1 #LyX 1.6.0svn 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 \fi % end if pdflatex is used
27 % Folgendes Problem lösen:
28 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
29 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
30 % die Kapitelnummer geschrieben.
31 % Als Lösung wird mehr Platz zwischen Nummer und
32 % Überschrift eingefügt.
33 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
34 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
36 % To be able to enter the character ° and · directly in LyX,
38 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
39 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
41 % increase link area for cross-references and autoname them,
42 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
44 \settowidth{\abc}{\space}
46 \renewcommand{\equationautorefname}{\hspace{-\abc}}
47 \renewcommand{\sectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
49 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
51 % don't load packages twice
52 % see first footnote in sec. 9.3
53 \@ifundefined{textcolor}{\usepackage{color}}{}
55 % the pages of the TOC are numbered roman
56 % and a PDF-bookmark for the TOC is added
58 \let\myTOC\tableofcontents
59 \renewcommand{\tableofcontents}{%
61 \pdfbookmark[1]{\contentsname}{}
64 \pagenumbering{arabic}}
66 % insert additional vertical space of 1.5 mm between footnotes,
68 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
70 % provides caption formatting
71 \setkomafont{captionlabel}{\bfseries}
77 \usepackage[samesize]{cancel}
79 % enables calculation of values,
82 % for multiple table row and column cells
92 % center multirows (e.g. in sec. 13.3)
93 \renewcommand{\multirowsetup}{\centering}
95 % define a color, used in sec.9.3
96 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
98 % declare operators (see sec. 10.4 and sec. 15.2)
99 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
100 \DeclareMathOperator{\sgn}{sgn}
102 \newcommand{\spce}{\textvisiblespace}
104 % example definitions for sec. 20.1
105 \newcommand{\gr}{\Longrightarrow}
106 \newcommand{\us}[1]{\underline{#1}}
107 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
108 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
109 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
111 % example macro from sec. 19.4
112 %\def\tagform@#1{\maketag@@@{|#1|}}
114 % macro from sec. 10.2
115 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
116 \def\mathclap {\mathpalette \mathclapinternal}
117 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
119 % redefine the greyed out note
120 \renewenvironment{lyxgreyedout}
121 {\textcolor{blue}\bgroup}{\egroup}
123 % ------------------------------------
124 % used to check for needed LaTeX packages
127 % check for package eurosym
128 % used for the Euro symbol
130 \IfFileExists{eurosym.sty}
131 {\usepackage[gennarrow]{eurosym}
132 \setboolean{eurosym}{true}}
133 {\setboolean{eurosym}{false}}
135 % needed in sec. 22.4
136 % check for package braket
138 \IfFileExists{braket.sty}
140 \setboolean{braket}{true}}
141 {\setboolean{braket}{false}}
143 % needed in sec. 22.10
144 % check for package upgreek
146 \IfFileExists{upgreek.sty}
147 {\usepackage{upgreek}
148 \setboolean{upgreek}{true}}
149 {\setboolean{upgreek}{false}}
151 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
156 \font_typewriter default
157 \font_default_family default
167 \pdf_title "LyX's Math Manual"
168 \pdf_author "LyX Team, Uwe Stöhr"
169 \pdf_subject "LyX-documentation about math"
170 \pdf_keywords "LyX, Mathed"
172 \pdf_bookmarksnumbered true
173 \pdf_bookmarksopen true
174 \pdf_bookmarksopenlevel 1
175 \pdf_breaklinks false
179 \pdf_pagebackref false
180 \pdf_pdfusetitle false
181 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
188 \paperorientation portrait
191 \paragraph_separation skip
193 \quotes_language english
196 \paperpagestyle plain
200 \tracking_changes false
201 \output_changes false
209 LyX's detailed Math manual
217 \begin_layout Plain Layout
219 If you have comments or error corrections, please send them to the LyX Documenta
223 \begin_inset CommandInset href
225 name "lyx-docs@lists.lyx.org"
226 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
237 \begin_inset Note Note
240 \begin_layout Plain Layout
247 \begin_inset Newline newline
251 \begin_inset Newline newline
259 \begin_layout Standard
260 \begin_inset CommandInset toc
261 LatexCommand tableofcontents
268 \begin_layout Standard
269 \begin_inset Note Note
272 \begin_layout Plain Layout
273 To export this document to PDF, PS, or DVI the LaTeX-packages
286 If they are not installed you can export the document anyway but the sections
287 where the packages are required won't appear in the output.
290 \begin_layout Plain Layout
291 The latest PDF-version of this document can be found here:
292 \begin_inset Newline newline
297 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
305 \begin_layout Standard
306 \begin_inset Newpage newpage
312 \begin_layout Section
314 \begin_inset CommandInset label
316 name "sec:Introduction"
323 \begin_layout Standard
324 This document explains LyX's math features and is furthermore a collection
325 of LaTeX-commands used for mathematical characters and constructs.
326 The explanations are designed for the usage of commands.
327 It is therefore required that you have read the section
338 \begin_layout Standard
339 Most of the characters and many constructs explained in this manual are
340 also accessible via the menu
344 \SpecialChar \menuseparator
360 But everybody who has to write lots of formulas will notice that it is
361 much faster to use commands instead of the math toolbar.
362 Therefore this manual is focused on commands but also mentions the correspondin
363 g toolbar buttons when available.
366 \begin_layout Standard
367 If not specially mentioned the commands are only available within formulas.
368 To be able to use all commands explained in this document, the option
372 must be used in the document settings (menu
374 Document\SpecialChar \menuseparator
375 Settings\SpecialChar \menuseparator
386 \begin_layout Plain Layout
389 Use AMS math package automatically
395 \begin_layout Plain Layout
404 -math when math constructs are found that are supported by LyX.
412 \begin_layout Standard
413 This document doesn't list all
417 \begin_layout Plain Layout
430 \begin_layout Plain Layout
435 \begin_layout Plain Layout
444 -math commands is in the file
447 \begin_inset CommandInset href
450 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
456 , which is part of every LaTeX standard installation.
461 for lucidity reasons.
464 \begin_layout Section
466 \begin_inset CommandInset label
468 name "sec:General-Instructions"
475 \begin_layout Standard
476 To create an inline formula
480 \begin_layout Plain Layout
486 that is embedded into a text line, press
490 or the toolbar button
491 \begin_inset Graphics
492 filename ../images/math-mode.png
498 \begin_inset Newline newline
501 To create a display style formula
505 \begin_layout Plain Layout
506 Formula ! display style
511 that will appear bigger and in an own paragraph, press
518 \begin_layout Standard
519 To change a display style formula to an inline formula, set the cursor into
520 the formula and press
526 Edit\SpecialChar \menuseparator
527 Math\SpecialChar \menuseparator
531 The same way is used to change an inline formula to a display style formula.
534 \begin_layout Standard
535 To display parts of an inline formula in the size of a display style formula,
544 \begin_layout Plain Layout
555 Then a new blue box appears in which the desired formula part is inserted.
558 \begin_layout Standard
559 Only inline formulas are allowed inside tables.
562 \begin_layout Standard
567 can be turned on in the menu
569 View\SpecialChar \menuseparator
573 When you click there on
574 \begin_inset Quotes eld
578 \begin_inset Quotes erd
581 the toolbar will be shown permanently at the bottom; this state is visualized
586 menu with a checkmark.
587 When you click in this state again on
588 \begin_inset Quotes eld
592 \begin_inset Quotes erd
603 is only shown when the cursor is within a formula; this state is visualized
604 by the renaming of the menu entry from
605 \begin_inset Quotes eld
609 \begin_inset Quotes erd
613 \begin_inset Quotes eld
621 \begin_inset Quotes erd
627 \begin_layout Standard
632 \begin_layout Plain Layout
638 is invoked by pressing the toolbar button
639 \begin_inset Graphics
640 filename ../images/ert-insert.png
647 Insert\SpecialChar \menuseparator
652 \begin_layout Plain Layout
666 \begin_inset Note Note
669 \begin_layout Plain Layout
670 In LyX there are three
671 \begin_inset Quotes eld
675 \begin_inset Quotes erd
678 that appear in the output with sub- and superscript letters: TeX, LaTeX,
682 \begin_layout Plain Layout
683 To avoid that these names are recognized as proper names, a TeX-brace pair
692 \begin_layout Standard
693 To change the LaTeX-preamble
697 \begin_layout Plain Layout
705 Document\SpecialChar \menuseparator
706 Settings\SpecialChar \menuseparator
711 \begin_layout Plain Layout
727 \begin_layout Standard
728 To edit matrices, case differentiations, and multiline formulas subsequently,
731 Edit\SpecialChar \menuseparator
736 Edit\SpecialChar \menuseparator
738 \begin_inset space \thinspace{}
742 \begin_inset space \thinspace{}
752 When lines and columns are swapped via the menu, the column or line where
753 the cursor is in is exchanged with the column to the right or the line
755 Is the cursor in the last column or row, the exchange is done with the
756 column to the left or the line above.
759 \begin_layout Standard
760 To write text in formulas
764 \begin_layout Plain Layout
765 For multiline formulas the command
772 \begin_inset CommandInset ref
774 reference "sub:Text-in-multiline"
791 \begin_layout Plain Layout
801 \begin_layout Plain Layout
808 This mode is invoked with the the shortcut
816 or by the insertion of the command
824 \begin_layout Plain Layout
835 The text appears black in LyX and can therefore be distinguished from the
836 other formula parts that appear blue.
837 In the output mathematical text is set upright, in contrary to other formula
841 \begin_layout Subsection*
845 \begin_layout Standard
846 Most of the LaTeX-commands for math constructs have the following scheme:
849 \begin_layout Standard
865 \begin_layout Standard
866 A command starts always with a backslash
867 \begin_inset Quotes gld
877 \begin_inset Quotes grd
881 To omit optional arguments, also omit the associated brackets.
882 The braces around the required arguments are named in this document as
887 \begin_layout Plain Layout
894 If you add in a formula a left brace to a command name, LyX creates automatical
896 In all other cases TeX-braces are created in formulas with the command
904 TeX-braces appear red in LyX, in contrary to normal braces that appear
906 In TeX-mode no command is needed to get TeX-braces.
907 TeX-braces don't appear in the output.
910 \begin_layout Standard
911 When commands without arguments, like commands for symbols are entered in
912 TeX-mode, a space character must
916 be behind the command to end it.
917 This space doesn't appear in the output.
918 When the space should appear in the output, the space must be followed
919 by a protected space in normal text.
922 \begin_layout Standard
923 A protected space is inserted with
930 \begin_layout Subsection*
931 \begin_inset Newpage newpage
937 \begin_layout Itemize
942 \begin_layout Plain Layout
943 This visible space character can be created with the command
953 \begin_layout Plain Layout
961 , inserted in TeX-mode.
970 \begin_layout Plain Layout
983 denotes a space character to be input.
986 \begin_layout Itemize
988 \begin_inset Formula $\to$
991 denotes the usage of the corresponding arrow key on the keyboard.
994 \begin_layout Subsection*
998 \begin_layout Standard
1000 \begin_inset Float table
1006 \begin_layout Plain Layout
1008 \begin_inset Caption
1010 \begin_layout Plain Layout
1011 \begin_inset CommandInset label
1013 name "tab:Available-units"
1025 \begin_layout Plain Layout
1027 \begin_inset Tabular
1028 <lyxtabular version="3" rows="13" columns="2">
1030 <column alignment="center" valignment="top" width="0">
1031 <column alignment="center" valignment="top" width="0">
1033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1036 \begin_layout Plain Layout
1042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1045 \begin_layout Plain Layout
1053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1056 \begin_layout Plain Layout
1062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1065 \begin_layout Plain Layout
1073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1076 \begin_layout Plain Layout
1082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1085 \begin_layout Plain Layout
1093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1096 \begin_layout Plain Layout
1102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1105 \begin_layout Plain Layout
1107 \begin_inset space \thinspace{}
1111 \begin_inset space \thinspace{}
1121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1124 \begin_layout Plain Layout
1130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1133 \begin_layout Plain Layout
1135 \begin_inset space \thinspace{}
1139 \begin_inset space \thinspace{}
1149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1152 \begin_layout Plain Layout
1158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1161 \begin_layout Plain Layout
1163 \begin_inset space \thinspace{}
1167 \begin_inset space \thinspace{}
1177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1180 \begin_layout Plain Layout
1186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1189 \begin_layout Plain Layout
1191 \begin_inset space \thinspace{}
1195 \begin_inset space \thinspace{}
1205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1208 \begin_layout Plain Layout
1214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1217 \begin_layout Plain Layout
1219 \begin_inset space \thinspace{}
1223 \begin_inset space \thinspace{}
1233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1236 \begin_layout Plain Layout
1242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1245 \begin_layout Plain Layout
1247 \begin_inset space \thinspace{}
1251 \begin_inset Formula $\approx$
1255 \begin_inset space \thinspace{}
1265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1268 \begin_layout Plain Layout
1274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1277 \begin_layout Plain Layout
1279 \begin_inset space \thinspace{}
1283 \begin_inset space \thinspace{}
1293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1296 \begin_layout Plain Layout
1302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1305 \begin_layout Plain Layout
1309 \begin_inset Quotes eld
1315 \begin_inset Quotes erd
1325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1328 \begin_layout Plain Layout
1334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1337 \begin_layout Plain Layout
1339 \begin_inset Quotes eld
1347 \begin_inset Quotes erd
1357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1360 \begin_layout Plain Layout
1366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1369 \begin_layout Plain Layout
1371 \begin_inset space \thinspace{}
1375 \begin_inset Formula $\nicefrac{1}{18}$
1379 \begin_inset space \thinspace{}
1400 \begin_layout Standard
1401 \begin_inset Newpage newpage
1407 \begin_layout Section
1411 \begin_layout Subsection
1416 \begin_layout Plain Layout
1426 \begin_layout Plain Layout
1436 \begin_layout Plain Layout
1441 \begin_layout Plain Layout
1452 \begin_layout Plain Layout
1468 \begin_layout Plain Layout
1473 \begin_layout Plain Layout
1484 \begin_layout Plain Layout
1499 \begin_layout Standard
1500 Indices are created with an underscore
1501 \begin_inset Quotes eld
1505 \begin_inset Quotes erd
1508 or via the math toolbar button
1509 \begin_inset Graphics
1510 filename ../images/math-subscript.png
1515 , exponents with a caret
1516 \begin_inset Quotes eld
1520 \begin_inset Quotes erd
1523 or via the math toolbar button
1524 \begin_inset Graphics
1525 filename ../images/math-superscript.png
1533 \begin_layout Standard
1535 \begin_inset Tabular
1536 <lyxtabular version="3" rows="4" columns="2">
1538 <column alignment="center" valignment="top" width="0pt">
1539 <column alignment="center" valignment="top" width="0pt">
1541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1544 \begin_layout Plain Layout
1550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1553 \begin_layout Plain Layout
1555 \begin_inset Note Note
1558 \begin_layout Plain Layout
1565 is only used as spacer.
1577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1580 \begin_layout Plain Layout
1586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1589 \begin_layout Plain Layout
1590 \begin_inset Formula $B_{V}$
1600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1603 \begin_layout Plain Layout
1609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1612 \begin_layout Plain Layout
1613 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1626 \begin_layout Plain Layout
1631 \begin_layout Plain Layout
1645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1648 \begin_layout Plain Layout
1649 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1665 \begin_layout Standard
1666 As the caret is in some languages an accent, vowels will be accentuated
1667 in this case and not set as exponents
1671 \begin_layout Plain Layout
1672 Depending on the used keyboard settings this can also happen for other character
1679 To get in this case exponents, press
1683 after the caret as in the last example.
1686 \begin_layout Subsection
1688 \begin_inset CommandInset label
1690 name "sub:Fractions"
1698 \begin_layout Plain Layout
1707 \begin_layout Standard
1708 Fractions are generated with the command
1718 \begin_layout Plain Layout
1726 or via the math toolbar button
1727 \begin_inset Graphics
1728 filename ../images/math/frac.png
1734 The font size is adjusted automatically, depending on whether the fraction
1735 is in an inline or display style formula.
1736 With the math toolbar button
1737 \begin_inset Graphics
1738 filename ../images/math/frac-square.png
1743 you can select different fraction types.
1746 \begin_layout Standard
1755 \begin_layout Plain Layout
1765 a fraction can be created that has in any case the size of a display style
1775 \begin_layout Plain Layout
1785 the fraction appears always with the size of an inline formula.
1789 \begin_layout Standard
1790 A line with the fraction
1791 \begin_inset Formula $\frac{1}{2}$
1794 that was created with the command
1803 \begin_layout Standard
1804 A line with the fraction
1805 \begin_inset Formula $\dfrac{1}{2}$
1808 that was created with the command
1817 \begin_layout Standard
1819 \begin_inset Tabular
1820 <lyxtabular version="3" rows="4" columns="2">
1822 <column alignment="center" valignment="top" width="0pt">
1823 <column alignment="center" valignment="top" width="0pt">
1825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1828 \begin_layout Plain Layout
1834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1837 \begin_layout Plain Layout
1839 \begin_inset Note Note
1842 \begin_layout Plain Layout
1849 is only used as spacer.
1861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1864 \begin_layout Plain Layout
1871 \begin_layout Plain Layout
1881 \begin_inset Formula $\downarrow$
1889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1892 \begin_layout Plain Layout
1893 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1906 \begin_layout Plain Layout
1913 \begin_layout Plain Layout
1923 \begin_inset Formula $\downarrow$
1931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1934 \begin_layout Plain Layout
1935 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1948 \begin_layout Plain Layout
1955 \begin_layout Plain Layout
1968 \begin_layout Plain Layout
1983 \begin_layout Plain Layout
1993 \begin_inset Formula $\downarrow$
1997 \begin_inset Formula $\downarrow\downarrow$
2005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2008 \begin_layout Plain Layout
2009 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2025 \begin_layout Standard
2026 \begin_inset VSpace bigskip
2030 \begin_inset Newpage newpage
2033 For nested fractions the command
2043 \begin_layout Plain Layout
2053 \begin_inset VSpace -3mm
2059 \begin_layout Standard
2060 \begin_inset Formula \begin{align*}
2061 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2062 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2069 \begin_layout Standard
2070 The command for the example above is:
2073 \begin_layout Standard
2079 \begin_inset Formula $\to$
2089 \begin_inset Formula $\to$
2095 \begin_inset Formula $\to\to$
2103 \begin_layout Standard
2104 \begin_inset VSpace medskip
2110 \begin_layout Standard
2117 sets the fraction always in the size of a displayed formula, also when
2118 it is part of another fraction.
2125 has the following command scheme:
2128 \begin_layout Standard
2133 cfrac[numerator position]{numerator}{denominator}
2136 \begin_layout Standard
2137 The numerator position can be
2150 l or r aligns the numerator to the left or right, resp.
2151 \begin_inset space ~
2154 with the fraction stroke.
2159 or no position is given, the numerator appears centered.
2160 These fractions demonstrate the different alignments:
2161 \begin_inset Newline newline
2167 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2171 \begin_inset Formula $\cfrac{A}{B+C}$
2175 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2181 \begin_layout Standard
2182 \begin_inset VSpace medskip
2185 It is often advantageous to combine
2198 \begin_inset Formula \[
2199 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2206 \begin_layout Standard
2207 For inline fractions with a sloped fraction stroke you can use the command
2218 \begin_layout Plain Layout
2227 \begin_inset Formula $\nicefrac{5}{31}$
2240 \begin_layout Plain Layout
2249 \begin_inset Formula $\unitfrac{5}{31}$
2252 There is furthermore the command
2258 that offers to write a fraction in combination with a number:
2259 \begin_inset Formula $\unitfrac[2]{1}{3}$
2263 \begin_inset Newline newline
2272 is not a real LaTeX command but the command
2273 \begin_inset Newline newline
2280 unitfrac[number]{numerator}{denominator}
2282 , therefore you cannot use it in TeX code.
2285 \begin_layout Standard
2286 How to define own fractions where the fraction stroke can be changed, is
2288 \begin_inset CommandInset ref
2290 reference "sub:Self-defined-Fractions"
2297 \begin_layout Subsection
2302 \begin_layout Plain Layout
2311 \begin_layout Standard
2312 Square roots are created with
2322 \begin_layout Plain Layout
2330 or the math toolbar button
2331 \begin_inset Graphics
2332 filename ../images/math/sqrt.png
2337 , all other roots with the command
2347 \begin_layout Plain Layout
2355 or with the math toolbar button
2356 \begin_inset Graphics
2357 filename ../images/math/root.png
2365 \begin_layout Standard
2367 \begin_inset Tabular
2368 <lyxtabular version="3" rows="3" columns="2">
2370 <column alignment="center" valignment="top" width="0pt">
2371 <column alignment="center" valignment="top" width="0pt">
2373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2376 \begin_layout Plain Layout
2382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2385 \begin_layout Plain Layout
2387 \begin_inset Note Note
2390 \begin_layout Plain Layout
2397 is only used as spacer.
2409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2412 \begin_layout Plain Layout
2419 \begin_layout Plain Layout
2433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2436 \begin_layout Plain Layout
2437 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2447 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2450 \begin_layout Plain Layout
2457 \begin_layout Plain Layout
2467 \begin_inset Formula $\downarrow$
2475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2478 \begin_layout Plain Layout
2479 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2495 \begin_layout Standard
2496 A square root can also be created with
2502 when the root index field is left empty.
2505 \begin_layout Standard
2506 With certain indices the distance to the root is too small, like in this
2508 \begin_inset Formula $\sqrt[\beta]{B}$
2512 \begin_inset Newline newline
2516 \begin_inset Formula $\beta$
2520 To avoid this, the commands
2530 \begin_layout Plain Layout
2548 \begin_layout Plain Layout
2556 are used with the following scheme:
2559 \begin_layout Standard
2573 \begin_layout Standard
2574 Distance is the number of Big Points (unit bp;
2575 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2578 ), that the index should be moved to the left or top, resp..
2579 The commands are written to the index.
2580 This way the command
2581 \begin_inset Newline newline
2591 \begin_inset Formula $\to$
2597 \begin_inset Formula $\to$
2606 \begin_layout Plain Layout
2616 \begin_inset Formula $\to$
2620 \begin_inset Newline newline
2625 produces a correct typeset formula:
2626 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2632 \begin_layout Subsection
2633 Binomial coefficients
2637 \begin_layout Plain Layout
2638 Binomial coefficient s
2646 \begin_layout Standard
2647 Binomial coefficients are inserted with the command
2657 \begin_layout Plain Layout
2665 or with the submenu of the math toolbar button
2666 \begin_inset Graphics
2667 filename ../images/math/frac-square.png
2673 Analog to fractions (
2693 \begin_layout Plain Layout
2713 \begin_layout Plain Layout
2722 For other brackets around binomial coeficients there are the commands
2732 \begin_layout Plain Layout
2750 \begin_layout Plain Layout
2761 \begin_layout Standard
2763 \begin_inset Tabular
2764 <lyxtabular version="3" rows="6" columns="2">
2766 <column alignment="center" valignment="top" width="0pt">
2767 <column alignment="center" valignment="top" width="0pt">
2769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2772 \begin_layout Plain Layout
2778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2781 \begin_layout Plain Layout
2783 \begin_inset Note Note
2786 \begin_layout Plain Layout
2793 is only used as spacer.
2805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2808 \begin_layout Plain Layout
2815 \begin_layout Plain Layout
2825 \begin_inset Formula $\downarrow$
2833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2836 \begin_layout Plain Layout
2837 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2850 \begin_layout Plain Layout
2857 \begin_layout Plain Layout
2867 \begin_inset Formula $\downarrow$
2875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2878 \begin_layout Plain Layout
2879 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2892 \begin_layout Plain Layout
2899 \begin_layout Plain Layout
2909 \begin_inset Formula $\downarrow$
2917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2920 \begin_layout Plain Layout
2921 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2934 \begin_layout Plain Layout
2941 \begin_layout Plain Layout
2951 \begin_inset Formula $\downarrow$
2959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2962 \begin_layout Plain Layout
2963 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2976 \begin_layout Plain Layout
2983 \begin_layout Plain Layout
2993 \begin_inset Formula $\downarrow$
3001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3004 \begin_layout Plain Layout
3005 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3021 \begin_layout Subsection
3022 Case differentiations
3026 \begin_layout Plain Layout
3027 Case differentiations
3035 \begin_layout Standard
3037 \begin_inset Tabular
3038 <lyxtabular version="3" rows="3" columns="2">
3040 <column alignment="center" valignment="top" width="0pt">
3041 <column alignment="center" valignment="top" width="0pt">
3043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3046 \begin_layout Plain Layout
3052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3055 \begin_layout Plain Layout
3063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3066 \begin_layout Plain Layout
3073 \begin_layout Plain Layout
3083 \begin_inset Formula $\to$
3090 \begin_layout Plain Layout
3103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3106 \begin_layout Plain Layout
3107 \begin_inset Formula $\begin{cases}
3118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3121 \begin_layout Plain Layout
3128 \begin_layout Plain Layout
3142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3145 \begin_layout Plain Layout
3146 \begin_inset Formula $\begin{cases}
3147 A & \textrm{for }x>0\\
3148 B & \textrm{for }x=0\end{cases}$
3164 \begin_layout Standard
3171 or the usage of the math toolbar button
3172 \begin_inset Graphics
3173 filename ../images/math/cases.png
3178 you can create new lines with the shortcut
3182 or the table toolbar button
3183 \begin_inset Graphics
3184 filename ../images/tabular-feature_append-row.png
3192 \begin_layout Standard
3199 is also available via the menu
3201 Insert\SpecialChar \menuseparator
3202 Math\SpecialChar \menuseparator
3208 \begin_layout Subsection
3213 \begin_layout Plain Layout
3222 \begin_layout Standard
3233 \begin_layout Plain Layout
3241 every character can be displayed canceled.
3242 The characters are quasi accentuated by a slash.
3245 \begin_layout Standard
3247 \begin_inset Tabular
3248 <lyxtabular version="3" rows="4" columns="2">
3250 <column alignment="center" valignment="top" width="0pt">
3251 <column alignment="center" valignment="top" width="0pt">
3253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3256 \begin_layout Plain Layout
3262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3265 \begin_layout Plain Layout
3273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3276 \begin_layout Plain Layout
3284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3287 \begin_layout Plain Layout
3288 \begin_inset Formula $\not=$
3298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3301 \begin_layout Plain Layout
3311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3314 \begin_layout Plain Layout
3315 \begin_inset Formula $\not\le$
3325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3328 \begin_layout Plain Layout
3338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3341 \begin_layout Plain Layout
3342 \begin_inset Formula $\not\parallel$
3358 \begin_layout Standard
3359 The last example shows, that not all negations look good.
3360 Therefore there are for some negations special commands (see
3361 \begin_inset CommandInset ref
3363 reference "sub:Mathematical-Symbols"
3368 \begin_inset CommandInset ref
3370 reference "sec:Relations"
3377 \begin_layout Subsection
3379 \begin_inset CommandInset label
3381 name "sub:Placeholders"
3389 \begin_layout Plain Layout
3399 \begin_layout Plain Layout
3400 Chemical characters ! Isotopes
3409 \begin_layout Plain Layout
3414 \begin_layout Plain Layout
3425 \begin_layout Plain Layout
3440 \begin_layout Standard
3442 \begin_inset space \thinspace{}
3446 \begin_inset space ~
3453 \begin_layout Plain Layout
3454 More about chemical symbols is written in
3455 \begin_inset CommandInset ref
3457 reference "sub:Chemical-Symbols-and"
3466 the following problem occurs:
3469 \begin_layout Standard
3471 \begin_inset Tabular
3472 <lyxtabular version="3" rows="2" columns="2">
3474 <column alignment="center" valignment="top" width="0pt">
3475 <column alignment="center" valignment="top" width="0pt">
3477 <cell alignment="center" valignment="top" usebox="none">
3480 \begin_layout Plain Layout
3481 Indices created with sub- and superscripts:
3486 <cell alignment="center" valignment="top" usebox="none">
3489 \begin_layout Plain Layout
3490 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3500 <cell alignment="center" valignment="top" usebox="none">
3503 \begin_layout Plain Layout
3509 <cell alignment="center" valignment="top" usebox="none">
3512 \begin_layout Plain Layout
3513 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3527 \begin_inset Note Note
3530 \begin_layout Plain Layout
3537 is only used as spacer.
3545 \begin_layout Standard
3546 The shorter index is by default placed below or above the first character
3547 of the longer index.
3548 To avoid this there is the command
3558 \begin_layout Plain Layout
3566 or the math toolbar button
3567 \begin_inset space \thinspace{}
3574 \begin_layout Plain Layout
3575 can be found in the submenu of the toolbar button
3576 \begin_inset Graphics
3577 filename ../images/math/space.png
3588 \begin_inset Graphics
3589 filename ../images/math/phantom.png
3594 that creates one or more phantom characters.
3601 a small blue box appears that is superposed with two red arrows.
3602 The arrows indicate that the complete width and height of the box content
3603 will be created as placeholder.
3604 Phantom characters are accordingly placeholders with the size of the characters.
3607 \begin_layout Standard
3609 \begin_inset Tabular
3610 <lyxtabular version="3" rows="4" columns="2">
3612 <column alignment="center" valignment="top" width="0">
3613 <column alignment="center" valignment="top" width="0">
3615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3618 \begin_layout Plain Layout
3624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3627 \begin_layout Plain Layout
3629 \begin_inset Note Note
3632 \begin_layout Plain Layout
3639 is only used as spacer.
3651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3654 \begin_layout Plain Layout
3659 \begin_layout Plain Layout
3674 \begin_layout Plain Layout
3684 \begin_inset Formula $\to$
3691 \begin_layout Plain Layout
3705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3708 \begin_layout Plain Layout
3709 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3722 \begin_layout Plain Layout
3727 \begin_layout Plain Layout
3742 \begin_layout Plain Layout
3752 \begin_inset Formula $\to$
3759 \begin_layout Plain Layout
3773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3776 \begin_layout Plain Layout
3777 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3790 \begin_layout Plain Layout
3797 \begin_layout Plain Layout
3812 \begin_layout Plain Layout
3822 \begin_inset Formula $\to$
3829 \begin_layout Plain Layout
3843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3846 \begin_layout Plain Layout
3847 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3863 \begin_layout Standard
3864 Furthermore there are the commands
3874 \begin_layout Plain Layout
3883 \begin_inset space ~
3887 \begin_inset Graphics
3888 filename ../images/math/vphantom.png
3903 \begin_layout Plain Layout
3912 \begin_inset space ~
3916 \begin_inset Graphics
3917 filename ../images/math/hphantom.png
3929 creates only space for the maximal height of the characters in the box
3930 but not for its width.
3937 creates only space for the width of the box content.
3938 Therefore the boxes of both commands have only one red arrow.
3941 \begin_layout Standard
3952 \begin_layout Plain Layout
3967 space for the height of the integral sign,
3971 \begin_layout Plain Layout
3978 creates an integral sign, see
3979 \begin_inset CommandInset ref
3981 reference "sub:Big-Operators"
3990 because this is the larger character.
3991 An example application is in
3992 \begin_inset CommandInset ref
3994 reference "sub:Multiline-Brackets"
4001 \begin_layout Subsection
4006 \begin_layout Plain Layout
4016 \begin_layout Plain Layout
4017 Formula ! underlined
4025 \begin_layout Standard
4027 \begin_inset Tabular
4028 <lyxtabular version="3" rows="4" columns="2">
4030 <column alignment="center" valignment="top" width="0pt">
4031 <column alignment="center" valignment="top" width="0pt">
4033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4036 \begin_layout Plain Layout
4042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4045 \begin_layout Plain Layout
4047 \begin_inset Note Note
4050 \begin_layout Plain Layout
4057 is only used as spacer.
4069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4072 \begin_layout Plain Layout
4079 \begin_layout Plain Layout
4092 \begin_layout Plain Layout
4105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4108 \begin_layout Plain Layout
4109 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4119 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4122 \begin_layout Plain Layout
4129 \begin_layout Plain Layout
4142 \begin_layout Plain Layout
4155 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4158 \begin_layout Plain Layout
4159 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4172 \begin_layout Plain Layout
4179 \begin_layout Plain Layout
4194 \begin_layout Plain Layout
4208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4211 \begin_layout Plain Layout
4212 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4228 \begin_layout Standard
4229 In the last example it doesn't matter if first
4244 \begin_layout Standard
4245 To double underline e.
4246 \begin_inset space \thinspace{}
4259 \begin_layout Standard
4260 It is possible to place up to 6 lines above or below characters.
4263 \begin_layout Standard
4264 \begin_inset VSpace bigskip
4267 Custom lines can be created using the command
4273 which has the following scheme:
4276 \begin_layout Standard
4281 rule[vertical offset]{length}{thickness}
4284 \begin_layout Standard
4285 The optional vertical offset shifts the line upwards (or downwards, when
4286 the value is negative).
4288 \begin_inset CommandInset ref
4290 reference "tab:Available-units"
4294 can be used for the values.
4295 Here are two example lines created with the commands
4296 \begin_inset Newline newline
4303 rule[-2ex]{3cm}{2pt}
4314 \begin_layout Standard
4316 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4322 \begin_layout Standard
4329 can also be used for text when it is inserted in TeX-mode.
4332 \begin_layout Subsection
4334 \begin_inset CommandInset label
4344 \begin_layout Plain Layout
4353 \begin_layout Standard
4354 There are different types of ellipses available.
4358 \begin_layout Plain Layout
4359 In the math toolbar in the submenu of the button
4360 \begin_inset Graphics
4361 filename ../images/math/ldots.png
4371 For listings dots at the baseline are used (
4381 \begin_layout Plain Layout
4389 ), while for operations dots are needed that are on the same height as the
4400 \begin_layout Plain Layout
4409 When using the command
4419 \begin_layout Plain Layout
4427 , LaTeX decides on the basis of the next character what type is used.
4430 \begin_layout Standard
4432 \begin_inset Tabular
4433 <lyxtabular version="3" rows="8" columns="2">
4435 <column alignment="center" valignment="top" width="0pt">
4436 <column alignment="center" valignment="top" width="0pt">
4438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4441 \begin_layout Plain Layout
4447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4450 \begin_layout Plain Layout
4458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4461 \begin_layout Plain Layout
4466 \begin_layout Plain Layout
4481 \begin_layout Plain Layout
4495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4498 \begin_layout Plain Layout
4499 \begin_inset Formula $A_{1},\dots,A_{n}$
4509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4512 \begin_layout Plain Layout
4517 \begin_layout Plain Layout
4532 \begin_layout Plain Layout
4546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4549 \begin_layout Plain Layout
4550 \begin_inset Formula $A_{1}+\dots+A_{n}$
4560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4563 \begin_layout Plain Layout
4568 \begin_layout Plain Layout
4583 \begin_layout Plain Layout
4597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4600 \begin_layout Plain Layout
4601 \begin_inset Formula $A_{1},\ldots,A_{n}$
4611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4614 \begin_layout Plain Layout
4619 \begin_layout Plain Layout
4634 \begin_layout Plain Layout
4648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4651 \begin_layout Plain Layout
4652 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4665 \begin_layout Plain Layout
4673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4676 \begin_layout Plain Layout
4677 \begin_inset Formula $\vdots$
4687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4690 \begin_layout Plain Layout
4698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4701 \begin_layout Plain Layout
4702 \begin_inset Formula $\ddots$
4712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4715 \begin_layout Plain Layout
4717 \begin_inset space \thinspace{}
4720 matrix with the different dots
4725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4728 \begin_layout Plain Layout
4729 \begin_inset Formula $\begin{array}{ccc}
4730 A_{11} & \cdots & A_{1m}\\
4731 \vdots & \ddots & \vdots\\
4732 A_{n1} & \cdots & A_{nm}\end{array}$
4748 \begin_layout Standard
4749 The ellipses available in menu
4751 Insert\SpecialChar \menuseparator
4753 \begin_inset space ~
4767 \begin_layout Standard
4768 \begin_inset VSpace medskip
4771 Specially for matrices there are ellipses that span over several columns.
4772 They are created with the command
4782 \begin_layout Plain Layout
4790 , that has the following scheme:
4793 \begin_layout Standard
4798 hdotsfor[distance]{number of columns}
4801 \begin_layout Standard
4802 The number of columns specifies how many columns should be spanned.
4803 Distance is a factor for the distance between the dots.
4806 \begin_layout Standard
4807 In the following matrix the command
4813 was inserted in the first box of the second line, to get an ellipsis with
4814 a dot distance twice as long as with the command
4821 \begin_inset Formula \[
4822 \left(\begin{array}{cccc}
4825 q & w & e & r\end{array}\right)\]
4829 Note that the matrix fields that should be spanned must be empty, otherwise
4830 you get LaTeX-errors.
4833 \begin_layout Standard
4834 \begin_inset VSpace bigskip
4837 Furthermore you can fill with the command
4847 \begin_layout Plain Layout
4855 the rest of a line with dots.
4856 The effect of these commands is the same like with
4863 \begin_inset CommandInset ref
4865 reference "sub:Variable-Space"
4872 \begin_layout Standard
4873 For example the command
4881 \begin_layout Plain Layout
4895 \begin_layout Standard
4896 \begin_inset Formula $A\dotfill B$
4902 \begin_layout Standard
4909 there is for a line the command
4919 \begin_layout Plain Layout
4930 \begin_layout Standard
4931 \begin_inset Formula $A\hrulefill B$
4937 \begin_layout Standard
4938 To use the commands for text, they have to be inserted in TeX-mode.
4941 \begin_layout Section
4943 \begin_inset CommandInset label
4953 \begin_layout Plain Layout
4962 \begin_layout Standard
4963 Matrices can be inserted via the math toolbar button
4964 \begin_inset Graphics
4965 filename ../images/dialog-show_mathmatrix.png
4972 Insert\SpecialChar \menuseparator
4973 Math\SpecialChar \menuseparator
4977 You will be asked for the number of matrix columns and rows, and the alignment.
4978 The vertical alignment is hereby only of importance for matrices in inline
4982 \begin_layout Standard
4983 The first matrix is top
4984 \begin_inset Formula $\begin{array}[t]{cccc}
4987 C & F & I & L\end{array}$
4991 \begin_inset Formula $\begin{array}{cccc}
4994 C & F & I & L\end{array}$
4997 , and the third bottom
4998 \begin_inset Formula $\begin{array}[b]{cccc}
5001 C & F & I & L\end{array}$
5007 \begin_layout Standard
5008 The horizontal alignment specifies how the column entries should be aligned.
5009 It is set by entering a letter for every column.
5014 denotes left aligned,
5023 To create for example a 4
5028 \begin_inset space ~
5031 matrix where the first column is left aligned, the second and third are
5032 centered, and the last one is right aligned, one enters for the horizontal
5038 Normally are in a matrix all columns centered, therefore the default is
5039 for every column is a
5046 \begin_layout Standard
5047 Horizontal alignment:
5050 \begin_layout Standard
5056 \begin_inset Formula $\begin{array}{lll}
5059 C & F & 10000\end{array}$
5067 \begin_inset Formula $\begin{array}{ccc}
5070 C & F & 10000\end{array}$
5078 \begin_inset Formula $\begin{array}{rrr}
5081 C & F & 10000\end{array}$
5087 \begin_layout Standard
5088 To add or delete rows and columns subsequently, the math toolbar buttons
5090 \begin_inset Graphics
5091 filename ../images/tabular-feature_append-row.png
5097 \begin_inset Graphics
5098 filename ../images/tabular-feature_delete-row.png
5104 \begin_inset space \thinspace{}
5109 Edit\SpecialChar \menuseparator
5113 New rows can also be created with
5120 \begin_layout Standard
5121 \begin_inset VSpace bigskip
5124 Parentheses around a matrix can can either be created with the commands
5135 \begin_layout Plain Layout
5153 \begin_layout Plain Layout
5164 \begin_inset space ~
5170 \begin_inset CommandInset ref
5172 reference "sub:Automatic-Bracket-Size"
5176 , or by using the following commands:
5177 \begin_inset VSpace medskip
5183 \begin_layout Standard
5184 \begin_inset space \hfill{}
5188 \begin_inset Tabular
5189 <lyxtabular version="3" rows="4" columns="2">
5191 <column alignment="center" valignment="top" width="0">
5192 <column alignment="center" valignment="top" width="0">
5194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5197 \begin_layout Plain Layout
5203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5206 \begin_layout Plain Layout
5208 \begin_inset Note Note
5211 \begin_layout Plain Layout
5218 is only used as spacer.
5230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5233 \begin_layout Plain Layout
5240 \begin_layout Plain Layout
5254 \begin_inset space \thinspace{}
5262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5265 \begin_layout Plain Layout
5266 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5267 0 & \textrm{-}\mathrm{i}\\
5268 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5281 \begin_layout Plain Layout
5288 \begin_layout Plain Layout
5302 \begin_inset space \thinspace{}
5310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5313 \begin_layout Plain Layout
5314 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5315 0 & \textrm{-}\mathrm{i}\\
5316 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5329 \begin_layout Plain Layout
5336 \begin_layout Plain Layout
5350 \begin_inset space \thinspace{}
5358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5361 \begin_layout Plain Layout
5362 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5363 0 & \textrm{-}\mathrm{i}\\
5364 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5378 \begin_inset space \hfill{}
5382 \begin_inset Tabular
5383 <lyxtabular version="3" rows="4" columns="2">
5385 <column alignment="center" valignment="top" width="0">
5386 <column alignment="center" valignment="top" width="0">
5388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5391 \begin_layout Plain Layout
5397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5400 \begin_layout Plain Layout
5408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5411 \begin_layout Plain Layout
5418 \begin_layout Plain Layout
5432 \begin_inset space \thinspace{}
5440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5443 \begin_layout Plain Layout
5444 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5445 0 & \textrm{-}\mathrm{i}\\
5446 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5459 \begin_layout Plain Layout
5466 \begin_layout Plain Layout
5480 \begin_inset space \thinspace{}
5488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5491 \begin_layout Plain Layout
5492 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5493 0 & \textrm{-}\mathrm{i}\\
5494 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5507 \begin_layout Plain Layout
5514 \begin_layout Plain Layout
5528 \begin_inset space \thinspace{}
5536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5539 \begin_layout Plain Layout
5540 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5541 0 & \textrm{-}\mathrm{i}\\
5542 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5556 \begin_inset space \hfill{}
5562 \begin_layout Standard
5563 \begin_inset VSpace medskip
5567 \begin_inset space \thinspace{}
5571 \begin_inset space ~
5580 is inserted, a blue box appears between two vertical lines where the matrix
5584 \begin_layout Standard
5585 \begin_inset VSpace bigskip
5588 As all multiline formulas are matrices, the length
5598 \begin_layout Plain Layout
5606 that is described in
5607 \begin_inset CommandInset ref
5609 reference "sub:Column-Separation"
5613 can also be used to change the column separation of matrices.
5616 \begin_layout Standard
5617 To change the row separation, the command
5627 \begin_layout Plain Layout
5636 It is used as follows:
5639 \begin_layout Standard
5646 arraystretch}{stretch factor}
5650 \begin_layout Plain Layout
5661 \begin_layout Standard
5668 assigns the stretch factor to the predefined command
5676 \begin_inset space \thinspace{}
5680 \begin_inset space ~
5683 the row separation, use the factor 2.
5684 This is then used for all following matrices.
5685 To go back to the original separation, assign the factor 1 to
5694 \begin_layout Standard
5695 To set matrices into a text line, the command
5705 \begin_layout Plain Layout
5714 When it is inserted a blue box with two dashed lines appears.
5715 In this box the matrix is inserted.
5718 \begin_layout Standard
5720 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5721 C & D\end{smallmatrix}\right)$
5727 \begin_layout Section
5728 Brackets and Delimiters
5732 \begin_layout Plain Layout
5742 \begin_layout Plain Layout
5751 \begin_layout Subsection
5752 Vertical Brackets and Delimiters
5756 \begin_layout Plain Layout
5765 \begin_layout Standard
5766 \begin_inset space \hfill{}
5770 \begin_inset Tabular
5771 <lyxtabular version="3" rows="9" columns="2">
5773 <column alignment="center" valignment="top" width="0pt">
5774 <column alignment="center" valignment="top" width="0pt">
5776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5779 \begin_layout Plain Layout
5785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5788 \begin_layout Plain Layout
5796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5799 \begin_layout Plain Layout
5805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5808 \begin_layout Plain Layout
5809 \begin_inset Formula $($
5819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5822 \begin_layout Plain Layout
5828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5831 \begin_layout Plain Layout
5832 \begin_inset Formula $\{$
5842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5845 \begin_layout Plain Layout
5851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5854 \begin_layout Plain Layout
5855 \begin_inset Formula $[$
5865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5868 \begin_layout Plain Layout
5876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5879 \begin_layout Plain Layout
5880 \begin_inset Formula $\langle$
5890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5893 \begin_layout Plain Layout
5901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5904 \begin_layout Plain Layout
5905 \begin_inset Formula $\lceil$
5915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5918 \begin_layout Plain Layout
5926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5929 \begin_layout Plain Layout
5930 \begin_inset Formula $\lfloor$
5940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5943 \begin_layout Plain Layout
5949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5952 \begin_layout Plain Layout
5953 \begin_inset Formula $/$
5963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5966 \begin_layout Plain Layout
5972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5975 \begin_layout Plain Layout
5976 \begin_inset Formula $|$
5990 \begin_inset space \hfill{}
5994 \begin_inset Tabular
5995 <lyxtabular version="3" rows="9" columns="2">
5997 <column alignment="center" valignment="top" width="0pt">
5998 <column alignment="center" valignment="top" width="0pt">
6000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6003 \begin_layout Plain Layout
6009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6012 \begin_layout Plain Layout
6020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6023 \begin_layout Plain Layout
6029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6032 \begin_layout Plain Layout
6033 \begin_inset Formula $)$
6043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6046 \begin_layout Plain Layout
6052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6055 \begin_layout Plain Layout
6056 \begin_inset Formula $\}$
6066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6069 \begin_layout Plain Layout
6075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6078 \begin_layout Plain Layout
6079 \begin_inset Formula $]$
6089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6092 \begin_layout Plain Layout
6100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6103 \begin_layout Plain Layout
6104 \begin_inset Formula $\rangle$
6114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6117 \begin_layout Plain Layout
6125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6128 \begin_layout Plain Layout
6129 \begin_inset Formula $\rceil$
6139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6142 \begin_layout Plain Layout
6150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6153 \begin_layout Plain Layout
6154 \begin_inset Formula $\rfloor$
6164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6167 \begin_layout Plain Layout
6177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6180 \begin_layout Plain Layout
6181 \begin_inset Formula $\backslash$
6191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6194 \begin_layout Plain Layout
6202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6205 \begin_layout Plain Layout
6206 \begin_inset Formula $\|$
6220 \begin_inset space \hfill{}
6226 \begin_layout Standard
6229 \begin_inset Note Greyedout
6232 \begin_layout Plain Layout
6237 In TeX-mode the command
6247 \begin_layout Plain Layout
6255 must be used for the backslash, because the command
6263 produces there a line break.
6271 \begin_layout Standard
6272 For all characters listed above the size can be adjusted with the commands
6273 described in the following two subsections.
6274 When using these commands, the characters < and > can directly be used
6275 instead of the commands
6290 \begin_layout Subsubsection
6292 \begin_inset CommandInset label
6294 name "sub:Manual-Bracket-Size"
6302 \begin_layout Plain Layout
6303 Bracket size ! manual
6311 \begin_layout Standard
6312 The bracket size can be specified manually by the LaTeX-commands
6322 \begin_layout Plain Layout
6355 denotes the smallest and
6361 the largest bracket size.
6364 \begin_layout Standard
6365 These commands are used to emphasize levels of brackets:
6368 \begin_layout Standard
6370 \begin_inset Tabular
6371 <lyxtabular version="3" rows="2" columns="2">
6373 <column alignment="center" valignment="top" width="0pt">
6374 <column alignment="center" valignment="top" width="0pt">
6376 <cell alignment="center" valignment="top" usebox="none">
6379 \begin_layout Plain Layout
6380 all brackets in the same size:
6385 <cell alignment="center" valignment="top" usebox="none">
6388 \begin_layout Plain Layout
6389 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6399 <cell alignment="center" valignment="top" usebox="none">
6402 \begin_layout Plain Layout
6408 <cell alignment="center" valignment="top" usebox="none">
6411 \begin_layout Plain Layout
6412 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6426 \begin_inset Note Note
6429 \begin_layout Plain Layout
6436 is only used as spacer.
6444 \begin_layout Standard
6445 For the second formula the command
6455 \begin_layout Plain Layout
6469 \begin_layout Standard
6470 Here is an overview about all bracket sizes:
6473 \begin_layout Standard
6493 \begin_layout Plain Layout
6510 \begin_layout Plain Layout
6523 \begin_layout Plain Layout
6539 \begin_layout Standard
6541 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6547 \begin_layout Standard
6554 -commands there is the variant
6564 \begin_layout Plain Layout
6572 that adds a bit more space between the bracket and its content, and the
6589 \begin_layout Plain Layout
6599 , that don't add additional space.
6604 at the end of the command
6610 is for a left bracket; for a right bracket this will be replaced by an
6616 A left or right bracket can each be an opening or closing bracket.
6619 \begin_layout Standard
6620 In the following table is a comparison of the variants:
6623 \begin_layout Standard
6625 \begin_inset Tabular
6626 <lyxtabular version="3" rows="5" columns="2">
6628 <column alignment="center" valignment="middle" width="0">
6629 <column alignment="center" valignment="middle" width="0">
6631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6634 \begin_layout Plain Layout
6640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6643 \begin_layout Plain Layout
6645 \begin_inset Note Note
6648 \begin_layout Plain Layout
6655 is only used as spacer.
6667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6670 \begin_layout Plain Layout
6685 \begin_layout Plain Layout
6703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6706 \begin_layout Plain Layout
6707 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6720 \begin_layout Plain Layout
6735 \begin_layout Plain Layout
6753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6756 \begin_layout Plain Layout
6757 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6770 \begin_layout Plain Layout
6785 \begin_layout Plain Layout
6803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6806 \begin_layout Plain Layout
6807 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6820 \begin_layout Plain Layout
6832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6835 \begin_layout Plain Layout
6836 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6852 \begin_layout Subsubsection
6853 Automatic Bracket Size
6854 \begin_inset CommandInset label
6856 name "sub:Automatic-Bracket-Size"
6864 \begin_layout Plain Layout
6865 Bracket size ! automatic
6873 \begin_layout Standard
6874 Brackets with variable size can be inserted with the commands
6884 \begin_layout Plain Layout
6902 \begin_layout Plain Layout
6910 or via the math toolbar button
6911 \begin_inset Graphics
6912 filename ../images/dialog-show_mathdelimiter.png
6930 the wanted bracket must be inserted.
6931 The bracket size will then automatically be calculated for the output.
6934 \begin_layout Standard
6936 normal bracket: The command
6946 \begin_layout Plain Layout
6956 \begin_inset Formula $\downarrow$
6963 \begin_layout Plain Layout
6975 \begin_inset Formula \[
6983 \begin_layout Standard
6985 multiline bracket: The command
6997 \begin_layout Plain Layout
7007 \begin_inset Formula $\downarrow$
7014 \begin_layout Plain Layout
7028 \begin_inset Formula \[
7029 \ln\left(\frac{A}{C}\right)\]
7036 \begin_layout Standard
7052 \begin_inset space ~
7058 This has the advantage that you can see in LyX immediately the real bracket
7059 size and that the matching right bracket will be created too.
7060 \begin_inset Newline newline
7063 The command for the last example would then be:
7077 \begin_layout Plain Layout
7087 \begin_inset Formula $\downarrow$
7093 \begin_layout Standard
7094 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7095 For example the command
7105 \begin_layout Plain Layout
7115 \begin_inset Formula $\downarrow$
7122 \begin_layout Plain Layout
7138 \begin_inset Formula \[
7139 \left.\frac{A}{B}\right\} \]
7157 will be converted by LyX to brackets in the right size when the document
7158 is reloaded and an omitted bracket will appear as dashed line.
7161 \begin_layout Standard
7162 \begin_inset VSpace bigskip
7165 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7176 \begin_layout Plain Layout
7184 is additionally available for all brackets and limits.
7185 With this command the height of the following character is adapted to the
7186 one of the surrounding brackets, what is e.
7187 \begin_inset space \thinspace{}
7191 \begin_inset space ~
7194 needed for physical vectors:
7195 \begin_inset Formula \[
7196 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7200 For physical vectors there is a special LaTeX-package, described in
7201 \begin_inset CommandInset ref
7203 reference "sub:Physical-Vectors"
7210 \begin_layout Subsection
7215 \begin_layout Plain Layout
7216 Brackets ! horizontal
7224 \begin_layout Standard
7226 \begin_inset Tabular
7227 <lyxtabular version="3" rows="4" columns="2">
7229 <column alignment="center" valignment="top" width="0pt">
7230 <column alignment="center" valignment="top" width="0pt">
7232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7235 \begin_layout Plain Layout
7237 \begin_inset Note Note
7240 \begin_layout Plain Layout
7247 is only used as spacer.
7257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7260 \begin_layout Plain Layout
7268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7271 \begin_layout Plain Layout
7275 \begin_layout Plain Layout
7290 \begin_layout Plain Layout
7303 \begin_layout Plain Layout
7316 \begin_layout Plain Layout
7329 \begin_layout Plain Layout
7340 \begin_layout Plain Layout
7353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7356 \begin_layout Plain Layout
7357 \begin_inset Formula $\overbrace{A+B}^{3}$
7367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7370 \begin_layout Plain Layout
7374 \begin_layout Plain Layout
7389 \begin_layout Plain Layout
7402 \begin_layout Plain Layout
7415 \begin_layout Plain Layout
7426 \begin_layout Plain Layout
7439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7442 \begin_layout Plain Layout
7443 \begin_inset Formula $\underbrace{A+B}_{5}$
7453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7456 \begin_layout Plain Layout
7463 \begin_layout Plain Layout
7478 \begin_layout Plain Layout
7491 \begin_layout Plain Layout
7504 \begin_layout Plain Layout
7517 \begin_layout Plain Layout
7530 \begin_layout Plain Layout
7543 \begin_layout Plain Layout
7557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7560 \begin_layout Plain Layout
7561 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7577 \begin_layout Standard
7578 In the last example it doesn't matter if
7590 is inserted at first.
7593 \begin_layout Standard
7594 \begin_inset VSpace bigskip
7597 When brackets are needed that overlap each other, multiline formulas, as
7599 \begin_inset CommandInset ref
7601 reference "sec:Multiline-Formulas"
7606 \begin_inset Formula \begin{eqnarray*}
7607 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7608 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7612 In the first row the formula is inserted together with the first brace.
7613 It is hereby important that the space command
7617 \begin_layout Plain Layout
7618 Space commands are explained in
7619 \begin_inset CommandInset ref
7621 reference "sub:Predefined-Space"
7636 is inserted before the first
7637 \begin_inset Formula $d$
7640 , because the brace that ends behind the
7641 \begin_inset Formula $q$
7644 prevents that the following
7645 \begin_inset Quotes eld
7649 \begin_inset Quotes erd
7652 is surrounded by space.
7656 \begin_layout Plain Layout
7657 because a bracket is not handled as character, see
7658 \begin_inset CommandInset ref
7660 reference "sub:Binary-Operators"
7669 In the second row the second brace is inserted.
7670 As it should begin before the
7671 \begin_inset Formula $b$
7686 \begin_layout Plain Layout
7694 \begin_inset CommandInset ref
7696 reference "sub:Placeholders"
7705 This space is needed because the
7706 \begin_inset Quotes eld
7710 \begin_inset Quotes erd
7713 is also surrounded by space in the formula.
7714 The brace is placed under the command
7723 \begin_layout Standard
7724 It gets more complicated when brackets overlap each other, like in the following
7729 \begin_layout Plain Layout
7741 \begin_inset Formula \begin{eqnarray*}
7742 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7743 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7751 \begin_layout Plain Layout
7762 The first formula row is the same as the second row of the previous example,
7763 with the difference that the brace is above.
7764 The second row contains the formula together with the second brace.
7765 To avoid that there is space between the upper brace in the first row and
7766 the formula, the row spacing need to be reduced.
7767 This is not easily possible due to a bug in LyX
7771 \begin_layout Plain Layout
7772 \begin_inset CommandInset href
7774 name "LyX-bug #1505"
7775 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7785 As solution for the problem, the global formula row separation
7795 \begin_layout Plain Layout
7803 must be changed to -6
7804 \begin_inset space \thinspace{}
7807 pt before the formula with the command
7822 is set back after the formula to the standard value of 3
7823 \begin_inset space \thinspace{}
7826 pt using the same command.
7827 More about the row separation in formulas is explained in
7828 \begin_inset CommandInset ref
7830 reference "sub:Line-Separation"
7837 \begin_layout Section
7842 \begin_layout Plain Layout
7851 \begin_layout Standard
7852 Arrows can be inserted via the math toolbar button
7853 \begin_inset Graphics
7854 filename ../images/math/leftarrow.png
7859 or the commands listed in the following subsections.
7862 \begin_layout Standard
7863 \begin_inset Newpage newpage
7869 \begin_layout Subsection
7874 \begin_layout Plain Layout
7883 \begin_layout Standard
7884 \begin_inset space \hfill{}
7888 \begin_inset Tabular
7889 <lyxtabular version="3" rows="8" columns="2">
7891 <column alignment="center" valignment="top" width="0pt">
7892 <column alignment="center" valignment="top" width="0pt">
7894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7897 \begin_layout Plain Layout
7903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7906 \begin_layout Plain Layout
7914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7917 \begin_layout Plain Layout
7925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7928 \begin_layout Plain Layout
7929 \begin_inset Formula $\gets$
7939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7942 \begin_layout Plain Layout
7950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7953 \begin_layout Plain Layout
7954 \begin_inset Formula $\Leftarrow$
7964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7967 \begin_layout Plain Layout
7975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7978 \begin_layout Plain Layout
7979 \begin_inset Formula $\longleftarrow$
7989 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7992 \begin_layout Plain Layout
8000 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8003 \begin_layout Plain Layout
8004 \begin_inset Formula $\Longleftarrow$
8014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8017 \begin_layout Plain Layout
8025 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8028 \begin_layout Plain Layout
8029 \begin_inset Formula $\leftharpoonup$
8039 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8042 \begin_layout Plain Layout
8050 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8053 \begin_layout Plain Layout
8054 \begin_inset Formula $\leftharpoondown$
8064 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8067 \begin_layout Plain Layout
8075 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8078 \begin_layout Plain Layout
8079 \begin_inset Formula $\hookleftarrow$
8093 \begin_inset space \hfill{}
8097 \begin_inset Tabular
8098 <lyxtabular version="3" rows="8" columns="2">
8100 <column alignment="center" valignment="top" width="0pt">
8101 <column alignment="center" valignment="top" width="0pt">
8103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8106 \begin_layout Plain Layout
8112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8115 \begin_layout Plain Layout
8123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8126 \begin_layout Plain Layout
8134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8137 \begin_layout Plain Layout
8138 \begin_inset Formula $\to$
8148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8151 \begin_layout Plain Layout
8159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8162 \begin_layout Plain Layout
8163 \begin_inset Formula $\Rightarrow$
8173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8176 \begin_layout Plain Layout
8184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8187 \begin_layout Plain Layout
8188 \begin_inset Formula $\longrightarrow$
8198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8201 \begin_layout Plain Layout
8209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8212 \begin_layout Plain Layout
8213 \begin_inset Formula $\Longrightarrow$
8223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8226 \begin_layout Plain Layout
8234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8237 \begin_layout Plain Layout
8238 \begin_inset Formula $\rightharpoonup$
8248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8251 \begin_layout Plain Layout
8259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8262 \begin_layout Plain Layout
8263 \begin_inset Formula $\rightharpoondown$
8273 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8276 \begin_layout Plain Layout
8284 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8287 \begin_layout Plain Layout
8288 \begin_inset Formula $\hookrightarrow$
8302 \begin_inset space \hfill{}
8308 \begin_layout Standard
8309 \begin_inset space \hfill{}
8313 \begin_inset Tabular
8314 <lyxtabular version="3" rows="6" columns="2">
8316 <column alignment="center" valignment="top" width="0pt">
8317 <column alignment="center" valignment="top" width="0pt">
8319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8322 \begin_layout Plain Layout
8328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8331 \begin_layout Plain Layout
8339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8342 \begin_layout Plain Layout
8350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8353 \begin_layout Plain Layout
8354 \begin_inset Formula $\leftrightarrow$
8364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8367 \begin_layout Plain Layout
8375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8378 \begin_layout Plain Layout
8379 \begin_inset Formula $\Leftrightarrow$
8389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8392 \begin_layout Plain Layout
8400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8403 \begin_layout Plain Layout
8404 \begin_inset Formula $\longleftrightarrow$
8414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8417 \begin_layout Plain Layout
8425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8428 \begin_layout Plain Layout
8429 \begin_inset Formula $\Longleftrightarrow$
8439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8442 \begin_layout Plain Layout
8450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8453 \begin_layout Plain Layout
8454 \begin_inset Formula $\rightleftharpoons$
8468 \begin_inset space \hspace{}
8473 \begin_inset space \hfill{}
8477 \begin_inset Tabular
8478 <lyxtabular version="3" rows="5" columns="2">
8480 <column alignment="center" valignment="top" width="0pt">
8481 <column alignment="center" valignment="top" width="0pt">
8483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8486 \begin_layout Plain Layout
8492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8495 \begin_layout Plain Layout
8503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8506 \begin_layout Plain Layout
8514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8517 \begin_layout Plain Layout
8518 \begin_inset Formula $\mapsto$
8528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8531 \begin_layout Plain Layout
8539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8542 \begin_layout Plain Layout
8543 \begin_inset Formula $\longmapsto$
8553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8556 \begin_layout Plain Layout
8564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8567 \begin_layout Plain Layout
8568 \begin_inset Formula $\leadsto$
8578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8581 \begin_layout Plain Layout
8589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8592 \begin_layout Plain Layout
8593 \begin_inset Formula $\dasharrow$
8607 \begin_inset space \hfill{}
8613 \begin_layout Standard
8614 \begin_inset VSpace medskip
8617 Arrows used as accent like e.
8618 \begin_inset space \thinspace{}
8622 \begin_inset space ~
8625 vector arrows are listed in
8626 \begin_inset CommandInset ref
8628 reference "sec:Accents"
8635 \begin_layout Standard
8636 \begin_inset VSpace bigskip
8639 Furthermore there are the labeled arrows
8643 \begin_layout Plain Layout
8659 \begin_layout Plain Layout
8677 \begin_layout Plain Layout
8684 \begin_layout Plain Layout
8699 When inserting one of these commands in a formula, an arrow with two blue
8700 boxes appear where the label can be inserted.
8701 The length of the arrow adapts to the label width.
8704 \begin_layout Standard
8706 \begin_inset Tabular
8707 <lyxtabular version="3" rows="3" columns="2">
8709 <column alignment="center" valignment="top" width="0pt">
8710 <column alignment="center" valignment="top" width="0pt">
8712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8715 \begin_layout Plain Layout
8721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8724 \begin_layout Plain Layout
8726 \begin_inset Note Note
8729 \begin_layout Plain Layout
8736 is only used as spacer.
8748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8751 \begin_layout Plain Layout
8758 \begin_layout Plain Layout
8768 \begin_inset Formula $\downarrow$
8772 \begin_inset Formula $\to$
8780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8783 \begin_layout Plain Layout
8784 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8797 \begin_layout Plain Layout
8804 \begin_layout Plain Layout
8814 \begin_inset Formula $\downarrow$
8818 \begin_inset Formula $\to$
8826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8829 \begin_layout Plain Layout
8830 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8846 \begin_layout Subsection
8847 Vertical and diagonal Arrows
8851 \begin_layout Plain Layout
8861 \begin_layout Plain Layout
8870 \begin_layout Standard
8871 \begin_inset space \hfill{}
8875 \begin_inset Tabular
8876 <lyxtabular version="3" rows="7" columns="2">
8878 <column alignment="center" valignment="top" width="0pt">
8879 <column alignment="center" valignment="top" width="0pt">
8881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8884 \begin_layout Plain Layout
8890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8893 \begin_layout Plain Layout
8901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8904 \begin_layout Plain Layout
8912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8915 \begin_layout Plain Layout
8916 \begin_inset Formula $\uparrow$
8926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8929 \begin_layout Plain Layout
8937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8940 \begin_layout Plain Layout
8941 \begin_inset Formula $\Uparrow$
8951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8954 \begin_layout Plain Layout
8962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8965 \begin_layout Plain Layout
8966 \begin_inset Formula $\updownarrow$
8976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8979 \begin_layout Plain Layout
8987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8990 \begin_layout Plain Layout
8991 \begin_inset Formula $\Updownarrow$
9001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9004 \begin_layout Plain Layout
9012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9015 \begin_layout Plain Layout
9016 \begin_inset Formula $\Downarrow$
9026 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9029 \begin_layout Plain Layout
9037 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9040 \begin_layout Plain Layout
9041 \begin_inset Formula $\downarrow$
9055 \begin_inset space \hfill{}
9059 \begin_inset Tabular
9060 <lyxtabular version="3" rows="5" columns="2">
9062 <column alignment="center" valignment="top" width="0pt">
9063 <column alignment="center" valignment="top" width="0pt">
9065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9068 \begin_layout Plain Layout
9074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9077 \begin_layout Plain Layout
9085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9088 \begin_layout Plain Layout
9096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9099 \begin_layout Plain Layout
9100 \begin_inset Formula $\nearrow$
9110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9113 \begin_layout Plain Layout
9121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9124 \begin_layout Plain Layout
9125 \begin_inset Formula $\searrow$
9135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9138 \begin_layout Plain Layout
9146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9149 \begin_layout Plain Layout
9150 \begin_inset Formula $\swarrow$
9160 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9163 \begin_layout Plain Layout
9171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9174 \begin_layout Plain Layout
9175 \begin_inset Formula $\nwarrow$
9189 \begin_inset space \hfill{}
9195 \begin_layout Standard
9196 \begin_inset VSpace medskip
9199 Vertical arrows can be used also as delimiter together with the commands
9201 \begin_inset CommandInset ref
9203 reference "sub:Manual-Bracket-Size"
9208 \begin_inset CommandInset ref
9210 reference "sub:Automatic-Bracket-Size"
9217 \begin_layout Standard
9218 \begin_inset Newpage newpage
9224 \begin_layout Section
9226 \begin_inset CommandInset label
9236 \begin_layout Plain Layout
9245 \begin_layout Standard
9246 Accents can be inserted via the math toolbar button
9247 \begin_inset Graphics
9248 filename ../images/math/hat.png
9253 or the commands listed in the following subsections.
9256 \begin_layout Subsection
9257 Accents for one Character
9261 \begin_layout Plain Layout
9274 \begin_layout Plain Layout
9276 \begin_inset CommandInset ref
9278 reference "sub:Accents-in-Text"
9291 \begin_layout Plain Layout
9299 \begin_inset Note Note
9302 \begin_layout Plain Layout
9305 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9308 \begin_layout Plain Layout
9311 texorpdfstring is in section
9312 \begin_inset CommandInset ref
9314 reference "sub:Formulas-in-Section"
9324 \begin_inset CommandInset label
9326 name "sub:Accents-for-one"
9334 \begin_layout Plain Layout
9335 Accents ! for one character
9343 \begin_layout Standard
9344 \begin_inset space \hfill{}
9348 \begin_inset Tabular
9349 <lyxtabular version="3" rows="8" columns="2">
9351 <column alignment="center" valignment="top" width="0pt">
9352 <column alignment="center" valignment="top" width="0pt">
9354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9357 \begin_layout Plain Layout
9363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9366 \begin_layout Plain Layout
9368 \begin_inset Note Note
9371 \begin_layout Plain Layout
9378 is only used as spacer.
9390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9393 \begin_layout Plain Layout
9400 \begin_layout Plain Layout
9414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9417 \begin_layout Plain Layout
9418 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9428 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9431 \begin_layout Plain Layout
9438 \begin_layout Plain Layout
9452 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9455 \begin_layout Plain Layout
9456 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9466 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9469 \begin_layout Plain Layout
9476 \begin_layout Plain Layout
9490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9493 \begin_layout Plain Layout
9494 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9507 \begin_layout Plain Layout
9515 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9518 \begin_layout Plain Layout
9519 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9532 \begin_layout Plain Layout
9539 \begin_layout Plain Layout
9552 \begin_layout Plain Layout
9563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9566 \begin_layout Plain Layout
9567 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9580 \begin_layout Plain Layout
9587 \begin_layout Plain Layout
9601 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9604 \begin_layout Plain Layout
9605 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9618 \begin_layout Plain Layout
9625 \begin_layout Plain Layout
9639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9642 \begin_layout Plain Layout
9643 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9657 \begin_inset space \hfill{}
9661 \begin_inset Tabular
9662 <lyxtabular version="3" rows="7" columns="2">
9664 <column alignment="center" valignment="top" width="0pt">
9665 <column alignment="center" valignment="top" width="0pt">
9667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9670 \begin_layout Plain Layout
9676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9679 \begin_layout Plain Layout
9687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9690 \begin_layout Plain Layout
9697 \begin_layout Plain Layout
9711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9714 \begin_layout Plain Layout
9715 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9725 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9728 \begin_layout Plain Layout
9735 \begin_layout Plain Layout
9749 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9752 \begin_layout Plain Layout
9753 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9766 \begin_layout Plain Layout
9773 \begin_layout Plain Layout
9787 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9790 \begin_layout Plain Layout
9791 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9804 \begin_layout Plain Layout
9811 \begin_layout Plain Layout
9825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9828 \begin_layout Plain Layout
9829 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9842 \begin_layout Plain Layout
9849 \begin_layout Plain Layout
9863 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9866 \begin_layout Plain Layout
9867 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9877 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9880 \begin_layout Plain Layout
9887 \begin_layout Plain Layout
9901 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9904 \begin_layout Plain Layout
9905 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9919 \begin_inset space \hfill{}
9925 \begin_layout Standard
9926 \begin_inset VSpace bigskip
9933 \begin_layout Plain Layout
9939 in formulas, a quotation mark is inserted before the vowel.
9940 These two characters are then treated by LaTeX as
9944 character when the formula part with the umlaut is marked as German.
9952 \begin_inset Quotes eld
9956 \begin_inset Quotes erd
9959 umlauts are created as demonstrated in the following example:
9962 \begin_layout Standard
9963 \begin_inset VSpace -2mm
9969 \begin_layout Standard
9971 \begin_inset Tabular
9972 <lyxtabular version="3" rows="3" columns="2">
9974 <column alignment="center" valignment="top" width="0">
9975 <column alignment="center" valignment="top" width="0">
9977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9980 \begin_layout Plain Layout
9986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9989 \begin_layout Plain Layout
9991 \begin_inset Note Note
9994 \begin_layout Plain Layout
10001 is only used as spacer.
10013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10016 \begin_layout Plain Layout
10019 \begin_inset Quotes grd
10027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10030 \begin_layout Plain Layout
10033 \begin_inset Formula $"i$
10043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10046 \begin_layout Plain Layout
10053 \begin_layout Plain Layout
10067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10070 \begin_layout Plain Layout
10071 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10087 \begin_layout Standard
10088 Another advantage to
10094 is that umlauts can directly be converted to mathematical text because
10095 the accent commands above are
10101 in mathematical text
10104 To convert an accented character to mathematical text, only the character
10105 under the accent may be converted.
10106 This applies also for all other conversions, e.
10107 \begin_inset space \thinspace{}
10111 \begin_inset space ~
10117 \begin_layout Standard
10118 In mathematical text, umlauts and other accented characters can directly
10122 \begin_layout Subsection
10123 Accents for Operators
10127 \begin_layout Plain Layout
10128 Accents ! for operators
10136 \begin_layout Standard
10147 \begin_layout Plain Layout
10165 \begin_layout Plain Layout
10173 characters can be placed above or below an operator, respectively, to accent
10185 \begin_layout Plain Layout
10193 characters can be set before and behind an operator.
10194 The command scheme is:
10197 \begin_layout Standard
10213 \begin_layout Standard
10220 must always be before the operator that should be accented.
10221 You can accent with several characters and even with other operators and
10229 for example only characters behind an operator, write nothing between the
10230 first braces but don't omit the braces.
10233 \begin_layout Standard
10234 For example the command
10239 \begin_inset Formula $\to$
10249 \begin_inset Formula $\to$
10258 \begin_layout Plain Layout
10274 \begin_inset Formula \[
10275 \sideset{}{'}\sum_{k=1}^{n}\]
10282 \begin_layout Standard
10291 \begin_layout Plain Layout
10306 \begin_layout Plain Layout
10318 \begin_inset Formula $\uparrow$
10326 \begin_inset Formula \[
10327 \overset{a}{\maltese}\]
10331 As seen in the last example, with
10343 also symbols and characters can be accented; with
10349 this is not possible.
10352 \begin_layout Subsection
10353 Accents for several Characters
10354 \begin_inset CommandInset label
10356 name "sub:Accents-for-several"
10364 \begin_layout Plain Layout
10365 Accents ! for several characters
10373 \begin_layout Standard
10374 \begin_inset space \hfill{}
10378 \begin_inset Tabular
10379 <lyxtabular version="3" rows="5" columns="2">
10381 <column alignment="center" valignment="top" width="0pt">
10382 <column alignment="center" valignment="top" width="0pt">
10384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10387 \begin_layout Plain Layout
10393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10396 \begin_layout Plain Layout
10398 \begin_inset Note Note
10401 \begin_layout Plain Layout
10408 is only used as spacer.
10420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10423 \begin_layout Plain Layout
10430 \begin_layout Plain Layout
10444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10447 \begin_layout Plain Layout
10448 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10458 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10461 \begin_layout Plain Layout
10468 \begin_layout Plain Layout
10482 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10485 \begin_layout Plain Layout
10486 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10496 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10499 \begin_layout Plain Layout
10506 \begin_layout Plain Layout
10520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10523 \begin_layout Plain Layout
10524 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10537 \begin_layout Plain Layout
10540 underleftrightarrow
10544 \begin_layout Plain Layout
10558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10561 \begin_layout Plain Layout
10562 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10576 \begin_inset space \hfill{}
10580 \begin_inset Tabular
10581 <lyxtabular version="3" rows="5" columns="2">
10583 <column alignment="center" valignment="top" width="0pt">
10584 <column alignment="center" valignment="top" width="0pt">
10586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10589 \begin_layout Plain Layout
10595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10598 \begin_layout Plain Layout
10606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10609 \begin_layout Plain Layout
10616 \begin_layout Plain Layout
10630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10633 \begin_layout Plain Layout
10634 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10647 \begin_layout Plain Layout
10654 \begin_layout Plain Layout
10668 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10671 \begin_layout Plain Layout
10672 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10685 \begin_layout Plain Layout
10692 \begin_layout Plain Layout
10706 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10709 \begin_layout Plain Layout
10710 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10720 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10723 \begin_layout Plain Layout
10730 \begin_layout Plain Layout
10744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10747 \begin_layout Plain Layout
10748 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10762 \begin_inset space \hfill{}
10768 \begin_layout Standard
10769 \begin_inset VSpace medskip
10772 With these commands as many characters as you like can be accented.
10785 will only be set in the output with a length of three characters, as shown
10786 in the following example:
10787 \begin_inset Formula \[
10788 \widetilde{A+B=C-D}\]
10795 \begin_layout Standard
10806 \begin_layout Plain Layout
10824 \begin_layout Plain Layout
10832 described in the previous subsection it is also possible to accent several
10842 \begin_layout Plain Layout
10852 \begin_inset Formula $\downarrow$
10858 \begin_inset Formula \[
10859 \underset{***}{A=B}\]
10866 \begin_layout Section
10868 \begin_inset CommandInset label
10878 \begin_layout Plain Layout
10887 \begin_layout Subsection
10889 \begin_inset CommandInset label
10891 name "sub:Predefined-Space"
10899 \begin_layout Plain Layout
10900 Space ! horizontal ! predefined
10908 \begin_layout Standard
10909 Sometimes it is necessary to insert horizontal space to a formula.
10910 This is done by inserting a protected space (shortcut
10916 \begin_inset Quotes eld
10926 \begin_layout Plain Layout
10939 \begin_inset Quotes erd
10942 appears and by pressing
10946 several times one can select one of eight different space sizes.
10947 The spaces can also be inserted using the math toolbar button
10948 \begin_inset Graphics
10949 filename ../images/math/space.png
10954 or special commands.
10955 Independent from the inserted command, one can select the size again by
10963 \begin_layout Standard
10966 \begin_inset VSpace -5mm
10970 \begin_inset Tabular
10971 <lyxtabular version="3" rows="3" columns="7">
10973 <column alignment="center" valignment="middle" width="6.8cm">
10974 <column alignment="center" valignment="top" width="0">
10975 <column alignment="center" valignment="top" width="0">
10976 <column alignment="center" valignment="top" width="0">
10977 <column alignment="center" valignment="top" width="0">
10978 <column alignment="center" valignment="top" width="0">
10979 <column alignment="center" valignment="top" width="0">
10981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10984 \begin_layout Plain Layout
10990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10993 \begin_layout Plain Layout
11001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11004 \begin_layout Plain Layout
11012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11015 \begin_layout Plain Layout
11023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11026 \begin_layout Plain Layout
11034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11037 \begin_layout Plain Layout
11045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11048 \begin_layout Plain Layout
11058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11061 \begin_layout Plain Layout
11066 keystrokes after inserting the protected space
11071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11074 \begin_layout Plain Layout
11080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11083 \begin_layout Plain Layout
11089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11092 \begin_layout Plain Layout
11098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11101 \begin_layout Plain Layout
11107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11110 \begin_layout Plain Layout
11116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11119 \begin_layout Plain Layout
11127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11130 \begin_layout Plain Layout
11136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11139 \begin_layout Plain Layout
11140 \begin_inset Formula $A\, B$
11148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11151 \begin_layout Plain Layout
11152 \begin_inset Formula $A\: B$
11160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11163 \begin_layout Plain Layout
11164 \begin_inset Formula $A\; B$
11172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11175 \begin_layout Plain Layout
11176 \begin_inset Formula $A\quad B$
11184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11187 \begin_layout Plain Layout
11188 \begin_inset Formula $A\qquad B$
11196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11199 \begin_layout Plain Layout
11200 \begin_inset Formula $A\! B$
11216 \begin_layout Standard
11217 The last size seem to produce no space.
11218 It is displayed red in LyX contrary to the other sizes, because it is a
11220 There are two more negative spaces:
11223 \begin_layout Standard
11225 \begin_inset Tabular
11226 <lyxtabular version="3" rows="3" columns="3">
11228 <column alignment="center" valignment="middle" width="6.8cm">
11229 <column alignment="center" valignment="top" width="0pt">
11230 <column alignment="center" valignment="top" width="0pt">
11232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11235 \begin_layout Plain Layout
11241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11244 \begin_layout Plain Layout
11252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11255 \begin_layout Plain Layout
11265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11268 \begin_layout Plain Layout
11273 keystrokes after inserting the protected space
11278 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11281 \begin_layout Plain Layout
11287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11290 \begin_layout Plain Layout
11298 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11301 \begin_layout Plain Layout
11307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11310 \begin_layout Plain Layout
11311 \begin_inset Formula $A\negmedspace B$
11319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11322 \begin_layout Plain Layout
11323 \begin_inset Formula $A\negthickspace B$
11339 \begin_layout Standard
11340 Negative spaces can lead to characters overlapping each other.
11341 Thus they can be used to enforce ligatures, what is e.
11342 \begin_inset space \thinspace{}
11346 \begin_inset space ~
11349 useful for summation operators:
11352 \begin_layout Standard
11354 \begin_inset Tabular
11355 <lyxtabular version="3" rows="3" columns="2">
11357 <column alignment="center" valignment="top" width="0">
11358 <column alignment="center" valignment="top" width="0">
11360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11363 \begin_layout Plain Layout
11369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11372 \begin_layout Plain Layout
11374 \begin_inset Note Note
11377 \begin_layout Plain Layout
11384 is only used as spacer.
11396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11399 \begin_layout Plain Layout
11408 \begin_layout Plain Layout
11422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11425 \begin_layout Plain Layout
11426 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11439 \begin_layout Plain Layout
11450 \begin_layout Plain Layout
11464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11467 \begin_layout Plain Layout
11468 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11484 \begin_layout Standard
11485 Relations like for example equal signs, are always surrounded by space.
11486 To suppress this, the equal sign is placed into a TeX-brace.
11487 The following example demonstrates this:
11490 \begin_layout Standard
11492 \begin_inset Tabular
11493 <lyxtabular version="3" rows="2" columns="2">
11495 <column alignment="center" valignment="top" width="0pt">
11496 <column alignment="center" valignment="top" width="0pt">
11498 <cell alignment="center" valignment="top" usebox="none">
11501 \begin_layout Plain Layout
11507 <cell alignment="center" valignment="top" usebox="none">
11510 \begin_layout Plain Layout
11511 \begin_inset Formula $A=B$
11521 <cell alignment="center" valignment="top" usebox="none">
11524 \begin_layout Plain Layout
11525 \begin_inset Note Note
11528 \begin_layout Plain Layout
11535 is only used as spacer.
11541 \begin_inset Formula $\raisebox{5mm}{}$
11544 equation without space
11549 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11552 \begin_layout Plain Layout
11553 \begin_inset Formula $A{=}B$
11569 \begin_layout Standard
11571 The command for the last formula is:
11576 \begin_inset Formula $\to$
11582 \begin_layout Standard
11583 \begin_inset VSpace bigskip
11586 Spaces are needed for physical units, because the space between the value
11587 and the unit is the smallest one and not a normal space.
11588 For units in text, the smallest space is inserted via the menu
11590 Insert\SpecialChar \menuseparator
11591 Formatting\SpecialChar \menuseparator
11593 \begin_inset space ~
11605 \begin_layout Standard
11606 An example to visualize the difference:
11609 \begin_layout Standard
11610 \begin_inset Tabular
11611 <lyxtabular version="3" rows="2" columns="2">
11613 <column alignment="left" valignment="top" width="0">
11614 <column alignment="left" valignment="top" width="0">
11616 <cell alignment="center" valignment="top" usebox="none">
11619 \begin_layout Plain Layout
11621 \begin_inset Formula $\cdot$
11629 <cell alignment="center" valignment="top" usebox="none">
11632 \begin_layout Plain Layout
11633 space between value and unit
11640 <cell alignment="center" valignment="top" usebox="none">
11643 \begin_layout Plain Layout
11645 \begin_inset space \thinspace{}
11649 \begin_inset Formula $\cdot$
11657 <cell alignment="center" valignment="top" usebox="none">
11660 \begin_layout Plain Layout
11661 smallest space between value and unit
11674 \begin_layout Subsection
11679 \begin_layout Plain Layout
11692 \begin_layout Plain Layout
11693 for vertical space in formulas see
11694 \begin_inset CommandInset ref
11696 reference "sub:Line-Separation"
11709 \begin_layout Plain Layout
11717 \begin_inset Note Note
11720 \begin_layout Plain Layout
11723 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11726 \begin_layout Plain Layout
11729 texorpdfstring is in section
11730 \begin_inset CommandInset ref
11732 reference "sub:Formulas-in-Section"
11742 \begin_inset CommandInset label
11744 name "sub:Variable-Space"
11752 \begin_layout Plain Layout
11753 Space ! horizontal ! variable
11761 \begin_layout Standard
11762 Space with a defined length can be inserted in LyX with the command
11763 \begin_inset Newline newline
11776 \begin_layout Plain Layout
11785 For the length all units listed in
11786 \begin_inset CommandInset ref
11788 reference "tab:Available-units"
11792 are allowed, except of the unit
11793 \begin_inset Quotes eld
11797 \begin_inset Quotes erd
11801 The length may also be negative.
11802 To insert so many space that the formula uses all available space, the
11813 \begin_layout Plain Layout
11824 \begin_layout Standard
11825 \begin_inset VSpace -1mm
11831 \begin_layout Standard
11833 \begin_inset Tabular
11834 <lyxtabular version="3" rows="4" columns="2">
11836 <column alignment="center" valignment="top" width="0">
11837 <column alignment="center" valignment="top" width="0">
11839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11842 \begin_layout Plain Layout
11848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11851 \begin_layout Plain Layout
11859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11862 \begin_layout Plain Layout
11866 \begin_inset Formula $\to$
11876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11879 \begin_layout Plain Layout
11880 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11893 \begin_layout Plain Layout
11897 \begin_inset Formula $\to$
11907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11910 \begin_layout Plain Layout
11911 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11924 \begin_layout Plain Layout
11931 \begin_layout Plain Layout
11945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11948 \begin_layout Plain Layout
11949 \begin_inset Formula $A=A\hfill B=B$
11965 \begin_layout Standard
11966 In the last example the available space is given by the longest column entry
11968 In an inline formula the space depends on the length of the line in which
11976 Thus, when the line uses the full width, no space will be created.
11983 only has an effect on displayed formulas when the formula style
11988 (Formula styles are explained in
11989 \begin_inset CommandInset ref
11991 reference "sec:Formula-Styles"
11998 \begin_layout Standard
12005 , there are the commands
12017 that fill the space with a pattern, see
12018 \begin_inset CommandInset ref
12020 reference "sub:Ellipses"
12027 \begin_layout Standard
12028 For text, variable space can be inserted via the menu
12030 Insert\SpecialChar \menuseparator
12031 Formatting\SpecialChar \menuseparator
12033 \begin_inset space ~
12038 , what is not possible in formulas:
12041 \begin_layout Standard
12042 This is a line with
12043 \begin_inset space \hspace{}
12048 \begin_inset space \thinspace{}
12054 \begin_layout Standard
12055 This is a line with
12056 \begin_inset space \hfill{}
12062 \begin_layout Subsection
12063 Space besides inline Formulas
12067 \begin_layout Plain Layout
12068 Space ! besides inline formulas
12076 \begin_layout Standard
12077 The space that surrounds inline formulas can be adjusted with the length
12086 \begin_layout Plain Layout
12097 The value of a length is set with the command
12105 \begin_layout Plain Layout
12115 that has the following scheme:
12118 \begin_layout Standard
12123 setlength{length name}{value}
12126 \begin_layout Standard
12134 \begin_inset space \thinspace{}
12140 \begin_layout Standard
12150 \begin_layout Standard
12151 is inserted in TeX-mode.
12153 \begin_inset space \thinspace{}
12156 mm space will now be set around all inline formulas:
12160 \begin_layout Plain Layout
12174 \begin_layout Standard
12175 This is a line with an inline formula
12176 \begin_inset Formula $A=B$
12180 \begin_inset space \thinspace{}
12183 mm surrounding space.
12187 \begin_layout Plain Layout
12201 \begin_layout Standard
12202 To return to the predefined value,
12208 is set to the value 0
12209 \begin_inset space \thinspace{}
12215 \begin_layout Section
12220 \begin_layout Plain Layout
12230 \begin_layout Plain Layout
12235 \begin_layout Plain Layout
12246 \begin_layout Plain Layout
12261 \begin_layout Standard
12262 Boxes for text are described in chapter
12269 \begin_inset space ~
12277 \begin_layout Subsection
12279 \begin_inset CommandInset label
12281 name "sub:Boxes-with-Frame"
12289 \begin_layout Plain Layout
12298 \begin_layout Standard
12299 It is possible to frame formulas or parts of it with the commands
12309 \begin_layout Plain Layout
12327 \begin_layout Plain Layout
12338 \begin_layout Standard
12339 When one of these commands is inserted to a formula, a blue box appears
12340 within a frame to enter formula parts.
12347 an additional formula has to be created by
12355 \begin_layout Plain Layout
12356 Due to a bug in LyX it is not possible to create a new formula with
12361 \begin_inset CommandInset href
12363 name "LyX-bug #1435"
12364 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12373 , because the box content will otherwise be treated as mathematical text.
12380 is used, a new formula is automatically created inside the frame.
12383 \begin_layout Standard
12390 is not suitable to frame displayed formulas, because the formula will always
12391 be set in the size of the text.
12398 is in contrary not suitable to frame inline formulas, because the formula
12399 will always be set in the size of a displayed formula.
12402 \begin_layout Standard
12409 there is the command
12419 \begin_layout Plain Layout
12427 where additionally the frame width and the alignment can be specified.
12434 is used in the following scheme:
12437 \begin_layout Standard
12442 framebox[frame width][position]{box content}
12445 \begin_layout Standard
12446 The position can either be
12463 right aligns the formula in the box.
12464 When no position is given, the formula will be centered.
12465 \begin_inset Newline newline
12468 Is no width given, also no position can be given.
12469 In this case the frame width is adjusted to the box content like for
12478 \begin_layout Standard
12485 is inserted, a box appears containing three blue boxes.
12486 The first two boxes are surrounded by brackets and denote the two optional
12488 The third box is for formula parts like for
12497 \begin_layout Standard
12499 \begin_inset Note Note
12502 \begin_layout Plain Layout
12503 The table has been set into a minipage to make the footnote appearing.
12504 Otherwise the footnote text would not be displayed.
12510 \begin_inset Box Frameless
12519 height_special "totalheight"
12522 \begin_layout Plain Layout
12524 \begin_inset Tabular
12525 <lyxtabular version="3" rows="5" columns="2">
12527 <column alignment="center" valignment="top" width="0">
12528 <column alignment="center" valignment="top" width="0">
12530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12533 \begin_layout Plain Layout
12538 \begin_layout Plain Layout
12539 Due to a bug in LyX it is not possible to create a new formula with
12544 \begin_inset CommandInset href
12546 name "LyX-bug #1435"
12547 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12564 \begin_layout Plain Layout
12566 \begin_inset Note Note
12569 \begin_layout Plain Layout
12576 is only used as spacer.
12588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12591 \begin_layout Plain Layout
12598 \begin_layout Plain Layout
12617 \begin_layout Plain Layout
12631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12634 \begin_layout Plain Layout
12635 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
12646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12649 \begin_layout Plain Layout
12656 \begin_layout Plain Layout
12671 \begin_layout Plain Layout
12685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12688 \begin_layout Plain Layout
12689 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12702 \begin_layout Plain Layout
12709 \begin_layout Plain Layout
12723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12726 \begin_layout Plain Layout
12727 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12740 \begin_layout Plain Layout
12747 \begin_layout Plain Layout
12757 \begin_inset Formula $\to$
12761 \begin_inset Formula $\to$
12774 \begin_layout Plain Layout
12784 \begin_inset Formula $\downarrow$
12792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12795 \begin_layout Plain Layout
12796 \begin_inset Formula $\raisebox{6mm}{}$
12800 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12804 \begin_inset Formula $\raisebox{-4mm}{}$
12825 \begin_layout Standard
12826 The frame thickness can also be adjusted.
12827 To do this the following commands have to be inserted in TeX-mode before
12831 \begin_layout Standard
12841 \begin_inset Quotes eld
12845 \begin_inset Quotes erd
12859 \begin_inset Quotes eld
12863 \begin_inset Quotes erd
12869 \begin_layout Standard
12870 \begin_inset Quotes eld
12874 \begin_inset Quotes erd
12877 specifies the minimal distance between the frame and the first character
12879 An example for this is the following framed formula:
12883 \begin_layout Plain Layout
12895 \begin_inset Formula \[
12900 Before this formula the commands
12903 \begin_layout Standard
12925 \begin_layout Standard
12926 were inserted in TeX-mode.
12927 The given values are used for all following boxes.
12930 \begin_layout Standard
12931 To return to the standard frame size, the command
12934 \begin_layout Standard
12959 \begin_layout Plain Layout
12973 \begin_layout Standard
12974 is inserted in TeX-mode before the next formula.
12977 \begin_layout Subsection
12978 Boxes without Frame
12979 \begin_inset CommandInset label
12981 name "sub:Boxes-without-Frame"
12989 \begin_layout Plain Layout
12990 Boxes ! without frame
12998 \begin_layout Standard
12999 For boxes without a frame there are the following box commands:
13009 \begin_layout Plain Layout
13027 \begin_layout Plain Layout
13045 \begin_layout Plain Layout
13056 \begin_layout Standard
13063 a box can be super- or subscripted.
13064 But in contrary to normal super- and subscripting, the characters in the
13065 box keep their font size.
13072 is used in the following scheme:
13075 \begin_layout Standard
13080 raisebox{height}{box content}
13083 \begin_layout Standard
13084 When the box should contain a formula, an extra formula is needed like for
13094 \begin_layout Standard
13096 \begin_inset Tabular
13097 <lyxtabular version="3" rows="4" columns="2">
13099 <column alignment="center" valignment="top" width="0">
13100 <column alignment="center" valignment="top" width="0">
13102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13105 \begin_layout Plain Layout
13111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13114 \begin_layout Plain Layout
13122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13125 \begin_layout Plain Layout
13129 \begin_inset Formula $\to$
13135 \begin_inset Formula $\to$
13143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13146 \begin_layout Plain Layout
13147 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13160 \begin_layout Plain Layout
13164 \begin_inset Formula $\to$
13170 \begin_inset Formula $\to$
13178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13181 \begin_layout Plain Layout
13182 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13195 \begin_layout Plain Layout
13199 \begin_inset Formula $\to$
13214 \begin_layout Plain Layout
13228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13231 \begin_layout Plain Layout
13235 \begin_layout Plain Layout
13259 \begin_layout Standard
13260 The last formula can currently only be created using TeX-mode because LyX
13261 inserts a box instead of the needed extra formula.
13265 \begin_layout Plain Layout
13267 \begin_inset CommandInset href
13269 name "LyX-bug #1435"
13270 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13282 \begin_layout Standard
13307 , with the difference that there is no frame.
13310 \begin_layout Subsection
13312 \begin_inset CommandInset label
13314 name "sub:Colored-Boxes"
13322 \begin_layout Plain Layout
13331 \begin_layout Standard
13332 To be able to use all commands explained in this section, the LaTeX-package
13341 \begin_layout Plain Layout
13346 is part of every LaTeX standard installation.
13355 \begin_layout Plain Layout
13361 has to be loaded in the LaTeX-preamble with the line
13365 \begin_layout Plain Layout
13366 When text is colored somewhere in the document with a predefined color,
13367 LyX loads the LaTeX-package
13372 Thus it is possible that the package is loaded twice, but this doesn't
13379 \begin_inset Note Note
13382 \begin_layout Plain Layout
13383 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13392 \begin_layout Standard
13400 \begin_layout Standard
13401 \begin_inset VSpace medskip
13404 To color boxes, the command
13414 \begin_layout Plain Layout
13422 is used in the following scheme:
13425 \begin_layout Standard
13430 colorbox{color}{box content}
13433 \begin_layout Standard
13434 The box content can also be a box and a
13440 can also be part of another box (see the 2nd and 3rd example).
13441 When the box should contain a formula, an extra formula has to be created,
13452 \begin_layout Plain Layout
13453 This also applies for the command
13461 \begin_inset CommandInset href
13463 name "LyX-bug #1435"
13464 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13476 \begin_layout Standard
13477 One of the following predefined colors can be chosen:
13480 \begin_layout Standard
13514 \begin_layout Standard
13516 \begin_inset Tabular
13517 <lyxtabular version="3" rows="4" columns="2">
13519 <column alignment="center" valignment="top" width="0">
13520 <column alignment="center" valignment="top" width="0">
13522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13525 \begin_layout Plain Layout
13531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13534 \begin_layout Plain Layout
13536 \begin_inset Note Note
13539 \begin_layout Plain Layout
13546 is only used as spacer.
13558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13561 \begin_layout Plain Layout
13565 \begin_inset Formula $\to$
13575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13578 \begin_layout Plain Layout
13579 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13592 \begin_layout Plain Layout
13596 \begin_inset Formula $\to$
13607 \begin_layout Plain Layout
13621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13624 \begin_layout Plain Layout
13625 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13638 \begin_layout Plain Layout
13645 \begin_layout Plain Layout
13657 \begin_inset Formula $\to$
13667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13670 \begin_layout Plain Layout
13671 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13687 \begin_layout Standard
13694 only colors the box but not the characters in the box.
13695 To color all characters, the whole formula is highlighted and the wanted
13696 color is chosen in the
13699 \begin_inset space ~
13705 The dialog can be called with the toolbar button
13706 \begin_inset Graphics
13707 filename ../images/dialog-show_character.png
13714 Edit\SpecialChar \menuseparator
13716 \begin_inset space ~
13719 Style\SpecialChar \menuseparator
13723 The formula number has then the same color as the formula.
13724 When the formula number should get another color than the formula characters,
13725 the color must be changed within the formula.
13728 \begin_layout Standard
13732 \begin_layout Standard
13735 \begin_inset Formula \begin{equation}
13736 \int A=B\label{eq:red}\end{equation}
13743 \begin_inset Formula \begin{equation}
13744 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13751 \begin_layout Standard
13753 \begin_inset CommandInset ref
13759 is completely colored red.
13760 \begin_inset Newline newline
13764 \begin_inset CommandInset ref
13766 reference "eq:redgreen"
13770 was first completely colored green to set the color for the formula number.
13771 Subsequently the formula characters were colored red.
13774 \begin_layout Standard
13775 \begin_inset VSpace bigskip
13778 To color the frame different than the rest of the box, the command
13788 \begin_layout Plain Layout
13796 is used in the following scheme:
13799 \begin_layout Standard
13804 fcolorbox{frame color}{color}{box content}
13807 \begin_layout Standard
13814 is an extension of the command
13821 The frame width is set, like for
13844 \begin_layout Plain Layout
13856 \begin_inset Formula \[
13857 \fcolorbox{cyan}{magenta}{A=B}\]
13865 \begin_layout Plain Layout
13879 \begin_layout Standard
13880 This formula was created with the command
13881 \begin_inset Newline newline
13889 \begin_inset Formula $\to$
13895 \begin_inset Formula $\to$
13905 \begin_layout Standard
13906 \begin_inset VSpace bigskip
13909 To use other colors than the predefined ones, they have to be defined first.
13912 \begin_layout Standard
13913 One can for example define the color
13914 \begin_inset Quotes eld
13922 \begin_inset Quotes erd
13925 with the LaTeX-preamble line:
13928 \begin_layout Standard
13933 definecolor{darkgreen}{cmyk}{0.5,
13951 \begin_layout Plain Layout
13962 \begin_layout Standard
13967 is the color space that denotes the colors
13984 The four comma separated numbers are the portion factor for the corresponding
13985 colors of the color space.
13986 The factors can be in the range of 0
13987 \begin_inset space \thinspace{}
13991 \begin_inset space \thinspace{}
13999 also the color space
14003 can be used for definitions.
14020 , so that there are in this case three portion factors for the corresponding
14022 Furthermore there is the color space
14026 with one portion factor for the gray value.
14029 \begin_layout Standard
14030 As example a framed box with the new defined color
14034 where the characters have been colored
14039 \begin_inset Formula \begin{equation}
14040 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14047 \begin_layout Standard
14048 Self-defined colors can also be used for text with the help of the command
14059 \begin_layout Plain Layout
14068 \begin_layout Standard
14072 \begin_layout Plain Layout
14076 textcolor{darkgreen}{
14082 \begin_inset Quotes eld
14086 \begin_inset Quotes erd
14093 \begin_layout Plain Layout
14103 \begin_layout Standard
14114 \begin_layout Plain Layout
14122 is used in the scheme
14126 textcolor{color}{characters to color}
14131 \begin_layout Subsection
14133 \begin_inset CommandInset label
14135 name "sub:Paragraph-Boxes"
14143 \begin_layout Plain Layout
14144 Boxes ! as paragraph
14152 \begin_layout Standard
14153 A box that can contain several lines and paragraphs, a so called paragraph
14154 box (parbox), can be created with the menu
14156 Insert\SpecialChar \menuseparator
14159 or the toolbar button
14160 \begin_inset Graphics
14161 filename ../images/box-insert.png
14169 \begin_layout Standard
14170 The following example shows a framed parbox in a line:
14173 \begin_layout Standard
14174 \begin_inset VSpace medskip
14178 \begin_inset Box Boxed
14187 height_special "totalheight"
14190 \begin_layout Plain Layout
14191 This is a paragraph box.
14193 \begin_inset space \thinspace{}
14196 cm long and can also contain formulas:
14197 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14208 \begin_layout Standard
14209 \begin_inset VSpace medskip
14215 \begin_layout Standard
14216 Such a box is created by right-clicking on the gray box inset.
14217 A dialog pops up showing the box properties.
14231 \begin_inset space \thinspace{}
14236 Vertical Box Alignment
14241 \begin_layout Standard
14242 \begin_inset VSpace medskip
14245 In LaTeX a parbox is created with the command
14255 \begin_layout Plain Layout
14263 that has the following scheme:
14266 \begin_layout Standard
14271 parbox[position]{width}{box content}
14274 \begin_layout Standard
14288 for bottom means that the box is aligned within the surrounding text with
14294 for top this is done with the first line.
14295 When no position is given, the box will be vertically centered, see section
14303 \begin_inset space ~
14308 manual for examples.
14311 \begin_layout Standard
14312 \begin_inset VSpace bigskip
14315 To frame formulas completely, including the formula number, the formula
14316 must be set into a parbox.
14317 To do this, the command
14331 is inserted in TeX-mode before the formula.
14340 \begin_layout Plain Layout
14350 is hereby the line width set for the document.
14351 Because the frame is outside the parbox, 2
14352 \begin_inset space \thinspace{}
14355 times the frame separation and the frame thickness must be subtracted from
14357 As this is not automatically done by LyX due to a bug
14361 \begin_layout Plain Layout
14362 \begin_inset CommandInset href
14364 name "LyX-bug #4483"
14365 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14374 , TeX-mode has to be used.
14375 To be able to multiply and subtract in arguments, the LaTeX-package
14383 \begin_layout Plain Layout
14388 is part of every LaTeX standard installation.
14397 \begin_layout Plain Layout
14403 must be loaded in the LaTeX-preamble with the line
14406 \begin_layout Standard
14414 \begin_layout Standard
14415 Behind the formula both boxes are closed by entering
14420 Here is an example:
14424 \begin_layout Plain Layout
14438 \begin_layout Standard
14442 \begin_layout Plain Layout
14460 \begin_inset Formula \begin{equation}
14461 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14469 \begin_layout Plain Layout
14480 \begin_layout Plain Layout
14494 \begin_layout Standard
14495 \begin_inset VSpace medskip
14498 As a parbox is used as argument of
14504 , there is in this case no difference between
14519 \begin_layout Standard
14520 \begin_inset VSpace bigskip
14523 Paragraph boxes are very useful to comment formulas directly.
14530 is used in combination with the command
14544 \begin_inset CommandInset ref
14546 reference "sub:User-defined-Numbering"
14553 \begin_layout Standard
14554 An example of a formula commented with
14563 \begin_layout Standard
14567 \begin_layout Plain Layout
14580 This is a description.
14581 It is distinctly separated from the formula and multiline.
14585 \begin_layout Plain Layout
14597 \begin_layout Standard
14598 Such a formula must be inserted completely in TeX-mode because LyX does
14599 not yet support the command
14606 The formula is created with the following command sequence:
14609 \begin_layout Standard
14622 is inserted in TeX-mode.
14626 \begin_layout Plain Layout
14627 When the formula style
14639 can also be replaced by
14646 (formula styles see
14647 \begin_inset CommandInset ref
14649 reference "sec:Formula-Styles"
14658 Then the description follows as normal text, and finally
14664 is inserted in TeX-mode.
14677 hereby create a displayed formula.
14680 \begin_layout Standard
14687 can be seen in this example that was
14688 \begin_inset Quotes eld
14692 \begin_inset Quotes erd
14695 using the mathematical textmode:
14696 \begin_inset Formula \[
14697 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14704 \begin_layout Section
14709 \begin_layout Plain Layout
14718 \begin_layout Subsection
14720 \begin_inset CommandInset label
14722 name "sub:Big-Operators"
14730 \begin_layout Plain Layout
14740 \begin_layout Plain Layout
14750 \begin_layout Plain Layout
14759 \begin_layout Standard
14760 To be able to use all integral operators listed here, the option
14762 Use esint package automatically
14764 must be set in the document settings under
14767 \begin_inset space ~
14775 \begin_layout Standard
14776 \begin_inset space \hfill{}
14780 \begin_inset Tabular
14781 <lyxtabular version="3" rows="11" columns="2">
14783 <column alignment="center" valignment="top" width="0pt">
14784 <column alignment="center" valignment="top" width="0pt">
14786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14789 \begin_layout Plain Layout
14795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14798 \begin_layout Plain Layout
14806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14809 \begin_layout Plain Layout
14816 \begin_layout Plain Layout
14829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14832 \begin_layout Plain Layout
14833 \begin_inset Formula $\sum$
14843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14846 \begin_layout Plain Layout
14853 \begin_layout Plain Layout
14866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14869 \begin_layout Plain Layout
14870 \begin_inset Formula $\int$
14880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14883 \begin_layout Plain Layout
14891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14894 \begin_layout Plain Layout
14895 \begin_inset Formula $\intop$
14905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14908 \begin_layout Plain Layout
14916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14919 \begin_layout Plain Layout
14920 \begin_inset Formula $\oint$
14930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14933 \begin_layout Plain Layout
14941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14944 \begin_layout Plain Layout
14945 \begin_inset Formula $\ointop$
14955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14958 \begin_layout Plain Layout
14966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14969 \begin_layout Plain Layout
14970 \begin_inset Formula $\ointctrclockwise$
14980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14983 \begin_layout Plain Layout
14991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14994 \begin_layout Plain Layout
14995 \begin_inset Formula $\ointclockwise$
15005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15008 \begin_layout Plain Layout
15016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15019 \begin_layout Plain Layout
15020 \begin_inset Formula $\sqint$
15030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15033 \begin_layout Plain Layout
15041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15044 \begin_layout Plain Layout
15045 \begin_inset Formula $\bigcap$
15055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15058 \begin_layout Plain Layout
15066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15069 \begin_layout Plain Layout
15070 \begin_inset Formula $\bigcup$
15084 \begin_inset space \hfill{}
15088 \begin_inset Tabular
15089 <lyxtabular version="3" rows="10" columns="2">
15091 <column alignment="center" valignment="top" width="0pt">
15092 <column alignment="center" valignment="top" width="0pt">
15094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15097 \begin_layout Plain Layout
15103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15106 \begin_layout Plain Layout
15114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15117 \begin_layout Plain Layout
15124 \begin_layout Plain Layout
15137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15140 \begin_layout Plain Layout
15141 \begin_inset Formula $\prod$
15151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15154 \begin_layout Plain Layout
15162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15165 \begin_layout Plain Layout
15166 \begin_inset Formula $\coprod$
15176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15179 \begin_layout Plain Layout
15187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15190 \begin_layout Plain Layout
15191 \begin_inset Formula $\bigodot$
15201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15204 \begin_layout Plain Layout
15212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15215 \begin_layout Plain Layout
15216 \begin_inset Formula $\bigotimes$
15226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15229 \begin_layout Plain Layout
15237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15240 \begin_layout Plain Layout
15241 \begin_inset Formula $\bigoplus$
15251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15254 \begin_layout Plain Layout
15262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15265 \begin_layout Plain Layout
15266 \begin_inset Formula $\bigwedge$
15276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15279 \begin_layout Plain Layout
15287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15290 \begin_layout Plain Layout
15291 \begin_inset Formula $\bigvee$
15301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15304 \begin_layout Plain Layout
15312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15315 \begin_layout Plain Layout
15316 \begin_inset Formula $\bigsqcup$
15326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15329 \begin_layout Plain Layout
15337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15340 \begin_layout Plain Layout
15341 \begin_inset Formula $\biguplus$
15355 \begin_inset space \hfill{}
15361 \begin_layout Standard
15362 All big operators can also be inserted via the math toolbar button
15363 \begin_inset Graphics
15364 filename ../images/math/intop.png
15372 \begin_layout Standard
15373 The operators are called big because they are bigger than the sometimes
15374 equal looking binary operators.
15375 All big operators can have limits as described in the next subsection.
15378 \begin_layout Standard
15404 \begin_inset space ~
15407 in the style the operator limits are displayed, see
15408 \begin_inset CommandInset ref
15410 reference "sub:Operator-Limits"
15418 \begin_layout Subsubsection*
15419 Advices for Integrals
15422 \begin_layout Standard
15427 in an integral is an operator, that therefore has to be set upright.
15428 This is done by highlighting the
15432 and using the keyboard shortcut
15435 \begin_inset space ~
15444 \begin_layout Plain Layout
15450 \begin_inset CommandInset ref
15452 reference "sub:Font-Styles"
15462 Finally the smallest space is inserted before the
15466 , as this is usual for operators.
15470 \begin_layout Standard
15472 \begin_inset Formula $\int A(x)dx$
15476 \begin_inset Newline newline
15483 \begin_layout Plain Layout
15493 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15499 \begin_layout Standard
15500 For multiple integrals there are the following commands:
15501 \begin_inset VSpace medskip
15507 \begin_layout Standard
15508 \begin_inset space \hfill{}
15512 \begin_inset Tabular
15513 <lyxtabular version="3" rows="4" columns="2">
15515 <column alignment="center" valignment="top" width="0">
15516 <column alignment="center" valignment="top" width="0">
15518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15521 \begin_layout Plain Layout
15527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15530 \begin_layout Plain Layout
15532 \begin_inset Note Note
15535 \begin_layout Plain Layout
15542 is only used as spacer.
15554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15557 \begin_layout Plain Layout
15565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15568 \begin_layout Plain Layout
15569 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15582 \begin_layout Plain Layout
15590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15593 \begin_layout Plain Layout
15594 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15607 \begin_layout Plain Layout
15615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15618 \begin_layout Plain Layout
15619 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15633 \begin_inset space \hfill{}
15637 \begin_inset Tabular
15638 <lyxtabular version="3" rows="4" columns="2">
15640 <column alignment="center" valignment="top" width="0">
15641 <column alignment="center" valignment="top" width="0">
15643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15646 \begin_layout Plain Layout
15652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15655 \begin_layout Plain Layout
15663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15666 \begin_layout Plain Layout
15674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15677 \begin_layout Plain Layout
15678 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15691 \begin_layout Plain Layout
15699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15702 \begin_layout Plain Layout
15703 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15716 \begin_layout Plain Layout
15724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15727 \begin_layout Plain Layout
15728 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15742 \begin_inset space \hfill{}
15748 \begin_layout Subsection
15750 \begin_inset CommandInset label
15752 name "sub:Operator-Limits"
15760 \begin_layout Plain Layout
15769 \begin_layout Standard
15770 Limits are created by super- and subscripts:
15773 \begin_layout Standard
15775 \begin_inset Tabular
15776 <lyxtabular version="3" rows="2" columns="2">
15778 <column alignment="center" valignment="top" width="0pt">
15779 <column alignment="center" valignment="top" width="0pt">
15781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15784 \begin_layout Plain Layout
15790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15793 \begin_layout Plain Layout
15795 \begin_inset Note Note
15798 \begin_layout Plain Layout
15805 is only used as spacer.
15817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15820 \begin_layout Plain Layout
15829 \begin_layout Plain Layout
15839 \begin_inset Formula $\to$
15843 \begin_inset Formula $\to$
15851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15854 \begin_layout Plain Layout
15855 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15871 \begin_layout Standard
15872 Limits of inline formulas are set right beside the operator.
15873 Limits in displayed formulas are set above or below the operator, except
15874 of integral limits.
15877 \begin_layout Standard
15878 To force that the limits are set beside the operator, the cursor is set
15879 directly behind the operator and the limits type is changed with the menu
15882 Edit\SpecialChar \menuseparator
15883 Math\SpecialChar \menuseparator
15895 \begin_inset space ~
15904 \begin_layout Standard
15905 The default limits type is this:
15906 \begin_inset Formula \[
15907 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15911 This is how it looks when the limits type was changed to
15918 \begin_inset Formula \[
15919 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15923 For integrals, except of
15935 , the limits are by default set beside the operator.
15936 But for multiple integrals the limits are often set below the operator.
15937 In the following example the limits type was therefore set to
15941 and so set below the integrals:
15942 \begin_inset Formula \begin{equation}
15943 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15950 \begin_layout Standard
15951 \begin_inset VSpace medskip
15954 To specify conditions for limits, the commands
15964 \begin_layout Plain Layout
15982 \begin_layout Plain Layout
15991 To create for example this expression
15992 \begin_inset Formula \begin{equation}
15993 \sum_{\begin{subarray}{c}
15995 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16002 \begin_layout Standard
16003 the following has to be done:
16004 \begin_inset Newline newline
16019 \begin_layout Plain Layout
16031 One is now in a blue box under the summation operator and insert there
16040 \begin_layout Plain Layout
16052 The blue box is now within a purple box and now several lines can be written
16054 A new line is created by inserting a line break (
16060 \begin_inset Newline newline
16065 0<k<1000 Ctrl-Return
16066 \begin_inset Newline newline
16071 is typed in, a new box appears below for the new line.
16074 \begin_layout Standard
16075 The alignment of the lines can be changed to left aligned with the
16085 Edit\SpecialChar \menuseparator
16089 To get right alignment,
16097 \begin_layout Plain Layout
16108 is inserted at the beginning of the line.
16111 \begin_layout Standard
16124 with the difference that the lines are always centered.
16127 \begin_layout Standard
16128 \begin_inset VSpace bigskip
16132 \begin_inset CommandInset ref
16134 reference "eq:substack"
16138 there can be too much space beside an operator, because the characters
16139 following the operator are set beside the limits.
16142 \begin_layout Standard
16143 To avoid this, the following macro can be used in the LaTeX-preamble:
16146 \begin_layout Standard
16160 \begin_inset Newline newline
16172 \begin_inset Newline newline
16179 mathclapinternal #1#2{
16183 mathsurround =0pt #1{#2}$}}
16186 \begin_layout Standard
16187 This defines the command
16197 \begin_layout Plain Layout
16205 that sets the width of the limit to 0
16206 \begin_inset space \thinspace{}
16210 The command scheme is
16213 \begin_layout Standard
16221 \begin_layout Standard
16222 where the limit can consist of several conditions.
16225 \begin_layout Standard
16227 \begin_inset CommandInset ref
16229 reference "eq:substack"
16233 , one uses the command
16236 \begin_layout Standard
16249 \begin_layout Plain Layout
16258 0<k<1000 Ctrl-Enter
16261 \begin_layout Standard
16262 to create the lower limit.
16263 The summand is now directly behind the summation operator:
16264 \begin_inset Formula \[
16265 \sum_{\mathclap{\substack{0<k<1000\\
16266 \\k\,\in\,\mathbb{N}}
16274 \begin_layout Standard
16275 \begin_inset VSpace bigskip
16278 How to use one limit for several operators is described in
16279 \begin_inset CommandInset ref
16281 reference "sub:Self-defined-Operators"
16288 \begin_layout Standard
16289 \begin_inset Newpage newpage
16295 \begin_layout Subsection
16297 \begin_inset CommandInset label
16299 name "sub:Binary-Operators"
16307 \begin_layout Plain Layout
16316 \begin_layout Standard
16317 Binary operators are surrounded by space when there is a character before
16319 \begin_inset VSpace medskip
16325 \begin_layout Standard
16326 \begin_inset space \hfill{}
16330 \begin_inset Tabular
16331 <lyxtabular version="3" rows="13" columns="2">
16333 <column alignment="center" valignment="top" width="0pt">
16334 <column alignment="center" valignment="top" width="0pt">
16336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16339 \begin_layout Plain Layout
16341 \begin_inset Note Note
16344 \begin_layout Plain Layout
16351 is only used as spacer.
16361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16364 \begin_layout Plain Layout
16372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16375 \begin_layout Plain Layout
16381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16384 \begin_layout Plain Layout
16385 \begin_inset Formula $+$
16395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16398 \begin_layout Plain Layout
16404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16407 \begin_layout Plain Layout
16408 \begin_inset Formula $-$
16418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16421 \begin_layout Plain Layout
16429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16432 \begin_layout Plain Layout
16433 \begin_inset Formula $\pm$
16443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16446 \begin_layout Plain Layout
16454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16457 \begin_layout Plain Layout
16458 \begin_inset Formula $\mp$
16468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16471 \begin_layout Plain Layout
16479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16482 \begin_layout Plain Layout
16483 \begin_inset Formula $\cdot$
16493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16496 \begin_layout Plain Layout
16504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16507 \begin_layout Plain Layout
16508 \begin_inset Formula $\times$
16518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16521 \begin_layout Plain Layout
16529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16532 \begin_layout Plain Layout
16533 \begin_inset Formula $\div$
16543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16546 \begin_layout Plain Layout
16550 \begin_layout Plain Layout
16563 \begin_layout Plain Layout
16575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16578 \begin_layout Plain Layout
16579 \begin_inset Formula $*$
16589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16592 \begin_layout Plain Layout
16600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16603 \begin_layout Plain Layout
16604 \begin_inset Formula $\star$
16614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16617 \begin_layout Plain Layout
16625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16628 \begin_layout Plain Layout
16629 \begin_inset Formula $\circ$
16639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16642 \begin_layout Plain Layout
16650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16653 \begin_layout Plain Layout
16654 \begin_inset Formula $\diamond$
16664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16667 \begin_layout Plain Layout
16675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16678 \begin_layout Plain Layout
16679 \begin_inset Formula $\bullet$
16693 \begin_inset space \hfill{}
16697 \begin_inset Tabular
16698 <lyxtabular version="3" rows="13" columns="2">
16700 <column alignment="center" valignment="top" width="0pt">
16701 <column alignment="center" valignment="top" width="0pt">
16703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16706 \begin_layout Plain Layout
16712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16715 \begin_layout Plain Layout
16723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16726 \begin_layout Plain Layout
16734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16737 \begin_layout Plain Layout
16738 \begin_inset Formula $\nabla$
16748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16751 \begin_layout Plain Layout
16759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16762 \begin_layout Plain Layout
16763 \begin_inset Formula $\bigtriangledown$
16773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16776 \begin_layout Plain Layout
16784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16787 \begin_layout Plain Layout
16788 \begin_inset Formula $\bigtriangleup$
16798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16801 \begin_layout Plain Layout
16809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16812 \begin_layout Plain Layout
16813 \begin_inset Formula $\Box$
16823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16826 \begin_layout Plain Layout
16834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16837 \begin_layout Plain Layout
16838 \begin_inset Formula $\cap$
16848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16851 \begin_layout Plain Layout
16859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16862 \begin_layout Plain Layout
16863 \begin_inset Formula $\cup$
16873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16876 \begin_layout Plain Layout
16884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16887 \begin_layout Plain Layout
16888 \begin_inset Formula $\dagger$
16898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16901 \begin_layout Plain Layout
16909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16912 \begin_layout Plain Layout
16913 \begin_inset Formula $\ddagger$
16923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16926 \begin_layout Plain Layout
16934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16937 \begin_layout Plain Layout
16938 \begin_inset Formula $\wr$
16948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16951 \begin_layout Plain Layout
16959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16962 \begin_layout Plain Layout
16963 \begin_inset Formula $\bigcirc$
16973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16976 \begin_layout Plain Layout
16984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16987 \begin_layout Plain Layout
16988 \begin_inset Formula $\wedge$
16998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17001 \begin_layout Plain Layout
17009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17012 \begin_layout Plain Layout
17013 \begin_inset Formula $\vee$
17027 \begin_inset space \hfill{}
17031 \begin_inset Tabular
17032 <lyxtabular version="3" rows="13" columns="2">
17034 <column alignment="center" valignment="top" width="0pt">
17035 <column alignment="center" valignment="top" width="0pt">
17037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17040 \begin_layout Plain Layout
17046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17049 \begin_layout Plain Layout
17057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17060 \begin_layout Plain Layout
17068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17071 \begin_layout Plain Layout
17072 \begin_inset Formula $\oplus$
17082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17085 \begin_layout Plain Layout
17093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17096 \begin_layout Plain Layout
17097 \begin_inset Formula $\ominus$
17107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17110 \begin_layout Plain Layout
17118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17121 \begin_layout Plain Layout
17122 \begin_inset Formula $\otimes$
17132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17135 \begin_layout Plain Layout
17143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17146 \begin_layout Plain Layout
17147 \begin_inset Formula $\oslash$
17157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17160 \begin_layout Plain Layout
17168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17171 \begin_layout Plain Layout
17172 \begin_inset Formula $\odot$
17182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17185 \begin_layout Plain Layout
17193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17196 \begin_layout Plain Layout
17197 \begin_inset Formula $\amalg$
17207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17210 \begin_layout Plain Layout
17218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17221 \begin_layout Plain Layout
17222 \begin_inset Formula $\uplus$
17232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17235 \begin_layout Plain Layout
17243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17246 \begin_layout Plain Layout
17247 \begin_inset Formula $\setminus$
17257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17260 \begin_layout Plain Layout
17268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17271 \begin_layout Plain Layout
17272 \begin_inset Formula $\sqcap$
17282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17285 \begin_layout Plain Layout
17293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17296 \begin_layout Plain Layout
17297 \begin_inset Formula $\sqcup$
17307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17310 \begin_layout Plain Layout
17318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17321 \begin_layout Plain Layout
17322 \begin_inset Formula $\triangleleft$
17332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17335 \begin_layout Plain Layout
17343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17346 \begin_layout Plain Layout
17347 \begin_inset Formula $\triangleright$
17361 \begin_inset space \hfill{}
17367 \begin_layout Standard
17368 All binary operators can also be inserted via the math toolbar button
17369 \begin_inset Graphics
17370 filename ../images/math/pm.png
17378 \begin_layout Standard
17379 To typeset the Laplace operator also
17396 \begin_inset Formula $\nabla^{2}$
17399 ) can be used instead of
17408 \begin_layout Standard
17415 Insert\SpecialChar \menuseparator
17427 \begin_layout Subsection
17428 Self-defined Operators
17429 \begin_inset CommandInset label
17431 name "sub:Self-defined-Operators"
17439 \begin_layout Plain Layout
17440 Operators ! self-defined
17448 \begin_layout Standard
17449 With the help of the command
17453 DeclareMathOperator
17459 \begin_layout Plain Layout
17464 DeclareMathOperator
17469 custom operators can be defined in the LaTeX-preamble.
17470 Its command scheme is:
17473 \begin_layout Standard
17478 DeclareMathOperator{new command}{display}
17481 \begin_layout Standard
17482 Display can be characters or symbols that define how the operator looks
17484 To define a big operator a * is set behind the command.
17485 All self-defined big operators can have limits as described in
17486 \begin_inset CommandInset ref
17488 reference "sub:Operator-Limits"
17495 \begin_layout Standard
17496 For example the LaTeX-preamble line
17499 \begin_layout Standard
17504 DeclareMathOperator*{
17511 \begin_layout Standard
17512 defines the command
17518 , that inserts a big operator consisting of the lozenge symbol from
17519 \begin_inset CommandInset ref
17521 reference "sub:Miscellaneous-Symbols"
17526 \begin_inset Formula \[
17527 \Lozenge_{n=1}^{\infty}\]
17531 The command for this formula is:
17542 \begin_inset Formula $\to$
17548 \begin_layout Standard
17549 \begin_inset VSpace bigskip
17552 When self-defined operators are not used several times in the document,
17553 they can also be defined with the commands
17563 \begin_layout Plain Layout
17581 \begin_layout Plain Layout
17589 , which have the following scheme:
17592 \begin_layout Standard
17606 \begin_layout Standard
17613 defines big operators,
17622 \begin_layout Standard
17630 \begin_inset space \thinspace{}
17634 \begin_inset space ~
17637 be used to use one limit for several operators:
17640 \begin_layout Standard
17641 \begin_inset Formula \[
17642 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17649 \begin_layout Standard
17650 The command for the formula above is:
17651 \begin_inset Newline newline
17670 \begin_layout Plain Layout
17682 \begin_inset Formula $\to$
17691 \begin_layout Plain Layout
17705 \begin_layout Section
17710 \begin_layout Plain Layout
17719 \begin_layout Subsection
17721 \begin_inset CommandInset label
17723 name "sub:Font-Styles"
17731 \begin_layout Plain Layout
17740 \begin_layout Standard
17741 Latin letters in formulas can be set in one of the following font styles:
17742 \begin_inset VSpace -2mm
17748 \begin_layout Standard
17750 \begin_inset Tabular
17751 <lyxtabular version="3" rows="6" columns="3">
17753 <column alignment="center" valignment="top" width="0">
17754 <column alignment="center" valignment="top" width="0">
17755 <column alignment="center" valignment="top" width="0">
17757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17760 \begin_layout Plain Layout
17766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17769 \begin_layout Plain Layout
17775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17778 \begin_layout Plain Layout
17786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17789 \begin_layout Plain Layout
17798 \begin_layout Plain Layout
17814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17817 \begin_layout Plain Layout
17818 \begin_inset Formula $\mathbb{ABC}$
17826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17829 \begin_layout Plain Layout
17837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17840 \begin_layout Plain Layout
17849 \begin_layout Plain Layout
17865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17868 \begin_layout Plain Layout
17869 \begin_inset Formula $\mathbf{AbC}$
17877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17880 \begin_layout Plain Layout
17888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17891 \begin_layout Plain Layout
17900 \begin_layout Plain Layout
17916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17919 \begin_layout Plain Layout
17920 \begin_inset Formula $\boldsymbol{AbC}$
17928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17931 \begin_layout Plain Layout
17939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17942 \begin_layout Plain Layout
17951 \begin_layout Plain Layout
17967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17970 \begin_layout Plain Layout
17971 \begin_inset Formula $\mathcal{ABC}$
17979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17982 \begin_layout Plain Layout
17990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17993 \begin_layout Plain Layout
18002 \begin_layout Plain Layout
18018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18021 \begin_layout Plain Layout
18022 \begin_inset Formula $\mathfrak{AbC}$
18030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18033 \begin_layout Plain Layout
18047 \begin_layout Standard
18049 \begin_inset Tabular
18050 <lyxtabular version="3" rows="5" columns="3">
18052 <column alignment="center" valignment="top" width="0">
18053 <column alignment="center" valignment="top" width="0">
18054 <column alignment="center" valignment="top" width="0">
18056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18059 \begin_layout Plain Layout
18065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18068 \begin_layout Plain Layout
18074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18077 \begin_layout Plain Layout
18085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18088 \begin_layout Plain Layout
18097 \begin_layout Plain Layout
18113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18116 \begin_layout Plain Layout
18117 \begin_inset Formula $\mathit{AbC}$
18125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18128 \begin_layout Plain Layout
18136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18139 \begin_layout Plain Layout
18148 \begin_layout Plain Layout
18164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18167 \begin_layout Plain Layout
18168 \begin_inset Formula $\mathrm{AbC}$
18176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18179 \begin_layout Plain Layout
18187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18190 \begin_layout Plain Layout
18199 \begin_layout Plain Layout
18215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18218 \begin_layout Plain Layout
18219 \begin_inset Formula $\mathsf{AbC}$
18227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18230 \begin_layout Plain Layout
18238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18241 \begin_layout Plain Layout
18250 \begin_layout Plain Layout
18266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18269 \begin_layout Plain Layout
18270 \begin_inset Formula $\mathtt{AbC}$
18278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18281 \begin_layout Plain Layout
18295 \begin_layout Standard
18296 \begin_inset Note Greyedout
18299 \begin_layout Plain Layout
18316 can only be used for big letters.
18324 \begin_layout Standard
18325 Predefined is the style
18334 \begin_layout Standard
18335 The style commands work also for letters in mathematical constructs:
18336 \begin_inset Formula \[
18337 \mathfrak{A=\frac{b}{C}}\]
18344 \begin_layout Standard
18345 Characters in mathematical text don't appear in a math font style but in
18346 the text font style
18353 That their style can't be set correctly via the text style dialog is a
18358 \begin_layout Plain Layout
18359 \begin_inset CommandInset href
18361 name "LyX-bug #4091"
18362 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18374 \begin_layout Standard
18375 Instead of the style commands the dialog
18377 Edit\SpecialChar \menuseparator
18378 Math\SpecialChar \menuseparator
18381 or the toolbar button
18382 \begin_inset Graphics
18383 filename ../images/math/font.png
18391 \begin_layout Subsection
18393 \begin_inset CommandInset label
18395 name "sub:Bold-Formulas"
18403 \begin_layout Plain Layout
18412 \begin_layout Standard
18413 To make a complete formula bold, the command
18419 from the previous subsection cannot be used, because it doesn't work for
18420 small Greek letters.
18421 Furthermore it prints Latin letters always upright, like in the following
18425 \begin_layout Standard
18426 \begin_inset Formula \[
18427 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18434 \begin_layout Standard
18435 To display the formula correctly, the command
18442 \begin_inset Formula \[
18443 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18447 It is also possible to set the formula in a
18449 boldmath environment
18452 This environment is created by inserting the command
18460 \begin_layout Plain Layout
18471 To end the environment, the command
18479 \begin_layout Plain Layout
18489 is inserted in TeX-mode.
18493 \begin_layout Plain Layout
18503 \begin_inset Formula \[
18504 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18512 \begin_layout Plain Layout
18524 \begin_layout Subsection
18526 \begin_inset CommandInset label
18528 name "sub:Font-Sizes"
18536 \begin_layout Plain Layout
18545 \begin_layout Standard
18546 For characters in formulas there are, analog to characters in text, the
18547 following size commands:
18550 \begin_layout Standard
18594 \begin_inset Newline newline
18616 \begin_layout Standard
18617 The size produced by the commands depends on the document font size, that
18618 corresponds with the command
18625 The other commands produce smaller or larger sizes than
18632 The font size can however not exceed a certain value.
18633 Is for example the document font size 12
18634 \begin_inset space \thinspace{}
18643 switches to the same size as
18653 \begin_layout Standard
18654 A size command is inserted in TeX-mode before the formula and sets the size
18655 for all following formula and text characters.
18656 To switch back to the initial size, the command
18662 is inserted behind the formula in TeX-mode.
18665 \begin_layout Standard
18666 Within a formula the size can only be changed for symbols or letters in
18668 To do this, the size command is inserted in mathematical text.
18669 All following characters until the end of the mathematical text or until
18670 another size command will have the selected size.
18672 \begin_inset VSpace -2mm
18678 \begin_layout Standard
18682 \begin_layout Plain Layout
18692 \begin_inset Formula \[
18693 A=\frac{B}{c}\cdot\maltese\]
18698 \begin_inset Formula \[
18699 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18707 \begin_layout Plain Layout
18719 \begin_layout Standard
18720 \begin_inset VSpace medskip
18723 Before both formulas the command
18730 The command for the second formula is:
18731 \begin_inset Newline newline
18742 \begin_layout Plain Layout
18757 \begin_layout Plain Layout
18772 \begin_layout Plain Layout
18787 \begin_layout Plain Layout
18797 \begin_inset Formula $\to$
18801 \begin_inset Formula $\to$
18805 \begin_inset Newline newline
18809 \begin_inset space \hspace*{}
18823 \begin_layout Plain Layout
18838 \begin_layout Plain Layout
18853 \begin_layout Plain Layout
18865 \begin_layout Standard
18866 If a symbol cannot be displayed in different sizes, it will always be displayed
18867 in the default size.
18870 \begin_layout Section
18875 \begin_layout Plain Layout
18884 \begin_layout Standard
18885 All Greek letters can also be inserted via the toolbar button
18886 \begin_inset Graphics
18887 filename ../images/math/alpha.png
18895 \begin_layout Subsection
18897 \begin_inset CommandInset label
18899 name "sub:Small-Letters"
18907 \begin_layout Plain Layout
18908 Greek letters ! small
18916 \begin_layout Standard
18917 \begin_inset space \hfill{}
18921 \begin_inset Tabular
18922 <lyxtabular version="3" rows="11" columns="2">
18924 <column alignment="center" valignment="top" width="0pt">
18925 <column alignment="center" valignment="top" width="0pt">
18927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18930 \begin_layout Plain Layout
18936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18939 \begin_layout Plain Layout
18947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18950 \begin_layout Plain Layout
18958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18961 \begin_layout Plain Layout
18962 \begin_inset Formula $\alpha$
18972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18975 \begin_layout Plain Layout
18983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18986 \begin_layout Plain Layout
18987 \begin_inset Formula $\beta$
18997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19000 \begin_layout Plain Layout
19008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19011 \begin_layout Plain Layout
19012 \begin_inset Formula $\gamma$
19022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19025 \begin_layout Plain Layout
19033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19036 \begin_layout Plain Layout
19037 \begin_inset Formula $\delta$
19047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19050 \begin_layout Plain Layout
19058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19061 \begin_layout Plain Layout
19062 \begin_inset Formula $\epsilon$
19072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19075 \begin_layout Plain Layout
19083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19086 \begin_layout Plain Layout
19087 \begin_inset Formula $\varepsilon$
19097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19100 \begin_layout Plain Layout
19108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19111 \begin_layout Plain Layout
19112 \begin_inset Formula $\zeta$
19122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19125 \begin_layout Plain Layout
19133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19136 \begin_layout Plain Layout
19137 \begin_inset Formula $\eta$
19147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19150 \begin_layout Plain Layout
19158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19161 \begin_layout Plain Layout
19162 \begin_inset Formula $\theta$
19172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19175 \begin_layout Plain Layout
19183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19186 \begin_layout Plain Layout
19187 \begin_inset Formula $\vartheta$
19201 \begin_inset space \hfill{}
19205 \begin_inset Tabular
19206 <lyxtabular version="3" rows="12" columns="2">
19208 <column alignment="center" valignment="top" width="0pt">
19209 <column alignment="center" valignment="top" width="0pt">
19211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19214 \begin_layout Plain Layout
19220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19223 \begin_layout Plain Layout
19231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19234 \begin_layout Plain Layout
19242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19245 \begin_layout Plain Layout
19246 \begin_inset Formula $\iota$
19256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19259 \begin_layout Plain Layout
19267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19270 \begin_layout Plain Layout
19271 \begin_inset Formula $\kappa$
19281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19284 \begin_layout Plain Layout
19292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19295 \begin_layout Plain Layout
19296 \begin_inset Formula $\varkappa$
19306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19309 \begin_layout Plain Layout
19317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19320 \begin_layout Plain Layout
19321 \begin_inset Formula $\lambda$
19331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19334 \begin_layout Plain Layout
19342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19345 \begin_layout Plain Layout
19346 \begin_inset Formula $\mu$
19356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19359 \begin_layout Plain Layout
19367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19370 \begin_layout Plain Layout
19371 \begin_inset Formula $\nu$
19381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19384 \begin_layout Plain Layout
19392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19395 \begin_layout Plain Layout
19396 \begin_inset Formula $\xi$
19406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19409 \begin_layout Plain Layout
19415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19418 \begin_layout Plain Layout
19419 \begin_inset Formula $o$
19429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19432 \begin_layout Plain Layout
19440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19443 \begin_layout Plain Layout
19444 \begin_inset Formula $\pi$
19454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19457 \begin_layout Plain Layout
19465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19468 \begin_layout Plain Layout
19469 \begin_inset Formula $\varpi$
19479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19482 \begin_layout Plain Layout
19490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19493 \begin_layout Plain Layout
19494 \begin_inset Formula $\rho$
19508 \begin_inset space \hfill{}
19512 \begin_inset Tabular
19513 <lyxtabular version="3" rows="11" columns="2">
19515 <column alignment="center" valignment="top" width="0pt">
19516 <column alignment="center" valignment="top" width="0pt">
19518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19521 \begin_layout Plain Layout
19527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19530 \begin_layout Plain Layout
19538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19541 \begin_layout Plain Layout
19549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19552 \begin_layout Plain Layout
19553 \begin_inset Formula $\varrho$
19563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19566 \begin_layout Plain Layout
19574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19577 \begin_layout Plain Layout
19578 \begin_inset Formula $\sigma$
19588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19591 \begin_layout Plain Layout
19599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19602 \begin_layout Plain Layout
19603 \begin_inset Formula $\varsigma$
19613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19616 \begin_layout Plain Layout
19624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19627 \begin_layout Plain Layout
19628 \begin_inset Formula $\tau$
19638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19641 \begin_layout Plain Layout
19649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19652 \begin_layout Plain Layout
19653 \begin_inset Formula $\upsilon$
19663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19666 \begin_layout Plain Layout
19674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19677 \begin_layout Plain Layout
19678 \begin_inset Formula $\phi$
19688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19691 \begin_layout Plain Layout
19699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19702 \begin_layout Plain Layout
19703 \begin_inset Formula $\varphi$
19713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19716 \begin_layout Plain Layout
19724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19727 \begin_layout Plain Layout
19728 \begin_inset Formula $\chi$
19738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19741 \begin_layout Plain Layout
19749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19752 \begin_layout Plain Layout
19753 \begin_inset Formula $\psi$
19763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19766 \begin_layout Plain Layout
19774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19777 \begin_layout Plain Layout
19778 \begin_inset Formula $\omega$
19792 \begin_inset space \hfill{}
19798 \begin_layout Standard
19799 \begin_inset VSpace medskip
19805 \begin_layout Standard
19806 How to create upright Greek letters is explained in
19807 \begin_inset CommandInset ref
19809 reference "sub:Upright-small-Greek"
19816 \begin_layout Subsection
19821 \begin_layout Plain Layout
19822 Greek letters ! big
19830 \begin_layout Standard
19831 \begin_inset space \hfill{}
19835 \begin_inset Tabular
19836 <lyxtabular version="3" rows="7" columns="2">
19838 <column alignment="center" valignment="top" width="0pt">
19839 <column alignment="center" valignment="top" width="0pt">
19841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19844 \begin_layout Plain Layout
19850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19853 \begin_layout Plain Layout
19861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19864 \begin_layout Plain Layout
19872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19875 \begin_layout Plain Layout
19876 \begin_inset Formula $\Gamma$
19886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19889 \begin_layout Plain Layout
19897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19900 \begin_layout Plain Layout
19901 \begin_inset Formula $\Delta$
19911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19914 \begin_layout Plain Layout
19922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19925 \begin_layout Plain Layout
19926 \begin_inset Formula $\Theta$
19936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19939 \begin_layout Plain Layout
19947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19950 \begin_layout Plain Layout
19951 \begin_inset Formula $\Lambda$
19961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19964 \begin_layout Plain Layout
19972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19975 \begin_layout Plain Layout
19976 \begin_inset Formula $\Xi$
19986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19989 \begin_layout Plain Layout
19997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20000 \begin_layout Plain Layout
20001 \begin_inset Formula $\Pi$
20015 \begin_inset space \hfill{}
20019 \begin_inset Tabular
20020 <lyxtabular version="3" rows="6" columns="2">
20022 <column alignment="center" valignment="top" width="0pt">
20023 <column alignment="center" valignment="top" width="0pt">
20025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20028 \begin_layout Plain Layout
20034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20037 \begin_layout Plain Layout
20045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20048 \begin_layout Plain Layout
20056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20059 \begin_layout Plain Layout
20060 \begin_inset Formula $\Sigma$
20070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20073 \begin_layout Plain Layout
20081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20084 \begin_layout Plain Layout
20085 \begin_inset Formula $\Upsilon$
20095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20098 \begin_layout Plain Layout
20106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20109 \begin_layout Plain Layout
20110 \begin_inset Formula $\Phi$
20120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20123 \begin_layout Plain Layout
20131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20134 \begin_layout Plain Layout
20135 \begin_inset Formula $\Psi$
20145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20148 \begin_layout Plain Layout
20156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20159 \begin_layout Plain Layout
20160 \begin_inset Formula $\Omega$
20174 \begin_inset space \hfill{}
20180 \begin_layout Standard
20181 \begin_inset VSpace medskip
20184 That the big Greek letters appear upright is caused by a design bug when
20186 To get correct italic big letters, begin every command with
20191 For example the command
20198 \begin_inset Formula $\varGamma$
20204 \begin_layout Subsection
20209 \begin_layout Plain Layout
20210 Greek letters ! bold
20218 \begin_layout Standard
20219 Greek letters cannot be set with different font styles like Latin letters.
20220 They can only be made bold with the command
20230 \begin_layout Plain Layout
20241 \begin_layout Standard
20243 \begin_inset Tabular
20244 <lyxtabular version="3" rows="3" columns="2">
20246 <column alignment="center" valignment="top" width="0">
20247 <column alignment="center" valignment="top" width="0">
20249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20252 \begin_layout Plain Layout
20258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20261 \begin_layout Plain Layout
20269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20272 \begin_layout Plain Layout
20284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20287 \begin_layout Plain Layout
20288 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20301 \begin_layout Plain Layout
20313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20316 \begin_layout Plain Layout
20317 \begin_inset Formula $\theta\boldsymbol{\theta}$
20333 \begin_layout Section
20338 \begin_layout Plain Layout
20351 \begin_layout Plain Layout
20352 A list with all symbols of most of the LaTeX-packages can be found in
20353 \begin_inset CommandInset citation
20368 \begin_layout Plain Layout
20376 \begin_inset Note Note
20379 \begin_layout Plain Layout
20382 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20385 \begin_layout Plain Layout
20388 texorpdfstring is in section
20389 \begin_inset CommandInset ref
20391 reference "sub:Formulas-in-Section"
20404 \begin_layout Plain Layout
20413 \begin_layout Standard
20414 Many of the symbols listed in this section can also be inserted via the
20416 \begin_inset Graphics
20417 filename ../images/math/nabla.png
20423 \begin_inset Graphics
20424 filename ../images/math/digamma.png
20432 \begin_layout Subsection
20433 Mathematical Symbols
20434 \begin_inset CommandInset label
20436 name "sub:Mathematical-Symbols"
20444 \begin_layout Plain Layout
20445 Symbols ! mathematical
20453 \begin_layout Standard
20454 \begin_inset space \hfill{}
20458 \begin_inset Tabular
20459 <lyxtabular version="3" rows="10" columns="2">
20461 <column alignment="center" valignment="top" width="0pt">
20462 <column alignment="center" valignment="top" width="0pt">
20464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20467 \begin_layout Plain Layout
20473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20476 \begin_layout Plain Layout
20484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20487 \begin_layout Plain Layout
20495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20498 \begin_layout Plain Layout
20499 \begin_inset Formula $\neg$
20509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20512 \begin_layout Plain Layout
20520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20523 \begin_layout Plain Layout
20524 \begin_inset Formula $\Im$
20534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20537 \begin_layout Plain Layout
20545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20548 \begin_layout Plain Layout
20549 \begin_inset Formula $\Re$
20559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20562 \begin_layout Plain Layout
20570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20573 \begin_layout Plain Layout
20574 \begin_inset Formula $\aleph$
20584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20587 \begin_layout Plain Layout
20595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20598 \begin_layout Plain Layout
20599 \begin_inset Formula $\partial$
20609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20612 \begin_layout Plain Layout
20620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20623 \begin_layout Plain Layout
20624 \begin_inset Formula $\infty$
20634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20637 \begin_layout Plain Layout
20645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20648 \begin_layout Plain Layout
20649 \begin_inset Formula $\wp$
20659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20662 \begin_layout Plain Layout
20670 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20673 \begin_layout Plain Layout
20674 \begin_inset Formula $\imath$
20684 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20687 \begin_layout Plain Layout
20695 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20698 \begin_layout Plain Layout
20699 \begin_inset Formula $\jmath$
20713 \begin_inset space \hfill{}
20717 \begin_inset Tabular
20718 <lyxtabular version="3" rows="10" columns="2">
20720 <column alignment="center" valignment="top" width="0pt">
20721 <column alignment="center" valignment="top" width="0pt">
20723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20726 \begin_layout Plain Layout
20732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20735 \begin_layout Plain Layout
20737 \begin_inset Note Note
20740 \begin_layout Plain Layout
20747 is only used as spacer.
20759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20762 \begin_layout Plain Layout
20770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20773 \begin_layout Plain Layout
20774 \begin_inset Formula $\forall$
20784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20787 \begin_layout Plain Layout
20795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20798 \begin_layout Plain Layout
20799 \begin_inset Formula $\exists$
20809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20812 \begin_layout Plain Layout
20820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20823 \begin_layout Plain Layout
20824 \begin_inset Formula $\nexists$
20834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20837 \begin_layout Plain Layout
20845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20848 \begin_layout Plain Layout
20849 \begin_inset Formula $\emptyset$
20859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20862 \begin_layout Plain Layout
20870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20873 \begin_layout Plain Layout
20874 \begin_inset Formula $\varnothing$
20884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20887 \begin_layout Plain Layout
20895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20898 \begin_layout Plain Layout
20899 \begin_inset Formula $\dag$
20909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20912 \begin_layout Plain Layout
20920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20923 \begin_layout Plain Layout
20924 \begin_inset Formula $\ddag$
20934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20937 \begin_layout Plain Layout
20945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20948 \begin_layout Plain Layout
20952 \begin_layout Plain Layout
20962 \begin_inset Formula $\complement$
20969 \begin_layout Plain Layout
20983 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20986 \begin_layout Plain Layout
20994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20997 \begin_layout Plain Layout
20998 \begin_inset Formula $\Bbbk$
21012 \begin_inset space \hfill{}
21016 \begin_inset Tabular
21017 <lyxtabular version="3" rows="10" columns="2">
21019 <column alignment="center" valignment="top" width="0pt">
21020 <column alignment="center" valignment="top" width="0pt">
21022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21025 \begin_layout Plain Layout
21031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21034 \begin_layout Plain Layout
21042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21045 \begin_layout Plain Layout
21053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21056 \begin_layout Plain Layout
21057 \begin_inset Formula $\prime$
21067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21070 \begin_layout Plain Layout
21078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21081 \begin_layout Plain Layout
21082 \begin_inset Formula $\backprime$
21092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21095 \begin_layout Plain Layout
21103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21106 \begin_layout Plain Layout
21107 \begin_inset Formula $\mho$
21117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21120 \begin_layout Plain Layout
21128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21131 \begin_layout Plain Layout
21132 \begin_inset Formula $\triangle$
21142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21145 \begin_layout Plain Layout
21153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21156 \begin_layout Plain Layout
21157 \begin_inset Formula $\angle$
21167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21170 \begin_layout Plain Layout
21178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21181 \begin_layout Plain Layout
21182 \begin_inset Formula $\measuredangle$
21192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21195 \begin_layout Plain Layout
21203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21206 \begin_layout Plain Layout
21207 \begin_inset Formula $\sphericalangle$
21217 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21220 \begin_layout Plain Layout
21228 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21231 \begin_layout Plain Layout
21232 \begin_inset Formula $\top$
21242 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21245 \begin_layout Plain Layout
21253 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21256 \begin_layout Plain Layout
21257 \begin_inset Formula $\bot$
21271 \begin_inset space \hfill{}
21277 \begin_layout Standard
21278 \begin_inset Newpage newpage
21284 \begin_layout Subsection
21285 Miscellaneous Symbols
21286 \begin_inset CommandInset label
21288 name "sub:Miscellaneous-Symbols"
21296 \begin_layout Plain Layout
21297 Symbols ! miscellaneous
21305 \begin_layout Standard
21308 \begin_inset Tabular
21309 <lyxtabular version="3" rows="10" columns="2">
21311 <column alignment="center" valignment="top" width="0pt">
21312 <column alignment="center" valignment="top" width="0pt">
21314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21317 \begin_layout Plain Layout
21323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21326 \begin_layout Plain Layout
21334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21337 \begin_layout Plain Layout
21345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21348 \begin_layout Plain Layout
21349 \begin_inset Formula $\flat$
21359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21362 \begin_layout Plain Layout
21370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21373 \begin_layout Plain Layout
21374 \begin_inset Formula $\natural$
21384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21387 \begin_layout Plain Layout
21395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21398 \begin_layout Plain Layout
21399 \begin_inset Formula $\sharp$
21409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21412 \begin_layout Plain Layout
21420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21423 \begin_layout Plain Layout
21424 \begin_inset Formula $\surd$
21434 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21437 \begin_layout Plain Layout
21445 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21448 \begin_layout Plain Layout
21449 \begin_inset Formula $\checkmark$
21459 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21462 \begin_layout Plain Layout
21470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21473 \begin_layout Plain Layout
21474 \begin_inset Formula $\yen$
21484 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21487 \begin_layout Plain Layout
21495 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21498 \begin_layout Plain Layout
21499 \begin_inset Formula $\pounds$
21509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21512 \begin_layout Plain Layout
21518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21521 \begin_layout Plain Layout
21522 \begin_inset Formula $\$$
21532 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21535 \begin_layout Plain Layout
21541 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21544 \begin_layout Plain Layout
21545 \begin_inset Formula $§$
21559 \begin_inset Tabular
21560 <lyxtabular version="3" rows="10" columns="2">
21562 <column alignment="center" valignment="top" width="0">
21563 <column alignment="center" valignment="top" width="0">
21565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21568 \begin_layout Plain Layout
21574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21577 \begin_layout Plain Layout
21585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21588 \begin_layout Plain Layout
21596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21599 \begin_layout Plain Layout
21600 \begin_inset Formula $\hbar$
21610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21613 \begin_layout Plain Layout
21621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21624 \begin_layout Plain Layout
21625 \begin_inset Formula $\hslash$
21635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21638 \begin_layout Plain Layout
21646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21649 \begin_layout Plain Layout
21650 \begin_inset Formula $\clubsuit$
21660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21663 \begin_layout Plain Layout
21671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21674 \begin_layout Plain Layout
21675 \begin_inset Formula $\spadesuit$
21685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21688 \begin_layout Plain Layout
21696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21699 \begin_layout Plain Layout
21700 \begin_inset Formula $\bigstar$
21710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21713 \begin_layout Plain Layout
21721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21724 \begin_layout Plain Layout
21725 \begin_inset Formula $\blacklozenge$
21735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21738 \begin_layout Plain Layout
21746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21749 \begin_layout Plain Layout
21750 \begin_inset Formula $\blacktriangle$
21760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21763 \begin_layout Plain Layout
21771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21774 \begin_layout Plain Layout
21775 \begin_inset Formula $\blacktriangledown$
21785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21788 \begin_layout Plain Layout
21796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21799 \begin_layout Plain Layout
21800 \begin_inset Formula $\bullet$
21814 \begin_inset Tabular
21815 <lyxtabular version="3" rows="10" columns="2">
21817 <column alignment="center" valignment="top" width="0pt">
21818 <column alignment="center" valignment="top" width="0pt">
21820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21823 \begin_layout Plain Layout
21829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21832 \begin_layout Plain Layout
21840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21843 \begin_layout Plain Layout
21851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21854 \begin_layout Plain Layout
21855 \begin_inset Formula $\diamondsuit$
21865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21868 \begin_layout Plain Layout
21876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21879 \begin_layout Plain Layout
21880 \begin_inset Formula $\Diamond$
21890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21893 \begin_layout Plain Layout
21901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21904 \begin_layout Plain Layout
21905 \begin_inset Formula $\heartsuit$
21915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21918 \begin_layout Plain Layout
21926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21929 \begin_layout Plain Layout
21930 \begin_inset Formula $\P$
21940 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21943 \begin_layout Plain Layout
21951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21954 \begin_layout Plain Layout
21955 \begin_inset Formula $\copyright$
21965 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21968 \begin_layout Plain Layout
21976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21979 \begin_layout Plain Layout
21980 \begin_inset Formula $\circledR$
21990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21993 \begin_layout Plain Layout
22001 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22004 \begin_layout Plain Layout
22005 \begin_inset Formula $\maltese$
22015 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22018 \begin_layout Plain Layout
22026 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22029 \begin_layout Plain Layout
22030 \begin_inset Formula $\diagup$
22040 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22043 \begin_layout Plain Layout
22051 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22054 \begin_layout Plain Layout
22055 \begin_inset Formula $\diagdown$
22071 \begin_layout Standard
22072 \begin_inset VSpace medskip
22075 More symbols are listed in
22076 \begin_inset CommandInset ref
22078 reference "sub:Miscellaneous-Special-Characters"
22085 \begin_layout Standard
22086 Some symbols can be displayed in different sizes, see
22087 \begin_inset CommandInset ref
22089 reference "sub:Font-Sizes"
22096 \begin_layout Subsection
22101 \begin_layout Plain Layout
22102 Symbols ! Euro-symbol
22111 \begin_layout Plain Layout
22115 \begin_layout Plain Layout
22132 \begin_layout Standard
22133 To use the Euro symbol in formulas, the LaTeX-package
22141 \begin_layout Plain Layout
22147 must be installed and loaded with the LaTeX-preamble line
22150 \begin_layout Standard
22155 usepackage[gennarrow]{eurosym}
22158 \begin_layout Standard
22159 The Euro symbol can now be inserted with the command
22169 \begin_layout Plain Layout
22180 \begin_layout Standard
22181 The Euro symbol can directly be inserted with the € key in mathematical
22182 text, without having
22197 can also be inserted in TeX-mode.
22198 The official currency symbol can then be inserted with the command
22208 \begin_layout Plain Layout
22216 , that is only available in TeX-mode.
22219 \begin_layout Standard
22223 \begin_layout Plain Layout
22233 \begin_inset Note Note
22236 \begin_layout Plain Layout
22237 The following table will only be displayed when the LaTeX-package
22249 \begin_layout Standard
22250 An overview about the different Euro symbols:
22253 \begin_layout Standard
22255 \begin_inset Tabular
22256 <lyxtabular version="3" rows="4" columns="3">
22258 <column alignment="center" valignment="top" width="0pt">
22259 <column alignment="center" valignment="top" width="0pt">
22260 <column alignment="center" valignment="top" width="0pt">
22262 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22265 \begin_layout Plain Layout
22271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22274 \begin_layout Plain Layout
22280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22283 \begin_layout Plain Layout
22291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22294 \begin_layout Plain Layout
22300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22303 \begin_layout Plain Layout
22311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22314 \begin_layout Plain Layout
22315 \begin_inset Formula $\euro$
22325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22328 \begin_layout Plain Layout
22334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22337 \begin_layout Plain Layout
22343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22346 \begin_layout Plain Layout
22347 \begin_inset Formula $\mbox{€}$
22357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22360 \begin_layout Plain Layout
22366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22369 \begin_layout Plain Layout
22377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22380 \begin_layout Plain Layout
22384 \begin_layout Plain Layout
22406 \begin_layout Standard
22410 \begin_layout Plain Layout
22420 \begin_inset Note Note
22423 \begin_layout Plain Layout
22424 The following will be displayed when the LaTeX-package
22436 \begin_layout Standard
22437 You need to install the LaTeX-package
22441 to see the rest of this subsection in the output.
22444 \begin_layout Standard
22448 \begin_layout Plain Layout
22460 \begin_layout Section
22462 \begin_inset CommandInset label
22464 name "sec:Relations"
22472 \begin_layout Plain Layout
22482 \begin_layout Plain Layout
22487 \begin_layout Plain Layout
22498 \begin_layout Plain Layout
22513 \begin_layout Standard
22514 All relations can also be inserted via the toolbar button
22515 \begin_inset Graphics
22516 filename ../images/math/leq.png
22524 \begin_layout Standard
22525 \begin_inset space \hfill{}
22529 \begin_inset Tabular
22530 <lyxtabular version="3" rows="17" columns="2">
22532 <column alignment="center" valignment="top" width="0pt">
22533 <column alignment="center" valignment="top" width="0pt">
22535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22538 \begin_layout Plain Layout
22544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22547 \begin_layout Plain Layout
22555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22558 \begin_layout Plain Layout
22564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22567 \begin_layout Plain Layout
22568 \begin_inset Formula $<$
22578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22581 \begin_layout Plain Layout
22589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22592 \begin_layout Plain Layout
22593 \begin_inset Formula $\le$
22603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22606 \begin_layout Plain Layout
22614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22617 \begin_layout Plain Layout
22618 \begin_inset Formula $\ll$
22628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22631 \begin_layout Plain Layout
22639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22642 \begin_layout Plain Layout
22643 \begin_inset Formula $\prec$
22653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22656 \begin_layout Plain Layout
22664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22667 \begin_layout Plain Layout
22668 \begin_inset Formula $\preceq$
22678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22681 \begin_layout Plain Layout
22689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22692 \begin_layout Plain Layout
22693 \begin_inset Formula $\subset$
22703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22706 \begin_layout Plain Layout
22714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22717 \begin_layout Plain Layout
22718 \begin_inset Formula $\subseteq$
22728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22731 \begin_layout Plain Layout
22739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22742 \begin_layout Plain Layout
22743 \begin_inset Formula $\sqsubseteq$
22753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22756 \begin_layout Plain Layout
22764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22767 \begin_layout Plain Layout
22768 \begin_inset Formula $\in$
22778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22781 \begin_layout Plain Layout
22789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22792 \begin_layout Plain Layout
22793 \begin_inset Formula $\vdash$
22803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22806 \begin_layout Plain Layout
22814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22817 \begin_layout Plain Layout
22818 \begin_inset Formula $\smile$
22828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22831 \begin_layout Plain Layout
22839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22842 \begin_layout Plain Layout
22843 \begin_inset Formula $\lhd$
22853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22856 \begin_layout Plain Layout
22864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22867 \begin_layout Plain Layout
22868 \begin_inset Formula $\unlhd$
22878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22881 \begin_layout Plain Layout
22889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22892 \begin_layout Plain Layout
22893 \begin_inset Formula $\gtrless$
22903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22906 \begin_layout Plain Layout
22914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22917 \begin_layout Plain Layout
22918 \begin_inset Formula $\mid$
22928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22931 \begin_layout Plain Layout
22939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22942 \begin_layout Plain Layout
22943 \begin_inset Formula $\nmid$
22957 \begin_inset space \hfill{}
22961 \begin_inset Tabular
22962 <lyxtabular version="3" rows="17" columns="2">
22964 <column alignment="center" valignment="top" width="0pt">
22965 <column alignment="center" valignment="top" width="0pt">
22967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22970 \begin_layout Plain Layout
22976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22979 \begin_layout Plain Layout
22987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22990 \begin_layout Plain Layout
22996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22999 \begin_layout Plain Layout
23000 \begin_inset Formula $=$
23010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23013 \begin_layout Plain Layout
23021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23024 \begin_layout Plain Layout
23025 \begin_inset Formula $\not=$
23035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23038 \begin_layout Plain Layout
23046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23049 \begin_layout Plain Layout
23050 \begin_inset Formula $\equiv$
23060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23063 \begin_layout Plain Layout
23071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23074 \begin_layout Plain Layout
23075 \begin_inset Formula $\sim$
23085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23088 \begin_layout Plain Layout
23096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23099 \begin_layout Plain Layout
23100 \begin_inset Formula $\simeq$
23110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23113 \begin_layout Plain Layout
23121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23124 \begin_layout Plain Layout
23125 \begin_inset Formula $\approx$
23135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23138 \begin_layout Plain Layout
23146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23149 \begin_layout Plain Layout
23150 \begin_inset Formula $\cong$
23160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23163 \begin_layout Plain Layout
23171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23174 \begin_layout Plain Layout
23175 \begin_inset Formula $\bowtie$
23185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23188 \begin_layout Plain Layout
23196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23199 \begin_layout Plain Layout
23200 \begin_inset Formula $\notin$
23210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23213 \begin_layout Plain Layout
23221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23224 \begin_layout Plain Layout
23225 \begin_inset Formula $\perp$
23235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23238 \begin_layout Plain Layout
23246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23249 \begin_layout Plain Layout
23250 \begin_inset Formula $\propto$
23260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23263 \begin_layout Plain Layout
23271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23274 \begin_layout Plain Layout
23275 \begin_inset Formula $\asymp$
23285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23288 \begin_layout Plain Layout
23296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23299 \begin_layout Plain Layout
23300 \begin_inset Formula $\doteq$
23310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23313 \begin_layout Plain Layout
23321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23324 \begin_layout Plain Layout
23325 \begin_inset Formula $\circeq$
23335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23338 \begin_layout Plain Layout
23346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23349 \begin_layout Plain Layout
23350 \begin_inset Formula $\models$
23360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23363 \begin_layout Plain Layout
23371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23374 \begin_layout Plain Layout
23375 \begin_inset Formula $\widehat{=}$
23389 \begin_inset space \hfill{}
23393 \begin_inset Tabular
23394 <lyxtabular version="3" rows="17" columns="2">
23396 <column alignment="center" valignment="top" width="0pt">
23397 <column alignment="center" valignment="top" width="0pt">
23399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23402 \begin_layout Plain Layout
23408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23411 \begin_layout Plain Layout
23419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23422 \begin_layout Plain Layout
23428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23431 \begin_layout Plain Layout
23432 \begin_inset Formula $>$
23442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23445 \begin_layout Plain Layout
23453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23456 \begin_layout Plain Layout
23457 \begin_inset Formula $\ge$
23467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23470 \begin_layout Plain Layout
23478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23481 \begin_layout Plain Layout
23482 \begin_inset Formula $\gg$
23492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23495 \begin_layout Plain Layout
23503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23506 \begin_layout Plain Layout
23507 \begin_inset Formula $\succ$
23517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23520 \begin_layout Plain Layout
23528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23531 \begin_layout Plain Layout
23532 \begin_inset Formula $\succeq$
23542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23545 \begin_layout Plain Layout
23553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23556 \begin_layout Plain Layout
23557 \begin_inset Formula $\supset$
23567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23570 \begin_layout Plain Layout
23578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23581 \begin_layout Plain Layout
23582 \begin_inset Formula $\supseteq$
23592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23595 \begin_layout Plain Layout
23603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23606 \begin_layout Plain Layout
23607 \begin_inset Formula $\sqsupseteq$
23617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23620 \begin_layout Plain Layout
23628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23631 \begin_layout Plain Layout
23632 \begin_inset Formula $\ni$
23642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23645 \begin_layout Plain Layout
23653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23656 \begin_layout Plain Layout
23657 \begin_inset Formula $\dashv$
23667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23670 \begin_layout Plain Layout
23678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23681 \begin_layout Plain Layout
23682 \begin_inset Formula $\frown$
23692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23695 \begin_layout Plain Layout
23703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23706 \begin_layout Plain Layout
23707 \begin_inset Formula $\rhd$
23717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23720 \begin_layout Plain Layout
23728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23731 \begin_layout Plain Layout
23732 \begin_inset Formula $\unrhd$
23742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23745 \begin_layout Plain Layout
23753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23756 \begin_layout Plain Layout
23757 \begin_inset Formula $\lessgtr$
23767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23770 \begin_layout Plain Layout
23778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23781 \begin_layout Plain Layout
23782 \begin_inset Formula $\parallel$
23792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23795 \begin_layout Plain Layout
23803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23806 \begin_layout Plain Layout
23807 \begin_inset Formula $\nparallel$
23821 \begin_inset space \hfill{}
23827 \begin_layout Standard
23828 \begin_inset VSpace medskip
23843 are bigger than the equal looking operators
23858 \begin_layout Standard
23859 Relations are, in contrary to symbols, always surrounded by space.
23862 \begin_layout Standard
23863 Relations with labels can be created with the command
23873 \begin_layout Plain Layout
23884 \begin_layout Standard
23886 \begin_inset Tabular
23887 <lyxtabular version="3" rows="2" columns="2">
23889 <column alignment="center" valignment="top" width="0">
23890 <column alignment="center" valignment="top" width="0">
23892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23895 \begin_layout Plain Layout
23901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23904 \begin_layout Plain Layout
23906 \begin_inset Note Note
23909 \begin_layout Plain Layout
23916 is only used as spacer.
23928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23931 \begin_layout Plain Layout
23938 \begin_layout Plain Layout
23955 \begin_layout Plain Layout
23965 \begin_inset Formula $\downarrow$
23974 \begin_layout Plain Layout
23987 \begin_layout Plain Layout
24001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24004 \begin_layout Plain Layout
24005 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24021 \begin_layout Section
24025 \begin_layout Subsection
24026 Predefined Functions
24027 \begin_inset CommandInset label
24029 name "sub:Predefined-Functions"
24037 \begin_layout Plain Layout
24038 Functions ! predefined
24046 \begin_layout Standard
24047 In general, variables are set
24051 in mathematical expressions, but not function names, because
24052 \begin_inset Formula $sin$
24055 could be misunderstood as
24056 \begin_inset Formula $s\cdot i\cdot n$
24060 Therefore there are predefined functions, that are additionally a bit separated
24062 They are inserted as commands starting with a backslash before their name.
24065 \begin_layout Standard
24067 \begin_inset Tabular
24068 <lyxtabular version="3" rows="2" columns="4">
24070 <column alignment="center" valignment="top" width="0pt">
24071 <column alignment="center" valignment="top" width="0pt">
24072 <column alignment="center" valignment="top" width="0pt">
24073 <column alignment="center" valignment="top" width="0pt">
24075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24078 \begin_layout Plain Layout
24084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24087 \begin_layout Plain Layout
24093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24096 \begin_layout Plain Layout
24102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24105 \begin_layout Plain Layout
24113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24116 \begin_layout Plain Layout
24122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24125 \begin_layout Plain Layout
24126 \begin_inset Formula $Asin(x)+B$
24134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24137 \begin_layout Plain Layout
24145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24148 \begin_layout Plain Layout
24149 \begin_inset Formula $A\sin(x)+B$
24163 \begin_inset Newpage pagebreak
24169 \begin_layout Standard
24170 The following functions are predefined:
24173 \begin_layout Standard
24174 \begin_inset VSpace -2mm
24180 \begin_layout Standard
24182 \begin_inset Tabular
24183 <lyxtabular version="3" rows="9" columns="4">
24185 <column alignment="center" valignment="top" width="0pt">
24186 <column alignment="center" valignment="top" width="0pt">
24187 <column alignment="center" valignment="top" width="0pt">
24188 <column alignment="center" valignment="top" width="0pt">
24190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24193 \begin_layout Plain Layout
24199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24202 \begin_layout Plain Layout
24208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24211 \begin_layout Plain Layout
24217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24220 \begin_layout Plain Layout
24228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24231 \begin_layout Plain Layout
24239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24242 \begin_layout Plain Layout
24250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24253 \begin_layout Plain Layout
24261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24264 \begin_layout Plain Layout
24274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24277 \begin_layout Plain Layout
24285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24288 \begin_layout Plain Layout
24296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24299 \begin_layout Plain Layout
24307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24310 \begin_layout Plain Layout
24320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24323 \begin_layout Plain Layout
24331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24334 \begin_layout Plain Layout
24342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24345 \begin_layout Plain Layout
24353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24356 \begin_layout Plain Layout
24366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24369 \begin_layout Plain Layout
24377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24380 \begin_layout Plain Layout
24388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24391 \begin_layout Plain Layout
24399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24402 \begin_layout Plain Layout
24412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24415 \begin_layout Plain Layout
24423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24426 \begin_layout Plain Layout
24434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24437 \begin_layout Plain Layout
24445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24448 \begin_layout Plain Layout
24458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24461 \begin_layout Plain Layout
24469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24472 \begin_layout Plain Layout
24480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24483 \begin_layout Plain Layout
24491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24494 \begin_layout Plain Layout
24504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24507 \begin_layout Plain Layout
24515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24518 \begin_layout Plain Layout
24526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24529 \begin_layout Plain Layout
24537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24540 \begin_layout Plain Layout
24550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24553 \begin_layout Plain Layout
24561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24564 \begin_layout Plain Layout
24572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24575 \begin_layout Plain Layout
24583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24586 \begin_layout Plain Layout
24602 \begin_layout Standard
24603 They can also be inserted with the math toolbar button
24604 \begin_inset Graphics
24605 filename ../images/math/functions.png
24613 \begin_layout Subsection
24614 Self-defined Functions
24618 \begin_layout Plain Layout
24619 Functions ! self-defined
24627 \begin_layout Standard
24628 To use a function that is not predefined, like for example the sign function
24629 sgn(x), there are two possibilities:
24632 \begin_layout Itemize
24633 Define the function by inserting the following line to the LaTeX-preamble
24637 \begin_layout Plain Layout
24642 DeclareMathOperator
24645 \begin_inset CommandInset ref
24647 reference "sub:Self-defined-Operators"
24657 \begin_inset Newline newline
24661 \begin_inset VSpace -3mm
24665 \begin_inset Newline newline
24672 DeclareMathOperator{
24680 \begin_layout Plain Layout
24685 DeclareMathOperator
24691 \begin_inset Newline newline
24695 \begin_inset VSpace -2mm
24699 \begin_inset Newline newline
24702 Now the new defined function can be called with the command
24711 \begin_layout Itemize
24712 Write the the formula as usual, mark the formula name, in our example the
24717 , and change it to mathematical text.
24718 At last a space is inserted between prefactor and function.
24721 \begin_layout Standard
24722 The result is the same with both methods as with a predefined function
24726 \begin_layout Plain Layout
24727 In LyX self-defined functions are displayed red, predefined ones black.
24735 \begin_layout Standard
24737 \begin_inset Tabular
24738 <lyxtabular version="3" rows="3" columns="2">
24740 <column alignment="center" valignment="top" width="0pt">
24741 <column alignment="center" valignment="top" width="0pt">
24743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24746 \begin_layout Plain Layout
24752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24755 \begin_layout Plain Layout
24763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24766 \begin_layout Plain Layout
24774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24777 \begin_layout Plain Layout
24778 \begin_inset Formula $A\sgn(x)+B$
24788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24791 \begin_layout Plain Layout
24795 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24806 \begin_layout Plain Layout
24807 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24823 \begin_layout Standard
24824 The first method is more suitable when the self-defined function should
24825 be used several times.
24828 \begin_layout Subsection
24833 \begin_layout Plain Layout
24842 \begin_layout Standard
24843 For limits there are defined besides
24853 \begin_layout Plain Layout
24873 furthermore the following functions:
24876 \begin_layout Standard
24878 \begin_inset Tabular
24879 <lyxtabular version="3" rows="5" columns="2">
24881 <column alignment="center" valignment="top" width="0">
24882 <column alignment="center" valignment="top" width="0">
24884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24887 \begin_layout Plain Layout
24893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24896 \begin_layout Plain Layout
24898 \begin_inset Note Note
24901 \begin_layout Plain Layout
24908 is only used as spacer.
24920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24923 \begin_layout Plain Layout
24931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24934 \begin_layout Plain Layout
24935 \begin_inset Formula $\varliminf$
24945 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24948 \begin_layout Plain Layout
24956 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24959 \begin_layout Plain Layout
24960 \begin_inset Formula $\varlimsup$
24970 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24973 \begin_layout Plain Layout
24981 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24984 \begin_layout Plain Layout
24985 \begin_inset Formula $\varprojlim$
24995 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24998 \begin_layout Plain Layout
25006 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25009 \begin_layout Plain Layout
25010 \begin_inset Formula $\varinjlim$
25014 \begin_inset Formula $\raisebox{-2.5mm}{}$
25030 \begin_layout Standard
25031 \begin_inset VSpace medskip
25034 The limit is created by inserting a subscript.
25035 It is set right beside the function in an inline formula:
25038 \begin_layout Standard
25040 \begin_inset Tabular
25041 <lyxtabular version="3" rows="2" columns="2">
25043 <column alignment="center" valignment="top" width="0pt">
25044 <column alignment="center" valignment="top" width="0pt">
25046 <cell alignment="center" valignment="top" usebox="none">
25049 \begin_layout Plain Layout
25055 <cell alignment="center" valignment="top" usebox="none">
25058 \begin_layout Plain Layout
25059 \begin_inset space \hspace{}
25064 \begin_inset Note Note
25067 \begin_layout Plain Layout
25080 are used here as spacer.
25092 <cell alignment="center" valignment="top" usebox="none">
25095 \begin_layout Plain Layout
25104 \begin_layout Plain Layout
25117 \begin_layout Plain Layout
25131 <cell alignment="center" valignment="top" usebox="none">
25134 \begin_layout Plain Layout
25135 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25151 \begin_layout Standard
25152 In a displayed formula the limit is set below the formula, as usual:
25153 \begin_inset Formula \[
25161 \begin_layout Subsection
25166 \begin_layout Plain Layout
25167 Functions ! modulo-
25175 \begin_layout Standard
25176 The modulo-function is special, because it exists in four variants.
25179 \begin_layout Standard
25180 The variants in a displayed formula:
25181 \begin_inset Formula \begin{align*}
25182 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25183 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25184 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25185 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25186 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25193 \begin_layout Standard
25194 In an inline formula less space is set before the function names for all
25198 \begin_layout Section
25203 \begin_layout Plain Layout
25212 \begin_layout Subsection
25213 Special Characters in Mathematical Text
25216 \begin_layout Standard
25217 The following commands can only be used in mathematical text or in TeX-mode:
25220 \begin_layout Standard
25221 \begin_inset space \hfill{}
25225 \begin_inset Tabular
25226 <lyxtabular version="3" rows="8" columns="2">
25228 <column alignment="block" valignment="top" width="0">
25229 <column alignment="block" valignment="top" width="0">
25231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25234 \begin_layout Plain Layout
25240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25243 \begin_layout Plain Layout
25251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25254 \begin_layout Plain Layout
25262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25265 \begin_layout Plain Layout
25266 \begin_inset Formula $\textrm{œ}$
25276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25279 \begin_layout Plain Layout
25287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25290 \begin_layout Plain Layout
25291 \begin_inset Formula $\textrm{Œ}$
25301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25304 \begin_layout Plain Layout
25312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25315 \begin_layout Plain Layout
25316 \begin_inset Formula $\textrm{æ}$
25326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25329 \begin_layout Plain Layout
25337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25340 \begin_layout Plain Layout
25341 \begin_inset Formula $\textrm{Æ}$
25351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25354 \begin_layout Plain Layout
25362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25365 \begin_layout Plain Layout
25366 \begin_inset Formula $\textrm{\aa}$
25376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25379 \begin_layout Plain Layout
25386 \begin_layout Plain Layout
25390 \begin_layout Plain Layout
25413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25416 \begin_layout Plain Layout
25417 \begin_inset Formula $\textrm{Å}$
25427 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25430 \begin_layout Plain Layout
25438 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25441 \begin_layout Plain Layout
25442 \begin_inset Formula $\textrm{ı}$
25456 \begin_inset space \hfill{}
25460 \begin_inset Tabular
25461 <lyxtabular version="3" rows="8" columns="2">
25463 <column alignment="block" valignment="top" width="0">
25464 <column alignment="center" valignment="top" width="0">
25466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25469 \begin_layout Plain Layout
25471 \begin_inset Note Note
25474 \begin_layout Plain Layout
25481 is used for separation, because otherwise the output will be ¡ and ¿ respective
25492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25495 \begin_layout Plain Layout
25503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25506 \begin_layout Plain Layout
25514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25517 \begin_layout Plain Layout
25518 \begin_inset Formula $\textrm{ø}$
25528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25531 \begin_layout Plain Layout
25539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25542 \begin_layout Plain Layout
25543 \begin_inset Formula $\textrm{Ø}$
25553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25556 \begin_layout Plain Layout
25564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25567 \begin_layout Plain Layout
25568 \begin_inset Formula $\textrm{ł}$
25578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25581 \begin_layout Plain Layout
25589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25592 \begin_layout Plain Layout
25593 \begin_inset Formula $\textrm{Ł}$
25603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25606 \begin_layout Plain Layout
25608 \begin_inset space \hspace{}
25616 \begin_layout Plain Layout
25630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25633 \begin_layout Plain Layout
25634 \begin_inset Formula $\textrm{!`}$
25644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25647 \begin_layout Plain Layout
25649 \begin_inset space \hspace{}
25657 \begin_layout Plain Layout
25671 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25674 \begin_layout Plain Layout
25675 \begin_inset Formula $\textrm{?`}$
25685 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25688 \begin_layout Plain Layout
25696 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25699 \begin_layout Plain Layout
25700 \begin_inset Formula $\textrm{ȷ}$
25714 \begin_inset space \hfill{}
25720 \begin_layout Standard
25722 \begin_inset Formula $\textrm{\textrm{Å}}$
25726 \begin_inset Formula $\textrm{\textrm{Ø}}$
25729 can also be inserted via the math toolbar button
25730 \begin_inset Graphics
25731 filename ../images/math/digamma.png
25739 \begin_layout Standard
25740 An exception are the commands
25743 \begin_inset space \hspace{}
25752 \begin_inset space \hspace{}
25758 , because they can be inserted in LyX directly to text.
25761 \begin_layout Subsection
25763 \begin_inset CommandInset label
25765 name "sub:Accents-in-Text"
25773 \begin_layout Plain Layout
25782 \begin_layout Standard
25783 With the following commands all letters can be accented.
25784 The commands must be inserted in TeX-mode.
25787 \begin_layout Standard
25788 \begin_inset space \hfill{}
25792 \begin_inset Tabular
25793 <lyxtabular version="3" rows="8" columns="2">
25795 <column alignment="block" valignment="top" width="0">
25796 <column alignment="block" valignment="top" width="0">
25798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25801 \begin_layout Plain Layout
25807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25810 \begin_layout Plain Layout
25818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25821 \begin_layout Plain Layout
25825 \begin_inset Quotes grd
25833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25836 \begin_layout Plain Layout
25840 \begin_layout Plain Layout
25856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25859 \begin_layout Plain Layout
25867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25870 \begin_layout Plain Layout
25874 \begin_layout Plain Layout
25890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25893 \begin_layout Plain Layout
25900 \begin_layout Plain Layout
25914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25917 \begin_layout Plain Layout
25921 \begin_layout Plain Layout
25937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25940 \begin_layout Plain Layout
25948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25951 \begin_layout Plain Layout
25955 \begin_layout Plain Layout
25971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25974 \begin_layout Plain Layout
25981 \begin_layout Plain Layout
25995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25998 \begin_layout Plain Layout
26002 \begin_layout Plain Layout
26018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26021 \begin_layout Plain Layout
26028 \begin_layout Plain Layout
26042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26045 \begin_layout Plain Layout
26049 \begin_layout Plain Layout
26065 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26068 \begin_layout Plain Layout
26075 \begin_layout Plain Layout
26089 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26092 \begin_layout Plain Layout
26096 \begin_layout Plain Layout
26116 \begin_inset space \hfill{}
26120 \begin_inset Tabular
26121 <lyxtabular version="3" rows="8" columns="2">
26123 <column alignment="block" valignment="top" width="0">
26124 <column alignment="center" valignment="top" width="0">
26126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26129 \begin_layout Plain Layout
26135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26138 \begin_layout Plain Layout
26146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26149 \begin_layout Plain Layout
26156 \begin_layout Plain Layout
26170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26173 \begin_layout Plain Layout
26177 \begin_layout Plain Layout
26193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26196 \begin_layout Plain Layout
26204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26207 \begin_layout Plain Layout
26211 \begin_layout Plain Layout
26227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26230 \begin_layout Plain Layout
26237 \begin_layout Plain Layout
26248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26251 \begin_layout Plain Layout
26255 \begin_layout Plain Layout
26271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26274 \begin_layout Plain Layout
26282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26285 \begin_layout Plain Layout
26289 \begin_layout Plain Layout
26305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26308 \begin_layout Plain Layout
26315 \begin_layout Plain Layout
26329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26332 \begin_layout Plain Layout
26336 \begin_layout Plain Layout
26352 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26355 \begin_layout Plain Layout
26362 \begin_layout Plain Layout
26376 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26379 \begin_layout Plain Layout
26383 \begin_layout Plain Layout
26399 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26402 \begin_layout Plain Layout
26409 \begin_layout Plain Layout
26423 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26426 \begin_layout Plain Layout
26430 \begin_layout Plain Layout
26450 \begin_inset space \hfill{}
26456 \begin_layout Standard
26457 \begin_inset VSpace medskip
26466 also two different characters can be accented.
26475 \begin_layout Plain Layout
26490 \begin_layout Plain Layout
26502 \begin_layout Standard
26515 can in combination with vowels directly be inserted with the keyboard without
26517 The same applies for the tilde
26521 \begin_layout Plain Layout
26522 This only applies for keyboards where the tilde is defined as accent.
26531 in combination with
26546 \begin_layout Standard
26589 , and accents inserted directly with the keyboard are also available in
26591 For the other accents there are special math commands to be used in formulas,
26593 \begin_inset CommandInset ref
26595 reference "sub:Accents-for-one"
26602 \begin_layout Standard
26603 \begin_inset VSpace bigskip
26606 Furthermore, with the command
26616 \begin_layout Plain Layout
26624 all numbers and letters can be set into a circle, quasi accented with a
26625 circle, similar to the the copyright symbol.
26628 \begin_layout Standard
26630 \begin_inset Tabular
26631 <lyxtabular version="3" rows="3" columns="2">
26633 <column alignment="center" valignment="top" width="0">
26634 <column alignment="center" valignment="top" width="0">
26636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26639 \begin_layout Plain Layout
26645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26648 \begin_layout Plain Layout
26650 \begin_inset Note Note
26653 \begin_layout Plain Layout
26660 is only used as spacer.
26672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26675 \begin_layout Plain Layout
26683 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26686 \begin_layout Plain Layout
26690 \begin_layout Plain Layout
26706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26709 \begin_layout Plain Layout
26720 raisebox{-1.5pt}{W}}
26725 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26728 \begin_layout Plain Layout
26729 \begin_inset Formula $\raisebox{4.5mm}{}$
26736 \begin_layout Plain Layout
26754 \begin_inset Formula $\raisebox{-2mm}{}$
26770 \begin_layout Standard
26771 One has to take care that the character fits in the circle.
26782 \begin_layout Plain Layout
26784 \begin_inset CommandInset ref
26786 reference "sub:Font-Sizes"
26795 specifies thereby the size of the circle.
26806 \begin_layout Plain Layout
26808 \begin_inset CommandInset ref
26810 reference "sub:Boxes-without-Frame"
26819 the character can be centered.
26822 \begin_layout Subsection
26827 \begin_layout Plain Layout
26836 \begin_layout Standard
26837 Minuscule numbers are created with the command
26847 \begin_layout Plain Layout
26856 The command can be used in formulas and in TeX-mode.
26857 The command scheme is:
26860 \begin_layout Standard
26865 oldstylenums{number}
26868 \begin_layout Standard
26873 oldstylenums{0123456789
26876 \begin_inset Formula $\oldstylenums{0123456789}$
26882 \begin_layout Subsection
26883 Miscellaneous Special Characters
26884 \begin_inset CommandInset label
26886 name "sub:Miscellaneous-Special-Characters"
26894 \begin_layout Plain Layout
26895 Special characters ! miscellaneous
26903 \begin_layout Standard
26904 The following characters can only be inserted to formulas by using commands:
26907 \begin_layout Standard
26909 \begin_inset Tabular
26910 <lyxtabular version="3" rows="4" columns="2">
26912 <column alignment="center" valignment="top" width="0">
26913 <column alignment="center" valignment="top" width="0">
26915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26918 \begin_layout Plain Layout
26924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26927 \begin_layout Plain Layout
26935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26938 \begin_layout Plain Layout
26945 \begin_layout Plain Layout
26959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26962 \begin_layout Plain Layout
26963 \begin_inset Formula $\mathcircumflex$
26973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26976 \begin_layout Plain Layout
26984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26987 \begin_layout Plain Layout
26988 \begin_inset Formula $\_$
26998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27001 \begin_layout Plain Layout
27006 \begin_layout Plain Layout
27021 \begin_layout Plain Layout
27032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27035 \begin_layout Plain Layout
27036 \begin_inset Formula $^{\circ}$
27052 \begin_layout Standard
27053 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27054 contains the following line
27058 \begin_layout Plain Layout
27059 More about this is described in
27060 \begin_inset CommandInset ref
27062 reference "sub:Text-Characters-in"
27074 \begin_layout Standard
27079 DeclareInputtext{176}{
27092 \begin_layout Section
27094 \begin_inset CommandInset label
27096 name "sec:Formula-Styles"
27104 \begin_layout Plain Layout
27113 \begin_layout Itemize
27114 There are two different alignment styles:
27118 \begin_layout Description
27119 Centered is the predefined standard
27122 \begin_layout Description
27123 Indented for this the option
27127 must be inserted in the menu
27129 Document\SpecialChar \menuseparator
27135 \begin_inset space ~
27141 \begin_layout Standard
27146 is used, the indentation can be adjusted with the length
27156 \begin_layout Plain Layout
27165 Should the distance be 15
27166 \begin_inset space \thinspace{}
27169 mm, the following command line is inserted in the LaTeX-preamble
27172 \begin_layout Standard
27182 \begin_layout Standard
27183 When no length is specified, the predefined value of 30
27184 \begin_inset space \thinspace{}
27191 \begin_layout Itemize
27192 And two different numbering styles:
27196 \begin_layout Description
27197 Right is the predefined standard
27200 \begin_layout Description
27201 Left for this the option
27205 must be inserted in the menu
27207 Document\SpecialChar \menuseparator
27213 \begin_inset space ~
27220 \begin_layout Standard
27229 can also be used together.
27230 In this case both options are inserted, separated by a comma.
27233 \begin_layout Standard
27234 The chosen styles are used for all displayed formulas of the document.
27235 When both, centered and indented formulas should be created in a document,
27241 The indented formulas are then set in a flalign environment, see
27242 \begin_inset CommandInset ref
27244 reference "sub:Flalign-Environment"
27251 \begin_layout Section
27253 \begin_inset CommandInset label
27255 name "sec:Multiline-Formulas"
27263 \begin_layout Plain Layout
27264 Formula ! multiline
27272 \begin_layout Subsection
27276 \begin_layout Standard
27277 In LyX multiline formulas are created by pressing
27284 This creates either an
27286 eqnarray environment
27288 that is described in
27289 \begin_inset CommandInset ref
27291 reference "sub:Eqnarray-Environment"
27295 or, when the option
27297 Use AMS math package
27299 in the document settings is selected, an
27303 that is described in
27304 \begin_inset CommandInset ref
27306 reference "sub:Standard-align-Environment"
27313 \begin_layout Standard
27314 There are other multiline formula environments that can be created via the
27317 Insert\SpecialChar \menuseparator
27321 These environments are described in the following sections.
27324 \begin_layout Standard
27325 In all multiline formula environments a new line is created by pressing
27331 To add or delete lines, the math toolbar buttons
27332 \begin_inset Graphics
27333 filename ../images/tabular-feature_append-row.png
27339 \begin_inset Graphics
27340 filename ../images/tabular-feature_delete-row.png
27345 , respectively, or the menu
27347 Edit\SpecialChar \menuseparator
27353 \begin_layout Subsubsection
27355 \begin_inset CommandInset label
27357 name "sub:Line-Separation"
27365 \begin_layout Plain Layout
27366 Formula ! multiline ! Line separation
27374 \begin_layout Standard
27375 There is sometimes not enough space in multiline formulas between the lines:
27376 \begin_inset Formula \begin{eqnarray*}
27377 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}\\
27378 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*}
27385 \begin_layout Standard
27386 In LaTeX additional line space is specified as optional argument of the
27388 This is not yet possible in LyX
27392 \begin_layout Plain Layout
27394 \begin_inset CommandInset href
27396 name "LyX-bug #1505"
27397 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27406 , therefore the whole formula must be inserted in TeX-mode.
27407 To add in our example space, the command
27415 is inserted at the end of the first line.
27420 \begin_layout Plain Layout
27427 \begin_layout Plain Layout
27429 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27432 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27439 \begin_layout Plain Layout
27443 left(B^{2}+x_{0}^{2}
27451 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27456 \begin_layout Plain Layout
27468 \begin_layout Standard
27469 \begin_inset VSpace bigskip
27472 To set the the line separation for all lines in a formula, the length
27482 \begin_layout Plain Layout
27492 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27503 \begin_inset space \thinspace{}
27508 \begin_inset space \thinspace{}
27511 mm additional line separation as in the previous example, the command
27514 \begin_layout Standard
27524 \begin_layout Standard
27525 is inserted in TeX-mode before the formula.
27526 This requires that the LaTeX-package
27534 \begin_layout Plain Layout
27539 is part of every LaTeX standard installation.
27548 \begin_layout Plain Layout
27554 was loaded in LaTeX-preamble with the line
27557 \begin_layout Standard
27565 \begin_layout Standard
27570 \begin_layout Plain Layout
27582 \begin_inset Formula \begin{eqnarray*}
27583 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}\\
27584 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*}
27591 \begin_layout Standard
27595 \begin_layout Plain Layout
27606 To get back to the predefined distance,
27612 is set to the value 3
27613 \begin_inset space \thinspace{}
27619 \begin_layout Subsubsection
27621 \begin_inset CommandInset label
27623 name "sub:Column-Separation"
27631 \begin_layout Plain Layout
27632 Formula ! multiline ! Column separation
27640 \begin_layout Standard
27641 Multiline formulas form a matrix.
27642 A formula in the eqnarray environment is for example a matrix with three
27644 By changing the column separation in this environment, the space beside
27645 the relation sign can be changed.
27648 \begin_layout Standard
27649 The column separation is specified with the length
27659 \begin_layout Plain Layout
27668 \begin_inset Newline newline
27671 column separation = 2
27672 \begin_inset space \thinspace{}
27682 \begin_inset Newline newline
27688 \begin_layout Standard
27698 \begin_layout Standard
27699 inserted in TeX-mode, sets for all following formulas a column separation
27701 \begin_inset space \thinspace{}
27705 To get back to the predefined distance,
27712 \begin_inset space \thinspace{}
27718 \begin_layout Standard
27720 \begin_inset space \thinspace{}
27723 cm column separation:
27727 \begin_layout Plain Layout
27739 \begin_inset Formula \begin{eqnarray*}
27741 C & \ne & A\end{eqnarray*}
27745 A formula with the predefined column separation for matrices of 10
27746 \begin_inset space \thinspace{}
27753 \begin_layout Plain Layout
27765 \begin_inset Formula \begin{eqnarray*}
27767 C & \ne & A\end{eqnarray*}
27774 \begin_layout Subsubsection
27779 \begin_layout Plain Layout
27788 \begin_layout Standard
27789 Long formulas can be typeset using these methods:
27792 \begin_layout Itemize
27793 When one side of the equation is much shorther than the line width, this
27794 one is chosen for the left side and the right side is typeset over two
27799 \begin_layout Plain Layout
27809 \begin_inset Formula \begin{eqnarray}
27810 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 \\
27811 & & -\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}
27819 \begin_layout Plain Layout
27829 \begin_inset Newline newline
27832 The minus sign at the beginning of the second line does normally not appear
27833 as operator because it is the first character of the line.
27834 Thus it would not be surrounded by space and could not be distinguished
27835 from the fraction bar.
27836 To avoid this, space was inserted behind the minus sign with the command
27847 \begin_layout Plain Layout
27855 \begin_inset CommandInset ref
27857 reference "sub:Variable-Space"
27870 \begin_layout Plain Layout
27881 \begin_layout Itemize
27882 When both sides of the equation are too long, the command
27892 \begin_layout Plain Layout
27901 It is inserted to the first column of the first line and effects that all
27902 further insertions overwrite the following columns:
27906 \begin_layout Plain Layout
27916 \begin_inset Formula \begin{eqnarray}
27917 \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 \\
27918 & & -\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 \\
27919 & & =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}
27927 \begin_layout Plain Layout
27937 \begin_inset Newline newline
27940 After the insertion of
27946 , the cursor is in a purple box that is a bit shifted to the left from the
27948 In this the formula is inserted.
27952 \begin_layout Plain Layout
27962 \begin_inset Newline newline
27965 The content of the further lines is inserted to the second or another formula
27967 The greater the column number where it was inserted, the larger the indentation.
27971 \begin_layout Plain Layout
27981 \begin_inset Newline newline
27985 \begin_inset Note Greyedout
27988 \begin_layout Plain Layout
27989 Note the following when using
27998 \begin_layout Itemize
27999 The formula doesn't use the full page width.
28001 \begin_inset space \thinspace{}
28005 \begin_inset space ~
28009 \begin_inset Formula $-B^{2}$
28012 is added to the first line in the above example, it would have been outside
28014 To better use the width, negative space can be inserted at the beginning
28018 \begin_layout Itemize
28019 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28024 \begin_layout Plain Layout
28025 \begin_inset CommandInset href
28027 name "LyX-bug #1429"
28028 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28037 One can only set the cursor at the beginning of the line and move it with
28046 \begin_layout Itemize
28047 Other methods to set long formulas are offered by the environments described
28049 \begin_inset CommandInset ref
28051 reference "sub:Multline-Environment"
28056 \begin_inset CommandInset ref
28058 reference "sub:Multiline-Formula-Parts"
28065 \begin_layout Subsubsection
28067 \begin_inset CommandInset label
28069 name "sub:Multiline-Brackets"
28077 \begin_layout Plain Layout
28078 Brackets ! for multiline expressions
28086 \begin_layout Standard
28087 For brackets spanning multiple lines the following problem occurs:
28088 \begin_inset Formula \begin{eqnarray*}
28089 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28090 & & \left.\cdots+B-D\right]\end{eqnarray*}
28097 \begin_layout Standard
28098 The closing bracket is smaller than the opening bracket because brackets
28099 with variable size may not span multiple lines.
28102 \begin_layout Standard
28103 To set the bracket size for the second line correctly, the first line is
28114 \begin_layout Plain Layout
28122 and the second line with
28130 \begin_layout Plain Layout
28144 \begin_inset CommandInset ref
28146 reference "sub:Automatic-Bracket-Size"
28161 \begin_layout Plain Layout
28187 \begin_layout Plain Layout
28206 \begin_layout Plain Layout
28225 \begin_layout Plain Layout
28237 \begin_inset Formula $\downarrow$
28246 \begin_layout Plain Layout
28254 is inserted, because the multiplication operator with its limits is the
28255 largest symbol in the first line and this should be the size for the bracket
28256 in the second line.
28259 \begin_layout Standard
28260 The result is this:
28261 \begin_inset Formula \begin{eqnarray*}
28262 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28263 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28270 \begin_layout Subsection
28274 \begin_layout Standard
28275 Align environments can be used for every kind of multiline formulas.
28276 They are specially useful to set several formulas side by side.
28279 \begin_layout Standard
28280 Align environments consist of columns.
28281 The odd columns are right aligned, the even ones left aligned.
28282 Every line in an Align environment can be numbered.
28285 \begin_layout Standard
28286 Align environments are created via the menu
28288 Insert\SpecialChar \menuseparator
28294 Edit\SpecialChar \menuseparator
28295 Math\SpecialChar \menuseparator
28296 Change Formula Type
28298 already existing formulas can be converted to Align environments.
28301 \begin_layout Standard
28302 To add or delete columns, the math toolbar buttons
28303 \begin_inset Graphics
28304 filename ../images/tabular-feature_append-column.png
28310 \begin_inset Graphics
28311 filename ../images/tabular-feature_delete-column.png
28316 , respectively, or the menu
28318 Edit\SpecialChar \menuseparator
28324 \begin_layout Subsubsection
28325 Standard align Environment
28326 \begin_inset CommandInset label
28328 name "sub:Standard-align-Environment"
28336 \begin_layout Plain Layout
28337 Formula ! multiline ! align environment
28345 \begin_layout Standard
28346 This Align environment is created by presssing
28350 in a formula or by the menu
28352 Insert\SpecialChar \menuseparator
28353 Math\SpecialChar \menuseparator
28354 AMS align Environment
28359 \begin_layout Standard
28360 An example for two formulas set side by side, that are created with a four
28361 column align environment:
28362 \begin_inset Formula \begin{align*}
28363 A & =\sin(B) & C & =D\\
28364 C & \ne A & B & \ne D\end{align*}
28368 As it can be seen, the formulas in this environment are placed so as if
28377 \begin_layout Plain Layout
28385 \begin_inset CommandInset ref
28387 reference "sub:Variable-Space"
28398 before the first and after every even column.
28399 When the formula style
28405 \begin_layout Plain Layout
28407 \begin_inset CommandInset ref
28409 reference "sec:Formula-Styles"
28420 is used, the formula is set without the
28426 before the first column.
28429 \begin_layout Subsubsection
28430 Alignat Environment
28434 \begin_layout Plain Layout
28435 Formula ! multiline ! alignat environment
28443 \begin_layout Standard
28444 The alignat environment has no predefined column separation.
28445 It can be inserted manually with the spaces that are described
28446 \begin_inset CommandInset ref
28448 reference "sub:Space"
28455 \begin_layout Standard
28456 The above example in the alignat environment where 1
28457 \begin_inset space \thinspace{}
28460 cm space was inserted at the beginning of the second formula:
28461 \begin_inset Formula \begin{alignat*}{2}
28462 A & =\sin(B) & \hspace{1cm}C & =D\\
28463 C & \ne A & B & \ne D\end{alignat*}
28467 Because the column separation can be set separately for every column, this
28468 environment is especially suitable to set three and more formulas side
28472 \begin_layout Subsubsection
28473 Flalign Environment
28474 \begin_inset CommandInset label
28476 name "sub:Flalign-Environment"
28484 \begin_layout Plain Layout
28485 Formula ! multiline ! flalign environment
28493 \begin_layout Standard
28494 In this environment the first two columns are always set as much as possible
28495 to the left and the last two ones to the right.
28497 \begin_inset Formula \begin{flalign*}
28498 A & =1 & B & =2 & C & =3\\
28499 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28506 \begin_layout Standard
28507 By creating a flalign environment with an odd number of columns where an
28508 empty TeX-brace is inserted to the last column, several formulas in a document
28509 can be set to the left, although the formula style
28514 As example the indented formula
28515 \begin_inset CommandInset ref
28517 reference "eq:VolInt"
28522 \begin_inset Formula \begin{flalign}
28523 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28527 The first two columns contain the formula.
28528 To indent it as with the formula style
28533 \begin_inset space \thinspace{}
28536 pt space was inserted at the beginning of the first column.
28539 \begin_layout Subsection
28540 Eqnarray Environment
28541 \begin_inset CommandInset label
28543 name "sub:Eqnarray-Environment"
28551 \begin_layout Plain Layout
28552 Formula ! multiline ! eqnarray environment
28560 \begin_layout Standard
28561 When this environment has been created, three blue boxes appear.
28562 The content of the first box is right aligned, the content of the last
28564 The content of the middle box appears centered and a bit smaller, because
28565 it is designed to insert there only relation characters.
28566 \begin_inset Formula \begin{eqnarray*}
28567 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28569 A & = & A\end{eqnarray*}
28576 \begin_layout Subsection
28581 \begin_layout Plain Layout
28582 Formula ! multiline ! gather environment
28590 \begin_layout Standard
28591 This environment consists of only one centered column.
28592 Every line can be numbered.
28593 \begin_inset Formula \begin{gather}
28595 X=\textrm{-}1\end{gather}
28602 \begin_layout Subsection
28603 Multline Environment
28604 \begin_inset CommandInset label
28606 name "sub:Multline-Environment"
28614 \begin_layout Plain Layout
28615 Formula ! multiline ! multline environment
28623 \begin_layout Standard
28624 The multline environment consists, like the gather environment, of only
28626 But the first line is left aligned, the last one right aligned.
28627 All other lines are centered.
28628 Therefore this environment is suitable for long formulas.
28630 \begin_inset CommandInset ref
28632 reference "eq:lefteqn"
28636 in the multline environment:
28637 \begin_inset Formula \begin{multline}
28638 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}\\
28639 -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}\\
28640 =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}
28647 \begin_layout Standard
28648 In the output only the last (first) line of a multline environment appears
28649 numbered when the document numbering is right (left).
28653 \begin_layout Plain Layout
28654 numbering styles see
28655 \begin_inset CommandInset ref
28657 reference "sec:Formula-Styles"
28669 \begin_layout Standard
28678 \begin_layout Plain Layout
28696 \begin_layout Plain Layout
28706 a centered line can be right or left aligned, respectively.
28707 The commands are used as follows:
28710 \begin_layout Standard
28715 shoveright{line content}
28721 shoveleft{line content}
28724 \begin_layout Standard
28725 \begin_inset VSpace medskip
28736 \begin_layout Plain Layout
28746 specifies the distance of the first line from the left page margin.
28747 Predefined is the length 0
28748 \begin_inset space \thinspace{}
28754 \begin_layout Standard
28755 As example the above formula where the command
28758 \begin_layout Standard
28768 \begin_layout Standard
28769 was inserted in TeX-mode before:
28773 \begin_layout Plain Layout
28785 \begin_inset Formula \begin{multline}
28786 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}\\
28787 \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}}\\
28788 =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}
28796 \begin_layout Plain Layout
28807 The second line was left aligned using
28816 \begin_layout Subsection
28817 Multiline Formula Parts
28818 \begin_inset CommandInset label
28820 name "sub:Multiline-Formula-Parts"
28828 \begin_layout Plain Layout
28829 Formula ! multiline ! formula parts
28837 \begin_layout Standard
28838 To display only parts of a formula with multiple lines, one of the following
28839 environments are used:
28856 They can be inserted via the menu
28858 Insert\SpecialChar \menuseparator
28861 or by using the commands described in this section.
28864 \begin_layout Standard
28865 The first three have the same properties as the corresponding multiline
28866 formula environments, but it is possible to set further formula parts beside
28869 \begin_inset Formula \[
28870 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28871 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28872 \right\} \textrm{Uncertainty relations}\]
28879 \begin_layout Standard
28880 To get this formula, a displayed formula is created where the command
28888 \begin_layout Plain Layout
28899 A purple box appears around the blue formula box where now columns and
28900 lines can be added.
28901 Outside the multiline environment other formula parts can be set, like
28905 \begin_layout Standard
28906 The aligned environment is also suitable for long formulas whose lines are
28907 horizontally aligned.
28908 Using aligned in a displayed formula has the advantage that the formula
28909 number is vertically centered behind the lines.
28911 \begin_inset CommandInset ref
28913 reference "eq:kurzlang"
28917 in the aligned environment:
28918 \begin_inset Formula \begin{equation}
28919 \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}|}\\
28920 & -\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}
28928 \begin_layout Standard
28929 To use the environments
28951 \begin_layout Plain Layout
28969 \begin_layout Plain Layout
28987 \begin_layout Plain Layout
28995 are inserted, respectively.
28996 The split environment has the same properties as the aligned environment
28997 but it can only have two columns.
29000 \begin_layout Subsection
29001 Text in multiline Formulas
29002 \begin_inset CommandInset label
29004 name "sub:Text-in-multiline"
29012 \begin_layout Plain Layout
29022 \begin_layout Plain Layout
29023 Formula ! multiline ! text
29031 \begin_layout Standard
29032 In the Align environments, and the multline and gather environment, text
29033 can be inserted that will appear in a separate line and doesn't affect
29034 the column alignment.
29035 To do this, the command
29043 \begin_layout Plain Layout
29053 is used in the following scheme:
29056 \begin_layout Standard
29064 \begin_layout Standard
29065 The text should not be longer than a line because it cannot be hyphenated.
29066 As LyX doesn't yet support
29072 directly, the text is written as mathematical text.
29079 must hereby be at the beginning of a line and appears in the output above
29081 An example where the text was inserted at the beginning of the second line:
29082 \begin_inset Formula \begin{align}
29083 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29084 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29091 \begin_layout Section
29096 \begin_layout Plain Layout
29106 \begin_layout Plain Layout
29107 Formula ! numbering|see
29111 \begin_layout Plain Layout
29122 \begin_layout Plain Layout
29137 \begin_layout Subsection
29141 \begin_layout Standard
29142 Numbered formulas can be created with the menu
29144 Insert\SpecialChar \menuseparator
29145 Math\SpecialChar \menuseparator
29147 \begin_inset space ~
29155 \begin_inset space ~
29161 Existing formulas can be numbered with the menu
29163 Edit\SpecialChar \menuseparator
29164 Math\SpecialChar \menuseparator
29166 \begin_inset space ~
29174 \begin_inset space ~
29180 The formula number is displayed in LyX behind the formula as number sign
29182 The number sign is replaced in the output by the formula number.
29185 \begin_layout Standard
29186 When numbering is turned on in multiline formulas, all lines will be numbered.
29187 But the numbering can be controlled with the menu
29189 Edit\SpecialChar \menuseparator
29190 Math\SpecialChar \menuseparator
29192 \begin_inset space ~
29196 \begin_inset space ~
29200 \begin_inset space ~
29208 \begin_inset space ~
29216 \begin_layout Standard
29217 Except of inline formulas, all formulas can be numbered with two different
29219 \begin_inset CommandInset ref
29221 reference "sec:Formula-Styles"
29228 \begin_layout Subsection
29230 \begin_inset CommandInset label
29232 name "sub:Cross-References"
29240 \begin_layout Plain Layout
29241 Cross-references ! to formulas
29249 \begin_layout Standard
29250 All labeled formulas can be cross-referenced.
29251 A label is added by the menu
29253 Insert\SpecialChar \menuseparator
29256 or the toolbar button
29257 \begin_inset Graphics
29258 filename ../images/label-insert.png
29264 The cursor must hereby be inside a displayed formula.
29265 A dialog pops up displaying the prefix
29270 The label is inserted there behind the prefix.
29271 The predefined prefix means
29272 \begin_inset Quotes eld
29276 \begin_inset Quotes erd
29279 and makes it easier to find labels in large documents because it marks
29280 it as formula label to divide it from e.
29281 \begin_inset space \thinspace{}
29285 \begin_inset space ~
29289 To change a label, the menu
29291 Insert\SpecialChar \menuseparator
29297 \begin_layout Standard
29298 The name of the label is displayed in LyX within two parentheses behind
29300 A formula with a label is always numbered.
29303 \begin_layout Standard
29304 Cross-references are inserted via the menu
29306 Insert\SpecialChar \menuseparator
29309 or with the toolbar button
29310 \begin_inset Graphics
29311 filename ../images/dialog-show-new-inset_ref.png
29317 A formula cross-reference appears in the output as formula number.
29318 When in the cross-reference dialog window the format
29322 is chosen, the cross-reference appears in the output as formula number
29324 \begin_inset Newline newline
29327 By right-clicking on a cross-reference in LyX, one jumps to the formula
29328 that is referenced.
29331 \begin_layout Standard
29332 Here are as examples cross-references to formulas of the following subsections:
29333 \begin_inset Note Note
29336 \begin_layout Plain Layout
29337 Note the different cross-reference types.
29345 \begin_layout Standard
29347 \begin_inset CommandInset ref
29354 \begin_inset CommandInset ref
29362 \begin_inset CommandInset ref
29368 ) big Latin letters are used for the numbering in contrary to (
29369 \begin_inset CommandInset ref
29378 \begin_layout Standard
29379 \begin_inset VSpace medskip
29382 When the argument of
29390 \begin_layout Plain Layout
29398 \begin_inset CommandInset ref
29400 reference "sub:User-defined-Numbering"
29411 contains a box like in
29412 \begin_inset CommandInset ref
29414 reference "sub:Paragraph-Boxes"
29418 , the formula cannot be referenced.
29421 \begin_layout Subsection
29426 \begin_layout Plain Layout
29427 Formula numbering ! subnumbering
29435 \begin_layout Standard
29436 With the help of the commands
29440 begin{subequations}
29448 formulas can be subnumbered.
29449 Both commands are inserted in TeX-mode.
29452 \begin_layout Standard
29454 \begin_inset Formula \begin{equation}
29455 A=C-B\label{eq:a}\end{equation}
29463 \begin_layout Plain Layout
29467 addtocounter{equation}{-1}
29476 \begin_layout Plain Layout
29480 begin{subequations}
29486 \begin_inset VSpace -5mm
29490 \begin_inset Formula \begin{equation}
29491 B=C-A\label{eq:b}\end{equation}
29496 \begin_inset Formula \begin{equation}
29497 C=A+B\label{eq:c}\end{equation}
29504 \begin_layout Standard
29508 \begin_layout Plain Layout
29520 \begin_layout Standard
29521 To create the example, the following is done:
29524 \begin_layout Enumerate
29525 first formula is inserted
29528 \begin_layout Enumerate
29533 addtocounter{equation}{-1}
29535 begin{subequations}
29539 \begin_layout Plain Layout
29548 \begin_inset Newline newline
29553 is inserted after the first formula
29556 \begin_layout Enumerate
29557 second formula is inserted
29560 \begin_layout Enumerate
29561 third formula is inserted
29564 \begin_layout Enumerate
29571 is inserted after the third formula
29574 \begin_layout Standard
29575 Every formula between the commands
29587 is subnumbered as a, b,
29588 \begin_inset Newline linebreak
29591 c, \SpecialChar \ldots{}
29592 For multiline formulas every line will be subnumbered.
29593 All subnumbered formulas are treated as
29598 But as every numbered formula increases the counter
29602 by one, the command
29608 is needed to decrease it.
29609 Otherwise the formulas
29610 \begin_inset CommandInset ref
29617 \begin_inset CommandInset ref
29624 \begin_inset CommandInset ref
29630 would be numbered as
29631 \begin_inset CommandInset ref
29638 \begin_inset CommandInset ref
29645 \begin_inset CommandInset ref
29654 \begin_layout Standard
29655 By inserting the commands in TeX-mode, a space is created between the first
29658 \begin_inset space \thinspace{}
29661 mm vertical space is inserted after the command
29665 begin{subequations}
29668 When the formula style
29674 \begin_layout Plain Layout
29676 \begin_inset CommandInset ref
29678 reference "sec:Formula-Styles"
29690 \begin_inset space \thinspace{}
29693 mm space is inserted instead.
29696 \begin_layout Standard
29697 Here is an example for a multiline formula where the numbering was turned
29698 off for the second line:
29702 \begin_layout Plain Layout
29706 begin{subequations}
29712 \begin_inset Formula \begin{eqnarray}
29713 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29714 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29715 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29723 \begin_layout Plain Layout
29735 \begin_layout Subsection
29736 User-defined Numbering
29737 \begin_inset CommandInset label
29739 name "sub:User-defined-Numbering"
29747 \begin_layout Plain Layout
29748 Formula numbering ! user-defined
29756 \begin_layout Standard
29760 \begin_layout Plain Layout
29761 Formula numbering ! self-defined delimiters
29766 With the standard numbering parentheses are set around the formula number.
29767 To replace the parentheses for example by vertical bars, the following
29768 line is added to the LaTeX-preamble:
29771 \begin_layout Standard
29783 \begin_inset Note Note
29786 \begin_layout Plain Layout
29787 This macro is already declared in the LaTeX-preamble for testing.
29788 To activate it, remove the percent sign at the beginning.
29796 \begin_layout Standard
29797 To use other characters, the vertical bars besides the
29801 are replaced by one ore more characters.
29802 To get only the formula number the vertical bars are omitted.
29805 \begin_layout Standard
29806 \begin_inset VSpace bigskip
29809 When there should be an expression of your choice instead of the consecutive
29810 formula number in parentheses behind the formula, the command
29820 \begin_layout Plain Layout
29829 \begin_inset Formula \begin{equation}
29830 A+B=C\tag{something}\label{eq:tag}\end{equation}
29834 In this example the command
29842 \begin_layout Plain Layout
29853 was inserted to the formula.
29856 \begin_layout Standard
29865 \begin_layout Plain Layout
29876 is inserted instead, the star prevents the parentheses around the expression:
29877 \begin_inset Formula \[
29878 A+B=C\tag*{something}\]
29885 \begin_layout Standard
29886 \begin_inset VSpace bigskip
29889 To restart the formula numbering with new document parts or sections, the
29890 following command is used:
29893 \begin_layout Standard
29898 @addtoreset{equation}{part}
29904 \begin_layout Plain Layout
29909 \begin_layout Plain Layout
29920 \begin_layout Plain Layout
29933 \begin_layout Plain Layout
29944 \begin_layout Plain Layout
29957 \begin_inset Newline newline
29961 \begin_inset Newline newline
29968 @addtoreset{equation}{section}
29971 \begin_layout Standard
29972 To be able to use these commands in TeX-mode, the
29973 \begin_inset Quotes eld
29977 \begin_inset Quotes erd
29980 character has to be made
29981 \begin_inset Quotes eld
29985 \begin_inset Quotes erd
29988 for LaTeX using the command
30002 So the command sequence in TeX-mode is:
30005 \begin_layout Standard
30011 \begin_inset Newline newline
30016 @addtoreset{equation}{section}
30017 \begin_inset Newline newline
30025 \begin_layout Standard
30026 In the LaTeX-preamble
30038 can be omitted as they are automatically internally inserted by LyX.
30041 \begin_layout Standard
30056 \begin_layout Plain Layout
30061 is part of the LaTeX-package
30069 \begin_layout Plain Layout
30070 Packages ! carlisle
30075 that is part of every LaTeX standard installation.
30084 \begin_layout Plain Layout
30085 Packages ! remreset
30090 has to be loaded in the LaTeX-preamble with the line
30093 \begin_layout Standard
30098 usepackage{remreset}
30101 \begin_layout Standard
30112 \begin_layout Plain Layout
30117 \begin_layout Plain Layout
30128 \begin_layout Plain Layout
30141 \begin_layout Plain Layout
30152 \begin_layout Plain Layout
30164 can be used with the same scheme as
30173 \begin_layout Standard
30174 \begin_inset VSpace bigskip
30177 Sometimes formulas should be numbered in the following form:
30180 \begin_layout Standard
30183 (section number.formula number)
30186 \begin_layout Standard
30187 The formula number should start with every section with
30188 \begin_inset Quotes eld
30192 \begin_inset Quotes erd
30198 \begin_layout Standard
30199 For this case there is the command
30209 \begin_layout Plain Layout
30217 , which is used with the following scheme:
30220 \begin_layout Standard
30225 numberwithin{counter}{sectioning}
30228 \begin_layout Standard
30229 Counter denotes what kind of numbering is affected, sectioning denotes what
30230 number is before the dot.
30233 \begin_layout Standard
30234 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30237 \begin_layout Standard
30242 numberwithin{equation}{section}
30245 \begin_layout Standard
30246 This is the result:
30250 \begin_layout Plain Layout
30254 numberwithin{equation}{section}
30260 \begin_inset Formula \begin{equation}
30261 A+B=C\end{equation}
30268 \begin_layout Standard
30270 \begin_inset space \thinspace{}
30274 \begin_inset space ~
30277 tables so that the number of the part is the sectioning,
30278 \begin_inset Newline newline
30285 numberwithin{table}{part}
30290 \begin_layout Standard
30291 To go back to the standard numbering or to prevent this kind of numbering
30292 when it is defined by the document class, the following command is inserted
30293 as TeX-Code or to the LaTeX-preamble:
30296 \begin_layout Standard
30309 \begin_layout Plain Layout
30323 \begin_layout Plain Layout
30339 \begin_inset Newline newline
30347 \begin_inset Newline newline
30359 \begin_layout Standard
30366 uses internally the command
30372 , described above, that also needs to be reverted.
30376 \begin_layout Plain Layout
30383 \begin_layout Plain Layout
30387 @removefromreset{equation}{section}
30390 \begin_layout Plain Layout
30402 \begin_layout Subsection
30403 Numbering with Roman Numbers and Letters
30404 \begin_inset CommandInset label
30406 name "sub:Numbering-with-Roman"
30414 \begin_layout Plain Layout
30415 Formula numbering ! with letters
30424 \begin_layout Plain Layout
30425 Formula numbering ! with Roman numbers
30433 \begin_layout Standard
30434 Formulas can also be numbered with Roman numbers and Latin letters.
30435 To number for example with small Roman numbers, the command
30438 \begin_layout Standard
30450 \begin_layout Standard
30451 is inserted before the formula in TeX-mode.
30462 \begin_layout Plain Layout
30470 redefines the predefined command
30486 \begin_layout Plain Layout
30493 has the same scheme like the command
30499 that is described in
30500 \begin_inset CommandInset ref
30502 reference "sec:User-defined-commands"
30516 is the formula counter.
30523 is used as prefix for a counter, the value of the counter is output as
30525 When a formula is numbered, LaTeX sets internally the command
30531 behind the formula.
30540 \begin_layout Plain Layout
30550 outputs the counter as small Roman number.
30553 \begin_layout Standard
30554 All formulas behind the command
30564 are now numbered Roman.
30565 To switch to numbering with big Roman numbers, the command is inserted
30582 \begin_layout Plain Layout
30594 \begin_inset Quotes eld
30598 \begin_inset Quotes erd
30601 with small Latin letters there is the command
30611 \begin_layout Plain Layout
30619 , for big ones there is the command
30629 \begin_layout Plain Layout
30642 \begin_layout Standard
30643 \begin_inset Note Greyedout
30646 \begin_layout Plain Layout
30651 Only maximal 26 formulas can be numbered with Latin letters in one document.
30659 \begin_layout Standard
30663 \begin_layout Plain Layout
30679 \begin_layout Standard
30680 \begin_inset Formula \begin{equation}
30681 A=\textrm{small roman}\label{eq:rom}\end{equation}
30689 \begin_layout Plain Layout
30703 \begin_inset Formula \begin{equation}
30704 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30712 \begin_layout Plain Layout
30726 \begin_inset Formula \begin{equation}
30727 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30735 \begin_layout Plain Layout
30749 \begin_inset Formula \begin{equation}
30750 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30757 \begin_layout Standard
30758 To switch back to the default numbering, insert the command:
30761 \begin_layout Standard
30774 \begin_layout Plain Layout
30785 \begin_layout Standard
30789 \begin_layout Plain Layout
30803 \begin_inset Formula \begin{equation}
30804 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30811 \begin_layout Standard
30812 \begin_inset VSpace medskip
30815 As you see, formulas are numbered serially independent from the numbering
30817 When then numbering should start with
30818 \begin_inset Quotes eld
30822 \begin_inset Quotes erd
30825 when the style is changed, new equation counters have to be defined.
30826 A description about this can be found in the file
30827 \begin_inset CommandInset href
30829 target "Formula-numbering.lyx"
30836 \begin_layout Section
30837 User-defined commands
30838 \begin_inset CommandInset label
30840 name "sec:User-defined-commands"
30848 \begin_layout Plain Layout
30849 User-defined commands
30857 \begin_layout Standard
30858 Many LaTeX-commands are too long to be used frequently.
30859 But it is possible to define with the command
30869 \begin_layout Plain Layout
30877 new shorter commands.
30880 \begin_layout Standard
30881 The command scheme of
30890 \begin_layout Standard
30895 newcommand{new command name}[number of arguments][optional
30900 \begin_inset Newline newline
30907 \begin_layout Plain Layout
30922 \begin_layout Plain Layout
30929 {command definition}
30932 \begin_layout Standard
30933 \begin_inset Note Greyedout
30936 \begin_layout Plain Layout
30941 Assure that the name of the new command is not already used in your document
30942 or by LaTeX-packages that you use.
30943 When you for example define the command
30955 , you get an error message because
30961 is already defined as command for
30962 \begin_inset Quotes eld
30966 \begin_inset Formula $\le$
30970 \begin_inset Quotes erd
30981 \begin_layout Standard
30982 \begin_inset Note Greyedout
30985 \begin_layout Plain Layout
30990 The names of user-defined commands may only consist of Latin letters.
30998 \begin_layout Standard
30999 The number of arguments is an integer in the range 0
31000 \begin_inset space \thinspace{}
31004 \begin_inset space \thinspace{}
31007 9 and specifies how many arguments the new command should have.
31008 With the optional value a value for an optional argument can be predefined.
31009 When this is done, the
31017 rgument of the new command is automatically an optional one.
31020 \begin_layout Standard
31021 Here are some examples:
31024 \begin_layout Itemize
31025 To define the command
31037 , the LaTeX-preamble line is:
31041 \begin_layout Plain Layout
31053 \begin_inset Newline newline
31065 \begin_layout Itemize
31066 To define the command
31078 , the argument (that should be underlined) must be taken into account.
31079 For this the preamble line is:
31083 \begin_layout Plain Layout
31095 \begin_inset Newline newline
31110 \begin_layout Plain Layout
31122 \begin_inset Newline newline
31131 acts as argument placeholder, the
31135 behind it denotes that it is the placeholder for the first argument.
31138 \begin_layout Itemize
31146 \begin_inset space \thinspace{}
31150 \begin_inset space ~
31163 \begin_layout Plain Layout
31175 \begin_inset Newline newline
31184 framebox#1#2{$#3$}}
31190 \begin_layout Plain Layout
31202 \begin_inset Newline newline
31207 The two Dollar signs creates the extra formula needed for
31214 \begin_inset CommandInset ref
31216 reference "sub:Boxes-with-Frame"
31223 \begin_layout Itemize
31224 To create a new command for
31230 where the color for the box needn't to be specified, the argument for the
31231 color is defined optional:
31235 \begin_layout Plain Layout
31247 \begin_inset Newline newline
31256 fcolorbox{#2}{#1}{$#3$}}
31262 \begin_layout Plain Layout
31272 \begin_inset Newline newline
31275 When the color is not specified when using
31281 , the predefined color
31288 \begin_layout Standard
31289 A test of the new defined commands:
31292 \begin_layout Standard
31294 \begin_inset Tabular
31295 <lyxtabular version="3" rows="6" columns="2">
31297 <column alignment="center" valignment="top" width="0">
31298 <column alignment="center" valignment="top" width="0">
31300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31303 \begin_layout Plain Layout
31309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31312 \begin_layout Plain Layout
31314 \begin_inset Note Note
31317 \begin_layout Plain Layout
31324 is only used as spacer.
31336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31339 \begin_layout Plain Layout
31346 \begin_layout Plain Layout
31360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31363 \begin_layout Plain Layout
31364 \begin_inset Formula $A\gr B$
31374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31377 \begin_layout Plain Layout
31385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31388 \begin_layout Plain Layout
31389 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31402 \begin_layout Plain Layout
31406 \begin_inset Formula $\to$
31412 \begin_inset Formula $\to$
31423 \begin_layout Plain Layout
31437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31440 \begin_layout Plain Layout
31441 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31454 \begin_layout Plain Layout
31458 \begin_inset Formula $\to$
31469 \begin_layout Plain Layout
31483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31486 \begin_layout Plain Layout
31487 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31500 \begin_layout Plain Layout
31506 \begin_inset Formula $\to$
31517 \begin_layout Plain Layout
31531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31534 \begin_layout Plain Layout
31535 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31551 \begin_layout Section
31555 \begin_layout Standard
31556 LyX supports two types of commutative diagrams:
31564 that are explained in the following.
31567 \begin_layout Subsection
31572 \begin_layout Plain Layout
31581 \begin_layout Standard
31582 To create this type of diagrams, the LaTeX-package
31588 \begin_layout Plain Layout
31593 is part of every LaTeX standard installation.
31604 \begin_layout Plain Layout
31611 It is loaded in the LaTeX-preamble with the line
31614 \begin_layout Standard
31622 \begin_layout Standard
31623 Diagrams visualize relations and look like this:
31624 \begin_inset Formula \[
31625 \begin{CD}A@>>>B@>>>C\\
31627 F@<<<E@<<<D\end{CD}\]
31634 \begin_layout Standard
31635 To get them, the command
31643 \begin_layout Plain Layout
31653 is inserted to a formula.
31654 A blue box appears with two dashed lines where further commands can be
31660 a new line is created.
31661 Horizontal relations are inserted in odd, vertical in even formula lines.
31664 \begin_layout Standard
31665 To create the relations there are the following commands:
31668 \begin_layout Itemize
31673 creates a left arrow,
31684 \begin_layout Itemize
31689 creates an up arrow,
31697 a vertical equal sign
31700 \begin_layout Itemize
31706 is a placeholder for non-existent relations
31709 \begin_layout Standard
31710 All arrows can be labeled as follows:
31713 \begin_layout Itemize
31714 Is text inserted between the first and second < or >, resp., it is placed
31716 When it is inserted between the second and third one, it appears under
31720 \begin_layout Itemize
31721 When text for vertical arrows is inserted between the first and second A
31722 or V, resp., it is placed left beside the arrow.
31723 When it is inserted between the second and third one, it appears right
31725 If the text contains an A or V, these letters must be set into a TeX-brace.
31728 \begin_layout Standard
31729 As example a diagram with all possible relations:
31732 \begin_layout Standard
31733 \begin_inset Formula \[
31734 \begin{CD}A@>j>>B@>>k>C@=F\\
31736 D@<<j<E@>k>>F@=C\end{CD}\]
31743 \begin_layout Standard
31744 The command for this is:
31745 \begin_inset Newline newline
31756 \begin_layout Plain Layout
31765 A@>j>>B@>>k>C@=F Ctrl-Enter
31766 \begin_inset Newline newline
31773 \begin_layout Plain Layout
31788 \begin_layout Plain Layout
31801 \begin_layout Plain Layout
31813 \begin_inset Formula $\to$
31819 \begin_inset Newline newline
31826 \begin_layout Plain Layout
31841 \begin_layout Plain Layout
31854 \begin_layout Plain Layout
31864 \begin_layout Subsection
31869 \begin_layout Plain Layout
31870 Diagrams ! xymatrix
31878 \begin_layout Standard
31879 To be able to use xymatrices, the LaTeX-package
31884 A xymatrix is created by inserting the command
31891 Then you are able to add new matrix columns and rows like for normal matrices,
31893 \begin_inset CommandInset ref
31895 reference "sec:Matrices"
31902 \begin_layout Standard
31903 xymatrix offers many possibilities to create commutative diagrams and decoration
31904 s that are explained in detail in this manual:
31905 \begin_inset CommandInset href
31907 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31914 \begin_layout Standard
31915 \begin_inset Newpage newpage
31921 \begin_layout Section
31926 \begin_layout Plain Layout
31939 \begin_layout Plain Layout
31940 Other useful math tips can be found in
31941 \begin_inset CommandInset citation
31956 \begin_layout Plain Layout
31964 \begin_inset Note Note
31967 \begin_layout Plain Layout
31970 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31973 \begin_layout Plain Layout
31976 texorpdfstring is in section
31977 \begin_inset CommandInset ref
31979 reference "sub:Formulas-in-Section"
31992 \begin_layout Plain Layout
32002 \begin_layout Plain Layout
32007 \begin_layout Plain Layout
32014 Chemical characters
32018 \begin_layout Plain Layout
32033 \begin_layout Subsection
32034 Chemical Symbols and Equations
32035 \begin_inset CommandInset label
32037 name "sub:Chemical-Symbols-and"
32045 \begin_layout Plain Layout
32046 Chemical characters ! Symbols
32055 \begin_layout Plain Layout
32065 \begin_layout Plain Layout
32074 \begin_layout Standard
32075 An example text from chemistry:
32078 \begin_layout Quote
32080 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32083 -ion reacts with two
32084 \begin_inset Formula $\mathrm{Na^{+}}$
32087 -ions to sodium sulfate
32088 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32092 The chemical equation for this is:
32093 \begin_inset Formula \[
32094 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32101 \begin_layout Standard
32102 This chemical equation can directly be created as formula.
32103 To avoid that the symbols appear italic, everything is highlighted and
32104 changed by the shortcut
32107 \begin_inset space ~
32112 to the upright font style.
32116 \begin_layout Plain Layout
32122 \begin_inset CommandInset ref
32124 reference "sub:Font-Styles"
32136 \begin_layout Subsection
32141 \begin_layout Plain Layout
32150 \begin_layout Standard
32151 Negative numbers often look ugly in formulas because the minus sign before
32152 the number is set with the same length as the minus operator sign.
32153 When writing the negative number in normal text, the minus sign appears
32157 \begin_layout Standard
32158 Thus, the problem disappears when converting the minus sign to mathematical
32162 \begin_layout Standard
32163 An example to visualize the problem:
32166 \begin_layout Standard
32168 \begin_inset Tabular
32169 <lyxtabular version="3" rows="3" columns="2">
32171 <column alignment="right" valignment="top" width="0">
32172 <column alignment="left" valignment="top" width="0">
32174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32177 \begin_layout Plain Layout
32183 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32186 \begin_layout Plain Layout
32194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32197 \begin_layout Plain Layout
32203 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32206 \begin_layout Plain Layout
32207 \begin_inset Formula $x=-2$
32217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32220 \begin_layout Plain Layout
32226 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32229 \begin_layout Plain Layout
32230 \begin_inset Formula $x=\textrm{-}2$
32246 \begin_layout Subsection
32247 Comma as Decimal Separator
32251 \begin_layout Plain Layout
32260 \begin_layout Standard
32261 In LaTeX a comma inside a formula is used, according to the English convention,
32262 as number group separator.
32263 So there will be space added behind all commas in formulas.
32266 \begin_layout Standard
32267 To avoid this, the comma is highlighted and changed to mathematical text
32271 \begin_inset space ~
32279 \begin_layout Standard
32280 To use all formula commas in the document as decimal separator, the file
32289 \begin_layout Plain Layout
32294 is part of the LaTeX-package
32302 \begin_layout Plain Layout
32307 \begin_layout Plain Layout
32330 \begin_layout Plain Layout
32336 is loaded with the LaTeX-preamble line
32339 \begin_layout Standard
32347 \begin_layout Subsection
32349 \begin_inset CommandInset label
32351 name "sub:Physical-Vectors"
32359 \begin_layout Plain Layout
32368 \begin_layout Standard
32369 Predefined vectors are offered by the LaTeX-package
32377 \begin_layout Plain Layout
32382 should be part of every LaTeX standard installation.
32391 \begin_layout Plain Layout
32397 that is loaded with the LaTeX-preamble line
32400 \begin_layout Standard
32408 \begin_layout Standard
32412 \begin_layout Plain Layout
32422 \begin_inset Note Note
32425 \begin_layout Plain Layout
32426 The following table will only be displayed when the LaTeX-package
32435 The following commands are defined:
32438 \begin_layout Standard
32440 \begin_inset Tabular
32441 <lyxtabular version="3" rows="4" columns="2">
32443 <column alignment="center" valignment="top" width="0">
32444 <column alignment="center" valignment="top" width="0">
32446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32449 \begin_layout Plain Layout
32455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32458 \begin_layout Plain Layout
32466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32469 \begin_layout Plain Layout
32479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32482 \begin_layout Plain Layout
32483 \begin_inset Formula $\Bra{\psi}$
32493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32496 \begin_layout Plain Layout
32506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32509 \begin_layout Plain Layout
32510 \begin_inset Formula $\Ket{\psi}$
32520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32523 \begin_layout Plain Layout
32535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32538 \begin_layout Plain Layout
32539 \begin_inset Formula $\Braket{\psi|\phi}$
32555 \begin_layout Standard
32562 assures that all vertical bars are set in the size of the surrounding brackets:
32563 \begin_inset Formula \[
32564 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32572 \begin_layout Plain Layout
32582 \begin_inset Note Note
32585 \begin_layout Plain Layout
32586 The following will be displayed when the LaTeX-package
32598 \begin_layout Standard
32599 You need to install the LaTeX-package
32603 to see the rest of this subsection in the output.
32606 \begin_layout Standard
32610 \begin_layout Plain Layout
32622 \begin_layout Standard
32629 can also be achieved using the command
32635 , that is described in
32636 \begin_inset CommandInset ref
32638 reference "sub:Automatic-Bracket-Size"
32645 \begin_layout Subsection
32646 Self-defined Fractions
32647 \begin_inset CommandInset label
32649 name "sub:Self-defined-Fractions"
32657 \begin_layout Plain Layout
32658 Fractions ! self-defined
32666 \begin_layout Standard
32667 To define custom commands for fractions, the command
32677 \begin_layout Plain Layout
32685 is used in the following scheme:
32688 \begin_layout Standard
32701 bracket}{fraction bar thickness}{style}
32702 \begin_inset Newline newline
32709 \begin_layout Plain Layout
32724 \begin_layout Plain Layout
32731 {numerator}{denominator}
32734 \begin_layout Standard
32735 The style is a number in the range of 0
32736 \begin_inset space \thinspace{}
32740 \begin_inset space \thinspace{}
32746 \begin_layout Standard
32748 \begin_inset Tabular
32749 <lyxtabular version="3" rows="5" columns="2">
32751 <column alignment="center" valignment="top" width="0">
32752 <column alignment="center" valignment="top" width="0">
32754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32757 \begin_layout Plain Layout
32763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32766 \begin_layout Plain Layout
32774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32777 \begin_layout Plain Layout
32783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32786 \begin_layout Plain Layout
32787 display style formula
32794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32797 \begin_layout Plain Layout
32803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32806 \begin_layout Plain Layout
32814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32817 \begin_layout Plain Layout
32823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32826 \begin_layout Plain Layout
32834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32837 \begin_layout Plain Layout
32843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32846 \begin_layout Plain Layout
32860 \begin_layout Standard
32861 When no style is given, the size is adjusted to the surrounding environment
32862 like for the command
32871 \begin_layout Standard
32872 When no fraction bar thickness is given, the predefined value of 0.4
32873 \begin_inset space \thinspace{}
32879 \begin_layout Standard
32880 \begin_inset VSpace medskip
32883 For example, the commands
32896 \begin_inset CommandInset ref
32898 reference "sub:Fractions"
32902 are defined with the commands
32905 \begin_layout Standard
32914 genfrac{}{}{}{0}{#1}{#2}}
32917 \begin_layout Standard
32921 \begin_layout Standard
32930 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32933 \begin_layout Standard
32934 \begin_inset VSpace medskip
32937 To define a fraction where the fraction bar thickness can be given as optional
32938 argument, the following line is inserted to the LaTeX-preamble:
32941 \begin_layout Standard
32950 genfrac{}{}{#1}{}{#2}{#3}}
32953 \begin_layout Standard
32955 \begin_inset Formula \begin{align*}
32956 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32957 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32961 As one can see, the distance of the numerator and the denominator to the
32962 fraction bar is round about three times the bar thickness.
32965 \begin_layout Subsection
32967 \begin_inset CommandInset label
32969 name "sub:Canceled-Formulas"
32977 \begin_layout Plain Layout
32986 \begin_layout Standard
32987 To cancel formulas or formula parts, the LaTeX-package
32995 \begin_layout Plain Layout
33000 is part of every LaTeX standard installation.
33009 \begin_layout Plain Layout
33015 has to be loaded with the LaTeX-preamble line
33018 \begin_layout Standard
33023 usepackage[samesize]{cancel}
33026 \begin_layout Standard
33027 There are four ways to cancel formulas:
33030 \begin_layout Standard
33032 \begin_inset Tabular
33033 <lyxtabular version="3" rows="5" columns="2">
33035 <column alignment="center" valignment="top" width="0">
33036 <column alignment="center" valignment="top" width="0">
33038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33041 \begin_layout Plain Layout
33047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33050 \begin_layout Plain Layout
33052 \begin_inset Note Note
33055 \begin_layout Plain Layout
33068 are used here as spacer.
33080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33083 \begin_layout Plain Layout
33092 \begin_layout Plain Layout
33106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33109 \begin_layout Plain Layout
33110 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33123 \begin_layout Plain Layout
33132 \begin_layout Plain Layout
33146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33149 \begin_layout Plain Layout
33150 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33163 \begin_layout Plain Layout
33172 \begin_layout Plain Layout
33186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33189 \begin_layout Plain Layout
33190 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33203 \begin_layout Plain Layout
33207 \begin_inset Formula $\to$
33218 \begin_layout Plain Layout
33232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33235 \begin_layout Plain Layout
33236 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33252 \begin_layout Standard
33259 is especially suitable to visualize the reduction of fractions within formulas:
33260 \begin_inset Formula \[
33261 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33268 \begin_layout Subsection
33269 Formulas in Section Headings
33270 \begin_inset CommandInset label
33272 name "sub:Formulas-in-Section"
33280 \begin_layout Plain Layout
33281 Formula ! in section headings
33289 \begin_layout Standard
33290 When formulas are used in section headings, the following has to be taken
33294 \begin_layout Standard
33295 \begin_inset Note Greyedout
33298 \begin_layout Plain Layout
33307 \begin_layout Plain Layout
33308 Packages ! hyperref
33313 support is enabled in the document settings dialog under
33316 \begin_inset space ~
33321 , PDF-bookmarks are created for every section heading in the table of contents.
33322 If a section heading contains formulas, they are incorrectly displayed
33323 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33332 \begin_layout Standard
33333 Both problems can be solved by inserting at the end of the section heading
33334 a short title with the menu
33336 Insert\SpecialChar \menuseparator
33338 \begin_inset space ~
33344 Short titles are used as alternative for multiline section headings to
33345 keep the table of contents clearly arranged.
33346 Only the short title appears in the table of contents and therefore also
33347 in the PDF-bookmark.
33350 \begin_layout Standard
33351 When formulas should be used in the table of contents but
33355 is used, one can use the following command in TeX-mode:
33358 \begin_layout Standard
33363 texorpdfstring{part}{alternative}
33367 \begin_layout Plain Layout
33378 \begin_layout Standard
33379 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33380 This can be characters, formulas, footnotes, but also cross-references.
33381 The alternative is used instead of the part for the bookmark.
33384 \begin_layout Standard
33385 Here are two example headings:
33386 \begin_inset VSpace -3mm
33393 \begin_layout Plain Layout
33405 \begin_layout Subsubsection
33406 Heading without formula in table of contents
33407 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33411 \begin_inset OptArg
33414 \begin_layout Plain Layout
33415 Heading without formula in table of contents
33423 \begin_layout Subsubsection
33424 Heading with formula in table of contents
33428 \begin_layout Plain Layout
33438 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33445 \begin_layout Plain Layout
33455 \begin_layout Standard
33459 \begin_layout Plain Layout
33468 In the first heading a short title was used, in the second one
33477 \begin_layout Standard
33478 To get the same formatting as for the other headings, the complete heading
33487 \begin_layout Plain Layout
33489 \begin_inset CommandInset ref
33491 reference "sub:Bold-Formulas"
33503 \begin_layout Subsection
33504 Formulas in multi-column Text
33508 \begin_layout Plain Layout
33509 Formula ! in multi-column text
33517 \begin_layout Standard
33518 Formulas in multi-column text are often too wide to fit into a column and
33519 thus need to be set over the whole page width.
33520 This is done by using the LaTeX-package
33528 \begin_layout Plain Layout
33533 is part of every LaTeX standard installation.
33542 \begin_layout Plain Layout
33543 Packages ! multicol
33548 , that is loaded with the LaTeX-preamble line
33551 \begin_layout Standard
33556 usepackage{multicol}
33559 \begin_layout Standard
33560 \begin_inset Note Greyedout
33563 \begin_layout Plain Layout
33564 Note herby that the setting
33567 \begin_inset space ~
33574 Document\SpecialChar \menuseparator
33580 \begin_inset space ~
33600 \begin_layout Standard
33601 Before the multi-column text the command
33604 \begin_layout Standard
33609 begin{multicols}{column number}
33612 \begin_layout Standard
33613 is written in TeX-mode.
33614 The column number is a number in the range of 2
33615 \begin_inset space \thinspace{}
33619 \begin_inset space \thinspace{}
33623 Before the formula the multi-column text is ended by inserting the command
33626 \begin_layout Standard
33634 \begin_layout Standard
33638 \begin_layout Standard
33639 Due to the command some space is automatically added before the formula.
33641 \begin_inset space \thinspace{}
33644 mm vertical space is inserted before the formula.
33645 When the formula style
33651 \begin_layout Plain Layout
33653 \begin_inset CommandInset ref
33655 reference "sec:Formula-Styles"
33667 \begin_inset space \thinspace{}
33670 mm space is inserted instead.
33673 \begin_layout Standard
33674 As example a multi-column text with a displayed formula:
33677 \begin_layout Standard
33681 \begin_layout Plain Layout
33685 begin{multicols}{2}
33690 Das Spektrum wird fouriertransformiert.
33691 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33692 , Lösungsmittel) zu trennen.
33693 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33694 nun das Aussehen des Ausgangssignals.
33695 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33696 über alle Phasen integrieren muss.
33698 \begin_inset Formula $S$
33701 unser normiertes Ausgangssignal and
33702 \begin_inset Formula $P$
33705 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33709 \begin_layout Plain Layout
33719 \begin_inset VSpace -6mm
33723 \begin_inset Formula \begin{equation}
33724 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33732 \begin_layout Plain Layout
33736 begin{multicols}{2}
33742 \begin_inset Formula $S_{0}$
33745 das Signal ohne Gradient ist and the Normierungsbedingung
33746 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33750 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33752 \begin_inset Formula $\nicefrac{\pi}{2}$
33756 \begin_inset space \thinspace{}
33759 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33760 das Signal zusätzlich abschwächt.
33761 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33763 \begin_inset Formula $T_{2}$
33769 \begin_layout Standard
33773 \begin_layout Plain Layout
33785 \begin_layout Subsection
33786 Formulas with Description of Variables
33790 \begin_layout Plain Layout
33791 Formula ! with description of variables
33799 \begin_layout Standard
33800 To describe variables within a formula, like in formula
33801 \begin_inset CommandInset ref
33803 reference "eq:within"
33812 \begin_inset Formula $n$
33816 \begin_inset space ~
33819 matrix is used with left aligned columns for the
33820 \begin_inset Formula $n$
33827 \begin_layout Plain Layout
33829 \begin_inset CommandInset ref
33831 reference "sec:Matrices"
33840 To set the description in a smaller size, before the matrix e.
33841 \begin_inset space \thinspace{}
33845 \begin_inset space ~
33858 \begin_layout Plain Layout
33860 \begin_inset CommandInset ref
33862 reference "sub:Font-Sizes"
33874 \begin_layout Standard
33875 When the formula style
33881 \begin_layout Plain Layout
33883 \begin_inset CommandInset ref
33885 reference "sec:Formula-Styles"
33906 \begin_layout Plain Layout
33913 only works in formulas with the style
33918 \begin_inset CommandInset ref
33920 reference "sub:Variable-Space"
33929 is inserted before and after the matrix to have the same separation of
33930 the matrix from the equation and the side margin.
33933 \begin_layout Standard
33934 When the formula style
33938 is used, the method described in
33939 \begin_inset CommandInset ref
33941 reference "sub:Flalign-Environment"
33945 is used to indent formulas.
33947 \begin_inset CommandInset ref
33949 reference "eq:within"
33953 consists of five columns whereas in the first two columns contain the equation,
33954 the third the matrix, and the last one an empty TeX-brace.
33955 \begin_inset Formula \begin{flalign}
33956 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33957 \rho & \textrm{density}\\
33958 V & \textrm{volume}\\
33959 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33966 \begin_layout Subsection
33967 Upright small Greek Letters
33968 \begin_inset CommandInset label
33970 name "sub:Upright-small-Greek"
33978 \begin_layout Plain Layout
33979 Greek letters ! upright
33987 \begin_layout Standard
33988 Most of the math fonts only provide italic small Greek letters.
33989 But for symbols of elementary particles like pions and neutrinos, upright
33990 Greek letters are needed.
33999 \begin_layout Plain Layout
34004 is part of the LaTeX-package
34012 \begin_layout Plain Layout
34017 \begin_layout Plain Layout
34040 \begin_layout Plain Layout
34046 that is loaded with the LaTeX-preamble line
34049 \begin_layout Standard
34054 usepackage{upgreek}
34057 \begin_layout Standard
34063 \begin_layout Plain Layout
34073 \begin_inset Note Note
34076 \begin_layout Plain Layout
34077 The following table will only be displayed when the LaTeX-package
34086 They are created when the command for a small Greek letters is started
34092 For example the command
34099 \begin_inset Formula $\uptau$
34105 \begin_layout Standard
34106 With these commands reactions of elementary particles can be typeset:
34107 \begin_inset Formula \[
34108 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34115 \begin_layout Standard
34116 The upright letters are more bold and wider than the italic ones.
34117 They should therefore not be used for units like
34118 \begin_inset Quotes eld
34122 \begin_inset Quotes erd
34128 \begin_layout Standard
34132 \begin_layout Plain Layout
34142 \begin_inset Note Note
34145 \begin_layout Plain Layout
34146 The following will be displayed when the LaTeX-package
34158 \begin_layout Standard
34159 You need to install the LaTeX-package
34163 to see the rest of this subsection in the output.
34166 \begin_layout Standard
34170 \begin_layout Plain Layout
34182 \begin_layout Subsection
34183 Text Characters in Formulas
34184 \begin_inset CommandInset label
34186 name "sub:Text-Characters-in"
34194 \begin_layout Plain Layout
34203 \begin_layout Standard
34204 In some cases you might want to insert text characters directly into formulas.
34205 When for example the centered dot · is often used in formulas like
34206 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34209 , one would have to insert the command
34219 \begin_layout Plain Layout
34221 \begin_inset CommandInset ref
34223 reference "sub:Binary-Operators"
34232 all the time, because this character is defined in all encodings as text
34234 But the encoding can be changed by this LaTeX-preamble line:
34237 \begin_layout Standard
34242 Declare Inputtext{183}{
34252 f\SpecialChar \textcompwordmark{}
34256 \begin_layout Standard
34257 The character encoding (menu
34259 Document\SpecialChar \menuseparator
34260 Settings\SpecialChar \menuseparator
34263 ) specifies what character appears when a keyboard key is pressed.
34264 When the key for the character '·' is pressed, internally the command
34271 But this command is not available in a formula so that you would get LaTeX-erro
34273 With the changed encoding the right command is chosen automatically, depending
34274 on if the character was inserted into a formula or not.
34277 \begin_layout Standard
34278 The encoding of several characters is saved in definition files.
34279 Fore example the encoding
34283 is defined in the file
34287 that is in the installation folder of LaTeX.
34288 Encodings should only be changed via the LaTeX-preamble and not in the
34290 Otherwise own documents could not be edited by other LyX users working
34291 on other computers.
34294 \begin_layout Standard
34295 \begin_inset VSpace medskip
34298 Besides the centered dot, in this document the degree sign ° is defined
34299 with the following LaTeX-preamble line so that it can directly be inserted
34303 \begin_layout Standard
34308 DeclareInputtext{176}{
34318 f\SpecialChar \textcompwordmark{}
34322 \begin_layout Standard
34323 \begin_inset Newpage newpage
34329 \begin_layout Section
34331 Typographic Advises
34335 \begin_layout Plain Layout
34336 Typographic Advises
34344 \begin_layout Standard
34345 This section is a summary of the most important typographic rules, listed
34350 \begin_layout Plain Layout
34351 This collection was partly taken from the German semi-official dictionary
34353 \begin_inset Quotes eld
34357 \begin_inset Quotes erd
34361 \begin_inset CommandInset citation
34367 that lists some of the ISO rules.
34375 \begin_layout Itemize
34384 \begin_layout Plain Layout
34385 done with font styles, see
34386 \begin_inset CommandInset ref
34388 reference "sub:Font-Styles"
34398 \begin_inset space \thinspace{}
34402 \begin_inset Newline newline
34405 Between the value and the unit is the smallest space, see
34406 \begin_inset CommandInset ref
34408 reference "sub:Predefined-Space"
34413 \begin_inset Newline newline
34416 This convention is automatically fulfilled when the command
34423 When it is entered to a formula, two boxes appear.
34424 In the first one the value is inserted, in the second one the unit, and
34426 \begin_inset Formula $\unit[30]{km/h}$
34430 \begin_inset space \thinspace{}
34440 is not a real LaTeX command but the command
34446 , therefore you cannot use it in TeX code.
34449 \begin_layout Itemize
34450 Percent and perthousand signs are set like physical units:
34451 \begin_inset Newline newline
34455 \begin_inset space \thinspace{}
34461 \begin_layout Itemize
34462 The degree sign follows directly on the value: 15°, but not when it is used
34464 \begin_inset space \thinspace{}
34470 \begin_layout Itemize
34471 In numbers with more than four digits the smallest space is inserted before
34472 every third digit to group them:
34482 \begin_inset space \thinspace{}
34486 \begin_inset space \thinspace{}
34492 \begin_layout Itemize
34493 For dimensions like 120×90×40
34494 \begin_inset space \thinspace{}
34497 cm the multiplication sign
34498 \begin_inset Quotes eld
34502 \begin_inset Quotes erd
34506 It is available with the LaTeX-command
34512 , but can also directly be inserted with some keyboard definitions.
34515 \begin_layout Itemize
34516 Functions with names consisting of several letters are set upright to avoid
34518 \begin_inset CommandInset ref
34520 reference "sub:Predefined-Functions"
34527 \begin_layout Itemize
34528 Indices consisting of several letters, are set upright:
34529 \begin_inset Formula $E_{\mathrm{kin}}$
34533 \begin_inset Newline newline
34536 Components of matrices are set italic:
34537 \begin_inset Formula $\hat{H}_{kl}$
34543 \begin_layout Itemize
34544 The differentiation/integration operator 'd', the Euler's number 'e', and
34545 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34549 \begin_layout Standard
34550 \begin_inset Newpage newpage
34556 \begin_layout Section
34561 \begin_layout Plain Layout
34570 \begin_layout Standard
34571 Some characters and symbols can be created with several commands.
34572 Here is a list of the synonym commands:
34575 \begin_layout Standard
34576 \begin_inset VSpace bigskip
34580 \begin_inset space \hfill{}
34584 \begin_inset Tabular
34585 <lyxtabular version="3" rows="12" columns="2">
34587 <column alignment="center" valignment="top" width="0pt">
34588 <column alignment="center" valignment="top" width="0pt">
34590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34593 \begin_layout Plain Layout
34599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34602 \begin_layout Plain Layout
34604 \begin_inset Note Note
34607 \begin_layout Plain Layout
34614 is only used as spacer.
34626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34629 \begin_layout Plain Layout
34637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34640 \begin_layout Plain Layout
34644 \begin_layout Plain Layout
34657 \begin_layout Plain Layout
34671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34674 \begin_layout Plain Layout
34682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34685 \begin_layout Plain Layout
34695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34698 \begin_layout Plain Layout
34706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34709 \begin_layout Plain Layout
34719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34722 \begin_layout Plain Layout
34730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34733 \begin_layout Plain Layout
34741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34744 \begin_layout Plain Layout
34752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34755 \begin_layout Plain Layout
34763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34766 \begin_layout Plain Layout
34774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34777 \begin_layout Plain Layout
34787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34790 \begin_layout Plain Layout
34798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34801 \begin_layout Plain Layout
34811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34814 \begin_layout Plain Layout
34822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34825 \begin_layout Plain Layout
34835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34838 \begin_layout Plain Layout
34846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34849 \begin_layout Plain Layout
34859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34862 \begin_layout Plain Layout
34870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34873 \begin_layout Plain Layout
34881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34884 \begin_layout Plain Layout
34892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34895 \begin_layout Plain Layout
34907 \begin_inset space \hfill{}
34911 \begin_inset Tabular
34912 <lyxtabular version="3" rows="12" columns="2">
34914 <column alignment="center" valignment="top" width="0pt">
34915 <column alignment="center" valignment="top" width="0pt">
34917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34920 \begin_layout Plain Layout
34926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34929 \begin_layout Plain Layout
34937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34940 \begin_layout Plain Layout
34948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34951 \begin_layout Plain Layout
34963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34966 \begin_layout Plain Layout
34974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34977 \begin_layout Plain Layout
34987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34990 \begin_layout Plain Layout
34998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35001 \begin_layout Plain Layout
35011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35014 \begin_layout Plain Layout
35022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35025 \begin_layout Plain Layout
35033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35036 \begin_layout Plain Layout
35044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35047 \begin_layout Plain Layout
35055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35058 \begin_layout Plain Layout
35066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35069 \begin_layout Plain Layout
35079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35082 \begin_layout Plain Layout
35090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35093 \begin_layout Plain Layout
35103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35106 \begin_layout Plain Layout
35114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35117 \begin_layout Plain Layout
35127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35130 \begin_layout Plain Layout
35138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35141 \begin_layout Plain Layout
35151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35154 \begin_layout Plain Layout
35162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35165 \begin_layout Plain Layout
35175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35178 \begin_layout Plain Layout
35186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35189 \begin_layout Plain Layout
35203 \begin_inset space \hfill{}
35209 \begin_layout Standard
35210 \begin_inset Newpage newpage
35216 \begin_layout Bibliography
35217 \begin_inset CommandInset bibitem
35218 LatexCommand bibitem
35230 The LaTeX Companion
35233 Addison Wesley, 2004
35236 \begin_layout Bibliography
35237 \begin_inset CommandInset bibitem
35238 LatexCommand bibitem
35244 \begin_inset CommandInset href
35247 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35251 of LaTeX's math abilities
35254 \begin_layout Bibliography
35255 \begin_inset CommandInset bibitem
35256 LatexCommand bibitem
35261 LaTeX tips and tricks-
35262 \begin_inset CommandInset href
35265 target "http://tug.org/TeXnik/"
35272 \begin_layout Bibliography
35273 \begin_inset CommandInset bibitem
35274 LatexCommand bibitem
35280 \begin_inset CommandInset href
35283 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35291 \begin_layout Plain Layout
35303 \begin_layout Bibliography
35304 \begin_inset CommandInset bibitem
35305 LatexCommand bibitem
35311 \begin_inset CommandInset href
35314 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35318 of all symbols available with LaTeX-packages
35321 \begin_layout Bibliography
35322 \begin_inset CommandInset bibitem
35323 LatexCommand bibitem
35329 \begin_inset CommandInset href
35331 name "Documentation"
35332 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35336 of the LaTeX-package
35344 \begin_layout Plain Layout
35345 Packages ! hyperref
35353 \begin_layout Bibliography
35354 \begin_inset CommandInset bibitem
35355 LatexCommand bibitem
35361 \begin_inset CommandInset href
35364 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35375 \begin_inset CommandInset ref
35377 reference "sub:Operator-Limits"
35385 \begin_layout Plain Layout
35396 \begin_layout Bibliography
35397 \begin_inset CommandInset bibitem
35398 LatexCommand bibitem
35409 Auflage, Duden 2001
35412 \begin_layout Subsubsection*
35413 \begin_inset CommandInset index_print
35414 LatexCommand printindex