuseparator
27804 \begin_layout Standard
27805 The name of the label is displayed in LyX within two parentheses behind
27807 A formula with a label is always numbered.
27808 The label is deleted when the numbering is turned off.
27809 This is at the moment the only way to delete a label, see
27813 \begin_layout Standard
27817 href{http://bugzilla.lyx.org/show_bug.cgi?id=2556}{
27826 \begin_layout Standard
27836 \begin_layout Standard
27837 Cross-references are inserted via the menu
27839 Insert\SpecialChar \menuseparator
27842 or with the toolbar button
27843 \begin_inset Graphics
27844 filename ../images/dialog-show-new-inset_ref.png
27850 A formula cross-reference appears in the output as formula number.
27851 When in the cross-reference dialog window the format
27855 is chosen, the cross-reference appears in the output as formula number
27858 By right-clicking on a cross-reference in LyX, one jumps
27859 to the formula that is referenced.
27862 \begin_layout Standard
27863 Here are as examples cross-references to formulas of the following subsections:
27864 \begin_inset Note Note
27867 \begin_layout Standard
27868 Note the different cross-reference types.
27876 \begin_layout Standard
27878 \begin_inset LatexCommand eqref
27884 \begin_inset LatexCommand eqref
27891 \begin_inset LatexCommand ref
27896 ) big Latin letters are used for the numbering in contrary to (
27897 \begin_inset LatexCommand ref
27905 \begin_layout Standard
27906 \begin_inset VSpace medskip
27909 When the argument of
27917 \begin_layout Standard
27925 \begin_inset LatexCommand ref
27926 reference "sub:User-defined-Numbering"
27937 contains a box like in
27938 \begin_inset LatexCommand ref
27939 reference "sub:Paragraph-Boxes"
27943 , the formula cannot be referenced.
27946 \begin_layout Subsection
27948 \begin_inset LatexCommand index
27949 name "Formula numbering ! subnumbering"
27956 \begin_layout Standard
27957 With the help of the commands
27961 begin{subequations}
27969 formulas can be subnumbered.
27970 Both commands are inserted in TeX-mode.
27973 \begin_layout Standard
27975 \begin_inset Formula \begin{equation}
27976 A=C-B\label{eq:a}\end{equation}
27984 \begin_layout Standard
27988 addtocounter{equation}{-1}
27997 \begin_layout Standard
28001 begin{subequations}
28007 \begin_inset VSpace -5mm
28011 \begin_inset Formula \begin{equation}
28012 B=C-A\label{eq:b}\end{equation}
28017 \begin_inset Formula \begin{equation}
28018 C=A+B\label{eq:c}\end{equation}
28025 \begin_layout Standard
28029 \begin_layout Standard
28041 \begin_layout Standard
28042 To create the example, the following is done:
28045 \begin_layout Enumerate
28046 first formula is inserted
28049 \begin_layout Enumerate
28054 addtocounter{equation}{-1}
28056 begin{subequations}
28057 \begin_inset LatexCommand index
28058 name "Commands ! A ! \\textbackslash addtocounter"
28066 is inserted after the first formula
28069 \begin_layout Enumerate
28070 second formula is inserted
28073 \begin_layout Enumerate
28074 third formula is inserted
28077 \begin_layout Enumerate
28084 is inserted after the third formula
28087 \begin_layout Standard
28088 Every formula between the commands
28100 is subnumbered as a, b,
28104 \begin_layout Standard
28113 c, \SpecialChar \ldots{}
28114 For multiline formulas every line will be subnumbered.
28115 All subnumbered formulas are treated as
28120 But as every numbered formula increases the counter
28124 by one, the command
28130 is needed to decrease it.
28131 Otherwise the formulas
28132 \begin_inset LatexCommand eqref
28138 \begin_inset LatexCommand eqref
28144 \begin_inset LatexCommand eqref
28149 would be numbered as
28150 \begin_inset LatexCommand eqref
28156 \begin_inset LatexCommand eqref
28162 \begin_inset LatexCommand eqref
28170 \begin_layout Standard
28171 By inserting the commands in TeX-mode, a space is created between the first
28173 To revert this -5\InsetSpace \thinspace{}
28174 mm vertical space is inserted after the command
28178 begin{subequations}
28181 When the formula style
28187 \begin_layout Standard
28189 \begin_inset LatexCommand ref
28190 reference "sec:Formula-Styles"
28201 is used, -7\InsetSpace \thinspace{}
28202 mm space is inserted instead.
28205 \begin_layout Standard
28206 Here is an example for a multiline formula where the numbering was turned
28207 off for the second line:
28211 \begin_layout Standard
28215 begin{subequations}
28221 \begin_inset Formula \begin{eqnarray}
28222 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
28223 & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
28224 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
28232 \begin_layout Standard
28244 \begin_layout Subsection
28245 User-defined Numbering
28246 \begin_inset LatexCommand label
28247 name "sub:User-defined-Numbering"
28252 \begin_inset LatexCommand index
28253 name "Formula numbering ! user-defined"
28260 \begin_layout Standard
28261 \begin_inset LatexCommand index
28262 name "Formula numbering ! self-defined delimiters"
28266 With the standard numbering parentheses are set around the formula number.
28267 To replace the parentheses for example by vertical bars, the following
28268 line is added to the LaTeX-preamble:
28271 \begin_layout Standard
28283 \begin_inset Note Note
28286 \begin_layout Standard
28287 This macro is already declared in the LaTeX-preamble for testing.
28288 To activate it, remove the percent sign at the beginning.
28296 \begin_layout Standard
28297 To use other characters, the vertical bars besides the
28301 are replaced by one ore more characters.
28302 To get only the formula number the vertical bars are omitted.
28305 \begin_layout Standard
28306 \begin_inset VSpace bigskip
28309 When there should be an expression of your choice instead of the consecutive
28310 formula number in parentheses behind the formula, the command
28317 \begin_inset LatexCommand index
28318 name "Commands ! T ! \\textbackslash tag"
28323 \begin_inset Formula \begin{equation}
28324 A+B=C\tag{something}\label{eq:tag}\end{equation}
28328 In this example the command
28336 was inserted to the formula.
28339 \begin_layout Standard
28348 is inserted instead, the star prevents the parentheses around the expression:
28349 \begin_inset Formula \[
28350 A+B=C\tag*{something}\]
28357 \begin_layout Standard
28358 \begin_inset VSpace bigskip
28361 To restart the formula numbering with new document parts or sections, the
28362 following command is used:
28365 \begin_layout Standard
28370 @addtoreset{equation}{part}
28373 \begin_inset LatexCommand index
28374 name "Commands ! \"@\" ! \\textbackslash \"@\"addtoreset"
28386 @addtoreset{equation}{section}
28389 \begin_layout Standard
28390 To be able to use these commands in TeX-mode, the
28391 \begin_inset Quotes eld
28395 \begin_inset Quotes erd
28398 character has to be made
28399 \begin_inset Quotes eld
28403 \begin_inset Quotes erd
28406 for LaTeX using the command
28420 So the command sequence in TeX-mode is:
28423 \begin_layout Standard
28432 @addtoreset{equation}{section}
28439 \begin_layout Standard
28440 In the LaTeX-preamble
28452 can be omitted as they are automatically internally inserted by LyX.
28455 \begin_layout Standard
28470 \begin_layout Standard
28475 is part of the LaTeX-package
28480 \begin_inset LatexCommand index
28481 name "Packages ! carlisle"
28485 that is part of every LaTeX standard installation.
28491 \begin_inset LatexCommand index
28492 name "Packages ! remreset"
28496 has to be loaded in the LaTeX-preamble with the line
28499 \begin_layout Standard
28504 usepackage{remreset}
28507 \begin_layout Standard
28515 \begin_inset LatexCommand index
28516 name "Commands ! \"@\" ! \\textbackslash \"@\"removefromreset"
28520 can be used with the same scheme as
28529 \begin_layout Standard
28530 \begin_inset VSpace bigskip
28533 Sometimes formulas should be numbered in the following form:
28536 \begin_layout Standard
28539 (section number.formula number)
28542 \begin_layout Standard
28543 The formula number should start with every section with
28544 \begin_inset Quotes eld
28548 \begin_inset Quotes erd
28554 \begin_layout Standard
28555 For this case there is the command
28562 \begin_inset LatexCommand index
28563 name "Commands ! N ! \\textbackslash numberwithin"
28567 , which is used with the following scheme:
28570 \begin_layout Standard
28575 numberwithin{counter}{sectioning}
28578 \begin_layout Standard
28579 Counter denotes what kind of numbering is affected, sectioning denotes what
28580 number is before the dot.
28583 \begin_layout Standard
28584 Thus in our case the following LaTeX-preamble or ERT line is used:
28587 \begin_layout Standard
28592 numberwithin{equation}{section}
28595 \begin_layout Standard
28596 This is the result:
28600 \begin_layout Standard
28604 numberwithin{equation}{section}
28610 \begin_inset Formula \begin{equation}
28611 A+B=C\end{equation}
28618 \begin_layout Standard
28619 To number e.\InsetSpace \thinspace{}
28621 tables so that the number of the part is the sectioning,
28627 numberwithin{table}{part}
28632 \begin_layout Standard
28633 To go back to the standard numbering or to prevent this kind of numbering
28634 when it is defined by the document class, the following command is inserted
28635 as ERT or to the LaTeX-preamble:
28638 \begin_layout Standard
28648 \begin_inset LatexCommand index
28649 name "Commands ! A ! \\textbackslash arabic"
28659 \begin_layout Standard
28691 \begin_layout Standard
28698 uses internally the command
28704 , described above, that also needs to be reverted.
28708 \begin_layout Standard
28715 \begin_layout Standard
28719 @removefromreset{equation}{section}
28722 \begin_layout Standard
28734 \begin_layout Subsection
28735 Numbering with Roman Numbers and Letters
28736 \begin_inset LatexCommand label
28737 name "sub:Numbering-with-Roman"
28742 \begin_inset LatexCommand index
28743 name "Formula numbering ! with letters"
28748 \begin_inset LatexCommand index
28749 name "Formula numbering ! with Roman numbers"
28756 \begin_layout Standard
28757 Formulas can also be numbered with Roman numbers and Latin letters.
28758 To number for example with small Roman numbers, the command
28761 \begin_layout Standard
28773 \begin_layout Standard
28774 is inserted before the formula in TeX-mode.
28782 \begin_inset LatexCommand index
28783 name "Commands ! R ! \\textbackslash renewcommand"
28787 redefines the predefined command
28803 \begin_layout Standard
28810 has the same scheme like the command
28816 that is described in
28817 \begin_inset LatexCommand ref
28818 reference "sec:User-defined-commands"
28832 is the formula counter.
28839 is used as prefix for a counter, the value of the counter is output as
28841 When a formula is numbered, LaTeX sets internally the command
28847 behind the formula.
28853 \begin_inset LatexCommand index
28854 name "Commands ! R ! \\textbackslash roman"
28860 outputs the counter as small Roman number.
28863 \begin_layout Standard
28864 All formulas behind the command
28874 are now numbered Roman.
28875 To switch to numbering with big Roman numbers, the command is inserted
28889 \begin_inset LatexCommand index
28890 name "Commands ! R ! \\textbackslash roman@\\textbackslash Roman"
28896 \begin_inset Quotes eld
28900 \begin_inset Quotes erd
28903 with small Latin letters there is the command
28910 \begin_inset LatexCommand index
28911 name "Commands ! A ! \\textbackslash alph"
28915 , for big ones there is the command
28922 \begin_inset LatexCommand index
28923 name "Commands ! A ! \\textbackslash alph@\\textbackslash Alph"
28930 \begin_layout Standard
28931 \begin_inset Note Greyedout
28934 \begin_layout Standard
28939 Only maximal 26 formulas can be numbered with Latin letters in one document.
28947 \begin_layout Standard
28951 \begin_layout Standard
28967 \begin_layout Standard
28968 \begin_inset Formula \begin{equation}
28969 A=\textrm{small roman}\label{eq:rom}\end{equation}
28977 \begin_layout Standard
28991 \begin_inset Formula \begin{equation}
28992 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
29000 \begin_layout Standard
29014 \begin_inset Formula \begin{equation}
29015 C=\textrm{small Latin}\label{eq:lat}\end{equation}
29023 \begin_layout Standard
29037 \begin_inset Formula \begin{equation}
29038 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
29045 \begin_layout Standard
29046 To switch back to the default numbering, insert the command:
29049 \begin_layout Standard
29059 \begin_inset LatexCommand index
29060 name "Commands ! A ! \\textbackslash arabic"
29067 \begin_layout Standard
29071 \begin_layout Standard
29085 \begin_inset Formula \begin{equation}
29086 E=\textrm{Arabic}\label{eq:arab}\end{equation}
29093 \begin_layout Standard
29094 \begin_inset VSpace medskip
29097 As you see, formulas are numbered serially independent from the numbering
29099 When then numbering should start with
29100 \begin_inset Quotes eld
29104 \begin_inset Quotes erd
29107 when the style is changed, new equation counters have to be defined.
29108 A description about this can be found in the file
29112 \begin_layout Standard
29116 href{Formula-numbering.pdf}{
29121 Formula-numbering.pdf
29125 \begin_layout Standard
29133 \begin_inset Note Note
29136 \begin_layout Standard
29137 More about the command
29144 \begin_inset LatexCommand ref
29145 reference "sub:Links-in-DVI-"
29157 \begin_layout Section
29158 User-defined commands
29159 \begin_inset LatexCommand label
29160 name "sec:User-defined-commands"
29165 \begin_inset LatexCommand index
29166 name "User-defined commands"
29173 \begin_layout Standard
29174 Many LaTeX-commands are too long to be used frequently.
29175 But it is possible to define with the command
29182 \begin_inset LatexCommand index
29183 name "Commands ! N ! \\textbackslash newcommand"
29187 new shorter commands.
29190 \begin_layout Standard
29191 The command scheme of
29200 \begin_layout Standard
29205 newcommand{new command name}[number of arguments][optional
29215 \begin_layout Standard
29230 \begin_layout Standard
29237 {command definition}
29240 \begin_layout Standard
29241 \begin_inset Note Greyedout
29244 \begin_layout Standard
29249 Assure that the name of the new command is not already used in your document
29250 or by LaTeX-packages that you use.
29251 When you for example define the command
29263 , you get an error message because
29269 is already defined as command for
29270 \begin_inset Quotes eld
29274 \begin_inset Formula $\le$
29278 \begin_inset Quotes erd
29289 \begin_layout Standard
29290 \begin_inset Note Greyedout
29293 \begin_layout Standard
29298 The names of user-defined commands may only consist of Latin letters.
29306 \begin_layout Standard
29307 The number of arguments is an integer in the range 0\InsetSpace \thinspace{}
29308 -\InsetSpace \thinspace{}
29309 9 and specifies how
29310 many arguments the new command should have.
29311 With the optional value a value for an optional argument can be predefined.
29312 When this is done, the
29320 rgument of the new command is automatically an optional one.
29323 \begin_layout Standard
29324 Here are some examples:
29327 \begin_layout Itemize
29328 To define the command
29340 , the LaTeX-preamble line is:
29344 \begin_layout Standard
29366 \begin_layout Itemize
29367 To define the command
29379 , the argument (that should be underlined) must be taken into account.
29380 For this the preamble line is:
29384 \begin_layout Standard
29409 \begin_layout Standard
29428 acts as argument placeholder, the
29432 behind it denotes that it is the placeholder for the first argument.
29435 \begin_layout Itemize
29442 one can e.\InsetSpace \thinspace{}
29454 \begin_layout Standard
29473 framebox#1#2{$#3$}}
29479 \begin_layout Standard
29494 The two Dollar signs creates the extra formula needed for
29501 \begin_inset LatexCommand ref
29502 reference "sub:Boxes-with-Frame"
29509 \begin_layout Itemize
29510 To create a new command for
29516 where the color for the box needn't to be specified, the argument for the
29517 color is defined optional:
29521 \begin_layout Standard
29540 fcolorbox{#2}{#1}{$#3$}}
29546 \begin_layout Standard
29557 When the color is not specified when using
29563 , the predefined color
29570 \begin_layout Standard
29571 A test of the new defined commands:
29574 \begin_layout Standard
29576 \begin_inset Tabular
29577 <lyxtabular version="3" rows="6" columns="2">
29579 <column alignment="center" valignment="top" leftline="true" width="0">
29580 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
29581 <row topline="true" bottomline="true">
29582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29585 \begin_layout Standard
29591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29594 \begin_layout Standard
29596 \begin_inset Note Note
29599 \begin_layout Standard
29606 is only used as spacer.
29617 <row topline="true">
29618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29621 \begin_layout Standard
29628 \begin_layout Standard
29642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29645 \begin_layout Standard
29646 \begin_inset Formula $A\gr B$
29655 <row topline="true">
29656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29659 \begin_layout Standard
29667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29670 \begin_layout Standard
29671 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
29680 <row topline="true">
29681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29684 \begin_layout Standard
29688 \begin_inset Formula $\to$
29694 \begin_inset Formula $\to$
29705 \begin_layout Standard
29719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29722 \begin_layout Standard
29723 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
29732 <row topline="true">
29733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29736 \begin_layout Standard
29740 \begin_inset Formula $\to$
29751 \begin_layout Standard
29765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29768 \begin_layout Standard
29769 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
29778 <row topline="true" bottomline="true">
29779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29782 \begin_layout Standard
29788 \begin_inset Formula $\to$
29799 \begin_layout Standard
29813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29816 \begin_layout Standard
29817 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
29833 \begin_layout Section
29835 \begin_inset LatexCommand index
29843 \begin_layout Standard
29844 To create diagrams, the LaTeX-package
29850 \begin_layout Standard
29855 is part of every LaTeX standard installation.
29863 \begin_inset LatexCommand index
29864 name "Packages ! amscd"
29869 It is loaded in the LaTeX-preamble with the line
29872 \begin_layout Standard
29880 \begin_layout Standard
29881 Diagrams visualize relations and look like this:
29882 \begin_inset Formula \[
29883 \begin{CD}A@>>>B@>>>C\\
29885 F@<<<E@<<<D\end{CD}\]
29892 \begin_layout Standard
29893 To get them, the command
29898 \begin_inset LatexCommand index
29899 name "Commands ! C ! \\textbackslash CD"
29905 is inserted to a formula.
29906 A blue box appears with two dashed lines where further commands can be
29912 a new line is created.
29913 Horizontal relations are inserted in odd, vertical in even formula lines.
29916 \begin_layout Standard
29917 To create the relations there are the following commands:
29920 \begin_layout Itemize
29925 creates a left arrow,
29936 \begin_layout Itemize
29941 creates an up arrow,
29949 a vertical equal sign
29952 \begin_layout Itemize
29958 is a placeholder for non-existent relations
29961 \begin_layout Standard
29962 All arrows can be labeled as follows:
29965 \begin_layout Itemize
29966 Is text inserted between the first and second < or >, resp., it is placed
29968 When it is inserted between the second and third one, it appears under
29972 \begin_layout Itemize
29973 When text for vertical arrows is inserted between the first and second A
29974 or V, resp., it is placed left beside the arrow.
29975 When it is inserted between the second and third one, it appears right
29977 If the text contains an A or V, these letters must be set into a TeX-brace.
29980 \begin_layout Standard
29981 As example a diagram with all possible relations:
29984 \begin_layout Standard
29985 \begin_inset Formula \[
29986 \begin{CD}A@>j>>B@>>k>C@=F\\
29988 D@<<j<E@>k>>F@=C\end{CD}\]
29995 \begin_layout Standard
29996 The command for this is:
30006 \begin_layout Standard
30015 A@>j>>B@>>k>C@=F Ctrl-Enter
30021 \begin_layout Standard
30036 \begin_layout Standard
30049 \begin_layout Standard
30061 \begin_inset Formula $\to$
30072 \begin_layout Standard
30087 \begin_layout Standard
30100 \begin_layout Standard
30110 \begin_layout Standard
30116 \begin_layout Section
30121 \begin_layout Standard
30134 \begin_layout Standard
30135 Other useful math tips can be found in
30136 \begin_inset LatexCommand cite
30150 \begin_layout Standard
30158 \begin_inset Note Note
30161 \begin_layout Standard
30164 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
30167 \begin_layout Standard
30170 texorpdfstring is in section
30171 \begin_inset LatexCommand ref
30172 reference "sub:Formulas-in-Section"
30182 \begin_inset LatexCommand index
30188 \begin_inset LatexCommand index
30189 name "Ions|see{Chemical characters}"
30196 \begin_layout Subsection
30197 Chemical Symbols and Equations
30198 \begin_inset LatexCommand label
30199 name "sub:Chemical-Symbols-and"
30204 \begin_inset LatexCommand index
30205 name "Chemical characters ! Symbols"
30210 \begin_inset LatexCommand index
30211 name "Chemical equations"
30216 \begin_inset LatexCommand index
30217 name "Symbols ! chemical"
30224 \begin_layout Standard
30225 An example text from chemistry:
30228 \begin_layout Quote
30230 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30233 -ion reacts with two
30234 \begin_inset Formula $\mathrm{Na^{+}}$
30237 -ions to sodium sulfate
30238 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30242 The chemical equation for this is:
30243 \begin_inset Formula \[
30244 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
30251 \begin_layout Standard
30252 This chemical equation can directly be created as formula.
30253 To avoid that the symbols appear italic, everything is highlighted and
30254 changed by the shortcut
30259 to the upright font style.
30263 \begin_layout Standard
30269 \begin_inset LatexCommand ref
30270 reference "sub:Font-Styles"
30282 \begin_layout Subsection
30284 \begin_inset LatexCommand index
30285 name "Numbers ! negative"
30292 \begin_layout Standard
30293 Negative numbers often look ugly in formulas because the minus sign before
30294 the number is set with the same length as the minus operator sign.
30295 When writing the negative number in normal text, the minus sign appears
30299 \begin_layout Standard
30300 Thus, the problem disappears when converting the minus sign to mathematical
30304 \begin_layout Standard
30305 An example to visualize the problem:
30308 \begin_layout Standard
30310 \begin_inset Tabular
30311 <lyxtabular version="3" rows="3" columns="2">
30313 <column alignment="right" valignment="top" leftline="true" width="0">
30314 <column alignment="left" valignment="top" rightline="true" width="0">
30315 <row topline="true">
30316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30319 \begin_layout Standard
30325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30328 \begin_layout Standard
30335 <row topline="true" bottomline="true">
30336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30339 \begin_layout Standard
30345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30348 \begin_layout Standard
30349 \begin_inset Formula $x=-2$
30358 <row topline="true" bottomline="true">
30359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30362 \begin_layout Standard
30368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30371 \begin_layout Standard
30372 \begin_inset Formula $x=\textrm{-}2$
30388 \begin_layout Subsection
30389 Comma as Decimal Separator
30390 \begin_inset LatexCommand index
30398 \begin_layout Standard
30399 In LaTeX a comma inside a formula is used, according to the English convention,
30400 as number group separator.
30401 So there will be space added behind all commas in formulas.
30404 \begin_layout Standard
30405 To avoid this, the comma is highlighted and changed to mathematical text
30414 \begin_layout Standard
30415 To use all formula commas in the document as decimal separator, the file
30424 \begin_layout Standard
30429 is part of the LaTeX-package
30434 \begin_inset LatexCommand index
30435 name "Packages ! was\\vspace{4mm}"
30445 \begin_inset LatexCommand index
30446 name "Packages ! icomma"
30450 is loaded with the LaTeX-preamble line
30453 \begin_layout Standard
30461 \begin_layout Subsection
30463 \begin_inset LatexCommand label
30464 name "sub:Physical-Vectors"
30469 \begin_inset LatexCommand index
30470 name "Vectors ! physical"
30477 \begin_layout Standard
30478 Predefined vectors are offered by the LaTeX-package
30486 \begin_layout Standard
30491 is part of every LaTeX standard installation.
30497 \begin_inset LatexCommand index
30498 name "Packages ! braket"
30502 that is loaded with the LaTeX-preamble line
30505 \begin_layout Standard
30513 \begin_layout Standard
30514 The following commands are defined:
30517 \begin_layout Standard
30519 \begin_inset Tabular
30520 <lyxtabular version="3" rows="4" columns="2">
30522 <column alignment="center" valignment="top" leftline="true" width="0">
30523 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30524 <row topline="true" bottomline="true">
30525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30528 \begin_layout Standard
30534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30537 \begin_layout Standard
30544 <row topline="true">
30545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30548 \begin_layout Standard
30558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30561 \begin_layout Standard
30562 \begin_inset Formula $\Bra{\psi}$
30571 <row topline="true">
30572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30575 \begin_layout Standard
30585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30588 \begin_layout Standard
30589 \begin_inset Formula $\Ket{\psi}$
30598 <row topline="true" bottomline="true">
30599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30602 \begin_layout Standard
30614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30617 \begin_layout Standard
30618 \begin_inset Formula $\Braket{\psi|\phi}$
30634 \begin_layout Standard
30641 assures that all vertical bars are set in the size of the surrounding brackets:
30642 \begin_inset Formula \[
30643 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
30650 \begin_layout Standard
30657 can also be achieved using the command
30663 , that is described in
30664 \begin_inset LatexCommand ref
30665 reference "sub:Automatic-Bracket-Size"
30672 \begin_layout Subsection
30673 Self-defined Fractions
30674 \begin_inset LatexCommand label
30675 name "sub:Self-defined-Fractions"
30680 \begin_inset LatexCommand index
30681 name "Fractions ! self-defined"
30688 \begin_layout Standard
30689 To define custom commands for fractions, the command
30696 \begin_inset LatexCommand index
30697 name "Commands ! G ! \\textbackslash genfrac"
30701 is used in the following scheme:
30704 \begin_layout Standard
30717 bracket}{fraction bar thickness}{style}
30723 \begin_layout Standard
30738 \begin_layout Standard
30745 {numerator}{denominator}
30748 \begin_layout Standard
30749 The style is a number in the range of 0\InsetSpace \thinspace{}
30750 -\InsetSpace \thinspace{}
30754 \begin_layout Standard
30756 \begin_inset Tabular
30757 <lyxtabular version="3" rows="5" columns="2">
30759 <column alignment="center" valignment="top" leftline="true" width="0">
30760 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30761 <row topline="true" bottomline="true">
30762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30765 \begin_layout Standard
30771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30774 \begin_layout Standard
30781 <row topline="true">
30782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30785 \begin_layout Standard
30791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30794 \begin_layout Standard
30795 display style formula
30801 <row topline="true">
30802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30805 \begin_layout Standard
30811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30814 \begin_layout Standard
30821 <row topline="true">
30822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30825 \begin_layout Standard
30831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30834 \begin_layout Standard
30841 <row topline="true" bottomline="true">
30842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30845 \begin_layout Standard
30851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30854 \begin_layout Standard
30868 \begin_layout Standard
30869 When no style is given, the size is adjusted to the surrounding environment
30870 like for the command
30879 \begin_layout Standard
30880 When no fraction bar thickness is given, the predefined value of 0.4\InsetSpace \thinspace{}
30885 \begin_layout Standard
30886 \begin_inset VSpace medskip
30889 For example, the commands
30902 \begin_inset LatexCommand ref
30903 reference "sub:Fractions"
30907 are defined with the commands
30910 \begin_layout Standard
30919 genfrac{}{}{}{0}{#1}{#2}}
30922 \begin_layout Standard
30926 \begin_layout Standard
30935 genfrac{(}{)}{0pt}{1}{#1}{#2}}
30938 \begin_layout Standard
30939 \begin_inset VSpace medskip
30942 To define a fraction where the fraction bar thickness can be given as optional
30943 argument, the following line is inserted to the LaTeX-preamble:
30946 \begin_layout Standard
30955 genfrac{}{}{#1}{}{#2}{#3}}
30958 \begin_layout Standard
30960 \begin_inset Formula \begin{align*}
30961 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
30962 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
30966 As one can see, the distance of the numerator and the denominator to the
30967 fraction bar is round about three times the bar thickness.
30970 \begin_layout Subsection
30972 \begin_inset LatexCommand label
30973 name "sub:Canceled-Formulas"
30978 \begin_inset LatexCommand index
30979 name "Formula ! canceled"
30986 \begin_layout Standard
30987 To cancel formulas or formula parts, the LaTeX-package
30995 \begin_layout Standard
31000 is part of every LaTeX standard installation.
31006 \begin_inset LatexCommand index
31007 name "Packages ! cancel"
31011 has to be loaded with the LaTeX-preamble line
31014 \begin_layout Standard
31019 usepackage[samesize]{cancel}
31022 \begin_layout Standard
31023 There are four ways to cancel formulas:
31026 \begin_layout Standard
31028 \begin_inset Tabular
31029 <lyxtabular version="3" rows="5" columns="2">
31031 <column alignment="center" valignment="top" leftline="true" width="0">
31032 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
31033 <row topline="true" bottomline="true">
31034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31037 \begin_layout Standard
31043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31046 \begin_layout Standard
31048 \begin_inset Note Note
31051 \begin_layout Standard
31064 are used here as spacer.
31075 <row topline="true">
31076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31079 \begin_layout Standard
31088 \begin_layout Standard
31102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31105 \begin_layout Standard
31106 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
31115 <row topline="true">
31116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31119 \begin_layout Standard
31128 \begin_layout Standard
31142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31145 \begin_layout Standard
31146 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
31155 <row topline="true" bottomline="true">
31156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31159 \begin_layout Standard
31168 \begin_layout Standard
31182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31185 \begin_layout Standard
31186 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
31195 <row topline="true" bottomline="true">
31196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31199 \begin_layout Standard
31203 \begin_inset Formula $\to$
31214 \begin_layout Standard
31228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31231 \begin_layout Standard
31232 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
31248 \begin_layout Standard
31255 is especially suitable to visualize the reduction of fractions within formulas:
31256 \begin_inset Formula \[
31257 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
31264 \begin_layout Subsection
31265 Formulas in Section Headings
31266 \begin_inset LatexCommand label
31267 name "sub:Formulas-in-Section"
31272 \begin_inset LatexCommand index
31273 name "Formula ! in section headings"
31280 \begin_layout Standard
31281 When formulas are used in section headings, the following has to be taken
31285 \begin_layout Standard
31286 \begin_inset Note Greyedout
31289 \begin_layout Standard
31290 When the LaTeX-package
31295 \begin_inset LatexCommand index
31296 name "Packages ! hyperref"
31300 is used, PDF-bookmarks are automatically created for every section heading
31301 in the table of contents.
31302 If a section heading contains formulas, they are incorrectly displayed
31303 in the bookmark text, because formulas in bookmarks infringe the PDF convention
31312 \begin_layout Standard
31313 Both problems can be solved by inserting at the end of the section heading
31314 a short title with the menu
31316 Insert\SpecialChar \menuseparator
31321 Short titles are used as alternative for multiline section headings to
31322 keep the table of contents clearly arranged.
31323 Only the short title appears in the table of contents and therefore also
31324 in the PDF-bookmark.
31327 \begin_layout Standard
31328 When formulas should be used in the table of contents but
31332 is used, one can use the following command in TeX-mode:
31335 \begin_layout Standard
31340 texorpdfstring{part}{alternative}
31341 \begin_inset LatexCommand index
31342 name "Commands ! T ! \\textbackslash texorpdfstring"
31349 \begin_layout Standard
31350 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
31351 This can be characters, formulas, footnotes, but also cross-references.
31352 The alternative is used instead of the part for the bookmark.
31355 \begin_layout Standard
31356 Here are two example headings:
31357 \begin_inset VSpace -3mm
31364 \begin_layout Standard
31376 \begin_layout Subsubsection
31377 Heading without formula in table of contents
31378 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31382 \begin_inset OptArg
31385 \begin_layout Standard
31386 Heading without formula in table of contents
31394 \begin_layout Subsubsection
31395 Heading with formula in table of contents
31399 \begin_layout Standard
31409 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31416 \begin_layout Standard
31426 \begin_layout Standard
31430 \begin_layout Standard
31439 In the first heading a short title was used, in the second one
31448 \begin_layout Standard
31449 To get the same formatting as for the other headings, the complete heading
31452 boldmath environment
31458 \begin_layout Standard
31460 \begin_inset LatexCommand ref
31461 reference "sub:Bold-Formulas"
31473 \begin_layout Subsection
31474 Formulas in multi-column Text
31475 \begin_inset LatexCommand index
31476 name "Formula ! in multi-column text"
31483 \begin_layout Standard
31484 Formulas in multi-column text are often too wide to fit into a column and
31485 thus need to be set over the whole page width.
31486 This is done by using the LaTeX-package
31494 \begin_layout Standard
31499 is part of every LaTeX standard installation.
31505 \begin_inset LatexCommand index
31506 name "Packages ! multicol"
31510 , that is loaded with the LaTeX-preamble line
31513 \begin_layout Standard
31518 usepackage{multicol}
31521 \begin_layout Standard
31522 \begin_inset Note Greyedout
31525 \begin_layout Standard
31526 Note herby that the setting
31528 Two-column\InsetSpace ~
31533 Document\SpecialChar \menuseparator
31556 \begin_layout Standard
31557 Before the multi-column text the command
31560 \begin_layout Standard
31565 begin{multicols}{column number}
31568 \begin_layout Standard
31569 is written in TeX-mode.
31570 The column number is a number in the range of 2\InsetSpace \thinspace{}
31571 -\InsetSpace \thinspace{}
31573 Before the formula the multi-column text is ended by inserting the command
31576 \begin_layout Standard
31584 \begin_layout Standard
31588 \begin_layout Standard
31589 Due to the command some space is automatically added before the formula.
31590 To revert this, -6\InsetSpace \thinspace{}
31591 mm vertical space is inserted before the formula.
31592 When the formula style
31598 \begin_layout Standard
31600 \begin_inset LatexCommand ref
31601 reference "sec:Formula-Styles"
31612 is used, -9\InsetSpace \thinspace{}
31613 mm space is inserted instead.
31616 \begin_layout Standard
31617 As example a multi-column text with a displayed formula:
31620 \begin_layout Standard
31624 \begin_layout Standard
31628 begin{multicols}{2}
31633 Das Spektrum wird fouriertransformiert.
31634 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
31635 , Lösungsmittel) zu trennen.
31636 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
31637 nun das Aussehen des Ausgangssignals.
31638 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
31639 über alle Phasen integrieren muss.
31641 \begin_inset Formula $S$
31644 unser normiertes Ausgangssignal and
31645 \begin_inset Formula $P$
31648 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
31652 \begin_layout Standard
31662 \begin_inset VSpace -6mm
31666 \begin_inset Formula \begin{equation}
31667 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
31675 \begin_layout Standard
31679 begin{multicols}{2}
31685 \begin_inset Formula $S_{0}$
31688 das Signal ohne Gradient ist and the Normierungsbedingung
31689 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
31693 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
31695 \begin_inset Formula $\nicefrac{\pi}{2}$
31698 \InsetSpace \thinspace{}
31699 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
31700 das Signal zusätzlich abschwächt.
31701 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
31703 \begin_inset Formula $T_{2}$
31709 \begin_layout Standard
31713 \begin_layout Standard
31725 \begin_layout Subsection
31726 Formulas with Description of Variables
31727 \begin_inset LatexCommand index
31728 name "Formula ! with description of variables"
31735 \begin_layout Standard
31736 To describe variables within a formula, like in formula
31737 \begin_inset LatexCommand eqref
31738 reference "eq:within"
31747 \begin_inset Formula $n$
31751 matrix is used with left aligned columns for the
31752 \begin_inset Formula $n$
31759 \begin_layout Standard
31761 \begin_inset LatexCommand ref
31762 reference "sec:Matrices"
31771 To set the description in a smaller size, before the matrix e.\InsetSpace \thinspace{}
31784 \begin_layout Standard
31786 \begin_inset LatexCommand ref
31787 reference "sub:Font-Sizes"
31799 \begin_layout Standard
31800 When the formula style
31806 \begin_layout Standard
31808 \begin_inset LatexCommand ref
31809 reference "sec:Formula-Styles"
31830 \begin_layout Standard
31837 only works in formulas with the style
31842 \begin_inset LatexCommand ref
31843 reference "sub:Variable-Space"
31852 is inserted before and after the matrix to have the same separation of
31853 the matrix from the equation and the side margin.
31856 \begin_layout Standard
31857 When the formula style
31861 is used, the method described in
31862 \begin_inset LatexCommand ref
31863 reference "sub:Flalign-Environment"
31867 is used to indent formulas.
31869 \begin_inset LatexCommand eqref
31870 reference "eq:within"
31874 consists of five columns whereas in the first two columns contain the equation,
31875 the third the matrix, and the last one an empty TeX-brace.
31876 \begin_inset Formula \begin{flalign}
31877 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
31878 \rho & \textrm{density}\\
31879 V & \textrm{volume}\\
31880 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
31887 \begin_layout Subsection
31888 Upright small Greek Letters
31889 \begin_inset LatexCommand label
31890 name "sub:Upright-small-Greek"
31895 \begin_inset LatexCommand index
31896 name "Greek letters ! upright"
31903 \begin_layout Standard
31904 Most of the math fonts only provide italic small Greek letters.
31905 But for symbols of elementary particles like pions and neutrinos, upright
31906 Greek letters are needed.
31915 \begin_layout Standard
31920 is part of the LaTeX-package
31925 \begin_inset LatexCommand index
31926 name "Packages ! was\\vspace{4mm}"
31936 \begin_inset LatexCommand index
31937 name "Packages ! upgreek"
31941 that is loaded with the LaTeX-preamble line
31944 \begin_layout Standard
31949 usepackage{upgreek}
31952 \begin_layout Standard
31958 \begin_layout Standard
31968 \begin_inset Note Note
31971 \begin_layout Standard
31972 The following table will only be displayed when the LaTeX-package
31981 They are created when the command for a small Greek letters is started
31987 For example the command
31994 \begin_inset Formula $\uptau$
32000 \begin_layout Standard
32001 With these commands reactions of elementary particles can be typeset:
32002 \begin_inset Formula \[
32003 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
32010 \begin_layout Standard
32011 The upright letters are more bold and wider than the italic ones.
32012 They should therefore not be used for units like
32013 \begin_inset Quotes eld
32017 \begin_inset Quotes erd
32023 \begin_layout Standard
32027 \begin_layout Standard
32037 \begin_inset Note Note
32040 \begin_layout Standard
32041 The following will be displayed when the LaTeX-package
32053 \begin_layout Standard
32054 You need to install the package
32058 to see the rest of this subsection in the output.
32061 \begin_layout Standard
32065 \begin_layout Standard
32077 \begin_layout Subsection
32078 Text Characters in Formulas
32079 \begin_inset LatexCommand label
32080 name "sub:Text-Characters-in"
32085 \begin_inset LatexCommand index
32086 name "Text ! in formulas"
32093 \begin_layout Standard
32094 In some cases you might want to insert text characters directly into formulas.
32095 When for example the centered dot · is often used in formulas like
32096 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
32099 , one would have to insert the command
32109 \begin_layout Standard
32111 \begin_inset LatexCommand ref
32112 reference "sub:Binary-Operators"
32121 all the time, because this character is defined in all encodings as text
32123 But the encoding can be changed by this LaTeX-preamble line:
32126 \begin_layout Standard
32131 Declare Inputtext{183}{
32141 f\SpecialChar \textcompwordmark{}
32145 \begin_layout Standard
32146 The character encoding (menu
32148 Document\SpecialChar \menuseparator
32149 Settings\SpecialChar \menuseparator
32152 ) specifies what character appears when a keyboard key is pressed.
32153 When the key for the character '·' is pressed, internally the command
32160 But this command is not available in a formula so that you would get LaTeX-erro
32162 With the changed encoding the right command is chosen automatically, depending
32163 on if the character was inserted into a formula or not.
32166 \begin_layout Standard
32167 The encoding of several characters is saved in definition files.
32168 Fore example the encoding
32172 is defined in the file
32176 that is in the installation folder of LaTeX.
32177 Encodings should only be changed via the LaTeX-preamble and not in the
32179 Otherwise own documents could not be edited by other LyX users working
32180 on other computers.
32183 \begin_layout Standard
32184 \begin_inset VSpace medskip
32187 Besides the centered dot, in this document the degree sign ° is defined
32188 with the following LaTeX-preamble line so that it can directly be inserted
32192 \begin_layout Standard
32197 DeclareInputtext{176}{
32207 f\SpecialChar \textcompwordmark{}
32211 \begin_layout Standard
32217 \begin_layout Section
32219 Typographic Advises
32220 \begin_inset LatexCommand index
32221 name "Typographic Advises"
32228 \begin_layout Standard
32229 This section is a summary of the most important typographic rules, listed
32234 \begin_layout Standard
32235 This collection was partly taken from the German semi-official dictionary
32237 \begin_inset Quotes eld
32241 \begin_inset Quotes erd
32245 \begin_inset LatexCommand cite
32250 that lists some of the ISO rules.
32258 \begin_layout Itemize
32267 \begin_layout Standard
32268 done with font styles, see
32269 \begin_inset LatexCommand ref
32270 reference "sub:Font-Styles"
32279 : 30\InsetSpace \thinspace{}
32282 Between the value and the unit is the smallest space, see
32283 \begin_inset LatexCommand ref
32284 reference "sub:Predefined-Space"
32291 \begin_layout Itemize
32292 Percent and perthousand signs are set like physical units:
32294 1,2\InsetSpace \thinspace{}
32299 \begin_layout Standard
32312 \begin_layout Itemize
32313 The degree sign follows directly on the value: 15°, but not when it is used
32314 in units: 15\InsetSpace \thinspace{}
32318 \begin_layout Itemize
32319 In numbers with more than four digits the smallest space is inserted before
32320 every third digit to group them:
32329 18\InsetSpace \thinspace{}
32330 473\InsetSpace \thinspace{}
32334 \begin_layout Itemize
32335 For dimensionings like 120×90×40\InsetSpace \thinspace{}
32336 cm the multiplication sign
32337 \begin_inset Quotes eld
32341 \begin_inset Quotes erd
32345 It is available with the LaTeX-command
32351 , but can also directly be inserted with some keyboard definitions.
32354 \begin_layout Itemize
32355 Functions with names consisting of several letters are set upright to avoid
32357 \begin_inset LatexCommand ref
32358 reference "sub:Predefined-Functions"
32365 \begin_layout Itemize
32366 Indices consisting of several letters, are set upright:
32367 \begin_inset Formula $E_{\mathrm{kin}}$
32372 Components of matrices are set italic:
32373 \begin_inset Formula $\hat{H}_{kl}$
32379 \begin_layout Itemize
32380 The differentiation/integration operator 'd', the Euler's number 'e', and
32381 the imaginary unit 'i' should be set upright, to avoid mixing them up with
32385 \begin_layout Standard
32391 \begin_layout Section
32393 \begin_inset LatexCommand index
32401 \begin_layout Standard
32402 Some characters and symbols can be created with several commands.
32403 Here is a list of the synonym commands:
32406 \begin_layout Standard
32407 \begin_inset VSpace bigskip
32413 \begin_inset Tabular
32414 <lyxtabular version="3" rows="12" columns="2">
32416 <column alignment="center" valignment="top" leftline="true" width="0pt">
32417 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
32418 <row topline="true" bottomline="true">
32419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32422 \begin_layout Standard
32428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32431 \begin_layout Standard
32433 \begin_inset Note Note
32436 \begin_layout Standard
32443 is only used as spacer.
32454 <row topline="true">
32455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32458 \begin_layout Standard
32466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32469 \begin_layout Standard
32473 \begin_layout Standard
32486 \begin_layout Standard
32499 <row topline="true">
32500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32503 \begin_layout Standard
32511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32514 \begin_layout Standard
32523 <row topline="true">
32524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32527 \begin_layout Standard
32535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32538 \begin_layout Standard
32547 <row topline="true">
32548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32551 \begin_layout Standard
32559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32562 \begin_layout Standard
32569 <row topline="true">
32570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32573 \begin_layout Standard
32581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32584 \begin_layout Standard
32591 <row topline="true">
32592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32595 \begin_layout Standard
32603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32606 \begin_layout Standard
32615 <row topline="true">
32616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32619 \begin_layout Standard
32627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32630 \begin_layout Standard
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32702 \begin_layout Standard
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32920 \begin_layout Standard
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32933 \begin_layout Standard
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32968 \begin_layout Standard
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32992 \begin_layout Standard
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33034 \begin_layout Standard
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33053 The LaTeX Companion
33056 Addison Wesley, 2004
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33069 \begin_layout Standard
33073 href{ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf}{
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33089 of LaTeX's math abilities
33092 \begin_layout Bibliography
33093 \begin_inset LatexCommand bibitem
33098 LaTeX tips and tricks-
33102 \begin_layout Standard
33106 href{http://tug.org/TeXnik/}{
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33125 \begin_layout Bibliography
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33139 href{ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf}{
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33159 \begin_layout Standard
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33181 \begin_layout Standard
33185 href{ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}{
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33201 of all symbols available with LaTeX-packages
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33218 href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{
33227 \begin_layout Standard
33234 of the LaTeX-package
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33240 name "Packages ! hyperref"
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33261 href{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}{
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33284 \begin_inset LatexCommand ref
33285 reference "sub:Operator-Limits"
33290 \begin_inset LatexCommand index
33291 name "Commands ! M ! \\textbackslash mathclap"
33298 \begin_layout Bibliography
33299 \begin_inset LatexCommand bibitem
33310 Auflage, Duden 2001
33313 \begin_layout Subsubsection*
33314 \begin_inset LatexCommand printindex