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. 22.4
151 % check for package braket
153 \IfFileExists{braket.sty}
155 \setboolean{braket}{true}}
156 {\setboolean{braket}{false}}
158 % needed in sec. 22.10
159 % check for package upgreek
161 \IfFileExists{upgreek.sty}
162 {\usepackage{upgreek}
163 \setboolean{upgreek}{true}}
164 {\setboolean{upgreek}{false}}
166 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
171 \font_typewriter default
172 \font_default_family default
186 \paperorientation portrait
189 \paragraph_separation skip
191 \quotes_language english
194 \paperpagestyle plain
198 \tracking_changes false
199 \output_changes false
207 LyX's detailed Math manual
215 \begin_layout Standard
217 If you have comments or error corrections, please send them to the LyX Documenta
224 \begin_layout Standard
228 href{mailto:lyx-docs@lists.lyx.org?subject=LyX's Math manual}{
233 lyx-docs@lists.lyx.org
237 \begin_layout Standard
250 \begin_inset Note Note
253 \begin_layout Standard
270 \begin_layout Standard
271 \begin_inset LatexCommand tableofcontents
278 \begin_layout Standard
279 \begin_inset Note Note
282 \begin_layout Standard
283 To export this document to PDF, PS, or DVI the LaTeX-packages
296 If they are not installed you can export the document anyway but the sections
297 where the packages are required won't appear in the output.
300 \begin_layout Standard
301 The latest PDF-version of this document can be found here:
305 http://wiki.lyx.org/LyX/DocumentationDevelopment#EmbeddedObjects
313 \begin_layout Standard
319 \begin_layout Section
321 \begin_inset LatexCommand label
322 name "sec:Introduction"
329 \begin_layout Standard
330 This document explains LyX's math features and is furthermore a collection
331 of LaTeX-commands used for mathematical characters and constructs.
332 The explanations are designed for the usage of commands.
333 It is therefore required that you have read the section
335 Mathematical\InsetSpace ~
341 \begin_layout Standard
342 Most of the characters and many constructs explained in this manual are
343 also accessible via the menu
347 \SpecialChar \menuseparator
363 But everybody who has to write lots of formulas will notice that it is
364 much faster to use commands instead of the math toolbar.
365 Therefore this manual is focused on commands but also mentions the correspondin
366 g toolbar buttons when available.
369 \begin_layout Standard
370 If not specially mentioned the commands are only available within formulas.
371 To be able to use all commands explained in this document, the option
375 must be used in the document settings (menu
377 Document\SpecialChar \menuseparator
378 Settings\SpecialChar \menuseparator
386 \begin_layout Standard
389 Use AMS math package automatically
395 \begin_layout Standard
404 -math when math constructs are found that are supported by LyX.
412 \begin_layout Standard
413 This document doesn't list all
417 \begin_layout Standard
430 \begin_layout Standard
435 \begin_layout Standard
444 -math commands is in the file
448 \begin_layout Standard
452 href{ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps}{
465 \begin_layout Standard
472 , which is part of every LaTeX standard installation.
477 for lucidity reasons.
480 \begin_layout Section
482 \begin_inset LatexCommand label
483 name "sec:General-Instructions"
490 \begin_layout Standard
491 To create an inline formula
492 \begin_inset LatexCommand index
493 name "Formula ! inline"
497 that is embedded into a text line, press
501 or the toolbar button
502 \begin_inset Graphics
503 filename ../images/math-mode.png
510 To create a display style formula
511 \begin_inset LatexCommand index
512 name "Formula ! display style"
516 that will appear bigger and in an own paragraph, press
523 \begin_layout Standard
524 To change a display style formula to an inline formula, set the cursor into
525 the formula and press
531 Edit\SpecialChar \menuseparator
532 Math\SpecialChar \menuseparator
536 The same way is used to change an inline formula to a display style formula.
539 \begin_layout Standard
540 To display parts of an inline formula in the size of a display style formula,
546 \begin_inset LatexCommand index
547 name "Commands ! D ! \\textbackslash displaystyle"
554 Then a new blue box appears in which the desired formula part is inserted.
557 \begin_layout Standard
558 Only inline formulas are allowed inside tables.
561 \begin_layout Standard
566 can be turned on in the menu
568 View\SpecialChar \menuseparator
572 When you click there on
573 \begin_inset Quotes eld
577 \begin_inset Quotes erd
580 the toolbar will be shown permanently at the bottom; this state is visualized
585 menu with a checkmark.
586 When you click in this state again on
587 \begin_inset Quotes eld
591 \begin_inset Quotes erd
602 is only shown when the cursor is within a formula; this state is visualized
603 by the renaming of the menu entry from
604 \begin_inset Quotes eld
608 \begin_inset Quotes erd
612 \begin_inset Quotes eld
617 \begin_inset Quotes erd
623 \begin_layout Standard
625 \begin_inset LatexCommand index
630 is invoked by pressing the toolbar button
631 \begin_inset Graphics
632 filename ../images/ert-insert.png
639 Insert\SpecialChar \menuseparator
644 \begin_layout Standard
655 \begin_layout Standard
669 \begin_inset Note Note
672 \begin_layout Standard
673 In LyX there are three
674 \begin_inset Quotes eld
678 \begin_inset Quotes erd
681 that appear in the output with sub- and superscript letters: TeX, LaTeX,
685 \begin_layout Standard
686 To avoid that these names are recognized as proper names, TeX-braces are
687 set around one of the letters of the name.
695 \begin_layout Standard
696 To change the LaTeX-preamble
697 \begin_inset LatexCommand index
698 name "L@\\LaTeX-preamble"
704 Document\SpecialChar \menuseparator
705 Settings\SpecialChar \menuseparator
710 \begin_layout Standard
721 \begin_layout Standard
737 \begin_layout Standard
738 To edit matrices, case differentiations, and multiline formulas subsequently,
741 Edit\SpecialChar \menuseparator
746 Edit\SpecialChar \menuseparator
747 Rows\InsetSpace \thinspace{}
748 &\InsetSpace \thinspace{}
756 When lines and columns are swapped via the menu, the column or line where
757 the cursor is in is exchanged with the column to the right or the line
759 Is the cursor in the last column or row, the exchange is done with the
760 column to the left or the line above.
763 \begin_layout Standard
764 To write text in formulas
768 \begin_layout Standard
769 For multiline formulas the command
776 \begin_inset LatexCommand ref
777 reference "sub:Text-in-multiline"
791 \begin_inset LatexCommand index
792 name "Text ! in formulas"
797 \begin_inset LatexCommand index
798 name "Mathematical text"
803 This mode is invoked with the the shortcut
808 or by the insertion of the command
813 \begin_inset LatexCommand index
814 name "Commands ! T ! \\textbackslash text"
821 The text appears black in LyX and can therefore be distinguished from the
822 other formula parts that appear blue.
823 In the output mathematical text is set upright, in contrary to other formula
827 \begin_layout Subsection*
831 \begin_layout Standard
832 Most of the LaTeX-commands for math constructs have the following scheme:
835 \begin_layout Standard
851 \begin_layout Standard
852 A command starts always with a backslash
853 \begin_inset Quotes gld
863 \begin_inset Quotes grd
867 To omit optional arguments, also omit the associated brackets.
868 The braces around the required arguments are named in this document as
870 \begin_inset LatexCommand index
871 name "T@\\TeX-braces"
876 If you add in a formula a left brace to a command name, LyX creates automatical
878 In all other cases TeX-braces are created in formulas with the command
886 TeX-braces appear red in LyX, in contrary to normal braces that appear
888 In TeX-mode no command is needed to get TeX-braces.
889 TeX-braces don't appear in the output.
892 \begin_layout Standard
893 When commands without arguments, like commands for symbols are entered in
894 TeX-mode, a space character must
898 be behind the command to end it.
899 This space doesn't appear in the output.
900 When the space should appear in the output, the space must be followed
901 by a protected space in normal text.
904 \begin_layout Standard
905 A protected space is inserted with
912 \begin_layout Subsection*
918 \begin_layout Itemize
923 \begin_layout Standard
924 This visible space character can be created with the command
931 \begin_inset LatexCommand index
932 name "Commands ! T ! \\textbackslash textvisiblespace"
936 , inserted in TeX-mode.
945 \begin_layout Standard
955 denotes a space character to be input.
958 \begin_layout Itemize
960 \begin_inset Formula $\to$
963 denotes the usage of the corresponding arrow key on the keyboard.
966 \begin_layout Subsection*
970 \begin_layout Standard
972 \begin_inset Float table
978 \begin_layout Standard
982 \begin_layout Standard
983 \begin_inset LatexCommand label
984 name "tab:Used-units"
996 \begin_layout Standard
999 <lyxtabular version="3" rows="13" columns="2">
1001 <column alignment="center" valignment="top" leftline="true" width="0">
1002 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
1003 <row topline="true" bottomline="true">
1004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1007 \begin_layout Standard
1013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1016 \begin_layout Standard
1023 <row topline="true">
1024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1027 \begin_layout Standard
1033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1036 \begin_layout Standard
1043 <row topline="true">
1044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1047 \begin_layout Standard
1053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1056 \begin_layout Standard
1063 <row topline="true">
1064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1067 \begin_layout Standard
1073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1076 \begin_layout Standard
1077 Inch (1\InsetSpace \thinspace{}
1078 in = 2,54\InsetSpace \thinspace{}
1085 <row topline="true">
1086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1089 \begin_layout Standard
1095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1098 \begin_layout Standard
1099 Point (72.27\InsetSpace \thinspace{}
1100 pt = 1\InsetSpace \thinspace{}
1107 <row topline="true">
1108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1111 \begin_layout Standard
1117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1120 \begin_layout Standard
1121 Pica (1\InsetSpace \thinspace{}
1122 pc = 12\InsetSpace \thinspace{}
1129 <row topline="true">
1130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1133 \begin_layout Standard
1139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1142 \begin_layout Standard
1143 scaled point (65536\InsetSpace \thinspace{}
1144 sp = 1\InsetSpace \thinspace{}
1151 <row topline="true">
1152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1155 \begin_layout Standard
1161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1164 \begin_layout Standard
1165 big point (72\InsetSpace \thinspace{}
1166 bp = 1\InsetSpace \thinspace{}
1173 <row topline="true">
1174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1177 \begin_layout Standard
1183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1186 \begin_layout Standard
1187 Didot (1\InsetSpace \thinspace{}
1189 \begin_inset Formula $\approx$
1192 0.376\InsetSpace \thinspace{}
1199 <row topline="true">
1200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1203 \begin_layout Standard
1209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1212 \begin_layout Standard
1213 Cicero (1\InsetSpace \thinspace{}
1214 cc = 12\InsetSpace \thinspace{}
1221 <row topline="true">
1222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1225 \begin_layout Standard
1231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1234 \begin_layout Standard
1238 \begin_inset Quotes eld
1244 \begin_inset Quotes erd
1253 <row topline="true">
1254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1257 \begin_layout Standard
1263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1266 \begin_layout Standard
1268 \begin_inset Quotes eld
1276 \begin_inset Quotes erd
1285 <row topline="true" bottomline="true">
1286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1289 \begin_layout Standard
1295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1298 \begin_layout Standard
1299 math unit (1\InsetSpace \thinspace{}
1301 \begin_inset Formula $\nicefrac{1}{18}$
1304 \InsetSpace \thinspace{}
1306 \begin_inset Note Note
1309 \begin_layout Standard
1316 is explained in sec.\InsetSpace \thinspace{}
1318 \begin_inset LatexCommand ref
1319 reference "sub:Self-defined-Fractions"
1346 \begin_layout Standard
1352 \begin_layout Section
1356 \begin_layout Subsection
1358 \begin_inset LatexCommand index
1364 \begin_inset LatexCommand index
1370 \begin_inset LatexCommand index
1371 name "Superscripts|see{Exponents}"
1376 \begin_inset LatexCommand index
1377 name "Subscripts|see{Indices}"
1384 \begin_layout Standard
1385 Indices are created with an underscore
1386 \begin_inset Quotes eld
1390 \begin_inset Quotes erd
1393 or via the math toolbar button
1394 \begin_inset Graphics
1395 filename ../images/math-subscript.png
1400 , exponents with a caret
1401 \begin_inset Quotes eld
1405 \begin_inset Quotes erd
1408 or via the math toolbar button
1409 \begin_inset Graphics
1410 filename ../images/math-superscript.png
1418 \begin_layout Standard
1420 \begin_inset Tabular
1421 <lyxtabular version="3" rows="4" columns="2">
1423 <column alignment="center" valignment="top" leftline="true" width="0pt">
1424 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
1425 <row topline="true" bottomline="true">
1426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1429 \begin_layout Standard
1435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1438 \begin_layout Standard
1440 \begin_inset Note Note
1443 \begin_layout Standard
1450 is only used as spacer.
1461 <row topline="true">
1462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1465 \begin_layout Standard
1471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1474 \begin_layout Standard
1475 \begin_inset Formula $B_{V}$
1484 <row topline="true" bottomline="true">
1485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1488 \begin_layout Standard
1494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1497 \begin_layout Standard
1498 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1507 <row topline="true" bottomline="true">
1508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1511 \begin_layout Standard
1516 \begin_layout Standard
1530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1533 \begin_layout Standard
1534 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1550 \begin_layout Standard
1551 As the caret is in some languages an accent, vowels will be accentuated
1552 in this case and not set as exponents
1556 \begin_layout Standard
1557 Depending on the used keyboard settings this can also happen for other character
1564 To get in this case exponents, press
1568 after the caret as in the last example.
1571 \begin_layout Subsection
1573 \begin_inset LatexCommand label
1574 name "sub:Fractions"
1579 \begin_inset LatexCommand index
1587 \begin_layout Standard
1588 Fractions are generated with the command
1595 \begin_inset LatexCommand index
1596 name "Commands ! F ! \\textbackslash frac"
1600 or via the math toolbar button
1601 \begin_inset Graphics
1602 filename ../images/math/frac.png
1608 The font size is adjusted automatically, depending on whether the fraction
1609 is in an inline or display style formula.
1610 With the math toolbar button
1611 \begin_inset Graphics
1612 filename ../images/math/frac-square.png
1617 you can select different fraction types.
1620 \begin_layout Standard
1626 \begin_inset LatexCommand index
1627 name "Commands ! D ! \\textbackslash dfrac"
1633 a fraction can be created that has in any case the size of a display style
1640 \begin_inset LatexCommand index
1641 name "Commands ! T ! \\textbackslash tfrac"
1647 the fraction appears always with the size of an inline formula.
1651 \begin_layout Standard
1652 A line with the fraction
1653 \begin_inset Formula $\frac{1}{2}$
1656 that was created with the command
1665 \begin_layout Standard
1666 A line with the fraction
1667 \begin_inset Formula $\dfrac{1}{2}$
1670 that was created with the command
1679 \begin_layout Standard
1681 \begin_inset Tabular
1682 <lyxtabular version="3" rows="4" columns="2">
1684 <column alignment="center" valignment="top" leftline="true" width="0pt">
1685 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
1686 <row topline="true" bottomline="true">
1687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1690 \begin_layout Standard
1696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1699 \begin_layout Standard
1701 \begin_inset Note Note
1704 \begin_layout Standard
1711 is only used as spacer.
1722 <row topline="true">
1723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1726 \begin_layout Standard
1733 \begin_layout Standard
1743 \begin_inset Formula $\downarrow$
1751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1754 \begin_layout Standard
1755 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1764 <row topline="true">
1765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1768 \begin_layout Standard
1775 \begin_layout Standard
1785 \begin_inset Formula $\downarrow$
1793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1796 \begin_layout Standard
1797 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1806 <row topline="true" bottomline="true">
1807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1810 \begin_layout Standard
1817 \begin_layout Standard
1830 \begin_layout Standard
1845 \begin_layout Standard
1855 \begin_inset Formula $\downarrow$
1859 \begin_inset Formula $\downarrow\downarrow$
1867 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1870 \begin_layout Standard
1871 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1887 \begin_layout Standard
1888 \begin_inset VSpace bigskip
1893 For nested fractions the command
1900 \begin_inset LatexCommand index
1901 name "Commands ! C ! \\textbackslash cfrac"
1907 \begin_inset VSpace -3mm
1913 \begin_layout Standard
1914 \begin_inset Formula \begin{align*}
1915 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1916 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
1923 \begin_layout Standard
1924 The command for the example above is:
1927 \begin_layout Standard
1933 \begin_inset Formula $\to$
1943 \begin_inset Formula $\to$
1949 \begin_inset Formula $\to\to$
1957 \begin_layout Standard
1958 \begin_inset VSpace medskip
1964 \begin_layout Standard
1971 sets the fraction always in the size of a displayed formula, also when
1972 it is part of another fraction.
1979 has the following command scheme:
1982 \begin_layout Standard
1987 cfrac[numerator position]{numerator}{denominator}
1990 \begin_layout Standard
1991 The numerator position can be
2004 l or r aligns the numerator to the left or right, resp.\InsetSpace ~
2011 or no position is given, the numerator appears centered.
2012 These fractions demonstrate the different alignments:
2017 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2021 \begin_inset Formula $\cfrac{A}{B+C}$
2025 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2031 \begin_layout Standard
2032 \begin_inset VSpace medskip
2035 It is often advantageous to combine
2048 \begin_inset Formula \[
2049 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2056 \begin_layout Standard
2057 For inline fractions with a sloped fraction stroke you can use the command
2063 \begin_inset LatexCommand index
2064 name "Commands ! N ! \\textbackslash nicefrac"
2071 \begin_inset Formula $\nicefrac{5}{31}$
2077 \begin_layout Standard
2078 How to define own fractions where the fraction stroke can be changed, is
2080 \begin_inset LatexCommand ref
2081 reference "sub:Self-defined-Fractions"
2088 \begin_layout Subsection
2090 \begin_inset LatexCommand index
2098 \begin_layout Standard
2099 Square roots are created with
2106 \begin_inset LatexCommand index
2107 name "Commands ! S ! \\textbackslash sqrt"
2111 or the math toolbar button
2112 \begin_inset Graphics
2113 filename ../images/math/sqrt.png
2118 , all other roots with the command
2125 \begin_inset LatexCommand index
2126 name "Commands ! R ! \\textbackslash root"
2130 or with the math toolbar button
2131 \begin_inset Graphics
2132 filename ../images/math/root.png
2140 \begin_layout Standard
2142 \begin_inset Tabular
2143 <lyxtabular version="3" rows="3" columns="2">
2145 <column alignment="center" valignment="top" leftline="true" width="0pt">
2146 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2147 <row topline="true" bottomline="true">
2148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2151 \begin_layout Standard
2157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2160 \begin_layout Standard
2162 \begin_inset Note Note
2165 \begin_layout Standard
2172 is only used as spacer.
2183 <row topline="true" bottomline="true">
2184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2187 \begin_layout Standard
2194 \begin_layout Standard
2208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
2211 \begin_layout Standard
2212 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2221 <row bottomline="true">
2222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2225 \begin_layout Standard
2232 \begin_layout Standard
2242 \begin_inset Formula $\downarrow$
2250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2253 \begin_layout Standard
2254 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2270 \begin_layout Standard
2271 A square root can also be created with
2277 when the root index field is left empty.
2280 \begin_layout Standard
2281 With certain indices the distance to the root is too small, like in this
2283 \begin_inset Formula $\sqrt[\beta]{B}$
2289 \begin_inset Formula $\beta$
2293 To avoid this, the commands
2300 \begin_inset LatexCommand index
2301 name "Commands ! L ! \\textbackslash leftroot"
2312 \begin_inset LatexCommand index
2313 name "Commands ! U ! \\textbackslash uproot"
2317 are used with the following scheme:
2320 \begin_layout Standard
2334 \begin_layout Standard
2335 Distance is the number of Big Points (unit bp;
2336 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2339 ), that the index should be moved to the left or top, resp..
2340 The commands are written to the index.
2341 This way the command
2350 \begin_inset Formula $\to$
2356 \begin_inset Formula $\to$
2365 \begin_layout Standard
2375 \begin_inset Formula $\to$
2382 produces a correct typeset formula:
2383 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2389 \begin_layout Subsection
2390 Binomial coefficients
2391 \begin_inset LatexCommand index
2392 name "Binomial coefficient s"
2399 \begin_layout Standard
2400 Binomial coefficients are inserted with the command
2407 \begin_inset LatexCommand index
2408 name "Commands ! B ! \\textbackslash binom"
2412 or with the submenu of the math toolbar button
2413 \begin_inset Graphics
2414 filename ../images/math/frac-square.png
2422 \begin_layout Standard
2424 \begin_inset Tabular
2425 <lyxtabular version="3" rows="3" columns="2">
2427 <column alignment="center" valignment="top" leftline="true" width="0pt">
2428 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2429 <row topline="true" bottomline="true">
2430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2433 \begin_layout Standard
2439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2442 \begin_layout Standard
2444 \begin_inset Note Note
2447 \begin_layout Standard
2454 is only used as spacer.
2465 <row topline="true">
2466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2469 \begin_layout Standard
2476 \begin_layout Standard
2486 \begin_inset Formula $\downarrow$
2494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2497 \begin_layout Standard
2498 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2507 <row topline="true" bottomline="true">
2508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2511 \begin_layout Standard
2515 \begin_inset Formula $\to$
2525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2528 \begin_layout Standard
2529 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2545 \begin_layout Standard
2546 Analog to fractions (
2563 \begin_inset LatexCommand index
2564 name "Commands ! D ! \\textbackslash dbinom"
2577 \begin_inset LatexCommand index
2578 name "Commands ! T ! \\textbackslash tbinom"
2582 with the following command scheme:
2585 \begin_layout Standard
2590 dbinom{numerator}{denominator}
2598 tbinom{numerator}{denominator}
2601 \begin_layout Subsection
2602 Case differentiations
2603 \begin_inset LatexCommand index
2604 name "Case differentiations "
2611 \begin_layout Standard
2613 \begin_inset Tabular
2614 <lyxtabular version="3" rows="3" columns="2">
2616 <column alignment="center" valignment="top" leftline="true" width="0pt">
2617 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2618 <row topline="true" bottomline="true">
2619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2622 \begin_layout Standard
2628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2631 \begin_layout Standard
2638 <row topline="true">
2639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2642 \begin_layout Standard
2649 \begin_layout Standard
2659 \begin_inset Formula $\to$
2663 \begin_inset LatexCommand index
2664 name "Commands ! C ! \\textbackslash cases"
2673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2676 \begin_layout Standard
2677 \begin_inset Formula $\begin{cases}
2687 <row topline="true" bottomline="true">
2688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2691 \begin_layout Standard
2698 \begin_layout Standard
2712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2715 \begin_layout Standard
2716 \begin_inset Formula $\begin{cases}
2717 A & \textrm{for }x>0\\
2718 B & \textrm{for }x=0\end{cases}$
2734 \begin_layout Standard
2741 or the usage of the math toolbar button
2742 \begin_inset Graphics
2743 filename ../images/math/cases.png
2748 you can create new lines with the shortcut
2752 or the table toolbar button
2753 \begin_inset Graphics
2754 filename ../images/tabular-feature_append-row.png
2762 \begin_layout Standard
2769 is also available via the menu
2771 Insert\SpecialChar \menuseparator
2772 Math\SpecialChar \menuseparator
2778 \begin_layout Subsection
2780 \begin_inset LatexCommand index
2788 \begin_layout Standard
2796 \begin_inset LatexCommand index
2797 name "Commands ! N ! \\textbackslash not"
2801 every character can be displayed canceled.
2802 The characters are quasi accentuated by a slash.
2805 \begin_layout Standard
2807 \begin_inset Tabular
2808 <lyxtabular version="3" rows="4" columns="2">
2810 <column alignment="center" valignment="top" leftline="true" width="0pt">
2811 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
2812 <row topline="true" bottomline="true">
2813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2816 \begin_layout Standard
2822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2825 \begin_layout Standard
2832 <row topline="true">
2833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2836 \begin_layout Standard
2844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2847 \begin_layout Standard
2848 \begin_inset Formula $\not=$
2857 <row topline="true" bottomline="true">
2858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2861 \begin_layout Standard
2871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2874 \begin_layout Standard
2875 \begin_inset Formula $\not\le$
2884 <row topline="true" bottomline="true">
2885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2888 \begin_layout Standard
2898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2901 \begin_layout Standard
2902 \begin_inset Formula $\not\parallel$
2918 \begin_layout Standard
2919 The last example shows, that not all negations look good.
2920 Therefore there are for some negations special commands (see
2921 \begin_inset LatexCommand ref
2922 reference "sub:Mathematical-Symbols"
2927 \begin_inset LatexCommand ref
2928 reference "sec:Relations"
2935 \begin_layout Subsection
2937 \begin_inset LatexCommand label
2938 name "sub:Placeholders"
2943 \begin_inset LatexCommand index
2949 \begin_inset LatexCommand index
2950 name "Chemical characters ! Isotopes"
2955 \begin_inset LatexCommand index
2956 name "Isotopes|see{Chemical characters}"
2963 \begin_layout Standard
2964 When displaying e.\InsetSpace \thinspace{}
2970 \begin_layout Standard
2971 More about chemical symbols is written in
2972 \begin_inset LatexCommand ref
2973 reference "sub:Chemical-Symbols-and"
2982 the following problem occurs:
2985 \begin_layout Standard
2987 \begin_inset Tabular
2988 <lyxtabular version="3" rows="2" columns="2">
2990 <column alignment="center" valignment="top" width="0pt">
2991 <column alignment="center" valignment="top" width="0pt">
2993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2996 \begin_layout Standard
2997 Indices created with sub- and superscripts:
3002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3005 \begin_layout Standard
3006 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3019 \begin_layout Standard
3025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3028 \begin_layout Standard
3029 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3043 \begin_inset Note Note
3046 \begin_layout Standard
3053 is only used as spacer.
3061 \begin_layout Standard
3062 The shorter index is by default placed below or above the first character
3063 of the longer index.
3064 To avoid this there is the command
3071 \begin_inset LatexCommand index
3072 name "Commands ! P ! \\textbackslash phantom"
3076 or the math toolbar button\InsetSpace \thinspace{}
3081 \begin_layout Standard
3082 can be found in the submenu of the toolbar button
3083 \begin_inset Graphics
3084 filename ../images/math/space.png
3095 \begin_inset Graphics
3096 filename ../images/math/phantom.png
3101 that creates one or more phantom characters.
3108 a small blue box appears that is superposed with two red arrows.
3109 The arrows indicate that the complete width and height of the box content
3110 will be created as placeholder.
3111 Phantom characters are accordingly placeholders with the size of the characters.
3114 \begin_layout Standard
3116 \begin_inset Tabular
3117 <lyxtabular version="3" rows="4" columns="2">
3119 <column alignment="center" valignment="top" leftline="true" width="0">
3120 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
3121 <row topline="true" bottomline="true">
3122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3125 \begin_layout Standard
3131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3134 \begin_layout Standard
3136 \begin_inset Note Note
3139 \begin_layout Standard
3146 is only used as spacer.
3157 <row topline="true">
3158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3161 \begin_layout Standard
3166 \begin_layout Standard
3181 \begin_layout Standard
3191 \begin_inset Formula $\to$
3198 \begin_layout Standard
3212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3215 \begin_layout Standard
3216 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3225 <row topline="true" bottomline="true">
3226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3229 \begin_layout Standard
3234 \begin_layout Standard
3249 \begin_layout Standard
3259 \begin_inset Formula $\to$
3266 \begin_layout Standard
3280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3283 \begin_layout Standard
3284 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3293 <row topline="true" bottomline="true">
3294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3297 \begin_layout Standard
3304 \begin_layout Standard
3319 \begin_layout Standard
3329 \begin_inset Formula $\to$
3336 \begin_layout Standard
3350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3353 \begin_layout Standard
3354 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3370 \begin_layout Standard
3371 Furthermore there are the commands
3378 \begin_inset LatexCommand index
3379 name "Commands ! V ! \\textbackslash vphantom"
3383 (toolbar button \InsetSpace ~
3385 \begin_inset Graphics
3386 filename ../images/math/vphantom.png
3398 \begin_inset LatexCommand index
3399 name "Commands ! H ! \\textbackslash hphantom"
3403 (toolbar button \InsetSpace ~
3405 \begin_inset Graphics
3406 filename ../images/math/hphantom.png
3418 creates only space for the maximal height of the characters in the box
3419 but not for its width.
3426 creates only space for the width of the box content.
3427 Therefore the boxes of both commands have only one red arrow.
3430 \begin_layout Standard
3441 \begin_layout Standard
3456 space for the height of the integral sign,
3460 \begin_layout Standard
3467 creates an integral sign, see
3468 \begin_inset LatexCommand ref
3469 reference "sub:Big-Operators"
3478 because this is the larger character.
3479 An example application is in
3480 \begin_inset LatexCommand ref
3481 reference "sub:Multiline-Brackets"
3488 \begin_layout Subsection
3490 \begin_inset LatexCommand index
3496 \begin_inset LatexCommand index
3497 name "Formula ! underlined"
3504 \begin_layout Standard
3506 \begin_inset Tabular
3507 <lyxtabular version="3" rows="4" columns="2">
3509 <column alignment="center" valignment="top" leftline="true" width="0pt">
3510 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3511 <row topline="true" bottomline="true">
3512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3515 \begin_layout Standard
3521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3524 \begin_layout Standard
3526 \begin_inset Note Note
3529 \begin_layout Standard
3536 is only used as spacer.
3547 <row topline="true" bottomline="true">
3548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3551 \begin_layout Standard
3558 \begin_layout Standard
3568 \begin_inset LatexCommand index
3569 name "Commands ! O ! \\textbackslash overline"
3578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3581 \begin_layout Standard
3582 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3591 <row bottomline="true">
3592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3595 \begin_layout Standard
3602 \begin_layout Standard
3612 \begin_inset LatexCommand index
3613 name "Commands ! U ! \\textbackslash underline"
3622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3625 \begin_layout Standard
3626 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3635 <row topline="true" bottomline="true">
3636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3639 \begin_layout Standard
3646 \begin_layout Standard
3661 \begin_layout Standard
3675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3678 \begin_layout Standard
3679 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
3695 \begin_layout Standard
3696 In the last example it doesn't matter if first
3711 \begin_layout Standard
3712 To double underline e.\InsetSpace \thinspace{}
3723 \begin_layout Standard
3724 It is possible to place up to 6 lines above or below characters.
3727 \begin_layout Subsection
3729 \begin_inset LatexCommand index
3737 \begin_layout Standard
3738 There are different types of ellipses available.
3742 \begin_layout Standard
3743 In the math toolbar in the submenu of the button
3744 \begin_inset Graphics
3745 filename ../images/math/ldots.png
3755 For listings dots at the baseline are used (
3762 \begin_inset LatexCommand index
3763 name "Commands ! L ! \\textbackslash ldots"
3767 ), while for operations dots are needed that are on the same height as the
3775 \begin_inset LatexCommand index
3776 name "Commands ! C ! \\textbackslash cdots"
3781 When using the command
3788 \begin_inset LatexCommand index
3789 name "Commands ! D ! \\textbackslash dots"
3793 , LaTeX decides on the basis of the next character what type is used.
3796 \begin_layout Standard
3798 \begin_inset Tabular
3799 <lyxtabular version="3" rows="8" columns="2">
3801 <column alignment="center" valignment="top" leftline="true" width="0pt">
3802 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
3803 <row topline="true" bottomline="true">
3804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3807 \begin_layout Standard
3813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3816 \begin_layout Standard
3823 <row topline="true">
3824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3827 \begin_layout Standard
3832 \begin_layout Standard
3847 \begin_layout Standard
3861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3864 \begin_layout Standard
3865 \begin_inset Formula $A_{1},\dots,A_{n}$
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 $A_{1},\ldots,A_{n}$
3976 <row topline="true" bottomline="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 $A_{1}+\cdots+A_{n}$
4027 <row topline="true">
4028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4031 \begin_layout Standard
4039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4042 \begin_layout Standard
4043 \begin_inset Formula $\vdots$
4052 <row topline="true" bottomline="true">
4053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4056 \begin_layout Standard
4064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4067 \begin_layout Standard
4068 \begin_inset Formula $\ddots$
4077 <row topline="true" bottomline="true">
4078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4081 \begin_layout Standard
4082 3×3\InsetSpace \thinspace{}
4083 matrix with the different dots
4088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4091 \begin_layout Standard
4092 \begin_inset Formula $\begin{array}{ccc}
4093 A_{11} & \cdots & A_{1m}\\
4094 \vdots & \ddots & \vdots\\
4095 A_{n1} & \cdots & A_{nm}\end{array}$
4111 \begin_layout Standard
4112 The ellipses available in menu
4114 Insert\SpecialChar \menuseparator
4115 Special\InsetSpace ~
4127 \begin_layout Standard
4128 \begin_inset VSpace medskip
4131 Specially for matrices there are ellipses that span over several columns.
4132 They are created with the command
4139 \begin_inset LatexCommand index
4140 name "Commands ! H ! \\textbackslash hdotsfor"
4144 , that has the following scheme:
4147 \begin_layout Standard
4152 hdotsfor[distance]{number of columns}
4155 \begin_layout Standard
4156 The number of columns specifies how many columns should be spanned.
4157 Distance is a factor for the distance between the dots.
4160 \begin_layout Standard
4161 In the following matrix the command
4167 was inserted in the first box of the second line, to get an ellipsis with
4168 a dot distance twice as long as with the command
4175 \begin_inset Formula \[
4176 \left(\begin{array}{cccc}
4179 q & w & e & r\end{array}\right)\]
4183 Note that the matrix fields that should be spanned must be empty, otherwise
4184 you get LaTeX-errors.
4187 \begin_layout Standard
4188 \begin_inset VSpace bigskip
4191 Furthermore you can fill with the command
4198 \begin_inset LatexCommand index
4199 name "Commands ! D ! \\textbackslash dotfill"
4203 the rest of a line with dots.
4204 The effect of these commands is the same like with
4211 \begin_inset LatexCommand ref
4212 reference "sub:Variable-Space"
4219 \begin_layout Standard
4220 For example the command
4228 \begin_layout Standard
4242 \begin_layout Standard
4243 \begin_inset Formula $A\dotfill B$
4249 \begin_layout Standard
4256 there is for a line the command
4263 \begin_inset LatexCommand index
4264 name "Commands ! H ! \\textbackslash hrulefill"
4271 \begin_layout Standard
4272 \begin_inset Formula $A\hrulefill B$
4278 \begin_layout Standard
4279 To use the commands for text, they have to be inserted in TeX-mode.
4282 \begin_layout Section
4284 \begin_inset LatexCommand label
4290 \begin_inset LatexCommand index
4298 \begin_layout Standard
4299 Matrices can be inserted via the math toolbar button
4300 \begin_inset Graphics
4301 filename ../images/dialog-show_mathmatrix.png
4308 Insert\SpecialChar \menuseparator
4309 Math\SpecialChar \menuseparator
4313 You will be asked for the number of matrix columns and rows, and the alignment.
4314 The vertical alignment is hereby only of importance for matrices in inline
4318 \begin_layout Standard
4319 The first matrix is top
4320 \begin_inset Formula $\begin{array}[t]{cccc}
4323 C & F & I & L\end{array}$
4327 \begin_inset Formula $\begin{array}{cccc}
4330 C & F & I & L\end{array}$
4333 , and the third bottom
4334 \begin_inset Formula $\begin{array}[b]{cccc}
4337 C & F & I & L\end{array}$
4343 \begin_layout Standard
4344 The horizontal alignment specifies how the column entries should be aligned.
4345 It is set by entering a letter for every column.
4350 denotes left aligned,
4359 To create for example a 4
4364 matrix where the first column is left aligned, the second and third are
4365 centered, and the last one is right aligned, one enters for the horizontal
4371 Normally are in a matrix all columns centered, therefore the default is
4372 for every column is a
4379 \begin_layout Standard
4380 Horizontal alignment:
4383 \begin_layout Standard
4389 \begin_inset Formula $\begin{array}{lll}
4392 C & F & 10000\end{array}$
4400 \begin_inset Formula $\begin{array}{ccc}
4403 C & F & 10000\end{array}$
4411 \begin_inset Formula $\begin{array}{rrr}
4414 C & F & 10000\end{array}$
4420 \begin_layout Standard
4421 To add or delete rows and columns subsequently, the math toolbar buttons
4423 \begin_inset Graphics
4424 filename ../images/tabular-feature_append-row.png
4430 \begin_inset Graphics
4431 filename ../images/tabular-feature_delete-row.png
4436 , etc.\InsetSpace \thinspace{}
4439 Edit\SpecialChar \menuseparator
4443 New rows can also be created with
4450 \begin_layout Standard
4451 \begin_inset VSpace bigskip
4454 Parentheses around a matrix can can either be created with the commands
4462 \begin_inset LatexCommand index
4463 name "Commands ! L ! \\textbackslash left"
4474 \begin_inset LatexCommand index
4475 name "Commands ! R ! \\textbackslash right"
4485 \begin_inset LatexCommand ref
4486 reference "sub:Automatic-Bracket-Size"
4490 , or by using the following commands:
4491 \begin_inset VSpace medskip
4497 \begin_layout Standard
4501 \begin_inset Tabular
4502 <lyxtabular version="3" rows="4" columns="2">
4504 <column alignment="center" valignment="top" leftline="true" width="0">
4505 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4506 <row topline="true" bottomline="true">
4507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4510 \begin_layout Standard
4516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4519 \begin_layout Standard
4521 \begin_inset Note Note
4524 \begin_layout Standard
4531 is only used as spacer.
4542 <row topline="true">
4543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4546 \begin_layout Standard
4553 \begin_layout Standard
4566 2\InsetSpace \thinspace{}
4572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4575 \begin_layout Standard
4576 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
4577 0 & \textrm{-}\mathrm{i}\\
4578 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
4587 <row topline="true">
4588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4591 \begin_layout Standard
4598 \begin_layout Standard
4611 2\InsetSpace \thinspace{}
4617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4620 \begin_layout Standard
4621 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
4622 0 & \textrm{-}\mathrm{i}\\
4623 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
4632 <row topline="true" bottomline="true">
4633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4636 \begin_layout Standard
4643 \begin_layout Standard
4656 2\InsetSpace \thinspace{}
4662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4665 \begin_layout Standard
4666 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
4667 0 & \textrm{-}\mathrm{i}\\
4668 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
4684 \begin_inset Tabular
4685 <lyxtabular version="3" rows="4" columns="2">
4687 <column alignment="center" valignment="top" leftline="true" width="0">
4688 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
4689 <row topline="true" bottomline="true">
4690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4693 \begin_layout Standard
4699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4702 \begin_layout Standard
4709 <row topline="true">
4710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4713 \begin_layout Standard
4720 \begin_layout Standard
4733 2\InsetSpace \thinspace{}
4739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4742 \begin_layout Standard
4743 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
4744 0 & \textrm{-}\mathrm{i}\\
4745 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
4754 <row topline="true" bottomline="true">
4755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4758 \begin_layout Standard
4765 \begin_layout Standard
4778 2\InsetSpace \thinspace{}
4784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4787 \begin_layout Standard
4788 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
4789 0 & \textrm{-}\mathrm{i}\\
4790 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
4799 <row topline="true" bottomline="true">
4800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4803 \begin_layout Standard
4810 \begin_layout Standard
4823 2\InsetSpace \thinspace{}
4829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4832 \begin_layout Standard
4833 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
4834 0 & \textrm{-}\mathrm{i}\\
4835 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
4853 \begin_layout Standard
4854 \begin_inset VSpace medskip
4857 When e.\InsetSpace \thinspace{}
4865 is inserted, a blue box appears between two vertical lines where the matrix
4869 \begin_layout Standard
4870 \begin_inset VSpace bigskip
4873 As all multiline formulas are matrices, the length
4880 \begin_inset LatexCommand index
4881 name "Commands ! A ! \\textbackslash arraycolsep"
4885 that is described in
4886 \begin_inset LatexCommand ref
4887 reference "sub:Column-Separation"
4891 can also be used to change the column separation of matrices.
4894 \begin_layout Standard
4895 To change the row separation, the command
4902 \begin_inset LatexCommand index
4903 name "Commands ! A ! \\textbackslash arraystretch"
4908 It is used as follows:
4911 \begin_layout Standard
4918 arraystretch}{stretch factor}
4919 \begin_inset LatexCommand index
4920 name "Commands ! R ! \\textbackslash renewcommand"
4927 \begin_layout Standard
4934 assigns the stretch factor to the predefined command
4941 To double e.\InsetSpace \thinspace{}
4943 the row separation, use the factor 2.
4944 This is then used for all following matrices.
4945 To go back to the original separation, assign the factor 1 to
4954 \begin_layout Standard
4955 To set matrices into a text line, the command
4962 \begin_inset LatexCommand index
4963 name "Commands ! S ! \\textbackslash smallmatrix"
4968 When it is inserted a blue box with two dashed lines appears.
4969 In this box the matrix is inserted.
4972 \begin_layout Standard
4974 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
4975 C & D\end{smallmatrix}\right)$
4981 \begin_layout Section
4982 Brackets and Delimiters
4983 \begin_inset LatexCommand index
4989 \begin_inset LatexCommand index
4997 \begin_layout Subsection
4998 Vertical Brackets and Delimiters
4999 \begin_inset LatexCommand index
5000 name "Brackets ! vertical"
5007 \begin_layout Standard
5011 \begin_inset Tabular
5012 <lyxtabular version="3" rows="9" columns="2">
5014 <column alignment="center" valignment="top" leftline="true" width="0pt">
5015 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5016 <row topline="true" bottomline="true">
5017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5020 \begin_layout Standard
5026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5029 \begin_layout Standard
5036 <row topline="true">
5037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5040 \begin_layout Standard
5046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5049 \begin_layout Standard
5050 \begin_inset Formula $($
5059 <row topline="true">
5060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5063 \begin_layout Standard
5069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5072 \begin_layout Standard
5073 \begin_inset Formula $\{$
5082 <row topline="true">
5083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5086 \begin_layout Standard
5092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5095 \begin_layout Standard
5096 \begin_inset Formula $[$
5105 <row topline="true">
5106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5109 \begin_layout Standard
5117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5120 \begin_layout Standard
5121 \begin_inset Formula $\langle$
5130 <row topline="true">
5131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5134 \begin_layout Standard
5142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5145 \begin_layout Standard
5146 \begin_inset Formula $\lceil$
5155 <row topline="true">
5156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5159 \begin_layout Standard
5167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5170 \begin_layout Standard
5171 \begin_inset Formula $\lfloor$
5180 <row topline="true">
5181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5184 \begin_layout Standard
5190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5193 \begin_layout Standard
5194 \begin_inset Formula $/$
5203 <row topline="true" bottomline="true">
5204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5207 \begin_layout Standard
5213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5216 \begin_layout Standard
5217 \begin_inset Formula $|$
5233 \begin_inset Tabular
5234 <lyxtabular version="3" rows="9" columns="2">
5236 <column alignment="center" valignment="top" leftline="true" width="0pt">
5237 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
5238 <row topline="true" bottomline="true">
5239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5242 \begin_layout Standard
5248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5251 \begin_layout Standard
5258 <row topline="true">
5259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5262 \begin_layout Standard
5268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5271 \begin_layout Standard
5272 \begin_inset Formula $)$
5281 <row topline="true">
5282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5285 \begin_layout Standard
5291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5294 \begin_layout Standard
5295 \begin_inset Formula $\}$
5304 <row topline="true">
5305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5308 \begin_layout Standard
5314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5317 \begin_layout Standard
5318 \begin_inset Formula $]$
5327 <row topline="true">
5328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5331 \begin_layout Standard
5339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5342 \begin_layout Standard
5343 \begin_inset Formula $\rangle$
5352 <row topline="true">
5353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5356 \begin_layout Standard
5364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5367 \begin_layout Standard
5368 \begin_inset Formula $\rceil$
5377 <row topline="true">
5378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5381 \begin_layout Standard
5389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5392 \begin_layout Standard
5393 \begin_inset Formula $\rfloor$
5402 <row topline="true">
5403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5406 \begin_layout Standard
5416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5419 \begin_layout Standard
5420 \begin_inset Formula $\backslash$
5429 <row topline="true" bottomline="true">
5430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5433 \begin_layout Standard
5441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5444 \begin_layout Standard
5445 \begin_inset Formula $\|$
5463 \begin_layout Standard
5466 \begin_inset Note Greyedout
5469 \begin_layout Standard
5474 In TeX-mode the command
5481 \begin_inset LatexCommand index
5482 name "Commands ! T ! \\textbackslash textbackslash"
5486 must be used for the backslash, because the command
5494 produces there a line break.
5502 \begin_layout Standard
5503 For all characters listed above the size can be adjusted with the commands
5504 described in the following two subsections.
5505 When using these commands, the characters < and > can directly be used
5506 instead of the commands
5521 \begin_layout Subsubsection
5523 \begin_inset LatexCommand label
5524 name "sub:Manual-Bracket-Size"
5529 \begin_inset LatexCommand index
5530 name "Bracket size ! manual"
5537 \begin_layout Standard
5538 The bracket size can be specified manually by the LaTeX-commands
5545 \begin_inset LatexCommand index
5546 name "Commands ! B ! \\textbackslash big"
5575 denotes the smallest and
5581 the largest bracket size.
5584 \begin_layout Standard
5585 These commands are used to emphasize levels of brackets:
5588 \begin_layout Standard
5590 \begin_inset Tabular
5591 <lyxtabular version="3" rows="2" columns="2">
5593 <column alignment="center" valignment="top" width="0pt">
5594 <column alignment="center" valignment="top" width="0pt">
5596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5599 \begin_layout Standard
5600 all brackets in the same size:
5605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5608 \begin_layout Standard
5609 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
5619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5622 \begin_layout Standard
5628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5631 \begin_layout Standard
5632 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
5646 \begin_inset Note Note
5649 \begin_layout Standard
5656 is only used as spacer.
5664 \begin_layout Standard
5665 For the second formula the command
5675 \begin_layout Standard
5689 \begin_layout Standard
5690 Here is an overview about all bracket sizes:
5693 \begin_layout Standard
5713 \begin_layout Standard
5730 \begin_layout Standard
5743 \begin_layout Standard
5759 \begin_layout Standard
5761 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
5767 \begin_layout Standard
5776 -commands there is the variant
5783 \begin_inset LatexCommand index
5784 name "Commands ! B ! \\textbackslash bigm"
5788 that adds a bit more space between the bracket and its content, and the
5802 \begin_inset LatexCommand index
5803 name "Commands ! B ! \\textbackslash bigl - \\textbackslash bigr"
5807 , that don't add additional space.
5812 at the end of the command
5818 is for a left bracket; for a right bracket this will be replaced by an
5824 A left or right bracket can each be an opening or closing bracket.
5827 \begin_layout Standard
5828 In the following table is a comparison of the variants:
5831 \begin_layout Standard
5833 \begin_inset Tabular
5834 <lyxtabular version="3" rows="5" columns="2">
5836 <column alignment="center" valignment="middle" leftline="true" width="0">
5837 <column alignment="center" valignment="middle" leftline="true" rightline="true" width="0">
5838 <row topline="true" bottomline="true">
5839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5842 \begin_layout Standard
5848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5851 \begin_layout Standard
5853 \begin_inset Note Note
5856 \begin_layout Standard
5863 is only used as spacer.
5874 <row topline="true">
5875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5878 \begin_layout Standard
5893 \begin_layout Standard
5911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5914 \begin_layout Standard
5915 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
5924 <row topline="true">
5925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5928 \begin_layout Standard
5943 \begin_layout Standard
5961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5964 \begin_layout Standard
5965 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
5974 <row topline="true" bottomline="true">
5975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5978 \begin_layout Standard
5993 \begin_layout Standard
6011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6014 \begin_layout Standard
6015 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6024 <row topline="true" bottomline="true">
6025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6028 \begin_layout Standard
6040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6043 \begin_layout Standard
6044 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6060 \begin_layout Subsubsection
6061 Automatic Bracket Size
6062 \begin_inset LatexCommand label
6063 name "sub:Automatic-Bracket-Size"
6068 \begin_inset LatexCommand index
6069 name "Bracket size ! automatic"
6076 \begin_layout Standard
6077 Brackets with variable size can be inserted with the commands
6084 \begin_inset LatexCommand index
6085 name "Commands ! L ! \\textbackslash left"
6096 \begin_inset LatexCommand index
6097 name "Commands ! R ! \\textbackslash right"
6101 or via the math toolbar button
6102 \begin_inset Graphics
6103 filename ../images/dialog-show_mathdelimiter.png
6121 the wanted bracket must be inserted.
6122 The bracket size will then automatically be calculated for the output.
6125 \begin_layout Standard
6127 normal bracket: The command
6137 \begin_layout Standard
6147 \begin_inset Formula $\downarrow$
6154 \begin_layout Standard
6166 \begin_inset Formula \[
6174 \begin_layout Standard
6176 multiline bracket: The command
6188 \begin_layout Standard
6198 \begin_inset Formula $\downarrow$
6205 \begin_layout Standard
6219 \begin_inset Formula \[
6220 \ln\left(\frac{A}{C}\right)\]
6227 \begin_layout Standard
6246 This has the advantage that you can see in LyX immediately the real bracket
6247 size and that the matching right bracket will be created too.
6250 for the last example would then be:
6264 \begin_layout Standard
6274 \begin_inset Formula $\downarrow$
6280 \begin_layout Standard
6281 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6282 For example the command
6292 \begin_layout Standard
6302 \begin_inset Formula $\downarrow$
6309 \begin_layout Standard
6325 \begin_inset Formula \[
6326 \left.\frac{A}{B}\right\} \]
6344 will be converted by LyX to brackets in the right size when the document
6345 is reloaded and an omitted bracket will appear as dashed line.
6348 \begin_layout Standard
6349 \begin_inset VSpace bigskip
6352 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6360 \begin_inset LatexCommand index
6361 name "Commands ! M ! \\textbackslash middle"
6365 is additionally available for all brackets and limits.
6366 With this command the height of the following character is adapted to the
6367 one of the surrounding brackets, what is e.\InsetSpace \thinspace{}
6369 needed for physical vectors:
6370 \begin_inset Formula \[
6371 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
6375 For physical vectors there is a special LaTeX-package, described in
6376 \begin_inset LatexCommand ref
6377 reference "sub:Physical-Vectors"
6384 \begin_layout Subsection
6386 \begin_inset LatexCommand index
6387 name "Brackets ! horizontal"
6394 \begin_layout Standard
6396 \begin_inset Tabular
6397 <lyxtabular version="3" rows="4" columns="2">
6399 <column alignment="center" valignment="top" leftline="true" width="0pt">
6400 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
6401 <row topline="true" bottomline="true">
6402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6405 \begin_layout Standard
6407 \begin_inset Note Note
6410 \begin_layout Standard
6417 is only used as spacer.
6427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6430 \begin_layout Standard
6437 <row topline="true">
6438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6441 \begin_layout Standard
6445 \begin_layout Standard
6460 \begin_layout Standard
6473 \begin_layout Standard
6486 \begin_layout Standard
6499 \begin_layout Standard
6507 \begin_inset LatexCommand index
6508 name "Commands ! O ! \\textbackslash overbrace"
6517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6520 \begin_layout Standard
6521 \begin_inset Formula $\overbrace{A+B}^{3}$
6530 <row topline="true" bottomline="true">
6531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6534 \begin_layout Standard
6538 \begin_layout Standard
6553 \begin_layout Standard
6566 \begin_layout Standard
6579 \begin_layout Standard
6587 \begin_inset LatexCommand index
6588 name "Commands ! U ! \\textbackslash underbrace"
6597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6600 \begin_layout Standard
6601 \begin_inset Formula $\underbrace{A+B}_{5}$
6610 <row topline="true" bottomline="true">
6611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6614 \begin_layout Standard
6623 \begin_layout Standard
6636 \begin_layout Standard
6649 \begin_layout Standard
6662 \begin_layout Standard
6675 \begin_layout Standard
6688 \begin_layout Standard
6702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6705 \begin_layout Standard
6706 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6722 \begin_layout Standard
6723 In the last example it doesn't matter if
6735 is inserted at first.
6738 \begin_layout Standard
6739 \begin_inset VSpace bigskip
6742 When brackets are needed that overlap each other, multiline formulas, as
6744 \begin_inset LatexCommand ref
6745 reference "sec:Multiline-Formulas"
6750 \begin_inset Formula \begin{eqnarray*}
6751 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
6752 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
6756 In the first row the formula is inserted together with the first brace.
6757 It is hereby important that the space command
6761 \begin_layout Standard
6762 Space commands are explained in
6763 \begin_inset LatexCommand ref
6764 reference "sub:Predefined-Space"
6779 is inserted before the first
6780 \begin_inset Formula $d$
6783 , because the brace that ends behind the
6784 \begin_inset Formula $q$
6787 prevents that the following
6788 \begin_inset Quotes eld
6792 \begin_inset Quotes erd
6795 is surrounded by space.
6799 \begin_layout Standard
6800 because a bracket is not handled as character, see
6801 \begin_inset LatexCommand ref
6802 reference "sub:Binary-Operators"
6811 In the second row the second brace is inserted.
6812 As it should begin before the
6813 \begin_inset Formula $b$
6828 \begin_layout Standard
6836 \begin_inset LatexCommand ref
6837 reference "sub:Placeholders"
6846 This space is needed because the
6847 \begin_inset Quotes eld
6851 \begin_inset Quotes erd
6854 is also surrounded by space in the formula.
6855 The brace is placed under the command
6864 \begin_layout Standard
6865 It gets more complicated when brackets overlap each other, like in the following
6870 \begin_layout Standard
6882 \begin_inset Formula \begin{eqnarray*}
6883 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
6884 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
6892 \begin_layout Standard
6903 The first formula row is the same as the second row of the previous example,
6904 with the difference that the brace is above.
6905 The second row contains the formula together with the second brace.
6906 To avoid that there is space between the upper brace in the first row and
6907 the formula, the row spacing need to be reduced.
6908 This is not easily possible due to a bug in LyX
6912 \begin_layout Standard
6916 \begin_layout Standard
6920 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
6929 \begin_layout Standard
6942 As solution for the problem, the global formula row separation
6949 \begin_inset LatexCommand index
6950 name "Commands ! J ! \\textbackslash jot"
6954 must be changed to -6\InsetSpace \thinspace{}
6955 pt before the formula with the command
6970 is set back after the formula to the standard value of 3\InsetSpace \thinspace{}
6973 More about the row separation in formulas is explained in
6974 \begin_inset LatexCommand ref
6975 reference "sub:Line-Separation"
6982 \begin_layout Section
6984 \begin_inset LatexCommand index
6992 \begin_layout Standard
6993 Arrows can be inserted via the math toolbar button
6994 \begin_inset Graphics
6995 filename ../images/math/leftarrow.png
7000 or the commands listed in the following subsections.
7003 \begin_layout Subsection
7005 \begin_inset LatexCommand index
7006 name "Arrows ! horizontal"
7013 \begin_layout Standard
7017 \begin_inset Tabular
7018 <lyxtabular version="3" rows="8" columns="2">
7020 <column alignment="center" valignment="top" leftline="true" width="0pt">
7021 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7022 <row topline="true" bottomline="true">
7023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7026 \begin_layout Standard
7032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7035 \begin_layout Standard
7042 <row topline="true">
7043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7046 \begin_layout Standard
7054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7057 \begin_layout Standard
7058 \begin_inset Formula $\gets$
7067 <row topline="true">
7068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7071 \begin_layout Standard
7079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7082 \begin_layout Standard
7083 \begin_inset Formula $\Leftarrow$
7092 <row topline="true" bottomline="true">
7093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7096 \begin_layout Standard
7104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7107 \begin_layout Standard
7108 \begin_inset Formula $\longleftarrow$
7117 <row bottomline="true">
7118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7121 \begin_layout Standard
7129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7132 \begin_layout Standard
7133 \begin_inset Formula $\Longleftarrow$
7142 <row bottomline="true">
7143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7146 \begin_layout Standard
7154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7157 \begin_layout Standard
7158 \begin_inset Formula $\leftharpoonup$
7167 <row bottomline="true">
7168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7171 \begin_layout Standard
7179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7182 \begin_layout Standard
7183 \begin_inset Formula $\leftharpoondown$
7192 <row bottomline="true">
7193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7196 \begin_layout Standard
7204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7207 \begin_layout Standard
7208 \begin_inset Formula $\hookleftarrow$
7224 \begin_inset Tabular
7225 <lyxtabular version="3" rows="8" columns="2">
7227 <column alignment="center" valignment="top" leftline="true" width="0pt">
7228 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7229 <row topline="true" bottomline="true">
7230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7233 \begin_layout Standard
7239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7242 \begin_layout Standard
7249 <row topline="true">
7250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7253 \begin_layout Standard
7261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7264 \begin_layout Standard
7265 \begin_inset Formula $\to$
7274 <row topline="true">
7275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7278 \begin_layout Standard
7286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7289 \begin_layout Standard
7290 \begin_inset Formula $\Rightarrow$
7299 <row topline="true">
7300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7303 \begin_layout Standard
7311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7314 \begin_layout Standard
7315 \begin_inset Formula $\longrightarrow$
7324 <row topline="true">
7325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7328 \begin_layout Standard
7336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7339 \begin_layout Standard
7340 \begin_inset Formula $\Longrightarrow$
7349 <row topline="true">
7350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7353 \begin_layout Standard
7361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7364 \begin_layout Standard
7365 \begin_inset Formula $\rightharpoonup$
7374 <row topline="true" bottomline="true">
7375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7378 \begin_layout Standard
7386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7389 \begin_layout Standard
7390 \begin_inset Formula $\rightharpoondown$
7399 <row bottomline="true">
7400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7403 \begin_layout Standard
7411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7414 \begin_layout Standard
7415 \begin_inset Formula $\hookrightarrow$
7433 \begin_layout Standard
7437 \begin_inset Tabular
7438 <lyxtabular version="3" rows="6" columns="2">
7440 <column alignment="center" valignment="top" leftline="true" width="0pt">
7441 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7442 <row topline="true" bottomline="true">
7443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7446 \begin_layout Standard
7452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7455 \begin_layout Standard
7462 <row topline="true">
7463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7466 \begin_layout Standard
7474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7477 \begin_layout Standard
7478 \begin_inset Formula $\leftrightarrow$
7487 <row topline="true">
7488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7491 \begin_layout Standard
7499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7502 \begin_layout Standard
7503 \begin_inset Formula $\Leftrightarrow$
7512 <row topline="true">
7513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7516 \begin_layout Standard
7524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7527 \begin_layout Standard
7528 \begin_inset Formula $\longleftrightarrow$
7537 <row topline="true">
7538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7541 \begin_layout Standard
7549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7552 \begin_layout Standard
7553 \begin_inset Formula $\Longleftrightarrow$
7562 <row topline="true" bottomline="true">
7563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7566 \begin_layout Standard
7574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7577 \begin_layout Standard
7578 \begin_inset Formula $\rightleftharpoons$
7595 \begin_layout Standard
7607 \begin_inset Tabular
7608 <lyxtabular version="3" rows="5" columns="2">
7610 <column alignment="center" valignment="top" leftline="true" width="0pt">
7611 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7612 <row topline="true" bottomline="true">
7613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7616 \begin_layout Standard
7622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7625 \begin_layout Standard
7632 <row topline="true">
7633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7636 \begin_layout Standard
7644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7647 \begin_layout Standard
7648 \begin_inset Formula $\mapsto$
7657 <row topline="true">
7658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7661 \begin_layout Standard
7669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7672 \begin_layout Standard
7673 \begin_inset Formula $\longmapsto$
7682 <row topline="true">
7683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7686 \begin_layout Standard
7694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7697 \begin_layout Standard
7698 \begin_inset Formula $\leadsto$
7707 <row topline="true" bottomline="true">
7708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7711 \begin_layout Standard
7719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7722 \begin_layout Standard
7723 \begin_inset Formula $\dasharrow$
7741 \begin_layout Standard
7742 \begin_inset VSpace medskip
7745 Arrows used as accent like e.\InsetSpace \thinspace{}
7747 vector arrows are listed in
7748 \begin_inset LatexCommand ref
7749 reference "sec:Accents"
7756 \begin_layout Standard
7757 \begin_inset VSpace bigskip
7760 Furthermore there are the labeled arrows
7761 \begin_inset LatexCommand index
7762 name "Arrows ! labeled"
7773 \begin_inset LatexCommand index
7774 name "Commands ! X ! \\textbackslash xleftarrow"
7785 \begin_inset LatexCommand index
7786 name "Commands ! X ! \\textbackslash xrightarrow\\vspace{4mm}"
7791 When inserting one of these commands in a formula, an arrow with two blue
7792 boxes appear where the label can be inserted.
7793 The length of the arrow adapts to the label width.
7796 \begin_layout Standard
7798 \begin_inset Tabular
7799 <lyxtabular version="3" rows="3" columns="2">
7801 <column alignment="center" valignment="top" leftline="true" width="0pt">
7802 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7803 <row topline="true" bottomline="true">
7804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7807 \begin_layout Standard
7813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7816 \begin_layout Standard
7818 \begin_inset Note Note
7821 \begin_layout Standard
7828 is only used as spacer.
7839 <row topline="true">
7840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7843 \begin_layout Standard
7850 \begin_layout Standard
7860 \begin_inset Formula $\downarrow$
7864 \begin_inset Formula $\to$
7872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7875 \begin_layout Standard
7876 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
7885 <row topline="true" bottomline="true">
7886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7889 \begin_layout Standard
7896 \begin_layout Standard
7906 \begin_inset Formula $\downarrow$
7910 \begin_inset Formula $\to$
7918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7921 \begin_layout Standard
7922 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
7938 \begin_layout Subsection
7939 Vertical and diagonal Arrows
7940 \begin_inset LatexCommand index
7941 name "Arrows ! diagonal"
7946 \begin_inset LatexCommand index
7947 name "Arrows ! vertical"
7954 \begin_layout Standard
7958 \begin_inset Tabular
7959 <lyxtabular version="3" rows="7" columns="2">
7961 <column alignment="center" valignment="top" leftline="true" width="0pt">
7962 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
7963 <row topline="true" bottomline="true">
7964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7967 \begin_layout Standard
7973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7976 \begin_layout Standard
7983 <row topline="true">
7984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7987 \begin_layout Standard
7995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7998 \begin_layout Standard
7999 \begin_inset Formula $\uparrow$
8008 <row topline="true">
8009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8012 \begin_layout Standard
8020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8023 \begin_layout Standard
8024 \begin_inset Formula $\Uparrow$
8033 <row topline="true">
8034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8037 \begin_layout Standard
8045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8048 \begin_layout Standard
8049 \begin_inset Formula $\updownarrow$
8058 <row topline="true">
8059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8062 \begin_layout Standard
8070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8073 \begin_layout Standard
8074 \begin_inset Formula $\Updownarrow$
8083 <row topline="true" bottomline="true">
8084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8087 \begin_layout Standard
8095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8098 \begin_layout Standard
8099 \begin_inset Formula $\Downarrow$
8108 <row bottomline="true">
8109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8112 \begin_layout Standard
8120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8123 \begin_layout Standard
8124 \begin_inset Formula $\downarrow$
8140 \begin_inset Tabular
8141 <lyxtabular version="3" rows="5" columns="2">
8143 <column alignment="center" valignment="top" leftline="true" width="0pt">
8144 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8145 <row topline="true" bottomline="true">
8146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8149 \begin_layout Standard
8155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8158 \begin_layout Standard
8165 <row topline="true">
8166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8169 \begin_layout Standard
8177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8180 \begin_layout Standard
8181 \begin_inset Formula $\nearrow$
8190 <row topline="true">
8191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8194 \begin_layout Standard
8202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8205 \begin_layout Standard
8206 \begin_inset Formula $\searrow$
8215 <row topline="true" bottomline="true">
8216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8219 \begin_layout Standard
8227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8230 \begin_layout Standard
8231 \begin_inset Formula $\swarrow$
8240 <row bottomline="true">
8241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8244 \begin_layout Standard
8252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8255 \begin_layout Standard
8256 \begin_inset Formula $\nwarrow$
8274 \begin_layout Standard
8275 \begin_inset VSpace medskip
8278 Vertical arrows can be used also as delimiter together with the commands
8280 \begin_inset LatexCommand ref
8281 reference "sub:Manual-Bracket-Size"
8286 \begin_inset LatexCommand ref
8287 reference "sub:Automatic-Bracket-Size"
8294 \begin_layout Standard
8300 \begin_layout Section
8302 \begin_inset LatexCommand label
8308 \begin_inset LatexCommand index
8316 \begin_layout Standard
8317 Accents can be inserted via the math toolbar button
8318 \begin_inset Graphics
8319 filename ../images/math/hat.png
8324 or the commands listed in the following subsections.
8327 \begin_layout Subsection
8328 Accents for one Character
8332 \begin_layout Standard
8345 \begin_layout Standard
8347 \begin_inset LatexCommand ref
8348 reference "sub:Accents-in-Text"
8361 \begin_layout Standard
8369 \begin_inset Note Note
8372 \begin_layout Standard
8375 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
8378 \begin_layout Standard
8381 texorpdfstring is in section
8382 \begin_inset LatexCommand ref
8383 reference "sub:Formulas-in-Section"
8393 \begin_inset LatexCommand label
8394 name "sub:Accents-for-one"
8399 \begin_inset LatexCommand index
8400 name "Accents ! for one character"
8407 \begin_layout Standard
8411 \begin_inset Tabular
8412 <lyxtabular version="3" rows="8" columns="2">
8414 <column alignment="center" valignment="top" leftline="true" width="0pt">
8415 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8416 <row topline="true" bottomline="true">
8417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8420 \begin_layout Standard
8426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8429 \begin_layout Standard
8431 \begin_inset Note Note
8434 \begin_layout Standard
8441 is only used as spacer.
8452 <row topline="true" bottomline="true">
8453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8456 \begin_layout Standard
8463 \begin_layout Standard
8477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8480 \begin_layout Standard
8481 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8490 <row bottomline="true">
8491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8494 \begin_layout Standard
8501 \begin_layout Standard
8515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8518 \begin_layout Standard
8519 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8528 <row bottomline="true">
8529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8532 \begin_layout Standard
8539 \begin_layout Standard
8553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8556 \begin_layout Standard
8557 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8566 <row bottomline="true">
8567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8570 \begin_layout Standard
8578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8581 \begin_layout Standard
8582 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
8591 <row bottomline="true">
8592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8595 \begin_layout Standard
8602 \begin_layout Standard
8612 \begin_inset LatexCommand index
8622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8625 \begin_layout Standard
8626 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
8635 <row bottomline="true">
8636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8639 \begin_layout Standard
8646 \begin_layout Standard
8660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8663 \begin_layout Standard
8664 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
8673 <row bottomline="true">
8674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8677 \begin_layout Standard
8684 \begin_layout Standard
8698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8701 \begin_layout Standard
8702 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
8718 \begin_inset Tabular
8719 <lyxtabular version="3" rows="7" columns="2">
8721 <column alignment="center" valignment="top" leftline="true" width="0pt">
8722 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
8723 <row topline="true" bottomline="true">
8724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8727 \begin_layout Standard
8733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8736 \begin_layout Standard
8743 <row topline="true" bottomline="true">
8744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8747 \begin_layout Standard
8754 \begin_layout Standard
8768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8771 \begin_layout Standard
8772 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
8781 <row bottomline="true">
8782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8785 \begin_layout Standard
8792 \begin_layout Standard
8806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8809 \begin_layout Standard
8810 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
8819 <row bottomline="true">
8820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8823 \begin_layout Standard
8830 \begin_layout Standard
8844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8847 \begin_layout Standard
8848 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
8857 <row bottomline="true">
8858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8861 \begin_layout Standard
8868 \begin_layout Standard
8882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8885 \begin_layout Standard
8886 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
8895 <row bottomline="true">
8896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8899 \begin_layout Standard
8906 \begin_layout Standard
8920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8923 \begin_layout Standard
8924 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
8933 <row bottomline="true">
8934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8937 \begin_layout Standard
8944 \begin_layout Standard
8958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8961 \begin_layout Standard
8962 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
8980 \begin_layout Standard
8981 \begin_inset VSpace bigskip
8985 \begin_inset LatexCommand index
8990 in formulas, a quotation mark is inserted before the vowel.
8991 These two characters are then treated by LaTeX as
8995 character when the formula part with the umlaut is marked as German.
9003 \begin_inset Quotes eld
9007 \begin_inset Quotes erd
9010 umlauts are created as demonstrated in the following example:
9013 \begin_layout Standard
9014 \begin_inset VSpace -2mm
9020 \begin_layout Standard
9022 \begin_inset Tabular
9023 <lyxtabular version="3" rows="3" columns="2">
9025 <column alignment="center" valignment="top" leftline="true" width="0">
9026 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
9027 <row topline="true" bottomline="true">
9028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9031 \begin_layout Standard
9037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9040 \begin_layout Standard
9042 \begin_inset Note Note
9045 \begin_layout Standard
9052 is only used as spacer.
9063 <row topline="true">
9064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9067 \begin_layout Standard
9070 \begin_inset Quotes grd
9078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9081 \begin_layout Standard
9084 \begin_inset Formula $"i$
9093 <row topline="true" bottomline="true">
9094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9097 \begin_layout Standard
9104 \begin_layout Standard
9118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9121 \begin_layout Standard
9122 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9138 \begin_layout Standard
9139 Another advantage to
9145 is that umlauts can directly be converted to mathematical text because
9146 the accent commands above are
9152 in mathematical text
9155 To convert an accented character to mathematical text, only the character
9156 under the accent may be converted.
9157 This applies also for all other conversions, e.\InsetSpace \thinspace{}
9162 \begin_layout Standard
9163 In mathematical text, umlauts and other accented characters can directly
9167 \begin_layout Subsection
9168 Accents for Operators
9169 \begin_inset LatexCommand index
9170 name "Accents ! for operators"
9177 \begin_layout Standard
9185 \begin_inset LatexCommand index
9186 name "Commands ! O ! \\textbackslash overset"
9197 \begin_inset LatexCommand index
9198 name "Commands ! U ! \\textbackslash underset"
9202 characters can be placed above or below an operator, respectively, to accent
9211 \begin_inset LatexCommand index
9212 name "Commands ! S ! \\textbackslash sideset"
9216 characters can be set before and behind an operator.
9217 The command scheme is:
9220 \begin_layout Standard
9236 \begin_layout Standard
9243 must always be before the operator that should be accented.
9244 You can accent with several characters and even with other operators and
9252 for example only characters behind an operator, write nothing between the
9253 first braces but don't omit the braces.
9256 \begin_layout Standard
9257 For example the command
9262 \begin_inset Formula $\to$
9272 \begin_inset Formula $\to$
9281 \begin_layout Standard
9297 \begin_inset Formula \[
9298 \sideset{}{'}\sum_{k=1}^{n}\]
9305 \begin_layout Standard
9314 \begin_layout Standard
9329 \begin_layout Standard
9341 \begin_inset Formula $\uparrow$
9349 \begin_inset Formula \[
9350 \overset{a}{\maltese}\]
9354 As seen in the last example, with
9366 also symbols and characters can be accented; with
9372 this is not possible.
9375 \begin_layout Subsection
9376 Accents for several Characters
9377 \begin_inset LatexCommand label
9378 name "sub:Accents-for-several"
9383 \begin_inset LatexCommand index
9384 name "Accents ! for several characters"
9391 \begin_layout Standard
9395 \begin_inset Tabular
9396 <lyxtabular version="3" rows="5" columns="2">
9398 <column alignment="center" valignment="top" leftline="true" width="0pt">
9399 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9400 <row topline="true" bottomline="true">
9401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9404 \begin_layout Standard
9410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9413 \begin_layout Standard
9415 \begin_inset Note Note
9418 \begin_layout Standard
9425 is only used as spacer.
9436 <row topline="true" bottomline="true">
9437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9440 \begin_layout Standard
9447 \begin_layout Standard
9461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9464 \begin_layout Standard
9465 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9474 <row bottomline="true">
9475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9478 \begin_layout Standard
9485 \begin_layout Standard
9499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9502 \begin_layout Standard
9503 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9512 <row bottomline="true">
9513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9516 \begin_layout Standard
9523 \begin_layout Standard
9537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9540 \begin_layout Standard
9541 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9550 <row bottomline="true">
9551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9554 \begin_layout Standard
9561 \begin_layout Standard
9575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9578 \begin_layout Standard
9579 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9595 \begin_inset Tabular
9596 <lyxtabular version="3" rows="5" columns="2">
9598 <column alignment="center" valignment="top" leftline="true" width="0pt">
9599 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
9600 <row topline="true" bottomline="true">
9601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9604 \begin_layout Standard
9610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9613 \begin_layout Standard
9620 <row topline="true" bottomline="true">
9621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9624 \begin_layout Standard
9631 \begin_layout Standard
9645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9648 \begin_layout Standard
9649 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9658 <row bottomline="true">
9659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9662 \begin_layout Standard
9669 \begin_layout Standard
9683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9686 \begin_layout Standard
9687 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9696 <row bottomline="true">
9697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9700 \begin_layout Standard
9707 \begin_layout Standard
9721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9724 \begin_layout Standard
9725 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9734 <row bottomline="true">
9735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9738 \begin_layout Standard
9745 \begin_layout Standard
9759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9762 \begin_layout Standard
9763 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
9781 \begin_layout Standard
9782 \begin_inset VSpace medskip
9785 With these commands as many characters as you like can be accented.
9798 will only be set in the output with a length of three characters, as shown
9799 in the following example:
9800 \begin_inset Formula \[
9801 \widetilde{A+B=C-D}\]
9808 \begin_layout Standard
9816 \begin_inset LatexCommand index
9817 name "Commands ! O ! \\textbackslash overset"
9828 \begin_inset LatexCommand index
9829 name "Commands ! U ! \\textbackslash underset"
9833 described in the previous subsection it is also possible to accent several
9843 \begin_layout Standard
9853 \begin_inset Formula $\downarrow$
9859 \begin_inset Formula \[
9860 \underset{***}{A=B}\]
9867 \begin_layout Section
9869 \begin_inset LatexCommand label
9875 \begin_inset LatexCommand index
9876 name "Space ! horizontal"
9883 \begin_layout Subsection
9885 \begin_inset LatexCommand label
9886 name "sub:Predefined-Space"
9891 \begin_inset LatexCommand index
9892 name "Space ! horizontal ! predefined"
9899 \begin_layout Standard
9900 Sometimes it is necessary to insert horizontal space to a formula.
9901 This is done by inserting a protected space (shortcut
9907 \begin_inset Quotes eld
9917 \begin_layout Standard
9930 \begin_inset Quotes erd
9933 appears and by pressing
9937 several times one can select one of eight different space sizes.
9938 The spaces can also be inserted using the math toolbar button
9939 \begin_inset Graphics
9940 filename ../images/math/space.png
9945 or special commands.
9946 Independent from the inserted command, one can select the size again by
9954 \begin_layout Standard
9957 \begin_inset VSpace -5mm
9961 \begin_inset Tabular
9962 <lyxtabular version="3" rows="3" columns="7">
9964 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
9965 <column alignment="center" valignment="top" leftline="true" width="0">
9966 <column alignment="center" valignment="top" leftline="true" width="0">
9967 <column alignment="center" valignment="top" leftline="true" width="0">
9968 <column alignment="center" valignment="top" leftline="true" width="0">
9969 <column alignment="center" valignment="top" leftline="true" width="0">
9970 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
9971 <row topline="true">
9972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9975 \begin_layout Standard
9981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9984 \begin_layout Standard
9992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9995 \begin_layout Standard
10003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10006 \begin_layout Standard
10014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10017 \begin_layout Standard
10025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10028 \begin_layout Standard
10036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10039 \begin_layout Standard
10048 <row topline="true">
10049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10052 \begin_layout Standard
10057 keystrokes after inserting the protected space
10062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10065 \begin_layout Standard
10071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10074 \begin_layout Standard
10080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10083 \begin_layout Standard
10089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10092 \begin_layout Standard
10098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10101 \begin_layout Standard
10107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10110 \begin_layout Standard
10117 <row topline="true" bottomline="true">
10118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10121 \begin_layout Standard
10127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10130 \begin_layout Standard
10131 \begin_inset Formula $A\, B$
10139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10142 \begin_layout Standard
10143 \begin_inset Formula $A\: B$
10151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10154 \begin_layout Standard
10155 \begin_inset Formula $A\; B$
10163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10166 \begin_layout Standard
10167 \begin_inset Formula $A\quad B$
10175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10178 \begin_layout Standard
10179 \begin_inset Formula $A\qquad B$
10187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10190 \begin_layout Standard
10191 \begin_inset Formula $A\! B$
10207 \begin_layout Standard
10208 The last size seem to produce no space.
10209 It is displayed red in LyX contrary to the other sizes, because it is a
10211 There are two more negative spaces:
10214 \begin_layout Standard
10216 \begin_inset Tabular
10217 <lyxtabular version="3" rows="3" columns="3">
10219 <column alignment="center" valignment="middle" leftline="true" width="6.8cm">
10220 <column alignment="center" valignment="top" leftline="true" width="0pt">
10221 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
10222 <row topline="true" bottomline="true">
10223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10226 \begin_layout Standard
10232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10235 \begin_layout Standard
10243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10246 \begin_layout Standard
10255 <row bottomline="true">
10256 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10259 \begin_layout Standard
10264 keystrokes after inserting the protected space
10269 <cell alignment="center" valignment="top" leftline="true" usebox="none">
10272 \begin_layout Standard
10278 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10281 \begin_layout Standard
10288 <row bottomline="true">
10289 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10292 \begin_layout Standard
10298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10301 \begin_layout Standard
10302 \begin_inset Formula $A\negmedspace B$
10310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10313 \begin_layout Standard
10314 \begin_inset Formula $A\negthickspace B$
10330 \begin_layout Standard
10331 Negative spaces can lead to characters overlapping each other.
10332 Thus they can be used to enforce ligatures, what is e.\InsetSpace \thinspace{}
10334 useful for summation
10338 \begin_layout Standard
10340 \begin_inset Tabular
10341 <lyxtabular version="3" rows="3" columns="2">
10343 <column alignment="center" valignment="top" leftline="true" width="0">
10344 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10345 <row topline="true" bottomline="true">
10346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10349 \begin_layout Standard
10355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10358 \begin_layout Standard
10360 \begin_inset Note Note
10363 \begin_layout Standard
10370 is only used as spacer.
10381 <row topline="true">
10382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10385 \begin_layout Standard
10394 \begin_layout Standard
10408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10411 \begin_layout Standard
10412 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10421 <row topline="true" bottomline="true">
10422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10425 \begin_layout Standard
10436 \begin_layout Standard
10450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10453 \begin_layout Standard
10454 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10470 \begin_layout Standard
10471 Relations like for example equal signs, are always surrounded by space.
10472 To suppress this, the equal sign is placed into a TeX-brace.
10473 The following example demonstrates this:
10476 \begin_layout Standard
10478 \begin_inset Tabular
10479 <lyxtabular version="3" rows="2" columns="2">
10481 <column alignment="center" valignment="top" width="0pt">
10482 <column alignment="center" valignment="top" width="0pt">
10484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10487 \begin_layout Standard
10493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10496 \begin_layout Standard
10497 \begin_inset Formula $A=B$
10507 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10510 \begin_layout Standard
10511 \begin_inset Note Note
10514 \begin_layout Standard
10521 is only used as spacer.
10527 \begin_inset Formula $\raisebox{5mm}{}$
10530 equation without space
10535 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" usebox="none">
10538 \begin_layout Standard
10539 \begin_inset Formula $A{=}B$
10555 \begin_layout Standard
10557 The command for the last formula is:
10562 \begin_inset Formula $\to$
10568 \begin_layout Standard
10569 \begin_inset VSpace bigskip
10572 Spaces are needed for physical units, because the space between the value
10573 and the unit is the smallest one and not a normal space.
10574 For units in text, the smallest space is inserted via the menu
10576 Insert\SpecialChar \menuseparator
10577 Formatting\SpecialChar \menuseparator
10588 \begin_layout Standard
10589 An example to visualize the difference:
10592 \begin_layout Standard
10593 \begin_inset Tabular
10594 <lyxtabular version="3" rows="2" columns="2">
10596 <column alignment="left" valignment="top" width="0">
10597 <column alignment="left" valignment="top" width="0">
10599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10602 \begin_layout Standard
10604 \begin_inset Formula $\cdot$
10612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10615 \begin_layout Standard
10616 space between value and unit
10623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10626 \begin_layout Standard
10627 24\InsetSpace \thinspace{}
10629 \begin_inset Formula $\cdot$
10637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10640 \begin_layout Standard
10641 smallest space between value and unit
10654 \begin_layout Subsection
10659 \begin_layout Standard
10672 \begin_layout Standard
10673 for vertical space in formulas see
10674 \begin_inset LatexCommand ref
10675 reference "sub:Line-Separation"
10688 \begin_layout Standard
10696 \begin_inset Note Note
10699 \begin_layout Standard
10702 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
10705 \begin_layout Standard
10708 texorpdfstring is in section
10709 \begin_inset LatexCommand ref
10710 reference "sub:Formulas-in-Section"
10720 \begin_inset LatexCommand label
10721 name "sub:Variable-Space"
10726 \begin_inset LatexCommand index
10727 name "Space ! horizontal ! variable"
10734 \begin_layout Standard
10735 Space with a defined length can be inserted in LyX with the command
10744 \begin_inset LatexCommand index
10745 name "Commands ! H ! \\textbackslash hspace"
10750 For the length all units listed in
10751 \begin_inset LatexCommand ref
10752 reference "tab:Used-units"
10756 are allowed, except of the unit
10757 \begin_inset Quotes eld
10761 \begin_inset Quotes erd
10765 The length may also be negative.
10766 To insert so many space that the formula uses all available space, the
10774 \begin_inset LatexCommand index
10775 name "Commands ! H ! \\textbackslash hfill"
10782 \begin_layout Standard
10783 \begin_inset VSpace -1mm
10789 \begin_layout Standard
10791 \begin_inset Tabular
10792 <lyxtabular version="3" rows="4" columns="2">
10794 <column alignment="center" valignment="top" leftline="true" width="0">
10795 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
10796 <row topline="true" bottomline="true">
10797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10800 \begin_layout Standard
10806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10809 \begin_layout Standard
10816 <row topline="true">
10817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10820 \begin_layout Standard
10824 \begin_inset Formula $\to$
10834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10837 \begin_layout Standard
10838 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
10847 <row topline="true" bottomline="true">
10848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10851 \begin_layout Standard
10855 \begin_inset Formula $\to$
10865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10868 \begin_layout Standard
10869 \begin_inset Formula $A\hspace{-1mm}A\not=A$
10878 <row topline="true" bottomline="true">
10879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10882 \begin_layout Standard
10889 \begin_layout Standard
10903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10906 \begin_layout Standard
10907 \begin_inset Formula $A=A\hfill B=B$
10923 \begin_layout Standard
10924 In the last example the available space is given by the longest column entry
10926 In an inline formula the space depends on the length of the line in which
10934 Thus, when the line uses the full width, no space will be created.
10941 has only an effect on displayed formulas when the formula style
10946 (Formula styles are explained in
10947 \begin_inset LatexCommand ref
10948 reference "sec:Formula-Styles"
10955 \begin_layout Standard
10968 can also be inserted in TeX-mode to use them for text:
10971 \begin_layout Standard
10972 This is a line with
10976 \begin_layout Standard
10985 2\InsetSpace \thinspace{}
10989 \begin_layout Standard
10990 This is a line with
10995 \begin_layout Standard
10996 In the last example
11002 was inserted via the menu
11004 Insert\SpecialChar \menuseparator
11005 Formatting\SpecialChar \menuseparator
11006 Horizontal\InsetSpace ~
11009 , what is not possible in formulas.
11010 This has the advantage that one can directly see in LyX that this is a
11014 \begin_layout Standard
11015 When the commands are at the begin of a text line but not at the beginning
11016 of a paragraph, they will be ignored by LaTeX.
11017 To avoid that, the command
11030 To get the same with
11036 , a line break and an empty placeholder
11042 \begin_layout Standard
11043 for placeholders see
11044 \begin_inset LatexCommand ref
11045 reference "sub:Placeholders"
11056 is inserted in TeX-mode with the command
11072 \begin_layout Subsection
11073 Space besides inline Formulas
11074 \begin_inset LatexCommand index
11075 name "Space ! besides inline formulas"
11082 \begin_layout Standard
11083 The space that surrounds inline formulas can be adjusted with the length
11089 \begin_inset LatexCommand index
11090 name "Commands ! M ! \\textbackslash mathsurround"
11097 The value of a length is set with the command
11102 \begin_inset LatexCommand index
11103 name "Commands ! S ! \\textbackslash setlength"
11109 that has the following scheme:
11112 \begin_layout Standard
11117 setlength{length name}{value}
11120 \begin_layout Standard
11127 to the value 5\InsetSpace \thinspace{}
11131 \begin_layout Standard
11141 \begin_layout Standard
11142 is inserted in TeX-mode.
11143 5\InsetSpace \thinspace{}
11144 mm space will now be set around all inline formulas:
11148 \begin_layout Standard
11162 \begin_layout Standard
11163 This is a line with an inline formula
11164 \begin_inset Formula $A=B$
11167 with 5\InsetSpace \thinspace{}
11168 mm surrounding space.
11172 \begin_layout Standard
11186 \begin_layout Standard
11187 To return to the predefined value,
11193 is set to the value 0\InsetSpace \thinspace{}
11197 \begin_layout Section
11199 \begin_inset LatexCommand index
11205 \begin_inset LatexCommand index
11206 name "Frames | see {Boxes}"
11213 \begin_layout Standard
11214 Boxes for text are described in chapter
11220 Embedded\InsetSpace ~
11226 \begin_layout Subsection
11228 \begin_inset LatexCommand label
11229 name "sub:Boxes-with-Frame"
11234 \begin_inset LatexCommand index
11235 name "Boxes ! with frame"
11242 \begin_layout Standard
11243 It is possible to frame formulas or parts of it with the commands
11250 \begin_inset LatexCommand index
11251 name "Commands ! F ! \\textbackslash fbox"
11262 \begin_inset LatexCommand index
11263 name "Commands ! B ! \\textbackslash boxed"
11270 \begin_layout Standard
11271 When one of these commands is inserted to a formula, a blue box appears
11272 within a frame to enter formula parts.
11279 an additional formula has to be created by
11287 \begin_layout Standard
11288 Due to a bug in LyX it is not possible to create a new formula with
11296 \begin_layout Standard
11300 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11309 \begin_layout Standard
11321 , because the box content will otherwise be treated as mathematical text.
11328 is used, a new formula is automatically created inside the frame.
11331 \begin_layout Standard
11338 is not suitable to frame displayed formulas, because the formula will always
11339 be set in the size of the text.
11346 is in contrary not suitable to frame inline formulas, because the formula
11347 will always be set in the size of a displayed formula.
11350 \begin_layout Standard
11357 there is the command
11364 \begin_inset LatexCommand index
11365 name "Commands ! F ! \\textbackslash framebox"
11369 where additionally the frame width and the alignment can be specified.
11376 is used in the following scheme:
11379 \begin_layout Standard
11384 framebox[frame width][position]{box content}
11387 \begin_layout Standard
11388 The position can either be
11405 right aligns the formula in the box.
11406 When no position is given, the formula will be centered.
11409 also no position can be given.
11410 In this case the frame width is adjusted to the box content like for
11419 \begin_layout Standard
11426 is inserted, a box appears containing three blue boxes.
11430 \begin_layout Standard
11431 Due to a bug in LyX the cursor has to be placed left beside blue the boxes
11436 \begin_layout Standard
11440 href{http://bugzilla.lyx.org/show_bug.cgi?id=2461}{
11449 \begin_layout Standard
11461 The first two boxes are surrounded by brackets and denote the two optional
11463 The third box is for formula parts like for
11472 \begin_layout Standard
11474 \begin_inset Note Note
11477 \begin_layout Standard
11478 The table has been set into a minipage to make the footnote appearing.
11479 Otherwise the footnote text would not be displayed.
11485 \begin_inset Box Frameless
11494 height_special "totalheight"
11497 \begin_layout Standard
11499 \begin_inset Tabular
11500 <lyxtabular version="3" rows="5" columns="2">
11502 <column alignment="center" valignment="top" leftline="true" width="0">
11503 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
11504 <row topline="true" bottomline="true">
11505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11508 \begin_layout Standard
11513 \begin_layout Standard
11514 Due to a bug in LyX it is not possible to create a new formula with
11522 \begin_layout Standard
11526 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
11535 \begin_layout Standard
11552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11555 \begin_layout Standard
11557 \begin_inset Note Note
11560 \begin_layout Standard
11567 is only used as spacer.
11578 <row topline="true">
11579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11582 \begin_layout Standard
11589 \begin_layout Standard
11608 \begin_layout Standard
11622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11625 \begin_layout Standard
11626 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
11636 <row topline="true">
11637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11640 \begin_layout Standard
11647 \begin_layout Standard
11662 \begin_layout Standard
11676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11679 \begin_layout Standard
11680 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
11689 <row topline="true">
11690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11693 \begin_layout Standard
11700 \begin_layout Standard
11714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11717 \begin_layout Standard
11718 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
11727 <row topline="true" bottomline="true">
11728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11731 \begin_layout Standard
11738 \begin_layout Standard
11748 \begin_inset Formula $\to$
11752 \begin_inset Formula $\to$
11765 \begin_layout Standard
11775 \begin_inset Formula $\downarrow$
11783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11786 \begin_layout Standard
11787 \begin_inset Formula $\raisebox{6mm}{}$
11791 \begin_inset Formula $\framebox[20mm]{$\frac{A}{B}$}$
11795 \begin_inset Formula $\raisebox{-4mm}{}$
11816 \begin_layout Standard
11817 The frame thickness can also be adjusted.
11818 To do this the following commands have to be inserted in TeX-mode before
11822 \begin_layout Standard
11832 \begin_inset Quotes eld
11836 \begin_inset Quotes erd
11850 \begin_inset Quotes eld
11854 \begin_inset Quotes erd
11860 \begin_layout Standard
11861 \begin_inset Quotes eld
11865 \begin_inset Quotes erd
11868 specifies the minimal distance between the frame and the first character
11870 An example for this is the following framed formula:
11874 \begin_layout Standard
11886 \begin_inset Formula \[
11891 Before this formula the commands
11894 \begin_layout Standard
11916 \begin_layout Standard
11917 were inserted in TeX-mode.
11918 The given values are used for all following boxes.
11921 \begin_layout Standard
11922 To return to the standard frame size, the command
11925 \begin_layout Standard
11950 \begin_layout Standard
11964 \begin_layout Standard
11965 is inserted in TeX-mode before the next formula.
11968 \begin_layout Subsection
11969 Boxes without Frame
11970 \begin_inset LatexCommand label
11971 name "sub:Boxes-without-Frame"
11976 \begin_inset LatexCommand index
11977 name "Boxes ! without frame"
11984 \begin_layout Standard
11985 For boxes without a frame there are the following box commands:
11992 \begin_inset LatexCommand index
11993 name "Commands ! M ! \\textbackslash mbox"
12004 \begin_inset LatexCommand index
12005 name "Commands ! M ! \\textbackslash makebox"
12016 \begin_inset LatexCommand index
12017 name "Commands ! R ! \\textbackslash raisebox"
12024 \begin_layout Standard
12031 a box can be super- or subscripted.
12032 But in contrary to normal super- and subscripting, the characters in the
12033 box keep their font size.
12040 is used in the following scheme:
12043 \begin_layout Standard
12048 raisebox{height}{box content}
12051 \begin_layout Standard
12052 When the box should contain a formula, an extra formula is needed like for
12062 \begin_layout Standard
12064 \begin_inset Tabular
12065 <lyxtabular version="3" rows="4" columns="2">
12067 <column alignment="center" valignment="top" leftline="true" width="0">
12068 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12069 <row topline="true" bottomline="true">
12070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12073 \begin_layout Standard
12079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12082 \begin_layout Standard
12089 <row topline="true">
12090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12093 \begin_layout Standard
12097 \begin_inset Formula $\to$
12103 \begin_inset Formula $\to$
12111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12114 \begin_layout Standard
12115 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12124 <row topline="true" bottomline="true">
12125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12128 \begin_layout Standard
12132 \begin_inset Formula $\to$
12138 \begin_inset Formula $\to$
12146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12149 \begin_layout Standard
12150 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12159 <row topline="true" bottomline="true">
12160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12163 \begin_layout Standard
12167 \begin_inset Formula $\to$
12182 \begin_layout Standard
12196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12199 \begin_layout Standard
12203 \begin_layout Standard
12227 \begin_layout Standard
12228 The last formula can currently only be created using TeX-mode because LyX
12229 inserts a box instead of the needed extra formula.
12233 \begin_layout Standard
12238 \begin_layout Standard
12242 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12251 \begin_layout Standard
12266 \begin_layout Standard
12291 , with the difference that there is no frame.
12294 \begin_layout Subsection
12296 \begin_inset LatexCommand label
12297 name "sub:Colored-Boxes"
12302 \begin_inset LatexCommand index
12303 name "Boxes ! colored"
12310 \begin_layout Standard
12311 To be able to use all commands explained in this section, the LaTeX-package
12320 \begin_layout Standard
12325 is part of every LaTeX standard installation.
12331 \begin_inset LatexCommand index
12332 name "Packages ! color"
12336 has to be loaded in the LaTeX-preamble with the line
12340 \begin_layout Standard
12341 When text is colored somewhere in the document with a predefined color,
12342 LyX loads the LaTeX-package
12347 Thus it is possible that the package is loaded twice, but this doesn't
12354 \begin_inset Note Note
12357 \begin_layout Standard
12358 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12367 \begin_layout Standard
12375 \begin_layout Standard
12376 \begin_inset VSpace medskip
12379 To color boxes, the command
12386 \begin_inset LatexCommand index
12387 name "Commands ! C ! \\textbackslash colorbox"
12391 is used in the following scheme:
12394 \begin_layout Standard
12399 colorbox{color}{box content}
12402 \begin_layout Standard
12403 The box content can also be a box and a
12409 can also be part of another box (see the 2nd and 3rd example).
12410 When the box should contain a formula, an extra formula has to be created,
12421 \begin_layout Standard
12422 This also applies for the command
12433 \begin_layout Standard
12437 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12446 \begin_layout Standard
12461 \begin_layout Standard
12462 One of the following predefined colors can be chosen:
12465 \begin_layout Standard
12499 \begin_layout Standard
12501 \begin_inset Tabular
12502 <lyxtabular version="3" rows="4" columns="2">
12504 <column alignment="center" valignment="top" leftline="true" width="0">
12505 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
12506 <row topline="true" bottomline="true">
12507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12510 \begin_layout Standard
12516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12519 \begin_layout Standard
12521 \begin_inset Note Note
12524 \begin_layout Standard
12531 is only used as spacer.
12542 <row topline="true">
12543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12546 \begin_layout Standard
12550 \begin_inset Formula $\to$
12560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12563 \begin_layout Standard
12564 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12573 <row topline="true">
12574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12577 \begin_layout Standard
12581 \begin_inset Formula $\to$
12592 \begin_layout Standard
12606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12609 \begin_layout Standard
12610 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
12619 <row topline="true" bottomline="true">
12620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12623 \begin_layout Standard
12630 \begin_layout Standard
12642 \begin_inset Formula $\to$
12652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12655 \begin_layout Standard
12656 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
12672 \begin_layout Standard
12679 only colors the box but not the characters in the box.
12680 To color all characters, the whole formula is highlighted and the wanted
12681 color is chosen in the
12687 The dialog can be called with the toolbar button
12688 \begin_inset Graphics
12689 filename ../images/dialog-show_character.png
12696 Edit\SpecialChar \menuseparator
12698 Style\SpecialChar \menuseparator
12702 The formula number has then the same color as the formula.
12703 When the formula number should get another color than the formula characters,
12704 the color must be changed within the formula.
12707 \begin_layout Standard
12711 \begin_layout Standard
12714 \begin_inset Formula \begin{equation}
12715 \int A=B\label{eq:red}\end{equation}
12722 \begin_inset Formula \begin{equation}
12723 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
12730 \begin_layout Standard
12732 \begin_inset LatexCommand eqref
12737 is completely colored red.
12740 \begin_inset LatexCommand eqref
12741 reference "eq:redgreen"
12745 was first completely colored green to set the color for the formula number.
12746 Subsequently the formula characters were colored red.
12749 \begin_layout Standard
12750 \begin_inset VSpace bigskip
12753 To color the frame different than the rest of the box, the command
12760 \begin_inset LatexCommand index
12761 name "Commands ! F ! \\textbackslash fcolorbox"
12765 is used in the following scheme:
12768 \begin_layout Standard
12773 fcolorbox{frame color}{color}{box content}
12776 \begin_layout Standard
12783 is an extension of the command
12790 The frame width is set, like for
12813 \begin_layout Standard
12825 \begin_inset Formula \[
12826 \fcolorbox{cyan}{magenta}{A=B}\]
12834 \begin_layout Standard
12848 \begin_layout Standard
12849 This formula was created with the command
12856 \begin_inset Formula $\to$
12862 \begin_inset Formula $\to$
12872 \begin_layout Standard
12873 \begin_inset VSpace bigskip
12876 To use other colors than the predefined ones, they have to be defined first.
12879 \begin_layout Standard
12880 One can for example define the color
12881 \begin_inset Quotes eld
12889 \begin_inset Quotes erd
12892 with the LaTeX-preamble line:
12895 \begin_layout Standard
12900 definecolor{darkgreen}{cmyk}{0.5,
12915 \begin_inset LatexCommand index
12916 name "Commands ! D ! \\textbackslash definecolor"
12923 \begin_layout Standard
12928 is the color space that denotes the colors
12945 The four comma separated numbers are the portion factor for the corresponding
12946 colors of the color space.
12947 The factors can be in the range of 0\InsetSpace \thinspace{}
12948 -\InsetSpace \thinspace{}
12954 also the color space
12958 can be used for definitions.
12975 , so that there are in this case three portion factors for the corresponding
12977 Furthermore there is the color space
12981 with one portion factor for the gray value.
12984 \begin_layout Standard
12985 As example a framed box with the new defined color
12989 where the characters have been colored
12994 \begin_inset Formula \begin{equation}
12995 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13002 \begin_layout Standard
13003 Self-defined colors can also be be used for text with the help of the command
13011 \begin_inset LatexCommand index
13012 name "Text ! colored"
13019 \begin_layout Standard
13023 \begin_layout Standard
13027 textcolor{darkgreen}{
13033 \begin_inset Quotes eld
13037 \begin_inset Quotes erd
13044 \begin_layout Standard
13054 \begin_layout Standard
13062 \begin_inset LatexCommand index
13063 name "Commands ! T ! \\textbackslash textcolor"
13067 is used in the scheme
13071 textcolor{color}{characters to color}
13076 \begin_layout Subsection
13078 \begin_inset LatexCommand label
13079 name "sub:Paragraph-Boxes"
13084 \begin_inset LatexCommand index
13085 name "Boxes ! as paragraph"
13092 \begin_layout Standard
13093 A box that can contain several lines and paragraphs, a so called paragraph
13094 box (parbox), can be created with the menu
13096 Insert\SpecialChar \menuseparator
13099 or the toolbar button
13100 \begin_inset Graphics
13101 filename ../images/box-insert.png
13109 \begin_layout Standard
13110 The following example shows a framed parbox in a line:
13113 \begin_layout Standard
13114 \begin_inset VSpace medskip
13118 \begin_inset Box Boxed
13127 height_special "totalheight"
13130 \begin_layout Standard
13131 This is a paragraph box.
13132 It is exactly 5\InsetSpace \thinspace{}
13133 cm long and can also contain formulas:
13134 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13145 \begin_layout Standard
13146 \begin_inset VSpace medskip
13152 \begin_layout Standard
13153 Such a box is created by right-clicking on the gray box inset.
13154 A dialog pops up showing the box properties.
13167 : 5\InsetSpace \thinspace{}
13170 Vertical Box Alignment
13175 \begin_layout Standard
13176 \begin_inset VSpace medskip
13179 In LaTeX a parbox is created with the command
13186 \begin_inset LatexCommand index
13187 name "Commands ! P ! \\textbackslash parbox"
13191 that has the following scheme:
13194 \begin_layout Standard
13199 parbox[position]{width}{box content}
13202 \begin_layout Standard
13216 for bottom means that the box is aligned within the surrounding text with
13222 for top this is done with the first line.
13223 When no position is given, the box will be vertically centered, see section
13230 Embedded\InsetSpace ~
13233 manual for examples.
13236 \begin_layout Standard
13237 \begin_inset VSpace bigskip
13240 To frame formulas completely, including the formula number, the formula
13241 must be set into a parbox.
13242 To do this, the command
13256 is inserted in TeX-mode before the formula.
13262 \begin_inset LatexCommand index
13263 name "Commands ! L ! \\textbackslash linewidth"
13269 is hereby the line width set for the document.
13270 Because the frame is outside the parbox, 2\InsetSpace \thinspace{}
13271 times the frame separation and
13272 the frame thickness must be subtracted from the line width.
13273 As this is not automatically done by LyX due to a bug
13277 \begin_layout Standard
13281 \begin_layout Standard
13285 href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
13294 \begin_layout Standard
13306 , TeX-mode has to be used.
13307 To be able to multiply and subtract in arguments, the LaTeX-package
13315 \begin_layout Standard
13320 is part of every LaTeX standard installation.
13326 \begin_inset LatexCommand index
13327 name "Packages ! calc"
13331 must be loaded in the LaTeX-preamble with the line
13334 \begin_layout Standard
13342 \begin_layout Standard
13343 Behind the formula both boxes are closed by entering
13348 Here is an example:
13352 \begin_layout Standard
13366 \begin_layout Standard
13370 \begin_layout Standard
13388 \begin_inset Formula \begin{equation}
13389 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
13397 \begin_layout Standard
13408 \begin_layout Standard
13422 \begin_layout Standard
13423 \begin_inset VSpace medskip
13426 As a parbox is used as argument of
13432 , there is in this case no difference between
13447 \begin_layout Standard
13448 \begin_inset VSpace bigskip
13451 Paragraph boxes are very useful to comment formulas directly.
13458 is used in combination with the command
13472 \begin_inset LatexCommand ref
13473 reference "sub:User-defined-Numbering"
13480 \begin_layout Standard
13481 An example of a formula commented with
13490 \begin_layout Standard
13494 \begin_layout Standard
13507 This is a description.
13508 It is distinctly separated from the formula and multiline.
13512 \begin_layout Standard
13524 \begin_layout Standard
13525 Such a formula must be inserted completely in TeX-mode because LyX does
13526 not yet support the command
13533 The formula is created with the following command sequence:
13536 \begin_layout Standard
13549 is inserted in TeX-mode.
13553 \begin_layout Standard
13554 When the formula style
13566 can also be replaced by
13573 (formula styles see
13574 \begin_inset LatexCommand ref
13575 reference "sec:Formula-Styles"
13584 Then the description follows as normal text, and finally
13590 is inserted in TeX-mode.
13603 hereby create a displayed formula.
13606 \begin_layout Standard
13613 can be seen in this example that was
13614 \begin_inset Quotes eld
13618 \begin_inset Quotes erd
13621 using the mathematical textmode:
13622 \begin_inset Formula \[
13623 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
13630 \begin_layout Section
13632 \begin_inset LatexCommand index
13640 \begin_layout Subsection
13642 \begin_inset LatexCommand label
13643 name "sub:Big-Operators"
13648 \begin_inset LatexCommand index
13649 name "Operators ! big"
13654 \begin_inset LatexCommand index
13660 \begin_inset LatexCommand index
13668 \begin_layout Standard
13669 To be able to use all integral operators listed here, the option
13671 Use esint package automatically
13673 must be set in the document settings under
13681 \begin_layout Standard
13685 \begin_inset Tabular
13686 <lyxtabular version="3" rows="11" columns="2">
13688 <column alignment="center" valignment="top" leftline="true" width="0pt">
13689 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13690 <row topline="true" bottomline="true">
13691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13694 \begin_layout Standard
13700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13703 \begin_layout Standard
13710 <row topline="true">
13711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13714 \begin_layout Standard
13718 \begin_inset LatexCommand index
13719 name "Commands ! S ! \\textbackslash sum"
13728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13731 \begin_layout Standard
13732 \begin_inset Formula $\sum$
13741 <row topline="true">
13742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13745 \begin_layout Standard
13749 \begin_inset LatexCommand index
13750 name "Commands ! I ! \\textbackslash int"
13759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13762 \begin_layout Standard
13763 \begin_inset Formula $\int$
13772 <row topline="true">
13773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13776 \begin_layout Standard
13784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13787 \begin_layout Standard
13788 \begin_inset Formula $\intop$
13797 <row topline="true">
13798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13801 \begin_layout Standard
13809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13812 \begin_layout Standard
13813 \begin_inset Formula $\oint$
13822 <row topline="true">
13823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13826 \begin_layout Standard
13834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13837 \begin_layout Standard
13838 \begin_inset Formula $\ointop$
13847 <row topline="true">
13848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13851 \begin_layout Standard
13859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13862 \begin_layout Standard
13863 \begin_inset Formula $\ointctrclockwise$
13872 <row topline="true">
13873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13876 \begin_layout Standard
13884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13887 \begin_layout Standard
13888 \begin_inset Formula $\ointclockwise$
13897 <row topline="true">
13898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13901 \begin_layout Standard
13909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13912 \begin_layout Standard
13913 \begin_inset Formula $\sqint$
13922 <row topline="true">
13923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13926 \begin_layout Standard
13934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13937 \begin_layout Standard
13938 \begin_inset Formula $\bigcap$
13947 <row topline="true" bottomline="true">
13948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13951 \begin_layout Standard
13959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13962 \begin_layout Standard
13963 \begin_inset Formula $\bigcup$
13979 \begin_inset Tabular
13980 <lyxtabular version="3" rows="10" columns="2">
13982 <column alignment="center" valignment="top" leftline="true" width="0pt">
13983 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
13984 <row topline="true" bottomline="true">
13985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13988 \begin_layout Standard
13994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13997 \begin_layout Standard
14004 <row topline="true">
14005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14008 \begin_layout Standard
14012 \begin_inset LatexCommand index
14013 name "Commands ! P ! \\textbackslash prod"
14022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14025 \begin_layout Standard
14026 \begin_inset Formula $\prod$
14035 <row topline="true">
14036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14039 \begin_layout Standard
14047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14050 \begin_layout Standard
14051 \begin_inset Formula $\coprod$
14060 <row topline="true">
14061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14064 \begin_layout Standard
14072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14075 \begin_layout Standard
14076 \begin_inset Formula $\bigodot$
14085 <row topline="true">
14086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14089 \begin_layout Standard
14097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14100 \begin_layout Standard
14101 \begin_inset Formula $\bigotimes$
14110 <row topline="true">
14111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14114 \begin_layout Standard
14122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14125 \begin_layout Standard
14126 \begin_inset Formula $\bigoplus$
14135 <row topline="true">
14136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14139 \begin_layout Standard
14147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14150 \begin_layout Standard
14151 \begin_inset Formula $\bigwedge$
14160 <row topline="true">
14161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14164 \begin_layout Standard
14172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14175 \begin_layout Standard
14176 \begin_inset Formula $\bigvee$
14185 <row topline="true">
14186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14189 \begin_layout Standard
14197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14200 \begin_layout Standard
14201 \begin_inset Formula $\bigsqcup$
14210 <row topline="true" bottomline="true">
14211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14214 \begin_layout Standard
14222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14225 \begin_layout Standard
14226 \begin_inset Formula $\biguplus$
14244 \begin_layout Standard
14245 All big operators can also be inserted via the math toolbar button
14246 \begin_inset Graphics
14247 filename ../images/math/intop.png
14255 \begin_layout Standard
14256 The operators are called big because they are bigger than the sometimes
14257 equal looking binary operators.
14258 All big operators can have limits as described in the next subsection.
14261 \begin_layout Standard
14286 , resp.\InsetSpace ~
14287 in the style the operator limits are displayed, see
14288 \begin_inset LatexCommand ref
14289 reference "sub:Operator-Limits"
14297 \begin_layout Subsubsection*
14298 Advices for Integrals
14301 \begin_layout Standard
14306 in an integral is an operator, that therefore has to be set upright.
14307 This is done by highlighting the
14311 and using the keyboard shortcut
14320 \begin_layout Standard
14326 \begin_inset LatexCommand ref
14327 reference "sub:Font-Styles"
14337 Finally the smallest space is inserted before the
14341 , as this is usual for operators.
14345 \begin_layout Standard
14347 \begin_inset Formula $\int A(x)dx$
14356 \begin_layout Standard
14366 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14372 \begin_layout Standard
14373 For multiple integrals there are the following commands:
14374 \begin_inset VSpace medskip
14380 \begin_layout Standard
14384 \begin_inset Tabular
14385 <lyxtabular version="3" rows="4" columns="2">
14387 <column alignment="center" valignment="top" leftline="true" width="0">
14388 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14389 <row topline="true" bottomline="true">
14390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14393 \begin_layout Standard
14399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14402 \begin_layout Standard
14404 \begin_inset Note Note
14407 \begin_layout Standard
14414 is only used as spacer.
14425 <row topline="true">
14426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14429 \begin_layout Standard
14437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14440 \begin_layout Standard
14441 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
14450 <row topline="true">
14451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14454 \begin_layout Standard
14462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14465 \begin_layout Standard
14466 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
14475 <row topline="true" bottomline="true">
14476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14479 \begin_layout Standard
14487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14490 \begin_layout Standard
14491 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
14507 \begin_inset Tabular
14508 <lyxtabular version="3" rows="4" columns="2">
14510 <column alignment="center" valignment="top" leftline="true" width="0">
14511 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
14512 <row topline="true" bottomline="true">
14513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14516 \begin_layout Standard
14522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14525 \begin_layout Standard
14532 <row topline="true">
14533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14536 \begin_layout Standard
14544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14547 \begin_layout Standard
14548 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
14557 <row topline="true">
14558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14561 \begin_layout Standard
14569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14572 \begin_layout Standard
14573 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
14582 <row topline="true" bottomline="true">
14583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14586 \begin_layout Standard
14594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14597 \begin_layout Standard
14598 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
14616 \begin_layout Subsection
14618 \begin_inset LatexCommand label
14619 name "sub:Operator-Limits"
14624 \begin_inset LatexCommand index
14625 name "Operators ! Limits"
14632 \begin_layout Standard
14633 Limits are created by super- and subscripts:
14636 \begin_layout Standard
14638 \begin_inset Tabular
14639 <lyxtabular version="3" rows="2" columns="2">
14641 <column alignment="center" valignment="top" leftline="true" width="0pt">
14642 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
14643 <row topline="true" bottomline="true">
14644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14647 \begin_layout Standard
14653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14656 \begin_layout Standard
14658 \begin_inset Note Note
14661 \begin_layout Standard
14668 is only used as spacer.
14679 <row topline="true" bottomline="true">
14680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14683 \begin_layout Standard
14692 \begin_layout Standard
14702 \begin_inset Formula $\to$
14706 \begin_inset Formula $\to$
14714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14717 \begin_layout Standard
14718 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
14734 \begin_layout Standard
14735 Limits of inline formulas are set right beside the operator.
14736 Limits in displayed formulas are set above or below the operator, except
14737 of integral limits.
14740 \begin_layout Standard
14741 To force that the limits are set beside the operator, the cursor is set
14742 directly behind the operator and the limits type is changed with the menu
14745 Edit\SpecialChar \menuseparator
14746 Math\SpecialChar \menuseparator
14764 \begin_layout Standard
14765 The default limits type is this:
14766 \begin_inset Formula \[
14767 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
14771 This is how it looks when the limits type was changed to
14778 \begin_inset Formula \[
14779 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
14783 For integrals, except of
14795 , the limits are by default set beside the operator.
14796 But for multiple integrals the limits are often set below the operator.
14797 In the following example the limits type was therefore set to
14801 and so set below the integrals:
14802 \begin_inset Formula \begin{equation}
14803 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
14810 \begin_layout Standard
14811 \begin_inset VSpace medskip
14814 To specify conditions for limits, the commands
14821 \begin_inset LatexCommand index
14822 name "Commands ! S ! \\textbackslash subarray"
14833 \begin_inset LatexCommand index
14834 name "Commands ! S ! \\textbackslash substack"
14839 To create for example this expression
14840 \begin_inset Formula \begin{equation}
14841 \sum_{\begin{subarray}{c}
14843 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
14850 \begin_layout Standard
14851 the following has to be done:
14865 \begin_layout Standard
14877 One is now in a blue box under the summation operator and insert there
14886 \begin_layout Standard
14898 The blue box is now within a purple box and now several lines can be written
14900 A new line is created by inserting a line break (
14909 0<k<1000 Ctrl-Return
14913 is typed in, a new box appears below for the new line.
14916 \begin_layout Standard
14917 The alignment of the lines can be changed to left aligned with the
14927 Edit\SpecialChar \menuseparator
14931 To get right alignment,
14939 \begin_layout Standard
14950 is inserted at the beginning of the line.
14953 \begin_layout Standard
14966 with the difference that the lines are always centered.
14969 \begin_layout Standard
14970 \begin_inset VSpace bigskip
14974 \begin_inset LatexCommand eqref
14975 reference "eq:substack"
14979 there can be too much space beside an operator, because the characters
14980 following the operator are set beside the limits.
14983 \begin_layout Standard
14984 To avoid this, the following macro can be used in the LaTeX-preamble:
14987 \begin_layout Standard
15016 mathclapinternal #1#2{
15020 mathsurround =0pt #1{#2}$}}
15023 \begin_layout Standard
15024 This defines the command
15031 \begin_inset LatexCommand index
15032 name "Commands ! M ! \\textbackslash mathclap"
15036 that sets the width of the limit to 0\InsetSpace \thinspace{}
15038 The command scheme is
15041 \begin_layout Standard
15049 \begin_layout Standard
15050 where the limit can consist of several conditions.
15053 \begin_layout Standard
15055 \begin_inset LatexCommand eqref
15056 reference "eq:substack"
15060 , one uses the command
15063 \begin_layout Standard
15076 \begin_layout Standard
15085 0<k<1000 Ctrl-Enter
15088 \begin_layout Standard
15089 to create the lower limit.
15090 The summand is now directly behind the summation operator:
15091 \begin_inset Formula \[
15092 \sum_{\mathclap{\substack{0<k<1000\\
15093 \\k\,\in\,\mathbb{N}}
15101 \begin_layout Standard
15102 \begin_inset VSpace bigskip
15105 How to use one limit for several operators is described in
15106 \begin_inset LatexCommand ref
15107 reference "sub:Self-defined-Operators"
15114 \begin_layout Subsection
15116 \begin_inset LatexCommand label
15117 name "sub:Binary-Operators"
15122 \begin_inset LatexCommand index
15123 name "Operators ! binary"
15130 \begin_layout Standard
15131 Binary operators are surrounded by space when there is a character before
15133 \begin_inset VSpace medskip
15139 \begin_layout Standard
15143 \begin_inset Tabular
15144 <lyxtabular version="3" rows="13" columns="2">
15146 <column alignment="center" valignment="top" leftline="true" width="0pt">
15147 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15148 <row topline="true" bottomline="true">
15149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15152 \begin_layout Standard
15154 \begin_inset Note Note
15157 \begin_layout Standard
15164 is only used as spacer.
15174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15177 \begin_layout Standard
15184 <row topline="true">
15185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15188 \begin_layout Standard
15194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15197 \begin_layout Standard
15198 \begin_inset Formula $+$
15207 <row topline="true">
15208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15211 \begin_layout Standard
15217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15220 \begin_layout Standard
15221 \begin_inset Formula $-$
15230 <row topline="true">
15231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15234 \begin_layout Standard
15242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15245 \begin_layout Standard
15246 \begin_inset Formula $\pm$
15255 <row topline="true">
15256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15259 \begin_layout Standard
15267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15270 \begin_layout Standard
15271 \begin_inset Formula $\mp$
15280 <row topline="true">
15281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15284 \begin_layout Standard
15292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15295 \begin_layout Standard
15296 \begin_inset Formula $\cdot$
15305 <row topline="true">
15306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15309 \begin_layout Standard
15317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15320 \begin_layout Standard
15321 \begin_inset Formula $\times$
15330 <row topline="true">
15331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15334 \begin_layout Standard
15342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15345 \begin_layout Standard
15346 \begin_inset Formula $\div$
15355 <row topline="true">
15356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15359 \begin_layout Standard
15363 \begin_layout Standard
15376 \begin_layout Standard
15388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15391 \begin_layout Standard
15392 \begin_inset Formula $*$
15401 <row topline="true">
15402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15405 \begin_layout Standard
15413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15416 \begin_layout Standard
15417 \begin_inset Formula $\star$
15426 <row topline="true">
15427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15430 \begin_layout Standard
15438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15441 \begin_layout Standard
15442 \begin_inset Formula $\circ$
15451 <row topline="true">
15452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15455 \begin_layout Standard
15463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15466 \begin_layout Standard
15467 \begin_inset Formula $\diamond$
15476 <row topline="true" bottomline="true">
15477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15480 \begin_layout Standard
15488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15491 \begin_layout Standard
15492 \begin_inset Formula $\bullet$
15508 \begin_inset Tabular
15509 <lyxtabular version="3" rows="13" columns="2">
15511 <column alignment="center" valignment="top" leftline="true" width="0pt">
15512 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15513 <row topline="true" bottomline="true">
15514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15517 \begin_layout Standard
15523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15526 \begin_layout Standard
15533 <row topline="true">
15534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15537 \begin_layout Standard
15545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15548 \begin_layout Standard
15549 \begin_inset Formula $\nabla$
15558 <row topline="true">
15559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15562 \begin_layout Standard
15570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15573 \begin_layout Standard
15574 \begin_inset Formula $\bigtriangledown$
15583 <row topline="true">
15584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15587 \begin_layout Standard
15595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15598 \begin_layout Standard
15599 \begin_inset Formula $\bigtriangleup$
15608 <row topline="true">
15609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15612 \begin_layout Standard
15620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15623 \begin_layout Standard
15624 \begin_inset Formula $\Box$
15633 <row topline="true">
15634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15637 \begin_layout Standard
15645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15648 \begin_layout Standard
15649 \begin_inset Formula $\cap$
15658 <row topline="true">
15659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15662 \begin_layout Standard
15670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15673 \begin_layout Standard
15674 \begin_inset Formula $\cup$
15683 <row topline="true">
15684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15687 \begin_layout Standard
15695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15698 \begin_layout Standard
15699 \begin_inset Formula $\dagger$
15708 <row topline="true">
15709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15712 \begin_layout Standard
15720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15723 \begin_layout Standard
15724 \begin_inset Formula $\ddagger$
15733 <row topline="true">
15734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15737 \begin_layout Standard
15745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15748 \begin_layout Standard
15749 \begin_inset Formula $\wr$
15758 <row topline="true">
15759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15762 \begin_layout Standard
15770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15773 \begin_layout Standard
15774 \begin_inset Formula $\bigcirc$
15783 <row topline="true">
15784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15787 \begin_layout Standard
15795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15798 \begin_layout Standard
15799 \begin_inset Formula $\wedge$
15808 <row topline="true" bottomline="true">
15809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15812 \begin_layout Standard
15820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15823 \begin_layout Standard
15824 \begin_inset Formula $\vee$
15840 \begin_inset Tabular
15841 <lyxtabular version="3" rows="13" columns="2">
15843 <column alignment="center" valignment="top" leftline="true" width="0pt">
15844 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
15845 <row topline="true" bottomline="true">
15846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15849 \begin_layout Standard
15855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15858 \begin_layout Standard
15865 <row topline="true">
15866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15869 \begin_layout Standard
15877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15880 \begin_layout Standard
15881 \begin_inset Formula $\oplus$
15890 <row topline="true">
15891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15894 \begin_layout Standard
15902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15905 \begin_layout Standard
15906 \begin_inset Formula $\ominus$
15915 <row topline="true">
15916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15919 \begin_layout Standard
15927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15930 \begin_layout Standard
15931 \begin_inset Formula $\otimes$
15940 <row topline="true">
15941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15944 \begin_layout Standard
15952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15955 \begin_layout Standard
15956 \begin_inset Formula $\oslash$
15965 <row topline="true">
15966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15969 \begin_layout Standard
15977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15980 \begin_layout Standard
15981 \begin_inset Formula $\odot$
15990 <row topline="true">
15991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15994 \begin_layout Standard
16002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16005 \begin_layout Standard
16006 \begin_inset Formula $\amalg$
16015 <row topline="true">
16016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16019 \begin_layout Standard
16027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16030 \begin_layout Standard
16031 \begin_inset Formula $\uplus$
16040 <row topline="true">
16041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16044 \begin_layout Standard
16052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16055 \begin_layout Standard
16056 \begin_inset Formula $\setminus$
16065 <row topline="true">
16066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16069 \begin_layout Standard
16077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16080 \begin_layout Standard
16081 \begin_inset Formula $\sqcap$
16090 <row topline="true">
16091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16094 \begin_layout Standard
16102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16105 \begin_layout Standard
16106 \begin_inset Formula $\sqcup$
16115 <row topline="true">
16116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16119 \begin_layout Standard
16127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16130 \begin_layout Standard
16131 \begin_inset Formula $\triangleleft$
16140 <row topline="true" bottomline="true">
16141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16144 \begin_layout Standard
16152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16155 \begin_layout Standard
16156 \begin_inset Formula $\triangleright$
16174 \begin_layout Standard
16175 All binary operators can also be inserted via the math toolbar button
16176 \begin_inset Graphics
16177 filename ../images/math/pm.png
16185 \begin_layout Standard
16186 To typeset the Laplace operator also
16203 \begin_inset Formula $\nabla^{2}$
16206 ) can be used instead of
16215 \begin_layout Standard
16222 Insert\SpecialChar \menuseparator
16234 \begin_layout Subsection
16235 Self-defined Operators
16236 \begin_inset LatexCommand label
16237 name "sub:Self-defined-Operators"
16242 \begin_inset LatexCommand index
16243 name "Operators ! self-defined"
16250 \begin_layout Standard
16251 With the help of the command
16255 DeclareMathOperator
16258 \begin_inset LatexCommand index
16259 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
16263 custom operators can be defined in the LaTeX-preamble.
16264 Its command scheme is:
16267 \begin_layout Standard
16272 DeclareMathOperator{new command}{display}
16275 \begin_layout Standard
16276 Display can be characters or symbols that define how the operator looks
16278 To define a big operator a * is set behind the command.
16279 All self-defined big operators can have limits as described in
16280 \begin_inset LatexCommand ref
16281 reference "sub:Operator-Limits"
16288 \begin_layout Standard
16289 For example the LaTeX-preamble line
16292 \begin_layout Standard
16297 DeclareMathOperator*{
16304 \begin_layout Standard
16305 defines the command
16311 , that inserts a big operator consisting of the lozenge symbol from
16312 \begin_inset LatexCommand ref
16313 reference "sub:Miscellaneous-Symbols"
16318 \begin_inset Formula \[
16319 \Lozenge_{n=1}^{\infty}\]
16323 The command for this formula is:
16334 \begin_inset Formula $\to$
16340 \begin_layout Standard
16341 \begin_inset VSpace bigskip
16344 When self-defined operators are not used several times in the document,
16345 they can also be defined with the commands
16352 \begin_inset LatexCommand index
16353 name "Commands ! M ! \\textbackslash mathop"
16364 \begin_inset LatexCommand index
16365 name "Commands ! M ! \\textbackslash mathbin"
16369 , which have the following scheme:
16372 \begin_layout Standard
16386 \begin_layout Standard
16393 defines big operators,
16402 \begin_layout Standard
16409 can e.\InsetSpace \thinspace{}
16411 be used to use one limit for several operators:
16414 \begin_layout Standard
16415 \begin_inset Formula \[
16416 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
16423 \begin_layout Standard
16424 The command for the formula above is:
16442 \begin_layout Standard
16454 \begin_inset Formula $\to$
16463 \begin_layout Standard
16477 \begin_layout Section
16479 \begin_inset LatexCommand index
16487 \begin_layout Subsection
16489 \begin_inset LatexCommand label
16490 name "sub:Font-Styles"
16495 \begin_inset LatexCommand index
16496 name "Font ! style"
16503 \begin_layout Standard
16504 Latin letters in formulas can be set in one of the following font styles:
16505 \begin_inset VSpace -2mm
16511 \begin_layout Standard
16513 \begin_inset Tabular
16514 <lyxtabular version="3" rows="6" columns="3">
16516 <column alignment="center" valignment="top" leftline="true" width="0">
16517 <column alignment="center" valignment="top" leftline="true" width="0">
16518 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16519 <row topline="true" bottomline="true">
16520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16523 \begin_layout Standard
16529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16532 \begin_layout Standard
16538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16541 \begin_layout Standard
16548 <row topline="true">
16549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16552 \begin_layout Standard
16561 \begin_layout Standard
16577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16580 \begin_layout Standard
16581 \begin_inset Formula $\mathbb{ABC}$
16589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16592 \begin_layout Standard
16599 <row topline="true">
16600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16603 \begin_layout Standard
16612 \begin_layout Standard
16628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16631 \begin_layout Standard
16632 \begin_inset Formula $\mathbf{AbC}$
16640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16643 \begin_layout Standard
16650 <row topline="true">
16651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16654 \begin_layout Standard
16663 \begin_layout Standard
16679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16682 \begin_layout Standard
16683 \begin_inset Formula $\boldsymbol{AbC}$
16691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16694 \begin_layout Standard
16701 <row topline="true">
16702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16705 \begin_layout Standard
16714 \begin_layout Standard
16730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16733 \begin_layout Standard
16734 \begin_inset Formula $\mathcal{ABC}$
16742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16745 \begin_layout Standard
16752 <row topline="true" bottomline="true">
16753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16756 \begin_layout Standard
16765 \begin_layout Standard
16781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16784 \begin_layout Standard
16785 \begin_inset Formula $\mathfrak{AbC}$
16793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16796 \begin_layout Standard
16810 \begin_layout Standard
16812 \begin_inset Tabular
16813 <lyxtabular version="3" rows="5" columns="3">
16815 <column alignment="center" valignment="top" leftline="true" width="0">
16816 <column alignment="center" valignment="top" leftline="true" width="0">
16817 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
16818 <row topline="true" bottomline="true">
16819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16822 \begin_layout Standard
16828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16831 \begin_layout Standard
16837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16840 \begin_layout Standard
16847 <row topline="true">
16848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16851 \begin_layout Standard
16860 \begin_layout Standard
16876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16879 \begin_layout Standard
16880 \begin_inset Formula $\mathit{AbC}$
16888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16891 \begin_layout Standard
16898 <row topline="true">
16899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16902 \begin_layout Standard
16911 \begin_layout Standard
16927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16930 \begin_layout Standard
16931 \begin_inset Formula $\mathrm{AbC}$
16939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16942 \begin_layout Standard
16949 <row topline="true">
16950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16953 \begin_layout Standard
16962 \begin_layout Standard
16978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16981 \begin_layout Standard
16982 \begin_inset Formula $\mathsf{AbC}$
16990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16993 \begin_layout Standard
17000 <row topline="true" bottomline="true">
17001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17004 \begin_layout Standard
17013 \begin_layout Standard
17029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17032 \begin_layout Standard
17033 \begin_inset Formula $\mathtt{AbC}$
17041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17044 \begin_layout Standard
17058 \begin_layout Standard
17059 \begin_inset Note Greyedout
17062 \begin_layout Standard
17079 can only be used for big letters.
17087 \begin_layout Standard
17088 Predefined is the style
17097 \begin_layout Standard
17098 The style commands work also for letters in mathematical constructs:
17099 \begin_inset Formula \[
17100 \mathfrak{A=\frac{b}{C}}\]
17107 \begin_layout Standard
17108 Characters in mathematical text don't appear in a math font style but in
17109 the text font style
17116 That their style can't be set correctly via the text style dialog is a
17121 \begin_layout Standard
17126 \begin_layout Standard
17130 href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
17139 \begin_layout Standard
17154 \begin_layout Standard
17155 Instead of the style commands the dialog
17157 Edit\SpecialChar \menuseparator
17158 Math\SpecialChar \menuseparator
17161 or the toolbar button
17162 \begin_inset Graphics
17163 filename ../images/math/font.png
17171 \begin_layout Subsection
17173 \begin_inset LatexCommand label
17174 name "sub:Bold-Formulas"
17179 \begin_inset LatexCommand index
17180 name "Formula ! bold"
17187 \begin_layout Standard
17188 To make a complete formula bold, the command
17194 from the previous subsection cannot be used, because it doesn't work for
17195 small Greek letters.
17196 Furthermore it prints Latin letters always upright, like in the following
17200 \begin_layout Standard
17201 \begin_inset Formula \[
17202 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
17209 \begin_layout Standard
17210 To display the formula correctly, the command
17217 \begin_inset Formula \[
17218 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
17222 It is also possible to set the formula in a
17224 boldmath environment
17227 This environment is created by inserting the command
17232 \begin_inset LatexCommand index
17233 name "Commands ! B ! \\textbackslash boldmath"
17240 To end the environment, the command
17245 \begin_inset LatexCommand index
17246 name "Commands ! U ! \\textbackslash unboldmath"
17252 is inserted in TeX-mode.
17256 \begin_layout Standard
17266 \begin_inset Formula \[
17267 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
17275 \begin_layout Standard
17287 \begin_layout Subsection
17289 \begin_inset LatexCommand label
17290 name "sub:Font-Sizes"
17295 \begin_inset LatexCommand index
17303 \begin_layout Standard
17304 For characters in formulas there are, analog to characters in text, the
17305 following size commands:
17308 \begin_layout Standard
17372 \begin_layout Standard
17373 The size produced by the commands depends on the document font size, that
17374 corresponds with the command
17381 The other commands produce smaller or larger sizes than
17388 The font size can however not exceed a certain value.
17389 Is for example the document font size 12\InsetSpace \thinspace{}
17396 switches to the same size as
17406 \begin_layout Standard
17407 A size command is inserted in TeX-mode before the formula and sets the size
17408 for all following formula and text characters.
17409 To switch back to the initial size, the command
17415 is inserted behind the formula in TeX-mode.
17418 \begin_layout Standard
17419 Within a formula the size can only be changed for symbols or letters in
17421 To do this, the size command is inserted in mathematical text.
17422 All following characters until the end of the mathematical text or until
17423 another size command will have the selected size.
17425 \begin_inset VSpace -2mm
17431 \begin_layout Standard
17435 \begin_layout Standard
17445 \begin_inset Formula \[
17446 A=\frac{B}{c}\cdot\maltese\]
17451 \begin_inset Formula \[
17452 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
17460 \begin_layout Standard
17472 \begin_layout Standard
17473 \begin_inset VSpace medskip
17476 Before both formulas the command
17483 The command for the second formula is:
17493 \begin_layout Standard
17508 \begin_layout Standard
17523 \begin_layout Standard
17538 \begin_layout Standard
17548 \begin_inset Formula $\to$
17552 \begin_inset Formula $\to$
17561 \begin_layout Standard
17580 \begin_layout Standard
17595 \begin_layout Standard
17610 \begin_layout Standard
17622 \begin_layout Standard
17623 If a symbol cannot be displayed in different sizes, it will always be displayed
17624 in the default size.
17627 \begin_layout Section
17629 \begin_inset LatexCommand index
17630 name "Greek letters"
17637 \begin_layout Standard
17638 All Greek letters can also be inserted via the toolbar button
17639 \begin_inset Graphics
17640 filename ../images/math/alpha.png
17648 \begin_layout Subsection
17650 \begin_inset LatexCommand label
17651 name "sub:Small-Letters"
17656 \begin_inset LatexCommand index
17657 name "Greek letters ! small"
17664 \begin_layout Standard
17668 \begin_inset Tabular
17669 <lyxtabular version="3" rows="11" columns="2">
17671 <column alignment="center" valignment="top" leftline="true" width="0pt">
17672 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17673 <row topline="true" bottomline="true">
17674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17677 \begin_layout Standard
17683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17686 \begin_layout Standard
17693 <row topline="true">
17694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17697 \begin_layout Standard
17705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17708 \begin_layout Standard
17709 \begin_inset Formula $\alpha$
17718 <row topline="true">
17719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17722 \begin_layout Standard
17730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17733 \begin_layout Standard
17734 \begin_inset Formula $\beta$
17743 <row topline="true">
17744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17747 \begin_layout Standard
17755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17758 \begin_layout Standard
17759 \begin_inset Formula $\gamma$
17768 <row topline="true">
17769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17772 \begin_layout Standard
17780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17783 \begin_layout Standard
17784 \begin_inset Formula $\delta$
17793 <row topline="true">
17794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17797 \begin_layout Standard
17805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17808 \begin_layout Standard
17809 \begin_inset Formula $\epsilon$
17818 <row topline="true">
17819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17822 \begin_layout Standard
17830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17833 \begin_layout Standard
17834 \begin_inset Formula $\varepsilon$
17843 <row topline="true">
17844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17847 \begin_layout Standard
17855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17858 \begin_layout Standard
17859 \begin_inset Formula $\zeta$
17868 <row topline="true">
17869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17872 \begin_layout Standard
17880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17883 \begin_layout Standard
17884 \begin_inset Formula $\eta$
17893 <row topline="true">
17894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17897 \begin_layout Standard
17905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17908 \begin_layout Standard
17909 \begin_inset Formula $\theta$
17918 <row topline="true" bottomline="true">
17919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17922 \begin_layout Standard
17930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17933 \begin_layout Standard
17934 \begin_inset Formula $\vartheta$
17950 \begin_inset Tabular
17951 <lyxtabular version="3" rows="12" columns="2">
17953 <column alignment="center" valignment="top" leftline="true" width="0pt">
17954 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
17955 <row topline="true" bottomline="true">
17956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17959 \begin_layout Standard
17965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17968 \begin_layout Standard
17975 <row topline="true">
17976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17979 \begin_layout Standard
17987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17990 \begin_layout Standard
17991 \begin_inset Formula $\iota$
18000 <row topline="true">
18001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18004 \begin_layout Standard
18012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18015 \begin_layout Standard
18016 \begin_inset Formula $\kappa$
18025 <row topline="true">
18026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18029 \begin_layout Standard
18037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18040 \begin_layout Standard
18041 \begin_inset Formula $\varkappa$
18050 <row topline="true">
18051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18054 \begin_layout Standard
18062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18065 \begin_layout Standard
18066 \begin_inset Formula $\lambda$
18075 <row topline="true">
18076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18079 \begin_layout Standard
18087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18090 \begin_layout Standard
18091 \begin_inset Formula $\mu$
18100 <row topline="true">
18101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18104 \begin_layout Standard
18112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18115 \begin_layout Standard
18116 \begin_inset Formula $\nu$
18125 <row topline="true">
18126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18129 \begin_layout Standard
18137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18140 \begin_layout Standard
18141 \begin_inset Formula $\xi$
18150 <row topline="true">
18151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18154 \begin_layout Standard
18160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18163 \begin_layout Standard
18164 \begin_inset Formula $o$
18173 <row topline="true">
18174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18177 \begin_layout Standard
18185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18188 \begin_layout Standard
18189 \begin_inset Formula $\pi$
18198 <row topline="true">
18199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18202 \begin_layout Standard
18210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18213 \begin_layout Standard
18214 \begin_inset Formula $\varpi$
18223 <row topline="true" bottomline="true">
18224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18227 \begin_layout Standard
18235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18238 \begin_layout Standard
18239 \begin_inset Formula $\rho$
18255 \begin_inset Tabular
18256 <lyxtabular version="3" rows="11" columns="2">
18258 <column alignment="center" valignment="top" leftline="true" width="0pt">
18259 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18260 <row topline="true" bottomline="true">
18261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18264 \begin_layout Standard
18270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18273 \begin_layout Standard
18280 <row topline="true">
18281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18284 \begin_layout Standard
18292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18295 \begin_layout Standard
18296 \begin_inset Formula $\varrho$
18305 <row topline="true">
18306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18309 \begin_layout Standard
18317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18320 \begin_layout Standard
18321 \begin_inset Formula $\sigma$
18330 <row topline="true">
18331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18334 \begin_layout Standard
18342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18345 \begin_layout Standard
18346 \begin_inset Formula $\varsigma$
18355 <row topline="true">
18356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18359 \begin_layout Standard
18367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18370 \begin_layout Standard
18371 \begin_inset Formula $\tau$
18380 <row topline="true">
18381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18384 \begin_layout Standard
18392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18395 \begin_layout Standard
18396 \begin_inset Formula $\upsilon$
18405 <row topline="true">
18406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18409 \begin_layout Standard
18417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18420 \begin_layout Standard
18421 \begin_inset Formula $\phi$
18430 <row topline="true">
18431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18434 \begin_layout Standard
18442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18445 \begin_layout Standard
18446 \begin_inset Formula $\varphi$
18455 <row topline="true">
18456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18459 \begin_layout Standard
18467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18470 \begin_layout Standard
18471 \begin_inset Formula $\chi$
18480 <row topline="true">
18481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18484 \begin_layout Standard
18492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18495 \begin_layout Standard
18496 \begin_inset Formula $\psi$
18505 <row topline="true" bottomline="true">
18506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18509 \begin_layout Standard
18517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18520 \begin_layout Standard
18521 \begin_inset Formula $\omega$
18539 \begin_layout Standard
18540 \begin_inset VSpace medskip
18546 \begin_layout Standard
18547 How to create upright Greek letters is explained in
18548 \begin_inset LatexCommand ref
18549 reference "sub:Upright-small-Greek"
18556 \begin_layout Subsection
18558 \begin_inset LatexCommand index
18559 name "Greek letters ! big"
18566 \begin_layout Standard
18570 \begin_inset Tabular
18571 <lyxtabular version="3" rows="7" columns="2">
18573 <column alignment="center" valignment="top" leftline="true" width="0pt">
18574 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18575 <row topline="true" bottomline="true">
18576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18579 \begin_layout Standard
18585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18588 \begin_layout Standard
18595 <row topline="true">
18596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18599 \begin_layout Standard
18607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18610 \begin_layout Standard
18611 \begin_inset Formula $\Gamma$
18620 <row topline="true">
18621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18624 \begin_layout Standard
18632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18635 \begin_layout Standard
18636 \begin_inset Formula $\Delta$
18645 <row topline="true">
18646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18649 \begin_layout Standard
18657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18660 \begin_layout Standard
18661 \begin_inset Formula $\Theta$
18670 <row topline="true">
18671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18674 \begin_layout Standard
18682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18685 \begin_layout Standard
18686 \begin_inset Formula $\Lambda$
18695 <row topline="true">
18696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18699 \begin_layout Standard
18707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18710 \begin_layout Standard
18711 \begin_inset Formula $\Xi$
18720 <row topline="true" bottomline="true">
18721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18724 \begin_layout Standard
18732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18735 \begin_layout Standard
18736 \begin_inset Formula $\Pi$
18752 \begin_inset Tabular
18753 <lyxtabular version="3" rows="6" columns="2">
18755 <column alignment="center" valignment="top" leftline="true" width="0pt">
18756 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
18757 <row topline="true" bottomline="true">
18758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18761 \begin_layout Standard
18767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18770 \begin_layout Standard
18777 <row topline="true">
18778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18781 \begin_layout Standard
18789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18792 \begin_layout Standard
18793 \begin_inset Formula $\Sigma$
18802 <row topline="true">
18803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18806 \begin_layout Standard
18814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18817 \begin_layout Standard
18818 \begin_inset Formula $\Upsilon$
18827 <row topline="true">
18828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18831 \begin_layout Standard
18839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18842 \begin_layout Standard
18843 \begin_inset Formula $\Phi$
18852 <row topline="true">
18853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18856 \begin_layout Standard
18864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18867 \begin_layout Standard
18868 \begin_inset Formula $\Psi$
18877 <row topline="true" bottomline="true">
18878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18881 \begin_layout Standard
18889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18892 \begin_layout Standard
18893 \begin_inset Formula $\Omega$
18911 \begin_layout Standard
18912 \begin_inset VSpace medskip
18915 That the big Greek letters appear upright is caused by a design bug when
18917 To get correct italic big letters, begin every command with
18922 For example the command
18929 \begin_inset Formula $\varGamma$
18935 \begin_layout Subsection
18937 \begin_inset LatexCommand index
18938 name "Greek letters ! bold"
18945 \begin_layout Standard
18946 Greek letters cannot be set with different font styles like Latin letters.
18947 They can only be made bold with the command
18954 \begin_inset LatexCommand index
18955 name "Commands ! B ! \\textbackslash boldsymbol"
18962 \begin_layout Standard
18964 \begin_inset Tabular
18965 <lyxtabular version="3" rows="3" columns="2">
18967 <column alignment="center" valignment="top" leftline="true" width="0">
18968 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
18969 <row topline="true" bottomline="true">
18970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18973 \begin_layout Standard
18979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18982 \begin_layout Standard
18989 <row topline="true">
18990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18993 \begin_layout Standard
19005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19008 \begin_layout Standard
19009 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
19018 <row topline="true" bottomline="true">
19019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19022 \begin_layout Standard
19034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19037 \begin_layout Standard
19038 \begin_inset Formula $\theta\boldsymbol{\theta}$
19054 \begin_layout Section
19059 \begin_layout Standard
19072 \begin_layout Standard
19073 A list with all symbols of most of the LaTeX-packages can be found in
19074 \begin_inset LatexCommand cite
19088 \begin_layout Standard
19096 \begin_inset Note Note
19099 \begin_layout Standard
19102 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
19105 \begin_layout Standard
19108 texorpdfstring is in section
19109 \begin_inset LatexCommand ref
19110 reference "sub:Formulas-in-Section"
19120 \begin_inset LatexCommand index
19128 \begin_layout Standard
19129 Many of the symbols listed in this section can also be inserted via the
19131 \begin_inset Graphics
19132 filename ../images/math/nabla.png
19138 \begin_inset Graphics
19139 filename ../images/math/digamma.png
19147 \begin_layout Subsection
19148 Mathematical Symbols
19149 \begin_inset LatexCommand label
19150 name "sub:Mathematical-Symbols"
19155 \begin_inset LatexCommand index
19156 name "Symbols ! mathematical"
19163 \begin_layout Standard
19167 \begin_inset Tabular
19168 <lyxtabular version="3" rows="10" columns="2">
19170 <column alignment="center" valignment="top" leftline="true" width="0pt">
19171 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19172 <row topline="true" bottomline="true">
19173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19176 \begin_layout Standard
19182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19185 \begin_layout Standard
19192 <row topline="true">
19193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19196 \begin_layout Standard
19204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19207 \begin_layout Standard
19208 \begin_inset Formula $\neg$
19217 <row topline="true">
19218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19221 \begin_layout Standard
19229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19232 \begin_layout Standard
19233 \begin_inset Formula $\Im$
19242 <row topline="true">
19243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19246 \begin_layout Standard
19254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19257 \begin_layout Standard
19258 \begin_inset Formula $\Re$
19267 <row topline="true">
19268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19271 \begin_layout Standard
19279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19282 \begin_layout Standard
19283 \begin_inset Formula $\aleph$
19292 <row topline="true">
19293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19296 \begin_layout Standard
19304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19307 \begin_layout Standard
19308 \begin_inset Formula $\partial$
19317 <row topline="true">
19318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19321 \begin_layout Standard
19329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19332 \begin_layout Standard
19333 \begin_inset Formula $\infty$
19342 <row topline="true" bottomline="true">
19343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19346 \begin_layout Standard
19354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19357 \begin_layout Standard
19358 \begin_inset Formula $\wp$
19367 <row bottomline="true">
19368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19371 \begin_layout Standard
19379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19382 \begin_layout Standard
19383 \begin_inset Formula $\imath$
19392 <row bottomline="true">
19393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19396 \begin_layout Standard
19404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19407 \begin_layout Standard
19408 \begin_inset Formula $\jmath$
19424 \begin_inset Tabular
19425 <lyxtabular version="3" rows="10" columns="2">
19427 <column alignment="center" valignment="top" leftline="true" width="0pt">
19428 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19429 <row topline="true" bottomline="true">
19430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19433 \begin_layout Standard
19439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19442 \begin_layout Standard
19444 \begin_inset Note Note
19447 \begin_layout Standard
19454 is only used as spacer.
19465 <row topline="true">
19466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19469 \begin_layout Standard
19477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19480 \begin_layout Standard
19481 \begin_inset Formula $\forall$
19490 <row topline="true">
19491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19494 \begin_layout Standard
19502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19505 \begin_layout Standard
19506 \begin_inset Formula $\exists$
19515 <row topline="true">
19516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19519 \begin_layout Standard
19527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19530 \begin_layout Standard
19531 \begin_inset Formula $\nexists$
19540 <row topline="true">
19541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19544 \begin_layout Standard
19552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19555 \begin_layout Standard
19556 \begin_inset Formula $\emptyset$
19565 <row topline="true">
19566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19569 \begin_layout Standard
19577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19580 \begin_layout Standard
19581 \begin_inset Formula $\varnothing$
19590 <row topline="true">
19591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19594 \begin_layout Standard
19602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19605 \begin_layout Standard
19606 \begin_inset Formula $\dag$
19615 <row topline="true" bottomline="true">
19616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19619 \begin_layout Standard
19627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19630 \begin_layout Standard
19631 \begin_inset Formula $\ddag$
19640 <row bottomline="true">
19641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19644 \begin_layout Standard
19652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19655 \begin_layout Standard
19659 \begin_layout Standard
19669 \begin_inset Formula $\complement$
19676 \begin_layout Standard
19689 <row bottomline="true">
19690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19693 \begin_layout Standard
19701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19704 \begin_layout Standard
19705 \begin_inset Formula $\Bbbk$
19721 \begin_inset Tabular
19722 <lyxtabular version="3" rows="10" columns="2">
19724 <column alignment="center" valignment="top" leftline="true" width="0pt">
19725 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
19726 <row topline="true" bottomline="true">
19727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19730 \begin_layout Standard
19736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19739 \begin_layout Standard
19746 <row topline="true">
19747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19750 \begin_layout Standard
19758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19761 \begin_layout Standard
19762 \begin_inset Formula $\prime$
19771 <row topline="true">
19772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19775 \begin_layout Standard
19783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19786 \begin_layout Standard
19787 \begin_inset Formula $\backprime$
19796 <row topline="true">
19797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19800 \begin_layout Standard
19808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19811 \begin_layout Standard
19812 \begin_inset Formula $\mho$
19821 <row topline="true">
19822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19825 \begin_layout Standard
19833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19836 \begin_layout Standard
19837 \begin_inset Formula $\triangle$
19846 <row topline="true">
19847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19850 \begin_layout Standard
19858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19861 \begin_layout Standard
19862 \begin_inset Formula $\angle$
19871 <row topline="true">
19872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19875 \begin_layout Standard
19883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19886 \begin_layout Standard
19887 \begin_inset Formula $\measuredangle$
19896 <row topline="true" bottomline="true">
19897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19900 \begin_layout Standard
19908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19911 \begin_layout Standard
19912 \begin_inset Formula $\sphericalangle$
19921 <row bottomline="true">
19922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19925 \begin_layout Standard
19933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19936 \begin_layout Standard
19937 \begin_inset Formula $\top$
19946 <row bottomline="true">
19947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19950 \begin_layout Standard
19958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19961 \begin_layout Standard
19962 \begin_inset Formula $\bot$
19980 \begin_layout Standard
19986 \begin_layout Subsection
19987 Miscellaneous Symbols
19988 \begin_inset LatexCommand label
19989 name "sub:Miscellaneous-Symbols"
19994 \begin_inset LatexCommand index
19995 name "Symbols ! miscellaneous"
20002 \begin_layout Standard
20003 \begin_inset Tabular
20004 <lyxtabular version="3" rows="10" columns="2">
20006 <column alignment="center" valignment="top" leftline="true" width="0pt">
20007 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20008 <row topline="true" bottomline="true">
20009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20012 \begin_layout Standard
20018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20021 \begin_layout Standard
20028 <row topline="true">
20029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20032 \begin_layout Standard
20040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20043 \begin_layout Standard
20044 \begin_inset Formula $\flat$
20053 <row topline="true">
20054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20057 \begin_layout Standard
20065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20068 \begin_layout Standard
20069 \begin_inset Formula $\natural$
20078 <row topline="true">
20079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20082 \begin_layout Standard
20090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20093 \begin_layout Standard
20094 \begin_inset Formula $\sharp$
20103 <row topline="true" bottomline="true">
20104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20107 \begin_layout Standard
20115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20118 \begin_layout Standard
20119 \begin_inset Formula $\surd$
20128 <row bottomline="true">
20129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20132 \begin_layout Standard
20140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20143 \begin_layout Standard
20144 \begin_inset Formula $\checkmark$
20153 <row bottomline="true">
20154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20157 \begin_layout Standard
20165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20168 \begin_layout Standard
20169 \begin_inset Formula $\yen$
20178 <row bottomline="true">
20179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20182 \begin_layout Standard
20190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20193 \begin_layout Standard
20194 \begin_inset Formula $\pounds$
20203 <row bottomline="true">
20204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20207 \begin_layout Standard
20213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20216 \begin_layout Standard
20217 \begin_inset Formula $\$$
20226 <row bottomline="true">
20227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20230 \begin_layout Standard
20236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20239 \begin_layout Standard
20240 \begin_inset Formula $§$
20254 \begin_inset Tabular
20255 <lyxtabular version="3" rows="10" columns="2">
20257 <column alignment="center" valignment="top" leftline="true" width="0">
20258 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
20259 <row topline="true" bottomline="true">
20260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20263 \begin_layout Standard
20269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20272 \begin_layout Standard
20279 <row topline="true">
20280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20283 \begin_layout Standard
20291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20294 \begin_layout Standard
20295 \begin_inset Formula $\hbar$
20304 <row topline="true">
20305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20308 \begin_layout Standard
20316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20319 \begin_layout Standard
20320 \begin_inset Formula $\hslash$
20329 <row topline="true">
20330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20333 \begin_layout Standard
20341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20344 \begin_layout Standard
20345 \begin_inset Formula $\clubsuit$
20354 <row topline="true">
20355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20358 \begin_layout Standard
20366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20369 \begin_layout Standard
20370 \begin_inset Formula $\spadesuit$
20379 <row topline="true">
20380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20383 \begin_layout Standard
20391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20394 \begin_layout Standard
20395 \begin_inset Formula $\bigstar$
20404 <row topline="true">
20405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20408 \begin_layout Standard
20416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20419 \begin_layout Standard
20420 \begin_inset Formula $\blacklozenge$
20429 <row topline="true">
20430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20433 \begin_layout Standard
20441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20444 \begin_layout Standard
20445 \begin_inset Formula $\blacktriangle$
20454 <row topline="true">
20455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20458 \begin_layout Standard
20466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20469 \begin_layout Standard
20470 \begin_inset Formula $\blacktriangledown$
20479 <row topline="true" bottomline="true">
20480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20483 \begin_layout Standard
20491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20494 \begin_layout Standard
20495 \begin_inset Formula $\bullet$
20509 \begin_inset Tabular
20510 <lyxtabular version="3" rows="10" columns="2">
20512 <column alignment="center" valignment="top" leftline="true" width="0pt">
20513 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20514 <row topline="true" bottomline="true">
20515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20518 \begin_layout Standard
20524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20527 \begin_layout Standard
20534 <row topline="true">
20535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20538 \begin_layout Standard
20546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20549 \begin_layout Standard
20550 \begin_inset Formula $\diamondsuit$
20559 <row topline="true">
20560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20563 \begin_layout Standard
20571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20574 \begin_layout Standard
20575 \begin_inset Formula $\Diamond$
20584 <row topline="true">
20585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20588 \begin_layout Standard
20596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20599 \begin_layout Standard
20600 \begin_inset Formula $\heartsuit$
20609 <row topline="true" bottomline="true">
20610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20613 \begin_layout Standard
20621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20624 \begin_layout Standard
20625 \begin_inset Formula $\P$
20634 <row bottomline="true">
20635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20638 \begin_layout Standard
20646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20649 \begin_layout Standard
20650 \begin_inset Formula $\copyright$
20659 <row bottomline="true">
20660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20663 \begin_layout Standard
20671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20674 \begin_layout Standard
20675 \begin_inset Formula $\circledR$
20684 <row bottomline="true">
20685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20688 \begin_layout Standard
20696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20699 \begin_layout Standard
20700 \begin_inset Formula $\maltese$
20709 <row bottomline="true">
20710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20713 \begin_layout Standard
20721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20724 \begin_layout Standard
20725 \begin_inset Formula $\diagup$
20734 <row bottomline="true">
20735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20738 \begin_layout Standard
20746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20749 \begin_layout Standard
20750 \begin_inset Formula $\diagdown$
20766 \begin_layout Standard
20767 \begin_inset VSpace medskip
20770 More symbols are listed in
20771 \begin_inset LatexCommand ref
20772 reference "sub:Miscellaneous-Special-Characters"
20779 \begin_layout Standard
20780 Some symbols can be displayed in different sizes, see
20781 \begin_inset LatexCommand ref
20782 reference "sub:Font-Sizes"
20789 \begin_layout Subsection
20791 \begin_inset LatexCommand index
20792 name "Symbols ! Euro-symbol"
20797 \begin_inset LatexCommand index
20798 name "\\textcent@\\officialeuro"
20805 \begin_layout Standard
20806 To use the Euro symbol in formulas, the LaTeX-package
20811 \begin_inset LatexCommand index
20812 name "Packages ! eurosym"
20816 must be installed and loaded with the LaTeX-preamble line
20819 \begin_layout Standard
20824 usepackage[gennarrow]{eurosym}
20827 \begin_layout Standard
20828 The Euro symbol can now be inserted with the command
20835 \begin_inset LatexCommand index
20836 name "Commands ! E ! \\textbackslash euro"
20843 \begin_layout Standard
20844 The Euro symbol can directly be inserted with the € key in mathematical
20845 text, without having
20860 can also be inserted in TeX-mode.
20861 The official currency symbol can then be inserted with the command
20868 \begin_inset LatexCommand index
20869 name "Commands ! O ! \\textbackslash officialeuro"
20873 , that is only available in TeX-mode.
20876 \begin_layout Standard
20880 \begin_layout Standard
20890 \begin_inset Note Note
20893 \begin_layout Standard
20894 The following table will only be displayed when the LaTeX-package
20906 \begin_layout Standard
20907 An overview about the different Euro symbols:
20910 \begin_layout Standard
20912 \begin_inset Tabular
20913 <lyxtabular version="3" rows="4" columns="3">
20915 <column alignment="center" valignment="top" leftline="true" width="0pt">
20916 <column alignment="center" valignment="top" leftline="true" width="0pt">
20917 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
20918 <row topline="true" bottomline="true">
20919 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
20922 \begin_layout Standard
20928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20931 \begin_layout Standard
20937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20940 \begin_layout Standard
20947 <row topline="true">
20948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20951 \begin_layout Standard
20957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20960 \begin_layout Standard
20968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20971 \begin_layout Standard
20972 \begin_inset Formula $\euro$
20981 <row topline="true">
20982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20985 \begin_layout Standard
20991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20994 \begin_layout Standard
21000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21003 \begin_layout Standard
21004 \begin_inset Formula $\mbox{€}$
21013 <row topline="true" bottomline="true">
21014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21017 \begin_layout Standard
21023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21026 \begin_layout Standard
21034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21037 \begin_layout Standard
21041 \begin_layout Standard
21063 \begin_layout Standard
21067 \begin_layout Standard
21077 \begin_inset Note Note
21080 \begin_layout Standard
21081 The following will be displayed when the LaTeX-package
21093 \begin_layout Standard
21094 You need to install the LaTeX-package
21098 to see the rest of this subsection in the output.
21101 \begin_layout Standard
21105 \begin_layout Standard
21117 \begin_layout Section
21119 \begin_inset LatexCommand label
21120 name "sec:Relations"
21125 \begin_inset LatexCommand index
21131 \begin_inset LatexCommand index
21132 name "Comparisons|see{Relations}"
21139 \begin_layout Standard
21140 All relations can also be inserted via the toolbar button
21141 \begin_inset Graphics
21142 filename ../images/math/leq.png
21150 \begin_layout Standard
21154 \begin_inset Tabular
21155 <lyxtabular version="3" rows="17" columns="2">
21157 <column alignment="center" valignment="top" leftline="true" width="0pt">
21158 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21159 <row topline="true" bottomline="true">
21160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21163 \begin_layout Standard
21169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21172 \begin_layout Standard
21179 <row topline="true">
21180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21183 \begin_layout Standard
21189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21192 \begin_layout Standard
21193 \begin_inset Formula $<$
21202 <row topline="true">
21203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21206 \begin_layout Standard
21214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21217 \begin_layout Standard
21218 \begin_inset Formula $\le$
21227 <row topline="true">
21228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21231 \begin_layout Standard
21239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21242 \begin_layout Standard
21243 \begin_inset Formula $\ll$
21252 <row topline="true">
21253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21256 \begin_layout Standard
21264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21267 \begin_layout Standard
21268 \begin_inset Formula $\prec$
21277 <row topline="true">
21278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21281 \begin_layout Standard
21289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21292 \begin_layout Standard
21293 \begin_inset Formula $\preceq$
21302 <row topline="true">
21303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21306 \begin_layout Standard
21314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21317 \begin_layout Standard
21318 \begin_inset Formula $\subset$
21327 <row topline="true">
21328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21331 \begin_layout Standard
21339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21342 \begin_layout Standard
21343 \begin_inset Formula $\subseteq$
21352 <row topline="true">
21353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21356 \begin_layout Standard
21364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21367 \begin_layout Standard
21368 \begin_inset Formula $\sqsubseteq$
21377 <row topline="true">
21378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21381 \begin_layout Standard
21389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21392 \begin_layout Standard
21393 \begin_inset Formula $\in$
21402 <row topline="true">
21403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21406 \begin_layout Standard
21414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21417 \begin_layout Standard
21418 \begin_inset Formula $\vdash$
21427 <row topline="true">
21428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21431 \begin_layout Standard
21439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21442 \begin_layout Standard
21443 \begin_inset Formula $\smile$
21452 <row topline="true">
21453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21456 \begin_layout Standard
21464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21467 \begin_layout Standard
21468 \begin_inset Formula $\lhd$
21477 <row topline="true">
21478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21481 \begin_layout Standard
21489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21492 \begin_layout Standard
21493 \begin_inset Formula $\unlhd$
21502 <row topline="true">
21503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21506 \begin_layout Standard
21514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21517 \begin_layout Standard
21518 \begin_inset Formula $\gtrless$
21527 <row topline="true">
21528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21531 \begin_layout Standard
21539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21542 \begin_layout Standard
21543 \begin_inset Formula $\mid$
21552 <row topline="true" bottomline="true">
21553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21556 \begin_layout Standard
21564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21567 \begin_layout Standard
21568 \begin_inset Formula $\nmid$
21584 \begin_inset Tabular
21585 <lyxtabular version="3" rows="17" columns="2">
21587 <column alignment="center" valignment="top" leftline="true" width="0pt">
21588 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
21589 <row topline="true" bottomline="true">
21590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21593 \begin_layout Standard
21599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21602 \begin_layout Standard
21609 <row topline="true">
21610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21613 \begin_layout Standard
21619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21622 \begin_layout Standard
21623 \begin_inset Formula $=$
21632 <row topline="true">
21633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21636 \begin_layout Standard
21644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21647 \begin_layout Standard
21648 \begin_inset Formula $\not=$
21657 <row topline="true">
21658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21661 \begin_layout Standard
21669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21672 \begin_layout Standard
21673 \begin_inset Formula $\equiv$
21682 <row topline="true">
21683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21686 \begin_layout Standard
21694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21697 \begin_layout Standard
21698 \begin_inset Formula $\sim$
21707 <row topline="true">
21708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21711 \begin_layout Standard
21719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21722 \begin_layout Standard
21723 \begin_inset Formula $\simeq$
21732 <row topline="true">
21733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21736 \begin_layout Standard
21744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21747 \begin_layout Standard
21748 \begin_inset Formula $\approx$
21757 <row topline="true">
21758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21761 \begin_layout Standard
21769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21772 \begin_layout Standard
21773 \begin_inset Formula $\cong$
21782 <row topline="true">
21783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21786 \begin_layout Standard
21794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21797 \begin_layout Standard
21798 \begin_inset Formula $\bowtie$
21807 <row topline="true">
21808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21811 \begin_layout Standard
21819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21822 \begin_layout Standard
21823 \begin_inset Formula $\notin$
21832 <row topline="true">
21833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21836 \begin_layout Standard
21844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21847 \begin_layout Standard
21848 \begin_inset Formula $\perp$
21857 <row topline="true">
21858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21861 \begin_layout Standard
21869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21872 \begin_layout Standard
21873 \begin_inset Formula $\propto$
21882 <row topline="true">
21883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21886 \begin_layout Standard
21894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21897 \begin_layout Standard
21898 \begin_inset Formula $\asymp$
21907 <row topline="true">
21908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21911 \begin_layout Standard
21919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21922 \begin_layout Standard
21923 \begin_inset Formula $\doteq$
21932 <row topline="true">
21933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21936 \begin_layout Standard
21944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21947 \begin_layout Standard
21948 \begin_inset Formula $\circeq$
21957 <row topline="true">
21958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21961 \begin_layout Standard
21969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21972 \begin_layout Standard
21973 \begin_inset Formula $\models$
21982 <row topline="true" bottomline="true">
21983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21986 \begin_layout Standard
21994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21997 \begin_layout Standard
21998 \begin_inset Formula $\widehat{=}$
22014 \begin_inset Tabular
22015 <lyxtabular version="3" rows="17" columns="2">
22017 <column alignment="center" valignment="top" leftline="true" width="0pt">
22018 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22019 <row topline="true" bottomline="true">
22020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22023 \begin_layout Standard
22029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22032 \begin_layout Standard
22039 <row topline="true">
22040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22043 \begin_layout Standard
22049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22052 \begin_layout Standard
22053 \begin_inset Formula $>$
22062 <row topline="true">
22063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22066 \begin_layout Standard
22074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22077 \begin_layout Standard
22078 \begin_inset Formula $\ge$
22087 <row topline="true">
22088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22091 \begin_layout Standard
22099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22102 \begin_layout Standard
22103 \begin_inset Formula $\gg$
22112 <row topline="true">
22113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22116 \begin_layout Standard
22124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22127 \begin_layout Standard
22128 \begin_inset Formula $\succ$
22137 <row topline="true">
22138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22141 \begin_layout Standard
22149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22152 \begin_layout Standard
22153 \begin_inset Formula $\succeq$
22162 <row topline="true">
22163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22166 \begin_layout Standard
22174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22177 \begin_layout Standard
22178 \begin_inset Formula $\supset$
22187 <row topline="true">
22188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22191 \begin_layout Standard
22199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22202 \begin_layout Standard
22203 \begin_inset Formula $\supseteq$
22212 <row topline="true">
22213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22216 \begin_layout Standard
22224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22227 \begin_layout Standard
22228 \begin_inset Formula $\sqsupseteq$
22237 <row topline="true">
22238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22241 \begin_layout Standard
22249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22252 \begin_layout Standard
22253 \begin_inset Formula $\ni$
22262 <row topline="true">
22263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22266 \begin_layout Standard
22274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22277 \begin_layout Standard
22278 \begin_inset Formula $\dashv$
22287 <row topline="true">
22288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22291 \begin_layout Standard
22299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22302 \begin_layout Standard
22303 \begin_inset Formula $\frown$
22312 <row topline="true">
22313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22316 \begin_layout Standard
22324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22327 \begin_layout Standard
22328 \begin_inset Formula $\rhd$
22337 <row topline="true">
22338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22341 \begin_layout Standard
22349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22352 \begin_layout Standard
22353 \begin_inset Formula $\unrhd$
22362 <row topline="true">
22363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22366 \begin_layout Standard
22374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22377 \begin_layout Standard
22378 \begin_inset Formula $\lessgtr$
22387 <row topline="true">
22388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22391 \begin_layout Standard
22399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22402 \begin_layout Standard
22403 \begin_inset Formula $\parallel$
22412 <row topline="true" bottomline="true">
22413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22416 \begin_layout Standard
22424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22427 \begin_layout Standard
22428 \begin_inset Formula $\nparallel$
22446 \begin_layout Standard
22447 \begin_inset VSpace medskip
22462 are bigger than the equal looking operators
22477 \begin_layout Standard
22478 Relations are, in contrary to symbols, always surrounded by space.
22481 \begin_layout Standard
22482 Relations with labels can be created with the command
22489 \begin_inset LatexCommand index
22490 name "Commands ! S ! \\textbackslash stackrel"
22497 \begin_layout Standard
22499 \begin_inset Tabular
22500 <lyxtabular version="3" rows="2" columns="2">
22502 <column alignment="center" valignment="top" leftline="true" width="0">
22503 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
22504 <row topline="true" bottomline="true">
22505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22508 \begin_layout Standard
22514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22517 \begin_layout Standard
22519 \begin_inset Note Note
22522 \begin_layout Standard
22529 is only used as spacer.
22540 <row topline="true" bottomline="true">
22541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22544 \begin_layout Standard
22551 \begin_layout Standard
22568 \begin_layout Standard
22578 \begin_inset Formula $\downarrow$
22587 \begin_layout Standard
22600 \begin_layout Standard
22614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22617 \begin_layout Standard
22618 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
22634 \begin_layout Section
22638 \begin_layout Subsection
22639 Predefined Functions
22640 \begin_inset LatexCommand label
22641 name "sub:Predefined-Functions"
22646 \begin_inset LatexCommand index
22647 name "Functions ! predefined"
22654 \begin_layout Standard
22655 In general, variables are set
22659 in mathematical expressions, but not function names, because
22660 \begin_inset Formula $sin$
22663 could be misunderstood as
22664 \begin_inset Formula $s\cdot i\cdot n$
22668 Therefore there are predefined functions, that are additionally a bit separated
22670 They are inserted as commands starting with a backslash before their name.
22673 \begin_layout Standard
22675 \begin_inset Tabular
22676 <lyxtabular version="3" rows="2" columns="4">
22678 <column alignment="center" valignment="top" leftline="true" width="0pt">
22679 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22680 <column alignment="center" valignment="top" leftline="true" width="0pt">
22681 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22682 <row topline="true" bottomline="true">
22683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22686 \begin_layout Standard
22692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22695 \begin_layout Standard
22701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22704 \begin_layout Standard
22710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22713 \begin_layout Standard
22720 <row topline="true" bottomline="true">
22721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22724 \begin_layout Standard
22730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22733 \begin_layout Standard
22734 \begin_inset Formula $Asin(x)+B$
22742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22745 \begin_layout Standard
22753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22756 \begin_layout Standard
22757 \begin_inset Formula $A\sin(x)+B$
22774 \begin_layout Standard
22786 \begin_layout Standard
22787 The following functions are predefined:
22790 \begin_layout Standard
22791 \begin_inset VSpace -2mm
22797 \begin_layout Standard
22799 \begin_inset Tabular
22800 <lyxtabular version="3" rows="9" columns="4">
22802 <column alignment="center" valignment="top" leftline="true" width="0pt">
22803 <column alignment="center" valignment="top" leftline="true" width="0pt">
22804 <column alignment="center" valignment="top" leftline="true" width="0pt">
22805 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
22806 <row topline="true" bottomline="true">
22807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22810 \begin_layout Standard
22816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22819 \begin_layout Standard
22825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22828 \begin_layout Standard
22834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22837 \begin_layout Standard
22844 <row topline="true">
22845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22848 \begin_layout Standard
22856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22859 \begin_layout Standard
22867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22870 \begin_layout Standard
22878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22881 \begin_layout Standard
22890 <row topline="true">
22891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22894 \begin_layout Standard
22902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22905 \begin_layout Standard
22913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22916 \begin_layout Standard
22924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22927 \begin_layout Standard
22936 <row topline="true">
22937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22940 \begin_layout Standard
22948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22951 \begin_layout Standard
22959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22962 \begin_layout Standard
22970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22973 \begin_layout Standard
22982 <row topline="true">
22983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22986 \begin_layout Standard
22994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22997 \begin_layout Standard
23005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23008 \begin_layout Standard
23016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23019 \begin_layout Standard
23028 <row topline="true">
23029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23032 \begin_layout Standard
23040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23043 \begin_layout Standard
23051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23054 \begin_layout Standard
23062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23065 \begin_layout Standard
23074 <row topline="true">
23075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23078 \begin_layout Standard
23086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23089 \begin_layout Standard
23097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23100 \begin_layout Standard
23108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23111 \begin_layout Standard
23120 <row topline="true">
23121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23124 \begin_layout Standard
23132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23135 \begin_layout Standard
23143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23146 \begin_layout Standard
23154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23157 \begin_layout Standard
23166 <row topline="true" bottomline="true">
23167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23170 \begin_layout Standard
23178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23181 \begin_layout Standard
23189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23192 \begin_layout Standard
23200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23203 \begin_layout Standard
23219 \begin_layout Standard
23220 They can also be inserted with the math toolbar button
23221 \begin_inset Graphics
23222 filename ../images/math/functions.png
23230 \begin_layout Subsection
23231 Self-defined Functions
23232 \begin_inset LatexCommand index
23233 name "Functions ! self-defined"
23240 \begin_layout Standard
23241 To use a function that is not predefined, like for example the sign function
23242 sgn(x), there are two possibilities:
23245 \begin_layout Itemize
23246 Define the function by inserting the following line to the LaTeX-preamble
23250 \begin_layout Standard
23255 DeclareMathOperator
23258 \begin_inset LatexCommand ref
23259 reference "sub:Self-defined-Operators"
23271 \begin_inset VSpace -3mm
23280 DeclareMathOperator{
23285 \begin_inset LatexCommand index
23286 name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
23293 \begin_inset VSpace -2mm
23298 Now the new defined function can be called with the command
23307 \begin_layout Itemize
23308 Write the the formula as usual, mark the formula name, in our example the
23313 , and change it to mathematical text.
23314 At last a space is inserted between prefactor and function.
23317 \begin_layout Standard
23318 The result is the same with both methods as with a predefined function
23322 \begin_layout Standard
23323 In LyX self-defined functions are displayed red, predefined ones black.
23331 \begin_layout Standard
23333 \begin_inset Tabular
23334 <lyxtabular version="3" rows="3" columns="2">
23336 <column alignment="center" valignment="top" leftline="true" width="0pt">
23337 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
23338 <row topline="true" bottomline="true">
23339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23342 \begin_layout Standard
23348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23351 \begin_layout Standard
23358 <row topline="true" bottomline="true">
23359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23362 \begin_layout Standard
23370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23373 \begin_layout Standard
23374 \begin_inset Formula $A\sgn(x)+B$
23383 <row topline="true" bottomline="true">
23384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23387 \begin_layout Standard
23391 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
23399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23402 \begin_layout Standard
23403 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
23419 \begin_layout Standard
23420 The first method is more suitable when the self-defined function should
23421 be used several times.
23424 \begin_layout Subsection
23426 \begin_inset LatexCommand index
23434 \begin_layout Standard
23435 For limits there are defined besides
23442 \begin_inset LatexCommand index
23443 name "Commands ! L ! \\textbackslash lim"
23459 furthermore the following functions:
23462 \begin_layout Standard
23464 \begin_inset Tabular
23465 <lyxtabular version="3" rows="5" columns="2">
23467 <column alignment="center" valignment="top" leftline="true" width="0">
23468 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
23469 <row topline="true" bottomline="true">
23470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23473 \begin_layout Standard
23479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23482 \begin_layout Standard
23484 \begin_inset Note Note
23487 \begin_layout Standard
23494 is only used as spacer.
23505 <row topline="true">
23506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23509 \begin_layout Standard
23517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23520 \begin_layout Standard
23521 \begin_inset Formula $\varliminf$
23531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23534 \begin_layout Standard
23542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23545 \begin_layout Standard
23546 \begin_inset Formula $\varlimsup$
23556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23559 \begin_layout Standard
23567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23570 \begin_layout Standard
23571 \begin_inset Formula $\varprojlim$
23580 <row bottomline="true">
23581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23584 \begin_layout Standard
23592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23595 \begin_layout Standard
23596 \begin_inset Formula $\varinjlim$
23600 \begin_inset Formula $\raisebox{-2.5mm}{}$
23616 \begin_layout Standard
23617 \begin_inset VSpace medskip
23620 The limit is created by inserting a subscript.
23621 It is set right beside the function in an inline formula:
23624 \begin_layout Standard
23626 \begin_inset Tabular
23627 <lyxtabular version="3" rows="2" columns="2">
23629 <column alignment="center" valignment="top" width="0pt">
23630 <column alignment="center" valignment="top" width="0pt">
23632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23635 \begin_layout Standard
23641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23644 \begin_layout Standard
23648 \begin_layout Standard
23658 \begin_inset Note Note
23661 \begin_layout Standard
23674 are used here as spacer.
23686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23689 \begin_layout Standard
23698 \begin_layout Standard
23711 \begin_layout Standard
23725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23728 \begin_layout Standard
23729 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
23745 \begin_layout Standard
23746 In a displayed formula the limit is set below the formula, as usual:
23747 \begin_inset Formula \[
23755 \begin_layout Subsection
23757 \begin_inset LatexCommand index
23758 name "Functions ! modulo-"
23765 \begin_layout Standard
23766 The modulo-function is special, because it exists in four variants.
23769 \begin_layout Standard
23770 The variants in a displayed formula:
23771 \begin_inset Formula \begin{align*}
23772 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
23773 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
23774 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
23775 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
23776 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
23783 \begin_layout Standard
23784 In an inline formula less space is set before the function names for all
23788 \begin_layout Section
23790 \begin_inset LatexCommand index
23791 name "Special characters"
23798 \begin_layout Subsection
23799 Special Characters in Mathematical Text
23802 \begin_layout Standard
23803 The following commands can only be used in mathematical text or in TeX-mode:
23806 \begin_layout Standard
23810 \begin_inset Tabular
23811 <lyxtabular version="3" rows="8" columns="2">
23813 <column alignment="block" valignment="top" leftline="true" width="0">
23814 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
23815 <row topline="true" bottomline="true">
23816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23819 \begin_layout Standard
23825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23828 \begin_layout Standard
23835 <row topline="true">
23836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23839 \begin_layout Standard
23847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23850 \begin_layout Standard
23851 \begin_inset Formula $\textrm{\oe}$
23860 <row topline="true">
23861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23864 \begin_layout Standard
23872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23875 \begin_layout Standard
23876 \begin_inset Formula $\textrm{\OE}$
23885 <row topline="true">
23886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23889 \begin_layout Standard
23897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23900 \begin_layout Standard
23901 \begin_inset Formula $\textrm{\ae}$
23910 <row topline="true">
23911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23914 \begin_layout Standard
23922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23925 \begin_layout Standard
23926 \begin_inset Formula $\textrm{\AE}$
23935 <row topline="true">
23936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23939 \begin_layout Standard
23947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23950 \begin_layout Standard
23951 \begin_inset Formula $\textrm{\aa}$
23960 <row topline="true" bottomline="true">
23961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23964 \begin_layout Standard
23968 \begin_inset LatexCommand index
23969 name "\\@\\textrm{\\AA}"
23978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23981 \begin_layout Standard
23982 \begin_inset Formula $\textrm{\AA}$
23991 <row bottomline="true">
23992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23995 \begin_layout Standard
24003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24006 \begin_layout Standard
24007 \begin_inset Formula $\textrm{\i}$
24023 \begin_inset Tabular
24024 <lyxtabular version="3" rows="8" columns="2">
24026 <column alignment="block" valignment="top" leftline="true" width="0">
24027 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24028 <row topline="true" bottomline="true">
24029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24032 \begin_layout Standard
24034 \begin_inset Note Note
24037 \begin_layout Standard
24044 is used for separation, because otherwise the output will be ¡ and ¿ respective
24055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24058 \begin_layout Standard
24065 <row topline="true">
24066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24069 \begin_layout Standard
24077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24080 \begin_layout Standard
24081 \begin_inset Formula $\textrm{\o}$
24090 <row topline="true">
24091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24094 \begin_layout Standard
24102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24105 \begin_layout Standard
24106 \begin_inset Formula $\textrm{\O}$
24115 <row topline="true">
24116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24119 \begin_layout Standard
24127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24130 \begin_layout Standard
24131 \begin_inset Formula $\textrm{\l}$
24140 <row topline="true">
24141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24144 \begin_layout Standard
24152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24155 \begin_layout Standard
24156 \begin_inset Formula $\textrm{\L}$
24165 <row topline="true" bottomline="true">
24166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24169 \begin_layout Standard
24174 \begin_layout Standard
24187 \begin_layout Standard
24201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24204 \begin_layout Standard
24205 \begin_inset Formula $\textrm{!`}$
24214 <row bottomline="true">
24215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24218 \begin_layout Standard
24223 \begin_layout Standard
24236 \begin_layout Standard
24250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24253 \begin_layout Standard
24254 \begin_inset Formula $\textrm{?`}$
24263 <row bottomline="true">
24264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24267 \begin_layout Standard
24275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24278 \begin_layout Standard
24279 \begin_inset Formula $\textrm{\j}$
24297 \begin_layout Standard
24299 \begin_inset Formula $\textrm{\textrm{Å}}$
24303 \begin_inset Formula $\textrm{\textrm{Ø}}$
24306 can also be inserted via the math toolbar button
24307 \begin_inset Graphics
24308 filename ../images/math/digamma.png
24316 \begin_layout Standard
24317 An exception are the commands
24323 \begin_layout Standard
24340 \begin_layout Standard
24351 , because they can be inserted in LyX directly to text.
24354 \begin_layout Subsection
24356 \begin_inset LatexCommand label
24357 name "sub:Accents-in-Text"
24362 \begin_inset LatexCommand index
24363 name "Accents ! in text"
24370 \begin_layout Standard
24371 With the following commands all letters can be accented.
24372 The commands must be inserted in TeX-mode.
24375 \begin_layout Standard
24379 \begin_inset Tabular
24380 <lyxtabular version="3" rows="8" columns="2">
24382 <column alignment="block" valignment="top" leftline="true" width="0">
24383 <column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
24384 <row topline="true" bottomline="true">
24385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24388 \begin_layout Standard
24394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24397 \begin_layout Standard
24404 <row topline="true">
24405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24408 \begin_layout Standard
24412 \begin_inset Quotes grd
24420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24423 \begin_layout Standard
24427 \begin_layout Standard
24442 <row topline="true">
24443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24446 \begin_layout Standard
24454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24457 \begin_layout Standard
24461 \begin_layout Standard
24476 <row topline="true">
24477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24480 \begin_layout Standard
24487 \begin_layout Standard
24501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24504 \begin_layout Standard
24508 \begin_layout Standard
24523 <row topline="true">
24524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24527 \begin_layout Standard
24535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24538 \begin_layout Standard
24542 \begin_layout Standard
24557 <row topline="true">
24558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24561 \begin_layout Standard
24568 \begin_layout Standard
24582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24585 \begin_layout Standard
24589 \begin_layout Standard
24604 <row topline="true" bottomline="true">
24605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24608 \begin_layout Standard
24615 \begin_layout Standard
24629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24632 \begin_layout Standard
24636 \begin_layout Standard
24651 <row bottomline="true">
24652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24655 \begin_layout Standard
24662 \begin_layout Standard
24676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24679 \begin_layout Standard
24683 \begin_layout Standard
24705 \begin_inset Tabular
24706 <lyxtabular version="3" rows="8" columns="2">
24708 <column alignment="block" valignment="top" leftline="true" width="0">
24709 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
24710 <row topline="true" bottomline="true">
24711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24714 \begin_layout Standard
24720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24723 \begin_layout Standard
24730 <row topline="true">
24731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24734 \begin_layout Standard
24741 \begin_layout Standard
24755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24758 \begin_layout Standard
24762 \begin_layout Standard
24777 <row topline="true">
24778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24781 \begin_layout Standard
24789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24792 \begin_layout Standard
24796 \begin_layout Standard
24811 <row topline="true">
24812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24815 \begin_layout Standard
24819 \begin_inset LatexCommand index
24829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24832 \begin_layout Standard
24836 \begin_layout Standard
24851 <row topline="true">
24852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24855 \begin_layout Standard
24863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24866 \begin_layout Standard
24870 \begin_layout Standard
24885 <row topline="true" bottomline="true">
24886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24889 \begin_layout Standard
24896 \begin_layout Standard
24910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24913 \begin_layout Standard
24917 \begin_layout Standard
24932 <row bottomline="true">
24933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24936 \begin_layout Standard
24943 \begin_layout Standard
24957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24960 \begin_layout Standard
24964 \begin_layout Standard
24979 <row bottomline="true">
24980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24983 \begin_layout Standard
24990 \begin_layout Standard
25004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25007 \begin_layout Standard
25011 \begin_layout Standard
25035 \begin_layout Standard
25036 \begin_inset VSpace medskip
25045 also two different characters can be accented.
25054 \begin_layout Standard
25069 \begin_layout Standard
25081 \begin_layout Standard
25094 can in combination with vowels directly be inserted with the keyboard without
25096 The same applies for the tilde
25100 \begin_layout Standard
25101 This only applies for keyboards where the tilde is defined as accent.
25110 in combination with
25125 \begin_layout Standard
25168 , and accents inserted directly with the keyboard are also available in
25170 For the other accents there are special math commands to be used in formulas,
25172 \begin_inset LatexCommand ref
25173 reference "sub:Accents-for-one"
25180 \begin_layout Standard
25181 \begin_inset VSpace bigskip
25184 Furthermore, with the command
25191 \begin_inset LatexCommand index
25192 name "Commands ! T ! \\textbackslash textcircled"
25196 all numbers and letters can be set into a circle, quasi accented with a
25197 circle, similar to the the copyright symbol.
25200 \begin_layout Standard
25202 \begin_inset Tabular
25203 <lyxtabular version="3" rows="3" columns="2">
25205 <column alignment="center" valignment="top" leftline="true" width="0">
25206 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25207 <row topline="true" bottomline="true">
25208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25211 \begin_layout Standard
25217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25220 \begin_layout Standard
25222 \begin_inset Note Note
25225 \begin_layout Standard
25232 is only used as spacer.
25243 <row topline="true">
25244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25247 \begin_layout Standard
25255 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25258 \begin_layout Standard
25262 \begin_layout Standard
25277 <row topline="true" bottomline="true">
25278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25281 \begin_layout Standard
25292 raisebox{-1.5pt}{W}}
25297 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25300 \begin_layout Standard
25301 \begin_inset Formula $\raisebox{4.5mm}{}$
25308 \begin_layout Standard
25326 \begin_inset Formula $\raisebox{-2mm}{}$
25342 \begin_layout Standard
25343 One has to take care that the character fits in the circle.
25354 \begin_layout Standard
25356 \begin_inset LatexCommand ref
25357 reference "sub:Font-Sizes"
25366 specifies thereby the size of the circle.
25377 \begin_layout Standard
25379 \begin_inset LatexCommand ref
25380 reference "sub:Boxes-without-Frame"
25389 the character can be centered.
25392 \begin_layout Subsection
25394 \begin_inset LatexCommand index
25395 name "Minuscule numbers"
25402 \begin_layout Standard
25403 Minuscule numbers are created with the command
25410 \begin_inset LatexCommand index
25411 name "Commands ! O ! \\textbackslash oldstylenums"
25416 The command can be used in formulas and in TeX-mode.
25417 The command scheme is:
25420 \begin_layout Standard
25425 oldstylenums{number}
25428 \begin_layout Standard
25433 oldstylenums{0123456789
25436 \begin_inset Formula $\oldstylenums{0123456789}$
25442 \begin_layout Subsection
25443 Miscellaneous Special Characters
25444 \begin_inset LatexCommand label
25445 name "sub:Miscellaneous-Special-Characters"
25450 \begin_inset LatexCommand index
25451 name "Special characters ! miscellaneous"
25458 \begin_layout Standard
25459 The following characters can only be inserted to formulas by using commands:
25462 \begin_layout Standard
25464 \begin_inset Tabular
25465 <lyxtabular version="3" rows="4" columns="2">
25467 <column alignment="center" valignment="top" leftline="true" width="0">
25468 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
25469 <row topline="true" bottomline="true">
25470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25473 \begin_layout Standard
25479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25482 \begin_layout Standard
25489 <row topline="true">
25490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25493 \begin_layout Standard
25500 \begin_layout Standard
25514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25517 \begin_layout Standard
25518 \begin_inset Formula $\mathcircumflex$
25527 <row topline="true">
25528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25531 \begin_layout Standard
25539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25542 \begin_layout Standard
25543 \begin_inset Formula $\_$
25552 <row topline="true" bottomline="true">
25553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25556 \begin_layout Standard
25561 \begin_layout Standard
25573 \begin_inset LatexCommand index
25583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25586 \begin_layout Standard
25587 \begin_inset Formula $^{\circ}$
25603 \begin_layout Standard
25604 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
25605 contains the following line
25609 \begin_layout Standard
25610 More about this is described in
25611 \begin_inset LatexCommand ref
25612 reference "sub:Text-Characters-in"
25624 \begin_layout Standard
25629 DeclareInputtext{176}{
25639 f\SpecialChar \textcompwordmark{}
25643 \begin_layout Standard
25644 \begin_inset VSpace bigskip
25648 \begin_inset LatexCommand index
25653 is designed as accent, thus is looks alone a bit misplaced: ~
25656 addresses (URLs) sometimes a single tilde is needed.
25657 In this case the relation sign
25665 \begin_layout Standard
25667 \begin_inset LatexCommand ref
25668 reference "sec:Relations"
25679 is used in a formula.
25680 As a formula cannot be created in an URL-box (menu
25682 Insert\SpecialChar \menuseparator
25685 ), the URL is inserted as normal text with the font style '
25690 Should the URL be a hyperlink in the DVI- or PDF-output, the command
25700 \begin_layout Standard
25707 can only be used together with the LaTeX-package
25712 \begin_inset LatexCommand index
25713 name "Packages ! hyperref"
25724 is written in the section
25730 Embedded\InsetSpace ~
25739 \begin_inset LatexCommand index
25740 name "Commands ! H ! \\textbackslash href"
25747 \begin_layout Standard
25748 As example an URL with a tilde:
25751 \begin_layout Standard
25754 http://www.lyx.org/
25755 \begin_inset Formula $\sim$
25761 \begin_layout Standard
25772 \begin_layout Standard
25776 href{http://www.lyx.org/~mustermann}{
25781 http://www.lyx.org/
25782 \begin_inset Formula $\sim$
25789 \begin_layout Standard
25799 \begin_layout Section
25801 \begin_inset LatexCommand label
25802 name "sec:Formula-Styles"
25807 \begin_inset LatexCommand index
25808 name "Formula ! styles"
25815 \begin_layout Itemize
25816 There are two different alignment styles:
25820 \begin_layout Description
25821 Centered is the predefined standard
25824 \begin_layout Description
25825 Indented for this the option
25829 must be inserted in the menu
25831 Document\SpecialChar \menuseparator
25836 Document\InsetSpace ~
25840 \begin_layout Standard
25845 is used, the indentation can be adjusted with the length
25852 \begin_inset LatexCommand index
25853 name "Commands ! M ! \\textbackslash mathindent"
25858 Should the distance be 15\InsetSpace \thinspace{}
25859 mm, the following command line is inserted in
25863 \begin_layout Standard
25873 \begin_layout Standard
25874 When no length is specified, the predefined value of 30\InsetSpace \thinspace{}
25879 \begin_layout Itemize
25880 And two different numbering styles:
25884 \begin_layout Description
25885 Right is the predefined standard
25888 \begin_layout Description
25889 Left for this the option
25893 must be inserted in the menu
25895 Document\SpecialChar \menuseparator
25900 Document\InsetSpace ~
25905 \begin_layout Standard
25914 can also be used together.
25915 In this case both options are inserted, separated by a comma.
25918 \begin_layout Standard
25919 The chosen styles are used for all displayed formulas of the document.
25920 When both, centered and indented formulas should be created in a document,
25926 The indented formulas are then set in a flalign environment, see
25927 \begin_inset LatexCommand ref
25928 reference "sub:Flalign-Environment"
25935 \begin_layout Section
25937 \begin_inset LatexCommand label
25938 name "sec:Multiline-Formulas"
25943 \begin_inset LatexCommand index
25944 name "Formula ! multiline"
25951 \begin_layout Subsection
25955 \begin_layout Standard
25956 In LyX multiline formulas are created by pressing
25967 that is described in
25968 \begin_inset LatexCommand ref
25969 reference "sub:Standard-align-Environment"
25976 \begin_layout Standard
25977 There are other multiline formula environments that can be created via the
25980 Insert\SpecialChar \menuseparator
25984 These environments are described in the following sections.
25987 \begin_layout Standard
25988 In all multiline formula environments a new line is created by pressing
25994 To add or delete lines, the math toolbar buttons
25995 \begin_inset Graphics
25996 filename ../images/tabular-feature_append-row.png
26002 \begin_inset Graphics
26003 filename ../images/tabular-feature_delete-row.png
26008 , respectively, or the menu
26010 Edit\SpecialChar \menuseparator
26016 \begin_layout Subsubsection
26018 \begin_inset LatexCommand label
26019 name "sub:Line-Separation"
26024 \begin_inset LatexCommand index
26025 name "Formula ! multiline ! Line separation"
26032 \begin_layout Standard
26033 There is sometimes not enough space in multiline formulas between the lines:
26034 \begin_inset Formula \begin{eqnarray*}
26035 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}\\
26036 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*}
26043 \begin_layout Standard
26044 In LaTeX additional line space is specified as optional argument of the
26046 This is not yet possible in LyX
26050 \begin_layout Standard
26055 \begin_layout Standard
26059 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
26068 \begin_layout Standard
26080 , therefore the whole formula must be inserted in TeX-mode.
26081 To add in our example space, the command
26089 is inserted at the end of the first line.
26094 \begin_layout Standard
26101 \begin_layout Standard
26103 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26106 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26113 \begin_layout Standard
26117 left(B^{2}+x_{0}^{2}
26125 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26130 \begin_layout Standard
26142 \begin_layout Standard
26143 \begin_inset VSpace bigskip
26146 To set the the line separation for all lines in a formula, the length
26153 \begin_inset LatexCommand index
26154 name "Commands ! J ! \\textbackslash jot"
26160 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26170 is the value 3\InsetSpace \thinspace{}
26172 To create 3\InsetSpace \thinspace{}
26173 mm additional line separation as in the previous example, the
26177 \begin_layout Standard
26187 \begin_layout Standard
26188 is inserted in TeX-mode before the formula.
26189 This requires that the LaTeX-package
26197 \begin_layout Standard
26202 is part of every LaTeX standard installation.
26208 \begin_inset LatexCommand index
26209 name "Packages ! calc"
26213 was loaded in LaTeX-preamble with the line
26216 \begin_layout Standard
26224 \begin_layout Standard
26229 \begin_layout Standard
26241 \begin_inset Formula \begin{eqnarray*}
26242 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}\\
26243 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*}
26250 \begin_layout Standard
26254 \begin_layout Standard
26265 To get back to the predefined distance,
26271 is set to the value 3\InsetSpace \thinspace{}
26275 \begin_layout Subsubsection
26277 \begin_inset LatexCommand label
26278 name "sub:Column-Separation"
26283 \begin_inset LatexCommand index
26284 name "Formula ! multiline ! Column separation"
26291 \begin_layout Standard
26292 Multiline formulas form a matrix.
26293 A formula in the eqnarray environment is for example a matrix with three
26295 By changing the column separation in this environment, the space beside
26296 the relation sign can be changed.
26299 \begin_layout Standard
26300 The column separation is specified with the length
26307 \begin_inset LatexCommand index
26308 name "Commands ! A ! \\textbackslash arraycolsep"
26314 column separation = 2\InsetSpace \thinspace{}
26326 \begin_layout Standard
26336 \begin_layout Standard
26337 inserted in TeX-mode, sets for all following formulas a column separation
26338 of 2\InsetSpace \thinspace{}
26340 To get back to the predefined distance,
26346 is set to 5\InsetSpace \thinspace{}
26350 \begin_layout Standard
26351 A formula with 2\InsetSpace \thinspace{}
26352 cm column separation:
26356 \begin_layout Standard
26368 \begin_inset Formula \begin{eqnarray*}
26370 C & \ne & A\end{eqnarray*}
26374 A formula with the predefined column separation for matrices of 10\InsetSpace \thinspace{}
26379 \begin_layout Standard
26391 \begin_inset Formula \begin{eqnarray*}
26393 C & \ne & A\end{eqnarray*}
26400 \begin_layout Subsubsection
26402 \begin_inset LatexCommand index
26403 name "Formula ! long"
26410 \begin_layout Standard
26411 Long formulas can be typeset using these methods:
26414 \begin_layout Itemize
26415 When one side of the equation is much shorther than the line width, this
26416 one is chosen for the left side and the right side is typeset over two
26421 \begin_layout Standard
26431 \begin_inset Formula \begin{eqnarray}
26432 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 \\
26433 & & -\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}
26441 \begin_layout Standard
26452 The minus sign at the beginning of the second line does normally not appear
26453 as operator because it is the first character of the line.
26454 Thus it would not be surrounded by space and could not be distinguished
26455 from the fraction bar.
26456 To avoid this, space was inserted behind the minus sign with the command
26467 \begin_layout Standard
26475 \begin_inset LatexCommand ref
26476 reference "sub:Variable-Space"
26486 \begin_inset LatexCommand index
26487 name "Commands ! H ! \\textbackslash hspace"
26494 \begin_layout Itemize
26495 When both sides of the equation are too long, the command
26502 \begin_inset LatexCommand index
26503 name "Commands ! L ! \\textbackslash lefteqn"
26508 It is inserted to the first column of the first line and effects that all
26509 further insertions overwrite the following columns:
26513 \begin_layout Standard
26523 \begin_inset Formula \begin{eqnarray}
26524 \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 \\
26525 & & -\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 \\
26526 & & =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}
26534 \begin_layout Standard
26545 After the insertion of
26551 , the cursor is in a purple box that is a bit shifted to the left from the
26553 In this the formula is inserted.
26557 \begin_layout Standard
26568 The content of the further lines is inserted to the second or another formula
26570 The greater the column number where it was inserted, the larger the indentation.
26574 \begin_layout Standard
26586 \begin_inset Note Greyedout
26589 \begin_layout Standard
26590 Note the following when using
26599 \begin_layout Itemize
26600 The formula doesn't use the full page width.
26601 When e.\InsetSpace \thinspace{}
26604 \begin_inset Formula $-B^{2}$
26607 is added to the first line in the above example, it would have been outside
26609 To better use the width, negative space can be inserted at the beginning
26613 \begin_layout Itemize
26614 Due to a bug in LyX the cursor cannot be set with the mouse into the first
26619 \begin_layout Standard
26623 \begin_layout Standard
26627 href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
26636 \begin_layout Standard
26648 One can only set the cursor at the beginning of the line and move it with
26657 \begin_layout Itemize
26658 Other methods to set long formulas are offered by the environments described
26660 \begin_inset LatexCommand ref
26661 reference "sub:Multline-Environment"
26666 \begin_inset LatexCommand ref
26667 reference "sub:Multiline-Formula-Parts"
26674 \begin_layout Subsubsection
26676 \begin_inset LatexCommand label
26677 name "sub:Multiline-Brackets"
26682 \begin_inset LatexCommand index
26683 name "Brackets ! for multiline expressions"
26690 \begin_layout Standard
26691 For brackets spanning multiple lines the following problem occurs:
26692 \begin_inset Formula \begin{eqnarray*}
26693 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26694 & & \left.\cdots+B-D\right]\end{eqnarray*}
26701 \begin_layout Standard
26702 The closing bracket is smaller than the opening bracket because brackets
26703 with variable size may not span multiple lines.
26706 \begin_layout Standard
26707 To set the bracket size for the second line correctly, the first line is
26715 \begin_inset LatexCommand index
26716 name "Commands ! R ! \\textbackslash right"
26720 and the second line with
26728 \begin_layout Standard
26742 \begin_inset LatexCommand ref
26743 reference "sub:Automatic-Bracket-Size"
26755 \begin_inset LatexCommand index
26756 name "Commands ! L ! \\textbackslash left"
26778 \begin_layout Standard
26797 \begin_layout Standard
26816 \begin_layout Standard
26828 \begin_inset Formula $\downarrow$
26834 \begin_inset LatexCommand index
26835 name "Commands ! V ! \\textbackslash vphantom"
26839 is inserted, because the multiplication operator with its limits is the
26840 largest symbol in the first line and this should be the size for the bracket
26841 in the second line.
26844 \begin_layout Standard
26845 The result is this:
26846 \begin_inset Formula \begin{eqnarray*}
26847 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
26848 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
26855 \begin_layout Subsection
26859 \begin_layout Standard
26860 Align environments can be used for every kind of multiline formulas.
26861 They are specially useful to set several formulas side by side.
26864 \begin_layout Standard
26865 Align environments consist of columns.
26866 The odd columns are right aligned, the even ones left aligned.
26867 Every line in an Align environment can be numbered.
26870 \begin_layout Standard
26871 Align environments are created via the menu
26873 Insert\SpecialChar \menuseparator
26879 Edit\SpecialChar \menuseparator
26880 Math\SpecialChar \menuseparator
26881 Change Formula Type
26883 already existing existing formulas can be converted to Align environments.
26886 \begin_layout Standard
26887 To add or delete columns, the math toolbar buttons
26888 \begin_inset Graphics
26889 filename ../images/tabular-feature_append-column.png
26895 \begin_inset Graphics
26896 filename ../images/tabular-feature_delete-column.png
26901 , respectively, or the menu
26903 Edit\SpecialChar \menuseparator
26909 \begin_layout Subsubsection
26910 Standard align Environment
26911 \begin_inset LatexCommand label
26912 name "sub:Standard-align-Environment"
26917 \begin_inset LatexCommand index
26918 name "Formula ! multiline ! align environment"
26925 \begin_layout Standard
26926 This Align environment is created by presssing
26930 in a formula or by the menu
26932 Insert\SpecialChar \menuseparator
26933 Math\SpecialChar \menuseparator
26934 AMS align Environment
26939 \begin_layout Standard
26940 An example for two formulas set side by side, that are created with a four
26941 column align environment:
26942 \begin_inset Formula \begin{align*}
26943 A & =\sin(B) & C & =D\\
26944 C & \ne A & B & \ne D\end{align*}
26948 As it can be seen, the formulas in this environment are placed so as if
26957 \begin_layout Standard
26965 \begin_inset LatexCommand ref
26966 reference "sub:Variable-Space"
26977 before the first and after every even column.
26978 When the formula style
26984 \begin_layout Standard
26986 \begin_inset LatexCommand ref
26987 reference "sec:Formula-Styles"
26998 is used, the formula is set without the
27004 before the first column.
27007 \begin_layout Subsubsection
27008 Alignat Environment
27009 \begin_inset LatexCommand index
27010 name "Formula ! multiline ! alignat environment"
27017 \begin_layout Standard
27018 The alignat environment has no predefined column separation.
27019 It can be inserted manually with the spaces that are described
27020 \begin_inset LatexCommand ref
27021 reference "sub:Space"
27028 \begin_layout Standard
27029 The above example in the alignat environment where 1\InsetSpace \thinspace{}
27030 cm space was inserted
27031 at the beginning of the second formula:
27032 \begin_inset Formula \begin{alignat*}{2}
27033 A & =\sin(B) & \hspace{1cm}C & =D\\
27034 C & \ne A & B & \ne D\end{alignat*}
27038 Because the column separation can be set separately for every column, this
27039 environment is especially suitable to set three and more formulas side
27043 \begin_layout Subsubsection
27044 Flalign Environment
27045 \begin_inset LatexCommand label
27046 name "sub:Flalign-Environment"
27051 \begin_inset LatexCommand index
27052 name "Formula ! multiline ! flalign environment"
27059 \begin_layout Standard
27060 In this environment the first two columns are always set as much as possible
27061 to the left and the last two ones to the right.
27063 \begin_inset Formula \begin{flalign*}
27064 A & =1 & B & =2 & C & =3\\
27065 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
27072 \begin_layout Standard
27073 By creating a flalign environment with an odd number of columns where an
27074 empty TeX-brace is inserted to the last column, several formulas in a document
27075 can be set to the left, although the formula style
27080 As example the indented formula
27081 \begin_inset LatexCommand eqref
27082 reference "eq:VolInt"
27087 \begin_inset Formula \begin{flalign}
27088 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
27092 The first two columns contain the formula.
27093 To indent it as with the formula style
27097 , 30\InsetSpace \thinspace{}
27098 pt space was inserted at the beginning of the first column.
27101 \begin_layout Subsection
27102 Eqnarray Environment
27103 \begin_inset LatexCommand index
27104 name "Formula ! multiline ! eqnarray environment"
27111 \begin_layout Standard
27112 When this environment has been created, three blue boxes appear.
27113 The content of the first box is right aligned, the content of the last
27115 The content of the middle box appears centered and a bit smaller, because
27116 it is designed to insert there only relation characters.
27117 \begin_inset Formula \begin{eqnarray*}
27118 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27120 A & = & A\end{eqnarray*}
27127 \begin_layout Subsection
27129 \begin_inset LatexCommand index
27130 name "Formula ! multiline ! gather environment"
27137 \begin_layout Standard
27138 This environment consists of only one centered column.
27139 Every line can be numbered.
27140 \begin_inset Formula \begin{gather}
27142 X=\textrm{-}1\end{gather}
27149 \begin_layout Subsection
27150 Multline Environment
27151 \begin_inset LatexCommand label
27152 name "sub:Multline-Environment"
27157 \begin_inset LatexCommand index
27158 name "Formula ! multiline ! multline environment"
27165 \begin_layout Standard
27166 The multline environment consists, like the gather environment, of only
27168 But the first line is left aligned, the last one right aligned.
27169 All other lines are centered.
27170 Therefore this environment is suitable for long formulas.
27172 \begin_inset LatexCommand eqref
27173 reference "eq:lefteqn"
27177 in the multline environment:
27178 \begin_inset Formula \begin{multline}
27179 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}\\
27180 -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}\\
27181 =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}
27188 \begin_layout Standard
27189 In the output only the the last (first) line of a multline environment appears
27190 numbered when the document numbering is right (left).
27194 \begin_layout Standard
27195 numbering styles see
27196 \begin_inset LatexCommand ref
27197 reference "sec:Formula-Styles"
27206 This is also the case when there is a formula number displayed after every
27211 \begin_layout Standard
27216 \begin_layout Standard
27220 href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
27229 \begin_layout Standard
27244 \begin_layout Standard
27250 \begin_inset LatexCommand index
27251 name "Commands ! S ! \\textbackslash shoveright"
27262 \begin_inset LatexCommand index
27263 name "Commands ! S ! \\textbackslash shoveleft"
27269 a centered line can be right or left aligned, respectively.
27270 The commands are used as follows:
27273 \begin_layout Standard
27278 shoveright{line content}
27284 shoveleft{line content}
27287 \begin_layout Standard
27288 \begin_inset VSpace medskip
27296 \begin_inset LatexCommand index
27297 name "Commands ! M ! \\textbackslash multlinegap"
27303 specifies the distance of the first line from the left page margin.
27304 Predefined is the length 0\InsetSpace \thinspace{}
27308 \begin_layout Standard
27309 As example the above formula where the command
27312 \begin_layout Standard
27322 \begin_layout Standard
27323 was inserted in TeX-mode before:
27327 \begin_layout Standard
27339 \begin_inset Formula \begin{multline}
27340 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}\\
27341 \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}}\\
27342 =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}
27350 \begin_layout Standard
27361 The second line was left aligned using
27370 \begin_layout Subsection
27371 Multiline Formula Parts
27372 \begin_inset LatexCommand label
27373 name "sub:Multiline-Formula-Parts"
27378 \begin_inset LatexCommand index
27379 name "Formula ! multiline ! formula parts"
27386 \begin_layout Standard
27387 To display only parts of a formula with multiple lines, one of the following
27388 environments are used:
27405 They can be inserted via the menu
27407 Insert\SpecialChar \menuseparator
27410 or by using the commands described in this section.
27413 \begin_layout Standard
27414 The first three have the same properties as the corresponding multiline
27415 formula environments, but it is possible to set further formula parts beside
27418 \begin_inset Formula \[
27419 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
27420 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
27421 \right\} \textrm{Uncertainty relations}\]
27428 \begin_layout Standard
27429 To get this formula, a displayed formula is created where the command
27434 \begin_inset LatexCommand index
27435 name "Commands ! A ! \\textbackslash aligned"
27442 A purple box appears around the blue formula box where now columns and
27443 lines can be added.
27444 Outside the multiline environment other formula parts can be set, like
27448 \begin_layout Standard
27449 The aligned environment is also suitable for long formulas whose lines are
27450 horizontally aligned.
27451 Using aligned in a displayed formula has the advantage that the formula
27452 number is vertically centered behind the lines.
27454 \begin_inset LatexCommand eqref
27455 reference "eq:kurzlang"
27459 in the aligned environment:
27460 \begin_inset Formula \begin{equation}
27461 \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}|}\\
27462 & -\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}
27470 \begin_layout Standard
27471 To use the environments
27490 \begin_inset LatexCommand index
27491 name "Commands ! A ! \\textbackslash alignedat"
27502 \begin_inset LatexCommand index
27503 name "Commands ! G ! \\textbackslash gathered"
27514 \begin_inset LatexCommand index
27515 name "Commands ! S ! \\textbackslash split"
27519 are inserted, respectively.
27520 The split environment has the same properties as the aligned environment
27521 but it can only have two columns.
27524 \begin_layout Subsection
27525 Text in multiline Formulas
27526 \begin_inset LatexCommand label
27527 name "sub:Text-in-multiline"
27532 \begin_inset LatexCommand index
27533 name "Text ! in formulas"
27538 \begin_inset LatexCommand index
27539 name "Formula ! multiline ! text"
27546 \begin_layout Standard
27547 In the Align environments, and the multline and gather environment, text
27548 can be inserted that will appear in a separate line and doesn't affect
27549 the column alignment.
27550 To do this, the command
27555 \begin_inset LatexCommand index
27556 name "Commands ! I ! \\textbackslash intertext"
27562 is used in the following scheme:
27565 \begin_layout Standard
27573 \begin_layout Standard
27574 The text should not be longer than a line because it cannot be hyphenated.
27575 As LyX doesn't yet support
27581 directly, the text is written as mathematical text.
27588 must hereby be at the beginning of a line and appears in the output above
27590 An example where the text was inserted at the beginning of the second line:
27591 \begin_inset Formula \begin{align}
27592 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
27593 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
27600 \begin_layout Section
27602 \begin_inset LatexCommand index
27603 name "Formula numbering"
27608 \begin_inset LatexCommand index
27609 name "Formula ! numbering|see{Formula numbering}"
27616 \begin_layout Subsection
27620 \begin_layout Standard
27621 Numbered formulas can be created with the menu
27623 Insert\SpecialChar \menuseparator
27624 Math\SpecialChar \menuseparator
27625 Numbered\InsetSpace ~
27630 Ctrl-Alt\InsetSpace ~
27634 Existing formulas can be numbered with the menu
27636 Edit\SpecialChar \menuseparator
27637 Math\SpecialChar \menuseparator
27638 Toggle\InsetSpace ~
27647 The formula number is displayed in LyX behind the formula as number sign
27649 The number sign is replaced in the output by the formula number.
27652 \begin_layout Standard
27653 When numbering is turned on in multiline formulas, all lines will be numbered.
27654 But the numbering can be controlled with the menu
27656 Edit\SpecialChar \menuseparator
27657 Math\SpecialChar \menuseparator
27658 Toggle\InsetSpace ~
27659 Numbering\InsetSpace ~
27671 \begin_layout Standard
27672 Except of inline formulas, all formulas can be numbered with two different
27674 \begin_inset LatexCommand ref
27675 reference "sec:Formula-Styles"
27682 \begin_layout Subsection
27684 \begin_inset LatexCommand label
27685 name "sub:Cross-References"
27690 \begin_inset LatexCommand index
27691 name "Cross-references ! to formulas"
27698 \begin_layout Standard
27699 All labeled formulas can be cross-referenced.
27700 A label is added by the menu
27702 Insert\SpecialChar \menuseparator
27705 or the toolbar button
27706 \begin_inset Graphics
27707 filename ../images/label-insert.png
27713 The cursor must hereby be inside a displayed formula.
27714 A dialog pops up displaying the prefix
27719 The label is inserted there behind the prefix.
27720 The predefined prefix means
27721 \begin_inset Quotes eld
27725 \begin_inset Quotes erd
27728 and makes it easier to find labels in large documents because it marks
27729 it as formula label to divide it from e.\InsetSpace \thinspace{}
27732 To change a label, the menu
27734 Insert\SpecialChar \menuseparator
27740 \begin_layout Standard
27741 The name of the label is displayed in LyX within two parentheses behind
27743 A formula with a label is always numbered.
27744 The label is deleted when the numbering is turned off.
27745 This is at the moment the only way to delete a label, see
27749 \begin_layout Standard
27753 href{http://bugzilla.lyx.org/show_bug.cgi?id=2556}{
27762 \begin_layout Standard
27772 \begin_layout Standard
27773 Cross-references are inserted via the menu
27775 Insert\SpecialChar \menuseparator
27778 or with the toolbar button
27779 \begin_inset Graphics
27780 filename ../images/dialog-show-new-inset_ref.png
27786 A formula cross-reference appears in the output as formula number.
27787 When in the cross-reference dialog window the format
27791 is chosen, the cross-reference appears in the output as formula number
27794 By right-clicking on a cross-reference in LyX, one jumps
27795 to the formula that is referenced.
27798 \begin_layout Standard
27799 Here are as examples cross-references to formulas of the following subsections:
27800 \begin_inset Note Note
27803 \begin_layout Standard
27804 Note the different cross-reference types.
27812 \begin_layout Standard
27814 \begin_inset LatexCommand eqref
27820 \begin_inset LatexCommand eqref
27827 \begin_inset LatexCommand ref
27832 ) big Latin letters are used for the numbering in contrary to (
27833 \begin_inset LatexCommand ref
27841 \begin_layout Standard
27842 \begin_inset VSpace medskip
27845 When the argument of
27853 \begin_layout Standard
27861 \begin_inset LatexCommand ref
27862 reference "sub:User-defined-Numbering"
27873 contains a box like in
27874 \begin_inset LatexCommand ref
27875 reference "sub:Paragraph-Boxes"
27879 , the formula cannot be referenced.
27882 \begin_layout Subsection
27884 \begin_inset LatexCommand index
27885 name "Formula numbering ! subnumbering"
27892 \begin_layout Standard
27893 With the help of the commands
27897 begin{subequations}
27905 formulas can be subnumbered.
27906 Both commands are inserted in TeX-mode.
27909 \begin_layout Standard
27911 \begin_inset Formula \begin{equation}
27912 A=C-B\label{eq:a}\end{equation}
27920 \begin_layout Standard
27924 addtocounter{equation}{-1}
27933 \begin_layout Standard
27937 begin{subequations}
27943 \begin_inset VSpace -5mm
27947 \begin_inset Formula \begin{equation}
27948 B=C-A\label{eq:b}\end{equation}
27953 \begin_inset Formula \begin{equation}
27954 C=A+B\label{eq:c}\end{equation}
27961 \begin_layout Standard
27965 \begin_layout Standard
27977 \begin_layout Standard
27978 To create the example, the following is done:
27981 \begin_layout Enumerate
27982 first formula is inserted
27985 \begin_layout Enumerate
27990 addtocounter{equation}{-1}
27992 begin{subequations}
27993 \begin_inset LatexCommand index
27994 name "Commands ! A ! \\textbackslash addtocounter"
28002 is inserted after the first formula
28005 \begin_layout Enumerate
28006 second formula is inserted
28009 \begin_layout Enumerate
28010 third formula is inserted
28013 \begin_layout Enumerate
28020 is inserted after the third formula
28023 \begin_layout Standard
28024 Every formula between the commands
28036 is subnumbered as a, b,
28040 \begin_layout Standard
28049 c, \SpecialChar \ldots{}
28050 For multiline formulas every line will be subnumbered.
28051 All subnumbered formulas are treated as
28056 But as every numbered formula increases the counter
28060 by one, the command
28066 is needed to decrease it.
28067 Otherwise the formulas
28068 \begin_inset LatexCommand eqref
28074 \begin_inset LatexCommand eqref
28080 \begin_inset LatexCommand eqref
28085 would be numbered as
28086 \begin_inset LatexCommand eqref
28092 \begin_inset LatexCommand eqref
28098 \begin_inset LatexCommand eqref
28106 \begin_layout Standard
28107 By inserting the commands in TeX-mode, a space is created between the first
28109 To revert this -5\InsetSpace \thinspace{}
28110 mm vertical space is inserted after the command
28114 begin{subequations}
28117 When the formula style
28123 \begin_layout Standard
28125 \begin_inset LatexCommand ref
28126 reference "sec:Formula-Styles"
28137 is used, -7\InsetSpace \thinspace{}
28138 mm space is inserted instead.
28141 \begin_layout Standard
28142 Here is an example for a multiline formula where the numbering was turned
28143 off for the second line:
28147 \begin_layout Standard
28151 begin{subequations}
28157 \begin_inset Formula \begin{eqnarray}
28158 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
28159 & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
28160 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
28168 \begin_layout Standard
28180 \begin_layout Subsection
28181 User-defined Numbering
28182 \begin_inset LatexCommand label
28183 name "sub:User-defined-Numbering"
28188 \begin_inset LatexCommand index
28189 name "Formula numbering ! user-defined"
28196 \begin_layout Standard
28197 \begin_inset LatexCommand index
28198 name "Formula numbering ! self-defined delimiters"
28202 With the standard numbering parentheses are set around the formula number.
28203 To replace the parentheses for example by vertical bars, the following
28204 line is added to the LaTeX-preamble:
28207 \begin_layout Standard
28219 \begin_inset Note Note
28222 \begin_layout Standard
28223 This macro is already declared in the LaTeX-preamble for testing.
28224 To activate it, remove the percent sign at the beginning.
28232 \begin_layout Standard
28233 To use other characters, the vertical bars besides the
28237 are replaced by one ore more characters.
28238 To get only the formula number the vertical bars are omitted.
28241 \begin_layout Standard
28242 \begin_inset VSpace bigskip
28245 When there should be an expression of your choice instead of the consecutive
28246 formula number in parentheses behind the formula, the command
28253 \begin_inset LatexCommand index
28254 name "Commands ! T ! \\textbackslash tag"
28259 \begin_inset Formula \begin{equation}
28260 A+B=C\tag{something}\label{eq:tag}\end{equation}
28264 In this example the command
28272 was inserted to the formula.
28275 \begin_layout Standard
28284 is inserted instead, the star prevents the parentheses around the expression:
28285 \begin_inset Formula \[
28286 A+B=C\tag*{something}\]
28293 \begin_layout Standard
28294 \begin_inset VSpace bigskip
28297 To restart the formula numbering with new document parts or sections, the
28298 following command is used:
28301 \begin_layout Standard
28306 @addtoreset{equation}{part}
28309 \begin_inset LatexCommand index
28310 name "Commands ! \"@\" ! \\textbackslash \"@\"addtoreset"
28322 @addtoreset{equation}{section}
28325 \begin_layout Standard
28326 To be able to use these commands in TeX-mode, the
28327 \begin_inset Quotes eld
28331 \begin_inset Quotes erd
28334 character has to be made
28335 \begin_inset Quotes eld
28339 \begin_inset Quotes erd
28342 for LaTeX using the command
28356 So the command sequence in TeX-mode is:
28359 \begin_layout Standard
28368 @addtoreset{equation}{section}
28375 \begin_layout Standard
28376 In the LaTeX-preamble
28388 can be omitted as they are automatically internally inserted by LyX.
28391 \begin_layout Standard
28406 \begin_layout Standard
28411 is part of the LaTeX-package
28416 \begin_inset LatexCommand index
28417 name "Packages ! carlisle"
28421 that is part of every LaTeX standard installation.
28427 \begin_inset LatexCommand index
28428 name "Packages ! remreset"
28432 has to be loaded in the LaTeX-preamble with the line
28435 \begin_layout Standard
28440 usepackage{remreset}
28443 \begin_layout Standard
28451 \begin_inset LatexCommand index
28452 name "Commands ! \"@\" ! \\textbackslash \"@\"removefromreset"
28456 can be used with the same scheme as
28465 \begin_layout Standard
28466 \begin_inset VSpace bigskip
28469 Sometimes formulas should be numbered in the following form:
28472 \begin_layout Standard
28475 (section number.formula number)
28478 \begin_layout Standard
28479 The formula number should start with every section with
28480 \begin_inset Quotes eld
28484 \begin_inset Quotes erd
28490 \begin_layout Standard
28491 For this case there is the command
28498 \begin_inset LatexCommand index
28499 name "Commands ! N ! \\textbackslash numberwithin"
28503 , which is used with the following scheme:
28506 \begin_layout Standard
28511 numberwithin{counter}{sectioning}
28514 \begin_layout Standard
28515 Counter denotes what kind of numbering is affected, sectioning denotes what
28516 number is before the dot.
28519 \begin_layout Standard
28520 Thus in our case the following LaTeX-preamble or ERT line is used:
28523 \begin_layout Standard
28528 numberwithin{equation}{section}
28531 \begin_layout Standard
28532 This is the result:
28536 \begin_layout Standard
28540 numberwithin{equation}{section}
28546 \begin_inset Formula \begin{equation}
28547 A+B=C\end{equation}
28554 \begin_layout Standard
28555 To number e.\InsetSpace \thinspace{}
28557 tables so that the number of the part is the sectioning,
28563 numberwithin{table}{part}
28568 \begin_layout Standard
28569 To go back to the standard numbering or to prevent this kind of numbering
28570 when it is defined by the document class, the following command is inserted
28571 as ERT or to the LaTeX-preamble:
28574 \begin_layout Standard
28584 \begin_inset LatexCommand index
28585 name "Commands ! A ! \\textbackslash arabic"
28595 \begin_layout Standard
28627 \begin_layout Standard
28634 uses internally the command
28640 , described above, that also needs to be reverted.
28644 \begin_layout Standard
28651 \begin_layout Standard
28655 @removefromreset{equation}{section}
28658 \begin_layout Standard
28670 \begin_layout Subsection
28671 Numbering with Roman Numbers and Letters
28672 \begin_inset LatexCommand label
28673 name "sub:Numbering-with-Roman"
28678 \begin_inset LatexCommand index
28679 name "Formula numbering ! with letters"
28684 \begin_inset LatexCommand index
28685 name "Formula numbering ! with Roman numbers"
28692 \begin_layout Standard
28693 Formulas can also be numbered with Roman numbers and Latin letters.
28694 To number for example with small Roman numbers, the command
28697 \begin_layout Standard
28709 \begin_layout Standard
28710 is inserted before the formula in TeX-mode.
28718 \begin_inset LatexCommand index
28719 name "Commands ! R ! \\textbackslash renewcommand"
28723 redefines the predefined command
28739 \begin_layout Standard
28746 has the same scheme like the command
28752 that is described in
28753 \begin_inset LatexCommand ref
28754 reference "sec:User-defined-commands"
28768 is the formula counter.
28775 is used as prefix for a counter, the value of the counter is output as
28777 When a formula is numbered, LaTeX sets internally the command
28783 behind the formula.
28789 \begin_inset LatexCommand index
28790 name "Commands ! R ! \\textbackslash roman"
28796 outputs the counter as small Roman number.
28799 \begin_layout Standard
28800 All formulas behind the command
28810 are now numbered Roman.
28811 To switch to numbering with big Roman numbers, the command is inserted
28825 \begin_inset LatexCommand index
28826 name "Commands ! R ! \\textbackslash roman@\\textbackslash Roman"
28832 \begin_inset Quotes eld
28836 \begin_inset Quotes erd
28839 with small Latin letters there is the command
28846 \begin_inset LatexCommand index
28847 name "Commands ! A ! \\textbackslash alph"
28851 , for big ones there is the command
28858 \begin_inset LatexCommand index
28859 name "Commands ! A ! \\textbackslash alph@\\textbackslash Alph"
28866 \begin_layout Standard
28867 \begin_inset Note Greyedout
28870 \begin_layout Standard
28875 Only maximal 26 formulas can be numbered with Latin letters in one document.
28883 \begin_layout Standard
28887 \begin_layout Standard
28903 \begin_layout Standard
28904 \begin_inset Formula \begin{equation}
28905 A=\textrm{small roman}\label{eq:rom}\end{equation}
28913 \begin_layout Standard
28927 \begin_inset Formula \begin{equation}
28928 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
28936 \begin_layout Standard
28950 \begin_inset Formula \begin{equation}
28951 C=\textrm{small Latin}\label{eq:lat}\end{equation}
28959 \begin_layout Standard
28973 \begin_inset Formula \begin{equation}
28974 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
28981 \begin_layout Standard
28982 To switch back to the default numbering, insert the command:
28985 \begin_layout Standard
28995 \begin_inset LatexCommand index
28996 name "Commands ! A ! \\textbackslash arabic"
29003 \begin_layout Standard
29007 \begin_layout Standard
29021 \begin_inset Formula \begin{equation}
29022 E=\textrm{Arabic}\label{eq:arab}\end{equation}
29029 \begin_layout Standard
29030 \begin_inset VSpace medskip
29033 As you see, formulas are numbered serially independent from the numbering
29035 When then numbering should start with
29036 \begin_inset Quotes eld
29040 \begin_inset Quotes erd
29043 when the style is changed, new equation counters have to be defined.
29044 A description about this can be found in the file
29048 \begin_layout Standard
29052 href{Formula-numbering.pdf}{
29057 Formula-numbering.pdf
29061 \begin_layout Standard
29069 \begin_inset Note Note
29072 \begin_layout Standard
29073 More about the command
29080 \begin_inset LatexCommand ref
29081 reference "sub:Links-in-DVI-"
29093 \begin_layout Section
29094 User-defined commands
29095 \begin_inset LatexCommand label
29096 name "sec:User-defined-commands"
29101 \begin_inset LatexCommand index
29102 name "User-defined commands"
29109 \begin_layout Standard
29110 Many LaTeX-commands are too long to be used frequently.
29111 But it is possible to define with the command
29118 \begin_inset LatexCommand index
29119 name "Commands ! N ! \\textbackslash newcommand"
29123 new shorter commands.
29126 \begin_layout Standard
29127 The command scheme of
29136 \begin_layout Standard
29141 newcommand{new command name}[number of arguments][optional
29151 \begin_layout Standard
29166 \begin_layout Standard
29173 {command definition}
29176 \begin_layout Standard
29177 \begin_inset Note Greyedout
29180 \begin_layout Standard
29185 Assure that the name of the new command is not already used in your document
29186 or by LaTeX-packages that you use.
29187 When you for example define the command
29199 , you get an error message because
29205 is already defined as command for
29206 \begin_inset Quotes eld
29210 \begin_inset Formula $\le$
29214 \begin_inset Quotes erd
29225 \begin_layout Standard
29226 \begin_inset Note Greyedout
29229 \begin_layout Standard
29234 The names of user-defined commands may only consist of Latin letters.
29242 \begin_layout Standard
29243 The number of arguments is an integer in the range 0\InsetSpace \thinspace{}
29244 -\InsetSpace \thinspace{}
29245 9 and specifies how
29246 many arguments the new command should have.
29247 With the optional value a value for an optional argument can be predefined.
29248 When this is done, the
29256 rgument of the new command is automatically an optional one.
29259 \begin_layout Standard
29260 Here are some examples:
29263 \begin_layout Itemize
29264 To define the command
29276 , the LaTeX-preamble line is:
29280 \begin_layout Standard
29302 \begin_layout Itemize
29303 To define the command
29315 , the argument (that should be underlined) must be taken into account.
29316 For this the preamble line is:
29320 \begin_layout Standard
29345 \begin_layout Standard
29364 acts as argument placeholder, the
29368 behind it denotes that it is the placeholder for the first argument.
29371 \begin_layout Itemize
29378 one can e.\InsetSpace \thinspace{}
29390 \begin_layout Standard
29409 framebox#1#2{$#3$}}
29415 \begin_layout Standard
29430 The two Dollar signs creates the extra formula needed for
29437 \begin_inset LatexCommand ref
29438 reference "sub:Boxes-with-Frame"
29445 \begin_layout Itemize
29446 To create a new command for
29452 where the color for the box needn't to be specified, the argument for the
29453 color is defined optional:
29457 \begin_layout Standard
29476 fcolorbox{#2}{#1}{$#3$}}
29482 \begin_layout Standard
29493 When the color is not specified when using
29499 , the predefined color
29506 \begin_layout Standard
29507 A test of the new defined commands:
29510 \begin_layout Standard
29512 \begin_inset Tabular
29513 <lyxtabular version="3" rows="6" columns="2">
29515 <column alignment="center" valignment="top" leftline="true" width="0">
29516 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
29517 <row topline="true" bottomline="true">
29518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29521 \begin_layout Standard
29527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29530 \begin_layout Standard
29532 \begin_inset Note Note
29535 \begin_layout Standard
29542 is only used as spacer.
29553 <row topline="true">
29554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29557 \begin_layout Standard
29564 \begin_layout Standard
29578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29581 \begin_layout Standard
29582 \begin_inset Formula $A\gr B$
29591 <row topline="true">
29592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29595 \begin_layout Standard
29603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29606 \begin_layout Standard
29607 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
29616 <row topline="true">
29617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29620 \begin_layout Standard
29624 \begin_inset Formula $\to$
29630 \begin_inset Formula $\to$
29641 \begin_layout Standard
29655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29658 \begin_layout Standard
29659 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
29668 <row topline="true">
29669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29672 \begin_layout Standard
29676 \begin_inset Formula $\to$
29687 \begin_layout Standard
29701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29704 \begin_layout Standard
29705 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
29714 <row topline="true" bottomline="true">
29715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29718 \begin_layout Standard
29724 \begin_inset Formula $\to$
29735 \begin_layout Standard
29749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
29752 \begin_layout Standard
29753 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
29769 \begin_layout Section
29771 \begin_inset LatexCommand index
29779 \begin_layout Standard
29780 To create diagrams, the LaTeX-package
29786 \begin_layout Standard
29791 is part of every LaTeX standard installation.
29799 \begin_inset LatexCommand index
29800 name "Packages ! amscd"
29805 It is loaded in the LaTeX-preamble with the line
29808 \begin_layout Standard
29816 \begin_layout Standard
29817 Diagrams visualize relations and look like this:
29818 \begin_inset Formula \[
29819 \begin{CD}A@>>>B@>>>C\\
29821 F@<<<E@<<<D\end{CD}\]
29828 \begin_layout Standard
29829 To get them, the command
29834 \begin_inset LatexCommand index
29835 name "Commands ! C ! \\textbackslash CD"
29841 is inserted to a formula.
29842 A blue box appears with two dashed lines where further commands can be
29848 a new line is created.
29849 Horizontal relations are inserted in odd, vertical in even formula lines.
29852 \begin_layout Standard
29853 To create the relations there are the following commands:
29856 \begin_layout Itemize
29861 creates a left arrow,
29872 \begin_layout Itemize
29877 creates an up arrow,
29885 a vertical equal sign
29888 \begin_layout Itemize
29894 is a placeholder for non-existent relations
29897 \begin_layout Standard
29898 All arrows can be labeled as follows:
29901 \begin_layout Itemize
29902 Is text inserted between the first and second < or >, resp., it is placed
29904 When it is inserted between the second and third one, it appears under
29908 \begin_layout Itemize
29909 When text for vertical arrows is inserted between the first and second A
29910 or V, resp., it is placed left beside the arrow.
29911 When it is inserted between the second and third one, it appears right
29913 If the text contains an A or V, these letters must be set into a TeX-brace.
29916 \begin_layout Standard
29917 As example a diagram with all possible relations:
29920 \begin_layout Standard
29921 \begin_inset Formula \[
29922 \begin{CD}A@>j>>B@>>k>C@=F\\
29924 D@<<j<E@>k>>F@=C\end{CD}\]
29931 \begin_layout Standard
29932 The command for this is:
29942 \begin_layout Standard
29951 A@>j>>B@>>k>C@=F Ctrl-Enter
29957 \begin_layout Standard
29972 \begin_layout Standard
29985 \begin_layout Standard
29997 \begin_inset Formula $\to$
30008 \begin_layout Standard
30023 \begin_layout Standard
30036 \begin_layout Standard
30046 \begin_layout Standard
30052 \begin_layout Section
30057 \begin_layout Standard
30070 \begin_layout Standard
30071 Other useful math tips can be found in
30072 \begin_inset LatexCommand cite
30086 \begin_layout Standard
30094 \begin_inset Note Note
30097 \begin_layout Standard
30100 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
30103 \begin_layout Standard
30106 texorpdfstring is in section
30107 \begin_inset LatexCommand ref
30108 reference "sub:Formulas-in-Section"
30118 \begin_inset LatexCommand index
30124 \begin_inset LatexCommand index
30125 name "Ions|see{Chemical characters}"
30132 \begin_layout Subsection
30133 Chemical Symbols and Equations
30134 \begin_inset LatexCommand label
30135 name "sub:Chemical-Symbols-and"
30140 \begin_inset LatexCommand index
30141 name "Chemical characters ! Symbols"
30146 \begin_inset LatexCommand index
30147 name "Chemical equations"
30152 \begin_inset LatexCommand index
30153 name "Symbols ! chemical"
30160 \begin_layout Standard
30161 An example text from chemistry:
30164 \begin_layout Quote
30166 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30169 -ion reacts with two
30170 \begin_inset Formula $\mathrm{Na^{+}}$
30173 -ions to sodium sulfate
30174 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30178 The chemical equation for this is:
30179 \begin_inset Formula \[
30180 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
30187 \begin_layout Standard
30188 This chemical equation can directly be created as formula.
30189 To avoid that the symbols appear italic, everything is highlighted and
30190 changed by the shortcut
30195 to the upright font style.
30199 \begin_layout Standard
30205 \begin_inset LatexCommand ref
30206 reference "sub:Font-Styles"
30218 \begin_layout Subsection
30220 \begin_inset LatexCommand index
30221 name "Numbers ! negative"
30228 \begin_layout Standard
30229 Negative numbers often look ugly in formulas because the minus sign before
30230 the number is set with the same length as the minus operator sign.
30231 When writing the negative number in normal text, the minus sign appears
30235 \begin_layout Standard
30236 Thus, the problem disappears when converting the minus sign to mathematical
30240 \begin_layout Standard
30241 An example to visualize the problem:
30244 \begin_layout Standard
30246 \begin_inset Tabular
30247 <lyxtabular version="3" rows="3" columns="2">
30249 <column alignment="right" valignment="top" leftline="true" width="0">
30250 <column alignment="left" valignment="top" rightline="true" width="0">
30251 <row topline="true">
30252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30255 \begin_layout Standard
30261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30264 \begin_layout Standard
30271 <row topline="true" bottomline="true">
30272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30275 \begin_layout Standard
30281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30284 \begin_layout Standard
30285 \begin_inset Formula $x=-2$
30294 <row topline="true" bottomline="true">
30295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30298 \begin_layout Standard
30304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30307 \begin_layout Standard
30308 \begin_inset Formula $x=\textrm{-}2$
30324 \begin_layout Subsection
30325 Comma as Decimal Separator
30326 \begin_inset LatexCommand index
30334 \begin_layout Standard
30335 In LaTeX a comma inside a formula is used, according to the English convention,
30336 as number group separator.
30337 So there will be space added behind all commas in formulas.
30340 \begin_layout Standard
30341 To avoid this, the comma is highlighted and changed to mathematical text
30350 \begin_layout Standard
30351 To use all formula commas in the document as decimal separator, the file
30360 \begin_layout Standard
30365 is part of the LaTeX-package
30370 \begin_inset LatexCommand index
30371 name "Packages ! was\\vspace{4mm}"
30381 \begin_inset LatexCommand index
30382 name "Packages ! icomma"
30386 is loaded with the LaTeX-preamble line
30389 \begin_layout Standard
30397 \begin_layout Subsection
30399 \begin_inset LatexCommand label
30400 name "sub:Physical-Vectors"
30405 \begin_inset LatexCommand index
30406 name "Vectors ! physical"
30413 \begin_layout Standard
30414 Predefined vectors are offered by the LaTeX-package
30422 \begin_layout Standard
30427 should be part of every LaTeX standard installation.
30433 \begin_inset LatexCommand index
30434 name "Packages ! braket"
30438 that is loaded with the LaTeX-preamble line
30441 \begin_layout Standard
30449 \begin_layout Standard
30453 \begin_layout Standard
30463 \begin_inset Note Note
30466 \begin_layout Standard
30467 The following table will only be displayed when the LaTeX-package
30476 The following commands are defined:
30479 \begin_layout Standard
30481 \begin_inset Tabular
30482 <lyxtabular version="3" rows="4" columns="2">
30484 <column alignment="center" valignment="top" leftline="true" width="0">
30485 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30486 <row topline="true" bottomline="true">
30487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30490 \begin_layout Standard
30496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30499 \begin_layout Standard
30506 <row topline="true">
30507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30510 \begin_layout Standard
30520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30523 \begin_layout Standard
30524 \begin_inset Formula $\Bra{\psi}$
30533 <row topline="true">
30534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30537 \begin_layout Standard
30547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30550 \begin_layout Standard
30551 \begin_inset Formula $\Ket{\psi}$
30560 <row topline="true" bottomline="true">
30561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30564 \begin_layout Standard
30576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30579 \begin_layout Standard
30580 \begin_inset Formula $\Braket{\psi|\phi}$
30596 \begin_layout Standard
30603 assures that all vertical bars are set in the size of the surrounding brackets:
30604 \begin_inset Formula \[
30605 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
30613 \begin_layout Standard
30623 \begin_inset Note Note
30626 \begin_layout Standard
30627 The following will be displayed when the LaTeX-package
30639 \begin_layout Standard
30640 You need to install the LaTeX-package
30644 to see the rest of this subsection in the output.
30647 \begin_layout Standard
30651 \begin_layout Standard
30663 \begin_layout Standard
30670 can also be achieved using the command
30676 , that is described in
30677 \begin_inset LatexCommand ref
30678 reference "sub:Automatic-Bracket-Size"
30685 \begin_layout Subsection
30686 Self-defined Fractions
30687 \begin_inset LatexCommand label
30688 name "sub:Self-defined-Fractions"
30693 \begin_inset LatexCommand index
30694 name "Fractions ! self-defined"
30701 \begin_layout Standard
30702 To define custom commands for fractions, the command
30709 \begin_inset LatexCommand index
30710 name "Commands ! G ! \\textbackslash genfrac"
30714 is used in the following scheme:
30717 \begin_layout Standard
30730 bracket}{fraction bar thickness}{style}
30736 \begin_layout Standard
30751 \begin_layout Standard
30758 {numerator}{denominator}
30761 \begin_layout Standard
30762 The style is a number in the range of 0\InsetSpace \thinspace{}
30763 -\InsetSpace \thinspace{}
30767 \begin_layout Standard
30769 \begin_inset Tabular
30770 <lyxtabular version="3" rows="5" columns="2">
30772 <column alignment="center" valignment="top" leftline="true" width="0">
30773 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
30774 <row topline="true" bottomline="true">
30775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30778 \begin_layout Standard
30784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30787 \begin_layout Standard
30794 <row topline="true">
30795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30798 \begin_layout Standard
30804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30807 \begin_layout Standard
30808 display style formula
30814 <row topline="true">
30815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30818 \begin_layout Standard
30824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30827 \begin_layout Standard
30834 <row topline="true">
30835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30838 \begin_layout Standard
30844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30847 \begin_layout Standard
30854 <row topline="true" bottomline="true">
30855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30858 \begin_layout Standard
30864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30867 \begin_layout Standard
30881 \begin_layout Standard
30882 When no style is given, the size is adjusted to the surrounding environment
30883 like for the command
30892 \begin_layout Standard
30893 When no fraction bar thickness is given, the predefined value of 0.4\InsetSpace \thinspace{}
30898 \begin_layout Standard
30899 \begin_inset VSpace medskip
30902 For example, the commands
30915 \begin_inset LatexCommand ref
30916 reference "sub:Fractions"
30920 are defined with the commands
30923 \begin_layout Standard
30932 genfrac{}{}{}{0}{#1}{#2}}
30935 \begin_layout Standard
30939 \begin_layout Standard
30948 genfrac{(}{)}{0pt}{1}{#1}{#2}}
30951 \begin_layout Standard
30952 \begin_inset VSpace medskip
30955 To define a fraction where the fraction bar thickness can be given as optional
30956 argument, the following line is inserted to the LaTeX-preamble:
30959 \begin_layout Standard
30968 genfrac{}{}{#1}{}{#2}{#3}}
30971 \begin_layout Standard
30973 \begin_inset Formula \begin{align*}
30974 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
30975 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
30979 As one can see, the distance of the numerator and the denominator to the
30980 fraction bar is round about three times the bar thickness.
30983 \begin_layout Subsection
30985 \begin_inset LatexCommand label
30986 name "sub:Canceled-Formulas"
30991 \begin_inset LatexCommand index
30992 name "Formula ! canceled"
30999 \begin_layout Standard
31000 To cancel formulas or formula parts, the LaTeX-package
31008 \begin_layout Standard
31013 is part of every LaTeX standard installation.
31019 \begin_inset LatexCommand index
31020 name "Packages ! cancel"
31024 has to be loaded with the LaTeX-preamble line
31027 \begin_layout Standard
31032 usepackage[samesize]{cancel}
31035 \begin_layout Standard
31036 There are four ways to cancel formulas:
31039 \begin_layout Standard
31041 \begin_inset Tabular
31042 <lyxtabular version="3" rows="5" columns="2">
31044 <column alignment="center" valignment="top" leftline="true" width="0">
31045 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
31046 <row topline="true" bottomline="true">
31047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31050 \begin_layout Standard
31056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31059 \begin_layout Standard
31061 \begin_inset Note Note
31064 \begin_layout Standard
31077 are used here as spacer.
31088 <row topline="true">
31089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31092 \begin_layout Standard
31101 \begin_layout Standard
31115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31118 \begin_layout Standard
31119 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
31128 <row topline="true">
31129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31132 \begin_layout Standard
31141 \begin_layout Standard
31155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31158 \begin_layout Standard
31159 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
31168 <row topline="true" bottomline="true">
31169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31172 \begin_layout Standard
31181 \begin_layout Standard
31195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31198 \begin_layout Standard
31199 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
31208 <row topline="true" bottomline="true">
31209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31212 \begin_layout Standard
31216 \begin_inset Formula $\to$
31227 \begin_layout Standard
31241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31244 \begin_layout Standard
31245 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
31261 \begin_layout Standard
31268 is especially suitable to visualize the reduction of fractions within formulas:
31269 \begin_inset Formula \[
31270 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
31277 \begin_layout Subsection
31278 Formulas in Section Headings
31279 \begin_inset LatexCommand label
31280 name "sub:Formulas-in-Section"
31285 \begin_inset LatexCommand index
31286 name "Formula ! in section headings"
31293 \begin_layout Standard
31294 When formulas are used in section headings, the following has to be taken
31298 \begin_layout Standard
31299 \begin_inset Note Greyedout
31302 \begin_layout Standard
31303 When the LaTeX-package
31308 \begin_inset LatexCommand index
31309 name "Packages ! hyperref"
31313 is used, PDF-bookmarks are automatically created for every section heading
31314 in the table of contents.
31315 If a section heading contains formulas, they are incorrectly displayed
31316 in the bookmark text, because formulas in bookmarks infringe the PDF convention
31325 \begin_layout Standard
31326 Both problems can be solved by inserting at the end of the section heading
31327 a short title with the menu
31329 Insert\SpecialChar \menuseparator
31334 Short titles are used as alternative for multiline section headings to
31335 keep the table of contents clearly arranged.
31336 Only the short title appears in the table of contents and therefore also
31337 in the PDF-bookmark.
31340 \begin_layout Standard
31341 When formulas should be used in the table of contents but
31345 is used, one can use the following command in TeX-mode:
31348 \begin_layout Standard
31353 texorpdfstring{part}{alternative}
31354 \begin_inset LatexCommand index
31355 name "Commands ! T ! \\textbackslash texorpdfstring"
31362 \begin_layout Standard
31363 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
31364 This can be characters, formulas, footnotes, but also cross-references.
31365 The alternative is used instead of the part for the bookmark.
31368 \begin_layout Standard
31369 Here are two example headings:
31370 \begin_inset VSpace -3mm
31377 \begin_layout Standard
31389 \begin_layout Subsubsection
31390 Heading without formula in table of contents
31391 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31395 \begin_inset OptArg
31398 \begin_layout Standard
31399 Heading without formula in table of contents
31407 \begin_layout Subsubsection
31408 Heading with formula in table of contents
31412 \begin_layout Standard
31422 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
31429 \begin_layout Standard
31439 \begin_layout Standard
31443 \begin_layout Standard
31452 In the first heading a short title was used, in the second one
31461 \begin_layout Standard
31462 To get the same formatting as for the other headings, the complete heading
31465 boldmath environment
31471 \begin_layout Standard
31473 \begin_inset LatexCommand ref
31474 reference "sub:Bold-Formulas"
31486 \begin_layout Subsection
31487 Formulas in multi-column Text
31488 \begin_inset LatexCommand index
31489 name "Formula ! in multi-column text"
31496 \begin_layout Standard
31497 Formulas in multi-column text are often too wide to fit into a column and
31498 thus need to be set over the whole page width.
31499 This is done by using the LaTeX-package
31507 \begin_layout Standard
31512 is part of every LaTeX standard installation.
31518 \begin_inset LatexCommand index
31519 name "Packages ! multicol"
31523 , that is loaded with the LaTeX-preamble line
31526 \begin_layout Standard
31531 usepackage{multicol}
31534 \begin_layout Standard
31535 \begin_inset Note Greyedout
31538 \begin_layout Standard
31539 Note herby that the setting
31541 Two-column\InsetSpace ~
31546 Document\SpecialChar \menuseparator
31569 \begin_layout Standard
31570 Before the multi-column text the command
31573 \begin_layout Standard
31578 begin{multicols}{column number}
31581 \begin_layout Standard
31582 is written in TeX-mode.
31583 The column number is a number in the range of 2\InsetSpace \thinspace{}
31584 -\InsetSpace \thinspace{}
31586 Before the formula the multi-column text is ended by inserting the command
31589 \begin_layout Standard
31597 \begin_layout Standard
31601 \begin_layout Standard
31602 Due to the command some space is automatically added before the formula.
31603 To revert this, -6\InsetSpace \thinspace{}
31604 mm vertical space is inserted before the formula.
31605 When the formula style
31611 \begin_layout Standard
31613 \begin_inset LatexCommand ref
31614 reference "sec:Formula-Styles"
31625 is used, -9\InsetSpace \thinspace{}
31626 mm space is inserted instead.
31629 \begin_layout Standard
31630 As example a multi-column text with a displayed formula:
31633 \begin_layout Standard
31637 \begin_layout Standard
31641 begin{multicols}{2}
31646 Das Spektrum wird fouriertransformiert.
31647 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
31648 , Lösungsmittel) zu trennen.
31649 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
31650 nun das Aussehen des Ausgangssignals.
31651 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
31652 über alle Phasen integrieren muss.
31654 \begin_inset Formula $S$
31657 unser normiertes Ausgangssignal and
31658 \begin_inset Formula $P$
31661 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
31665 \begin_layout Standard
31675 \begin_inset VSpace -6mm
31679 \begin_inset Formula \begin{equation}
31680 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
31688 \begin_layout Standard
31692 begin{multicols}{2}
31698 \begin_inset Formula $S_{0}$
31701 das Signal ohne Gradient ist and the Normierungsbedingung
31702 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
31706 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
31708 \begin_inset Formula $\nicefrac{\pi}{2}$
31711 \InsetSpace \thinspace{}
31712 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
31713 das Signal zusätzlich abschwächt.
31714 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
31716 \begin_inset Formula $T_{2}$
31722 \begin_layout Standard
31726 \begin_layout Standard
31738 \begin_layout Subsection
31739 Formulas with Description of Variables
31740 \begin_inset LatexCommand index
31741 name "Formula ! with description of variables"
31748 \begin_layout Standard
31749 To describe variables within a formula, like in formula
31750 \begin_inset LatexCommand eqref
31751 reference "eq:within"
31760 \begin_inset Formula $n$
31764 matrix is used with left aligned columns for the
31765 \begin_inset Formula $n$
31772 \begin_layout Standard
31774 \begin_inset LatexCommand ref
31775 reference "sec:Matrices"
31784 To set the description in a smaller size, before the matrix e.\InsetSpace \thinspace{}
31797 \begin_layout Standard
31799 \begin_inset LatexCommand ref
31800 reference "sub:Font-Sizes"
31812 \begin_layout Standard
31813 When the formula style
31819 \begin_layout Standard
31821 \begin_inset LatexCommand ref
31822 reference "sec:Formula-Styles"
31843 \begin_layout Standard
31850 only works in formulas with the style
31855 \begin_inset LatexCommand ref
31856 reference "sub:Variable-Space"
31865 is inserted before and after the matrix to have the same separation of
31866 the matrix from the equation and the side margin.
31869 \begin_layout Standard
31870 When the formula style
31874 is used, the method described in
31875 \begin_inset LatexCommand ref
31876 reference "sub:Flalign-Environment"
31880 is used to indent formulas.
31882 \begin_inset LatexCommand eqref
31883 reference "eq:within"
31887 consists of five columns whereas in the first two columns contain the equation,
31888 the third the matrix, and the last one an empty TeX-brace.
31889 \begin_inset Formula \begin{flalign}
31890 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
31891 \rho & \textrm{density}\\
31892 V & \textrm{volume}\\
31893 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
31900 \begin_layout Subsection
31901 Upright small Greek Letters
31902 \begin_inset LatexCommand label
31903 name "sub:Upright-small-Greek"
31908 \begin_inset LatexCommand index
31909 name "Greek letters ! upright"
31916 \begin_layout Standard
31917 Most of the math fonts only provide italic small Greek letters.
31918 But for symbols of elementary particles like pions and neutrinos, upright
31919 Greek letters are needed.
31928 \begin_layout Standard
31933 is part of the LaTeX-package
31938 \begin_inset LatexCommand index
31939 name "Packages ! was\\vspace{4mm}"
31949 \begin_inset LatexCommand index
31950 name "Packages ! upgreek"
31954 that is loaded with the LaTeX-preamble line
31957 \begin_layout Standard
31962 usepackage{upgreek}
31965 \begin_layout Standard
31971 \begin_layout Standard
31981 \begin_inset Note Note
31984 \begin_layout Standard
31985 The following table will only be displayed when the LaTeX-package
31994 They are created when the command for a small Greek letters is started
32000 For example the command
32007 \begin_inset Formula $\uptau$
32013 \begin_layout Standard
32014 With these commands reactions of elementary particles can be typeset:
32015 \begin_inset Formula \[
32016 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
32023 \begin_layout Standard
32024 The upright letters are more bold and wider than the italic ones.
32025 They should therefore not be used for units like
32026 \begin_inset Quotes eld
32030 \begin_inset Quotes erd
32036 \begin_layout Standard
32040 \begin_layout Standard
32050 \begin_inset Note Note
32053 \begin_layout Standard
32054 The following will be displayed when the LaTeX-package
32066 \begin_layout Standard
32067 You need to install the LaTeX-package
32071 to see the rest of this subsection in the output.
32074 \begin_layout Standard
32078 \begin_layout Standard
32090 \begin_layout Subsection
32091 Text Characters in Formulas
32092 \begin_inset LatexCommand label
32093 name "sub:Text-Characters-in"
32098 \begin_inset LatexCommand index
32099 name "Text ! in formulas"
32106 \begin_layout Standard
32107 In some cases you might want to insert text characters directly into formulas.
32108 When for example the centered dot · is often used in formulas like
32109 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
32112 , one would have to insert the command
32122 \begin_layout Standard
32124 \begin_inset LatexCommand ref
32125 reference "sub:Binary-Operators"
32134 all the time, because this character is defined in all encodings as text
32136 But the encoding can be changed by this LaTeX-preamble line:
32139 \begin_layout Standard
32144 Declare Inputtext{183}{
32154 f\SpecialChar \textcompwordmark{}
32158 \begin_layout Standard
32159 The character encoding (menu
32161 Document\SpecialChar \menuseparator
32162 Settings\SpecialChar \menuseparator
32165 ) specifies what character appears when a keyboard key is pressed.
32166 When the key for the character '·' is pressed, internally the command
32173 But this command is not available in a formula so that you would get LaTeX-erro
32175 With the changed encoding the right command is chosen automatically, depending
32176 on if the character was inserted into a formula or not.
32179 \begin_layout Standard
32180 The encoding of several characters is saved in definition files.
32181 Fore example the encoding
32185 is defined in the file
32189 that is in the installation folder of LaTeX.
32190 Encodings should only be changed via the LaTeX-preamble and not in the
32192 Otherwise own documents could not be edited by other LyX users working
32193 on other computers.
32196 \begin_layout Standard
32197 \begin_inset VSpace medskip
32200 Besides the centered dot, in this document the degree sign ° is defined
32201 with the following LaTeX-preamble line so that it can directly be inserted
32205 \begin_layout Standard
32210 DeclareInputtext{176}{
32220 f\SpecialChar \textcompwordmark{}
32224 \begin_layout Standard
32230 \begin_layout Section
32232 Typographic Advises
32233 \begin_inset LatexCommand index
32234 name "Typographic Advises"
32241 \begin_layout Standard
32242 This section is a summary of the most important typographic rules, listed
32247 \begin_layout Standard
32248 This collection was partly taken from the German semi-official dictionary
32250 \begin_inset Quotes eld
32254 \begin_inset Quotes erd
32258 \begin_inset LatexCommand cite
32263 that lists some of the ISO rules.
32271 \begin_layout Itemize
32280 \begin_layout Standard
32281 done with font styles, see
32282 \begin_inset LatexCommand ref
32283 reference "sub:Font-Styles"
32292 : 30\InsetSpace \thinspace{}
32295 Between the value and the unit is the smallest space, see
32296 \begin_inset LatexCommand ref
32297 reference "sub:Predefined-Space"
32304 \begin_layout Itemize
32305 Percent and perthousand signs are set like physical units:
32307 1,2\InsetSpace \thinspace{}
32312 \begin_layout Standard
32325 \begin_layout Itemize
32326 The degree sign follows directly on the value: 15°, but not when it is used
32327 in units: 15\InsetSpace \thinspace{}
32331 \begin_layout Itemize
32332 In numbers with more than four digits the smallest space is inserted before
32333 every third digit to group them:
32342 18\InsetSpace \thinspace{}
32343 473\InsetSpace \thinspace{}
32347 \begin_layout Itemize
32348 For dimensionings like 120×90×40\InsetSpace \thinspace{}
32349 cm the multiplication sign
32350 \begin_inset Quotes eld
32354 \begin_inset Quotes erd
32358 It is available with the LaTeX-command
32364 , but can also directly be inserted with some keyboard definitions.
32367 \begin_layout Itemize
32368 Functions with names consisting of several letters are set upright to avoid
32370 \begin_inset LatexCommand ref
32371 reference "sub:Predefined-Functions"
32378 \begin_layout Itemize
32379 Indices consisting of several letters, are set upright:
32380 \begin_inset Formula $E_{\mathrm{kin}}$
32385 Components of matrices are set italic:
32386 \begin_inset Formula $\hat{H}_{kl}$
32392 \begin_layout Itemize
32393 The differentiation/integration operator 'd', the Euler's number 'e', and
32394 the imaginary unit 'i' should be set upright, to avoid mixing them up with
32398 \begin_layout Standard
32404 \begin_layout Section
32406 \begin_inset LatexCommand index
32414 \begin_layout Standard
32415 Some characters and symbols can be created with several commands.
32416 Here is a list of the synonym commands:
32419 \begin_layout Standard
32420 \begin_inset VSpace bigskip
32426 \begin_inset Tabular
32427 <lyxtabular version="3" rows="12" columns="2">
32429 <column alignment="center" valignment="top" leftline="true" width="0pt">
32430 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
32431 <row topline="true" bottomline="true">
32432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32435 \begin_layout Standard
32441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32444 \begin_layout Standard
32446 \begin_inset Note Note
32449 \begin_layout Standard
32456 is only used as spacer.
32467 <row topline="true">
32468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32471 \begin_layout Standard
32479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32482 \begin_layout Standard
32486 \begin_layout Standard
32499 \begin_layout Standard
32512 <row topline="true">
32513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32516 \begin_layout Standard
32524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32527 \begin_layout Standard
32536 <row topline="true">
32537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32540 \begin_layout Standard
32548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32551 \begin_layout Standard
32560 <row topline="true">
32561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32564 \begin_layout Standard
32572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32575 \begin_layout Standard
32582 <row topline="true">
32583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32586 \begin_layout Standard
32594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32597 \begin_layout Standard
32604 <row topline="true">
32605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32608 \begin_layout Standard
32616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32619 \begin_layout Standard
32628 <row topline="true">
32629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32632 \begin_layout Standard
32640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32643 \begin_layout Standard
32652 <row topline="true">
32653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32656 \begin_layout Standard
32664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32667 \begin_layout Standard
32676 <row topline="true">
32677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32680 \begin_layout Standard
32688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32691 \begin_layout Standard
32700 <row topline="true">
32701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32704 \begin_layout Standard
32712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32715 \begin_layout Standard
32722 <row topline="true" bottomline="true">
32723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32726 \begin_layout Standard
32734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32737 \begin_layout Standard
32751 \begin_inset Tabular
32752 <lyxtabular version="3" rows="12" columns="2">
32754 <column alignment="center" valignment="top" leftline="true" width="0pt">
32755 <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
32756 <row topline="true" bottomline="true">
32757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32760 \begin_layout Standard
32766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32769 \begin_layout Standard
32776 <row topline="true">
32777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32780 \begin_layout Standard
32788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32791 \begin_layout Standard
32802 <row topline="true">
32803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32806 \begin_layout Standard
32814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32817 \begin_layout Standard
32826 <row topline="true">
32827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32830 \begin_layout Standard
32838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32841 \begin_layout Standard
32850 <row topline="true">
32851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32854 \begin_layout Standard
32862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32865 \begin_layout Standard
32872 <row topline="true">
32873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32876 \begin_layout Standard
32884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32887 \begin_layout Standard
32894 <row topline="true">
32895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32898 \begin_layout Standard
32906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32909 \begin_layout Standard
32918 <row topline="true">
32919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32922 \begin_layout Standard
32930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32933 \begin_layout Standard
32942 <row topline="true">
32943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32946 \begin_layout Standard
32954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32957 \begin_layout Standard
32966 <row topline="true">
32967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32970 \begin_layout Standard
32978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32981 \begin_layout Standard
32990 <row topline="true">
32991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32994 \begin_layout Standard
33002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33005 \begin_layout Standard
33014 <row topline="true" bottomline="true">
33015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33018 \begin_layout Standard
33026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33029 \begin_layout Standard
33047 \begin_layout Standard
33053 \begin_layout Bibliography
33054 \begin_inset LatexCommand bibitem
33066 The LaTeX Companion
33069 Addison Wesley, 2004
33072 \begin_layout Bibliography
33073 \begin_inset LatexCommand bibitem
33082 \begin_layout Standard
33086 href{ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf}{
33095 \begin_layout Standard
33102 of LaTeX's math abilities
33105 \begin_layout Bibliography
33106 \begin_inset LatexCommand bibitem
33111 LaTeX tips and tricks-
33115 \begin_layout Standard
33119 href{http://tug.org/TeXnik/}{
33128 \begin_layout Standard
33138 \begin_layout Bibliography
33139 \begin_inset LatexCommand bibitem
33148 \begin_layout Standard
33152 href{ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf}{
33161 \begin_layout Standard
33172 \begin_layout Standard
33184 \begin_layout Bibliography
33185 \begin_inset LatexCommand bibitem
33194 \begin_layout Standard
33198 href{ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}{
33207 \begin_layout Standard
33214 of all symbols available with LaTeX-packages
33217 \begin_layout Bibliography
33218 \begin_inset LatexCommand bibitem
33227 \begin_layout Standard
33231 href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{
33240 \begin_layout Standard
33247 of the LaTeX-package
33252 \begin_inset LatexCommand index
33253 name "Packages ! hyperref"
33260 \begin_layout Bibliography
33261 \begin_inset LatexCommand bibitem
33270 \begin_layout Standard
33274 href{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}{
33283 \begin_layout Standard
33297 \begin_inset LatexCommand ref
33298 reference "sub:Operator-Limits"
33303 \begin_inset LatexCommand index
33304 name "Commands ! M ! \\textbackslash mathclap"
33311 \begin_layout Bibliography
33312 \begin_inset LatexCommand bibitem
33323 Auflage, Duden 2001
33326 \begin_layout Subsubsection*
33327 \begin_inset LatexCommand printindex