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:Used-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
2216 \begin_layout Plain Layout
2227 \begin_inset Formula $\nicefrac{5}{31}$
2233 \begin_layout Standard
2234 How to define own fractions where the fraction stroke can be changed, is
2236 \begin_inset CommandInset ref
2238 reference "sub:Self-defined-Fractions"
2245 \begin_layout Subsection
2250 \begin_layout Plain Layout
2259 \begin_layout Standard
2260 Square roots are created with
2270 \begin_layout Plain Layout
2278 or the math toolbar button
2279 \begin_inset Graphics
2280 filename ../images/math/sqrt.png
2285 , all other roots with the command
2295 \begin_layout Plain Layout
2303 or with the math toolbar button
2304 \begin_inset Graphics
2305 filename ../images/math/root.png
2313 \begin_layout Standard
2315 \begin_inset Tabular
2316 <lyxtabular version="3" rows="3" columns="2">
2318 <column alignment="center" valignment="top" width="0pt">
2319 <column alignment="center" valignment="top" width="0pt">
2321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2324 \begin_layout Plain Layout
2330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2333 \begin_layout Plain Layout
2335 \begin_inset Note Note
2338 \begin_layout Plain Layout
2345 is only used as spacer.
2357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2360 \begin_layout Plain Layout
2367 \begin_layout Plain Layout
2381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2384 \begin_layout Plain Layout
2385 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2398 \begin_layout Plain Layout
2405 \begin_layout Plain Layout
2415 \begin_inset Formula $\downarrow$
2423 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2426 \begin_layout Plain Layout
2427 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2443 \begin_layout Standard
2444 A square root can also be created with
2450 when the root index field is left empty.
2453 \begin_layout Standard
2454 With certain indices the distance to the root is too small, like in this
2456 \begin_inset Formula $\sqrt[\beta]{B}$
2460 \begin_inset Newline newline
2464 \begin_inset Formula $\beta$
2468 To avoid this, the commands
2478 \begin_layout Plain Layout
2496 \begin_layout Plain Layout
2504 are used with the following scheme:
2507 \begin_layout Standard
2521 \begin_layout Standard
2522 Distance is the number of Big Points (unit bp;
2523 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2526 ), that the index should be moved to the left or top, resp..
2527 The commands are written to the index.
2528 This way the command
2529 \begin_inset Newline newline
2539 \begin_inset Formula $\to$
2545 \begin_inset Formula $\to$
2554 \begin_layout Plain Layout
2564 \begin_inset Formula $\to$
2568 \begin_inset Newline newline
2573 produces a correct typeset formula:
2574 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2580 \begin_layout Subsection
2581 Binomial coefficients
2585 \begin_layout Plain Layout
2586 Binomial coefficient s
2594 \begin_layout Standard
2595 Binomial coefficients are inserted with the command
2605 \begin_layout Plain Layout
2613 or with the submenu of the math toolbar button
2614 \begin_inset Graphics
2615 filename ../images/math/frac-square.png
2621 Analog to fractions (
2641 \begin_layout Plain Layout
2661 \begin_layout Plain Layout
2670 For other brackets around binomial coeficients there are the commands
2680 \begin_layout Plain Layout
2698 \begin_layout Plain Layout
2709 \begin_layout Standard
2711 \begin_inset Tabular
2712 <lyxtabular version="3" rows="6" columns="2">
2714 <column alignment="center" valignment="top" width="0pt">
2715 <column alignment="center" valignment="top" width="0pt">
2717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2720 \begin_layout Plain Layout
2726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2729 \begin_layout Plain Layout
2731 \begin_inset Note Note
2734 \begin_layout Plain Layout
2741 is only used as spacer.
2753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2756 \begin_layout Plain Layout
2763 \begin_layout Plain Layout
2773 \begin_inset Formula $\downarrow$
2781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2784 \begin_layout Plain Layout
2785 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2798 \begin_layout Plain Layout
2805 \begin_layout Plain Layout
2815 \begin_inset Formula $\downarrow$
2823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2826 \begin_layout Plain Layout
2827 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2840 \begin_layout Plain Layout
2847 \begin_layout Plain Layout
2857 \begin_inset Formula $\downarrow$
2865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2868 \begin_layout Plain Layout
2869 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2882 \begin_layout Plain Layout
2889 \begin_layout Plain Layout
2899 \begin_inset Formula $\downarrow$
2907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2910 \begin_layout Plain Layout
2911 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2924 \begin_layout Plain Layout
2931 \begin_layout Plain Layout
2941 \begin_inset Formula $\downarrow$
2949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2952 \begin_layout Plain Layout
2953 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2969 \begin_layout Subsection
2970 Case differentiations
2974 \begin_layout Plain Layout
2975 Case differentiations
2983 \begin_layout Standard
2985 \begin_inset Tabular
2986 <lyxtabular version="3" rows="3" columns="2">
2988 <column alignment="center" valignment="top" width="0pt">
2989 <column alignment="center" valignment="top" width="0pt">
2991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2994 \begin_layout Plain Layout
3000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3003 \begin_layout Plain Layout
3011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3014 \begin_layout Plain Layout
3021 \begin_layout Plain Layout
3031 \begin_inset Formula $\to$
3038 \begin_layout Plain Layout
3051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3054 \begin_layout Plain Layout
3055 \begin_inset Formula $\begin{cases}
3066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3069 \begin_layout Plain Layout
3076 \begin_layout Plain Layout
3090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3093 \begin_layout Plain Layout
3094 \begin_inset Formula $\begin{cases}
3095 A & \textrm{for }x>0\\
3096 B & \textrm{for }x=0\end{cases}$
3112 \begin_layout Standard
3119 or the usage of the math toolbar button
3120 \begin_inset Graphics
3121 filename ../images/math/cases.png
3126 you can create new lines with the shortcut
3130 or the table toolbar button
3131 \begin_inset Graphics
3132 filename ../images/tabular-feature_append-row.png
3140 \begin_layout Standard
3147 is also available via the menu
3149 Insert\SpecialChar \menuseparator
3150 Math\SpecialChar \menuseparator
3156 \begin_layout Subsection
3161 \begin_layout Plain Layout
3170 \begin_layout Standard
3181 \begin_layout Plain Layout
3189 every character can be displayed canceled.
3190 The characters are quasi accentuated by a slash.
3193 \begin_layout Standard
3195 \begin_inset Tabular
3196 <lyxtabular version="3" rows="4" columns="2">
3198 <column alignment="center" valignment="top" width="0pt">
3199 <column alignment="center" valignment="top" width="0pt">
3201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3204 \begin_layout Plain Layout
3210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3213 \begin_layout Plain Layout
3221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3224 \begin_layout Plain Layout
3232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3235 \begin_layout Plain Layout
3236 \begin_inset Formula $\not=$
3246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3249 \begin_layout Plain Layout
3259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3262 \begin_layout Plain Layout
3263 \begin_inset Formula $\not\le$
3273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3276 \begin_layout Plain Layout
3286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3289 \begin_layout Plain Layout
3290 \begin_inset Formula $\not\parallel$
3306 \begin_layout Standard
3307 The last example shows, that not all negations look good.
3308 Therefore there are for some negations special commands (see
3309 \begin_inset CommandInset ref
3311 reference "sub:Mathematical-Symbols"
3316 \begin_inset CommandInset ref
3318 reference "sec:Relations"
3325 \begin_layout Subsection
3327 \begin_inset CommandInset label
3329 name "sub:Placeholders"
3337 \begin_layout Plain Layout
3347 \begin_layout Plain Layout
3348 Chemical characters ! Isotopes
3357 \begin_layout Plain Layout
3362 \begin_layout Plain Layout
3373 \begin_layout Plain Layout
3388 \begin_layout Standard
3390 \begin_inset space \thinspace{}
3394 \begin_inset space ~
3401 \begin_layout Plain Layout
3402 More about chemical symbols is written in
3403 \begin_inset CommandInset ref
3405 reference "sub:Chemical-Symbols-and"
3414 the following problem occurs:
3417 \begin_layout Standard
3419 \begin_inset Tabular
3420 <lyxtabular version="3" rows="2" columns="2">
3422 <column alignment="center" valignment="top" width="0pt">
3423 <column alignment="center" valignment="top" width="0pt">
3425 <cell alignment="center" valignment="top" usebox="none">
3428 \begin_layout Plain Layout
3429 Indices created with sub- and superscripts:
3434 <cell alignment="center" valignment="top" usebox="none">
3437 \begin_layout Plain Layout
3438 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3448 <cell alignment="center" valignment="top" usebox="none">
3451 \begin_layout Plain Layout
3457 <cell alignment="center" valignment="top" usebox="none">
3460 \begin_layout Plain Layout
3461 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3475 \begin_inset Note Note
3478 \begin_layout Plain Layout
3485 is only used as spacer.
3493 \begin_layout Standard
3494 The shorter index is by default placed below or above the first character
3495 of the longer index.
3496 To avoid this there is the command
3506 \begin_layout Plain Layout
3514 or the math toolbar button
3515 \begin_inset space \thinspace{}
3522 \begin_layout Plain Layout
3523 can be found in the submenu of the toolbar button
3524 \begin_inset Graphics
3525 filename ../images/math/space.png
3536 \begin_inset Graphics
3537 filename ../images/math/phantom.png
3542 that creates one or more phantom characters.
3549 a small blue box appears that is superposed with two red arrows.
3550 The arrows indicate that the complete width and height of the box content
3551 will be created as placeholder.
3552 Phantom characters are accordingly placeholders with the size of the characters.
3555 \begin_layout Standard
3557 \begin_inset Tabular
3558 <lyxtabular version="3" rows="4" columns="2">
3560 <column alignment="center" valignment="top" width="0">
3561 <column alignment="center" valignment="top" width="0">
3563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3566 \begin_layout Plain Layout
3572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3575 \begin_layout Plain Layout
3577 \begin_inset Note Note
3580 \begin_layout Plain Layout
3587 is only used as spacer.
3599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3602 \begin_layout Plain Layout
3607 \begin_layout Plain Layout
3622 \begin_layout Plain Layout
3632 \begin_inset Formula $\to$
3639 \begin_layout Plain Layout
3653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3656 \begin_layout Plain Layout
3657 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3670 \begin_layout Plain Layout
3675 \begin_layout Plain Layout
3690 \begin_layout Plain Layout
3700 \begin_inset Formula $\to$
3707 \begin_layout Plain Layout
3721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3724 \begin_layout Plain Layout
3725 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3738 \begin_layout Plain Layout
3745 \begin_layout Plain Layout
3760 \begin_layout Plain Layout
3770 \begin_inset Formula $\to$
3777 \begin_layout Plain Layout
3791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3794 \begin_layout Plain Layout
3795 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3811 \begin_layout Standard
3812 Furthermore there are the commands
3822 \begin_layout Plain Layout
3831 \begin_inset space ~
3835 \begin_inset Graphics
3836 filename ../images/math/vphantom.png
3851 \begin_layout Plain Layout
3860 \begin_inset space ~
3864 \begin_inset Graphics
3865 filename ../images/math/hphantom.png
3877 creates only space for the maximal height of the characters in the box
3878 but not for its width.
3885 creates only space for the width of the box content.
3886 Therefore the boxes of both commands have only one red arrow.
3889 \begin_layout Standard
3900 \begin_layout Plain Layout
3915 space for the height of the integral sign,
3919 \begin_layout Plain Layout
3926 creates an integral sign, see
3927 \begin_inset CommandInset ref
3929 reference "sub:Big-Operators"
3938 because this is the larger character.
3939 An example application is in
3940 \begin_inset CommandInset ref
3942 reference "sub:Multiline-Brackets"
3949 \begin_layout Subsection
3954 \begin_layout Plain Layout
3964 \begin_layout Plain Layout
3965 Formula ! underlined
3973 \begin_layout Standard
3975 \begin_inset Tabular
3976 <lyxtabular version="3" rows="4" columns="2">
3978 <column alignment="center" valignment="top" width="0pt">
3979 <column alignment="center" valignment="top" width="0pt">
3981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3984 \begin_layout Plain Layout
3990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3993 \begin_layout Plain Layout
3995 \begin_inset Note Note
3998 \begin_layout Plain Layout
4005 is only used as spacer.
4017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4020 \begin_layout Plain Layout
4027 \begin_layout Plain Layout
4040 \begin_layout Plain Layout
4053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4056 \begin_layout Plain Layout
4057 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4070 \begin_layout Plain Layout
4077 \begin_layout Plain Layout
4090 \begin_layout Plain Layout
4103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4106 \begin_layout Plain Layout
4107 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4120 \begin_layout Plain Layout
4127 \begin_layout Plain Layout
4142 \begin_layout Plain Layout
4156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4159 \begin_layout Plain Layout
4160 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4176 \begin_layout Standard
4177 In the last example it doesn't matter if first
4192 \begin_layout Standard
4193 To double underline e.
4194 \begin_inset space \thinspace{}
4207 \begin_layout Standard
4208 It is possible to place up to 6 lines above or below characters.
4211 \begin_layout Subsection
4216 \begin_layout Plain Layout
4225 \begin_layout Standard
4226 There are different types of ellipses available.
4230 \begin_layout Plain Layout
4231 In the math toolbar in the submenu of the button
4232 \begin_inset Graphics
4233 filename ../images/math/ldots.png
4243 For listings dots at the baseline are used (
4253 \begin_layout Plain Layout
4261 ), while for operations dots are needed that are on the same height as the
4272 \begin_layout Plain Layout
4281 When using the command
4291 \begin_layout Plain Layout
4299 , LaTeX decides on the basis of the next character what type is used.
4302 \begin_layout Standard
4304 \begin_inset Tabular
4305 <lyxtabular version="3" rows="8" columns="2">
4307 <column alignment="center" valignment="top" width="0pt">
4308 <column alignment="center" valignment="top" width="0pt">
4310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4313 \begin_layout Plain Layout
4319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4322 \begin_layout Plain Layout
4330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4333 \begin_layout Plain Layout
4338 \begin_layout Plain Layout
4353 \begin_layout Plain Layout
4367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4370 \begin_layout Plain Layout
4371 \begin_inset Formula $A_{1},\dots,A_{n}$
4381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4384 \begin_layout Plain Layout
4389 \begin_layout Plain Layout
4404 \begin_layout Plain Layout
4418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4421 \begin_layout Plain Layout
4422 \begin_inset Formula $A_{1}+\dots+A_{n}$
4432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4435 \begin_layout Plain Layout
4440 \begin_layout Plain Layout
4455 \begin_layout Plain Layout
4469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4472 \begin_layout Plain Layout
4473 \begin_inset Formula $A_{1},\ldots,A_{n}$
4483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4486 \begin_layout Plain Layout
4491 \begin_layout Plain Layout
4506 \begin_layout Plain Layout
4520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4523 \begin_layout Plain Layout
4524 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4537 \begin_layout Plain Layout
4545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4548 \begin_layout Plain Layout
4549 \begin_inset Formula $\vdots$
4559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4562 \begin_layout Plain Layout
4570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4573 \begin_layout Plain Layout
4574 \begin_inset Formula $\ddots$
4584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4587 \begin_layout Plain Layout
4589 \begin_inset space \thinspace{}
4592 matrix with the different dots
4597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4600 \begin_layout Plain Layout
4601 \begin_inset Formula $\begin{array}{ccc}
4602 A_{11} & \cdots & A_{1m}\\
4603 \vdots & \ddots & \vdots\\
4604 A_{n1} & \cdots & A_{nm}\end{array}$
4620 \begin_layout Standard
4621 The ellipses available in menu
4623 Insert\SpecialChar \menuseparator
4625 \begin_inset space ~
4639 \begin_layout Standard
4640 \begin_inset VSpace medskip
4643 Specially for matrices there are ellipses that span over several columns.
4644 They are created with the command
4654 \begin_layout Plain Layout
4662 , that has the following scheme:
4665 \begin_layout Standard
4670 hdotsfor[distance]{number of columns}
4673 \begin_layout Standard
4674 The number of columns specifies how many columns should be spanned.
4675 Distance is a factor for the distance between the dots.
4678 \begin_layout Standard
4679 In the following matrix the command
4685 was inserted in the first box of the second line, to get an ellipsis with
4686 a dot distance twice as long as with the command
4693 \begin_inset Formula \[
4694 \left(\begin{array}{cccc}
4697 q & w & e & r\end{array}\right)\]
4701 Note that the matrix fields that should be spanned must be empty, otherwise
4702 you get LaTeX-errors.
4705 \begin_layout Standard
4706 \begin_inset VSpace bigskip
4709 Furthermore you can fill with the command
4719 \begin_layout Plain Layout
4727 the rest of a line with dots.
4728 The effect of these commands is the same like with
4735 \begin_inset CommandInset ref
4737 reference "sub:Variable-Space"
4744 \begin_layout Standard
4745 For example the command
4753 \begin_layout Plain Layout
4767 \begin_layout Standard
4768 \begin_inset Formula $A\dotfill B$
4774 \begin_layout Standard
4781 there is for a line the command
4791 \begin_layout Plain Layout
4802 \begin_layout Standard
4803 \begin_inset Formula $A\hrulefill B$
4809 \begin_layout Standard
4810 To use the commands for text, they have to be inserted in TeX-mode.
4813 \begin_layout Section
4815 \begin_inset CommandInset label
4825 \begin_layout Plain Layout
4834 \begin_layout Standard
4835 Matrices can be inserted via the math toolbar button
4836 \begin_inset Graphics
4837 filename ../images/dialog-show_mathmatrix.png
4844 Insert\SpecialChar \menuseparator
4845 Math\SpecialChar \menuseparator
4849 You will be asked for the number of matrix columns and rows, and the alignment.
4850 The vertical alignment is hereby only of importance for matrices in inline
4854 \begin_layout Standard
4855 The first matrix is top
4856 \begin_inset Formula $\begin{array}[t]{cccc}
4859 C & F & I & L\end{array}$
4863 \begin_inset Formula $\begin{array}{cccc}
4866 C & F & I & L\end{array}$
4869 , and the third bottom
4870 \begin_inset Formula $\begin{array}[b]{cccc}
4873 C & F & I & L\end{array}$
4879 \begin_layout Standard
4880 The horizontal alignment specifies how the column entries should be aligned.
4881 It is set by entering a letter for every column.
4886 denotes left aligned,
4895 To create for example a 4
4900 \begin_inset space ~
4903 matrix where the first column is left aligned, the second and third are
4904 centered, and the last one is right aligned, one enters for the horizontal
4910 Normally are in a matrix all columns centered, therefore the default is
4911 for every column is a
4918 \begin_layout Standard
4919 Horizontal alignment:
4922 \begin_layout Standard
4928 \begin_inset Formula $\begin{array}{lll}
4931 C & F & 10000\end{array}$
4939 \begin_inset Formula $\begin{array}{ccc}
4942 C & F & 10000\end{array}$
4950 \begin_inset Formula $\begin{array}{rrr}
4953 C & F & 10000\end{array}$
4959 \begin_layout Standard
4960 To add or delete rows and columns subsequently, the math toolbar buttons
4962 \begin_inset Graphics
4963 filename ../images/tabular-feature_append-row.png
4969 \begin_inset Graphics
4970 filename ../images/tabular-feature_delete-row.png
4976 \begin_inset space \thinspace{}
4981 Edit\SpecialChar \menuseparator
4985 New rows can also be created with
4992 \begin_layout Standard
4993 \begin_inset VSpace bigskip
4996 Parentheses around a matrix can can either be created with the commands
5007 \begin_layout Plain Layout
5025 \begin_layout Plain Layout
5036 \begin_inset space ~
5042 \begin_inset CommandInset ref
5044 reference "sub:Automatic-Bracket-Size"
5048 , or by using the following commands:
5049 \begin_inset VSpace medskip
5055 \begin_layout Standard
5056 \begin_inset space \hfill{}
5060 \begin_inset Tabular
5061 <lyxtabular version="3" rows="4" columns="2">
5063 <column alignment="center" valignment="top" width="0">
5064 <column alignment="center" valignment="top" width="0">
5066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5069 \begin_layout Plain Layout
5075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5078 \begin_layout Plain Layout
5080 \begin_inset Note Note
5083 \begin_layout Plain Layout
5090 is only used as spacer.
5102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5105 \begin_layout Plain Layout
5112 \begin_layout Plain Layout
5126 \begin_inset space \thinspace{}
5134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5137 \begin_layout Plain Layout
5138 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5139 0 & \textrm{-}\mathrm{i}\\
5140 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5153 \begin_layout Plain Layout
5160 \begin_layout Plain Layout
5174 \begin_inset space \thinspace{}
5182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5185 \begin_layout Plain Layout
5186 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5187 0 & \textrm{-}\mathrm{i}\\
5188 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5201 \begin_layout Plain Layout
5208 \begin_layout Plain Layout
5222 \begin_inset space \thinspace{}
5230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5233 \begin_layout Plain Layout
5234 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5235 0 & \textrm{-}\mathrm{i}\\
5236 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5250 \begin_inset space \hfill{}
5254 \begin_inset Tabular
5255 <lyxtabular version="3" rows="4" columns="2">
5257 <column alignment="center" valignment="top" width="0">
5258 <column alignment="center" valignment="top" width="0">
5260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5263 \begin_layout Plain Layout
5269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5272 \begin_layout Plain Layout
5280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5283 \begin_layout Plain Layout
5290 \begin_layout Plain Layout
5304 \begin_inset space \thinspace{}
5312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5315 \begin_layout Plain Layout
5316 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5317 0 & \textrm{-}\mathrm{i}\\
5318 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5331 \begin_layout Plain Layout
5338 \begin_layout Plain Layout
5352 \begin_inset space \thinspace{}
5360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5363 \begin_layout Plain Layout
5364 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5365 0 & \textrm{-}\mathrm{i}\\
5366 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5379 \begin_layout Plain Layout
5386 \begin_layout Plain Layout
5400 \begin_inset space \thinspace{}
5408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5411 \begin_layout Plain Layout
5412 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5413 0 & \textrm{-}\mathrm{i}\\
5414 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5428 \begin_inset space \hfill{}
5434 \begin_layout Standard
5435 \begin_inset VSpace medskip
5439 \begin_inset space \thinspace{}
5443 \begin_inset space ~
5452 is inserted, a blue box appears between two vertical lines where the matrix
5456 \begin_layout Standard
5457 \begin_inset VSpace bigskip
5460 As all multiline formulas are matrices, the length
5470 \begin_layout Plain Layout
5478 that is described in
5479 \begin_inset CommandInset ref
5481 reference "sub:Column-Separation"
5485 can also be used to change the column separation of matrices.
5488 \begin_layout Standard
5489 To change the row separation, the command
5499 \begin_layout Plain Layout
5508 It is used as follows:
5511 \begin_layout Standard
5518 arraystretch}{stretch factor}
5522 \begin_layout Plain Layout
5533 \begin_layout Standard
5540 assigns the stretch factor to the predefined command
5548 \begin_inset space \thinspace{}
5552 \begin_inset space ~
5555 the row separation, use the factor 2.
5556 This is then used for all following matrices.
5557 To go back to the original separation, assign the factor 1 to
5566 \begin_layout Standard
5567 To set matrices into a text line, the command
5577 \begin_layout Plain Layout
5586 When it is inserted a blue box with two dashed lines appears.
5587 In this box the matrix is inserted.
5590 \begin_layout Standard
5592 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5593 C & D\end{smallmatrix}\right)$
5599 \begin_layout Section
5600 Brackets and Delimiters
5604 \begin_layout Plain Layout
5614 \begin_layout Plain Layout
5623 \begin_layout Subsection
5624 Vertical Brackets and Delimiters
5628 \begin_layout Plain Layout
5637 \begin_layout Standard
5638 \begin_inset space \hfill{}
5642 \begin_inset Tabular
5643 <lyxtabular version="3" rows="9" columns="2">
5645 <column alignment="center" valignment="top" width="0pt">
5646 <column alignment="center" valignment="top" width="0pt">
5648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5651 \begin_layout Plain Layout
5657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5660 \begin_layout Plain Layout
5668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5671 \begin_layout Plain Layout
5677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5680 \begin_layout Plain Layout
5681 \begin_inset Formula $($
5691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5694 \begin_layout Plain Layout
5700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5703 \begin_layout Plain Layout
5704 \begin_inset Formula $\{$
5714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5717 \begin_layout Plain Layout
5723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5726 \begin_layout Plain Layout
5727 \begin_inset Formula $[$
5737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5740 \begin_layout Plain Layout
5748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5751 \begin_layout Plain Layout
5752 \begin_inset Formula $\langle$
5762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5765 \begin_layout Plain Layout
5773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5776 \begin_layout Plain Layout
5777 \begin_inset Formula $\lceil$
5787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5790 \begin_layout Plain Layout
5798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5801 \begin_layout Plain Layout
5802 \begin_inset Formula $\lfloor$
5812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5815 \begin_layout Plain Layout
5821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5824 \begin_layout Plain Layout
5825 \begin_inset Formula $/$
5835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5838 \begin_layout Plain Layout
5844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5847 \begin_layout Plain Layout
5848 \begin_inset Formula $|$
5862 \begin_inset space \hfill{}
5866 \begin_inset Tabular
5867 <lyxtabular version="3" rows="9" columns="2">
5869 <column alignment="center" valignment="top" width="0pt">
5870 <column alignment="center" valignment="top" width="0pt">
5872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5875 \begin_layout Plain Layout
5881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5884 \begin_layout Plain Layout
5892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5895 \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 $)$
5915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5918 \begin_layout Plain Layout
5924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5927 \begin_layout Plain Layout
5928 \begin_inset Formula $\}$
5938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5941 \begin_layout Plain Layout
5947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5950 \begin_layout Plain Layout
5951 \begin_inset Formula $]$
5961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5964 \begin_layout Plain Layout
5972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5975 \begin_layout Plain Layout
5976 \begin_inset Formula $\rangle$
5986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5989 \begin_layout Plain Layout
5997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6000 \begin_layout Plain Layout
6001 \begin_inset Formula $\rceil$
6011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6014 \begin_layout Plain Layout
6022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6025 \begin_layout Plain Layout
6026 \begin_inset Formula $\rfloor$
6036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6039 \begin_layout Plain Layout
6049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6052 \begin_layout Plain Layout
6053 \begin_inset Formula $\backslash$
6063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6066 \begin_layout Plain Layout
6074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6077 \begin_layout Plain Layout
6078 \begin_inset Formula $\|$
6092 \begin_inset space \hfill{}
6098 \begin_layout Standard
6101 \begin_inset Note Greyedout
6104 \begin_layout Plain Layout
6109 In TeX-mode the command
6119 \begin_layout Plain Layout
6127 must be used for the backslash, because the command
6135 produces there a line break.
6143 \begin_layout Standard
6144 For all characters listed above the size can be adjusted with the commands
6145 described in the following two subsections.
6146 When using these commands, the characters < and > can directly be used
6147 instead of the commands
6162 \begin_layout Subsubsection
6164 \begin_inset CommandInset label
6166 name "sub:Manual-Bracket-Size"
6174 \begin_layout Plain Layout
6175 Bracket size ! manual
6183 \begin_layout Standard
6184 The bracket size can be specified manually by the LaTeX-commands
6194 \begin_layout Plain Layout
6227 denotes the smallest and
6233 the largest bracket size.
6236 \begin_layout Standard
6237 These commands are used to emphasize levels of brackets:
6240 \begin_layout Standard
6242 \begin_inset Tabular
6243 <lyxtabular version="3" rows="2" columns="2">
6245 <column alignment="center" valignment="top" width="0pt">
6246 <column alignment="center" valignment="top" width="0pt">
6248 <cell alignment="center" valignment="top" usebox="none">
6251 \begin_layout Plain Layout
6252 all brackets in the same size:
6257 <cell alignment="center" valignment="top" usebox="none">
6260 \begin_layout Plain Layout
6261 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6271 <cell alignment="center" valignment="top" usebox="none">
6274 \begin_layout Plain Layout
6280 <cell alignment="center" valignment="top" usebox="none">
6283 \begin_layout Plain Layout
6284 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6298 \begin_inset Note Note
6301 \begin_layout Plain Layout
6308 is only used as spacer.
6316 \begin_layout Standard
6317 For the second formula the command
6327 \begin_layout Plain Layout
6341 \begin_layout Standard
6342 Here is an overview about all bracket sizes:
6345 \begin_layout Standard
6365 \begin_layout Plain Layout
6382 \begin_layout Plain Layout
6395 \begin_layout Plain Layout
6411 \begin_layout Standard
6413 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6419 \begin_layout Standard
6420 \begin_inset Newpage newpage
6429 -commands there is the variant
6439 \begin_layout Plain Layout
6447 that adds a bit more space between the bracket and its content, and the
6464 \begin_layout Plain Layout
6474 , that don't add additional space.
6479 at the end of the command
6485 is for a left bracket; for a right bracket this will be replaced by an
6491 A left or right bracket can each be an opening or closing bracket.
6494 \begin_layout Standard
6495 In the following table is a comparison of the variants:
6498 \begin_layout Standard
6500 \begin_inset Tabular
6501 <lyxtabular version="3" rows="5" columns="2">
6503 <column alignment="center" valignment="middle" width="0">
6504 <column alignment="center" valignment="middle" width="0">
6506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6509 \begin_layout Plain Layout
6515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6518 \begin_layout Plain Layout
6520 \begin_inset Note Note
6523 \begin_layout Plain Layout
6530 is only used as spacer.
6542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6545 \begin_layout Plain Layout
6560 \begin_layout Plain Layout
6578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6581 \begin_layout Plain Layout
6582 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6595 \begin_layout Plain Layout
6610 \begin_layout Plain Layout
6628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6631 \begin_layout Plain Layout
6632 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6645 \begin_layout Plain Layout
6660 \begin_layout Plain Layout
6678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6681 \begin_layout Plain Layout
6682 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6695 \begin_layout Plain Layout
6707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6710 \begin_layout Plain Layout
6711 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6727 \begin_layout Subsubsection
6728 Automatic Bracket Size
6729 \begin_inset CommandInset label
6731 name "sub:Automatic-Bracket-Size"
6739 \begin_layout Plain Layout
6740 Bracket size ! automatic
6748 \begin_layout Standard
6749 Brackets with variable size can be inserted with the commands
6759 \begin_layout Plain Layout
6777 \begin_layout Plain Layout
6785 or via the math toolbar button
6786 \begin_inset Graphics
6787 filename ../images/dialog-show_mathdelimiter.png
6805 the wanted bracket must be inserted.
6806 The bracket size will then automatically be calculated for the output.
6809 \begin_layout Standard
6811 normal bracket: The command
6821 \begin_layout Plain Layout
6831 \begin_inset Formula $\downarrow$
6838 \begin_layout Plain Layout
6850 \begin_inset Formula \[
6858 \begin_layout Standard
6860 multiline bracket: The command
6872 \begin_layout Plain Layout
6882 \begin_inset Formula $\downarrow$
6889 \begin_layout Plain Layout
6903 \begin_inset Formula \[
6904 \ln\left(\frac{A}{C}\right)\]
6911 \begin_layout Standard
6927 \begin_inset space ~
6933 This has the advantage that you can see in LyX immediately the real bracket
6934 size and that the matching right bracket will be created too.
6935 \begin_inset Newline newline
6938 The command for the last example would then be:
6952 \begin_layout Plain Layout
6962 \begin_inset Formula $\downarrow$
6968 \begin_layout Standard
6969 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6970 For example the command
6980 \begin_layout Plain Layout
6990 \begin_inset Formula $\downarrow$
6997 \begin_layout Plain Layout
7013 \begin_inset Formula \[
7014 \left.\frac{A}{B}\right\} \]
7032 will be converted by LyX to brackets in the right size when the document
7033 is reloaded and an omitted bracket will appear as dashed line.
7036 \begin_layout Standard
7037 \begin_inset VSpace bigskip
7040 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7051 \begin_layout Plain Layout
7059 is additionally available for all brackets and limits.
7060 With this command the height of the following character is adapted to the
7061 one of the surrounding brackets, what is e.
7062 \begin_inset space \thinspace{}
7066 \begin_inset space ~
7069 needed for physical vectors:
7070 \begin_inset Formula \[
7071 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7075 For physical vectors there is a special LaTeX-package, described in
7076 \begin_inset CommandInset ref
7078 reference "sub:Physical-Vectors"
7085 \begin_layout Subsection
7090 \begin_layout Plain Layout
7091 Brackets ! horizontal
7099 \begin_layout Standard
7101 \begin_inset Tabular
7102 <lyxtabular version="3" rows="4" columns="2">
7104 <column alignment="center" valignment="top" width="0pt">
7105 <column alignment="center" valignment="top" width="0pt">
7107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7110 \begin_layout Plain Layout
7112 \begin_inset Note Note
7115 \begin_layout Plain Layout
7122 is only used as spacer.
7132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7135 \begin_layout Plain Layout
7143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7146 \begin_layout Plain Layout
7150 \begin_layout Plain Layout
7165 \begin_layout Plain Layout
7178 \begin_layout Plain Layout
7191 \begin_layout Plain Layout
7204 \begin_layout Plain Layout
7215 \begin_layout Plain Layout
7228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7231 \begin_layout Plain Layout
7232 \begin_inset Formula $\overbrace{A+B}^{3}$
7242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7245 \begin_layout Plain Layout
7249 \begin_layout Plain Layout
7264 \begin_layout Plain Layout
7277 \begin_layout Plain Layout
7290 \begin_layout Plain Layout
7301 \begin_layout Plain Layout
7314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7317 \begin_layout Plain Layout
7318 \begin_inset Formula $\underbrace{A+B}_{5}$
7328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7331 \begin_layout Plain Layout
7338 \begin_layout Plain Layout
7353 \begin_layout Plain Layout
7366 \begin_layout Plain Layout
7379 \begin_layout Plain Layout
7392 \begin_layout Plain Layout
7405 \begin_layout Plain Layout
7418 \begin_layout Plain Layout
7432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7435 \begin_layout Plain Layout
7436 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7452 \begin_layout Standard
7453 In the last example it doesn't matter if
7465 is inserted at first.
7468 \begin_layout Standard
7469 \begin_inset VSpace bigskip
7472 When brackets are needed that overlap each other, multiline formulas, as
7474 \begin_inset CommandInset ref
7476 reference "sec:Multiline-Formulas"
7481 \begin_inset Formula \begin{eqnarray*}
7482 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7483 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7487 In the first row the formula is inserted together with the first brace.
7488 It is hereby important that the space command
7492 \begin_layout Plain Layout
7493 Space commands are explained in
7494 \begin_inset CommandInset ref
7496 reference "sub:Predefined-Space"
7511 is inserted before the first
7512 \begin_inset Formula $d$
7515 , because the brace that ends behind the
7516 \begin_inset Formula $q$
7519 prevents that the following
7520 \begin_inset Quotes eld
7524 \begin_inset Quotes erd
7527 is surrounded by space.
7531 \begin_layout Plain Layout
7532 because a bracket is not handled as character, see
7533 \begin_inset CommandInset ref
7535 reference "sub:Binary-Operators"
7544 In the second row the second brace is inserted.
7545 As it should begin before the
7546 \begin_inset Formula $b$
7561 \begin_layout Plain Layout
7569 \begin_inset CommandInset ref
7571 reference "sub:Placeholders"
7580 This space is needed because the
7581 \begin_inset Quotes eld
7585 \begin_inset Quotes erd
7588 is also surrounded by space in the formula.
7589 The brace is placed under the command
7598 \begin_layout Standard
7599 It gets more complicated when brackets overlap each other, like in the following
7604 \begin_layout Plain Layout
7616 \begin_inset Formula \begin{eqnarray*}
7617 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7618 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7626 \begin_layout Plain Layout
7637 The first formula row is the same as the second row of the previous example,
7638 with the difference that the brace is above.
7639 The second row contains the formula together with the second brace.
7640 To avoid that there is space between the upper brace in the first row and
7641 the formula, the row spacing need to be reduced.
7642 This is not easily possible due to a bug in LyX
7646 \begin_layout Plain Layout
7647 \begin_inset CommandInset href
7649 name "LyX-bug #1505"
7650 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7660 As solution for the problem, the global formula row separation
7670 \begin_layout Plain Layout
7678 must be changed to -6
7679 \begin_inset space \thinspace{}
7682 pt before the formula with the command
7697 is set back after the formula to the standard value of 3
7698 \begin_inset space \thinspace{}
7701 pt using the same command.
7702 More about the row separation in formulas is explained in
7703 \begin_inset CommandInset ref
7705 reference "sub:Line-Separation"
7712 \begin_layout Section
7717 \begin_layout Plain Layout
7726 \begin_layout Standard
7727 Arrows can be inserted via the math toolbar button
7728 \begin_inset Graphics
7729 filename ../images/math/leftarrow.png
7734 or the commands listed in the following subsections.
7737 \begin_layout Subsection
7742 \begin_layout Plain Layout
7751 \begin_layout Standard
7752 \begin_inset space \hfill{}
7756 \begin_inset Tabular
7757 <lyxtabular version="3" rows="8" columns="2">
7759 <column alignment="center" valignment="top" width="0pt">
7760 <column alignment="center" valignment="top" width="0pt">
7762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7765 \begin_layout Plain Layout
7771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7774 \begin_layout Plain Layout
7782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7785 \begin_layout Plain Layout
7793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7796 \begin_layout Plain Layout
7797 \begin_inset Formula $\gets$
7807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7810 \begin_layout Plain Layout
7818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7821 \begin_layout Plain Layout
7822 \begin_inset Formula $\Leftarrow$
7832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7835 \begin_layout Plain Layout
7843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7846 \begin_layout Plain Layout
7847 \begin_inset Formula $\longleftarrow$
7857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7860 \begin_layout Plain Layout
7868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7871 \begin_layout Plain Layout
7872 \begin_inset Formula $\Longleftarrow$
7882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7885 \begin_layout Plain Layout
7893 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7896 \begin_layout Plain Layout
7897 \begin_inset Formula $\leftharpoonup$
7907 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7910 \begin_layout Plain Layout
7918 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7921 \begin_layout Plain Layout
7922 \begin_inset Formula $\leftharpoondown$
7932 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7935 \begin_layout Plain Layout
7943 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7946 \begin_layout Plain Layout
7947 \begin_inset Formula $\hookleftarrow$
7961 \begin_inset space \hfill{}
7965 \begin_inset Tabular
7966 <lyxtabular version="3" rows="8" columns="2">
7968 <column alignment="center" valignment="top" width="0pt">
7969 <column alignment="center" valignment="top" width="0pt">
7971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7974 \begin_layout Plain Layout
7980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7983 \begin_layout Plain Layout
7991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7994 \begin_layout Plain Layout
8002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8005 \begin_layout Plain Layout
8006 \begin_inset Formula $\to$
8016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8019 \begin_layout Plain Layout
8027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8030 \begin_layout Plain Layout
8031 \begin_inset Formula $\Rightarrow$
8041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8044 \begin_layout Plain Layout
8052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8055 \begin_layout Plain Layout
8056 \begin_inset Formula $\longrightarrow$
8066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8069 \begin_layout Plain Layout
8077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8080 \begin_layout Plain Layout
8081 \begin_inset Formula $\Longrightarrow$
8091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8094 \begin_layout Plain Layout
8102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8105 \begin_layout Plain Layout
8106 \begin_inset Formula $\rightharpoonup$
8116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8119 \begin_layout Plain Layout
8127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8130 \begin_layout Plain Layout
8131 \begin_inset Formula $\rightharpoondown$
8141 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8144 \begin_layout Plain Layout
8152 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8155 \begin_layout Plain Layout
8156 \begin_inset Formula $\hookrightarrow$
8170 \begin_inset space \hfill{}
8176 \begin_layout Standard
8177 \begin_inset space \hfill{}
8181 \begin_inset Tabular
8182 <lyxtabular version="3" rows="6" columns="2">
8184 <column alignment="center" valignment="top" width="0pt">
8185 <column alignment="center" valignment="top" width="0pt">
8187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8190 \begin_layout Plain Layout
8196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8199 \begin_layout Plain Layout
8207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8210 \begin_layout Plain Layout
8218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8221 \begin_layout Plain Layout
8222 \begin_inset Formula $\leftrightarrow$
8232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8235 \begin_layout Plain Layout
8243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8246 \begin_layout Plain Layout
8247 \begin_inset Formula $\Leftrightarrow$
8257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8260 \begin_layout Plain Layout
8268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8271 \begin_layout Plain Layout
8272 \begin_inset Formula $\longleftrightarrow$
8282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8285 \begin_layout Plain Layout
8293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8296 \begin_layout Plain Layout
8297 \begin_inset Formula $\Longleftrightarrow$
8307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8310 \begin_layout Plain Layout
8318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8321 \begin_layout Plain Layout
8322 \begin_inset Formula $\rightleftharpoons$
8336 \begin_inset space \hspace{}
8341 \begin_inset space \hfill{}
8345 \begin_inset Tabular
8346 <lyxtabular version="3" rows="5" columns="2">
8348 <column alignment="center" valignment="top" width="0pt">
8349 <column alignment="center" valignment="top" width="0pt">
8351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8354 \begin_layout Plain Layout
8360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8363 \begin_layout Plain Layout
8371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8374 \begin_layout Plain Layout
8382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8385 \begin_layout Plain Layout
8386 \begin_inset Formula $\mapsto$
8396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8399 \begin_layout Plain Layout
8407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8410 \begin_layout Plain Layout
8411 \begin_inset Formula $\longmapsto$
8421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8424 \begin_layout Plain Layout
8432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8435 \begin_layout Plain Layout
8436 \begin_inset Formula $\leadsto$
8446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8449 \begin_layout Plain Layout
8457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8460 \begin_layout Plain Layout
8461 \begin_inset Formula $\dasharrow$
8475 \begin_inset space \hfill{}
8481 \begin_layout Standard
8482 \begin_inset VSpace medskip
8485 Arrows used as accent like e.
8486 \begin_inset space \thinspace{}
8490 \begin_inset space ~
8493 vector arrows are listed in
8494 \begin_inset CommandInset ref
8496 reference "sec:Accents"
8503 \begin_layout Standard
8504 \begin_inset VSpace bigskip
8507 Furthermore there are the labeled arrows
8511 \begin_layout Plain Layout
8527 \begin_layout Plain Layout
8545 \begin_layout Plain Layout
8552 \begin_layout Plain Layout
8567 When inserting one of these commands in a formula, an arrow with two blue
8568 boxes appear where the label can be inserted.
8569 The length of the arrow adapts to the label width.
8572 \begin_layout Standard
8574 \begin_inset Tabular
8575 <lyxtabular version="3" rows="3" columns="2">
8577 <column alignment="center" valignment="top" width="0pt">
8578 <column alignment="center" valignment="top" width="0pt">
8580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8583 \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
8594 \begin_inset Note Note
8597 \begin_layout Plain Layout
8604 is only used as spacer.
8616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8619 \begin_layout Plain Layout
8626 \begin_layout Plain Layout
8636 \begin_inset Formula $\downarrow$
8640 \begin_inset Formula $\to$
8648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8651 \begin_layout Plain Layout
8652 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8665 \begin_layout Plain Layout
8672 \begin_layout Plain Layout
8682 \begin_inset Formula $\downarrow$
8686 \begin_inset Formula $\to$
8694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8697 \begin_layout Plain Layout
8698 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8714 \begin_layout Subsection
8715 Vertical and diagonal Arrows
8719 \begin_layout Plain Layout
8729 \begin_layout Plain Layout
8738 \begin_layout Standard
8739 \begin_inset space \hfill{}
8743 \begin_inset Tabular
8744 <lyxtabular version="3" rows="7" columns="2">
8746 <column alignment="center" valignment="top" width="0pt">
8747 <column alignment="center" valignment="top" width="0pt">
8749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8752 \begin_layout Plain Layout
8758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8761 \begin_layout Plain Layout
8769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8772 \begin_layout Plain Layout
8780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8783 \begin_layout Plain Layout
8784 \begin_inset Formula $\uparrow$
8794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8797 \begin_layout Plain Layout
8805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8808 \begin_layout Plain Layout
8809 \begin_inset Formula $\Uparrow$
8819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8822 \begin_layout Plain Layout
8830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8833 \begin_layout Plain Layout
8834 \begin_inset Formula $\updownarrow$
8844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8847 \begin_layout Plain Layout
8855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8858 \begin_layout Plain Layout
8859 \begin_inset Formula $\Updownarrow$
8869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8872 \begin_layout Plain Layout
8880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8883 \begin_layout Plain Layout
8884 \begin_inset Formula $\Downarrow$
8894 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8897 \begin_layout Plain Layout
8905 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8908 \begin_layout Plain Layout
8909 \begin_inset Formula $\downarrow$
8923 \begin_inset space \hfill{}
8927 \begin_inset Tabular
8928 <lyxtabular version="3" rows="5" columns="2">
8930 <column alignment="center" valignment="top" width="0pt">
8931 <column alignment="center" valignment="top" width="0pt">
8933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8936 \begin_layout Plain Layout
8942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8945 \begin_layout Plain Layout
8953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8956 \begin_layout Plain Layout
8964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8967 \begin_layout Plain Layout
8968 \begin_inset Formula $\nearrow$
8978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8981 \begin_layout Plain Layout
8989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8992 \begin_layout Plain Layout
8993 \begin_inset Formula $\searrow$
9003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9006 \begin_layout Plain Layout
9014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9017 \begin_layout Plain Layout
9018 \begin_inset Formula $\swarrow$
9028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9031 \begin_layout Plain Layout
9039 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9042 \begin_layout Plain Layout
9043 \begin_inset Formula $\nwarrow$
9057 \begin_inset space \hfill{}
9063 \begin_layout Standard
9064 \begin_inset VSpace medskip
9067 Vertical arrows can be used also as delimiter together with the commands
9069 \begin_inset CommandInset ref
9071 reference "sub:Manual-Bracket-Size"
9076 \begin_inset CommandInset ref
9078 reference "sub:Automatic-Bracket-Size"
9085 \begin_layout Standard
9086 \begin_inset Newpage newpage
9092 \begin_layout Section
9094 \begin_inset CommandInset label
9104 \begin_layout Plain Layout
9113 \begin_layout Standard
9114 Accents can be inserted via the math toolbar button
9115 \begin_inset Graphics
9116 filename ../images/math/hat.png
9121 or the commands listed in the following subsections.
9124 \begin_layout Subsection
9125 Accents for one Character
9129 \begin_layout Plain Layout
9142 \begin_layout Plain Layout
9144 \begin_inset CommandInset ref
9146 reference "sub:Accents-in-Text"
9159 \begin_layout Plain Layout
9167 \begin_inset Note Note
9170 \begin_layout Plain Layout
9173 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9176 \begin_layout Plain Layout
9179 texorpdfstring is in section
9180 \begin_inset CommandInset ref
9182 reference "sub:Formulas-in-Section"
9192 \begin_inset CommandInset label
9194 name "sub:Accents-for-one"
9202 \begin_layout Plain Layout
9203 Accents ! for one character
9211 \begin_layout Standard
9212 \begin_inset space \hfill{}
9216 \begin_inset Tabular
9217 <lyxtabular version="3" rows="8" columns="2">
9219 <column alignment="center" valignment="top" width="0pt">
9220 <column alignment="center" valignment="top" width="0pt">
9222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9225 \begin_layout Plain Layout
9231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9234 \begin_layout Plain Layout
9236 \begin_inset Note Note
9239 \begin_layout Plain Layout
9246 is only used as spacer.
9258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9261 \begin_layout Plain Layout
9268 \begin_layout Plain Layout
9282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9285 \begin_layout Plain Layout
9286 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9299 \begin_layout Plain Layout
9306 \begin_layout Plain Layout
9320 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9323 \begin_layout Plain Layout
9324 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9334 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9337 \begin_layout Plain Layout
9344 \begin_layout Plain Layout
9358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9361 \begin_layout Plain Layout
9362 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9372 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9375 \begin_layout Plain Layout
9383 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9386 \begin_layout Plain Layout
9387 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9400 \begin_layout Plain Layout
9407 \begin_layout Plain Layout
9420 \begin_layout Plain Layout
9431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9434 \begin_layout Plain Layout
9435 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9445 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9448 \begin_layout Plain Layout
9455 \begin_layout Plain Layout
9469 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9472 \begin_layout Plain Layout
9473 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9483 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9486 \begin_layout Plain Layout
9493 \begin_layout Plain Layout
9507 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9510 \begin_layout Plain Layout
9511 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9525 \begin_inset space \hfill{}
9529 \begin_inset Tabular
9530 <lyxtabular version="3" rows="7" columns="2">
9532 <column alignment="center" valignment="top" width="0pt">
9533 <column alignment="center" valignment="top" width="0pt">
9535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9538 \begin_layout Plain Layout
9544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9547 \begin_layout Plain Layout
9555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9558 \begin_layout Plain Layout
9565 \begin_layout Plain Layout
9579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9582 \begin_layout Plain Layout
9583 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9596 \begin_layout Plain Layout
9603 \begin_layout Plain Layout
9617 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9620 \begin_layout Plain Layout
9621 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9631 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9634 \begin_layout Plain Layout
9641 \begin_layout Plain Layout
9655 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9658 \begin_layout Plain Layout
9659 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9672 \begin_layout Plain Layout
9679 \begin_layout Plain Layout
9693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9696 \begin_layout Plain Layout
9697 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9707 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9710 \begin_layout Plain Layout
9717 \begin_layout Plain Layout
9731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9734 \begin_layout Plain Layout
9735 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9745 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9748 \begin_layout Plain Layout
9755 \begin_layout Plain Layout
9769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9772 \begin_layout Plain Layout
9773 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9787 \begin_inset space \hfill{}
9793 \begin_layout Standard
9794 \begin_inset VSpace bigskip
9801 \begin_layout Plain Layout
9807 in formulas, a quotation mark is inserted before the vowel.
9808 These two characters are then treated by LaTeX as
9812 character when the formula part with the umlaut is marked as German.
9820 \begin_inset Quotes eld
9824 \begin_inset Quotes erd
9827 umlauts are created as demonstrated in the following example:
9830 \begin_layout Standard
9831 \begin_inset VSpace -2mm
9837 \begin_layout Standard
9839 \begin_inset Tabular
9840 <lyxtabular version="3" rows="3" columns="2">
9842 <column alignment="center" valignment="top" width="0">
9843 <column alignment="center" valignment="top" width="0">
9845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9848 \begin_layout Plain Layout
9854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9857 \begin_layout Plain Layout
9859 \begin_inset Note Note
9862 \begin_layout Plain Layout
9869 is only used as spacer.
9881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9884 \begin_layout Plain Layout
9887 \begin_inset Quotes grd
9895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9898 \begin_layout Plain Layout
9901 \begin_inset Formula $"i$
9911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9914 \begin_layout Plain Layout
9921 \begin_layout Plain Layout
9935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9938 \begin_layout Plain Layout
9939 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9955 \begin_layout Standard
9956 Another advantage to
9962 is that umlauts can directly be converted to mathematical text because
9963 the accent commands above are
9969 in mathematical text
9972 To convert an accented character to mathematical text, only the character
9973 under the accent may be converted.
9974 This applies also for all other conversions, e.
9975 \begin_inset space \thinspace{}
9979 \begin_inset space ~
9985 \begin_layout Standard
9986 In mathematical text, umlauts and other accented characters can directly
9990 \begin_layout Subsection
9991 Accents for Operators
9995 \begin_layout Plain Layout
9996 Accents ! for operators
10004 \begin_layout Standard
10015 \begin_layout Plain Layout
10033 \begin_layout Plain Layout
10041 characters can be placed above or below an operator, respectively, to accent
10053 \begin_layout Plain Layout
10061 characters can be set before and behind an operator.
10062 The command scheme is:
10065 \begin_layout Standard
10081 \begin_layout Standard
10088 must always be before the operator that should be accented.
10089 You can accent with several characters and even with other operators and
10097 for example only characters behind an operator, write nothing between the
10098 first braces but don't omit the braces.
10101 \begin_layout Standard
10102 For example the command
10107 \begin_inset Formula $\to$
10117 \begin_inset Formula $\to$
10126 \begin_layout Plain Layout
10142 \begin_inset Formula \[
10143 \sideset{}{'}\sum_{k=1}^{n}\]
10150 \begin_layout Standard
10159 \begin_layout Plain Layout
10174 \begin_layout Plain Layout
10186 \begin_inset Formula $\uparrow$
10194 \begin_inset Formula \[
10195 \overset{a}{\maltese}\]
10199 As seen in the last example, with
10211 also symbols and characters can be accented; with
10217 this is not possible.
10220 \begin_layout Subsection
10221 Accents for several Characters
10222 \begin_inset CommandInset label
10224 name "sub:Accents-for-several"
10232 \begin_layout Plain Layout
10233 Accents ! for several characters
10241 \begin_layout Standard
10242 \begin_inset space \hfill{}
10246 \begin_inset Tabular
10247 <lyxtabular version="3" rows="5" columns="2">
10249 <column alignment="center" valignment="top" width="0pt">
10250 <column alignment="center" valignment="top" width="0pt">
10252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10255 \begin_layout Plain Layout
10261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10264 \begin_layout Plain Layout
10266 \begin_inset Note Note
10269 \begin_layout Plain Layout
10276 is only used as spacer.
10288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10291 \begin_layout Plain Layout
10298 \begin_layout Plain Layout
10312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10315 \begin_layout Plain Layout
10316 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10329 \begin_layout Plain Layout
10336 \begin_layout Plain Layout
10350 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10353 \begin_layout Plain Layout
10354 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10367 \begin_layout Plain Layout
10374 \begin_layout Plain Layout
10388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10391 \begin_layout Plain Layout
10392 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10402 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10405 \begin_layout Plain Layout
10408 underleftrightarrow
10412 \begin_layout Plain Layout
10426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10429 \begin_layout Plain Layout
10430 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10444 \begin_inset space \hfill{}
10448 \begin_inset Tabular
10449 <lyxtabular version="3" rows="5" columns="2">
10451 <column alignment="center" valignment="top" width="0pt">
10452 <column alignment="center" valignment="top" width="0pt">
10454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10457 \begin_layout Plain Layout
10463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10466 \begin_layout Plain Layout
10474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10477 \begin_layout Plain Layout
10484 \begin_layout Plain Layout
10498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10501 \begin_layout Plain Layout
10502 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10512 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10515 \begin_layout Plain Layout
10522 \begin_layout Plain Layout
10536 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10539 \begin_layout Plain Layout
10540 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10553 \begin_layout Plain Layout
10560 \begin_layout Plain Layout
10574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10577 \begin_layout Plain Layout
10578 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10588 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10591 \begin_layout Plain Layout
10598 \begin_layout Plain Layout
10612 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10615 \begin_layout Plain Layout
10616 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10630 \begin_inset space \hfill{}
10636 \begin_layout Standard
10637 \begin_inset VSpace medskip
10640 With these commands as many characters as you like can be accented.
10653 will only be set in the output with a length of three characters, as shown
10654 in the following example:
10655 \begin_inset Formula \[
10656 \widetilde{A+B=C-D}\]
10663 \begin_layout Standard
10674 \begin_layout Plain Layout
10692 \begin_layout Plain Layout
10700 described in the previous subsection it is also possible to accent several
10710 \begin_layout Plain Layout
10720 \begin_inset Formula $\downarrow$
10726 \begin_inset Formula \[
10727 \underset{***}{A=B}\]
10734 \begin_layout Section
10736 \begin_inset CommandInset label
10746 \begin_layout Plain Layout
10755 \begin_layout Subsection
10757 \begin_inset CommandInset label
10759 name "sub:Predefined-Space"
10767 \begin_layout Plain Layout
10768 Space ! horizontal ! predefined
10776 \begin_layout Standard
10777 Sometimes it is necessary to insert horizontal space to a formula.
10778 This is done by inserting a protected space (shortcut
10784 \begin_inset Quotes eld
10794 \begin_layout Plain Layout
10807 \begin_inset Quotes erd
10810 appears and by pressing
10814 several times one can select one of eight different space sizes.
10815 The spaces can also be inserted using the math toolbar button
10816 \begin_inset Graphics
10817 filename ../images/math/space.png
10822 or special commands.
10823 Independent from the inserted command, one can select the size again by
10831 \begin_layout Standard
10834 \begin_inset VSpace -5mm
10838 \begin_inset Tabular
10839 <lyxtabular version="3" rows="3" columns="7">
10841 <column alignment="center" valignment="middle" width="6.8cm">
10842 <column alignment="center" valignment="top" width="0">
10843 <column alignment="center" valignment="top" width="0">
10844 <column alignment="center" valignment="top" width="0">
10845 <column alignment="center" valignment="top" width="0">
10846 <column alignment="center" valignment="top" width="0">
10847 <column alignment="center" valignment="top" width="0">
10849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10852 \begin_layout Plain Layout
10858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10861 \begin_layout Plain Layout
10869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10872 \begin_layout Plain Layout
10880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10883 \begin_layout Plain Layout
10891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10894 \begin_layout Plain Layout
10902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10905 \begin_layout Plain Layout
10913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10916 \begin_layout Plain Layout
10926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10929 \begin_layout Plain Layout
10934 keystrokes after inserting the protected space
10939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10942 \begin_layout Plain Layout
10948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10951 \begin_layout Plain Layout
10957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10960 \begin_layout Plain Layout
10966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10969 \begin_layout Plain Layout
10975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10978 \begin_layout Plain Layout
10984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10987 \begin_layout Plain Layout
10995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10998 \begin_layout Plain Layout
11004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11007 \begin_layout Plain Layout
11008 \begin_inset Formula $A\, B$
11016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11019 \begin_layout Plain Layout
11020 \begin_inset Formula $A\: B$
11028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11031 \begin_layout Plain Layout
11032 \begin_inset Formula $A\; B$
11040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11043 \begin_layout Plain Layout
11044 \begin_inset Formula $A\quad B$
11052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11055 \begin_layout Plain Layout
11056 \begin_inset Formula $A\qquad B$
11064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11067 \begin_layout Plain Layout
11068 \begin_inset Formula $A\! B$
11084 \begin_layout Standard
11085 The last size seem to produce no space.
11086 It is displayed red in LyX contrary to the other sizes, because it is a
11088 There are two more negative spaces:
11091 \begin_layout Standard
11093 \begin_inset Tabular
11094 <lyxtabular version="3" rows="3" columns="3">
11096 <column alignment="center" valignment="middle" width="6.8cm">
11097 <column alignment="center" valignment="top" width="0pt">
11098 <column alignment="center" valignment="top" width="0pt">
11100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11103 \begin_layout Plain Layout
11109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11112 \begin_layout Plain Layout
11120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11123 \begin_layout Plain Layout
11133 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11136 \begin_layout Plain Layout
11141 keystrokes after inserting the protected space
11146 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11149 \begin_layout Plain Layout
11155 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11158 \begin_layout Plain Layout
11166 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11169 \begin_layout Plain Layout
11175 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11178 \begin_layout Plain Layout
11179 \begin_inset Formula $A\negmedspace B$
11187 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11190 \begin_layout Plain Layout
11191 \begin_inset Formula $A\negthickspace B$
11207 \begin_layout Standard
11208 Negative spaces can lead to characters overlapping each other.
11209 Thus they can be used to enforce ligatures, what is e.
11210 \begin_inset space \thinspace{}
11214 \begin_inset space ~
11217 useful for summation operators:
11220 \begin_layout Standard
11222 \begin_inset Tabular
11223 <lyxtabular version="3" rows="3" columns="2">
11225 <column alignment="center" valignment="top" width="0">
11226 <column alignment="center" valignment="top" width="0">
11228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11231 \begin_layout Plain Layout
11237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11240 \begin_layout Plain Layout
11242 \begin_inset Note Note
11245 \begin_layout Plain Layout
11252 is only used as spacer.
11264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11267 \begin_layout Plain Layout
11276 \begin_layout Plain Layout
11290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11293 \begin_layout Plain Layout
11294 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11307 \begin_layout Plain Layout
11318 \begin_layout Plain Layout
11332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11335 \begin_layout Plain Layout
11336 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11352 \begin_layout Standard
11353 Relations like for example equal signs, are always surrounded by space.
11354 To suppress this, the equal sign is placed into a TeX-brace.
11355 The following example demonstrates this:
11358 \begin_layout Standard
11360 \begin_inset Tabular
11361 <lyxtabular version="3" rows="2" columns="2">
11363 <column alignment="center" valignment="top" width="0pt">
11364 <column alignment="center" valignment="top" width="0pt">
11366 <cell alignment="center" valignment="top" usebox="none">
11369 \begin_layout Plain Layout
11375 <cell alignment="center" valignment="top" usebox="none">
11378 \begin_layout Plain Layout
11379 \begin_inset Formula $A=B$
11389 <cell alignment="center" valignment="top" usebox="none">
11392 \begin_layout Plain Layout
11393 \begin_inset Note Note
11396 \begin_layout Plain Layout
11403 is only used as spacer.
11409 \begin_inset Formula $\raisebox{5mm}{}$
11412 equation without space
11417 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11420 \begin_layout Plain Layout
11421 \begin_inset Formula $A{=}B$
11437 \begin_layout Standard
11439 The command for the last formula is:
11444 \begin_inset Formula $\to$
11450 \begin_layout Standard
11451 \begin_inset VSpace bigskip
11454 Spaces are needed for physical units, because the space between the value
11455 and the unit is the smallest one and not a normal space.
11456 For units in text, the smallest space is inserted via the menu
11458 Insert\SpecialChar \menuseparator
11459 Formatting\SpecialChar \menuseparator
11461 \begin_inset space ~
11473 \begin_layout Standard
11474 An example to visualize the difference:
11477 \begin_layout Standard
11478 \begin_inset Tabular
11479 <lyxtabular version="3" rows="2" columns="2">
11481 <column alignment="left" valignment="top" width="0">
11482 <column alignment="left" valignment="top" width="0">
11484 <cell alignment="center" valignment="top" usebox="none">
11487 \begin_layout Plain Layout
11489 \begin_inset Formula $\cdot$
11497 <cell alignment="center" valignment="top" usebox="none">
11500 \begin_layout Plain Layout
11501 space between value and unit
11508 <cell alignment="center" valignment="top" usebox="none">
11511 \begin_layout Plain Layout
11513 \begin_inset space \thinspace{}
11517 \begin_inset Formula $\cdot$
11525 <cell alignment="center" valignment="top" usebox="none">
11528 \begin_layout Plain Layout
11529 smallest space between value and unit
11542 \begin_layout Subsection
11547 \begin_layout Plain Layout
11560 \begin_layout Plain Layout
11561 for vertical space in formulas see
11562 \begin_inset CommandInset ref
11564 reference "sub:Line-Separation"
11577 \begin_layout Plain Layout
11585 \begin_inset Note Note
11588 \begin_layout Plain Layout
11591 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11594 \begin_layout Plain Layout
11597 texorpdfstring is in section
11598 \begin_inset CommandInset ref
11600 reference "sub:Formulas-in-Section"
11610 \begin_inset CommandInset label
11612 name "sub:Variable-Space"
11620 \begin_layout Plain Layout
11621 Space ! horizontal ! variable
11629 \begin_layout Standard
11630 Space with a defined length can be inserted in LyX with the command
11631 \begin_inset Newline newline
11644 \begin_layout Plain Layout
11653 For the length all units listed in
11654 \begin_inset CommandInset ref
11656 reference "tab:Used-units"
11660 are allowed, except of the unit
11661 \begin_inset Quotes eld
11665 \begin_inset Quotes erd
11669 The length may also be negative.
11670 To insert so many space that the formula uses all available space, the
11681 \begin_layout Plain Layout
11692 \begin_layout Standard
11693 \begin_inset VSpace -1mm
11699 \begin_layout Standard
11701 \begin_inset Tabular
11702 <lyxtabular version="3" rows="4" columns="2">
11704 <column alignment="center" valignment="top" width="0">
11705 <column alignment="center" valignment="top" width="0">
11707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11710 \begin_layout Plain Layout
11716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11719 \begin_layout Plain Layout
11727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11730 \begin_layout Plain Layout
11734 \begin_inset Formula $\to$
11744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11747 \begin_layout Plain Layout
11748 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11761 \begin_layout Plain Layout
11765 \begin_inset Formula $\to$
11775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11778 \begin_layout Plain Layout
11779 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11792 \begin_layout Plain Layout
11799 \begin_layout Plain Layout
11813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11816 \begin_layout Plain Layout
11817 \begin_inset Formula $A=A\hfill B=B$
11833 \begin_layout Standard
11834 In the last example the available space is given by the longest column entry
11836 In an inline formula the space depends on the length of the line in which
11844 Thus, when the line uses the full width, no space will be created.
11851 only has an effect on displayed formulas when the formula style
11856 (Formula styles are explained in
11857 \begin_inset CommandInset ref
11859 reference "sec:Formula-Styles"
11866 \begin_layout Standard
11867 For text, variable space can be inserted via the menu
11869 Insert\SpecialChar \menuseparator
11870 Formatting\SpecialChar \menuseparator
11872 \begin_inset space ~
11877 , what is not possible in formulas:
11880 \begin_layout Standard
11881 This is a line with
11882 \begin_inset space \hspace{}
11887 \begin_inset space \thinspace{}
11893 \begin_layout Standard
11894 This is a line with
11895 \begin_inset space \hfill{}
11901 \begin_layout Subsection
11902 Space besides inline Formulas
11906 \begin_layout Plain Layout
11907 Space ! besides inline formulas
11915 \begin_layout Standard
11916 The space that surrounds inline formulas can be adjusted with the length
11925 \begin_layout Plain Layout
11936 The value of a length is set with the command
11944 \begin_layout Plain Layout
11954 that has the following scheme:
11957 \begin_layout Standard
11962 setlength{length name}{value}
11965 \begin_layout Standard
11973 \begin_inset space \thinspace{}
11979 \begin_layout Standard
11989 \begin_layout Standard
11990 is inserted in TeX-mode.
11992 \begin_inset space \thinspace{}
11995 mm space will now be set around all inline formulas:
11999 \begin_layout Plain Layout
12013 \begin_layout Standard
12014 This is a line with an inline formula
12015 \begin_inset Formula $A=B$
12019 \begin_inset space \thinspace{}
12022 mm surrounding space.
12026 \begin_layout Plain Layout
12040 \begin_layout Standard
12041 To return to the predefined value,
12047 is set to the value 0
12048 \begin_inset space \thinspace{}
12054 \begin_layout Section
12059 \begin_layout Plain Layout
12069 \begin_layout Plain Layout
12074 \begin_layout Plain Layout
12085 \begin_layout Plain Layout
12100 \begin_layout Standard
12101 Boxes for text are described in chapter
12108 \begin_inset space ~
12116 \begin_layout Subsection
12118 \begin_inset CommandInset label
12120 name "sub:Boxes-with-Frame"
12128 \begin_layout Plain Layout
12137 \begin_layout Standard
12138 It is possible to frame formulas or parts of it with the commands
12148 \begin_layout Plain Layout
12166 \begin_layout Plain Layout
12177 \begin_layout Standard
12178 When one of these commands is inserted to a formula, a blue box appears
12179 within a frame to enter formula parts.
12186 an additional formula has to be created by
12194 \begin_layout Plain Layout
12195 Due to a bug in LyX it is not possible to create a new formula with
12200 \begin_inset CommandInset href
12202 name "LyX-bug #1435"
12203 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12212 , because the box content will otherwise be treated as mathematical text.
12219 is used, a new formula is automatically created inside the frame.
12222 \begin_layout Standard
12229 is not suitable to frame displayed formulas, because the formula will always
12230 be set in the size of the text.
12237 is in contrary not suitable to frame inline formulas, because the formula
12238 will always be set in the size of a displayed formula.
12241 \begin_layout Standard
12248 there is the command
12258 \begin_layout Plain Layout
12266 where additionally the frame width and the alignment can be specified.
12273 is used in the following scheme:
12276 \begin_layout Standard
12281 framebox[frame width][position]{box content}
12284 \begin_layout Standard
12285 The position can either be
12302 right aligns the formula in the box.
12303 When no position is given, the formula will be centered.
12304 \begin_inset Newline newline
12307 Is no width given, also no position can be given.
12308 In this case the frame width is adjusted to the box content like for
12317 \begin_layout Standard
12324 is inserted, a box appears containing three blue boxes.
12325 The first two boxes are surrounded by brackets and denote the two optional
12327 The third box is for formula parts like for
12336 \begin_layout Standard
12338 \begin_inset Note Note
12341 \begin_layout Plain Layout
12342 The table has been set into a minipage to make the footnote appearing.
12343 Otherwise the footnote text would not be displayed.
12349 \begin_inset Box Frameless
12358 height_special "totalheight"
12361 \begin_layout Plain Layout
12363 \begin_inset Tabular
12364 <lyxtabular version="3" rows="5" columns="2">
12366 <column alignment="center" valignment="top" width="0">
12367 <column alignment="center" valignment="top" width="0">
12369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12372 \begin_layout Plain Layout
12377 \begin_layout Plain Layout
12378 Due to a bug in LyX it is not possible to create a new formula with
12383 \begin_inset CommandInset href
12385 name "LyX-bug #1435"
12386 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12403 \begin_layout Plain Layout
12405 \begin_inset Note Note
12408 \begin_layout Plain Layout
12415 is only used as spacer.
12427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12430 \begin_layout Plain Layout
12437 \begin_layout Plain Layout
12456 \begin_layout Plain Layout
12470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12473 \begin_layout Plain Layout
12474 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
12485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12488 \begin_layout Plain Layout
12495 \begin_layout Plain Layout
12510 \begin_layout Plain Layout
12524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12527 \begin_layout Plain Layout
12528 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12541 \begin_layout Plain Layout
12548 \begin_layout Plain Layout
12562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12565 \begin_layout Plain Layout
12566 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12579 \begin_layout Plain Layout
12586 \begin_layout Plain Layout
12596 \begin_inset Formula $\to$
12600 \begin_inset Formula $\to$
12613 \begin_layout Plain Layout
12623 \begin_inset Formula $\downarrow$
12631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12634 \begin_layout Plain Layout
12635 \begin_inset Formula $\raisebox{6mm}{}$
12639 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12643 \begin_inset Formula $\raisebox{-4mm}{}$
12664 \begin_layout Standard
12665 The frame thickness can also be adjusted.
12666 To do this the following commands have to be inserted in TeX-mode before
12670 \begin_layout Standard
12680 \begin_inset Quotes eld
12684 \begin_inset Quotes erd
12698 \begin_inset Quotes eld
12702 \begin_inset Quotes erd
12708 \begin_layout Standard
12709 \begin_inset Quotes eld
12713 \begin_inset Quotes erd
12716 specifies the minimal distance between the frame and the first character
12718 An example for this is the following framed formula:
12722 \begin_layout Plain Layout
12734 \begin_inset Formula \[
12739 Before this formula the commands
12742 \begin_layout Standard
12764 \begin_layout Standard
12765 were inserted in TeX-mode.
12766 The given values are used for all following boxes.
12769 \begin_layout Standard
12770 To return to the standard frame size, the command
12773 \begin_layout Standard
12798 \begin_layout Plain Layout
12812 \begin_layout Standard
12813 is inserted in TeX-mode before the next formula.
12816 \begin_layout Subsection
12817 Boxes without Frame
12818 \begin_inset CommandInset label
12820 name "sub:Boxes-without-Frame"
12828 \begin_layout Plain Layout
12829 Boxes ! without frame
12837 \begin_layout Standard
12838 For boxes without a frame there are the following box commands:
12848 \begin_layout Plain Layout
12866 \begin_layout Plain Layout
12884 \begin_layout Plain Layout
12895 \begin_layout Standard
12902 a box can be super- or subscripted.
12903 But in contrary to normal super- and subscripting, the characters in the
12904 box keep their font size.
12911 is used in the following scheme:
12914 \begin_layout Standard
12919 raisebox{height}{box content}
12922 \begin_layout Standard
12923 When the box should contain a formula, an extra formula is needed like for
12933 \begin_layout Standard
12935 \begin_inset Tabular
12936 <lyxtabular version="3" rows="4" columns="2">
12938 <column alignment="center" valignment="top" width="0">
12939 <column alignment="center" valignment="top" width="0">
12941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12944 \begin_layout Plain Layout
12950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12953 \begin_layout Plain Layout
12961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12964 \begin_layout Plain Layout
12968 \begin_inset Formula $\to$
12974 \begin_inset Formula $\to$
12982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12985 \begin_layout Plain Layout
12986 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12999 \begin_layout Plain Layout
13003 \begin_inset Formula $\to$
13009 \begin_inset Formula $\to$
13017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13020 \begin_layout Plain Layout
13021 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13034 \begin_layout Plain Layout
13038 \begin_inset Formula $\to$
13053 \begin_layout Plain Layout
13067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13070 \begin_layout Plain Layout
13074 \begin_layout Plain Layout
13098 \begin_layout Standard
13099 The last formula can currently only be created using TeX-mode because LyX
13100 inserts a box instead of the needed extra formula.
13104 \begin_layout Plain Layout
13106 \begin_inset CommandInset href
13108 name "LyX-bug #1435"
13109 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13121 \begin_layout Standard
13146 , with the difference that there is no frame.
13149 \begin_layout Subsection
13151 \begin_inset CommandInset label
13153 name "sub:Colored-Boxes"
13161 \begin_layout Plain Layout
13170 \begin_layout Standard
13171 To be able to use all commands explained in this section, the LaTeX-package
13180 \begin_layout Plain Layout
13185 is part of every LaTeX standard installation.
13194 \begin_layout Plain Layout
13200 has to be loaded in the LaTeX-preamble with the line
13204 \begin_layout Plain Layout
13205 When text is colored somewhere in the document with a predefined color,
13206 LyX loads the LaTeX-package
13211 Thus it is possible that the package is loaded twice, but this doesn't
13218 \begin_inset Note Note
13221 \begin_layout Plain Layout
13222 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13231 \begin_layout Standard
13239 \begin_layout Standard
13240 \begin_inset VSpace medskip
13243 To color boxes, the command
13253 \begin_layout Plain Layout
13261 is used in the following scheme:
13264 \begin_layout Standard
13269 colorbox{color}{box content}
13272 \begin_layout Standard
13273 The box content can also be a box and a
13279 can also be part of another box (see the 2nd and 3rd example).
13280 When the box should contain a formula, an extra formula has to be created,
13291 \begin_layout Plain Layout
13292 This also applies for the command
13300 \begin_inset CommandInset href
13302 name "LyX-bug #1435"
13303 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13315 \begin_layout Standard
13316 One of the following predefined colors can be chosen:
13319 \begin_layout Standard
13353 \begin_layout Standard
13355 \begin_inset Tabular
13356 <lyxtabular version="3" rows="4" columns="2">
13358 <column alignment="center" valignment="top" width="0">
13359 <column alignment="center" valignment="top" width="0">
13361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13364 \begin_layout Plain Layout
13370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13373 \begin_layout Plain Layout
13375 \begin_inset Note Note
13378 \begin_layout Plain Layout
13385 is only used as spacer.
13397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13400 \begin_layout Plain Layout
13404 \begin_inset Formula $\to$
13414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13417 \begin_layout Plain Layout
13418 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13431 \begin_layout Plain Layout
13435 \begin_inset Formula $\to$
13446 \begin_layout Plain Layout
13460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13463 \begin_layout Plain Layout
13464 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13477 \begin_layout Plain Layout
13484 \begin_layout Plain Layout
13496 \begin_inset Formula $\to$
13506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13509 \begin_layout Plain Layout
13510 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13526 \begin_layout Standard
13533 only colors the box but not the characters in the box.
13534 To color all characters, the whole formula is highlighted and the wanted
13535 color is chosen in the
13538 \begin_inset space ~
13544 The dialog can be called with the toolbar button
13545 \begin_inset Graphics
13546 filename ../images/dialog-show_character.png
13553 Edit\SpecialChar \menuseparator
13555 \begin_inset space ~
13558 Style\SpecialChar \menuseparator
13562 The formula number has then the same color as the formula.
13563 When the formula number should get another color than the formula characters,
13564 the color must be changed within the formula.
13567 \begin_layout Standard
13571 \begin_layout Standard
13574 \begin_inset Formula \begin{equation}
13575 \int A=B\label{eq:red}\end{equation}
13582 \begin_inset Formula \begin{equation}
13583 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13590 \begin_layout Standard
13592 \begin_inset CommandInset ref
13598 is completely colored red.
13599 \begin_inset Newline newline
13603 \begin_inset CommandInset ref
13605 reference "eq:redgreen"
13609 was first completely colored green to set the color for the formula number.
13610 Subsequently the formula characters were colored red.
13613 \begin_layout Standard
13614 \begin_inset VSpace bigskip
13617 To color the frame different than the rest of the box, the command
13627 \begin_layout Plain Layout
13635 is used in the following scheme:
13638 \begin_layout Standard
13643 fcolorbox{frame color}{color}{box content}
13646 \begin_layout Standard
13653 is an extension of the command
13660 The frame width is set, like for
13683 \begin_layout Plain Layout
13695 \begin_inset Formula \[
13696 \fcolorbox{cyan}{magenta}{A=B}\]
13704 \begin_layout Plain Layout
13718 \begin_layout Standard
13719 This formula was created with the command
13720 \begin_inset Newline newline
13728 \begin_inset Formula $\to$
13734 \begin_inset Formula $\to$
13744 \begin_layout Standard
13745 \begin_inset VSpace bigskip
13748 To use other colors than the predefined ones, they have to be defined first.
13751 \begin_layout Standard
13752 One can for example define the color
13753 \begin_inset Quotes eld
13761 \begin_inset Quotes erd
13764 with the LaTeX-preamble line:
13767 \begin_layout Standard
13772 definecolor{darkgreen}{cmyk}{0.5,
13790 \begin_layout Plain Layout
13801 \begin_layout Standard
13806 is the color space that denotes the colors
13823 The four comma separated numbers are the portion factor for the corresponding
13824 colors of the color space.
13825 The factors can be in the range of 0
13826 \begin_inset space \thinspace{}
13830 \begin_inset space \thinspace{}
13838 also the color space
13842 can be used for definitions.
13859 , so that there are in this case three portion factors for the corresponding
13861 Furthermore there is the color space
13865 with one portion factor for the gray value.
13868 \begin_layout Standard
13869 As example a framed box with the new defined color
13873 where the characters have been colored
13878 \begin_inset Formula \begin{equation}
13879 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13886 \begin_layout Standard
13887 Self-defined colors can also be used for text with the help of the command
13898 \begin_layout Plain Layout
13907 \begin_layout Standard
13911 \begin_layout Plain Layout
13915 textcolor{darkgreen}{
13921 \begin_inset Quotes eld
13925 \begin_inset Quotes erd
13932 \begin_layout Plain Layout
13942 \begin_layout Standard
13953 \begin_layout Plain Layout
13961 is used in the scheme
13965 textcolor{color}{characters to color}
13970 \begin_layout Subsection
13972 \begin_inset CommandInset label
13974 name "sub:Paragraph-Boxes"
13982 \begin_layout Plain Layout
13983 Boxes ! as paragraph
13991 \begin_layout Standard
13992 A box that can contain several lines and paragraphs, a so called paragraph
13993 box (parbox), can be created with the menu
13995 Insert\SpecialChar \menuseparator
13998 or the toolbar button
13999 \begin_inset Graphics
14000 filename ../images/box-insert.png
14008 \begin_layout Standard
14009 The following example shows a framed parbox in a line:
14012 \begin_layout Standard
14013 \begin_inset VSpace medskip
14017 \begin_inset Box Boxed
14026 height_special "totalheight"
14029 \begin_layout Plain Layout
14030 This is a paragraph box.
14032 \begin_inset space \thinspace{}
14035 cm long and can also contain formulas:
14036 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14047 \begin_layout Standard
14048 \begin_inset VSpace medskip
14054 \begin_layout Standard
14055 Such a box is created by right-clicking on the gray box inset.
14056 A dialog pops up showing the box properties.
14070 \begin_inset space \thinspace{}
14075 Vertical Box Alignment
14080 \begin_layout Standard
14081 \begin_inset VSpace medskip
14084 In LaTeX a parbox is created with the command
14094 \begin_layout Plain Layout
14102 that has the following scheme:
14105 \begin_layout Standard
14110 parbox[position]{width}{box content}
14113 \begin_layout Standard
14127 for bottom means that the box is aligned within the surrounding text with
14133 for top this is done with the first line.
14134 When no position is given, the box will be vertically centered, see section
14142 \begin_inset space ~
14147 manual for examples.
14150 \begin_layout Standard
14151 \begin_inset VSpace bigskip
14154 To frame formulas completely, including the formula number, the formula
14155 must be set into a parbox.
14156 To do this, the command
14170 is inserted in TeX-mode before the formula.
14179 \begin_layout Plain Layout
14189 is hereby the line width set for the document.
14190 Because the frame is outside the parbox, 2
14191 \begin_inset space \thinspace{}
14194 times the frame separation and the frame thickness must be subtracted from
14196 As this is not automatically done by LyX due to a bug
14200 \begin_layout Plain Layout
14201 \begin_inset CommandInset href
14203 name "LyX-bug #4483"
14204 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14213 , TeX-mode has to be used.
14214 To be able to multiply and subtract in arguments, the LaTeX-package
14222 \begin_layout Plain Layout
14227 is part of every LaTeX standard installation.
14236 \begin_layout Plain Layout
14242 must be loaded in the LaTeX-preamble with the line
14245 \begin_layout Standard
14253 \begin_layout Standard
14254 Behind the formula both boxes are closed by entering
14259 Here is an example:
14263 \begin_layout Plain Layout
14277 \begin_layout Standard
14281 \begin_layout Plain Layout
14299 \begin_inset Formula \begin{equation}
14300 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14308 \begin_layout Plain Layout
14319 \begin_layout Plain Layout
14333 \begin_layout Standard
14334 \begin_inset VSpace medskip
14337 As a parbox is used as argument of
14343 , there is in this case no difference between
14358 \begin_layout Standard
14359 \begin_inset VSpace bigskip
14362 Paragraph boxes are very useful to comment formulas directly.
14369 is used in combination with the command
14383 \begin_inset CommandInset ref
14385 reference "sub:User-defined-Numbering"
14392 \begin_layout Standard
14393 An example of a formula commented with
14402 \begin_layout Standard
14406 \begin_layout Plain Layout
14419 This is a description.
14420 It is distinctly separated from the formula and multiline.
14424 \begin_layout Plain Layout
14436 \begin_layout Standard
14437 Such a formula must be inserted completely in TeX-mode because LyX does
14438 not yet support the command
14445 The formula is created with the following command sequence:
14448 \begin_layout Standard
14461 is inserted in TeX-mode.
14465 \begin_layout Plain Layout
14466 When the formula style
14478 can also be replaced by
14485 (formula styles see
14486 \begin_inset CommandInset ref
14488 reference "sec:Formula-Styles"
14497 Then the description follows as normal text, and finally
14503 is inserted in TeX-mode.
14516 hereby create a displayed formula.
14519 \begin_layout Standard
14526 can be seen in this example that was
14527 \begin_inset Quotes eld
14531 \begin_inset Quotes erd
14534 using the mathematical textmode:
14535 \begin_inset Formula \[
14536 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14543 \begin_layout Section
14548 \begin_layout Plain Layout
14557 \begin_layout Subsection
14559 \begin_inset CommandInset label
14561 name "sub:Big-Operators"
14569 \begin_layout Plain Layout
14579 \begin_layout Plain Layout
14589 \begin_layout Plain Layout
14598 \begin_layout Standard
14599 To be able to use all integral operators listed here, the option
14601 Use esint package automatically
14603 must be set in the document settings under
14606 \begin_inset space ~
14614 \begin_layout Standard
14615 \begin_inset space \hfill{}
14619 \begin_inset Tabular
14620 <lyxtabular version="3" rows="11" columns="2">
14622 <column alignment="center" valignment="top" width="0pt">
14623 <column alignment="center" valignment="top" width="0pt">
14625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14628 \begin_layout Plain Layout
14634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14637 \begin_layout Plain Layout
14645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14648 \begin_layout Plain Layout
14655 \begin_layout Plain Layout
14668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14671 \begin_layout Plain Layout
14672 \begin_inset Formula $\sum$
14682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14685 \begin_layout Plain Layout
14692 \begin_layout Plain Layout
14705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14708 \begin_layout Plain Layout
14709 \begin_inset Formula $\int$
14719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14722 \begin_layout Plain Layout
14730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14733 \begin_layout Plain Layout
14734 \begin_inset Formula $\intop$
14744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14747 \begin_layout Plain Layout
14755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14758 \begin_layout Plain Layout
14759 \begin_inset Formula $\oint$
14769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14772 \begin_layout Plain Layout
14780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14783 \begin_layout Plain Layout
14784 \begin_inset Formula $\ointop$
14794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14797 \begin_layout Plain Layout
14805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14808 \begin_layout Plain Layout
14809 \begin_inset Formula $\ointctrclockwise$
14819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14822 \begin_layout Plain Layout
14830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14833 \begin_layout Plain Layout
14834 \begin_inset Formula $\ointclockwise$
14844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14847 \begin_layout Plain Layout
14855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14858 \begin_layout Plain Layout
14859 \begin_inset Formula $\sqint$
14869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14872 \begin_layout Plain Layout
14880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14883 \begin_layout Plain Layout
14884 \begin_inset Formula $\bigcap$
14894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14897 \begin_layout Plain Layout
14905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14908 \begin_layout Plain Layout
14909 \begin_inset Formula $\bigcup$
14923 \begin_inset space \hfill{}
14927 \begin_inset Tabular
14928 <lyxtabular version="3" rows="10" columns="2">
14930 <column alignment="center" valignment="top" width="0pt">
14931 <column alignment="center" valignment="top" width="0pt">
14933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14936 \begin_layout Plain Layout
14942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14945 \begin_layout Plain Layout
14953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14956 \begin_layout Plain Layout
14963 \begin_layout Plain Layout
14976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14979 \begin_layout Plain Layout
14980 \begin_inset Formula $\prod$
14990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14993 \begin_layout Plain Layout
15001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15004 \begin_layout Plain Layout
15005 \begin_inset Formula $\coprod$
15015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15018 \begin_layout Plain Layout
15026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15029 \begin_layout Plain Layout
15030 \begin_inset Formula $\bigodot$
15040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15043 \begin_layout Plain Layout
15051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15054 \begin_layout Plain Layout
15055 \begin_inset Formula $\bigotimes$
15065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15068 \begin_layout Plain Layout
15076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15079 \begin_layout Plain Layout
15080 \begin_inset Formula $\bigoplus$
15090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15093 \begin_layout Plain Layout
15101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15104 \begin_layout Plain Layout
15105 \begin_inset Formula $\bigwedge$
15115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15118 \begin_layout Plain Layout
15126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15129 \begin_layout Plain Layout
15130 \begin_inset Formula $\bigvee$
15140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15143 \begin_layout Plain Layout
15151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15154 \begin_layout Plain Layout
15155 \begin_inset Formula $\bigsqcup$
15165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15168 \begin_layout Plain Layout
15176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15179 \begin_layout Plain Layout
15180 \begin_inset Formula $\biguplus$
15194 \begin_inset space \hfill{}
15200 \begin_layout Standard
15201 All big operators can also be inserted via the math toolbar button
15202 \begin_inset Graphics
15203 filename ../images/math/intop.png
15211 \begin_layout Standard
15212 The operators are called big because they are bigger than the sometimes
15213 equal looking binary operators.
15214 All big operators can have limits as described in the next subsection.
15217 \begin_layout Standard
15243 \begin_inset space ~
15246 in the style the operator limits are displayed, see
15247 \begin_inset CommandInset ref
15249 reference "sub:Operator-Limits"
15257 \begin_layout Subsubsection*
15258 Advices for Integrals
15261 \begin_layout Standard
15266 in an integral is an operator, that therefore has to be set upright.
15267 This is done by highlighting the
15271 and using the keyboard shortcut
15274 \begin_inset space ~
15283 \begin_layout Plain Layout
15289 \begin_inset CommandInset ref
15291 reference "sub:Font-Styles"
15301 Finally the smallest space is inserted before the
15305 , as this is usual for operators.
15309 \begin_layout Standard
15311 \begin_inset Formula $\int A(x)dx$
15315 \begin_inset Newline newline
15322 \begin_layout Plain Layout
15332 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15338 \begin_layout Standard
15339 For multiple integrals there are the following commands:
15340 \begin_inset VSpace medskip
15346 \begin_layout Standard
15347 \begin_inset space \hfill{}
15351 \begin_inset Tabular
15352 <lyxtabular version="3" rows="4" columns="2">
15354 <column alignment="center" valignment="top" width="0">
15355 <column alignment="center" valignment="top" width="0">
15357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15360 \begin_layout Plain Layout
15366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15369 \begin_layout Plain Layout
15371 \begin_inset Note Note
15374 \begin_layout Plain Layout
15381 is only used as spacer.
15393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15396 \begin_layout Plain Layout
15404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15407 \begin_layout Plain Layout
15408 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15421 \begin_layout Plain Layout
15429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15432 \begin_layout Plain Layout
15433 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15446 \begin_layout Plain Layout
15454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15457 \begin_layout Plain Layout
15458 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15472 \begin_inset space \hfill{}
15476 \begin_inset Tabular
15477 <lyxtabular version="3" rows="4" columns="2">
15479 <column alignment="center" valignment="top" width="0">
15480 <column alignment="center" valignment="top" width="0">
15482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15485 \begin_layout Plain Layout
15491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15494 \begin_layout Plain Layout
15502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15505 \begin_layout Plain Layout
15513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15516 \begin_layout Plain Layout
15517 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15530 \begin_layout Plain Layout
15538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15541 \begin_layout Plain Layout
15542 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15555 \begin_layout Plain Layout
15563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15566 \begin_layout Plain Layout
15567 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15581 \begin_inset space \hfill{}
15587 \begin_layout Subsection
15589 \begin_inset CommandInset label
15591 name "sub:Operator-Limits"
15599 \begin_layout Plain Layout
15608 \begin_layout Standard
15609 Limits are created by super- and subscripts:
15612 \begin_layout Standard
15614 \begin_inset Tabular
15615 <lyxtabular version="3" rows="2" columns="2">
15617 <column alignment="center" valignment="top" width="0pt">
15618 <column alignment="center" valignment="top" width="0pt">
15620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15623 \begin_layout Plain Layout
15629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15632 \begin_layout Plain Layout
15634 \begin_inset Note Note
15637 \begin_layout Plain Layout
15644 is only used as spacer.
15656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15659 \begin_layout Plain Layout
15668 \begin_layout Plain Layout
15678 \begin_inset Formula $\to$
15682 \begin_inset Formula $\to$
15690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15693 \begin_layout Plain Layout
15694 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15710 \begin_layout Standard
15711 Limits of inline formulas are set right beside the operator.
15712 Limits in displayed formulas are set above or below the operator, except
15713 of integral limits.
15716 \begin_layout Standard
15717 To force that the limits are set beside the operator, the cursor is set
15718 directly behind the operator and the limits type is changed with the menu
15721 Edit\SpecialChar \menuseparator
15722 Math\SpecialChar \menuseparator
15734 \begin_inset space ~
15743 \begin_layout Standard
15744 The default limits type is this:
15745 \begin_inset Formula \[
15746 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15750 This is how it looks when the limits type was changed to
15757 \begin_inset Formula \[
15758 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15762 For integrals, except of
15774 , the limits are by default set beside the operator.
15775 But for multiple integrals the limits are often set below the operator.
15776 In the following example the limits type was therefore set to
15780 and so set below the integrals:
15781 \begin_inset Formula \begin{equation}
15782 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15789 \begin_layout Standard
15790 \begin_inset VSpace medskip
15793 To specify conditions for limits, the commands
15803 \begin_layout Plain Layout
15821 \begin_layout Plain Layout
15830 To create for example this expression
15831 \begin_inset Formula \begin{equation}
15832 \sum_{\begin{subarray}{c}
15834 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
15841 \begin_layout Standard
15842 the following has to be done:
15843 \begin_inset Newline newline
15858 \begin_layout Plain Layout
15870 One is now in a blue box under the summation operator and insert there
15879 \begin_layout Plain Layout
15891 The blue box is now within a purple box and now several lines can be written
15893 A new line is created by inserting a line break (
15899 \begin_inset Newline newline
15904 0<k<1000 Ctrl-Return
15905 \begin_inset Newline newline
15910 is typed in, a new box appears below for the new line.
15913 \begin_layout Standard
15914 The alignment of the lines can be changed to left aligned with the
15924 Edit\SpecialChar \menuseparator
15928 To get right alignment,
15936 \begin_layout Plain Layout
15947 is inserted at the beginning of the line.
15950 \begin_layout Standard
15963 with the difference that the lines are always centered.
15966 \begin_layout Standard
15967 \begin_inset VSpace bigskip
15971 \begin_inset CommandInset ref
15973 reference "eq:substack"
15977 there can be too much space beside an operator, because the characters
15978 following the operator are set beside the limits.
15981 \begin_layout Standard
15982 To avoid this, the following macro can be used in the LaTeX-preamble:
15985 \begin_layout Standard
15999 \begin_inset Newline newline
16011 \begin_inset Newline newline
16018 mathclapinternal #1#2{
16022 mathsurround =0pt #1{#2}$}}
16025 \begin_layout Standard
16026 This defines the command
16036 \begin_layout Plain Layout
16044 that sets the width of the limit to 0
16045 \begin_inset space \thinspace{}
16049 The command scheme is
16052 \begin_layout Standard
16060 \begin_layout Standard
16061 where the limit can consist of several conditions.
16064 \begin_layout Standard
16066 \begin_inset CommandInset ref
16068 reference "eq:substack"
16072 , one uses the command
16075 \begin_layout Standard
16088 \begin_layout Plain Layout
16097 0<k<1000 Ctrl-Enter
16100 \begin_layout Standard
16101 to create the lower limit.
16102 The summand is now directly behind the summation operator:
16103 \begin_inset Formula \[
16104 \sum_{\mathclap{\substack{0<k<1000\\
16105 \\k\,\in\,\mathbb{N}}
16113 \begin_layout Standard
16114 \begin_inset VSpace bigskip
16117 How to use one limit for several operators is described in
16118 \begin_inset CommandInset ref
16120 reference "sub:Self-defined-Operators"
16127 \begin_layout Subsection
16129 \begin_inset CommandInset label
16131 name "sub:Binary-Operators"
16139 \begin_layout Plain Layout
16148 \begin_layout Standard
16149 Binary operators are surrounded by space when there is a character before
16151 \begin_inset VSpace medskip
16157 \begin_layout Standard
16158 \begin_inset space \hfill{}
16162 \begin_inset Tabular
16163 <lyxtabular version="3" rows="13" columns="2">
16165 <column alignment="center" valignment="top" width="0pt">
16166 <column alignment="center" valignment="top" width="0pt">
16168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16171 \begin_layout Plain Layout
16173 \begin_inset Note Note
16176 \begin_layout Plain Layout
16183 is only used as spacer.
16193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16196 \begin_layout Plain Layout
16204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16207 \begin_layout Plain Layout
16213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16216 \begin_layout Plain Layout
16217 \begin_inset Formula $+$
16227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16230 \begin_layout Plain Layout
16236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16239 \begin_layout Plain Layout
16240 \begin_inset Formula $-$
16250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16253 \begin_layout Plain Layout
16261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16264 \begin_layout Plain Layout
16265 \begin_inset Formula $\pm$
16275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16278 \begin_layout Plain Layout
16286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16289 \begin_layout Plain Layout
16290 \begin_inset Formula $\mp$
16300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16303 \begin_layout Plain Layout
16311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16314 \begin_layout Plain Layout
16315 \begin_inset Formula $\cdot$
16325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16328 \begin_layout Plain Layout
16336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16339 \begin_layout Plain Layout
16340 \begin_inset Formula $\times$
16350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16353 \begin_layout Plain Layout
16361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16364 \begin_layout Plain Layout
16365 \begin_inset Formula $\div$
16375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16378 \begin_layout Plain Layout
16382 \begin_layout Plain Layout
16395 \begin_layout Plain Layout
16407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16410 \begin_layout Plain Layout
16411 \begin_inset Formula $*$
16421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16424 \begin_layout Plain Layout
16432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16435 \begin_layout Plain Layout
16436 \begin_inset Formula $\star$
16446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16449 \begin_layout Plain Layout
16457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16460 \begin_layout Plain Layout
16461 \begin_inset Formula $\circ$
16471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16474 \begin_layout Plain Layout
16482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16485 \begin_layout Plain Layout
16486 \begin_inset Formula $\diamond$
16496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16499 \begin_layout Plain Layout
16507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16510 \begin_layout Plain Layout
16511 \begin_inset Formula $\bullet$
16525 \begin_inset space \hfill{}
16529 \begin_inset Tabular
16530 <lyxtabular version="3" rows="13" columns="2">
16532 <column alignment="center" valignment="top" width="0pt">
16533 <column alignment="center" valignment="top" width="0pt">
16535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16538 \begin_layout Plain Layout
16544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16547 \begin_layout Plain Layout
16555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16558 \begin_layout Plain Layout
16566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16569 \begin_layout Plain Layout
16570 \begin_inset Formula $\nabla$
16580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16583 \begin_layout Plain Layout
16591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16594 \begin_layout Plain Layout
16595 \begin_inset Formula $\bigtriangledown$
16605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16608 \begin_layout Plain Layout
16616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16619 \begin_layout Plain Layout
16620 \begin_inset Formula $\bigtriangleup$
16630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16633 \begin_layout Plain Layout
16641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16644 \begin_layout Plain Layout
16645 \begin_inset Formula $\Box$
16655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16658 \begin_layout Plain Layout
16666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16669 \begin_layout Plain Layout
16670 \begin_inset Formula $\cap$
16680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16683 \begin_layout Plain Layout
16691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16694 \begin_layout Plain Layout
16695 \begin_inset Formula $\cup$
16705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16708 \begin_layout Plain Layout
16716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16719 \begin_layout Plain Layout
16720 \begin_inset Formula $\dagger$
16730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16733 \begin_layout Plain Layout
16741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16744 \begin_layout Plain Layout
16745 \begin_inset Formula $\ddagger$
16755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16758 \begin_layout Plain Layout
16766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16769 \begin_layout Plain Layout
16770 \begin_inset Formula $\wr$
16780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16783 \begin_layout Plain Layout
16791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16794 \begin_layout Plain Layout
16795 \begin_inset Formula $\bigcirc$
16805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16808 \begin_layout Plain Layout
16816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16819 \begin_layout Plain Layout
16820 \begin_inset Formula $\wedge$
16830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16833 \begin_layout Plain Layout
16841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16844 \begin_layout Plain Layout
16845 \begin_inset Formula $\vee$
16859 \begin_inset space \hfill{}
16863 \begin_inset Tabular
16864 <lyxtabular version="3" rows="13" columns="2">
16866 <column alignment="center" valignment="top" width="0pt">
16867 <column alignment="center" valignment="top" width="0pt">
16869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16872 \begin_layout Plain Layout
16878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16881 \begin_layout Plain Layout
16889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16892 \begin_layout Plain Layout
16900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16903 \begin_layout Plain Layout
16904 \begin_inset Formula $\oplus$
16914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16917 \begin_layout Plain Layout
16925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16928 \begin_layout Plain Layout
16929 \begin_inset Formula $\ominus$
16939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16942 \begin_layout Plain Layout
16950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16953 \begin_layout Plain Layout
16954 \begin_inset Formula $\otimes$
16964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16967 \begin_layout Plain Layout
16975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16978 \begin_layout Plain Layout
16979 \begin_inset Formula $\oslash$
16989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16992 \begin_layout Plain Layout
17000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17003 \begin_layout Plain Layout
17004 \begin_inset Formula $\odot$
17014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17017 \begin_layout Plain Layout
17025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17028 \begin_layout Plain Layout
17029 \begin_inset Formula $\amalg$
17039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17042 \begin_layout Plain Layout
17050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17053 \begin_layout Plain Layout
17054 \begin_inset Formula $\uplus$
17064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17067 \begin_layout Plain Layout
17075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17078 \begin_layout Plain Layout
17079 \begin_inset Formula $\setminus$
17089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17092 \begin_layout Plain Layout
17100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17103 \begin_layout Plain Layout
17104 \begin_inset Formula $\sqcap$
17114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17117 \begin_layout Plain Layout
17125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17128 \begin_layout Plain Layout
17129 \begin_inset Formula $\sqcup$
17139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17142 \begin_layout Plain Layout
17150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17153 \begin_layout Plain Layout
17154 \begin_inset Formula $\triangleleft$
17164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17167 \begin_layout Plain Layout
17175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17178 \begin_layout Plain Layout
17179 \begin_inset Formula $\triangleright$
17193 \begin_inset space \hfill{}
17199 \begin_layout Standard
17200 All binary operators can also be inserted via the math toolbar button
17201 \begin_inset Graphics
17202 filename ../images/math/pm.png
17210 \begin_layout Standard
17211 To typeset the Laplace operator also
17228 \begin_inset Formula $\nabla^{2}$
17231 ) can be used instead of
17240 \begin_layout Standard
17247 Insert\SpecialChar \menuseparator
17259 \begin_layout Subsection
17260 Self-defined Operators
17261 \begin_inset CommandInset label
17263 name "sub:Self-defined-Operators"
17271 \begin_layout Plain Layout
17272 Operators ! self-defined
17280 \begin_layout Standard
17281 With the help of the command
17285 DeclareMathOperator
17291 \begin_layout Plain Layout
17296 DeclareMathOperator
17301 custom operators can be defined in the LaTeX-preamble.
17302 Its command scheme is:
17305 \begin_layout Standard
17310 DeclareMathOperator{new command}{display}
17313 \begin_layout Standard
17314 Display can be characters or symbols that define how the operator looks
17316 To define a big operator a * is set behind the command.
17317 All self-defined big operators can have limits as described in
17318 \begin_inset CommandInset ref
17320 reference "sub:Operator-Limits"
17327 \begin_layout Standard
17328 For example the LaTeX-preamble line
17331 \begin_layout Standard
17336 DeclareMathOperator*{
17343 \begin_layout Standard
17344 defines the command
17350 , that inserts a big operator consisting of the lozenge symbol from
17351 \begin_inset CommandInset ref
17353 reference "sub:Miscellaneous-Symbols"
17358 \begin_inset Formula \[
17359 \Lozenge_{n=1}^{\infty}\]
17363 The command for this formula is:
17374 \begin_inset Formula $\to$
17380 \begin_layout Standard
17381 \begin_inset VSpace bigskip
17384 When self-defined operators are not used several times in the document,
17385 they can also be defined with the commands
17395 \begin_layout Plain Layout
17413 \begin_layout Plain Layout
17421 , which have the following scheme:
17424 \begin_layout Standard
17438 \begin_layout Standard
17445 defines big operators,
17454 \begin_layout Standard
17462 \begin_inset space \thinspace{}
17466 \begin_inset space ~
17469 be used to use one limit for several operators:
17472 \begin_layout Standard
17473 \begin_inset Formula \[
17474 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17481 \begin_layout Standard
17482 The command for the formula above is:
17483 \begin_inset Newline newline
17502 \begin_layout Plain Layout
17514 \begin_inset Formula $\to$
17523 \begin_layout Plain Layout
17537 \begin_layout Section
17542 \begin_layout Plain Layout
17551 \begin_layout Subsection
17553 \begin_inset CommandInset label
17555 name "sub:Font-Styles"
17563 \begin_layout Plain Layout
17572 \begin_layout Standard
17573 Latin letters in formulas can be set in one of the following font styles:
17574 \begin_inset VSpace -2mm
17580 \begin_layout Standard
17582 \begin_inset Tabular
17583 <lyxtabular version="3" rows="6" columns="3">
17585 <column alignment="center" valignment="top" width="0">
17586 <column alignment="center" valignment="top" width="0">
17587 <column alignment="center" valignment="top" width="0">
17589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17592 \begin_layout Plain Layout
17598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17601 \begin_layout Plain Layout
17607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17610 \begin_layout Plain Layout
17618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17621 \begin_layout Plain Layout
17630 \begin_layout Plain Layout
17646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17649 \begin_layout Plain Layout
17650 \begin_inset Formula $\mathbb{ABC}$
17658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17661 \begin_layout Plain Layout
17669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17672 \begin_layout Plain Layout
17681 \begin_layout Plain Layout
17697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17700 \begin_layout Plain Layout
17701 \begin_inset Formula $\mathbf{AbC}$
17709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17712 \begin_layout Plain Layout
17720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17723 \begin_layout Plain Layout
17732 \begin_layout Plain Layout
17748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17751 \begin_layout Plain Layout
17752 \begin_inset Formula $\boldsymbol{AbC}$
17760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17763 \begin_layout Plain Layout
17771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17774 \begin_layout Plain Layout
17783 \begin_layout Plain Layout
17799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17802 \begin_layout Plain Layout
17803 \begin_inset Formula $\mathcal{ABC}$
17811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17814 \begin_layout Plain Layout
17822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17825 \begin_layout Plain Layout
17834 \begin_layout Plain Layout
17850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17853 \begin_layout Plain Layout
17854 \begin_inset Formula $\mathfrak{AbC}$
17862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17865 \begin_layout Plain Layout
17879 \begin_layout Standard
17881 \begin_inset Tabular
17882 <lyxtabular version="3" rows="5" columns="3">
17884 <column alignment="center" valignment="top" width="0">
17885 <column alignment="center" valignment="top" width="0">
17886 <column alignment="center" valignment="top" width="0">
17888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17891 \begin_layout Plain Layout
17897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17900 \begin_layout Plain Layout
17906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17909 \begin_layout Plain Layout
17917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17920 \begin_layout Plain Layout
17929 \begin_layout Plain Layout
17945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17948 \begin_layout Plain Layout
17949 \begin_inset Formula $\mathit{AbC}$
17957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17960 \begin_layout Plain Layout
17968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17971 \begin_layout Plain Layout
17980 \begin_layout Plain Layout
17996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17999 \begin_layout Plain Layout
18000 \begin_inset Formula $\mathrm{AbC}$
18008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18011 \begin_layout Plain Layout
18019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18022 \begin_layout Plain Layout
18031 \begin_layout Plain Layout
18047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18050 \begin_layout Plain Layout
18051 \begin_inset Formula $\mathsf{AbC}$
18059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18062 \begin_layout Plain Layout
18070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18073 \begin_layout Plain Layout
18082 \begin_layout Plain Layout
18098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18101 \begin_layout Plain Layout
18102 \begin_inset Formula $\mathtt{AbC}$
18110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18113 \begin_layout Plain Layout
18127 \begin_layout Standard
18128 \begin_inset Note Greyedout
18131 \begin_layout Plain Layout
18148 can only be used for big letters.
18156 \begin_layout Standard
18157 Predefined is the style
18166 \begin_layout Standard
18167 The style commands work also for letters in mathematical constructs:
18168 \begin_inset Formula \[
18169 \mathfrak{A=\frac{b}{C}}\]
18176 \begin_layout Standard
18177 Characters in mathematical text don't appear in a math font style but in
18178 the text font style
18185 That their style can't be set correctly via the text style dialog is a
18190 \begin_layout Plain Layout
18191 \begin_inset CommandInset href
18193 name "LyX-bug #4091"
18194 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18206 \begin_layout Standard
18207 Instead of the style commands the dialog
18209 Edit\SpecialChar \menuseparator
18210 Math\SpecialChar \menuseparator
18213 or the toolbar button
18214 \begin_inset Graphics
18215 filename ../images/math/font.png
18223 \begin_layout Subsection
18225 \begin_inset CommandInset label
18227 name "sub:Bold-Formulas"
18235 \begin_layout Plain Layout
18244 \begin_layout Standard
18245 To make a complete formula bold, the command
18251 from the previous subsection cannot be used, because it doesn't work for
18252 small Greek letters.
18253 Furthermore it prints Latin letters always upright, like in the following
18257 \begin_layout Standard
18258 \begin_inset Formula \[
18259 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18266 \begin_layout Standard
18267 To display the formula correctly, the command
18274 \begin_inset Formula \[
18275 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18279 It is also possible to set the formula in a
18281 boldmath environment
18284 This environment is created by inserting the command
18292 \begin_layout Plain Layout
18303 To end the environment, the command
18311 \begin_layout Plain Layout
18321 is inserted in TeX-mode.
18325 \begin_layout Plain Layout
18335 \begin_inset Formula \[
18336 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18344 \begin_layout Plain Layout
18356 \begin_layout Subsection
18358 \begin_inset CommandInset label
18360 name "sub:Font-Sizes"
18368 \begin_layout Plain Layout
18377 \begin_layout Standard
18378 For characters in formulas there are, analog to characters in text, the
18379 following size commands:
18382 \begin_layout Standard
18426 \begin_inset Newline newline
18448 \begin_layout Standard
18449 The size produced by the commands depends on the document font size, that
18450 corresponds with the command
18457 The other commands produce smaller or larger sizes than
18464 The font size can however not exceed a certain value.
18465 Is for example the document font size 12
18466 \begin_inset space \thinspace{}
18475 switches to the same size as
18485 \begin_layout Standard
18486 A size command is inserted in TeX-mode before the formula and sets the size
18487 for all following formula and text characters.
18488 To switch back to the initial size, the command
18494 is inserted behind the formula in TeX-mode.
18497 \begin_layout Standard
18498 Within a formula the size can only be changed for symbols or letters in
18500 To do this, the size command is inserted in mathematical text.
18501 All following characters until the end of the mathematical text or until
18502 another size command will have the selected size.
18504 \begin_inset VSpace -2mm
18510 \begin_layout Standard
18514 \begin_layout Plain Layout
18524 \begin_inset Formula \[
18525 A=\frac{B}{c}\cdot\maltese\]
18530 \begin_inset Formula \[
18531 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18539 \begin_layout Plain Layout
18551 \begin_layout Standard
18552 \begin_inset VSpace medskip
18555 Before both formulas the command
18562 The command for the second formula is:
18563 \begin_inset Newline newline
18574 \begin_layout Plain Layout
18589 \begin_layout Plain Layout
18604 \begin_layout Plain Layout
18619 \begin_layout Plain Layout
18629 \begin_inset Formula $\to$
18633 \begin_inset Formula $\to$
18637 \begin_inset Newline newline
18641 \begin_inset space \hspace*{}
18655 \begin_layout Plain Layout
18670 \begin_layout Plain Layout
18685 \begin_layout Plain Layout
18697 \begin_layout Standard
18698 If a symbol cannot be displayed in different sizes, it will always be displayed
18699 in the default size.
18702 \begin_layout Section
18707 \begin_layout Plain Layout
18716 \begin_layout Standard
18717 All Greek letters can also be inserted via the toolbar button
18718 \begin_inset Graphics
18719 filename ../images/math/alpha.png
18727 \begin_layout Subsection
18729 \begin_inset CommandInset label
18731 name "sub:Small-Letters"
18739 \begin_layout Plain Layout
18740 Greek letters ! small
18748 \begin_layout Standard
18749 \begin_inset space \hfill{}
18753 \begin_inset Tabular
18754 <lyxtabular version="3" rows="11" columns="2">
18756 <column alignment="center" valignment="top" width="0pt">
18757 <column alignment="center" valignment="top" width="0pt">
18759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18762 \begin_layout Plain Layout
18768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18771 \begin_layout Plain Layout
18779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18782 \begin_layout Plain Layout
18790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18793 \begin_layout Plain Layout
18794 \begin_inset Formula $\alpha$
18804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18807 \begin_layout Plain Layout
18815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18818 \begin_layout Plain Layout
18819 \begin_inset Formula $\beta$
18829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18832 \begin_layout Plain Layout
18840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18843 \begin_layout Plain Layout
18844 \begin_inset Formula $\gamma$
18854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18857 \begin_layout Plain Layout
18865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18868 \begin_layout Plain Layout
18869 \begin_inset Formula $\delta$
18879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18882 \begin_layout Plain Layout
18890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18893 \begin_layout Plain Layout
18894 \begin_inset Formula $\epsilon$
18904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18907 \begin_layout Plain Layout
18915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18918 \begin_layout Plain Layout
18919 \begin_inset Formula $\varepsilon$
18929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18932 \begin_layout Plain Layout
18940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18943 \begin_layout Plain Layout
18944 \begin_inset Formula $\zeta$
18954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18957 \begin_layout Plain Layout
18965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18968 \begin_layout Plain Layout
18969 \begin_inset Formula $\eta$
18979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18982 \begin_layout Plain Layout
18990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18993 \begin_layout Plain Layout
18994 \begin_inset Formula $\theta$
19004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19007 \begin_layout Plain Layout
19015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19018 \begin_layout Plain Layout
19019 \begin_inset Formula $\vartheta$
19033 \begin_inset space \hfill{}
19037 \begin_inset Tabular
19038 <lyxtabular version="3" rows="12" columns="2">
19040 <column alignment="center" valignment="top" width="0pt">
19041 <column alignment="center" valignment="top" width="0pt">
19043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19046 \begin_layout Plain Layout
19052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19055 \begin_layout Plain Layout
19063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19066 \begin_layout Plain Layout
19074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19077 \begin_layout Plain Layout
19078 \begin_inset Formula $\iota$
19088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19091 \begin_layout Plain Layout
19099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19102 \begin_layout Plain Layout
19103 \begin_inset Formula $\kappa$
19113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19116 \begin_layout Plain Layout
19124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19127 \begin_layout Plain Layout
19128 \begin_inset Formula $\varkappa$
19138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19141 \begin_layout Plain Layout
19149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19152 \begin_layout Plain Layout
19153 \begin_inset Formula $\lambda$
19163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19166 \begin_layout Plain Layout
19174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19177 \begin_layout Plain Layout
19178 \begin_inset Formula $\mu$
19188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19191 \begin_layout Plain Layout
19199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19202 \begin_layout Plain Layout
19203 \begin_inset Formula $\nu$
19213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19216 \begin_layout Plain Layout
19224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19227 \begin_layout Plain Layout
19228 \begin_inset Formula $\xi$
19238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19241 \begin_layout Plain Layout
19247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19250 \begin_layout Plain Layout
19251 \begin_inset Formula $o$
19261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19264 \begin_layout Plain Layout
19272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19275 \begin_layout Plain Layout
19276 \begin_inset Formula $\pi$
19286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19289 \begin_layout Plain Layout
19297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19300 \begin_layout Plain Layout
19301 \begin_inset Formula $\varpi$
19311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19314 \begin_layout Plain Layout
19322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19325 \begin_layout Plain Layout
19326 \begin_inset Formula $\rho$
19340 \begin_inset space \hfill{}
19344 \begin_inset Tabular
19345 <lyxtabular version="3" rows="11" columns="2">
19347 <column alignment="center" valignment="top" width="0pt">
19348 <column alignment="center" valignment="top" width="0pt">
19350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19353 \begin_layout Plain Layout
19359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19362 \begin_layout Plain Layout
19370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19373 \begin_layout Plain Layout
19381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19384 \begin_layout Plain Layout
19385 \begin_inset Formula $\varrho$
19395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19398 \begin_layout Plain Layout
19406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19409 \begin_layout Plain Layout
19410 \begin_inset Formula $\sigma$
19420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19423 \begin_layout Plain Layout
19431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19434 \begin_layout Plain Layout
19435 \begin_inset Formula $\varsigma$
19445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19448 \begin_layout Plain Layout
19456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19459 \begin_layout Plain Layout
19460 \begin_inset Formula $\tau$
19470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19473 \begin_layout Plain Layout
19481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19484 \begin_layout Plain Layout
19485 \begin_inset Formula $\upsilon$
19495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19498 \begin_layout Plain Layout
19506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19509 \begin_layout Plain Layout
19510 \begin_inset Formula $\phi$
19520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19523 \begin_layout Plain Layout
19531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19534 \begin_layout Plain Layout
19535 \begin_inset Formula $\varphi$
19545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19548 \begin_layout Plain Layout
19556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19559 \begin_layout Plain Layout
19560 \begin_inset Formula $\chi$
19570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19573 \begin_layout Plain Layout
19581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19584 \begin_layout Plain Layout
19585 \begin_inset Formula $\psi$
19595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19598 \begin_layout Plain Layout
19606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19609 \begin_layout Plain Layout
19610 \begin_inset Formula $\omega$
19624 \begin_inset space \hfill{}
19630 \begin_layout Standard
19631 \begin_inset VSpace medskip
19637 \begin_layout Standard
19638 How to create upright Greek letters is explained in
19639 \begin_inset CommandInset ref
19641 reference "sub:Upright-small-Greek"
19648 \begin_layout Subsection
19653 \begin_layout Plain Layout
19654 Greek letters ! big
19662 \begin_layout Standard
19663 \begin_inset space \hfill{}
19667 \begin_inset Tabular
19668 <lyxtabular version="3" rows="7" columns="2">
19670 <column alignment="center" valignment="top" width="0pt">
19671 <column alignment="center" valignment="top" width="0pt">
19673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19676 \begin_layout Plain Layout
19682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19685 \begin_layout Plain Layout
19693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19696 \begin_layout Plain Layout
19704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19707 \begin_layout Plain Layout
19708 \begin_inset Formula $\Gamma$
19718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19721 \begin_layout Plain Layout
19729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19732 \begin_layout Plain Layout
19733 \begin_inset Formula $\Delta$
19743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19746 \begin_layout Plain Layout
19754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19757 \begin_layout Plain Layout
19758 \begin_inset Formula $\Theta$
19768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19771 \begin_layout Plain Layout
19779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19782 \begin_layout Plain Layout
19783 \begin_inset Formula $\Lambda$
19793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19796 \begin_layout Plain Layout
19804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19807 \begin_layout Plain Layout
19808 \begin_inset Formula $\Xi$
19818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19821 \begin_layout Plain Layout
19829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19832 \begin_layout Plain Layout
19833 \begin_inset Formula $\Pi$
19847 \begin_inset space \hfill{}
19851 \begin_inset Tabular
19852 <lyxtabular version="3" rows="6" columns="2">
19854 <column alignment="center" valignment="top" width="0pt">
19855 <column alignment="center" valignment="top" width="0pt">
19857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19860 \begin_layout Plain Layout
19866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19869 \begin_layout Plain Layout
19877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19880 \begin_layout Plain Layout
19888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19891 \begin_layout Plain Layout
19892 \begin_inset Formula $\Sigma$
19902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19905 \begin_layout Plain Layout
19913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19916 \begin_layout Plain Layout
19917 \begin_inset Formula $\Upsilon$
19927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19930 \begin_layout Plain Layout
19938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19941 \begin_layout Plain Layout
19942 \begin_inset Formula $\Phi$
19952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19955 \begin_layout Plain Layout
19963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19966 \begin_layout Plain Layout
19967 \begin_inset Formula $\Psi$
19977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19980 \begin_layout Plain Layout
19988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19991 \begin_layout Plain Layout
19992 \begin_inset Formula $\Omega$
20006 \begin_inset space \hfill{}
20012 \begin_layout Standard
20013 \begin_inset VSpace medskip
20016 That the big Greek letters appear upright is caused by a design bug when
20018 To get correct italic big letters, begin every command with
20023 For example the command
20030 \begin_inset Formula $\varGamma$
20036 \begin_layout Subsection
20041 \begin_layout Plain Layout
20042 Greek letters ! bold
20050 \begin_layout Standard
20051 Greek letters cannot be set with different font styles like Latin letters.
20052 They can only be made bold with the command
20062 \begin_layout Plain Layout
20073 \begin_layout Standard
20075 \begin_inset Tabular
20076 <lyxtabular version="3" rows="3" columns="2">
20078 <column alignment="center" valignment="top" width="0">
20079 <column alignment="center" valignment="top" width="0">
20081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20084 \begin_layout Plain Layout
20090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20093 \begin_layout Plain Layout
20101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20104 \begin_layout Plain Layout
20116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20119 \begin_layout Plain Layout
20120 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20133 \begin_layout Plain Layout
20145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20148 \begin_layout Plain Layout
20149 \begin_inset Formula $\theta\boldsymbol{\theta}$
20165 \begin_layout Section
20170 \begin_layout Plain Layout
20183 \begin_layout Plain Layout
20184 A list with all symbols of most of the LaTeX-packages can be found in
20185 \begin_inset CommandInset citation
20200 \begin_layout Plain Layout
20208 \begin_inset Note Note
20211 \begin_layout Plain Layout
20214 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20217 \begin_layout Plain Layout
20220 texorpdfstring is in section
20221 \begin_inset CommandInset ref
20223 reference "sub:Formulas-in-Section"
20236 \begin_layout Plain Layout
20245 \begin_layout Standard
20246 Many of the symbols listed in this section can also be inserted via the
20248 \begin_inset Graphics
20249 filename ../images/math/nabla.png
20255 \begin_inset Graphics
20256 filename ../images/math/digamma.png
20264 \begin_layout Subsection
20265 Mathematical Symbols
20266 \begin_inset CommandInset label
20268 name "sub:Mathematical-Symbols"
20276 \begin_layout Plain Layout
20277 Symbols ! mathematical
20285 \begin_layout Standard
20286 \begin_inset space \hfill{}
20290 \begin_inset Tabular
20291 <lyxtabular version="3" rows="10" columns="2">
20293 <column alignment="center" valignment="top" width="0pt">
20294 <column alignment="center" valignment="top" width="0pt">
20296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20299 \begin_layout Plain Layout
20305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20308 \begin_layout Plain Layout
20316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20319 \begin_layout Plain Layout
20327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20330 \begin_layout Plain Layout
20331 \begin_inset Formula $\neg$
20341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20344 \begin_layout Plain Layout
20352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20355 \begin_layout Plain Layout
20356 \begin_inset Formula $\Im$
20366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20369 \begin_layout Plain Layout
20377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20380 \begin_layout Plain Layout
20381 \begin_inset Formula $\Re$
20391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20394 \begin_layout Plain Layout
20402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20405 \begin_layout Plain Layout
20406 \begin_inset Formula $\aleph$
20416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20419 \begin_layout Plain Layout
20427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20430 \begin_layout Plain Layout
20431 \begin_inset Formula $\partial$
20441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20444 \begin_layout Plain Layout
20452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20455 \begin_layout Plain Layout
20456 \begin_inset Formula $\infty$
20466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20469 \begin_layout Plain Layout
20477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20480 \begin_layout Plain Layout
20481 \begin_inset Formula $\wp$
20491 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20494 \begin_layout Plain Layout
20502 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20505 \begin_layout Plain Layout
20506 \begin_inset Formula $\imath$
20516 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20519 \begin_layout Plain Layout
20527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20530 \begin_layout Plain Layout
20531 \begin_inset Formula $\jmath$
20545 \begin_inset space \hfill{}
20549 \begin_inset Tabular
20550 <lyxtabular version="3" rows="10" columns="2">
20552 <column alignment="center" valignment="top" width="0pt">
20553 <column alignment="center" valignment="top" width="0pt">
20555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20558 \begin_layout Plain Layout
20564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20567 \begin_layout Plain Layout
20569 \begin_inset Note Note
20572 \begin_layout Plain Layout
20579 is only used as spacer.
20591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20594 \begin_layout Plain Layout
20602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20605 \begin_layout Plain Layout
20606 \begin_inset Formula $\forall$
20616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20619 \begin_layout Plain Layout
20627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20630 \begin_layout Plain Layout
20631 \begin_inset Formula $\exists$
20641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20644 \begin_layout Plain Layout
20652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20655 \begin_layout Plain Layout
20656 \begin_inset Formula $\nexists$
20666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20669 \begin_layout Plain Layout
20677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20680 \begin_layout Plain Layout
20681 \begin_inset Formula $\emptyset$
20691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20694 \begin_layout Plain Layout
20702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20705 \begin_layout Plain Layout
20706 \begin_inset Formula $\varnothing$
20716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20719 \begin_layout Plain Layout
20727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20730 \begin_layout Plain Layout
20731 \begin_inset Formula $\dag$
20741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20744 \begin_layout Plain Layout
20752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20755 \begin_layout Plain Layout
20756 \begin_inset Formula $\ddag$
20766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20769 \begin_layout Plain Layout
20777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20780 \begin_layout Plain Layout
20784 \begin_layout Plain Layout
20794 \begin_inset Formula $\complement$
20801 \begin_layout Plain Layout
20815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20818 \begin_layout Plain Layout
20826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20829 \begin_layout Plain Layout
20830 \begin_inset Formula $\Bbbk$
20844 \begin_inset space \hfill{}
20848 \begin_inset Tabular
20849 <lyxtabular version="3" rows="10" columns="2">
20851 <column alignment="center" valignment="top" width="0pt">
20852 <column alignment="center" valignment="top" width="0pt">
20854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20857 \begin_layout Plain Layout
20863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20866 \begin_layout Plain Layout
20874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20877 \begin_layout Plain Layout
20885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20888 \begin_layout Plain Layout
20889 \begin_inset Formula $\prime$
20899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20902 \begin_layout Plain Layout
20910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20913 \begin_layout Plain Layout
20914 \begin_inset Formula $\backprime$
20924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20927 \begin_layout Plain Layout
20935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20938 \begin_layout Plain Layout
20939 \begin_inset Formula $\mho$
20949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20952 \begin_layout Plain Layout
20960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20963 \begin_layout Plain Layout
20964 \begin_inset Formula $\triangle$
20974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20977 \begin_layout Plain Layout
20985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20988 \begin_layout Plain Layout
20989 \begin_inset Formula $\angle$
20999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21002 \begin_layout Plain Layout
21010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21013 \begin_layout Plain Layout
21014 \begin_inset Formula $\measuredangle$
21024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21027 \begin_layout Plain Layout
21035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21038 \begin_layout Plain Layout
21039 \begin_inset Formula $\sphericalangle$
21049 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21052 \begin_layout Plain Layout
21060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21063 \begin_layout Plain Layout
21064 \begin_inset Formula $\top$
21074 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21077 \begin_layout Plain Layout
21085 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21088 \begin_layout Plain Layout
21089 \begin_inset Formula $\bot$
21103 \begin_inset space \hfill{}
21109 \begin_layout Standard
21110 \begin_inset Newpage newpage
21116 \begin_layout Subsection
21117 Miscellaneous Symbols
21118 \begin_inset CommandInset label
21120 name "sub:Miscellaneous-Symbols"
21128 \begin_layout Plain Layout
21129 Symbols ! miscellaneous
21137 \begin_layout Standard
21140 \begin_inset Tabular
21141 <lyxtabular version="3" rows="10" columns="2">
21143 <column alignment="center" valignment="top" width="0pt">
21144 <column alignment="center" valignment="top" width="0pt">
21146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21149 \begin_layout Plain Layout
21155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21158 \begin_layout Plain Layout
21166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21169 \begin_layout Plain Layout
21177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21180 \begin_layout Plain Layout
21181 \begin_inset Formula $\flat$
21191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21194 \begin_layout Plain Layout
21202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21205 \begin_layout Plain Layout
21206 \begin_inset Formula $\natural$
21216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21219 \begin_layout Plain Layout
21227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21230 \begin_layout Plain Layout
21231 \begin_inset Formula $\sharp$
21241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21244 \begin_layout Plain Layout
21252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21255 \begin_layout Plain Layout
21256 \begin_inset Formula $\surd$
21266 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21269 \begin_layout Plain Layout
21277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21280 \begin_layout Plain Layout
21281 \begin_inset Formula $\checkmark$
21291 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21294 \begin_layout Plain Layout
21302 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21305 \begin_layout Plain Layout
21306 \begin_inset Formula $\yen$
21316 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21319 \begin_layout Plain Layout
21327 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21330 \begin_layout Plain Layout
21331 \begin_inset Formula $\pounds$
21341 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21344 \begin_layout Plain Layout
21350 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21353 \begin_layout Plain Layout
21354 \begin_inset Formula $\$$
21364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21367 \begin_layout Plain Layout
21373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21376 \begin_layout Plain Layout
21377 \begin_inset Formula $§$
21391 \begin_inset Tabular
21392 <lyxtabular version="3" rows="10" columns="2">
21394 <column alignment="center" valignment="top" width="0">
21395 <column alignment="center" valignment="top" width="0">
21397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21400 \begin_layout Plain Layout
21406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21409 \begin_layout Plain Layout
21417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21420 \begin_layout Plain Layout
21428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21431 \begin_layout Plain Layout
21432 \begin_inset Formula $\hbar$
21442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21445 \begin_layout Plain Layout
21453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21456 \begin_layout Plain Layout
21457 \begin_inset Formula $\hslash$
21467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21470 \begin_layout Plain Layout
21478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21481 \begin_layout Plain Layout
21482 \begin_inset Formula $\clubsuit$
21492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21495 \begin_layout Plain Layout
21503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21506 \begin_layout Plain Layout
21507 \begin_inset Formula $\spadesuit$
21517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21520 \begin_layout Plain Layout
21528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21531 \begin_layout Plain Layout
21532 \begin_inset Formula $\bigstar$
21542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21545 \begin_layout Plain Layout
21553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21556 \begin_layout Plain Layout
21557 \begin_inset Formula $\blacklozenge$
21567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21570 \begin_layout Plain Layout
21578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21581 \begin_layout Plain Layout
21582 \begin_inset Formula $\blacktriangle$
21592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21595 \begin_layout Plain Layout
21603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21606 \begin_layout Plain Layout
21607 \begin_inset Formula $\blacktriangledown$
21617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21620 \begin_layout Plain Layout
21628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21631 \begin_layout Plain Layout
21632 \begin_inset Formula $\bullet$
21646 \begin_inset Tabular
21647 <lyxtabular version="3" rows="10" columns="2">
21649 <column alignment="center" valignment="top" width="0pt">
21650 <column alignment="center" valignment="top" width="0pt">
21652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21655 \begin_layout Plain Layout
21661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21664 \begin_layout Plain Layout
21672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21675 \begin_layout Plain Layout
21683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21686 \begin_layout Plain Layout
21687 \begin_inset Formula $\diamondsuit$
21697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21700 \begin_layout Plain Layout
21708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21711 \begin_layout Plain Layout
21712 \begin_inset Formula $\Diamond$
21722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21725 \begin_layout Plain Layout
21733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21736 \begin_layout Plain Layout
21737 \begin_inset Formula $\heartsuit$
21747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21750 \begin_layout Plain Layout
21758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21761 \begin_layout Plain Layout
21762 \begin_inset Formula $\P$
21772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21775 \begin_layout Plain Layout
21783 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21786 \begin_layout Plain Layout
21787 \begin_inset Formula $\copyright$
21797 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21800 \begin_layout Plain Layout
21808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21811 \begin_layout Plain Layout
21812 \begin_inset Formula $\circledR$
21822 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21825 \begin_layout Plain Layout
21833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21836 \begin_layout Plain Layout
21837 \begin_inset Formula $\maltese$
21847 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21850 \begin_layout Plain Layout
21858 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21861 \begin_layout Plain Layout
21862 \begin_inset Formula $\diagup$
21872 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21875 \begin_layout Plain Layout
21883 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21886 \begin_layout Plain Layout
21887 \begin_inset Formula $\diagdown$
21903 \begin_layout Standard
21904 \begin_inset VSpace medskip
21907 More symbols are listed in
21908 \begin_inset CommandInset ref
21910 reference "sub:Miscellaneous-Special-Characters"
21917 \begin_layout Standard
21918 Some symbols can be displayed in different sizes, see
21919 \begin_inset CommandInset ref
21921 reference "sub:Font-Sizes"
21928 \begin_layout Subsection
21933 \begin_layout Plain Layout
21934 Symbols ! Euro-symbol
21943 \begin_layout Plain Layout
21947 \begin_layout Plain Layout
21964 \begin_layout Standard
21965 To use the Euro symbol in formulas, the LaTeX-package
21973 \begin_layout Plain Layout
21979 must be installed and loaded with the LaTeX-preamble line
21982 \begin_layout Standard
21987 usepackage[gennarrow]{eurosym}
21990 \begin_layout Standard
21991 The Euro symbol can now be inserted with the command
22001 \begin_layout Plain Layout
22012 \begin_layout Standard
22013 The Euro symbol can directly be inserted with the € key in mathematical
22014 text, without having
22029 can also be inserted in TeX-mode.
22030 The official currency symbol can then be inserted with the command
22040 \begin_layout Plain Layout
22048 , that is only available in TeX-mode.
22051 \begin_layout Standard
22055 \begin_layout Plain Layout
22065 \begin_inset Note Note
22068 \begin_layout Plain Layout
22069 The following table will only be displayed when the LaTeX-package
22081 \begin_layout Standard
22082 An overview about the different Euro symbols:
22085 \begin_layout Standard
22087 \begin_inset Tabular
22088 <lyxtabular version="3" rows="4" columns="3">
22090 <column alignment="center" valignment="top" width="0pt">
22091 <column alignment="center" valignment="top" width="0pt">
22092 <column alignment="center" valignment="top" width="0pt">
22094 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22097 \begin_layout Plain Layout
22103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22106 \begin_layout Plain Layout
22112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22115 \begin_layout Plain Layout
22123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22126 \begin_layout Plain Layout
22132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22135 \begin_layout Plain Layout
22143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22146 \begin_layout Plain Layout
22147 \begin_inset Formula $\euro$
22157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22160 \begin_layout Plain Layout
22166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22169 \begin_layout Plain Layout
22175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22178 \begin_layout Plain Layout
22179 \begin_inset Formula $\mbox{€}$
22189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22192 \begin_layout Plain Layout
22198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22201 \begin_layout Plain Layout
22209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22212 \begin_layout Plain Layout
22216 \begin_layout Plain Layout
22238 \begin_layout Standard
22242 \begin_layout Plain Layout
22252 \begin_inset Note Note
22255 \begin_layout Plain Layout
22256 The following will be displayed when the LaTeX-package
22268 \begin_layout Standard
22269 You need to install the LaTeX-package
22273 to see the rest of this subsection in the output.
22276 \begin_layout Standard
22280 \begin_layout Plain Layout
22292 \begin_layout Section
22294 \begin_inset CommandInset label
22296 name "sec:Relations"
22304 \begin_layout Plain Layout
22314 \begin_layout Plain Layout
22319 \begin_layout Plain Layout
22330 \begin_layout Plain Layout
22345 \begin_layout Standard
22346 All relations can also be inserted via the toolbar button
22347 \begin_inset Graphics
22348 filename ../images/math/leq.png
22356 \begin_layout Standard
22357 \begin_inset space \hfill{}
22361 \begin_inset Tabular
22362 <lyxtabular version="3" rows="17" columns="2">
22364 <column alignment="center" valignment="top" width="0pt">
22365 <column alignment="center" valignment="top" width="0pt">
22367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22370 \begin_layout Plain Layout
22376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22379 \begin_layout Plain Layout
22387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22390 \begin_layout Plain Layout
22396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22399 \begin_layout Plain Layout
22400 \begin_inset Formula $<$
22410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22413 \begin_layout Plain Layout
22421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22424 \begin_layout Plain Layout
22425 \begin_inset Formula $\le$
22435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22438 \begin_layout Plain Layout
22446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22449 \begin_layout Plain Layout
22450 \begin_inset Formula $\ll$
22460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22463 \begin_layout Plain Layout
22471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22474 \begin_layout Plain Layout
22475 \begin_inset Formula $\prec$
22485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22488 \begin_layout Plain Layout
22496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22499 \begin_layout Plain Layout
22500 \begin_inset Formula $\preceq$
22510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22513 \begin_layout Plain Layout
22521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22524 \begin_layout Plain Layout
22525 \begin_inset Formula $\subset$
22535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22538 \begin_layout Plain Layout
22546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22549 \begin_layout Plain Layout
22550 \begin_inset Formula $\subseteq$
22560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22563 \begin_layout Plain Layout
22571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22574 \begin_layout Plain Layout
22575 \begin_inset Formula $\sqsubseteq$
22585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22588 \begin_layout Plain Layout
22596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22599 \begin_layout Plain Layout
22600 \begin_inset Formula $\in$
22610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22613 \begin_layout Plain Layout
22621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22624 \begin_layout Plain Layout
22625 \begin_inset Formula $\vdash$
22635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22638 \begin_layout Plain Layout
22646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22649 \begin_layout Plain Layout
22650 \begin_inset Formula $\smile$
22660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22663 \begin_layout Plain Layout
22671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22674 \begin_layout Plain Layout
22675 \begin_inset Formula $\lhd$
22685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22688 \begin_layout Plain Layout
22696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22699 \begin_layout Plain Layout
22700 \begin_inset Formula $\unlhd$
22710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22713 \begin_layout Plain Layout
22721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22724 \begin_layout Plain Layout
22725 \begin_inset Formula $\gtrless$
22735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22738 \begin_layout Plain Layout
22746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22749 \begin_layout Plain Layout
22750 \begin_inset Formula $\mid$
22760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22763 \begin_layout Plain Layout
22771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22774 \begin_layout Plain Layout
22775 \begin_inset Formula $\nmid$
22789 \begin_inset space \hfill{}
22793 \begin_inset Tabular
22794 <lyxtabular version="3" rows="17" columns="2">
22796 <column alignment="center" valignment="top" width="0pt">
22797 <column alignment="center" valignment="top" width="0pt">
22799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22802 \begin_layout Plain Layout
22808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22811 \begin_layout Plain Layout
22819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22822 \begin_layout Plain Layout
22828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22831 \begin_layout Plain Layout
22832 \begin_inset Formula $=$
22842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22845 \begin_layout Plain Layout
22853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22856 \begin_layout Plain Layout
22857 \begin_inset Formula $\not=$
22867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22870 \begin_layout Plain Layout
22878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22881 \begin_layout Plain Layout
22882 \begin_inset Formula $\equiv$
22892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22895 \begin_layout Plain Layout
22903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22906 \begin_layout Plain Layout
22907 \begin_inset Formula $\sim$
22917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22920 \begin_layout Plain Layout
22928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22931 \begin_layout Plain Layout
22932 \begin_inset Formula $\simeq$
22942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22945 \begin_layout Plain Layout
22953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22956 \begin_layout Plain Layout
22957 \begin_inset Formula $\approx$
22967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22970 \begin_layout Plain Layout
22978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22981 \begin_layout Plain Layout
22982 \begin_inset Formula $\cong$
22992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22995 \begin_layout Plain Layout
23003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23006 \begin_layout Plain Layout
23007 \begin_inset Formula $\bowtie$
23017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23020 \begin_layout Plain Layout
23028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23031 \begin_layout Plain Layout
23032 \begin_inset Formula $\notin$
23042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23045 \begin_layout Plain Layout
23053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23056 \begin_layout Plain Layout
23057 \begin_inset Formula $\perp$
23067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23070 \begin_layout Plain Layout
23078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23081 \begin_layout Plain Layout
23082 \begin_inset Formula $\propto$
23092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23095 \begin_layout Plain Layout
23103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23106 \begin_layout Plain Layout
23107 \begin_inset Formula $\asymp$
23117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23120 \begin_layout Plain Layout
23128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23131 \begin_layout Plain Layout
23132 \begin_inset Formula $\doteq$
23142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23145 \begin_layout Plain Layout
23153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23156 \begin_layout Plain Layout
23157 \begin_inset Formula $\circeq$
23167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23170 \begin_layout Plain Layout
23178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23181 \begin_layout Plain Layout
23182 \begin_inset Formula $\models$
23192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23195 \begin_layout Plain Layout
23203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23206 \begin_layout Plain Layout
23207 \begin_inset Formula $\widehat{=}$
23221 \begin_inset space \hfill{}
23225 \begin_inset Tabular
23226 <lyxtabular version="3" rows="17" columns="2">
23228 <column alignment="center" valignment="top" width="0pt">
23229 <column alignment="center" valignment="top" width="0pt">
23231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23234 \begin_layout Plain Layout
23240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23243 \begin_layout Plain Layout
23251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23254 \begin_layout Plain Layout
23260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23263 \begin_layout Plain Layout
23264 \begin_inset Formula $>$
23274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23277 \begin_layout Plain Layout
23285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23288 \begin_layout Plain Layout
23289 \begin_inset Formula $\ge$
23299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23302 \begin_layout Plain Layout
23310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23313 \begin_layout Plain Layout
23314 \begin_inset Formula $\gg$
23324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23327 \begin_layout Plain Layout
23335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23338 \begin_layout Plain Layout
23339 \begin_inset Formula $\succ$
23349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23352 \begin_layout Plain Layout
23360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23363 \begin_layout Plain Layout
23364 \begin_inset Formula $\succeq$
23374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23377 \begin_layout Plain Layout
23385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23388 \begin_layout Plain Layout
23389 \begin_inset Formula $\supset$
23399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23402 \begin_layout Plain Layout
23410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23413 \begin_layout Plain Layout
23414 \begin_inset Formula $\supseteq$
23424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23427 \begin_layout Plain Layout
23435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23438 \begin_layout Plain Layout
23439 \begin_inset Formula $\sqsupseteq$
23449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23452 \begin_layout Plain Layout
23460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23463 \begin_layout Plain Layout
23464 \begin_inset Formula $\ni$
23474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23477 \begin_layout Plain Layout
23485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23488 \begin_layout Plain Layout
23489 \begin_inset Formula $\dashv$
23499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23502 \begin_layout Plain Layout
23510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23513 \begin_layout Plain Layout
23514 \begin_inset Formula $\frown$
23524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23527 \begin_layout Plain Layout
23535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23538 \begin_layout Plain Layout
23539 \begin_inset Formula $\rhd$
23549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23552 \begin_layout Plain Layout
23560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23563 \begin_layout Plain Layout
23564 \begin_inset Formula $\unrhd$
23574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23577 \begin_layout Plain Layout
23585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23588 \begin_layout Plain Layout
23589 \begin_inset Formula $\lessgtr$
23599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23602 \begin_layout Plain Layout
23610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23613 \begin_layout Plain Layout
23614 \begin_inset Formula $\parallel$
23624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23627 \begin_layout Plain Layout
23635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23638 \begin_layout Plain Layout
23639 \begin_inset Formula $\nparallel$
23653 \begin_inset space \hfill{}
23659 \begin_layout Standard
23660 \begin_inset VSpace medskip
23675 are bigger than the equal looking operators
23690 \begin_layout Standard
23691 Relations are, in contrary to symbols, always surrounded by space.
23694 \begin_layout Standard
23695 Relations with labels can be created with the command
23705 \begin_layout Plain Layout
23716 \begin_layout Standard
23718 \begin_inset Tabular
23719 <lyxtabular version="3" rows="2" columns="2">
23721 <column alignment="center" valignment="top" width="0">
23722 <column alignment="center" valignment="top" width="0">
23724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23727 \begin_layout Plain Layout
23733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23736 \begin_layout Plain Layout
23738 \begin_inset Note Note
23741 \begin_layout Plain Layout
23748 is only used as spacer.
23760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23763 \begin_layout Plain Layout
23770 \begin_layout Plain Layout
23787 \begin_layout Plain Layout
23797 \begin_inset Formula $\downarrow$
23806 \begin_layout Plain Layout
23819 \begin_layout Plain Layout
23833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23836 \begin_layout Plain Layout
23837 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23853 \begin_layout Section
23857 \begin_layout Subsection
23858 Predefined Functions
23859 \begin_inset CommandInset label
23861 name "sub:Predefined-Functions"
23869 \begin_layout Plain Layout
23870 Functions ! predefined
23878 \begin_layout Standard
23879 In general, variables are set
23883 in mathematical expressions, but not function names, because
23884 \begin_inset Formula $sin$
23887 could be misunderstood as
23888 \begin_inset Formula $s\cdot i\cdot n$
23892 Therefore there are predefined functions, that are additionally a bit separated
23894 They are inserted as commands starting with a backslash before their name.
23897 \begin_layout Standard
23899 \begin_inset Tabular
23900 <lyxtabular version="3" rows="2" columns="4">
23902 <column alignment="center" valignment="top" width="0pt">
23903 <column alignment="center" valignment="top" width="0pt">
23904 <column alignment="center" valignment="top" width="0pt">
23905 <column alignment="center" valignment="top" width="0pt">
23907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23910 \begin_layout Plain Layout
23916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23919 \begin_layout Plain Layout
23925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23928 \begin_layout Plain Layout
23934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23937 \begin_layout Plain Layout
23945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23948 \begin_layout Plain Layout
23954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23957 \begin_layout Plain Layout
23958 \begin_inset Formula $Asin(x)+B$
23966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23969 \begin_layout Plain Layout
23977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23980 \begin_layout Plain Layout
23981 \begin_inset Formula $A\sin(x)+B$
23995 \begin_inset Newpage pagebreak
24001 \begin_layout Standard
24002 The following functions are predefined:
24005 \begin_layout Standard
24006 \begin_inset VSpace -2mm
24012 \begin_layout Standard
24014 \begin_inset Tabular
24015 <lyxtabular version="3" rows="9" columns="4">
24017 <column alignment="center" valignment="top" width="0pt">
24018 <column alignment="center" valignment="top" width="0pt">
24019 <column alignment="center" valignment="top" width="0pt">
24020 <column alignment="center" valignment="top" width="0pt">
24022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24025 \begin_layout Plain Layout
24031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24034 \begin_layout Plain Layout
24040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24043 \begin_layout Plain Layout
24049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24052 \begin_layout Plain Layout
24060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24063 \begin_layout Plain Layout
24071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24074 \begin_layout Plain Layout
24082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24085 \begin_layout Plain Layout
24093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24096 \begin_layout Plain Layout
24106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24109 \begin_layout Plain Layout
24117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24120 \begin_layout Plain Layout
24128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24131 \begin_layout Plain Layout
24139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24142 \begin_layout Plain Layout
24152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24155 \begin_layout Plain Layout
24163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24166 \begin_layout Plain Layout
24174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24177 \begin_layout Plain Layout
24185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24188 \begin_layout Plain Layout
24198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24201 \begin_layout Plain Layout
24209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24212 \begin_layout Plain Layout
24220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24223 \begin_layout Plain Layout
24231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24234 \begin_layout Plain Layout
24244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24247 \begin_layout Plain Layout
24255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24258 \begin_layout Plain Layout
24266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24269 \begin_layout Plain Layout
24277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24280 \begin_layout Plain Layout
24290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24293 \begin_layout Plain Layout
24301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24304 \begin_layout Plain Layout
24312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24315 \begin_layout Plain Layout
24323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24326 \begin_layout Plain Layout
24336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24339 \begin_layout Plain Layout
24347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24350 \begin_layout Plain Layout
24358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24361 \begin_layout Plain Layout
24369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24372 \begin_layout Plain Layout
24382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24385 \begin_layout Plain Layout
24393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24396 \begin_layout Plain Layout
24404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24407 \begin_layout Plain Layout
24415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24418 \begin_layout Plain Layout
24434 \begin_layout Standard
24435 They can also be inserted with the math toolbar button
24436 \begin_inset Graphics
24437 filename ../images/math/functions.png
24445 \begin_layout Subsection
24446 Self-defined Functions
24450 \begin_layout Plain Layout
24451 Functions ! self-defined
24459 \begin_layout Standard
24460 To use a function that is not predefined, like for example the sign function
24461 sgn(x), there are two possibilities:
24464 \begin_layout Itemize
24465 Define the function by inserting the following line to the LaTeX-preamble
24469 \begin_layout Plain Layout
24474 DeclareMathOperator
24477 \begin_inset CommandInset ref
24479 reference "sub:Self-defined-Operators"
24489 \begin_inset Newline newline
24493 \begin_inset VSpace -3mm
24497 \begin_inset Newline newline
24504 DeclareMathOperator{
24512 \begin_layout Plain Layout
24517 DeclareMathOperator
24523 \begin_inset Newline newline
24527 \begin_inset VSpace -2mm
24531 \begin_inset Newline newline
24534 Now the new defined function can be called with the command
24543 \begin_layout Itemize
24544 Write the the formula as usual, mark the formula name, in our example the
24549 , and change it to mathematical text.
24550 At last a space is inserted between prefactor and function.
24553 \begin_layout Standard
24554 The result is the same with both methods as with a predefined function
24558 \begin_layout Plain Layout
24559 In LyX self-defined functions are displayed red, predefined ones black.
24567 \begin_layout Standard
24569 \begin_inset Tabular
24570 <lyxtabular version="3" rows="3" columns="2">
24572 <column alignment="center" valignment="top" width="0pt">
24573 <column alignment="center" valignment="top" width="0pt">
24575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24578 \begin_layout Plain Layout
24584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24587 \begin_layout Plain Layout
24595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24598 \begin_layout Plain Layout
24606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24609 \begin_layout Plain Layout
24610 \begin_inset Formula $A\sgn(x)+B$
24620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24623 \begin_layout Plain Layout
24627 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24638 \begin_layout Plain Layout
24639 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24655 \begin_layout Standard
24656 The first method is more suitable when the self-defined function should
24657 be used several times.
24660 \begin_layout Subsection
24665 \begin_layout Plain Layout
24674 \begin_layout Standard
24675 For limits there are defined besides
24685 \begin_layout Plain Layout
24705 furthermore the following functions:
24708 \begin_layout Standard
24710 \begin_inset Tabular
24711 <lyxtabular version="3" rows="5" columns="2">
24713 <column alignment="center" valignment="top" width="0">
24714 <column alignment="center" valignment="top" width="0">
24716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24719 \begin_layout Plain Layout
24725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24728 \begin_layout Plain Layout
24730 \begin_inset Note Note
24733 \begin_layout Plain Layout
24740 is only used as spacer.
24752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24755 \begin_layout Plain Layout
24763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24766 \begin_layout Plain Layout
24767 \begin_inset Formula $\varliminf$
24777 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24780 \begin_layout Plain Layout
24788 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24791 \begin_layout Plain Layout
24792 \begin_inset Formula $\varlimsup$
24802 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24805 \begin_layout Plain Layout
24813 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24816 \begin_layout Plain Layout
24817 \begin_inset Formula $\varprojlim$
24827 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24830 \begin_layout Plain Layout
24838 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24841 \begin_layout Plain Layout
24842 \begin_inset Formula $\varinjlim$
24846 \begin_inset Formula $\raisebox{-2.5mm}{}$
24862 \begin_layout Standard
24863 \begin_inset VSpace medskip
24866 The limit is created by inserting a subscript.
24867 It is set right beside the function in an inline formula:
24870 \begin_layout Standard
24872 \begin_inset Tabular
24873 <lyxtabular version="3" rows="2" columns="2">
24875 <column alignment="center" valignment="top" width="0pt">
24876 <column alignment="center" valignment="top" width="0pt">
24878 <cell alignment="center" valignment="top" usebox="none">
24881 \begin_layout Plain Layout
24887 <cell alignment="center" valignment="top" usebox="none">
24890 \begin_layout Plain Layout
24891 \begin_inset space \hspace{}
24896 \begin_inset Note Note
24899 \begin_layout Plain Layout
24912 are used here as spacer.
24924 <cell alignment="center" valignment="top" usebox="none">
24927 \begin_layout Plain Layout
24936 \begin_layout Plain Layout
24949 \begin_layout Plain Layout
24963 <cell alignment="center" valignment="top" usebox="none">
24966 \begin_layout Plain Layout
24967 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
24983 \begin_layout Standard
24984 In a displayed formula the limit is set below the formula, as usual:
24985 \begin_inset Formula \[
24993 \begin_layout Subsection
24998 \begin_layout Plain Layout
24999 Functions ! modulo-
25007 \begin_layout Standard
25008 The modulo-function is special, because it exists in four variants.
25011 \begin_layout Standard
25012 The variants in a displayed formula:
25013 \begin_inset Formula \begin{align*}
25014 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25015 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25016 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25017 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25018 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25025 \begin_layout Standard
25026 In an inline formula less space is set before the function names for all
25030 \begin_layout Section
25035 \begin_layout Plain Layout
25044 \begin_layout Subsection
25045 Special Characters in Mathematical Text
25048 \begin_layout Standard
25049 The following commands can only be used in mathematical text or in TeX-mode:
25052 \begin_layout Standard
25053 \begin_inset space \hfill{}
25057 \begin_inset Tabular
25058 <lyxtabular version="3" rows="8" columns="2">
25060 <column alignment="block" valignment="top" width="0">
25061 <column alignment="block" valignment="top" width="0">
25063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25066 \begin_layout Plain Layout
25072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25075 \begin_layout Plain Layout
25083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25086 \begin_layout Plain Layout
25094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25097 \begin_layout Plain Layout
25098 \begin_inset Formula $\textrm{œ}$
25108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25111 \begin_layout Plain Layout
25119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25122 \begin_layout Plain Layout
25123 \begin_inset Formula $\textrm{Œ}$
25133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25136 \begin_layout Plain Layout
25144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25147 \begin_layout Plain Layout
25148 \begin_inset Formula $\textrm{æ}$
25158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25161 \begin_layout Plain Layout
25169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25172 \begin_layout Plain Layout
25173 \begin_inset Formula $\textrm{Æ}$
25183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25186 \begin_layout Plain Layout
25194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25197 \begin_layout Plain Layout
25198 \begin_inset Formula $\textrm{\aa}$
25208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25211 \begin_layout Plain Layout
25218 \begin_layout Plain Layout
25222 \begin_layout Plain Layout
25245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25248 \begin_layout Plain Layout
25249 \begin_inset Formula $\textrm{Å}$
25259 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25262 \begin_layout Plain Layout
25270 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25273 \begin_layout Plain Layout
25274 \begin_inset Formula $\textrm{ı}$
25288 \begin_inset space \hfill{}
25292 \begin_inset Tabular
25293 <lyxtabular version="3" rows="8" columns="2">
25295 <column alignment="block" valignment="top" width="0">
25296 <column alignment="center" valignment="top" width="0">
25298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25301 \begin_layout Plain Layout
25303 \begin_inset Note Note
25306 \begin_layout Plain Layout
25313 is used for separation, because otherwise the output will be ¡ and ¿ respective
25324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25327 \begin_layout Plain Layout
25335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25338 \begin_layout Plain Layout
25346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25349 \begin_layout Plain Layout
25350 \begin_inset Formula $\textrm{ø}$
25360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25363 \begin_layout Plain Layout
25371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25374 \begin_layout Plain Layout
25375 \begin_inset Formula $\textrm{Ø}$
25385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25388 \begin_layout Plain Layout
25396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25399 \begin_layout Plain Layout
25400 \begin_inset Formula $\textrm{ł}$
25410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25413 \begin_layout Plain Layout
25421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25424 \begin_layout Plain Layout
25425 \begin_inset Formula $\textrm{Ł}$
25435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25438 \begin_layout Plain Layout
25440 \begin_inset space \hspace{}
25448 \begin_layout Plain Layout
25462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25465 \begin_layout Plain Layout
25466 \begin_inset Formula $\textrm{!`}$
25476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25479 \begin_layout Plain Layout
25481 \begin_inset space \hspace{}
25489 \begin_layout Plain Layout
25503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25506 \begin_layout Plain Layout
25507 \begin_inset Formula $\textrm{?`}$
25517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25520 \begin_layout Plain Layout
25528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25531 \begin_layout Plain Layout
25532 \begin_inset Formula $\textrm{ȷ}$
25546 \begin_inset space \hfill{}
25552 \begin_layout Standard
25554 \begin_inset Formula $\textrm{\textrm{Å}}$
25558 \begin_inset Formula $\textrm{\textrm{Ø}}$
25561 can also be inserted via the math toolbar button
25562 \begin_inset Graphics
25563 filename ../images/math/digamma.png
25571 \begin_layout Standard
25572 An exception are the commands
25575 \begin_inset space \hspace{}
25584 \begin_inset space \hspace{}
25590 , because they can be inserted in LyX directly to text.
25593 \begin_layout Subsection
25595 \begin_inset CommandInset label
25597 name "sub:Accents-in-Text"
25605 \begin_layout Plain Layout
25614 \begin_layout Standard
25615 With the following commands all letters can be accented.
25616 The commands must be inserted in TeX-mode.
25619 \begin_layout Standard
25620 \begin_inset space \hfill{}
25624 \begin_inset Tabular
25625 <lyxtabular version="3" rows="8" columns="2">
25627 <column alignment="block" valignment="top" width="0">
25628 <column alignment="block" valignment="top" width="0">
25630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25633 \begin_layout Plain Layout
25639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25642 \begin_layout Plain Layout
25650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25653 \begin_layout Plain Layout
25657 \begin_inset Quotes grd
25665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25668 \begin_layout Plain Layout
25672 \begin_layout Plain Layout
25688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25691 \begin_layout Plain Layout
25699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25702 \begin_layout Plain Layout
25706 \begin_layout Plain Layout
25722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25725 \begin_layout Plain Layout
25732 \begin_layout Plain Layout
25746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25749 \begin_layout Plain Layout
25753 \begin_layout Plain Layout
25769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25772 \begin_layout Plain Layout
25780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25783 \begin_layout Plain Layout
25787 \begin_layout Plain Layout
25803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25806 \begin_layout Plain Layout
25813 \begin_layout Plain Layout
25827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25830 \begin_layout Plain Layout
25834 \begin_layout Plain Layout
25850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25853 \begin_layout Plain Layout
25860 \begin_layout Plain Layout
25874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25877 \begin_layout Plain Layout
25881 \begin_layout Plain Layout
25897 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25900 \begin_layout Plain Layout
25907 \begin_layout Plain Layout
25921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25924 \begin_layout Plain Layout
25928 \begin_layout Plain Layout
25948 \begin_inset space \hfill{}
25952 \begin_inset Tabular
25953 <lyxtabular version="3" rows="8" columns="2">
25955 <column alignment="block" valignment="top" width="0">
25956 <column alignment="center" valignment="top" width="0">
25958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25961 \begin_layout Plain Layout
25967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25970 \begin_layout Plain Layout
25978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25981 \begin_layout Plain Layout
25988 \begin_layout Plain Layout
26002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26005 \begin_layout Plain Layout
26009 \begin_layout Plain Layout
26025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26028 \begin_layout Plain Layout
26036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26039 \begin_layout Plain Layout
26043 \begin_layout Plain Layout
26059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26062 \begin_layout Plain Layout
26069 \begin_layout Plain Layout
26080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26083 \begin_layout Plain Layout
26087 \begin_layout Plain Layout
26103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26106 \begin_layout Plain Layout
26114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26117 \begin_layout Plain Layout
26121 \begin_layout Plain Layout
26137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26140 \begin_layout Plain Layout
26147 \begin_layout Plain Layout
26161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26164 \begin_layout Plain Layout
26168 \begin_layout Plain Layout
26184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26187 \begin_layout Plain Layout
26194 \begin_layout Plain Layout
26208 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26211 \begin_layout Plain Layout
26215 \begin_layout Plain Layout
26231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26234 \begin_layout Plain Layout
26241 \begin_layout Plain Layout
26255 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26258 \begin_layout Plain Layout
26262 \begin_layout Plain Layout
26282 \begin_inset space \hfill{}
26288 \begin_layout Standard
26289 \begin_inset VSpace medskip
26298 also two different characters can be accented.
26307 \begin_layout Plain Layout
26322 \begin_layout Plain Layout
26334 \begin_layout Standard
26347 can in combination with vowels directly be inserted with the keyboard without
26349 The same applies for the tilde
26353 \begin_layout Plain Layout
26354 This only applies for keyboards where the tilde is defined as accent.
26363 in combination with
26378 \begin_layout Standard
26421 , and accents inserted directly with the keyboard are also available in
26423 For the other accents there are special math commands to be used in formulas,
26425 \begin_inset CommandInset ref
26427 reference "sub:Accents-for-one"
26434 \begin_layout Standard
26435 \begin_inset VSpace bigskip
26438 Furthermore, with the command
26448 \begin_layout Plain Layout
26456 all numbers and letters can be set into a circle, quasi accented with a
26457 circle, similar to the the copyright symbol.
26460 \begin_layout Standard
26462 \begin_inset Tabular
26463 <lyxtabular version="3" rows="3" columns="2">
26465 <column alignment="center" valignment="top" width="0">
26466 <column alignment="center" valignment="top" width="0">
26468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26471 \begin_layout Plain Layout
26477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26480 \begin_layout Plain Layout
26482 \begin_inset Note Note
26485 \begin_layout Plain Layout
26492 is only used as spacer.
26504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26507 \begin_layout Plain Layout
26515 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26518 \begin_layout Plain Layout
26522 \begin_layout Plain Layout
26538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26541 \begin_layout Plain Layout
26552 raisebox{-1.5pt}{W}}
26557 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26560 \begin_layout Plain Layout
26561 \begin_inset Formula $\raisebox{4.5mm}{}$
26568 \begin_layout Plain Layout
26586 \begin_inset Formula $\raisebox{-2mm}{}$
26602 \begin_layout Standard
26603 One has to take care that the character fits in the circle.
26614 \begin_layout Plain Layout
26616 \begin_inset CommandInset ref
26618 reference "sub:Font-Sizes"
26627 specifies thereby the size of the circle.
26638 \begin_layout Plain Layout
26640 \begin_inset CommandInset ref
26642 reference "sub:Boxes-without-Frame"
26651 the character can be centered.
26654 \begin_layout Subsection
26659 \begin_layout Plain Layout
26668 \begin_layout Standard
26669 Minuscule numbers are created with the command
26679 \begin_layout Plain Layout
26688 The command can be used in formulas and in TeX-mode.
26689 The command scheme is:
26692 \begin_layout Standard
26697 oldstylenums{number}
26700 \begin_layout Standard
26705 oldstylenums{0123456789
26708 \begin_inset Formula $\oldstylenums{0123456789}$
26714 \begin_layout Subsection
26715 Miscellaneous Special Characters
26716 \begin_inset CommandInset label
26718 name "sub:Miscellaneous-Special-Characters"
26726 \begin_layout Plain Layout
26727 Special characters ! miscellaneous
26735 \begin_layout Standard
26736 The following characters can only be inserted to formulas by using commands:
26739 \begin_layout Standard
26741 \begin_inset Tabular
26742 <lyxtabular version="3" rows="4" columns="2">
26744 <column alignment="center" valignment="top" width="0">
26745 <column alignment="center" valignment="top" width="0">
26747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26750 \begin_layout Plain Layout
26756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26759 \begin_layout Plain Layout
26767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26770 \begin_layout Plain Layout
26777 \begin_layout Plain Layout
26791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26794 \begin_layout Plain Layout
26795 \begin_inset Formula $\mathcircumflex$
26805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26808 \begin_layout Plain Layout
26816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26819 \begin_layout Plain Layout
26820 \begin_inset Formula $\_$
26830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26833 \begin_layout Plain Layout
26838 \begin_layout Plain Layout
26853 \begin_layout Plain Layout
26864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26867 \begin_layout Plain Layout
26868 \begin_inset Formula $^{\circ}$
26884 \begin_layout Standard
26885 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
26886 contains the following line
26890 \begin_layout Plain Layout
26891 More about this is described in
26892 \begin_inset CommandInset ref
26894 reference "sub:Text-Characters-in"
26906 \begin_layout Standard
26911 DeclareInputtext{176}{
26924 \begin_layout Section
26926 \begin_inset CommandInset label
26928 name "sec:Formula-Styles"
26936 \begin_layout Plain Layout
26945 \begin_layout Itemize
26946 There are two different alignment styles:
26950 \begin_layout Description
26951 Centered is the predefined standard
26954 \begin_layout Description
26955 Indented for this the option
26959 must be inserted in the menu
26961 Document\SpecialChar \menuseparator
26967 \begin_inset space ~
26973 \begin_layout Standard
26978 is used, the indentation can be adjusted with the length
26988 \begin_layout Plain Layout
26997 Should the distance be 15
26998 \begin_inset space \thinspace{}
27001 mm, the following command line is inserted in the LaTeX-preamble
27004 \begin_layout Standard
27014 \begin_layout Standard
27015 When no length is specified, the predefined value of 30
27016 \begin_inset space \thinspace{}
27023 \begin_layout Itemize
27024 And two different numbering styles:
27028 \begin_layout Description
27029 Right is the predefined standard
27032 \begin_layout Description
27033 Left for this the option
27037 must be inserted in the menu
27039 Document\SpecialChar \menuseparator
27045 \begin_inset space ~
27052 \begin_layout Standard
27061 can also be used together.
27062 In this case both options are inserted, separated by a comma.
27065 \begin_layout Standard
27066 The chosen styles are used for all displayed formulas of the document.
27067 When both, centered and indented formulas should be created in a document,
27073 The indented formulas are then set in a flalign environment, see
27074 \begin_inset CommandInset ref
27076 reference "sub:Flalign-Environment"
27083 \begin_layout Section
27085 \begin_inset CommandInset label
27087 name "sec:Multiline-Formulas"
27095 \begin_layout Plain Layout
27096 Formula ! multiline
27104 \begin_layout Subsection
27108 \begin_layout Standard
27109 In LyX multiline formulas are created by pressing
27116 This creates either an
27118 eqnarray environment
27120 that is described in
27121 \begin_inset CommandInset ref
27123 reference "sub:Eqnarray-Environment"
27127 or, when the option
27129 Use AMS math package
27131 in the document settings is selected, an
27135 that is described in
27136 \begin_inset CommandInset ref
27138 reference "sub:Standard-align-Environment"
27145 \begin_layout Standard
27146 There are other multiline formula environments that can be created via the
27149 Insert\SpecialChar \menuseparator
27153 These environments are described in the following sections.
27156 \begin_layout Standard
27157 In all multiline formula environments a new line is created by pressing
27163 To add or delete lines, the math toolbar buttons
27164 \begin_inset Graphics
27165 filename ../images/tabular-feature_append-row.png
27171 \begin_inset Graphics
27172 filename ../images/tabular-feature_delete-row.png
27177 , respectively, or the menu
27179 Edit\SpecialChar \menuseparator
27185 \begin_layout Subsubsection
27187 \begin_inset CommandInset label
27189 name "sub:Line-Separation"
27197 \begin_layout Plain Layout
27198 Formula ! multiline ! Line separation
27206 \begin_layout Standard
27207 There is sometimes not enough space in multiline formulas between the lines:
27208 \begin_inset Formula \begin{eqnarray*}
27209 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}\\
27210 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*}
27217 \begin_layout Standard
27218 In LaTeX additional line space is specified as optional argument of the
27220 This is not yet possible in LyX
27224 \begin_layout Plain Layout
27226 \begin_inset CommandInset href
27228 name "LyX-bug #1505"
27229 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27238 , therefore the whole formula must be inserted in TeX-mode.
27239 To add in our example space, the command
27247 is inserted at the end of the first line.
27252 \begin_layout Plain Layout
27259 \begin_layout Plain Layout
27261 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27264 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27271 \begin_layout Plain Layout
27275 left(B^{2}+x_{0}^{2}
27283 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27288 \begin_layout Plain Layout
27300 \begin_layout Standard
27301 \begin_inset VSpace bigskip
27304 To set the the line separation for all lines in a formula, the length
27314 \begin_layout Plain Layout
27324 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27335 \begin_inset space \thinspace{}
27340 \begin_inset space \thinspace{}
27343 mm additional line separation as in the previous example, the command
27346 \begin_layout Standard
27356 \begin_layout Standard
27357 is inserted in TeX-mode before the formula.
27358 This requires that the LaTeX-package
27366 \begin_layout Plain Layout
27371 is part of every LaTeX standard installation.
27380 \begin_layout Plain Layout
27386 was loaded in LaTeX-preamble with the line
27389 \begin_layout Standard
27397 \begin_layout Standard
27402 \begin_layout Plain Layout
27414 \begin_inset Formula \begin{eqnarray*}
27415 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}\\
27416 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*}
27423 \begin_layout Standard
27427 \begin_layout Plain Layout
27438 To get back to the predefined distance,
27444 is set to the value 3
27445 \begin_inset space \thinspace{}
27451 \begin_layout Subsubsection
27453 \begin_inset CommandInset label
27455 name "sub:Column-Separation"
27463 \begin_layout Plain Layout
27464 Formula ! multiline ! Column separation
27472 \begin_layout Standard
27473 Multiline formulas form a matrix.
27474 A formula in the eqnarray environment is for example a matrix with three
27476 By changing the column separation in this environment, the space beside
27477 the relation sign can be changed.
27480 \begin_layout Standard
27481 The column separation is specified with the length
27491 \begin_layout Plain Layout
27500 \begin_inset Newline newline
27503 column separation = 2
27504 \begin_inset space \thinspace{}
27514 \begin_inset Newline newline
27520 \begin_layout Standard
27530 \begin_layout Standard
27531 inserted in TeX-mode, sets for all following formulas a column separation
27533 \begin_inset space \thinspace{}
27537 To get back to the predefined distance,
27544 \begin_inset space \thinspace{}
27550 \begin_layout Standard
27552 \begin_inset space \thinspace{}
27555 cm column separation:
27559 \begin_layout Plain Layout
27571 \begin_inset Formula \begin{eqnarray*}
27573 C & \ne & A\end{eqnarray*}
27577 A formula with the predefined column separation for matrices of 10
27578 \begin_inset space \thinspace{}
27585 \begin_layout Plain Layout
27597 \begin_inset Formula \begin{eqnarray*}
27599 C & \ne & A\end{eqnarray*}
27606 \begin_layout Subsubsection
27611 \begin_layout Plain Layout
27620 \begin_layout Standard
27621 Long formulas can be typeset using these methods:
27624 \begin_layout Itemize
27625 When one side of the equation is much shorther than the line width, this
27626 one is chosen for the left side and the right side is typeset over two
27631 \begin_layout Plain Layout
27641 \begin_inset Formula \begin{eqnarray}
27642 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 \\
27643 & & -\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}
27651 \begin_layout Plain Layout
27661 \begin_inset Newline newline
27664 The minus sign at the beginning of the second line does normally not appear
27665 as operator because it is the first character of the line.
27666 Thus it would not be surrounded by space and could not be distinguished
27667 from the fraction bar.
27668 To avoid this, space was inserted behind the minus sign with the command
27679 \begin_layout Plain Layout
27687 \begin_inset CommandInset ref
27689 reference "sub:Variable-Space"
27702 \begin_layout Plain Layout
27713 \begin_layout Itemize
27714 When both sides of the equation are too long, the command
27724 \begin_layout Plain Layout
27733 It is inserted to the first column of the first line and effects that all
27734 further insertions overwrite the following columns:
27738 \begin_layout Plain Layout
27748 \begin_inset Formula \begin{eqnarray}
27749 \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 \\
27750 & & -\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 \\
27751 & & =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}
27759 \begin_layout Plain Layout
27769 \begin_inset Newline newline
27772 After the insertion of
27778 , the cursor is in a purple box that is a bit shifted to the left from the
27780 In this the formula is inserted.
27784 \begin_layout Plain Layout
27794 \begin_inset Newline newline
27797 The content of the further lines is inserted to the second or another formula
27799 The greater the column number where it was inserted, the larger the indentation.
27803 \begin_layout Plain Layout
27813 \begin_inset Newline newline
27817 \begin_inset Note Greyedout
27820 \begin_layout Plain Layout
27821 Note the following when using
27830 \begin_layout Itemize
27831 The formula doesn't use the full page width.
27833 \begin_inset space \thinspace{}
27837 \begin_inset space ~
27841 \begin_inset Formula $-B^{2}$
27844 is added to the first line in the above example, it would have been outside
27846 To better use the width, negative space can be inserted at the beginning
27850 \begin_layout Itemize
27851 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27856 \begin_layout Plain Layout
27857 \begin_inset CommandInset href
27859 name "LyX-bug #1429"
27860 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
27869 One can only set the cursor at the beginning of the line and move it with
27878 \begin_layout Itemize
27879 Other methods to set long formulas are offered by the environments described
27881 \begin_inset CommandInset ref
27883 reference "sub:Multline-Environment"
27888 \begin_inset CommandInset ref
27890 reference "sub:Multiline-Formula-Parts"
27897 \begin_layout Subsubsection
27899 \begin_inset CommandInset label
27901 name "sub:Multiline-Brackets"
27909 \begin_layout Plain Layout
27910 Brackets ! for multiline expressions
27918 \begin_layout Standard
27919 For brackets spanning multiple lines the following problem occurs:
27920 \begin_inset Formula \begin{eqnarray*}
27921 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27922 & & \left.\cdots+B-D\right]\end{eqnarray*}
27929 \begin_layout Standard
27930 The closing bracket is smaller than the opening bracket because brackets
27931 with variable size may not span multiple lines.
27934 \begin_layout Standard
27935 To set the bracket size for the second line correctly, the first line is
27946 \begin_layout Plain Layout
27954 and the second line with
27962 \begin_layout Plain Layout
27976 \begin_inset CommandInset ref
27978 reference "sub:Automatic-Bracket-Size"
27993 \begin_layout Plain Layout
28019 \begin_layout Plain Layout
28038 \begin_layout Plain Layout
28057 \begin_layout Plain Layout
28069 \begin_inset Formula $\downarrow$
28078 \begin_layout Plain Layout
28086 is inserted, because the multiplication operator with its limits is the
28087 largest symbol in the first line and this should be the size for the bracket
28088 in the second line.
28091 \begin_layout Standard
28092 The result is this:
28093 \begin_inset Formula \begin{eqnarray*}
28094 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28095 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28102 \begin_layout Subsection
28106 \begin_layout Standard
28107 Align environments can be used for every kind of multiline formulas.
28108 They are specially useful to set several formulas side by side.
28111 \begin_layout Standard
28112 Align environments consist of columns.
28113 The odd columns are right aligned, the even ones left aligned.
28114 Every line in an Align environment can be numbered.
28117 \begin_layout Standard
28118 Align environments are created via the menu
28120 Insert\SpecialChar \menuseparator
28126 Edit\SpecialChar \menuseparator
28127 Math\SpecialChar \menuseparator
28128 Change Formula Type
28130 already existing formulas can be converted to Align environments.
28133 \begin_layout Standard
28134 To add or delete columns, the math toolbar buttons
28135 \begin_inset Graphics
28136 filename ../images/tabular-feature_append-column.png
28142 \begin_inset Graphics
28143 filename ../images/tabular-feature_delete-column.png
28148 , respectively, or the menu
28150 Edit\SpecialChar \menuseparator
28156 \begin_layout Subsubsection
28157 Standard align Environment
28158 \begin_inset CommandInset label
28160 name "sub:Standard-align-Environment"
28168 \begin_layout Plain Layout
28169 Formula ! multiline ! align environment
28177 \begin_layout Standard
28178 This Align environment is created by presssing
28182 in a formula or by the menu
28184 Insert\SpecialChar \menuseparator
28185 Math\SpecialChar \menuseparator
28186 AMS align Environment
28191 \begin_layout Standard
28192 An example for two formulas set side by side, that are created with a four
28193 column align environment:
28194 \begin_inset Formula \begin{align*}
28195 A & =\sin(B) & C & =D\\
28196 C & \ne A & B & \ne D\end{align*}
28200 As it can be seen, the formulas in this environment are placed so as if
28209 \begin_layout Plain Layout
28217 \begin_inset CommandInset ref
28219 reference "sub:Variable-Space"
28230 before the first and after every even column.
28231 When the formula style
28237 \begin_layout Plain Layout
28239 \begin_inset CommandInset ref
28241 reference "sec:Formula-Styles"
28252 is used, the formula is set without the
28258 before the first column.
28261 \begin_layout Subsubsection
28262 Alignat Environment
28266 \begin_layout Plain Layout
28267 Formula ! multiline ! alignat environment
28275 \begin_layout Standard
28276 The alignat environment has no predefined column separation.
28277 It can be inserted manually with the spaces that are described
28278 \begin_inset CommandInset ref
28280 reference "sub:Space"
28287 \begin_layout Standard
28288 The above example in the alignat environment where 1
28289 \begin_inset space \thinspace{}
28292 cm space was inserted at the beginning of the second formula:
28293 \begin_inset Formula \begin{alignat*}{2}
28294 A & =\sin(B) & \hspace{1cm}C & =D\\
28295 C & \ne A & B & \ne D\end{alignat*}
28299 Because the column separation can be set separately for every column, this
28300 environment is especially suitable to set three and more formulas side
28304 \begin_layout Subsubsection
28305 Flalign Environment
28306 \begin_inset CommandInset label
28308 name "sub:Flalign-Environment"
28316 \begin_layout Plain Layout
28317 Formula ! multiline ! flalign environment
28325 \begin_layout Standard
28326 In this environment the first two columns are always set as much as possible
28327 to the left and the last two ones to the right.
28329 \begin_inset Formula \begin{flalign*}
28330 A & =1 & B & =2 & C & =3\\
28331 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28338 \begin_layout Standard
28339 By creating a flalign environment with an odd number of columns where an
28340 empty TeX-brace is inserted to the last column, several formulas in a document
28341 can be set to the left, although the formula style
28346 As example the indented formula
28347 \begin_inset CommandInset ref
28349 reference "eq:VolInt"
28354 \begin_inset Formula \begin{flalign}
28355 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28359 The first two columns contain the formula.
28360 To indent it as with the formula style
28365 \begin_inset space \thinspace{}
28368 pt space was inserted at the beginning of the first column.
28371 \begin_layout Subsection
28372 Eqnarray Environment
28373 \begin_inset CommandInset label
28375 name "sub:Eqnarray-Environment"
28383 \begin_layout Plain Layout
28384 Formula ! multiline ! eqnarray environment
28392 \begin_layout Standard
28393 When this environment has been created, three blue boxes appear.
28394 The content of the first box is right aligned, the content of the last
28396 The content of the middle box appears centered and a bit smaller, because
28397 it is designed to insert there only relation characters.
28398 \begin_inset Formula \begin{eqnarray*}
28399 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28401 A & = & A\end{eqnarray*}
28408 \begin_layout Subsection
28413 \begin_layout Plain Layout
28414 Formula ! multiline ! gather environment
28422 \begin_layout Standard
28423 This environment consists of only one centered column.
28424 Every line can be numbered.
28425 \begin_inset Formula \begin{gather}
28427 X=\textrm{-}1\end{gather}
28434 \begin_layout Subsection
28435 Multline Environment
28436 \begin_inset CommandInset label
28438 name "sub:Multline-Environment"
28446 \begin_layout Plain Layout
28447 Formula ! multiline ! multline environment
28455 \begin_layout Standard
28456 The multline environment consists, like the gather environment, of only
28458 But the first line is left aligned, the last one right aligned.
28459 All other lines are centered.
28460 Therefore this environment is suitable for long formulas.
28462 \begin_inset CommandInset ref
28464 reference "eq:lefteqn"
28468 in the multline environment:
28469 \begin_inset Formula \begin{multline}
28470 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}\\
28471 -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}\\
28472 =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}
28479 \begin_layout Standard
28480 In the output only the last (first) line of a multline environment appears
28481 numbered when the document numbering is right (left).
28485 \begin_layout Plain Layout
28486 numbering styles see
28487 \begin_inset CommandInset ref
28489 reference "sec:Formula-Styles"
28501 \begin_layout Standard
28510 \begin_layout Plain Layout
28528 \begin_layout Plain Layout
28538 a centered line can be right or left aligned, respectively.
28539 The commands are used as follows:
28542 \begin_layout Standard
28547 shoveright{line content}
28553 shoveleft{line content}
28556 \begin_layout Standard
28557 \begin_inset VSpace medskip
28568 \begin_layout Plain Layout
28578 specifies the distance of the first line from the left page margin.
28579 Predefined is the length 0
28580 \begin_inset space \thinspace{}
28586 \begin_layout Standard
28587 As example the above formula where the command
28590 \begin_layout Standard
28600 \begin_layout Standard
28601 was inserted in TeX-mode before:
28605 \begin_layout Plain Layout
28617 \begin_inset Formula \begin{multline}
28618 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}\\
28619 \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}}\\
28620 =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}
28628 \begin_layout Plain Layout
28639 The second line was left aligned using
28648 \begin_layout Subsection
28649 Multiline Formula Parts
28650 \begin_inset CommandInset label
28652 name "sub:Multiline-Formula-Parts"
28660 \begin_layout Plain Layout
28661 Formula ! multiline ! formula parts
28669 \begin_layout Standard
28670 To display only parts of a formula with multiple lines, one of the following
28671 environments are used:
28688 They can be inserted via the menu
28690 Insert\SpecialChar \menuseparator
28693 or by using the commands described in this section.
28696 \begin_layout Standard
28697 The first three have the same properties as the corresponding multiline
28698 formula environments, but it is possible to set further formula parts beside
28701 \begin_inset Formula \[
28702 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28703 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28704 \right\} \textrm{Uncertainty relations}\]
28711 \begin_layout Standard
28712 To get this formula, a displayed formula is created where the command
28720 \begin_layout Plain Layout
28731 A purple box appears around the blue formula box where now columns and
28732 lines can be added.
28733 Outside the multiline environment other formula parts can be set, like
28737 \begin_layout Standard
28738 The aligned environment is also suitable for long formulas whose lines are
28739 horizontally aligned.
28740 Using aligned in a displayed formula has the advantage that the formula
28741 number is vertically centered behind the lines.
28743 \begin_inset CommandInset ref
28745 reference "eq:kurzlang"
28749 in the aligned environment:
28750 \begin_inset Formula \begin{equation}
28751 \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}|}\\
28752 & -\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}
28760 \begin_layout Standard
28761 To use the environments
28783 \begin_layout Plain Layout
28801 \begin_layout Plain Layout
28819 \begin_layout Plain Layout
28827 are inserted, respectively.
28828 The split environment has the same properties as the aligned environment
28829 but it can only have two columns.
28832 \begin_layout Subsection
28833 Text in multiline Formulas
28834 \begin_inset CommandInset label
28836 name "sub:Text-in-multiline"
28844 \begin_layout Plain Layout
28854 \begin_layout Plain Layout
28855 Formula ! multiline ! text
28863 \begin_layout Standard
28864 In the Align environments, and the multline and gather environment, text
28865 can be inserted that will appear in a separate line and doesn't affect
28866 the column alignment.
28867 To do this, the command
28875 \begin_layout Plain Layout
28885 is used in the following scheme:
28888 \begin_layout Standard
28896 \begin_layout Standard
28897 The text should not be longer than a line because it cannot be hyphenated.
28898 As LyX doesn't yet support
28904 directly, the text is written as mathematical text.
28911 must hereby be at the beginning of a line and appears in the output above
28913 An example where the text was inserted at the beginning of the second line:
28914 \begin_inset Formula \begin{align}
28915 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28916 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
28923 \begin_layout Section
28928 \begin_layout Plain Layout
28938 \begin_layout Plain Layout
28939 Formula ! numbering|see
28943 \begin_layout Plain Layout
28954 \begin_layout Plain Layout
28969 \begin_layout Subsection
28973 \begin_layout Standard
28974 Numbered formulas can be created with the menu
28976 Insert\SpecialChar \menuseparator
28977 Math\SpecialChar \menuseparator
28979 \begin_inset space ~
28987 \begin_inset space ~
28993 Existing formulas can be numbered with the menu
28995 Edit\SpecialChar \menuseparator
28996 Math\SpecialChar \menuseparator
28998 \begin_inset space ~
29006 \begin_inset space ~
29012 The formula number is displayed in LyX behind the formula as number sign
29014 The number sign is replaced in the output by the formula number.
29017 \begin_layout Standard
29018 When numbering is turned on in multiline formulas, all lines will be numbered.
29019 But the numbering can be controlled with the menu
29021 Edit\SpecialChar \menuseparator
29022 Math\SpecialChar \menuseparator
29024 \begin_inset space ~
29028 \begin_inset space ~
29032 \begin_inset space ~
29040 \begin_inset space ~
29048 \begin_layout Standard
29049 Except of inline formulas, all formulas can be numbered with two different
29051 \begin_inset CommandInset ref
29053 reference "sec:Formula-Styles"
29060 \begin_layout Subsection
29062 \begin_inset CommandInset label
29064 name "sub:Cross-References"
29072 \begin_layout Plain Layout
29073 Cross-references ! to formulas
29081 \begin_layout Standard
29082 All labeled formulas can be cross-referenced.
29083 A label is added by the menu
29085 Insert\SpecialChar \menuseparator
29088 or the toolbar button
29089 \begin_inset Graphics
29090 filename ../images/label-insert.png
29096 The cursor must hereby be inside a displayed formula.
29097 A dialog pops up displaying the prefix
29102 The label is inserted there behind the prefix.
29103 The predefined prefix means
29104 \begin_inset Quotes eld
29108 \begin_inset Quotes erd
29111 and makes it easier to find labels in large documents because it marks
29112 it as formula label to divide it from e.
29113 \begin_inset space \thinspace{}
29117 \begin_inset space ~
29121 To change a label, the menu
29123 Insert\SpecialChar \menuseparator
29129 \begin_layout Standard
29130 The name of the label is displayed in LyX within two parentheses behind
29132 A formula with a label is always numbered.
29135 \begin_layout Standard
29136 Cross-references are inserted via the menu
29138 Insert\SpecialChar \menuseparator
29141 or with the toolbar button
29142 \begin_inset Graphics
29143 filename ../images/dialog-show-new-inset_ref.png
29149 A formula cross-reference appears in the output as formula number.
29150 When in the cross-reference dialog window the format
29154 is chosen, the cross-reference appears in the output as formula number
29156 \begin_inset Newline newline
29159 By right-clicking on a cross-reference in LyX, one jumps to the formula
29160 that is referenced.
29163 \begin_layout Standard
29164 Here are as examples cross-references to formulas of the following subsections:
29165 \begin_inset Note Note
29168 \begin_layout Plain Layout
29169 Note the different cross-reference types.
29177 \begin_layout Standard
29179 \begin_inset CommandInset ref
29186 \begin_inset CommandInset ref
29194 \begin_inset CommandInset ref
29200 ) big Latin letters are used for the numbering in contrary to (
29201 \begin_inset CommandInset ref
29210 \begin_layout Standard
29211 \begin_inset VSpace medskip
29214 When the argument of
29222 \begin_layout Plain Layout
29230 \begin_inset CommandInset ref
29232 reference "sub:User-defined-Numbering"
29243 contains a box like in
29244 \begin_inset CommandInset ref
29246 reference "sub:Paragraph-Boxes"
29250 , the formula cannot be referenced.
29253 \begin_layout Subsection
29258 \begin_layout Plain Layout
29259 Formula numbering ! subnumbering
29267 \begin_layout Standard
29268 With the help of the commands
29272 begin{subequations}
29280 formulas can be subnumbered.
29281 Both commands are inserted in TeX-mode.
29284 \begin_layout Standard
29286 \begin_inset Formula \begin{equation}
29287 A=C-B\label{eq:a}\end{equation}
29295 \begin_layout Plain Layout
29299 addtocounter{equation}{-1}
29308 \begin_layout Plain Layout
29312 begin{subequations}
29318 \begin_inset VSpace -5mm
29322 \begin_inset Formula \begin{equation}
29323 B=C-A\label{eq:b}\end{equation}
29328 \begin_inset Formula \begin{equation}
29329 C=A+B\label{eq:c}\end{equation}
29336 \begin_layout Standard
29340 \begin_layout Plain Layout
29352 \begin_layout Standard
29353 To create the example, the following is done:
29356 \begin_layout Enumerate
29357 first formula is inserted
29360 \begin_layout Enumerate
29365 addtocounter{equation}{-1}
29367 begin{subequations}
29371 \begin_layout Plain Layout
29380 \begin_inset Newline newline
29385 is inserted after the first formula
29388 \begin_layout Enumerate
29389 second formula is inserted
29392 \begin_layout Enumerate
29393 third formula is inserted
29396 \begin_layout Enumerate
29403 is inserted after the third formula
29406 \begin_layout Standard
29407 Every formula between the commands
29419 is subnumbered as a, b,
29420 \begin_inset Newline linebreak
29423 c, \SpecialChar \ldots{}
29424 For multiline formulas every line will be subnumbered.
29425 All subnumbered formulas are treated as
29430 But as every numbered formula increases the counter
29434 by one, the command
29440 is needed to decrease it.
29441 Otherwise the formulas
29442 \begin_inset CommandInset ref
29449 \begin_inset CommandInset ref
29456 \begin_inset CommandInset ref
29462 would be numbered as
29463 \begin_inset CommandInset ref
29470 \begin_inset CommandInset ref
29477 \begin_inset CommandInset ref
29486 \begin_layout Standard
29487 By inserting the commands in TeX-mode, a space is created between the first
29490 \begin_inset space \thinspace{}
29493 mm vertical space is inserted after the command
29497 begin{subequations}
29500 When the formula style
29506 \begin_layout Plain Layout
29508 \begin_inset CommandInset ref
29510 reference "sec:Formula-Styles"
29522 \begin_inset space \thinspace{}
29525 mm space is inserted instead.
29528 \begin_layout Standard
29529 Here is an example for a multiline formula where the numbering was turned
29530 off for the second line:
29534 \begin_layout Plain Layout
29538 begin{subequations}
29544 \begin_inset Formula \begin{eqnarray}
29545 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29546 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29547 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29555 \begin_layout Plain Layout
29567 \begin_layout Subsection
29568 User-defined Numbering
29569 \begin_inset CommandInset label
29571 name "sub:User-defined-Numbering"
29579 \begin_layout Plain Layout
29580 Formula numbering ! user-defined
29588 \begin_layout Standard
29592 \begin_layout Plain Layout
29593 Formula numbering ! self-defined delimiters
29598 With the standard numbering parentheses are set around the formula number.
29599 To replace the parentheses for example by vertical bars, the following
29600 line is added to the LaTeX-preamble:
29603 \begin_layout Standard
29615 \begin_inset Note Note
29618 \begin_layout Plain Layout
29619 This macro is already declared in the LaTeX-preamble for testing.
29620 To activate it, remove the percent sign at the beginning.
29628 \begin_layout Standard
29629 To use other characters, the vertical bars besides the
29633 are replaced by one ore more characters.
29634 To get only the formula number the vertical bars are omitted.
29637 \begin_layout Standard
29638 \begin_inset VSpace bigskip
29641 When there should be an expression of your choice instead of the consecutive
29642 formula number in parentheses behind the formula, the command
29652 \begin_layout Plain Layout
29661 \begin_inset Formula \begin{equation}
29662 A+B=C\tag{something}\label{eq:tag}\end{equation}
29666 In this example the command
29674 \begin_layout Plain Layout
29685 was inserted to the formula.
29688 \begin_layout Standard
29697 \begin_layout Plain Layout
29708 is inserted instead, the star prevents the parentheses around the expression:
29709 \begin_inset Formula \[
29710 A+B=C\tag*{something}\]
29717 \begin_layout Standard
29718 \begin_inset VSpace bigskip
29721 To restart the formula numbering with new document parts or sections, the
29722 following command is used:
29725 \begin_layout Standard
29730 @addtoreset{equation}{part}
29736 \begin_layout Plain Layout
29741 \begin_layout Plain Layout
29752 \begin_layout Plain Layout
29765 \begin_layout Plain Layout
29776 \begin_layout Plain Layout
29789 \begin_inset Newline newline
29793 \begin_inset Newline newline
29800 @addtoreset{equation}{section}
29803 \begin_layout Standard
29804 To be able to use these commands in TeX-mode, the
29805 \begin_inset Quotes eld
29809 \begin_inset Quotes erd
29812 character has to be made
29813 \begin_inset Quotes eld
29817 \begin_inset Quotes erd
29820 for LaTeX using the command
29834 So the command sequence in TeX-mode is:
29837 \begin_layout Standard
29843 \begin_inset Newline newline
29848 @addtoreset{equation}{section}
29849 \begin_inset Newline newline
29857 \begin_layout Standard
29858 In the LaTeX-preamble
29870 can be omitted as they are automatically internally inserted by LyX.
29873 \begin_layout Standard
29888 \begin_layout Plain Layout
29893 is part of the LaTeX-package
29901 \begin_layout Plain Layout
29902 Packages ! carlisle
29907 that is part of every LaTeX standard installation.
29916 \begin_layout Plain Layout
29917 Packages ! remreset
29922 has to be loaded in the LaTeX-preamble with the line
29925 \begin_layout Standard
29930 usepackage{remreset}
29933 \begin_layout Standard
29944 \begin_layout Plain Layout
29949 \begin_layout Plain Layout
29960 \begin_layout Plain Layout
29973 \begin_layout Plain Layout
29984 \begin_layout Plain Layout
29996 can be used with the same scheme as
30005 \begin_layout Standard
30006 \begin_inset VSpace bigskip
30009 Sometimes formulas should be numbered in the following form:
30012 \begin_layout Standard
30015 (section number.formula number)
30018 \begin_layout Standard
30019 The formula number should start with every section with
30020 \begin_inset Quotes eld
30024 \begin_inset Quotes erd
30030 \begin_layout Standard
30031 For this case there is the command
30041 \begin_layout Plain Layout
30049 , which is used with the following scheme:
30052 \begin_layout Standard
30057 numberwithin{counter}{sectioning}
30060 \begin_layout Standard
30061 Counter denotes what kind of numbering is affected, sectioning denotes what
30062 number is before the dot.
30065 \begin_layout Standard
30066 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30069 \begin_layout Standard
30074 numberwithin{equation}{section}
30077 \begin_layout Standard
30078 This is the result:
30082 \begin_layout Plain Layout
30086 numberwithin{equation}{section}
30092 \begin_inset Formula \begin{equation}
30093 A+B=C\end{equation}
30100 \begin_layout Standard
30102 \begin_inset space \thinspace{}
30106 \begin_inset space ~
30109 tables so that the number of the part is the sectioning,
30110 \begin_inset Newline newline
30117 numberwithin{table}{part}
30122 \begin_layout Standard
30123 To go back to the standard numbering or to prevent this kind of numbering
30124 when it is defined by the document class, the following command is inserted
30125 as TeX-Code or to the LaTeX-preamble:
30128 \begin_layout Standard
30141 \begin_layout Plain Layout
30155 \begin_layout Plain Layout
30171 \begin_inset Newline newline
30179 \begin_inset Newline newline
30191 \begin_layout Standard
30198 uses internally the command
30204 , described above, that also needs to be reverted.
30208 \begin_layout Plain Layout
30215 \begin_layout Plain Layout
30219 @removefromreset{equation}{section}
30222 \begin_layout Plain Layout
30234 \begin_layout Subsection
30235 Numbering with Roman Numbers and Letters
30236 \begin_inset CommandInset label
30238 name "sub:Numbering-with-Roman"
30246 \begin_layout Plain Layout
30247 Formula numbering ! with letters
30256 \begin_layout Plain Layout
30257 Formula numbering ! with Roman numbers
30265 \begin_layout Standard
30266 Formulas can also be numbered with Roman numbers and Latin letters.
30267 To number for example with small Roman numbers, the command
30270 \begin_layout Standard
30282 \begin_layout Standard
30283 is inserted before the formula in TeX-mode.
30294 \begin_layout Plain Layout
30302 redefines the predefined command
30318 \begin_layout Plain Layout
30325 has the same scheme like the command
30331 that is described in
30332 \begin_inset CommandInset ref
30334 reference "sec:User-defined-commands"
30348 is the formula counter.
30355 is used as prefix for a counter, the value of the counter is output as
30357 When a formula is numbered, LaTeX sets internally the command
30363 behind the formula.
30372 \begin_layout Plain Layout
30382 outputs the counter as small Roman number.
30385 \begin_layout Standard
30386 All formulas behind the command
30396 are now numbered Roman.
30397 To switch to numbering with big Roman numbers, the command is inserted
30414 \begin_layout Plain Layout
30426 \begin_inset Quotes eld
30430 \begin_inset Quotes erd
30433 with small Latin letters there is the command
30443 \begin_layout Plain Layout
30451 , for big ones there is the command
30461 \begin_layout Plain Layout
30474 \begin_layout Standard
30475 \begin_inset Note Greyedout
30478 \begin_layout Plain Layout
30483 Only maximal 26 formulas can be numbered with Latin letters in one document.
30491 \begin_layout Standard
30495 \begin_layout Plain Layout
30511 \begin_layout Standard
30512 \begin_inset Formula \begin{equation}
30513 A=\textrm{small roman}\label{eq:rom}\end{equation}
30521 \begin_layout Plain Layout
30535 \begin_inset Formula \begin{equation}
30536 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30544 \begin_layout Plain Layout
30558 \begin_inset Formula \begin{equation}
30559 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30567 \begin_layout Plain Layout
30581 \begin_inset Formula \begin{equation}
30582 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30589 \begin_layout Standard
30590 To switch back to the default numbering, insert the command:
30593 \begin_layout Standard
30606 \begin_layout Plain Layout
30617 \begin_layout Standard
30621 \begin_layout Plain Layout
30635 \begin_inset Formula \begin{equation}
30636 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30643 \begin_layout Standard
30644 \begin_inset VSpace medskip
30647 As you see, formulas are numbered serially independent from the numbering
30649 When then numbering should start with
30650 \begin_inset Quotes eld
30654 \begin_inset Quotes erd
30657 when the style is changed, new equation counters have to be defined.
30658 A description about this can be found in the file
30659 \begin_inset CommandInset href
30661 target "Formula-numbering.lyx"
30668 \begin_layout Section
30669 User-defined commands
30670 \begin_inset CommandInset label
30672 name "sec:User-defined-commands"
30680 \begin_layout Plain Layout
30681 User-defined commands
30689 \begin_layout Standard
30690 Many LaTeX-commands are too long to be used frequently.
30691 But it is possible to define with the command
30701 \begin_layout Plain Layout
30709 new shorter commands.
30712 \begin_layout Standard
30713 The command scheme of
30722 \begin_layout Standard
30727 newcommand{new command name}[number of arguments][optional
30732 \begin_inset Newline newline
30739 \begin_layout Plain Layout
30754 \begin_layout Plain Layout
30761 {command definition}
30764 \begin_layout Standard
30765 \begin_inset Note Greyedout
30768 \begin_layout Plain Layout
30773 Assure that the name of the new command is not already used in your document
30774 or by LaTeX-packages that you use.
30775 When you for example define the command
30787 , you get an error message because
30793 is already defined as command for
30794 \begin_inset Quotes eld
30798 \begin_inset Formula $\le$
30802 \begin_inset Quotes erd
30813 \begin_layout Standard
30814 \begin_inset Note Greyedout
30817 \begin_layout Plain Layout
30822 The names of user-defined commands may only consist of Latin letters.
30830 \begin_layout Standard
30831 The number of arguments is an integer in the range 0
30832 \begin_inset space \thinspace{}
30836 \begin_inset space \thinspace{}
30839 9 and specifies how many arguments the new command should have.
30840 With the optional value a value for an optional argument can be predefined.
30841 When this is done, the
30849 rgument of the new command is automatically an optional one.
30852 \begin_layout Standard
30853 Here are some examples:
30856 \begin_layout Itemize
30857 To define the command
30869 , the LaTeX-preamble line is:
30873 \begin_layout Plain Layout
30885 \begin_inset Newline newline
30897 \begin_layout Itemize
30898 To define the command
30910 , the argument (that should be underlined) must be taken into account.
30911 For this the preamble line is:
30915 \begin_layout Plain Layout
30927 \begin_inset Newline newline
30942 \begin_layout Plain Layout
30954 \begin_inset Newline newline
30963 acts as argument placeholder, the
30967 behind it denotes that it is the placeholder for the first argument.
30970 \begin_layout Itemize
30978 \begin_inset space \thinspace{}
30982 \begin_inset space ~
30995 \begin_layout Plain Layout
31007 \begin_inset Newline newline
31016 framebox#1#2{$#3$}}
31022 \begin_layout Plain Layout
31034 \begin_inset Newline newline
31039 The two Dollar signs creates the extra formula needed for
31046 \begin_inset CommandInset ref
31048 reference "sub:Boxes-with-Frame"
31055 \begin_layout Itemize
31056 To create a new command for
31062 where the color for the box needn't to be specified, the argument for the
31063 color is defined optional:
31067 \begin_layout Plain Layout
31079 \begin_inset Newline newline
31088 fcolorbox{#2}{#1}{$#3$}}
31094 \begin_layout Plain Layout
31104 \begin_inset Newline newline
31107 When the color is not specified when using
31113 , the predefined color
31120 \begin_layout Standard
31121 A test of the new defined commands:
31124 \begin_layout Standard
31126 \begin_inset Tabular
31127 <lyxtabular version="3" rows="6" columns="2">
31129 <column alignment="center" valignment="top" width="0">
31130 <column alignment="center" valignment="top" width="0">
31132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31135 \begin_layout Plain Layout
31141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31144 \begin_layout Plain Layout
31146 \begin_inset Note Note
31149 \begin_layout Plain Layout
31156 is only used as spacer.
31168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31171 \begin_layout Plain Layout
31178 \begin_layout Plain Layout
31192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31195 \begin_layout Plain Layout
31196 \begin_inset Formula $A\gr B$
31206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31209 \begin_layout Plain Layout
31217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31220 \begin_layout Plain Layout
31221 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31234 \begin_layout Plain Layout
31238 \begin_inset Formula $\to$
31244 \begin_inset Formula $\to$
31255 \begin_layout Plain Layout
31269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31272 \begin_layout Plain Layout
31273 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31286 \begin_layout Plain Layout
31290 \begin_inset Formula $\to$
31301 \begin_layout Plain Layout
31315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31318 \begin_layout Plain Layout
31319 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31332 \begin_layout Plain Layout
31338 \begin_inset Formula $\to$
31349 \begin_layout Plain Layout
31363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31366 \begin_layout Plain Layout
31367 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31383 \begin_layout Section
31388 \begin_layout Plain Layout
31397 \begin_layout Standard
31398 To create diagrams, the LaTeX-package
31404 \begin_layout Plain Layout
31409 is part of every LaTeX standard installation.
31420 \begin_layout Plain Layout
31427 It is loaded in the LaTeX-preamble with the line
31430 \begin_layout Standard
31438 \begin_layout Standard
31439 Diagrams visualize relations and look like this:
31440 \begin_inset Formula \[
31441 \begin{CD}A@>>>B@>>>C\\
31443 F@<<<E@<<<D\end{CD}\]
31450 \begin_layout Standard
31451 To get them, the command
31459 \begin_layout Plain Layout
31469 is inserted to a formula.
31470 A blue box appears with two dashed lines where further commands can be
31476 a new line is created.
31477 Horizontal relations are inserted in odd, vertical in even formula lines.
31480 \begin_layout Standard
31481 To create the relations there are the following commands:
31484 \begin_layout Itemize
31489 creates a left arrow,
31500 \begin_layout Itemize
31505 creates an up arrow,
31513 a vertical equal sign
31516 \begin_layout Itemize
31522 is a placeholder for non-existent relations
31525 \begin_layout Standard
31526 All arrows can be labeled as follows:
31529 \begin_layout Itemize
31530 Is text inserted between the first and second < or >, resp., it is placed
31532 When it is inserted between the second and third one, it appears under
31536 \begin_layout Itemize
31537 When text for vertical arrows is inserted between the first and second A
31538 or V, resp., it is placed left beside the arrow.
31539 When it is inserted between the second and third one, it appears right
31541 If the text contains an A or V, these letters must be set into a TeX-brace.
31544 \begin_layout Standard
31545 As example a diagram with all possible relations:
31548 \begin_layout Standard
31549 \begin_inset Formula \[
31550 \begin{CD}A@>j>>B@>>k>C@=F\\
31552 D@<<j<E@>k>>F@=C\end{CD}\]
31559 \begin_layout Standard
31560 The command for this is:
31561 \begin_inset Newline newline
31572 \begin_layout Plain Layout
31581 A@>j>>B@>>k>C@=F Ctrl-Enter
31582 \begin_inset Newline newline
31589 \begin_layout Plain Layout
31604 \begin_layout Plain Layout
31617 \begin_layout Plain Layout
31629 \begin_inset Formula $\to$
31635 \begin_inset Newline newline
31642 \begin_layout Plain Layout
31657 \begin_layout Plain Layout
31670 \begin_layout Plain Layout
31680 \begin_layout Standard
31681 \begin_inset Newpage newpage
31687 \begin_layout Section
31692 \begin_layout Plain Layout
31705 \begin_layout Plain Layout
31706 Other useful math tips can be found in
31707 \begin_inset CommandInset citation
31722 \begin_layout Plain Layout
31730 \begin_inset Note Note
31733 \begin_layout Plain Layout
31736 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31739 \begin_layout Plain Layout
31742 texorpdfstring is in section
31743 \begin_inset CommandInset ref
31745 reference "sub:Formulas-in-Section"
31758 \begin_layout Plain Layout
31768 \begin_layout Plain Layout
31773 \begin_layout Plain Layout
31780 Chemical characters
31784 \begin_layout Plain Layout
31799 \begin_layout Subsection
31800 Chemical Symbols and Equations
31801 \begin_inset CommandInset label
31803 name "sub:Chemical-Symbols-and"
31811 \begin_layout Plain Layout
31812 Chemical characters ! Symbols
31821 \begin_layout Plain Layout
31831 \begin_layout Plain Layout
31840 \begin_layout Standard
31841 An example text from chemistry:
31844 \begin_layout Quote
31846 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31849 -ion reacts with two
31850 \begin_inset Formula $\mathrm{Na^{+}}$
31853 -ions to sodium sulfate
31854 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31858 The chemical equation for this is:
31859 \begin_inset Formula \[
31860 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
31867 \begin_layout Standard
31868 This chemical equation can directly be created as formula.
31869 To avoid that the symbols appear italic, everything is highlighted and
31870 changed by the shortcut
31873 \begin_inset space ~
31878 to the upright font style.
31882 \begin_layout Plain Layout
31888 \begin_inset CommandInset ref
31890 reference "sub:Font-Styles"
31902 \begin_layout Subsection
31907 \begin_layout Plain Layout
31916 \begin_layout Standard
31917 Negative numbers often look ugly in formulas because the minus sign before
31918 the number is set with the same length as the minus operator sign.
31919 When writing the negative number in normal text, the minus sign appears
31923 \begin_layout Standard
31924 Thus, the problem disappears when converting the minus sign to mathematical
31928 \begin_layout Standard
31929 An example to visualize the problem:
31932 \begin_layout Standard
31934 \begin_inset Tabular
31935 <lyxtabular version="3" rows="3" columns="2">
31937 <column alignment="right" valignment="top" width="0">
31938 <column alignment="left" valignment="top" width="0">
31940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31943 \begin_layout Plain Layout
31949 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
31952 \begin_layout Plain Layout
31960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31963 \begin_layout Plain Layout
31969 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
31972 \begin_layout Plain Layout
31973 \begin_inset Formula $x=-2$
31983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31986 \begin_layout Plain Layout
31992 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
31995 \begin_layout Plain Layout
31996 \begin_inset Formula $x=\textrm{-}2$
32012 \begin_layout Subsection
32013 Comma as Decimal Separator
32017 \begin_layout Plain Layout
32026 \begin_layout Standard
32027 In LaTeX a comma inside a formula is used, according to the English convention,
32028 as number group separator.
32029 So there will be space added behind all commas in formulas.
32032 \begin_layout Standard
32033 To avoid this, the comma is highlighted and changed to mathematical text
32037 \begin_inset space ~
32045 \begin_layout Standard
32046 To use all formula commas in the document as decimal separator, the file
32055 \begin_layout Plain Layout
32060 is part of the LaTeX-package
32068 \begin_layout Plain Layout
32073 \begin_layout Plain Layout
32096 \begin_layout Plain Layout
32102 is loaded with the LaTeX-preamble line
32105 \begin_layout Standard
32113 \begin_layout Subsection
32115 \begin_inset CommandInset label
32117 name "sub:Physical-Vectors"
32125 \begin_layout Plain Layout
32134 \begin_layout Standard
32135 Predefined vectors are offered by the LaTeX-package
32143 \begin_layout Plain Layout
32148 should be part of every LaTeX standard installation.
32157 \begin_layout Plain Layout
32163 that is loaded with the LaTeX-preamble line
32166 \begin_layout Standard
32174 \begin_layout Standard
32178 \begin_layout Plain Layout
32188 \begin_inset Note Note
32191 \begin_layout Plain Layout
32192 The following table will only be displayed when the LaTeX-package
32201 The following commands are defined:
32204 \begin_layout Standard
32206 \begin_inset Tabular
32207 <lyxtabular version="3" rows="4" columns="2">
32209 <column alignment="center" valignment="top" width="0">
32210 <column alignment="center" valignment="top" width="0">
32212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32215 \begin_layout Plain Layout
32221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32224 \begin_layout Plain Layout
32232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32235 \begin_layout Plain Layout
32245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32248 \begin_layout Plain Layout
32249 \begin_inset Formula $\Bra{\psi}$
32259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32262 \begin_layout Plain Layout
32272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32275 \begin_layout Plain Layout
32276 \begin_inset Formula $\Ket{\psi}$
32286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32289 \begin_layout Plain Layout
32301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32304 \begin_layout Plain Layout
32305 \begin_inset Formula $\Braket{\psi|\phi}$
32321 \begin_layout Standard
32328 assures that all vertical bars are set in the size of the surrounding brackets:
32329 \begin_inset Formula \[
32330 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32338 \begin_layout Plain Layout
32348 \begin_inset Note Note
32351 \begin_layout Plain Layout
32352 The following will be displayed when the LaTeX-package
32364 \begin_layout Standard
32365 You need to install the LaTeX-package
32369 to see the rest of this subsection in the output.
32372 \begin_layout Standard
32376 \begin_layout Plain Layout
32388 \begin_layout Standard
32395 can also be achieved using the command
32401 , that is described in
32402 \begin_inset CommandInset ref
32404 reference "sub:Automatic-Bracket-Size"
32411 \begin_layout Subsection
32412 Self-defined Fractions
32413 \begin_inset CommandInset label
32415 name "sub:Self-defined-Fractions"
32423 \begin_layout Plain Layout
32424 Fractions ! self-defined
32432 \begin_layout Standard
32433 To define custom commands for fractions, the command
32443 \begin_layout Plain Layout
32451 is used in the following scheme:
32454 \begin_layout Standard
32467 bracket}{fraction bar thickness}{style}
32468 \begin_inset Newline newline
32475 \begin_layout Plain Layout
32490 \begin_layout Plain Layout
32497 {numerator}{denominator}
32500 \begin_layout Standard
32501 The style is a number in the range of 0
32502 \begin_inset space \thinspace{}
32506 \begin_inset space \thinspace{}
32512 \begin_layout Standard
32514 \begin_inset Tabular
32515 <lyxtabular version="3" rows="5" columns="2">
32517 <column alignment="center" valignment="top" width="0">
32518 <column alignment="center" valignment="top" width="0">
32520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32523 \begin_layout Plain Layout
32529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32532 \begin_layout Plain Layout
32540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32543 \begin_layout Plain Layout
32549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32552 \begin_layout Plain Layout
32553 display style formula
32560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32563 \begin_layout Plain Layout
32569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32572 \begin_layout Plain Layout
32580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32583 \begin_layout Plain Layout
32589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32592 \begin_layout Plain Layout
32600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32603 \begin_layout Plain Layout
32609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32612 \begin_layout Plain Layout
32626 \begin_layout Standard
32627 When no style is given, the size is adjusted to the surrounding environment
32628 like for the command
32637 \begin_layout Standard
32638 When no fraction bar thickness is given, the predefined value of 0.4
32639 \begin_inset space \thinspace{}
32645 \begin_layout Standard
32646 \begin_inset VSpace medskip
32649 For example, the commands
32662 \begin_inset CommandInset ref
32664 reference "sub:Fractions"
32668 are defined with the commands
32671 \begin_layout Standard
32680 genfrac{}{}{}{0}{#1}{#2}}
32683 \begin_layout Standard
32687 \begin_layout Standard
32696 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32699 \begin_layout Standard
32700 \begin_inset VSpace medskip
32703 To define a fraction where the fraction bar thickness can be given as optional
32704 argument, the following line is inserted to the LaTeX-preamble:
32707 \begin_layout Standard
32716 genfrac{}{}{#1}{}{#2}{#3}}
32719 \begin_layout Standard
32721 \begin_inset Formula \begin{align*}
32722 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32723 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32727 As one can see, the distance of the numerator and the denominator to the
32728 fraction bar is round about three times the bar thickness.
32731 \begin_layout Subsection
32733 \begin_inset CommandInset label
32735 name "sub:Canceled-Formulas"
32743 \begin_layout Plain Layout
32752 \begin_layout Standard
32753 To cancel formulas or formula parts, the LaTeX-package
32761 \begin_layout Plain Layout
32766 is part of every LaTeX standard installation.
32775 \begin_layout Plain Layout
32781 has to be loaded with the LaTeX-preamble line
32784 \begin_layout Standard
32789 usepackage[samesize]{cancel}
32792 \begin_layout Standard
32793 There are four ways to cancel formulas:
32796 \begin_layout Standard
32798 \begin_inset Tabular
32799 <lyxtabular version="3" rows="5" columns="2">
32801 <column alignment="center" valignment="top" width="0">
32802 <column alignment="center" valignment="top" width="0">
32804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32807 \begin_layout Plain Layout
32813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32816 \begin_layout Plain Layout
32818 \begin_inset Note Note
32821 \begin_layout Plain Layout
32834 are used here as spacer.
32846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32849 \begin_layout Plain Layout
32858 \begin_layout Plain Layout
32872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32875 \begin_layout Plain Layout
32876 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
32886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32889 \begin_layout Plain Layout
32898 \begin_layout Plain Layout
32912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32915 \begin_layout Plain Layout
32916 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
32926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32929 \begin_layout Plain Layout
32938 \begin_layout Plain Layout
32952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32955 \begin_layout Plain Layout
32956 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
32966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32969 \begin_layout Plain Layout
32973 \begin_inset Formula $\to$
32984 \begin_layout Plain Layout
32998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33001 \begin_layout Plain Layout
33002 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33018 \begin_layout Standard
33025 is especially suitable to visualize the reduction of fractions within formulas:
33026 \begin_inset Formula \[
33027 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33034 \begin_layout Subsection
33035 Formulas in Section Headings
33036 \begin_inset CommandInset label
33038 name "sub:Formulas-in-Section"
33046 \begin_layout Plain Layout
33047 Formula ! in section headings
33055 \begin_layout Standard
33056 When formulas are used in section headings, the following has to be taken
33060 \begin_layout Standard
33061 \begin_inset Note Greyedout
33064 \begin_layout Plain Layout
33073 \begin_layout Plain Layout
33074 Packages ! hyperref
33079 support is enabled in the document settings dialog under
33082 \begin_inset space ~
33087 , PDF-bookmarks are created for every section heading in the table of contents.
33088 If a section heading contains formulas, they are incorrectly displayed
33089 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33098 \begin_layout Standard
33099 Both problems can be solved by inserting at the end of the section heading
33100 a short title with the menu
33102 Insert\SpecialChar \menuseparator
33104 \begin_inset space ~
33110 Short titles are used as alternative for multiline section headings to
33111 keep the table of contents clearly arranged.
33112 Only the short title appears in the table of contents and therefore also
33113 in the PDF-bookmark.
33116 \begin_layout Standard
33117 When formulas should be used in the table of contents but
33121 is used, one can use the following command in TeX-mode:
33124 \begin_layout Standard
33129 texorpdfstring{part}{alternative}
33133 \begin_layout Plain Layout
33144 \begin_layout Standard
33145 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33146 This can be characters, formulas, footnotes, but also cross-references.
33147 The alternative is used instead of the part for the bookmark.
33150 \begin_layout Standard
33151 Here are two example headings:
33152 \begin_inset VSpace -3mm
33159 \begin_layout Plain Layout
33171 \begin_layout Subsubsection
33172 Heading without formula in table of contents
33173 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33177 \begin_inset OptArg
33180 \begin_layout Plain Layout
33181 Heading without formula in table of contents
33189 \begin_layout Subsubsection
33190 Heading with formula in table of contents
33194 \begin_layout Plain Layout
33204 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33211 \begin_layout Plain Layout
33221 \begin_layout Standard
33225 \begin_layout Plain Layout
33234 In the first heading a short title was used, in the second one
33243 \begin_layout Standard
33244 To get the same formatting as for the other headings, the complete heading
33253 \begin_layout Plain Layout
33255 \begin_inset CommandInset ref
33257 reference "sub:Bold-Formulas"
33269 \begin_layout Subsection
33270 Formulas in multi-column Text
33274 \begin_layout Plain Layout
33275 Formula ! in multi-column text
33283 \begin_layout Standard
33284 Formulas in multi-column text are often too wide to fit into a column and
33285 thus need to be set over the whole page width.
33286 This is done by using the LaTeX-package
33294 \begin_layout Plain Layout
33299 is part of every LaTeX standard installation.
33308 \begin_layout Plain Layout
33309 Packages ! multicol
33314 , that is loaded with the LaTeX-preamble line
33317 \begin_layout Standard
33322 usepackage{multicol}
33325 \begin_layout Standard
33326 \begin_inset Note Greyedout
33329 \begin_layout Plain Layout
33330 Note herby that the setting
33333 \begin_inset space ~
33340 Document\SpecialChar \menuseparator
33346 \begin_inset space ~
33366 \begin_layout Standard
33367 Before the multi-column text the command
33370 \begin_layout Standard
33375 begin{multicols}{column number}
33378 \begin_layout Standard
33379 is written in TeX-mode.
33380 The column number is a number in the range of 2
33381 \begin_inset space \thinspace{}
33385 \begin_inset space \thinspace{}
33389 Before the formula the multi-column text is ended by inserting the command
33392 \begin_layout Standard
33400 \begin_layout Standard
33404 \begin_layout Standard
33405 Due to the command some space is automatically added before the formula.
33407 \begin_inset space \thinspace{}
33410 mm vertical space is inserted before the formula.
33411 When the formula style
33417 \begin_layout Plain Layout
33419 \begin_inset CommandInset ref
33421 reference "sec:Formula-Styles"
33433 \begin_inset space \thinspace{}
33436 mm space is inserted instead.
33439 \begin_layout Standard
33440 As example a multi-column text with a displayed formula:
33443 \begin_layout Standard
33447 \begin_layout Plain Layout
33451 begin{multicols}{2}
33456 Das Spektrum wird fouriertransformiert.
33457 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33458 , Lösungsmittel) zu trennen.
33459 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33460 nun das Aussehen des Ausgangssignals.
33461 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33462 über alle Phasen integrieren muss.
33464 \begin_inset Formula $S$
33467 unser normiertes Ausgangssignal and
33468 \begin_inset Formula $P$
33471 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33475 \begin_layout Plain Layout
33485 \begin_inset VSpace -6mm
33489 \begin_inset Formula \begin{equation}
33490 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33498 \begin_layout Plain Layout
33502 begin{multicols}{2}
33508 \begin_inset Formula $S_{0}$
33511 das Signal ohne Gradient ist and the Normierungsbedingung
33512 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33516 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33518 \begin_inset Formula $\nicefrac{\pi}{2}$
33522 \begin_inset space \thinspace{}
33525 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33526 das Signal zusätzlich abschwächt.
33527 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33529 \begin_inset Formula $T_{2}$
33535 \begin_layout Standard
33539 \begin_layout Plain Layout
33551 \begin_layout Subsection
33552 Formulas with Description of Variables
33556 \begin_layout Plain Layout
33557 Formula ! with description of variables
33565 \begin_layout Standard
33566 To describe variables within a formula, like in formula
33567 \begin_inset CommandInset ref
33569 reference "eq:within"
33578 \begin_inset Formula $n$
33582 \begin_inset space ~
33585 matrix is used with left aligned columns for the
33586 \begin_inset Formula $n$
33593 \begin_layout Plain Layout
33595 \begin_inset CommandInset ref
33597 reference "sec:Matrices"
33606 To set the description in a smaller size, before the matrix e.
33607 \begin_inset space \thinspace{}
33611 \begin_inset space ~
33624 \begin_layout Plain Layout
33626 \begin_inset CommandInset ref
33628 reference "sub:Font-Sizes"
33640 \begin_layout Standard
33641 When the formula style
33647 \begin_layout Plain Layout
33649 \begin_inset CommandInset ref
33651 reference "sec:Formula-Styles"
33672 \begin_layout Plain Layout
33679 only works in formulas with the style
33684 \begin_inset CommandInset ref
33686 reference "sub:Variable-Space"
33695 is inserted before and after the matrix to have the same separation of
33696 the matrix from the equation and the side margin.
33699 \begin_layout Standard
33700 When the formula style
33704 is used, the method described in
33705 \begin_inset CommandInset ref
33707 reference "sub:Flalign-Environment"
33711 is used to indent formulas.
33713 \begin_inset CommandInset ref
33715 reference "eq:within"
33719 consists of five columns whereas in the first two columns contain the equation,
33720 the third the matrix, and the last one an empty TeX-brace.
33721 \begin_inset Formula \begin{flalign}
33722 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33723 \rho & \textrm{density}\\
33724 V & \textrm{volume}\\
33725 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33732 \begin_layout Subsection
33733 Upright small Greek Letters
33734 \begin_inset CommandInset label
33736 name "sub:Upright-small-Greek"
33744 \begin_layout Plain Layout
33745 Greek letters ! upright
33753 \begin_layout Standard
33754 Most of the math fonts only provide italic small Greek letters.
33755 But for symbols of elementary particles like pions and neutrinos, upright
33756 Greek letters are needed.
33765 \begin_layout Plain Layout
33770 is part of the LaTeX-package
33778 \begin_layout Plain Layout
33783 \begin_layout Plain Layout
33806 \begin_layout Plain Layout
33812 that is loaded with the LaTeX-preamble line
33815 \begin_layout Standard
33820 usepackage{upgreek}
33823 \begin_layout Standard
33829 \begin_layout Plain Layout
33839 \begin_inset Note Note
33842 \begin_layout Plain Layout
33843 The following table will only be displayed when the LaTeX-package
33852 They are created when the command for a small Greek letters is started
33858 For example the command
33865 \begin_inset Formula $\uptau$
33871 \begin_layout Standard
33872 With these commands reactions of elementary particles can be typeset:
33873 \begin_inset Formula \[
33874 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
33881 \begin_layout Standard
33882 The upright letters are more bold and wider than the italic ones.
33883 They should therefore not be used for units like
33884 \begin_inset Quotes eld
33888 \begin_inset Quotes erd
33894 \begin_layout Standard
33898 \begin_layout Plain Layout
33908 \begin_inset Note Note
33911 \begin_layout Plain Layout
33912 The following will be displayed when the LaTeX-package
33924 \begin_layout Standard
33925 You need to install the LaTeX-package
33929 to see the rest of this subsection in the output.
33932 \begin_layout Standard
33936 \begin_layout Plain Layout
33948 \begin_layout Subsection
33949 Text Characters in Formulas
33950 \begin_inset CommandInset label
33952 name "sub:Text-Characters-in"
33960 \begin_layout Plain Layout
33969 \begin_layout Standard
33970 In some cases you might want to insert text characters directly into formulas.
33971 When for example the centered dot · is often used in formulas like
33972 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
33975 , one would have to insert the command
33985 \begin_layout Plain Layout
33987 \begin_inset CommandInset ref
33989 reference "sub:Binary-Operators"
33998 all the time, because this character is defined in all encodings as text
34000 But the encoding can be changed by this LaTeX-preamble line:
34003 \begin_layout Standard
34008 Declare Inputtext{183}{
34018 f\SpecialChar \textcompwordmark{}
34022 \begin_layout Standard
34023 The character encoding (menu
34025 Document\SpecialChar \menuseparator
34026 Settings\SpecialChar \menuseparator
34029 ) specifies what character appears when a keyboard key is pressed.
34030 When the key for the character '·' is pressed, internally the command
34037 But this command is not available in a formula so that you would get LaTeX-erro
34039 With the changed encoding the right command is chosen automatically, depending
34040 on if the character was inserted into a formula or not.
34043 \begin_layout Standard
34044 The encoding of several characters is saved in definition files.
34045 Fore example the encoding
34049 is defined in the file
34053 that is in the installation folder of LaTeX.
34054 Encodings should only be changed via the LaTeX-preamble and not in the
34056 Otherwise own documents could not be edited by other LyX users working
34057 on other computers.
34060 \begin_layout Standard
34061 \begin_inset VSpace medskip
34064 Besides the centered dot, in this document the degree sign ° is defined
34065 with the following LaTeX-preamble line so that it can directly be inserted
34069 \begin_layout Standard
34074 DeclareInputtext{176}{
34084 f\SpecialChar \textcompwordmark{}
34088 \begin_layout Standard
34089 \begin_inset Newpage newpage
34095 \begin_layout Section
34097 Typographic Advises
34101 \begin_layout Plain Layout
34102 Typographic Advises
34110 \begin_layout Standard
34111 This section is a summary of the most important typographic rules, listed
34116 \begin_layout Plain Layout
34117 This collection was partly taken from the German semi-official dictionary
34119 \begin_inset Quotes eld
34123 \begin_inset Quotes erd
34127 \begin_inset CommandInset citation
34133 that lists some of the ISO rules.
34141 \begin_layout Itemize
34150 \begin_layout Plain Layout
34151 done with font styles, see
34152 \begin_inset CommandInset ref
34154 reference "sub:Font-Styles"
34164 \begin_inset space \thinspace{}
34168 \begin_inset Newline newline
34171 Between the value and the unit is the smallest space, see
34172 \begin_inset CommandInset ref
34174 reference "sub:Predefined-Space"
34181 \begin_layout Itemize
34182 Percent and perthousand signs are set like physical units:
34183 \begin_inset Newline newline
34187 \begin_inset space \thinspace{}
34193 \begin_layout Itemize
34194 The degree sign follows directly on the value: 15°, but not when it is used
34196 \begin_inset space \thinspace{}
34202 \begin_layout Itemize
34203 In numbers with more than four digits the smallest space is inserted before
34204 every third digit to group them:
34214 \begin_inset space \thinspace{}
34218 \begin_inset space \thinspace{}
34224 \begin_layout Itemize
34225 For dimensionings like 120×90×40
34226 \begin_inset space \thinspace{}
34229 cm the multiplication sign
34230 \begin_inset Quotes eld
34234 \begin_inset Quotes erd
34238 It is available with the LaTeX-command
34244 , but can also directly be inserted with some keyboard definitions.
34247 \begin_layout Itemize
34248 Functions with names consisting of several letters are set upright to avoid
34250 \begin_inset CommandInset ref
34252 reference "sub:Predefined-Functions"
34259 \begin_layout Itemize
34260 Indices consisting of several letters, are set upright:
34261 \begin_inset Formula $E_{\mathrm{kin}}$
34265 \begin_inset Newline newline
34268 Components of matrices are set italic:
34269 \begin_inset Formula $\hat{H}_{kl}$
34275 \begin_layout Itemize
34276 The differentiation/integration operator 'd', the Euler's number 'e', and
34277 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34281 \begin_layout Standard
34282 \begin_inset Newpage newpage
34288 \begin_layout Section
34293 \begin_layout Plain Layout
34302 \begin_layout Standard
34303 Some characters and symbols can be created with several commands.
34304 Here is a list of the synonym commands:
34307 \begin_layout Standard
34308 \begin_inset VSpace bigskip
34312 \begin_inset space \hfill{}
34316 \begin_inset Tabular
34317 <lyxtabular version="3" rows="12" columns="2">
34319 <column alignment="center" valignment="top" width="0pt">
34320 <column alignment="center" valignment="top" width="0pt">
34322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34325 \begin_layout Plain Layout
34331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34334 \begin_layout Plain Layout
34336 \begin_inset Note Note
34339 \begin_layout Plain Layout
34346 is only used as spacer.
34358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34361 \begin_layout Plain Layout
34369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34372 \begin_layout Plain Layout
34376 \begin_layout Plain Layout
34389 \begin_layout Plain Layout
34403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34406 \begin_layout Plain Layout
34414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34417 \begin_layout Plain Layout
34427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34430 \begin_layout Plain Layout
34438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34441 \begin_layout Plain Layout
34451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34454 \begin_layout Plain Layout
34462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34465 \begin_layout Plain Layout
34473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34476 \begin_layout Plain Layout
34484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34487 \begin_layout Plain Layout
34495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34498 \begin_layout Plain Layout
34506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34509 \begin_layout Plain Layout
34519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34522 \begin_layout Plain Layout
34530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34533 \begin_layout Plain Layout
34543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34546 \begin_layout Plain Layout
34554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34557 \begin_layout Plain Layout
34567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34570 \begin_layout Plain Layout
34578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34581 \begin_layout Plain Layout
34591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34594 \begin_layout Plain Layout
34602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34605 \begin_layout Plain Layout
34613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34616 \begin_layout Plain Layout
34624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34627 \begin_layout Plain Layout
34639 \begin_inset space \hfill{}
34643 \begin_inset Tabular
34644 <lyxtabular version="3" rows="12" columns="2">
34646 <column alignment="center" valignment="top" width="0pt">
34647 <column alignment="center" valignment="top" width="0pt">
34649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34652 \begin_layout Plain Layout
34658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34661 \begin_layout Plain Layout
34669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34672 \begin_layout Plain Layout
34680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34683 \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
34743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34746 \begin_layout Plain Layout
34754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34757 \begin_layout Plain Layout
34765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34768 \begin_layout Plain Layout
34776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34779 \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
34883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34886 \begin_layout Plain Layout
34894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34897 \begin_layout Plain Layout
34907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34910 \begin_layout Plain Layout
34918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34921 \begin_layout Plain Layout
34935 \begin_inset space \hfill{}
34941 \begin_layout Standard
34942 \begin_inset Newpage newpage
34948 \begin_layout Bibliography
34949 \begin_inset CommandInset bibitem
34950 LatexCommand bibitem
34962 The LaTeX Companion
34965 Addison Wesley, 2004
34968 \begin_layout Bibliography
34969 \begin_inset CommandInset bibitem
34970 LatexCommand bibitem
34976 \begin_inset CommandInset href
34979 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
34983 of LaTeX's math abilities
34986 \begin_layout Bibliography
34987 \begin_inset CommandInset bibitem
34988 LatexCommand bibitem
34993 LaTeX tips and tricks-
34994 \begin_inset CommandInset href
34997 target "http://tug.org/TeXnik/"
35004 \begin_layout Bibliography
35005 \begin_inset CommandInset bibitem
35006 LatexCommand bibitem
35012 \begin_inset CommandInset href
35015 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35023 \begin_layout Plain Layout
35035 \begin_layout Bibliography
35036 \begin_inset CommandInset bibitem
35037 LatexCommand bibitem
35043 \begin_inset CommandInset href
35046 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35050 of all symbols available with LaTeX-packages
35053 \begin_layout Bibliography
35054 \begin_inset CommandInset bibitem
35055 LatexCommand bibitem
35061 \begin_inset CommandInset href
35063 name "Documentation"
35064 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35068 of the LaTeX-package
35076 \begin_layout Plain Layout
35077 Packages ! hyperref
35085 \begin_layout Bibliography
35086 \begin_inset CommandInset bibitem
35087 LatexCommand bibitem
35093 \begin_inset CommandInset href
35096 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35107 \begin_inset CommandInset ref
35109 reference "sub:Operator-Limits"
35117 \begin_layout Plain Layout
35128 \begin_layout Bibliography
35129 \begin_inset CommandInset bibitem
35130 LatexCommand bibitem
35141 Auflage, Duden 2001
35144 \begin_layout Subsubsection*
35145 \begin_inset CommandInset index_print
35146 LatexCommand printindex