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}
74 \usepackage[samesize]{cancel}
76 % enables calculation of values,
79 % for multiple table row and column cells
86 % center multirows (e.g. in sec. 13.3)
87 \renewcommand{\multirowsetup}{\centering}
89 % define a color, used in sec.9.3
90 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
92 % declare operators (see sec. 10.4 and sec. 15.2)
93 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
94 \DeclareMathOperator{\sgn}{sgn}
96 \newcommand{\spce}{\textvisiblespace}
98 % example definitions for sec. 20.1
99 \newcommand{\gr}{\Longrightarrow}
100 \newcommand{\us}[1]{\underline{#1}}
101 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
102 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
103 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
105 % example macro from sec. 19.4
106 %\def\tagform@#1{\maketag@@@{|#1|}}
108 % macro from sec. 10.2
109 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
110 \def\mathclap {\mathpalette \mathclapinternal}
111 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
113 % redefine the greyed out note
114 \renewenvironment{lyxgreyedout}
115 {\textcolor{blue}\bgroup}{\egroup}
117 % ------------------------------------
118 % used to check for needed LaTeX packages
121 % check for package eurosym
122 % used for the Euro symbol
124 \IfFileExists{eurosym.sty}
125 {\usepackage[gennarrow]{eurosym}
126 \setboolean{eurosym}{true}}
127 {\setboolean{eurosym}{false}}
129 % needed in sec. 22.4
130 % check for package braket
132 \IfFileExists{braket.sty}
134 \setboolean{braket}{true}}
135 {\setboolean{braket}{false}}
137 % needed in sec. 22.10
138 % check for package upgreek
140 \IfFileExists{upgreek.sty}
141 {\usepackage{upgreek}
142 \setboolean{upgreek}{true}}
143 {\setboolean{upgreek}{false}}
145 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
150 \font_typewriter default
151 \font_default_family default
161 \pdf_title "LyX's Math Manual"
162 \pdf_author "LyX Team, Uwe Stöhr"
163 \pdf_subject "LyX-documentation about math"
164 \pdf_keywords "LyX, Mathed"
166 \pdf_bookmarksnumbered true
167 \pdf_bookmarksopen true
168 \pdf_bookmarksopenlevel 1
169 \pdf_breaklinks false
173 \pdf_pagebackref false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
182 \paperorientation portrait
185 \paragraph_separation skip
187 \quotes_language english
190 \paperpagestyle plain
194 \tracking_changes false
195 \output_changes false
203 LyX's detailed Math manual
211 \begin_layout Plain Layout
213 If you have comments or error corrections, please send them to the LyX Documenta
217 \begin_inset CommandInset href
219 name "lyx-docs@lists.lyx.org"
220 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
231 \begin_inset Note Note
234 \begin_layout Plain Layout
241 \begin_inset Newline newline
245 \begin_inset Newline newline
253 \begin_layout Standard
254 \begin_inset CommandInset toc
255 LatexCommand tableofcontents
262 \begin_layout Standard
263 \begin_inset Note Note
266 \begin_layout Plain Layout
267 To export this document to PDF, PS, or DVI the LaTeX-packages
280 If they are not installed you can export the document anyway but the sections
281 where the packages are required won't appear in the output.
284 \begin_layout Plain Layout
285 The latest PDF-version of this document can be found here:
286 \begin_inset Newline newline
291 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
299 \begin_layout Standard
300 \begin_inset Newpage newpage
306 \begin_layout Section
310 \begin_layout Standard
311 This document explains LyX's math features and is furthermore a collection
312 of LaTeX-commands used for mathematical characters and constructs.
313 The explanations are designed for the usage of commands.
314 It is therefore required that you have read the section
325 \begin_layout Standard
326 Most of the characters and many constructs explained in this manual are
327 also accessible via the menu
331 \SpecialChar \menuseparator
347 But everybody who has to write lots of formulas will notice that it is
348 much faster to use commands instead of the math toolbar.
349 Therefore this manual is focused on commands but also mentions the correspondin
350 g toolbar buttons when available.
353 \begin_layout Standard
354 If not specially mentioned the commands are only available within formulas.
355 To be able to use all commands explained in this document, the option
359 must be used in the document settings (menu
361 Document\SpecialChar \menuseparator
362 Settings\SpecialChar \menuseparator
373 \begin_layout Plain Layout
376 Use AMS math package automatically
382 \begin_layout Plain Layout
391 -math when math constructs are found that are supported by LyX.
399 \begin_layout Standard
400 This document doesn't list all
404 \begin_layout Plain Layout
417 \begin_layout Plain Layout
422 \begin_layout Plain Layout
431 -math commands is in the file
434 \begin_inset CommandInset href
437 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
443 , which is part of every LaTeX standard installation.
448 for lucidity reasons.
451 \begin_layout Section
455 \begin_layout Standard
456 To create an inline formula
460 \begin_layout Plain Layout
466 that is embedded into a text line, press
470 or the toolbar button
471 \begin_inset Graphics
472 filename ../images/math-mode.png
478 \begin_inset Newline newline
481 To create a display style formula
485 \begin_layout Plain Layout
486 Formula ! display style
491 that will appear bigger and in an own paragraph, press
498 \begin_layout Standard
499 To change a display style formula to an inline formula, set the cursor into
500 the formula and press
506 Edit\SpecialChar \menuseparator
507 Math\SpecialChar \menuseparator
511 The same way is used to change an inline formula to a display style formula.
514 \begin_layout Standard
515 To display parts of an inline formula in the size of a display style formula,
524 \begin_layout Plain Layout
535 Then a new blue box appears in which the desired formula part is inserted.
538 \begin_layout Standard
539 Only inline formulas are allowed inside tables.
542 \begin_layout Standard
547 can be turned on in the menu
549 View\SpecialChar \menuseparator
553 When you click there on
554 \begin_inset Quotes eld
558 \begin_inset Quotes erd
561 the toolbar will be shown permanently at the bottom; this state is visualized
566 menu with a checkmark.
567 When you click in this state again on
568 \begin_inset Quotes eld
572 \begin_inset Quotes erd
583 is only shown when the cursor is within a formula; this state is visualized
584 by the renaming of the menu entry from
585 \begin_inset Quotes eld
589 \begin_inset Quotes erd
593 \begin_inset Quotes eld
601 \begin_inset Quotes erd
607 \begin_layout Standard
612 \begin_layout Plain Layout
618 is invoked by pressing the toolbar button
619 \begin_inset Graphics
620 filename ../images/ert-insert.png
627 Insert\SpecialChar \menuseparator
632 \begin_layout Plain Layout
646 \begin_inset Note Note
649 \begin_layout Plain Layout
650 In LyX there are three
651 \begin_inset Quotes eld
655 \begin_inset Quotes erd
658 that appear in the output with sub- and superscript letters: TeX, LaTeX,
662 \begin_layout Plain Layout
663 To avoid that these names are recognized as proper names, a TeX-brace pair
672 \begin_layout Standard
673 To change the LaTeX-preamble
677 \begin_layout Plain Layout
685 Document\SpecialChar \menuseparator
686 Settings\SpecialChar \menuseparator
691 \begin_layout Plain Layout
707 \begin_layout Standard
708 To edit matrices, case differentiations, and multiline formulas subsequently,
711 Edit\SpecialChar \menuseparator
716 Edit\SpecialChar \menuseparator
718 \begin_inset space \thinspace{}
722 \begin_inset space \thinspace{}
732 When lines and columns are swapped via the menu, the column or line where
733 the cursor is in is exchanged with the column to the right or the line
735 Is the cursor in the last column or row, the exchange is done with the
736 column to the left or the line above.
739 \begin_layout Standard
740 To write text in formulas
744 \begin_layout Plain Layout
745 For multiline formulas the command
752 \begin_inset CommandInset ref
754 reference "sub:Text-in-multiline"
771 \begin_layout Plain Layout
781 \begin_layout Plain Layout
788 This mode is invoked with the the shortcut
796 or by the insertion of the command
804 \begin_layout Plain Layout
815 The text appears black in LyX and can therefore be distinguished from the
816 other formula parts that appear blue.
817 In the output mathematical text is set upright, in contrary to other formula
821 \begin_layout Subsection*
825 \begin_layout Standard
826 Most of the LaTeX-commands for math constructs have the following scheme:
829 \begin_layout Standard
845 \begin_layout Standard
846 A command starts always with a backslash
847 \begin_inset Quotes gld
857 \begin_inset Quotes grd
861 To omit optional arguments, also omit the associated brackets.
862 The braces around the required arguments are named in this document as
867 \begin_layout Plain Layout
874 If you add in a formula a left brace to a command name, LyX creates automatical
876 In all other cases TeX-braces are created in formulas with the command
884 TeX-braces appear red in LyX, in contrary to normal braces that appear
886 In TeX-mode no command is needed to get TeX-braces.
887 TeX-braces don't appear in the output.
890 \begin_layout Standard
891 When commands without arguments, like commands for symbols are entered in
892 TeX-mode, a space character must
896 be behind the command to end it.
897 This space doesn't appear in the output.
898 When the space should appear in the output, the space must be followed
899 by a protected space in normal text.
902 \begin_layout Standard
903 A protected space is inserted with
910 \begin_layout Subsection*
911 \begin_inset Newpage newpage
917 \begin_layout Itemize
922 \begin_layout Plain Layout
923 This visible space character can be created with the command
933 \begin_layout Plain Layout
941 , inserted in TeX-mode.
950 \begin_layout Plain Layout
963 denotes a space character to be input.
966 \begin_layout Itemize
968 \begin_inset Formula $\to$
971 denotes the usage of the corresponding arrow key on the keyboard.
974 \begin_layout Subsection*
978 \begin_layout Standard
980 \begin_inset Float table
986 \begin_layout Plain Layout
990 \begin_layout Plain Layout
991 \begin_inset CommandInset label
993 name "tab:Available-units"
1005 \begin_layout Plain Layout
1007 \begin_inset Tabular
1008 <lyxtabular version="3" rows="13" columns="2">
1010 <column alignment="center" valignment="top" width="0">
1011 <column alignment="center" valignment="top" width="0">
1013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1016 \begin_layout Plain Layout
1022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1025 \begin_layout Plain Layout
1033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1036 \begin_layout Plain Layout
1042 <cell alignment="center" valignment="top" topline="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
1087 \begin_inset space \thinspace{}
1091 \begin_inset space \thinspace{}
1101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1104 \begin_layout Plain Layout
1110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1113 \begin_layout Plain Layout
1115 \begin_inset space \thinspace{}
1119 \begin_inset space \thinspace{}
1129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1132 \begin_layout Plain Layout
1138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1141 \begin_layout Plain Layout
1143 \begin_inset space \thinspace{}
1147 \begin_inset space \thinspace{}
1157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1160 \begin_layout Plain Layout
1166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1169 \begin_layout Plain Layout
1171 \begin_inset space \thinspace{}
1175 \begin_inset space \thinspace{}
1185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1188 \begin_layout Plain Layout
1194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1197 \begin_layout Plain Layout
1199 \begin_inset space \thinspace{}
1203 \begin_inset space \thinspace{}
1213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1216 \begin_layout Plain Layout
1222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1225 \begin_layout Plain Layout
1227 \begin_inset space \thinspace{}
1231 \begin_inset Formula $\approx$
1235 \begin_inset space \thinspace{}
1245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1248 \begin_layout Plain Layout
1254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1257 \begin_layout Plain Layout
1259 \begin_inset space \thinspace{}
1263 \begin_inset space \thinspace{}
1273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1276 \begin_layout Plain Layout
1282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1285 \begin_layout Plain Layout
1289 \begin_inset Quotes eld
1295 \begin_inset Quotes erd
1305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1308 \begin_layout Plain Layout
1314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1317 \begin_layout Plain Layout
1319 \begin_inset Quotes eld
1327 \begin_inset Quotes erd
1337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1340 \begin_layout Plain Layout
1346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1349 \begin_layout Plain Layout
1351 \begin_inset space \thinspace{}
1355 \begin_inset Formula $\nicefrac{1}{18}$
1359 \begin_inset space \thinspace{}
1380 \begin_layout Standard
1381 \begin_inset Newpage newpage
1387 \begin_layout Section
1391 \begin_layout Subsection
1396 \begin_layout Plain Layout
1406 \begin_layout Plain Layout
1416 \begin_layout Plain Layout
1421 \begin_layout Plain Layout
1432 \begin_layout Plain Layout
1448 \begin_layout Plain Layout
1453 \begin_layout Plain Layout
1464 \begin_layout Plain Layout
1479 \begin_layout Standard
1480 Indices are created with an underscore
1481 \begin_inset Quotes eld
1485 \begin_inset Quotes erd
1488 or via the math toolbar button
1489 \begin_inset Graphics
1490 filename ../images/math-subscript.png
1495 , exponents with a caret
1496 \begin_inset Quotes eld
1500 \begin_inset Quotes erd
1503 or via the math toolbar button
1504 \begin_inset Graphics
1505 filename ../images/math-superscript.png
1513 \begin_layout Standard
1515 \begin_inset Tabular
1516 <lyxtabular version="3" rows="4" columns="2">
1518 <column alignment="center" valignment="top" width="0pt">
1519 <column alignment="center" valignment="top" width="0pt">
1521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1524 \begin_layout Plain Layout
1530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1533 \begin_layout Plain Layout
1535 \begin_inset Note Note
1538 \begin_layout Plain Layout
1545 is only used as spacer.
1557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1560 \begin_layout Plain Layout
1566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1569 \begin_layout Plain Layout
1570 \begin_inset Formula $B_{V}$
1580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1583 \begin_layout Plain Layout
1589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1592 \begin_layout Plain Layout
1593 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1606 \begin_layout Plain Layout
1611 \begin_layout Plain Layout
1625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1628 \begin_layout Plain Layout
1629 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1645 \begin_layout Standard
1646 As the caret is in some languages an accent, vowels will be accentuated
1647 in this case and not set as exponents
1651 \begin_layout Plain Layout
1652 Depending on the used keyboard settings this can also happen for other character
1659 To get in this case exponents, press
1663 after the caret as in the last example.
1666 \begin_layout Subsection
1668 \begin_inset CommandInset label
1670 name "sub:Fractions"
1678 \begin_layout Plain Layout
1687 \begin_layout Standard
1688 Fractions are generated with the command
1698 \begin_layout Plain Layout
1706 or via the math toolbar button
1707 \begin_inset Graphics
1708 filename ../images/math/frac.png
1714 The font size is adjusted automatically, depending on whether the fraction
1715 is in an inline or display style formula.
1716 With the math toolbar button
1717 \begin_inset Graphics
1718 filename ../images/math/frac-square.png
1723 you can select different fraction types.
1726 \begin_layout Standard
1735 \begin_layout Plain Layout
1745 a fraction can be created that has in any case the size of a display style
1755 \begin_layout Plain Layout
1765 the fraction appears always with the size of an inline formula.
1769 \begin_layout Standard
1770 A line with the fraction
1771 \begin_inset Formula $\frac{1}{2}$
1774 that was created with the command
1783 \begin_layout Standard
1784 A line with the fraction
1785 \begin_inset Formula $\dfrac{1}{2}$
1788 that was created with the command
1797 \begin_layout Standard
1799 \begin_inset Tabular
1800 <lyxtabular version="3" rows="4" columns="2">
1802 <column alignment="center" valignment="top" width="0pt">
1803 <column alignment="center" valignment="top" width="0pt">
1805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1808 \begin_layout Plain Layout
1814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1817 \begin_layout Plain Layout
1819 \begin_inset Note Note
1822 \begin_layout Plain Layout
1829 is only used as spacer.
1841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1844 \begin_layout Plain Layout
1851 \begin_layout Plain Layout
1861 \begin_inset Formula $\downarrow$
1869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1872 \begin_layout Plain Layout
1873 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1886 \begin_layout Plain Layout
1893 \begin_layout Plain Layout
1903 \begin_inset Formula $\downarrow$
1911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1914 \begin_layout Plain Layout
1915 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1928 \begin_layout Plain Layout
1935 \begin_layout Plain Layout
1948 \begin_layout Plain Layout
1963 \begin_layout Plain Layout
1973 \begin_inset Formula $\downarrow$
1977 \begin_inset Formula $\downarrow\downarrow$
1985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1988 \begin_layout Plain Layout
1989 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2005 \begin_layout Standard
2006 \begin_inset VSpace bigskip
2010 \begin_inset Newpage newpage
2013 For nested fractions the command
2023 \begin_layout Plain Layout
2033 \begin_inset VSpace -3mm
2039 \begin_layout Standard
2040 \begin_inset Formula \begin{align*}
2041 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2042 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2049 \begin_layout Standard
2050 The command for the example above is:
2053 \begin_layout Standard
2059 \begin_inset Formula $\to$
2069 \begin_inset Formula $\to$
2075 \begin_inset Formula $\to\to$
2083 \begin_layout Standard
2084 \begin_inset VSpace medskip
2090 \begin_layout Standard
2097 sets the fraction always in the size of a displayed formula, also when
2098 it is part of another fraction.
2105 has the following command scheme:
2108 \begin_layout Standard
2113 cfrac[numerator position]{numerator}{denominator}
2116 \begin_layout Standard
2117 The numerator position can be
2130 l or r aligns the numerator to the left or right, resp.
2131 \begin_inset space ~
2134 with the fraction stroke.
2139 or no position is given, the numerator appears centered.
2140 These fractions demonstrate the different alignments:
2141 \begin_inset Newline newline
2147 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2151 \begin_inset Formula $\cfrac{A}{B+C}$
2155 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2161 \begin_layout Standard
2162 \begin_inset VSpace medskip
2165 It is often advantageous to combine
2178 \begin_inset Formula \[
2179 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2186 \begin_layout Standard
2187 For inline fractions with a sloped fraction stroke you can use the command
2198 \begin_layout Plain Layout
2207 \begin_inset Formula $\nicefrac{5}{31}$
2220 \begin_layout Plain Layout
2229 \begin_inset Formula $\unitfrac{5}{31}$
2232 There is furthermore the command
2238 that offers to write a fraction in combination with a number:
2239 \begin_inset Formula $\unitfrac[2]{1}{3}$
2243 \begin_inset Newline newline
2252 is not a real LaTeX command but the command
2253 \begin_inset Newline newline
2260 unitfrac[number]{numerator}{denominator}
2262 , therefore you cannot use it in TeX code.
2265 \begin_layout Standard
2266 How to define own fractions where the fraction stroke can be changed, is
2268 \begin_inset CommandInset ref
2270 reference "sub:Self-defined-Fractions"
2277 \begin_layout Subsection
2282 \begin_layout Plain Layout
2291 \begin_layout Standard
2292 Square roots are created with
2302 \begin_layout Plain Layout
2310 or the math toolbar button
2311 \begin_inset Graphics
2312 filename ../images/math/sqrt.png
2317 , all other roots with the command
2327 \begin_layout Plain Layout
2335 or with the math toolbar button
2336 \begin_inset Graphics
2337 filename ../images/math/root.png
2345 \begin_layout Standard
2347 \begin_inset Tabular
2348 <lyxtabular version="3" rows="3" columns="2">
2350 <column alignment="center" valignment="top" width="0pt">
2351 <column alignment="center" valignment="top" width="0pt">
2353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2356 \begin_layout Plain Layout
2362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2365 \begin_layout Plain Layout
2367 \begin_inset Note Note
2370 \begin_layout Plain Layout
2377 is only used as spacer.
2389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2392 \begin_layout Plain Layout
2399 \begin_layout Plain Layout
2413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2416 \begin_layout Plain Layout
2417 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2427 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2430 \begin_layout Plain Layout
2437 \begin_layout Plain Layout
2447 \begin_inset Formula $\downarrow$
2455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2458 \begin_layout Plain Layout
2459 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2475 \begin_layout Standard
2476 A square root can also be created with
2482 when the root index field is left empty.
2485 \begin_layout Standard
2486 With certain indices the distance to the root is too small, like in this
2488 \begin_inset Formula $\sqrt[\beta]{B}$
2492 \begin_inset Newline newline
2496 \begin_inset Formula $\beta$
2500 To avoid this, the commands
2510 \begin_layout Plain Layout
2528 \begin_layout Plain Layout
2536 are used with the following scheme:
2539 \begin_layout Standard
2553 \begin_layout Standard
2554 Distance is the number of Big Points (unit bp;
2555 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2558 ), that the index should be moved to the left or top, resp..
2559 The commands are written to the index.
2560 This way the command
2561 \begin_inset Newline newline
2571 \begin_inset Formula $\to$
2577 \begin_inset Formula $\to$
2586 \begin_layout Plain Layout
2596 \begin_inset Formula $\to$
2600 \begin_inset Newline newline
2605 produces a correct typeset formula:
2606 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2612 \begin_layout Subsection
2613 Binomial Coefficients
2617 \begin_layout Plain Layout
2618 Binomial coefficients
2626 \begin_layout Standard
2627 Binomial coefficients are inserted with the command
2637 \begin_layout Plain Layout
2645 or with the submenu of the math toolbar button
2646 \begin_inset Graphics
2647 filename ../images/math/frac-square.png
2653 Analog to fractions (
2673 \begin_layout Plain Layout
2693 \begin_layout Plain Layout
2702 For other brackets around binomial coeficients there are the commands
2712 \begin_layout Plain Layout
2730 \begin_layout Plain Layout
2741 \begin_layout Standard
2743 \begin_inset Tabular
2744 <lyxtabular version="3" rows="6" columns="2">
2746 <column alignment="center" valignment="top" width="0pt">
2747 <column alignment="center" valignment="top" width="0pt">
2749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2752 \begin_layout Plain Layout
2758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2761 \begin_layout Plain Layout
2763 \begin_inset Note Note
2766 \begin_layout Plain Layout
2773 is only used as spacer.
2785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2788 \begin_layout Plain Layout
2795 \begin_layout Plain Layout
2805 \begin_inset Formula $\downarrow$
2813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2816 \begin_layout Plain Layout
2817 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2830 \begin_layout Plain Layout
2837 \begin_layout Plain Layout
2847 \begin_inset Formula $\downarrow$
2855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2858 \begin_layout Plain Layout
2859 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2872 \begin_layout Plain Layout
2879 \begin_layout Plain Layout
2889 \begin_inset Formula $\downarrow$
2897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2900 \begin_layout Plain Layout
2901 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2914 \begin_layout Plain Layout
2921 \begin_layout Plain Layout
2931 \begin_inset Formula $\downarrow$
2939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2942 \begin_layout Plain Layout
2943 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2956 \begin_layout Plain Layout
2963 \begin_layout Plain Layout
2973 \begin_inset Formula $\downarrow$
2981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2984 \begin_layout Plain Layout
2985 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3001 \begin_layout Subsection
3002 Case Differentiations
3006 \begin_layout Plain Layout
3007 Case differentiations
3015 \begin_layout Standard
3017 \begin_inset Tabular
3018 <lyxtabular version="3" rows="3" columns="2">
3020 <column alignment="center" valignment="top" width="0pt">
3021 <column alignment="center" valignment="top" width="0pt">
3023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3026 \begin_layout Plain Layout
3032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3035 \begin_layout Plain Layout
3043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3046 \begin_layout Plain Layout
3053 \begin_layout Plain Layout
3063 \begin_inset Formula $\to$
3070 \begin_layout Plain Layout
3083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3086 \begin_layout Plain Layout
3087 \begin_inset Formula $\begin{cases}
3098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3101 \begin_layout Plain Layout
3108 \begin_layout Plain Layout
3122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3125 \begin_layout Plain Layout
3126 \begin_inset Formula $\begin{cases}
3127 A & \textrm{for }x>0\\
3128 B & \textrm{for }x=0\end{cases}$
3144 \begin_layout Standard
3151 or the usage of the math toolbar button
3152 \begin_inset Graphics
3153 filename ../images/math/cases.png
3158 you can create new lines with the shortcut
3162 or the table toolbar button
3163 \begin_inset Graphics
3164 filename ../images/tabular-feature_append-row.png
3172 \begin_layout Standard
3179 is also available via the menu
3181 Insert\SpecialChar \menuseparator
3182 Math\SpecialChar \menuseparator
3188 \begin_layout Subsection
3193 \begin_layout Plain Layout
3202 \begin_layout Standard
3213 \begin_layout Plain Layout
3221 every character can be displayed canceled.
3222 The characters are quasi accentuated by a slash.
3225 \begin_layout Standard
3227 \begin_inset Tabular
3228 <lyxtabular version="3" rows="4" columns="2">
3230 <column alignment="center" valignment="top" width="0pt">
3231 <column alignment="center" valignment="top" width="0pt">
3233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3236 \begin_layout Plain Layout
3242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3245 \begin_layout Plain Layout
3253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3256 \begin_layout Plain Layout
3264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3267 \begin_layout Plain Layout
3268 \begin_inset Formula $\not=$
3278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3281 \begin_layout Plain Layout
3291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3294 \begin_layout Plain Layout
3295 \begin_inset Formula $\not\le$
3305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3308 \begin_layout Plain Layout
3318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3321 \begin_layout Plain Layout
3322 \begin_inset Formula $\not\parallel$
3338 \begin_layout Standard
3339 The last example shows, that not all negations look good.
3340 Therefore there are for some negations special commands (see
3341 \begin_inset CommandInset ref
3343 reference "sub:Mathematical-Symbols"
3348 \begin_inset CommandInset ref
3350 reference "sec:Relations"
3357 \begin_layout Subsection
3359 \begin_inset CommandInset label
3361 name "sub:Placeholders"
3369 \begin_layout Plain Layout
3379 \begin_layout Plain Layout
3380 Chemical characters ! Isotopes
3389 \begin_layout Plain Layout
3394 \begin_layout Plain Layout
3405 \begin_layout Plain Layout
3420 \begin_layout Standard
3422 \begin_inset space \thinspace{}
3426 \begin_inset space ~
3433 \begin_layout Plain Layout
3434 More about chemical symbols is written in
3435 \begin_inset CommandInset ref
3437 reference "sub:Chemical-Symbols-and"
3446 the following problem occurs:
3449 \begin_layout Standard
3451 \begin_inset Tabular
3452 <lyxtabular version="3" rows="2" columns="2">
3454 <column alignment="center" valignment="top" width="0pt">
3455 <column alignment="center" valignment="top" width="0pt">
3457 <cell alignment="center" valignment="top" usebox="none">
3460 \begin_layout Plain Layout
3461 Indices created with sub- and superscripts:
3466 <cell alignment="center" valignment="top" usebox="none">
3469 \begin_layout Plain Layout
3470 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3480 <cell alignment="center" valignment="top" usebox="none">
3483 \begin_layout Plain Layout
3489 <cell alignment="center" valignment="top" usebox="none">
3492 \begin_layout Plain Layout
3493 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3507 \begin_inset Note Note
3510 \begin_layout Plain Layout
3517 is only used as spacer.
3525 \begin_layout Standard
3526 The shorter index is by default placed below or above the first character
3527 of the longer index.
3528 To avoid this there is the command
3538 \begin_layout Plain Layout
3546 or the math toolbar button
3547 \begin_inset space \thinspace{}
3554 \begin_layout Plain Layout
3555 can be found in the submenu of the toolbar button
3556 \begin_inset Graphics
3557 filename ../images/math/space.png
3568 \begin_inset Graphics
3569 filename ../images/math/phantom.png
3574 that creates one or more phantom characters.
3581 a small blue box appears that is superposed with two red arrows.
3582 The arrows indicate that the complete width and height of the box content
3583 will be created as placeholder.
3584 Phantom characters are accordingly placeholders with the size of the characters.
3587 \begin_layout Standard
3589 \begin_inset Tabular
3590 <lyxtabular version="3" rows="4" columns="2">
3592 <column alignment="center" valignment="top" width="0">
3593 <column alignment="center" valignment="top" width="0">
3595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3598 \begin_layout Plain Layout
3604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3607 \begin_layout Plain Layout
3609 \begin_inset Note Note
3612 \begin_layout Plain Layout
3619 is only used as spacer.
3631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3634 \begin_layout Plain Layout
3639 \begin_layout Plain Layout
3654 \begin_layout Plain Layout
3664 \begin_inset Formula $\to$
3671 \begin_layout Plain Layout
3685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3688 \begin_layout Plain Layout
3689 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3702 \begin_layout Plain Layout
3707 \begin_layout Plain Layout
3722 \begin_layout Plain Layout
3732 \begin_inset Formula $\to$
3739 \begin_layout Plain Layout
3753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3756 \begin_layout Plain Layout
3757 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3770 \begin_layout Plain Layout
3777 \begin_layout Plain Layout
3792 \begin_layout Plain Layout
3802 \begin_inset Formula $\to$
3809 \begin_layout Plain Layout
3823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3826 \begin_layout Plain Layout
3827 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3843 \begin_layout Standard
3844 Furthermore there are the commands
3854 \begin_layout Plain Layout
3863 \begin_inset space ~
3867 \begin_inset Graphics
3868 filename ../images/math/vphantom.png
3883 \begin_layout Plain Layout
3892 \begin_inset space ~
3896 \begin_inset Graphics
3897 filename ../images/math/hphantom.png
3909 creates only space for the maximal height of the characters in the box
3910 but not for its width.
3917 creates only space for the width of the box content.
3918 Therefore the boxes of both commands have only one red arrow.
3921 \begin_layout Standard
3932 \begin_layout Plain Layout
3947 space for the height of the integral sign,
3951 \begin_layout Plain Layout
3958 creates an integral sign, see
3959 \begin_inset CommandInset ref
3961 reference "sub:Big-Operators"
3970 because this is the larger character.
3971 An example application is in
3972 \begin_inset CommandInset ref
3974 reference "sub:Multiline-Brackets"
3981 \begin_layout Subsection
3986 \begin_layout Plain Layout
3996 \begin_layout Plain Layout
3997 Formula ! underlined
4005 \begin_layout Standard
4007 \begin_inset Tabular
4008 <lyxtabular version="3" rows="4" columns="2">
4010 <column alignment="center" valignment="top" width="0pt">
4011 <column alignment="center" valignment="top" width="0pt">
4013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4016 \begin_layout Plain Layout
4022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4025 \begin_layout Plain Layout
4027 \begin_inset Note Note
4030 \begin_layout Plain Layout
4037 is only used as spacer.
4049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4052 \begin_layout Plain Layout
4059 \begin_layout Plain Layout
4072 \begin_layout Plain Layout
4085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4088 \begin_layout Plain Layout
4089 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4099 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4102 \begin_layout Plain Layout
4109 \begin_layout Plain Layout
4122 \begin_layout Plain Layout
4135 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4138 \begin_layout Plain Layout
4139 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4152 \begin_layout Plain Layout
4159 \begin_layout Plain Layout
4174 \begin_layout Plain Layout
4188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4191 \begin_layout Plain Layout
4192 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4208 \begin_layout Standard
4209 In the last example it doesn't matter if first
4224 \begin_layout Standard
4225 To double underline e.
4226 \begin_inset space \thinspace{}
4239 \begin_layout Standard
4240 It is possible to place up to 6 lines above or below characters.
4243 \begin_layout Standard
4244 \begin_inset VSpace bigskip
4247 Custom lines can be created using the command
4257 \begin_layout Plain Layout
4265 which has the following scheme:
4268 \begin_layout Standard
4273 rule[vertical offset]{length}{thickness}
4276 \begin_layout Standard
4277 The optional vertical offset shifts the line upwards (or downwards, when
4278 the value is negative).
4280 \begin_inset CommandInset ref
4282 reference "tab:Available-units"
4286 can be used for the values.
4287 Here are two example lines created with the commands
4288 \begin_inset Newline newline
4295 rule[-2ex]{3cm}{2pt}
4306 \begin_layout Standard
4308 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4314 \begin_layout Standard
4321 can also be used for text when it is inserted in TeX-mode.
4324 \begin_layout Subsection
4326 \begin_inset CommandInset label
4336 \begin_layout Plain Layout
4345 \begin_layout Standard
4346 There are different types of ellipses available.
4350 \begin_layout Plain Layout
4351 In the math toolbar in the submenu of the button
4352 \begin_inset Graphics
4353 filename ../images/math/ldots.png
4363 For listings dots at the baseline are used (
4373 \begin_layout Plain Layout
4381 ), while for operations dots are needed that are on the same height as the
4392 \begin_layout Plain Layout
4401 When using the command
4411 \begin_layout Plain Layout
4419 , LaTeX decides on the basis of the next character what type is used.
4422 \begin_layout Standard
4424 \begin_inset Tabular
4425 <lyxtabular version="3" rows="8" columns="2">
4427 <column alignment="center" valignment="top" width="0pt">
4428 <column alignment="center" valignment="top" width="0pt">
4430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4433 \begin_layout Plain Layout
4439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4442 \begin_layout Plain Layout
4450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4453 \begin_layout Plain Layout
4458 \begin_layout Plain Layout
4473 \begin_layout Plain Layout
4487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4490 \begin_layout Plain Layout
4491 \begin_inset Formula $A_{1},\dots,A_{n}$
4501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4504 \begin_layout Plain Layout
4509 \begin_layout Plain Layout
4524 \begin_layout Plain Layout
4538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4541 \begin_layout Plain Layout
4542 \begin_inset Formula $A_{1}+\dots+A_{n}$
4552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4555 \begin_layout Plain Layout
4560 \begin_layout Plain Layout
4575 \begin_layout Plain Layout
4589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4592 \begin_layout Plain Layout
4593 \begin_inset Formula $A_{1},\ldots,A_{n}$
4603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4606 \begin_layout Plain Layout
4611 \begin_layout Plain Layout
4626 \begin_layout Plain Layout
4640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4643 \begin_layout Plain Layout
4644 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4657 \begin_layout Plain Layout
4665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4668 \begin_layout Plain Layout
4669 \begin_inset Formula $\vdots$
4679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4682 \begin_layout Plain Layout
4690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4693 \begin_layout Plain Layout
4694 \begin_inset Formula $\ddots$
4704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4707 \begin_layout Plain Layout
4709 \begin_inset space \thinspace{}
4712 matrix with the different dots
4717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4720 \begin_layout Plain Layout
4721 \begin_inset Formula $\begin{array}{ccc}
4722 A_{11} & \cdots & A_{1m}\\
4723 \vdots & \ddots & \vdots\\
4724 A_{n1} & \cdots & A_{nm}\end{array}$
4740 \begin_layout Standard
4741 The ellipses available in menu
4743 Insert\SpecialChar \menuseparator
4745 \begin_inset space ~
4759 \begin_layout Standard
4760 \begin_inset VSpace medskip
4763 Specially for matrices there are ellipses that span over several columns.
4764 They are created with the command
4774 \begin_layout Plain Layout
4782 , that has the following scheme:
4785 \begin_layout Standard
4790 hdotsfor[distance]{number of columns}
4793 \begin_layout Standard
4794 The number of columns specifies how many columns should be spanned.
4795 Distance is a factor for the distance between the dots.
4798 \begin_layout Standard
4799 In the following matrix the command
4805 was inserted in the first box of the second line, to get an ellipsis with
4806 a dot distance twice as long as with the command
4813 \begin_inset Formula \[
4814 \left(\begin{array}{cccc}
4817 q & w & e & r\end{array}\right)\]
4821 Note that the matrix fields that should be spanned must be empty, otherwise
4822 you get LaTeX-errors.
4825 \begin_layout Standard
4826 \begin_inset VSpace bigskip
4829 Furthermore you can fill with the command
4839 \begin_layout Plain Layout
4847 the rest of a line with dots.
4848 The effect of these commands is the same like with
4855 \begin_inset CommandInset ref
4857 reference "sub:Variable-Space"
4864 \begin_layout Standard
4865 For example the command
4873 \begin_layout Plain Layout
4887 \begin_layout Standard
4888 \begin_inset Formula $A\dotfill B$
4894 \begin_layout Standard
4901 there is for a line the command
4911 \begin_layout Plain Layout
4922 \begin_layout Standard
4923 \begin_inset Formula $A\hrulefill B$
4929 \begin_layout Standard
4930 To use the commands for text, they have to be inserted in TeX-mode.
4933 \begin_layout Section
4935 \begin_inset CommandInset label
4945 \begin_layout Plain Layout
4954 \begin_layout Standard
4955 Matrices can be inserted via the math toolbar button
4956 \begin_inset Graphics
4957 filename ../images/dialog-show_mathmatrix.png
4964 Insert\SpecialChar \menuseparator
4965 Math\SpecialChar \menuseparator
4969 You will be asked for the number of matrix columns and rows, and the alignment.
4970 The vertical alignment is hereby only of importance for matrices in inline
4974 \begin_layout Standard
4975 The first matrix is top
4976 \begin_inset Formula $\begin{array}[t]{cccc}
4979 C & F & I & L\end{array}$
4983 \begin_inset Formula $\begin{array}{cccc}
4986 C & F & I & L\end{array}$
4989 , and the third bottom
4990 \begin_inset Formula $\begin{array}[b]{cccc}
4993 C & F & I & L\end{array}$
4999 \begin_layout Standard
5000 The horizontal alignment specifies how the column entries should be aligned.
5001 It is set by entering a letter for every column.
5006 denotes left aligned,
5015 To create for example a 4
5020 \begin_inset space ~
5023 matrix where the first column is left aligned, the second and third are
5024 centered, and the last one is right aligned, one enters for the horizontal
5030 Normally are in a matrix all columns centered, therefore the default is
5031 for every column is a
5038 \begin_layout Standard
5039 Horizontal alignment:
5042 \begin_layout Standard
5048 \begin_inset Formula $\begin{array}{lll}
5051 C & F & 10000\end{array}$
5059 \begin_inset Formula $\begin{array}{ccc}
5062 C & F & 10000\end{array}$
5070 \begin_inset Formula $\begin{array}{rrr}
5073 C & F & 10000\end{array}$
5079 \begin_layout Standard
5080 To add or delete rows and columns subsequently, the math toolbar buttons
5082 \begin_inset Graphics
5083 filename ../images/tabular-feature_append-row.png
5089 \begin_inset Graphics
5090 filename ../images/tabular-feature_delete-row.png
5096 \begin_inset space \thinspace{}
5101 Edit\SpecialChar \menuseparator
5105 New rows can also be created with
5112 \begin_layout Standard
5113 \begin_inset VSpace bigskip
5116 Parentheses around a matrix can can either be created with the commands
5127 \begin_layout Plain Layout
5145 \begin_layout Plain Layout
5156 \begin_inset space ~
5162 \begin_inset CommandInset ref
5164 reference "sub:Automatic-Bracket-Size"
5168 , or by using the following commands:
5169 \begin_inset VSpace medskip
5175 \begin_layout Standard
5176 \begin_inset space \hfill{}
5180 \begin_inset Tabular
5181 <lyxtabular version="3" rows="4" columns="2">
5183 <column alignment="center" valignment="top" width="0">
5184 <column alignment="center" valignment="top" width="0">
5186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5189 \begin_layout Plain Layout
5195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5198 \begin_layout Plain Layout
5200 \begin_inset Note Note
5203 \begin_layout Plain Layout
5210 is only used as spacer.
5222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5225 \begin_layout Plain Layout
5232 \begin_layout Plain Layout
5246 \begin_inset space \thinspace{}
5254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5257 \begin_layout Plain Layout
5258 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5259 0 & \textrm{-}\mathrm{i}\\
5260 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5273 \begin_layout Plain Layout
5280 \begin_layout Plain Layout
5294 \begin_inset space \thinspace{}
5302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5305 \begin_layout Plain Layout
5306 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5307 0 & \textrm{-}\mathrm{i}\\
5308 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5321 \begin_layout Plain Layout
5328 \begin_layout Plain Layout
5342 \begin_inset space \thinspace{}
5350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5353 \begin_layout Plain Layout
5354 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5355 0 & \textrm{-}\mathrm{i}\\
5356 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5370 \begin_inset space \hfill{}
5374 \begin_inset Tabular
5375 <lyxtabular version="3" rows="4" columns="2">
5377 <column alignment="center" valignment="top" width="0">
5378 <column alignment="center" valignment="top" width="0">
5380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5383 \begin_layout Plain Layout
5389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5392 \begin_layout Plain Layout
5400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5403 \begin_layout Plain Layout
5410 \begin_layout Plain Layout
5424 \begin_inset space \thinspace{}
5432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5435 \begin_layout Plain Layout
5436 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5437 0 & \textrm{-}\mathrm{i}\\
5438 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5451 \begin_layout Plain Layout
5458 \begin_layout Plain Layout
5472 \begin_inset space \thinspace{}
5480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5483 \begin_layout Plain Layout
5484 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5485 0 & \textrm{-}\mathrm{i}\\
5486 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5499 \begin_layout Plain Layout
5506 \begin_layout Plain Layout
5520 \begin_inset space \thinspace{}
5528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5531 \begin_layout Plain Layout
5532 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5533 0 & \textrm{-}\mathrm{i}\\
5534 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5548 \begin_inset space \hfill{}
5554 \begin_layout Standard
5555 \begin_inset VSpace medskip
5559 \begin_inset space \thinspace{}
5563 \begin_inset space ~
5572 is inserted, a blue box appears between two vertical lines where the matrix
5576 \begin_layout Standard
5577 \begin_inset VSpace bigskip
5580 As all multiline formulas are matrices, the length
5590 \begin_layout Plain Layout
5598 that is described in
5599 \begin_inset CommandInset ref
5601 reference "sub:Column-Separation"
5605 can also be used to change the column separation of matrices.
5608 \begin_layout Standard
5609 To change the row separation, the command
5619 \begin_layout Plain Layout
5628 It is used as follows:
5631 \begin_layout Standard
5638 arraystretch}{stretch factor}
5642 \begin_layout Plain Layout
5653 \begin_layout Standard
5660 assigns the stretch factor to the predefined command
5668 \begin_inset space \thinspace{}
5672 \begin_inset space ~
5675 the row separation, use the factor 2.
5676 This is then used for all following matrices.
5677 To go back to the original separation, assign the factor 1 to
5686 \begin_layout Standard
5687 To set matrices into a text line, the command
5697 \begin_layout Plain Layout
5706 When it is inserted a blue box with two dashed lines appears.
5707 In this box the matrix is inserted.
5710 \begin_layout Standard
5712 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5713 C & D\end{smallmatrix}\right)$
5719 \begin_layout Section
5720 Brackets and Delimiters
5724 \begin_layout Plain Layout
5734 \begin_layout Plain Layout
5743 \begin_layout Subsection
5744 Vertical Brackets and Delimiters
5748 \begin_layout Plain Layout
5757 \begin_layout Standard
5758 \begin_inset space \hfill{}
5762 \begin_inset Tabular
5763 <lyxtabular version="3" rows="9" columns="2">
5765 <column alignment="center" valignment="top" width="0pt">
5766 <column alignment="center" valignment="top" width="0pt">
5768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5771 \begin_layout Plain Layout
5777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5780 \begin_layout Plain Layout
5788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5791 \begin_layout Plain Layout
5797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5800 \begin_layout Plain Layout
5801 \begin_inset Formula $($
5811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5814 \begin_layout Plain Layout
5820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5823 \begin_layout Plain Layout
5824 \begin_inset Formula $\{$
5834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5837 \begin_layout Plain Layout
5843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5846 \begin_layout Plain Layout
5847 \begin_inset Formula $[$
5857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5860 \begin_layout Plain Layout
5868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5871 \begin_layout Plain Layout
5872 \begin_inset Formula $\langle$
5882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5885 \begin_layout Plain Layout
5893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5896 \begin_layout Plain Layout
5897 \begin_inset Formula $\lceil$
5907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5910 \begin_layout Plain Layout
5918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5921 \begin_layout Plain Layout
5922 \begin_inset Formula $\lfloor$
5932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5935 \begin_layout Plain Layout
5941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5944 \begin_layout Plain Layout
5945 \begin_inset Formula $/$
5955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5958 \begin_layout Plain Layout
5964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5967 \begin_layout Plain Layout
5968 \begin_inset Formula $|$
5982 \begin_inset space \hfill{}
5986 \begin_inset Tabular
5987 <lyxtabular version="3" rows="9" columns="2">
5989 <column alignment="center" valignment="top" width="0pt">
5990 <column alignment="center" valignment="top" width="0pt">
5992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5995 \begin_layout Plain Layout
6001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6004 \begin_layout Plain Layout
6012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6015 \begin_layout Plain Layout
6021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6024 \begin_layout Plain Layout
6025 \begin_inset Formula $)$
6035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6038 \begin_layout Plain Layout
6044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6047 \begin_layout Plain Layout
6048 \begin_inset Formula $\}$
6058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6061 \begin_layout Plain Layout
6067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6070 \begin_layout Plain Layout
6071 \begin_inset Formula $]$
6081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6084 \begin_layout Plain Layout
6092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6095 \begin_layout Plain Layout
6096 \begin_inset Formula $\rangle$
6106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6109 \begin_layout Plain Layout
6117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6120 \begin_layout Plain Layout
6121 \begin_inset Formula $\rceil$
6131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6134 \begin_layout Plain Layout
6142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6145 \begin_layout Plain Layout
6146 \begin_inset Formula $\rfloor$
6156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6159 \begin_layout Plain Layout
6169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6172 \begin_layout Plain Layout
6173 \begin_inset Formula $\backslash$
6183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6186 \begin_layout Plain Layout
6194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6197 \begin_layout Plain Layout
6198 \begin_inset Formula $\|$
6212 \begin_inset space \hfill{}
6218 \begin_layout Standard
6221 \begin_inset Note Greyedout
6224 \begin_layout Plain Layout
6229 In TeX-mode the command
6239 \begin_layout Plain Layout
6247 must be used for the backslash, because the command
6255 produces there a line break.
6263 \begin_layout Standard
6264 For all characters listed above the size can be adjusted with the commands
6265 described in the following two subsections.
6266 When using these commands, the characters < and > can directly be used
6267 instead of the commands
6282 \begin_layout Subsubsection
6284 \begin_inset CommandInset label
6286 name "sub:Manual-Bracket-Size"
6294 \begin_layout Plain Layout
6295 Bracket size ! manual
6303 \begin_layout Standard
6304 The bracket size can be specified manually by the LaTeX-commands
6314 \begin_layout Plain Layout
6347 denotes the smallest and
6353 the largest bracket size.
6356 \begin_layout Standard
6357 These commands are used to emphasize levels of brackets:
6360 \begin_layout Standard
6362 \begin_inset Tabular
6363 <lyxtabular version="3" rows="2" columns="2">
6365 <column alignment="center" valignment="top" width="0pt">
6366 <column alignment="center" valignment="top" width="0pt">
6368 <cell alignment="center" valignment="top" usebox="none">
6371 \begin_layout Plain Layout
6372 all brackets in the same size:
6377 <cell alignment="center" valignment="top" usebox="none">
6380 \begin_layout Plain Layout
6381 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6391 <cell alignment="center" valignment="top" usebox="none">
6394 \begin_layout Plain Layout
6400 <cell alignment="center" valignment="top" usebox="none">
6403 \begin_layout Plain Layout
6404 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6418 \begin_inset Note Note
6421 \begin_layout Plain Layout
6428 is only used as spacer.
6436 \begin_layout Standard
6437 For the second formula the command
6447 \begin_layout Plain Layout
6461 \begin_layout Standard
6462 Here is an overview about all bracket sizes:
6465 \begin_layout Standard
6485 \begin_layout Plain Layout
6502 \begin_layout Plain Layout
6515 \begin_layout Plain Layout
6531 \begin_layout Standard
6533 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6539 \begin_layout Standard
6546 -commands there is the variant
6556 \begin_layout Plain Layout
6564 that adds a bit more space between the bracket and its content, and the
6581 \begin_layout Plain Layout
6591 , that don't add additional space.
6596 at the end of the command
6602 is for a left bracket; for a right bracket this will be replaced by an
6608 A left or right bracket can each be an opening or closing bracket.
6611 \begin_layout Standard
6612 In the following table is a comparison of the variants:
6615 \begin_layout Standard
6617 \begin_inset Tabular
6618 <lyxtabular version="3" rows="5" columns="2">
6620 <column alignment="center" valignment="middle" width="0">
6621 <column alignment="center" valignment="middle" width="0">
6623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6626 \begin_layout Plain Layout
6632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6635 \begin_layout Plain Layout
6637 \begin_inset Note Note
6640 \begin_layout Plain Layout
6647 is only used as spacer.
6659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6662 \begin_layout Plain Layout
6677 \begin_layout Plain Layout
6695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6698 \begin_layout Plain Layout
6699 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6712 \begin_layout Plain Layout
6727 \begin_layout Plain Layout
6745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6748 \begin_layout Plain Layout
6749 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6762 \begin_layout Plain Layout
6777 \begin_layout Plain Layout
6795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6798 \begin_layout Plain Layout
6799 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6812 \begin_layout Plain Layout
6824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6827 \begin_layout Plain Layout
6828 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6844 \begin_layout Subsubsection
6845 Automatic Bracket Size
6846 \begin_inset CommandInset label
6848 name "sub:Automatic-Bracket-Size"
6856 \begin_layout Plain Layout
6857 Bracket size ! automatic
6865 \begin_layout Standard
6866 Brackets with variable size can be inserted with the commands
6876 \begin_layout Plain Layout
6894 \begin_layout Plain Layout
6902 or via the math toolbar button
6903 \begin_inset Graphics
6904 filename ../images/dialog-show_mathdelimiter.png
6922 the wanted bracket must be inserted.
6923 The bracket size will then automatically be calculated for the output.
6926 \begin_layout Standard
6928 normal bracket: The command
6938 \begin_layout Plain Layout
6948 \begin_inset Formula $\downarrow$
6955 \begin_layout Plain Layout
6967 \begin_inset Formula \[
6975 \begin_layout Standard
6977 multiline bracket: The command
6989 \begin_layout Plain Layout
6999 \begin_inset Formula $\downarrow$
7006 \begin_layout Plain Layout
7020 \begin_inset Formula \[
7021 \ln\left(\frac{A}{C}\right)\]
7028 \begin_layout Standard
7044 \begin_inset space ~
7050 This has the advantage that you can see in LyX immediately the real bracket
7051 size and that the matching right bracket will be created too.
7052 \begin_inset Newline newline
7055 The command for the last example would then be:
7069 \begin_layout Plain Layout
7079 \begin_inset Formula $\downarrow$
7085 \begin_layout Standard
7086 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7087 For example the command
7097 \begin_layout Plain Layout
7107 \begin_inset Formula $\downarrow$
7114 \begin_layout Plain Layout
7130 \begin_inset Formula \[
7131 \left.\frac{A}{B}\right\} \]
7149 will be converted by LyX to brackets in the right size when the document
7150 is reloaded and an omitted bracket will appear as dashed line.
7153 \begin_layout Standard
7154 \begin_inset VSpace bigskip
7157 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7168 \begin_layout Plain Layout
7176 is additionally available for all brackets and limits.
7177 With this command the height of the following character is adapted to the
7178 one of the surrounding brackets, what is e.
7179 \begin_inset space \thinspace{}
7183 \begin_inset space ~
7186 needed for physical vectors:
7187 \begin_inset Formula \[
7188 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7192 For physical vectors there is a special LaTeX-package, described in
7193 \begin_inset CommandInset ref
7195 reference "sub:Physical-Vectors"
7202 \begin_layout Subsection
7207 \begin_layout Plain Layout
7208 Brackets ! horizontal
7216 \begin_layout Standard
7218 \begin_inset Tabular
7219 <lyxtabular version="3" rows="4" columns="2">
7221 <column alignment="center" valignment="top" width="0pt">
7222 <column alignment="center" valignment="top" width="0pt">
7224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7227 \begin_layout Plain Layout
7229 \begin_inset Note Note
7232 \begin_layout Plain Layout
7239 is only used as spacer.
7249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7252 \begin_layout Plain Layout
7260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7263 \begin_layout Plain Layout
7267 \begin_layout Plain Layout
7282 \begin_layout Plain Layout
7295 \begin_layout Plain Layout
7308 \begin_layout Plain Layout
7321 \begin_layout Plain Layout
7332 \begin_layout Plain Layout
7345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7348 \begin_layout Plain Layout
7349 \begin_inset Formula $\overbrace{A+B}^{3}$
7359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7362 \begin_layout Plain Layout
7366 \begin_layout Plain Layout
7381 \begin_layout Plain Layout
7394 \begin_layout Plain Layout
7407 \begin_layout Plain Layout
7418 \begin_layout Plain Layout
7431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7434 \begin_layout Plain Layout
7435 \begin_inset Formula $\underbrace{A+B}_{5}$
7445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7448 \begin_layout Plain Layout
7455 \begin_layout Plain Layout
7470 \begin_layout Plain Layout
7483 \begin_layout Plain Layout
7496 \begin_layout Plain Layout
7509 \begin_layout Plain Layout
7522 \begin_layout Plain Layout
7535 \begin_layout Plain Layout
7549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7552 \begin_layout Plain Layout
7553 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7569 \begin_layout Standard
7570 In the last example it doesn't matter if
7582 is inserted at first.
7585 \begin_layout Standard
7586 \begin_inset VSpace bigskip
7589 When brackets are needed that overlap each other, multiline formulas, as
7591 \begin_inset CommandInset ref
7593 reference "sec:Multiline-Formulas"
7598 \begin_inset Formula \begin{eqnarray*}
7599 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7600 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7604 In the first row the formula is inserted together with the first brace.
7605 It is hereby important that the space command
7609 \begin_layout Plain Layout
7610 Space commands are explained in
7611 \begin_inset CommandInset ref
7613 reference "sub:Predefined-Space"
7628 is inserted before the first
7629 \begin_inset Formula $d$
7632 , because the brace that ends behind the
7633 \begin_inset Formula $q$
7636 prevents that the following
7637 \begin_inset Quotes eld
7641 \begin_inset Quotes erd
7644 is surrounded by space.
7648 \begin_layout Plain Layout
7649 because a bracket is not handled as character, see
7650 \begin_inset CommandInset ref
7652 reference "sub:Binary-Operators"
7661 In the second row the second brace is inserted.
7662 As it should begin before the
7663 \begin_inset Formula $b$
7678 \begin_layout Plain Layout
7686 \begin_inset CommandInset ref
7688 reference "sub:Placeholders"
7697 This space is needed because the
7698 \begin_inset Quotes eld
7702 \begin_inset Quotes erd
7705 is also surrounded by space in the formula.
7706 The brace is placed under the command
7715 \begin_layout Standard
7716 It gets more complicated when brackets overlap each other, like in the following
7721 \begin_layout Plain Layout
7733 \begin_inset Formula \begin{eqnarray*}
7734 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7735 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7743 \begin_layout Plain Layout
7754 The first formula row is the same as the second row of the previous example,
7755 with the difference that the brace is above.
7756 The second row contains the formula together with the second brace.
7757 To avoid that there is space between the upper brace in the first row and
7758 the formula, the row spacing need to be reduced.
7759 This is not easily possible due to a bug in LyX
7763 \begin_layout Plain Layout
7764 \begin_inset CommandInset href
7766 name "LyX-bug #1505"
7767 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7777 As solution for the problem, the global formula row separation
7787 \begin_layout Plain Layout
7795 must be changed to -6
7796 \begin_inset space \thinspace{}
7799 pt before the formula with the command
7814 is set back after the formula to the standard value of 3
7815 \begin_inset space \thinspace{}
7818 pt using the same command.
7819 More about the row separation in formulas is explained in
7820 \begin_inset CommandInset ref
7822 reference "sub:Line-Separation"
7829 \begin_layout Section
7834 \begin_layout Plain Layout
7843 \begin_layout Standard
7844 Arrows can be inserted via the math toolbar button
7845 \begin_inset Graphics
7846 filename ../images/math/leftarrow.png
7851 or the commands listed in the following subsections.
7854 \begin_layout Standard
7855 \begin_inset Newpage newpage
7861 \begin_layout Subsection
7866 \begin_layout Plain Layout
7875 \begin_layout Standard
7876 \begin_inset space \hfill{}
7880 \begin_inset Tabular
7881 <lyxtabular version="3" rows="8" columns="2">
7883 <column alignment="center" valignment="top" width="0pt">
7884 <column alignment="center" valignment="top" width="0pt">
7886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7889 \begin_layout Plain Layout
7895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7898 \begin_layout Plain Layout
7906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7909 \begin_layout Plain Layout
7917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7920 \begin_layout Plain Layout
7921 \begin_inset Formula $\gets$
7931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7934 \begin_layout Plain Layout
7942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7945 \begin_layout Plain Layout
7946 \begin_inset Formula $\Leftarrow$
7956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7959 \begin_layout Plain Layout
7967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7970 \begin_layout Plain Layout
7971 \begin_inset Formula $\longleftarrow$
7981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7984 \begin_layout Plain Layout
7992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7995 \begin_layout Plain Layout
7996 \begin_inset Formula $\Longleftarrow$
8006 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8009 \begin_layout Plain Layout
8017 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8020 \begin_layout Plain Layout
8021 \begin_inset Formula $\leftharpoonup$
8031 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8034 \begin_layout Plain Layout
8042 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8045 \begin_layout Plain Layout
8046 \begin_inset Formula $\leftharpoondown$
8056 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8059 \begin_layout Plain Layout
8067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8070 \begin_layout Plain Layout
8071 \begin_inset Formula $\hookleftarrow$
8085 \begin_inset space \hfill{}
8089 \begin_inset Tabular
8090 <lyxtabular version="3" rows="8" columns="2">
8092 <column alignment="center" valignment="top" width="0pt">
8093 <column alignment="center" valignment="top" width="0pt">
8095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8098 \begin_layout Plain Layout
8104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8107 \begin_layout Plain Layout
8115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8118 \begin_layout Plain Layout
8126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8129 \begin_layout Plain Layout
8130 \begin_inset Formula $\to$
8140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8143 \begin_layout Plain Layout
8151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8154 \begin_layout Plain Layout
8155 \begin_inset Formula $\Rightarrow$
8165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8168 \begin_layout Plain Layout
8176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8179 \begin_layout Plain Layout
8180 \begin_inset Formula $\longrightarrow$
8190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8193 \begin_layout Plain Layout
8201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8204 \begin_layout Plain Layout
8205 \begin_inset Formula $\Longrightarrow$
8215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8218 \begin_layout Plain Layout
8226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8229 \begin_layout Plain Layout
8230 \begin_inset Formula $\rightharpoonup$
8240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8243 \begin_layout Plain Layout
8251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8254 \begin_layout Plain Layout
8255 \begin_inset Formula $\rightharpoondown$
8265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8268 \begin_layout Plain Layout
8276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8279 \begin_layout Plain Layout
8280 \begin_inset Formula $\hookrightarrow$
8294 \begin_inset space \hfill{}
8300 \begin_layout Standard
8301 \begin_inset space \hfill{}
8305 \begin_inset Tabular
8306 <lyxtabular version="3" rows="6" columns="2">
8308 <column alignment="center" valignment="top" width="0pt">
8309 <column alignment="center" valignment="top" width="0pt">
8311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8314 \begin_layout Plain Layout
8320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8323 \begin_layout Plain Layout
8331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8334 \begin_layout Plain Layout
8342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8345 \begin_layout Plain Layout
8346 \begin_inset Formula $\leftrightarrow$
8356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8359 \begin_layout Plain Layout
8367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8370 \begin_layout Plain Layout
8371 \begin_inset Formula $\Leftrightarrow$
8381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8384 \begin_layout Plain Layout
8392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8395 \begin_layout Plain Layout
8396 \begin_inset Formula $\longleftrightarrow$
8406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8409 \begin_layout Plain Layout
8417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8420 \begin_layout Plain Layout
8421 \begin_inset Formula $\Longleftrightarrow$
8431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8434 \begin_layout Plain Layout
8442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8445 \begin_layout Plain Layout
8446 \begin_inset Formula $\rightleftharpoons$
8460 \begin_inset space \hspace{}
8465 \begin_inset space \hfill{}
8469 \begin_inset Tabular
8470 <lyxtabular version="3" rows="5" columns="2">
8472 <column alignment="center" valignment="top" width="0pt">
8473 <column alignment="center" valignment="top" width="0pt">
8475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8478 \begin_layout Plain Layout
8484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8487 \begin_layout Plain Layout
8495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8498 \begin_layout Plain Layout
8506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8509 \begin_layout Plain Layout
8510 \begin_inset Formula $\mapsto$
8520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8523 \begin_layout Plain Layout
8531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8534 \begin_layout Plain Layout
8535 \begin_inset Formula $\longmapsto$
8545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8548 \begin_layout Plain Layout
8556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8559 \begin_layout Plain Layout
8560 \begin_inset Formula $\leadsto$
8570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8573 \begin_layout Plain Layout
8581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8584 \begin_layout Plain Layout
8585 \begin_inset Formula $\dasharrow$
8599 \begin_inset space \hfill{}
8605 \begin_layout Standard
8606 \begin_inset VSpace medskip
8609 Arrows used as accent like e.
8610 \begin_inset space \thinspace{}
8614 \begin_inset space ~
8617 vector arrows are listed in
8618 \begin_inset CommandInset ref
8620 reference "sec:Accents"
8627 \begin_layout Standard
8628 \begin_inset VSpace bigskip
8631 Furthermore there are the labeled arrows
8635 \begin_layout Plain Layout
8651 \begin_layout Plain Layout
8669 \begin_layout Plain Layout
8676 \begin_layout Plain Layout
8691 When inserting one of these commands in a formula, an arrow with two blue
8692 boxes appear where the label can be inserted.
8693 The length of the arrow adapts to the label width.
8696 \begin_layout Standard
8698 \begin_inset Tabular
8699 <lyxtabular version="3" rows="3" columns="2">
8701 <column alignment="center" valignment="top" width="0pt">
8702 <column alignment="center" valignment="top" width="0pt">
8704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8707 \begin_layout Plain Layout
8713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8716 \begin_layout Plain Layout
8718 \begin_inset Note Note
8721 \begin_layout Plain Layout
8728 is only used as spacer.
8740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8743 \begin_layout Plain Layout
8750 \begin_layout Plain Layout
8760 \begin_inset Formula $\downarrow$
8764 \begin_inset Formula $\to$
8772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8775 \begin_layout Plain Layout
8776 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8789 \begin_layout Plain Layout
8796 \begin_layout Plain Layout
8806 \begin_inset Formula $\downarrow$
8810 \begin_inset Formula $\to$
8818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8821 \begin_layout Plain Layout
8822 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8838 \begin_layout Subsection
8839 Vertical and diagonal Arrows
8843 \begin_layout Plain Layout
8853 \begin_layout Plain Layout
8862 \begin_layout Standard
8863 \begin_inset space \hfill{}
8867 \begin_inset Tabular
8868 <lyxtabular version="3" rows="7" columns="2">
8870 <column alignment="center" valignment="top" width="0pt">
8871 <column alignment="center" valignment="top" width="0pt">
8873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8876 \begin_layout Plain Layout
8882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8885 \begin_layout Plain Layout
8893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8896 \begin_layout Plain Layout
8904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8907 \begin_layout Plain Layout
8908 \begin_inset Formula $\uparrow$
8918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8921 \begin_layout Plain Layout
8929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8932 \begin_layout Plain Layout
8933 \begin_inset Formula $\Uparrow$
8943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8946 \begin_layout Plain Layout
8954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8957 \begin_layout Plain Layout
8958 \begin_inset Formula $\updownarrow$
8968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8971 \begin_layout Plain Layout
8979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8982 \begin_layout Plain Layout
8983 \begin_inset Formula $\Updownarrow$
8993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8996 \begin_layout Plain Layout
9004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9007 \begin_layout Plain Layout
9008 \begin_inset Formula $\Downarrow$
9018 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9021 \begin_layout Plain Layout
9029 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9032 \begin_layout Plain Layout
9033 \begin_inset Formula $\downarrow$
9047 \begin_inset space \hfill{}
9051 \begin_inset Tabular
9052 <lyxtabular version="3" rows="5" columns="2">
9054 <column alignment="center" valignment="top" width="0pt">
9055 <column alignment="center" valignment="top" width="0pt">
9057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9060 \begin_layout Plain Layout
9066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9069 \begin_layout Plain Layout
9077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9080 \begin_layout Plain Layout
9088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9091 \begin_layout Plain Layout
9092 \begin_inset Formula $\nearrow$
9102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9105 \begin_layout Plain Layout
9113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9116 \begin_layout Plain Layout
9117 \begin_inset Formula $\searrow$
9127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9130 \begin_layout Plain Layout
9138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9141 \begin_layout Plain Layout
9142 \begin_inset Formula $\swarrow$
9152 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9155 \begin_layout Plain Layout
9163 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9166 \begin_layout Plain Layout
9167 \begin_inset Formula $\nwarrow$
9181 \begin_inset space \hfill{}
9187 \begin_layout Standard
9188 \begin_inset VSpace medskip
9191 Vertical arrows can be used also as delimiter together with the commands
9193 \begin_inset CommandInset ref
9195 reference "sub:Manual-Bracket-Size"
9200 \begin_inset CommandInset ref
9202 reference "sub:Automatic-Bracket-Size"
9209 \begin_layout Standard
9210 \begin_inset Newpage newpage
9216 \begin_layout Section
9218 \begin_inset CommandInset label
9228 \begin_layout Plain Layout
9237 \begin_layout Standard
9238 Accents can be inserted via the math toolbar button
9239 \begin_inset Graphics
9240 filename ../images/math/hat.png
9245 or the commands listed in the following subsections.
9248 \begin_layout Subsection
9249 Accents for one Character
9253 \begin_layout Plain Layout
9266 \begin_layout Plain Layout
9268 \begin_inset CommandInset ref
9270 reference "sub:Accents-in-Text"
9283 \begin_layout Plain Layout
9291 \begin_inset Note Note
9294 \begin_layout Plain Layout
9297 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9300 \begin_layout Plain Layout
9303 texorpdfstring is in section
9304 \begin_inset CommandInset ref
9306 reference "sub:Formulas-in-Section"
9316 \begin_inset CommandInset label
9318 name "sub:Accents-for-one"
9326 \begin_layout Plain Layout
9327 Accents ! for one character
9335 \begin_layout Standard
9336 \begin_inset space \hfill{}
9340 \begin_inset Tabular
9341 <lyxtabular version="3" rows="8" columns="2">
9343 <column alignment="center" valignment="top" width="0pt">
9344 <column alignment="center" valignment="top" width="0pt">
9346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9349 \begin_layout Plain Layout
9355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9358 \begin_layout Plain Layout
9360 \begin_inset Note Note
9363 \begin_layout Plain Layout
9370 is only used as spacer.
9382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9385 \begin_layout Plain Layout
9392 \begin_layout Plain Layout
9406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9409 \begin_layout Plain Layout
9410 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9423 \begin_layout Plain Layout
9430 \begin_layout Plain Layout
9444 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9447 \begin_layout Plain Layout
9448 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9458 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9461 \begin_layout Plain Layout
9468 \begin_layout Plain Layout
9482 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9485 \begin_layout Plain Layout
9486 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9496 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9499 \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 $\raisebox{5mm}{}\ddddot{A}$
9521 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9524 \begin_layout Plain Layout
9531 \begin_layout Plain Layout
9544 \begin_layout Plain Layout
9555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9558 \begin_layout Plain Layout
9559 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9572 \begin_layout Plain Layout
9579 \begin_layout Plain Layout
9593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9596 \begin_layout Plain Layout
9597 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9610 \begin_layout Plain Layout
9617 \begin_layout Plain Layout
9631 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9634 \begin_layout Plain Layout
9635 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9649 \begin_inset space \hfill{}
9653 \begin_inset Tabular
9654 <lyxtabular version="3" rows="7" columns="2">
9656 <column alignment="center" valignment="top" width="0pt">
9657 <column alignment="center" valignment="top" width="0pt">
9659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9662 \begin_layout Plain Layout
9668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9671 \begin_layout Plain Layout
9679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9682 \begin_layout Plain Layout
9689 \begin_layout Plain Layout
9703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9706 \begin_layout Plain Layout
9707 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9717 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9720 \begin_layout Plain Layout
9727 \begin_layout Plain Layout
9741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9744 \begin_layout Plain Layout
9745 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9758 \begin_layout Plain Layout
9765 \begin_layout Plain Layout
9779 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9782 \begin_layout Plain Layout
9783 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9796 \begin_layout Plain Layout
9803 \begin_layout Plain Layout
9817 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9820 \begin_layout Plain Layout
9821 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9831 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9834 \begin_layout Plain Layout
9841 \begin_layout Plain Layout
9855 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9858 \begin_layout Plain Layout
9859 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9869 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9872 \begin_layout Plain Layout
9879 \begin_layout Plain Layout
9893 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9896 \begin_layout Plain Layout
9897 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9911 \begin_inset space \hfill{}
9917 \begin_layout Standard
9918 \begin_inset VSpace bigskip
9925 \begin_layout Plain Layout
9931 in formulas, a quotation mark is inserted before the vowel.
9932 These two characters are then treated by LaTeX as
9936 character when the formula part with the umlaut is marked as German.
9944 \begin_inset Quotes eld
9948 \begin_inset Quotes erd
9951 umlauts are created as demonstrated in the following example:
9954 \begin_layout Standard
9955 \begin_inset VSpace -2mm
9961 \begin_layout Standard
9963 \begin_inset Tabular
9964 <lyxtabular version="3" rows="3" columns="2">
9966 <column alignment="center" valignment="top" width="0">
9967 <column alignment="center" valignment="top" width="0">
9969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9972 \begin_layout Plain Layout
9978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9981 \begin_layout Plain Layout
9983 \begin_inset Note Note
9986 \begin_layout Plain Layout
9994 \begin_inset space \thinspace{}
9997 pt space are only used as spacer.
10009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10012 \begin_layout Plain Layout
10015 \begin_inset Quotes grd
10023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10026 \begin_layout Plain Layout
10027 \begin_inset space \hspace{}
10034 \begin_inset Formula $"i$
10044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10047 \begin_layout Plain Layout
10054 \begin_layout Plain Layout
10068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10071 \begin_layout Plain Layout
10072 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10088 \begin_layout Standard
10089 Another advantage to
10095 is that umlauts can directly be converted to mathematical text because
10096 the accent commands above are
10102 in mathematical text
10105 To convert an accented character to mathematical text, only the character
10106 under the accent may be converted.
10107 This applies also for all other conversions, e.
10108 \begin_inset space \thinspace{}
10112 \begin_inset space ~
10118 \begin_layout Standard
10119 In mathematical text, umlauts and other accented characters can directly
10123 \begin_layout Subsection
10124 Accents for Operators
10128 \begin_layout Plain Layout
10129 Accents ! for operators
10137 \begin_layout Standard
10148 \begin_layout Plain Layout
10166 \begin_layout Plain Layout
10174 characters can be placed above or below an operator, respectively, to accent
10186 \begin_layout Plain Layout
10194 characters can be set before and behind an operator.
10195 The command scheme is:
10198 \begin_layout Standard
10214 \begin_layout Standard
10221 must always be before the operator that should be accented.
10222 You can accent with several characters and even with other operators and
10230 for example only characters behind an operator, write nothing between the
10231 first braces but don't omit the braces.
10234 \begin_layout Standard
10235 For example the command
10240 \begin_inset Formula $\to$
10250 \begin_inset Formula $\to$
10259 \begin_layout Plain Layout
10275 \begin_inset Formula \[
10276 \sideset{}{'}\sum_{k=1}^{n}\]
10283 \begin_layout Standard
10292 \begin_layout Plain Layout
10307 \begin_layout Plain Layout
10319 \begin_inset Formula $\uparrow$
10327 \begin_inset Formula \[
10328 \overset{a}{\maltese}\]
10332 As seen in the last example, with
10344 also symbols and characters can be accented; with
10350 this is not possible.
10353 \begin_layout Subsection
10354 Accents for several Characters
10358 \begin_layout Plain Layout
10359 Accents ! for several characters
10367 \begin_layout Standard
10368 \begin_inset space \hfill{}
10372 \begin_inset Tabular
10373 <lyxtabular version="3" rows="5" columns="2">
10375 <column alignment="center" valignment="top" width="0pt">
10376 <column alignment="center" valignment="top" width="0pt">
10378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10381 \begin_layout Plain Layout
10387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10390 \begin_layout Plain Layout
10392 \begin_inset Note Note
10395 \begin_layout Plain Layout
10402 is only used as spacer.
10414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10417 \begin_layout Plain Layout
10424 \begin_layout Plain Layout
10438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10441 \begin_layout Plain Layout
10442 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10452 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10455 \begin_layout Plain Layout
10462 \begin_layout Plain Layout
10476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10479 \begin_layout Plain Layout
10480 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10493 \begin_layout Plain Layout
10500 \begin_layout Plain Layout
10514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10517 \begin_layout Plain Layout
10518 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10531 \begin_layout Plain Layout
10534 underleftrightarrow
10538 \begin_layout Plain Layout
10552 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10555 \begin_layout Plain Layout
10556 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10570 \begin_inset space \hfill{}
10574 \begin_inset Tabular
10575 <lyxtabular version="3" rows="5" columns="2">
10577 <column alignment="center" valignment="top" width="0pt">
10578 <column alignment="center" valignment="top" width="0pt">
10580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10583 \begin_layout Plain Layout
10589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10592 \begin_layout Plain Layout
10600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10603 \begin_layout Plain Layout
10610 \begin_layout Plain Layout
10624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10627 \begin_layout Plain Layout
10628 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10638 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10641 \begin_layout Plain Layout
10648 \begin_layout Plain Layout
10662 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10665 \begin_layout Plain Layout
10666 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10679 \begin_layout Plain Layout
10686 \begin_layout Plain Layout
10700 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10703 \begin_layout Plain Layout
10704 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10714 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10717 \begin_layout Plain Layout
10724 \begin_layout Plain Layout
10738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10741 \begin_layout Plain Layout
10742 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10756 \begin_inset space \hfill{}
10762 \begin_layout Standard
10763 \begin_inset VSpace medskip
10766 With these commands as many characters as you like can be accented.
10779 will only be set in the output with a length of three characters, as shown
10780 in the following example:
10781 \begin_inset Formula \[
10782 \widetilde{A+B=C-D}\]
10789 \begin_layout Standard
10800 \begin_layout Plain Layout
10818 \begin_layout Plain Layout
10826 described in the previous subsection it is also possible to accent several
10836 \begin_layout Plain Layout
10846 \begin_inset Formula $\downarrow$
10852 \begin_inset Formula \[
10853 \underset{***}{A=B}\]
10860 \begin_layout Section
10862 \begin_inset CommandInset label
10872 \begin_layout Plain Layout
10881 \begin_layout Subsection
10883 \begin_inset CommandInset label
10885 name "sub:Predefined-Space"
10893 \begin_layout Plain Layout
10894 Space ! horizontal ! predefined
10902 \begin_layout Standard
10903 Sometimes it is necessary to insert horizontal space to a formula.
10904 This is done by inserting a protected space (shortcut
10910 \begin_inset Quotes eld
10920 \begin_layout Plain Layout
10933 \begin_inset Quotes erd
10936 appears and by pressing
10940 several times one can select one of eight different space sizes.
10941 The spaces can also be inserted using the math toolbar button
10942 \begin_inset Graphics
10943 filename ../images/math/space.png
10948 or special commands.
10949 Independent from the inserted command, one can select the size again by
10957 \begin_layout Standard
10960 \begin_inset VSpace -5mm
10964 \begin_inset Tabular
10965 <lyxtabular version="3" rows="3" columns="7">
10967 <column alignment="center" valignment="middle" width="6.8cm">
10968 <column alignment="center" valignment="top" width="0">
10969 <column alignment="center" valignment="top" width="0">
10970 <column alignment="center" valignment="top" width="0">
10971 <column alignment="center" valignment="top" width="0">
10972 <column alignment="center" valignment="top" width="0">
10973 <column alignment="center" valignment="top" width="0">
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" usebox="none">
10987 \begin_layout Plain Layout
10995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10998 \begin_layout Plain Layout
11006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11009 \begin_layout Plain Layout
11017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11020 \begin_layout Plain Layout
11028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11031 \begin_layout Plain Layout
11039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11042 \begin_layout Plain Layout
11052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11055 \begin_layout Plain Layout
11060 keystrokes after inserting the protected space
11065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11068 \begin_layout Plain Layout
11074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11077 \begin_layout Plain Layout
11083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11086 \begin_layout Plain Layout
11092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11095 \begin_layout Plain Layout
11101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11104 \begin_layout Plain Layout
11110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11113 \begin_layout Plain Layout
11121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11124 \begin_layout Plain Layout
11130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11133 \begin_layout Plain Layout
11134 \begin_inset Formula $A\, B$
11142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11145 \begin_layout Plain Layout
11146 \begin_inset Formula $A\: B$
11154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11157 \begin_layout Plain Layout
11158 \begin_inset Formula $A\; B$
11166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11169 \begin_layout Plain Layout
11170 \begin_inset Formula $A\quad B$
11178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11181 \begin_layout Plain Layout
11182 \begin_inset Formula $A\qquad B$
11190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11193 \begin_layout Plain Layout
11194 \begin_inset Formula $A\! B$
11210 \begin_layout Standard
11211 The last size seem to produce no space.
11212 It is displayed red in LyX contrary to the other sizes, because it is a
11214 There are two more negative spaces:
11217 \begin_layout Standard
11219 \begin_inset Tabular
11220 <lyxtabular version="3" rows="3" columns="3">
11222 <column alignment="center" valignment="middle" width="6.8cm">
11223 <column alignment="center" valignment="top" width="0pt">
11224 <column alignment="center" valignment="top" width="0pt">
11226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11229 \begin_layout Plain Layout
11235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11238 \begin_layout Plain Layout
11246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11249 \begin_layout Plain Layout
11259 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11262 \begin_layout Plain Layout
11267 keystrokes after inserting the protected space
11272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11275 \begin_layout Plain Layout
11281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11284 \begin_layout Plain Layout
11292 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11295 \begin_layout Plain Layout
11301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11304 \begin_layout Plain Layout
11305 \begin_inset Formula $A\negmedspace B$
11313 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11316 \begin_layout Plain Layout
11317 \begin_inset Formula $A\negthickspace B$
11333 \begin_layout Standard
11334 Negative spaces can lead to characters overlapping each other.
11335 Thus they can be used to enforce ligatures, what is e.
11336 \begin_inset space \thinspace{}
11340 \begin_inset space ~
11343 useful for summation operators:
11346 \begin_layout Standard
11348 \begin_inset Tabular
11349 <lyxtabular version="3" rows="3" columns="2">
11351 <column alignment="center" valignment="top" width="0">
11352 <column alignment="center" valignment="top" width="0">
11354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11357 \begin_layout Plain Layout
11363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11366 \begin_layout Plain Layout
11368 \begin_inset Note Note
11371 \begin_layout Plain Layout
11378 is only used as spacer.
11390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11393 \begin_layout Plain Layout
11402 \begin_layout Plain Layout
11416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11419 \begin_layout Plain Layout
11420 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11433 \begin_layout Plain Layout
11444 \begin_layout Plain Layout
11458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11461 \begin_layout Plain Layout
11462 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11478 \begin_layout Standard
11479 Relations like for example equal signs, are always surrounded by space.
11480 To suppress this, the equal sign is placed into a TeX-brace.
11481 The following example demonstrates this:
11484 \begin_layout Standard
11486 \begin_inset Tabular
11487 <lyxtabular version="3" rows="2" columns="2">
11489 <column alignment="center" valignment="top" width="0pt">
11490 <column alignment="center" valignment="top" width="0pt">
11492 <cell alignment="center" valignment="top" usebox="none">
11495 \begin_layout Plain Layout
11501 <cell alignment="center" valignment="top" usebox="none">
11504 \begin_layout Plain Layout
11505 \begin_inset Formula $A=B$
11515 <cell alignment="center" valignment="top" usebox="none">
11518 \begin_layout Plain Layout
11519 \begin_inset Note Note
11522 \begin_layout Plain Layout
11529 is only used as spacer.
11535 \begin_inset Formula $\raisebox{5mm}{}$
11538 equation without space
11543 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11546 \begin_layout Plain Layout
11547 \begin_inset Formula $A{=}B$
11563 \begin_layout Standard
11565 The command for the last formula is:
11570 \begin_inset Formula $\to$
11576 \begin_layout Standard
11577 \begin_inset VSpace bigskip
11580 Spaces are needed for physical units, because the space between the value
11581 and the unit is the smallest one and not a normal space.
11582 For units in text, the smallest space is inserted via the menu
11584 Insert\SpecialChar \menuseparator
11585 Formatting\SpecialChar \menuseparator
11587 \begin_inset space ~
11599 \begin_layout Standard
11600 An example to visualize the difference:
11603 \begin_layout Standard
11604 \begin_inset Tabular
11605 <lyxtabular version="3" rows="2" columns="2">
11607 <column alignment="left" valignment="top" width="0">
11608 <column alignment="left" valignment="top" width="0">
11610 <cell alignment="center" valignment="top" usebox="none">
11613 \begin_layout Plain Layout
11615 \begin_inset Formula $\cdot$
11623 <cell alignment="center" valignment="top" usebox="none">
11626 \begin_layout Plain Layout
11627 space between value and unit
11634 <cell alignment="center" valignment="top" usebox="none">
11637 \begin_layout Plain Layout
11639 \begin_inset space \thinspace{}
11643 \begin_inset Formula $\cdot$
11651 <cell alignment="center" valignment="top" usebox="none">
11654 \begin_layout Plain Layout
11655 smallest space between value and unit
11668 \begin_layout Subsection
11673 \begin_layout Plain Layout
11686 \begin_layout Plain Layout
11687 for vertical space in formulas see
11688 \begin_inset CommandInset ref
11690 reference "sub:Line-Separation"
11703 \begin_layout Plain Layout
11711 \begin_inset Note Note
11714 \begin_layout Plain Layout
11717 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11720 \begin_layout Plain Layout
11723 texorpdfstring is in section
11724 \begin_inset CommandInset ref
11726 reference "sub:Formulas-in-Section"
11736 \begin_inset CommandInset label
11738 name "sub:Variable-Space"
11746 \begin_layout Plain Layout
11747 Space ! horizontal ! variable
11755 \begin_layout Standard
11756 Space with a defined length can be inserted in LyX with the command
11757 \begin_inset Newline newline
11770 \begin_layout Plain Layout
11779 For the length all units listed in
11780 \begin_inset CommandInset ref
11782 reference "tab:Available-units"
11786 are allowed, except of the unit
11787 \begin_inset Quotes eld
11791 \begin_inset Quotes erd
11795 The length may also be negative.
11796 To insert so many space that the formula uses all available space, the
11807 \begin_layout Plain Layout
11818 \begin_layout Standard
11819 \begin_inset VSpace -1mm
11825 \begin_layout Standard
11827 \begin_inset Tabular
11828 <lyxtabular version="3" rows="4" columns="2">
11830 <column alignment="center" valignment="top" width="0">
11831 <column alignment="center" valignment="top" width="0">
11833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11836 \begin_layout Plain Layout
11842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11845 \begin_layout Plain Layout
11853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11856 \begin_layout Plain Layout
11860 \begin_inset Formula $\to$
11870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11873 \begin_layout Plain Layout
11874 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11887 \begin_layout Plain Layout
11891 \begin_inset Formula $\to$
11901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11904 \begin_layout Plain Layout
11905 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11918 \begin_layout Plain Layout
11925 \begin_layout Plain Layout
11939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11942 \begin_layout Plain Layout
11943 \begin_inset Formula $A=A\hfill B=B$
11959 \begin_layout Standard
11960 In the last example the available space is given by the longest column entry
11962 In an inline formula the space depends on the length of the line in which
11970 Thus, when the line uses the full width, no space will be created.
11977 only has an effect on displayed formulas when the formula style
11982 (Formula styles are explained in
11983 \begin_inset CommandInset ref
11985 reference "sec:Formula-Styles"
11992 \begin_layout Standard
11999 , there are the commands
12011 that fill the space with a pattern, see
12012 \begin_inset CommandInset ref
12014 reference "sub:Ellipses"
12021 \begin_layout Standard
12022 For text, variable space can be inserted via the menu
12024 Insert\SpecialChar \menuseparator
12025 Formatting\SpecialChar \menuseparator
12027 \begin_inset space ~
12032 , what is not possible in formulas:
12035 \begin_layout Standard
12036 This is a line with
12037 \begin_inset space \hspace{}
12042 \begin_inset space \thinspace{}
12048 \begin_layout Standard
12049 This is a line with
12050 \begin_inset space \hfill{}
12056 \begin_layout Subsection
12057 Space besides inline Formulas
12061 \begin_layout Plain Layout
12062 Space ! besides inline formulas
12070 \begin_layout Standard
12071 The space that surrounds inline formulas can be adjusted with the length
12080 \begin_layout Plain Layout
12091 The value of a length is set with the command
12099 \begin_layout Plain Layout
12109 that has the following scheme:
12112 \begin_layout Standard
12117 setlength{length name}{value}
12120 \begin_layout Standard
12128 \begin_inset space \thinspace{}
12134 \begin_layout Standard
12144 \begin_layout Standard
12145 is inserted in TeX-mode.
12147 \begin_inset space \thinspace{}
12150 mm space will now be set around all inline formulas:
12154 \begin_layout Plain Layout
12168 \begin_layout Standard
12169 This is a line with an inline formula
12170 \begin_inset Formula $A=B$
12174 \begin_inset space \thinspace{}
12177 mm surrounding space.
12181 \begin_layout Plain Layout
12195 \begin_layout Standard
12196 To return to the predefined value,
12202 is set to the value 0
12203 \begin_inset space \thinspace{}
12209 \begin_layout Section
12214 \begin_layout Plain Layout
12224 \begin_layout Plain Layout
12229 \begin_layout Plain Layout
12240 \begin_layout Plain Layout
12255 \begin_layout Standard
12256 Boxes for text are described in chapter
12263 \begin_inset space ~
12271 \begin_layout Subsection
12273 \begin_inset CommandInset label
12275 name "sub:Boxes-with-Frame"
12283 \begin_layout Plain Layout
12292 \begin_layout Standard
12293 It is possible to frame formulas or parts of it with the commands
12303 \begin_layout Plain Layout
12321 \begin_layout Plain Layout
12332 \begin_layout Standard
12333 When one of these commands is inserted to a formula, a blue box appears
12334 within a frame to enter formula parts.
12341 an additional formula has to be created by
12349 \begin_layout Plain Layout
12350 Due to a bug in LyX it is not possible to create a new formula with
12355 \begin_inset CommandInset href
12357 name "LyX-bug #1435"
12358 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12367 , because the box content will otherwise be treated as mathematical text.
12374 is used, a new formula is automatically created inside the frame.
12377 \begin_layout Standard
12384 is not suitable to frame displayed formulas, because the formula will always
12385 be set in the size of the text.
12392 is in contrary not suitable to frame inline formulas, because the formula
12393 will always be set in the size of a displayed formula.
12396 \begin_layout Standard
12403 there is the command
12413 \begin_layout Plain Layout
12421 where additionally the frame width and the alignment can be specified.
12428 is used in the following scheme:
12431 \begin_layout Standard
12436 framebox[frame width][position]{box content}
12439 \begin_layout Standard
12440 The position can either be
12457 right aligns the formula in the box.
12458 When no position is given, the formula will be centered.
12459 \begin_inset Newline newline
12462 Is no width given, also no position can be given.
12463 In this case the frame width is adjusted to the box content like for
12472 \begin_layout Standard
12479 is inserted, a box appears containing three blue boxes.
12480 The first two boxes are surrounded by brackets and denote the two optional
12482 The third box is for formula parts like for
12491 \begin_layout Standard
12493 \begin_inset Note Note
12496 \begin_layout Plain Layout
12497 The table has been set into a minipage to make the footnote appearing.
12498 Otherwise the footnote text would not be displayed.
12504 \begin_inset Box Frameless
12513 height_special "totalheight"
12516 \begin_layout Plain Layout
12518 \begin_inset Tabular
12519 <lyxtabular version="3" rows="5" columns="2">
12521 <column alignment="center" valignment="top" width="0">
12522 <column alignment="center" valignment="top" width="0">
12524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12527 \begin_layout Plain Layout
12532 \begin_layout Plain Layout
12533 Due to a bug in LyX it is not possible to create a new formula with
12538 \begin_inset CommandInset href
12540 name "LyX-bug #1435"
12541 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12558 \begin_layout Plain Layout
12560 \begin_inset Note Note
12563 \begin_layout Plain Layout
12570 is only used as spacer.
12582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12585 \begin_layout Plain Layout
12592 \begin_layout Plain Layout
12611 \begin_layout Plain Layout
12625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12628 \begin_layout Plain Layout
12629 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12642 \begin_layout Plain Layout
12649 \begin_layout Plain Layout
12664 \begin_layout Plain Layout
12678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12681 \begin_layout Plain Layout
12682 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12695 \begin_layout Plain Layout
12702 \begin_layout Plain Layout
12716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12719 \begin_layout Plain Layout
12720 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12733 \begin_layout Plain Layout
12740 \begin_layout Plain Layout
12750 \begin_inset Formula $\to$
12754 \begin_inset Formula $\to$
12767 \begin_layout Plain Layout
12777 \begin_inset Formula $\downarrow$
12785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12788 \begin_layout Plain Layout
12789 \begin_inset Formula $\raisebox{6mm}{}$
12793 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12797 \begin_inset Formula $\raisebox{-4mm}{}$
12818 \begin_layout Standard
12819 The frame thickness can also be adjusted.
12820 To do this the following commands have to be inserted in TeX-mode before
12824 \begin_layout Standard
12834 \begin_inset Quotes eld
12838 \begin_inset Quotes erd
12852 \begin_inset Quotes eld
12856 \begin_inset Quotes erd
12862 \begin_layout Standard
12863 \begin_inset Quotes eld
12867 \begin_inset Quotes erd
12870 specifies the minimal distance between the frame and the first character
12872 An example for this is the following framed formula:
12876 \begin_layout Plain Layout
12888 \begin_inset Formula \[
12893 Before this formula the commands
12896 \begin_layout Standard
12918 \begin_layout Standard
12919 were inserted in TeX-mode.
12920 The given values are used for all following boxes.
12923 \begin_layout Standard
12924 To return to the standard frame size, the command
12927 \begin_layout Standard
12952 \begin_layout Plain Layout
12966 \begin_layout Standard
12967 is inserted in TeX-mode before the next formula.
12970 \begin_layout Subsection
12971 Boxes without Frame
12972 \begin_inset CommandInset label
12974 name "sub:Boxes-without-Frame"
12982 \begin_layout Plain Layout
12983 Boxes ! without frame
12991 \begin_layout Standard
12992 For boxes without a frame there are the following box commands:
13002 \begin_layout Plain Layout
13020 \begin_layout Plain Layout
13038 \begin_layout Plain Layout
13049 \begin_layout Standard
13056 a box can be super- or subscripted.
13057 But in contrary to normal super- and subscripting, the characters in the
13058 box keep their font size.
13065 is used in the following scheme:
13068 \begin_layout Standard
13073 raisebox{height}{box content}
13076 \begin_layout Standard
13077 When the box should contain a formula, an extra formula is needed like for
13087 \begin_layout Standard
13089 \begin_inset Tabular
13090 <lyxtabular version="3" rows="4" columns="2">
13092 <column alignment="center" valignment="top" width="0">
13093 <column alignment="center" valignment="top" width="0">
13095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13098 \begin_layout Plain Layout
13104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13107 \begin_layout Plain Layout
13115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13118 \begin_layout Plain Layout
13122 \begin_inset Formula $\to$
13128 \begin_inset Formula $\to$
13136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13139 \begin_layout Plain Layout
13140 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13153 \begin_layout Plain Layout
13157 \begin_inset Formula $\to$
13163 \begin_inset Formula $\to$
13171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13174 \begin_layout Plain Layout
13175 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13188 \begin_layout Plain Layout
13192 \begin_inset Formula $\to$
13207 \begin_layout Plain Layout
13221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13224 \begin_layout Plain Layout
13228 \begin_layout Plain Layout
13252 \begin_layout Standard
13253 The last formula can currently only be created using TeX-mode because LyX
13254 inserts a box instead of the needed extra formula.
13258 \begin_layout Plain Layout
13260 \begin_inset CommandInset href
13262 name "LyX-bug #1435"
13263 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13275 \begin_layout Standard
13300 , with the difference that there is no frame.
13303 \begin_layout Subsection
13305 \begin_inset CommandInset label
13307 name "sub:Colored-Boxes"
13315 \begin_layout Plain Layout
13324 \begin_layout Standard
13325 To be able to use all commands explained in this section, the LaTeX-package
13334 \begin_layout Plain Layout
13339 is part of every LaTeX standard installation.
13348 \begin_layout Plain Layout
13354 has to be loaded in the LaTeX-preamble with the line
13358 \begin_layout Plain Layout
13359 When text is colored somewhere in the document with a predefined color,
13360 LyX loads the LaTeX-package
13365 Thus it is possible that the package is loaded twice, but this doesn't
13372 \begin_inset Note Note
13375 \begin_layout Plain Layout
13376 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13385 \begin_layout Standard
13393 \begin_layout Standard
13394 \begin_inset VSpace medskip
13397 To color boxes, the command
13407 \begin_layout Plain Layout
13415 is used in the following scheme:
13418 \begin_layout Standard
13423 colorbox{color}{box content}
13426 \begin_layout Standard
13427 The box content can also be a box and a
13433 can also be part of another box (see the 2nd and 3rd example).
13434 When the box should contain a formula, an extra formula has to be created,
13445 \begin_layout Plain Layout
13446 This also applies for the command
13454 \begin_inset CommandInset href
13456 name "LyX-bug #1435"
13457 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13469 \begin_layout Standard
13470 One of the following predefined colors can be chosen:
13473 \begin_layout Standard
13507 \begin_layout Standard
13509 \begin_inset Tabular
13510 <lyxtabular version="3" rows="4" columns="2">
13512 <column alignment="center" valignment="top" width="0">
13513 <column alignment="center" valignment="top" width="0">
13515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13518 \begin_layout Plain Layout
13524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13527 \begin_layout Plain Layout
13529 \begin_inset Note Note
13532 \begin_layout Plain Layout
13539 is only used as spacer.
13551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13554 \begin_layout Plain Layout
13558 \begin_inset Formula $\to$
13568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13571 \begin_layout Plain Layout
13572 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13585 \begin_layout Plain Layout
13589 \begin_inset Formula $\to$
13600 \begin_layout Plain Layout
13614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13617 \begin_layout Plain Layout
13618 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13631 \begin_layout Plain Layout
13638 \begin_layout Plain Layout
13650 \begin_inset Formula $\to$
13660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13663 \begin_layout Plain Layout
13664 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13680 \begin_layout Standard
13687 only colors the box but not the characters in the box.
13688 To color all characters, the whole formula is highlighted and the wanted
13689 color is chosen in the
13692 \begin_inset space ~
13698 The dialog can be called with the toolbar button
13699 \begin_inset Graphics
13700 filename ../images/dialog-show_character.png
13707 Edit\SpecialChar \menuseparator
13709 \begin_inset space ~
13712 Style\SpecialChar \menuseparator
13716 The formula number has then the same color as the formula.
13717 When the formula number should get another color than the formula characters,
13718 the color must be changed within the formula.
13721 \begin_layout Standard
13725 \begin_layout Standard
13728 \begin_inset Formula \begin{equation}
13729 \int A=B\label{eq:red}\end{equation}
13736 \begin_inset Formula \begin{equation}
13737 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13744 \begin_layout Standard
13746 \begin_inset CommandInset ref
13752 is completely colored red.
13753 \begin_inset Newline newline
13757 \begin_inset CommandInset ref
13759 reference "eq:redgreen"
13763 was first completely colored green to set the color for the formula number.
13764 Subsequently the formula characters were colored red.
13767 \begin_layout Standard
13768 \begin_inset VSpace bigskip
13771 To color the frame different than the rest of the box, the command
13781 \begin_layout Plain Layout
13789 is used in the following scheme:
13792 \begin_layout Standard
13797 fcolorbox{frame color}{color}{box content}
13800 \begin_layout Standard
13807 is an extension of the command
13814 The frame width is set, like for
13837 \begin_layout Plain Layout
13849 \begin_inset Formula \[
13850 \fcolorbox{cyan}{magenta}{A=B}\]
13858 \begin_layout Plain Layout
13872 \begin_layout Standard
13873 This formula was created with the command
13874 \begin_inset Newline newline
13882 \begin_inset Formula $\to$
13888 \begin_inset Formula $\to$
13898 \begin_layout Standard
13899 \begin_inset VSpace bigskip
13902 To use other colors than the predefined ones, they have to be defined first.
13905 \begin_layout Standard
13906 One can for example define the color
13907 \begin_inset Quotes eld
13915 \begin_inset Quotes erd
13918 with the LaTeX-preamble line:
13921 \begin_layout Standard
13926 definecolor{darkgreen}{cmyk}{0.5,
13944 \begin_layout Plain Layout
13955 \begin_layout Standard
13960 is the color space that denotes the colors
13977 The four comma separated numbers are the portion factor for the corresponding
13978 colors of the color space.
13979 The factors can be in the range of 0
13980 \begin_inset space \thinspace{}
13984 \begin_inset space \thinspace{}
13992 also the color space
13996 can be used for definitions.
14013 , so that there are in this case three portion factors for the corresponding
14015 Furthermore there is the color space
14019 with one portion factor for the gray value.
14022 \begin_layout Standard
14023 As example a framed box with the new defined color
14027 where the characters have been colored
14032 \begin_inset Formula \begin{equation}
14033 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14040 \begin_layout Standard
14041 Self-defined colors can also be used for text with the help of the command
14052 \begin_layout Plain Layout
14061 \begin_layout Standard
14065 \begin_layout Plain Layout
14069 textcolor{darkgreen}{
14075 \begin_inset Quotes eld
14079 \begin_inset Quotes erd
14086 \begin_layout Plain Layout
14096 \begin_layout Standard
14107 \begin_layout Plain Layout
14115 is used in the scheme
14119 textcolor{color}{characters to color}
14124 \begin_layout Subsection
14126 \begin_inset CommandInset label
14128 name "sub:Paragraph-Boxes"
14136 \begin_layout Plain Layout
14137 Boxes ! as paragraph
14145 \begin_layout Standard
14146 A box that can contain several lines and paragraphs, a so called paragraph
14147 box (parbox), can be created with the menu
14149 Insert\SpecialChar \menuseparator
14152 or the toolbar button
14153 \begin_inset Graphics
14154 filename ../images/box-insert.png
14162 \begin_layout Standard
14163 The following example shows a framed parbox in a line:
14166 \begin_layout Standard
14167 \begin_inset VSpace medskip
14171 \begin_inset Box Boxed
14180 height_special "totalheight"
14183 \begin_layout Plain Layout
14184 This is a paragraph box.
14186 \begin_inset space \thinspace{}
14189 cm long and can also contain formulas:
14190 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14201 \begin_layout Standard
14202 \begin_inset VSpace medskip
14208 \begin_layout Standard
14209 Such a box is created by right-clicking on the gray box inset.
14210 A dialog pops up showing the box properties.
14224 \begin_inset space \thinspace{}
14229 Vertical Box Alignment
14234 \begin_layout Standard
14235 \begin_inset VSpace medskip
14238 In LaTeX a parbox is created with the command
14248 \begin_layout Plain Layout
14256 that has the following scheme:
14259 \begin_layout Standard
14264 parbox[position]{width}{box content}
14267 \begin_layout Standard
14281 for bottom means that the box is aligned within the surrounding text with
14287 for top this is done with the first line.
14288 When no position is given, the box will be vertically centered, see section
14296 \begin_inset space ~
14301 manual for examples.
14304 \begin_layout Standard
14305 \begin_inset VSpace bigskip
14308 To frame formulas completely, including the formula number, the formula
14309 must be set into a parbox.
14310 To do this, the command
14324 is inserted in TeX-mode before the formula.
14333 \begin_layout Plain Layout
14343 is hereby the line width set for the document.
14344 Because the frame is outside the parbox, 2
14345 \begin_inset space \thinspace{}
14348 times the frame separation and the frame thickness must be subtracted from
14350 As this is not automatically done by LyX due to a bug
14354 \begin_layout Plain Layout
14355 \begin_inset CommandInset href
14357 name "LyX-bug #4483"
14358 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14367 , TeX-mode has to be used.
14368 To be able to multiply and subtract in arguments, the LaTeX-package
14376 \begin_layout Plain Layout
14381 is part of every LaTeX standard installation.
14390 \begin_layout Plain Layout
14396 must be loaded in the LaTeX-preamble with the line
14399 \begin_layout Standard
14407 \begin_layout Standard
14408 Behind the formula both boxes are closed by entering
14413 Here is an example:
14417 \begin_layout Plain Layout
14431 \begin_layout Standard
14435 \begin_layout Plain Layout
14453 \begin_inset Formula \begin{equation}
14454 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14462 \begin_layout Plain Layout
14473 \begin_layout Plain Layout
14487 \begin_layout Standard
14488 \begin_inset VSpace medskip
14491 As a parbox is used as argument of
14497 , there is in this case no difference between
14512 \begin_layout Standard
14513 \begin_inset VSpace bigskip
14516 Paragraph boxes are very useful to comment formulas directly.
14523 is used in combination with the command
14537 \begin_inset CommandInset ref
14539 reference "sub:User-defined-Numbering"
14546 \begin_layout Standard
14547 An example of a formula commented with
14556 \begin_layout Standard
14560 \begin_layout Plain Layout
14573 This is a description.
14574 It is distinctly separated from the formula and multiline.
14578 \begin_layout Plain Layout
14590 \begin_layout Standard
14591 Such a formula must be inserted completely in TeX-mode because LyX does
14592 not yet support the command
14599 The formula is created with the following command sequence:
14602 \begin_layout Standard
14615 is inserted in TeX-mode.
14619 \begin_layout Plain Layout
14620 When the formula style
14632 can also be replaced by
14639 (formula styles see
14640 \begin_inset CommandInset ref
14642 reference "sec:Formula-Styles"
14651 Then the description follows as normal text, and finally
14657 is inserted in TeX-mode.
14670 hereby create a displayed formula.
14673 \begin_layout Standard
14680 can be seen in this example that was
14681 \begin_inset Quotes eld
14685 \begin_inset Quotes erd
14688 using the mathematical textmode:
14689 \begin_inset Formula \[
14690 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14697 \begin_layout Section
14702 \begin_layout Plain Layout
14711 \begin_layout Subsection
14713 \begin_inset CommandInset label
14715 name "sub:Big-Operators"
14723 \begin_layout Plain Layout
14733 \begin_layout Plain Layout
14743 \begin_layout Plain Layout
14752 \begin_layout Standard
14753 To be able to use all integral operators listed here, the option
14755 Use esint package automatically
14757 must be set in the document settings under
14760 \begin_inset space ~
14768 \begin_layout Standard
14769 \begin_inset space \hfill{}
14773 \begin_inset Tabular
14774 <lyxtabular version="3" rows="11" columns="2">
14776 <column alignment="center" valignment="top" width="0pt">
14777 <column alignment="center" valignment="top" width="0pt">
14779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14782 \begin_layout Plain Layout
14788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14791 \begin_layout Plain Layout
14799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14802 \begin_layout Plain Layout
14809 \begin_layout Plain Layout
14822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14825 \begin_layout Plain Layout
14826 \begin_inset Formula $\sum$
14836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14839 \begin_layout Plain Layout
14846 \begin_layout Plain Layout
14859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14862 \begin_layout Plain Layout
14863 \begin_inset Formula $\int$
14873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14876 \begin_layout Plain Layout
14884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14887 \begin_layout Plain Layout
14888 \begin_inset Formula $\intop$
14898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14901 \begin_layout Plain Layout
14909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14912 \begin_layout Plain Layout
14913 \begin_inset Formula $\oint$
14923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14926 \begin_layout Plain Layout
14934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14937 \begin_layout Plain Layout
14938 \begin_inset Formula $\ointop$
14948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14951 \begin_layout Plain Layout
14959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14962 \begin_layout Plain Layout
14963 \begin_inset Formula $\ointctrclockwise$
14973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14976 \begin_layout Plain Layout
14984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14987 \begin_layout Plain Layout
14988 \begin_inset Formula $\ointclockwise$
14998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15001 \begin_layout Plain Layout
15009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15012 \begin_layout Plain Layout
15013 \begin_inset Formula $\sqint$
15023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15026 \begin_layout Plain Layout
15034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15037 \begin_layout Plain Layout
15038 \begin_inset Formula $\bigcap$
15048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15051 \begin_layout Plain Layout
15059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15062 \begin_layout Plain Layout
15063 \begin_inset Formula $\bigcup$
15077 \begin_inset space \hfill{}
15081 \begin_inset Tabular
15082 <lyxtabular version="3" rows="10" columns="2">
15084 <column alignment="center" valignment="top" width="0pt">
15085 <column alignment="center" valignment="top" width="0pt">
15087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15090 \begin_layout Plain Layout
15096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15099 \begin_layout Plain Layout
15107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15110 \begin_layout Plain Layout
15117 \begin_layout Plain Layout
15130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15133 \begin_layout Plain Layout
15134 \begin_inset Formula $\prod$
15144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15147 \begin_layout Plain Layout
15155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15158 \begin_layout Plain Layout
15159 \begin_inset Formula $\coprod$
15169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15172 \begin_layout Plain Layout
15180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15183 \begin_layout Plain Layout
15184 \begin_inset Formula $\bigodot$
15194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15197 \begin_layout Plain Layout
15205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15208 \begin_layout Plain Layout
15209 \begin_inset Formula $\bigotimes$
15219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15222 \begin_layout Plain Layout
15230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15233 \begin_layout Plain Layout
15234 \begin_inset Formula $\bigoplus$
15244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15247 \begin_layout Plain Layout
15255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15258 \begin_layout Plain Layout
15259 \begin_inset Formula $\bigwedge$
15269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15272 \begin_layout Plain Layout
15280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15283 \begin_layout Plain Layout
15284 \begin_inset Formula $\bigvee$
15294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15297 \begin_layout Plain Layout
15305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15308 \begin_layout Plain Layout
15309 \begin_inset Formula $\bigsqcup$
15319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15322 \begin_layout Plain Layout
15330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15333 \begin_layout Plain Layout
15334 \begin_inset Formula $\biguplus$
15348 \begin_inset space \hfill{}
15354 \begin_layout Standard
15355 All big operators can also be inserted via the math toolbar button
15356 \begin_inset Graphics
15357 filename ../images/math/intop.png
15365 \begin_layout Standard
15366 The operators are called big because they are bigger than the sometimes
15367 equal looking binary operators.
15368 All big operators can have limits as described in the next subsection.
15371 \begin_layout Standard
15397 \begin_inset space ~
15400 in the style the operator limits are displayed, see
15401 \begin_inset CommandInset ref
15403 reference "sub:Operator-Limits"
15411 \begin_layout Subsubsection*
15412 Advices for Integrals
15415 \begin_layout Standard
15420 in an integral is an operator, that therefore has to be set upright.
15421 This is done by highlighting the
15425 and using the keyboard shortcut
15428 \begin_inset space ~
15437 \begin_layout Plain Layout
15443 \begin_inset CommandInset ref
15445 reference "sub:Font-Styles"
15455 Finally the smallest space is inserted before the
15459 , as this is usual for operators.
15463 \begin_layout Standard
15465 \begin_inset Formula $\int A(x)dx$
15469 \begin_inset Newline newline
15476 \begin_layout Plain Layout
15486 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15492 \begin_layout Standard
15493 For multiple integrals there are the following commands:
15494 \begin_inset VSpace medskip
15500 \begin_layout Standard
15501 \begin_inset space \hfill{}
15505 \begin_inset Tabular
15506 <lyxtabular version="3" rows="4" columns="2">
15508 <column alignment="center" valignment="top" width="0">
15509 <column alignment="center" valignment="top" width="0">
15511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15514 \begin_layout Plain Layout
15520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15523 \begin_layout Plain Layout
15525 \begin_inset Note Note
15528 \begin_layout Plain Layout
15535 is only used as spacer.
15547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15550 \begin_layout Plain Layout
15558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15561 \begin_layout Plain Layout
15562 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15575 \begin_layout Plain Layout
15583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15586 \begin_layout Plain Layout
15587 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15600 \begin_layout Plain Layout
15608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15611 \begin_layout Plain Layout
15612 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15626 \begin_inset space \hfill{}
15630 \begin_inset Tabular
15631 <lyxtabular version="3" rows="4" columns="2">
15633 <column alignment="center" valignment="top" width="0">
15634 <column alignment="center" valignment="top" width="0">
15636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15639 \begin_layout Plain Layout
15645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15648 \begin_layout Plain Layout
15656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15659 \begin_layout Plain Layout
15667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15670 \begin_layout Plain Layout
15671 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15684 \begin_layout Plain Layout
15692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15695 \begin_layout Plain Layout
15696 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15709 \begin_layout Plain Layout
15717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15720 \begin_layout Plain Layout
15721 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15735 \begin_inset space \hfill{}
15741 \begin_layout Subsection
15743 \begin_inset CommandInset label
15745 name "sub:Operator-Limits"
15753 \begin_layout Plain Layout
15762 \begin_layout Standard
15763 Limits are created by super- and subscripts:
15766 \begin_layout Standard
15768 \begin_inset Tabular
15769 <lyxtabular version="3" rows="2" columns="2">
15771 <column alignment="center" valignment="top" width="0pt">
15772 <column alignment="center" valignment="top" width="0pt">
15774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15777 \begin_layout Plain Layout
15783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15786 \begin_layout Plain Layout
15788 \begin_inset Note Note
15791 \begin_layout Plain Layout
15798 is only used as spacer.
15810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15813 \begin_layout Plain Layout
15822 \begin_layout Plain Layout
15832 \begin_inset Formula $\to$
15836 \begin_inset Formula $\to$
15844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15847 \begin_layout Plain Layout
15848 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15864 \begin_layout Standard
15865 Limits of inline formulas are set right beside the operator.
15866 Limits in displayed formulas are set above or below the operator, except
15867 of integral limits.
15870 \begin_layout Standard
15871 To force that the limits are set beside the operator, the cursor is set
15872 directly behind the operator and the limits type is changed with the menu
15875 Edit\SpecialChar \menuseparator
15876 Math\SpecialChar \menuseparator
15888 \begin_inset space ~
15897 \begin_layout Standard
15898 The default limits type is this:
15899 \begin_inset Formula \[
15900 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15904 This is how it looks when the limits type was changed to
15911 \begin_inset Formula \[
15912 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15916 For integrals, except of
15928 , the limits are by default set beside the operator.
15929 But for multiple integrals the limits are often set below the operator.
15930 In the following example the limits type was therefore set to
15934 and so set below the integrals:
15935 \begin_inset Formula \begin{equation}
15936 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15943 \begin_layout Standard
15944 \begin_inset VSpace medskip
15947 To specify conditions for limits, the commands
15957 \begin_layout Plain Layout
15975 \begin_layout Plain Layout
15984 To create for example this expression
15985 \begin_inset Formula \begin{equation}
15986 \sum_{\begin{subarray}{c}
15988 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
15995 \begin_layout Standard
15996 the following has to be done:
15997 \begin_inset Newline newline
16012 \begin_layout Plain Layout
16024 One is now in a blue box under the summation operator and insert there
16033 \begin_layout Plain Layout
16045 The blue box is now within a purple box and now several lines can be written
16047 A new line is created by inserting a line break (
16053 \begin_inset Newline newline
16058 0<k<1000 Ctrl-Return
16059 \begin_inset Newline newline
16064 is typed in, a new box appears below for the new line.
16067 \begin_layout Standard
16068 The alignment of the lines can be changed to left aligned with the
16078 Edit\SpecialChar \menuseparator
16082 To get right alignment,
16090 \begin_layout Plain Layout
16101 is inserted at the beginning of the line.
16104 \begin_layout Standard
16117 with the difference that the lines are always centered.
16120 \begin_layout Standard
16121 \begin_inset VSpace bigskip
16125 \begin_inset CommandInset ref
16127 reference "eq:substack"
16131 there can be too much space beside an operator, because the characters
16132 following the operator are set beside the limits.
16135 \begin_layout Standard
16136 To avoid this, the following macro can be used in the LaTeX-preamble:
16139 \begin_layout Standard
16153 \begin_inset Newline newline
16165 \begin_inset Newline newline
16172 mathclapinternal #1#2{
16176 mathsurround =0pt #1{#2}$}}
16179 \begin_layout Standard
16180 This defines the command
16190 \begin_layout Plain Layout
16198 that sets the width of the limit to 0
16199 \begin_inset space \thinspace{}
16203 The command scheme is
16206 \begin_layout Standard
16214 \begin_layout Standard
16215 where the limit can consist of several conditions.
16218 \begin_layout Standard
16220 \begin_inset CommandInset ref
16222 reference "eq:substack"
16226 , one uses the command
16229 \begin_layout Standard
16242 \begin_layout Plain Layout
16251 0<k<1000 Ctrl-Enter
16254 \begin_layout Standard
16255 to create the lower limit.
16256 The summand is now directly behind the summation operator:
16257 \begin_inset Formula \[
16258 \sum_{\mathclap{\substack{0<k<1000\\
16259 \\k\,\in\,\mathbb{N}}
16267 \begin_layout Standard
16268 \begin_inset VSpace bigskip
16271 How to use one limit for several operators is described in
16272 \begin_inset CommandInset ref
16274 reference "sub:Self-defined-Operators"
16281 \begin_layout Standard
16282 \begin_inset Newpage newpage
16288 \begin_layout Subsection
16290 \begin_inset CommandInset label
16292 name "sub:Binary-Operators"
16300 \begin_layout Plain Layout
16309 \begin_layout Standard
16310 Binary operators are surrounded by space when there is a character before
16312 \begin_inset VSpace medskip
16318 \begin_layout Standard
16319 \begin_inset space \hfill{}
16323 \begin_inset Tabular
16324 <lyxtabular version="3" rows="13" columns="2">
16326 <column alignment="center" valignment="top" width="0pt">
16327 <column alignment="center" valignment="top" width="0pt">
16329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16332 \begin_layout Plain Layout
16334 \begin_inset Note Note
16337 \begin_layout Plain Layout
16344 is only used as spacer.
16354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16357 \begin_layout Plain Layout
16365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16368 \begin_layout Plain Layout
16374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16377 \begin_layout Plain Layout
16378 \begin_inset Formula $+$
16388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16391 \begin_layout Plain Layout
16397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16400 \begin_layout Plain Layout
16401 \begin_inset Formula $-$
16411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16414 \begin_layout Plain Layout
16422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16425 \begin_layout Plain Layout
16426 \begin_inset Formula $\pm$
16436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16439 \begin_layout Plain Layout
16447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16450 \begin_layout Plain Layout
16451 \begin_inset Formula $\mp$
16461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16464 \begin_layout Plain Layout
16472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16475 \begin_layout Plain Layout
16476 \begin_inset Formula $\cdot$
16486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16489 \begin_layout Plain Layout
16497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16500 \begin_layout Plain Layout
16501 \begin_inset Formula $\times$
16511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16514 \begin_layout Plain Layout
16522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16525 \begin_layout Plain Layout
16526 \begin_inset Formula $\div$
16536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16539 \begin_layout Plain Layout
16543 \begin_layout Plain Layout
16556 \begin_layout Plain Layout
16568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16571 \begin_layout Plain Layout
16572 \begin_inset Formula $*$
16582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16585 \begin_layout Plain Layout
16593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16596 \begin_layout Plain Layout
16597 \begin_inset Formula $\star$
16607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16610 \begin_layout Plain Layout
16618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16621 \begin_layout Plain Layout
16622 \begin_inset Formula $\circ$
16632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16635 \begin_layout Plain Layout
16643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16646 \begin_layout Plain Layout
16647 \begin_inset Formula $\diamond$
16657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16660 \begin_layout Plain Layout
16668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16671 \begin_layout Plain Layout
16672 \begin_inset Formula $\bullet$
16686 \begin_inset space \hfill{}
16690 \begin_inset Tabular
16691 <lyxtabular version="3" rows="13" columns="2">
16693 <column alignment="center" valignment="top" width="0pt">
16694 <column alignment="center" valignment="top" width="0pt">
16696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16699 \begin_layout Plain Layout
16705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16708 \begin_layout Plain Layout
16716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16719 \begin_layout Plain Layout
16727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16730 \begin_layout Plain Layout
16731 \begin_inset Formula $\nabla$
16741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16744 \begin_layout Plain Layout
16752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16755 \begin_layout Plain Layout
16756 \begin_inset Formula $\bigtriangledown$
16766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16769 \begin_layout Plain Layout
16777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16780 \begin_layout Plain Layout
16781 \begin_inset Formula $\bigtriangleup$
16791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16794 \begin_layout Plain Layout
16802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16805 \begin_layout Plain Layout
16806 \begin_inset Formula $\Box$
16816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16819 \begin_layout Plain Layout
16827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16830 \begin_layout Plain Layout
16831 \begin_inset Formula $\cap$
16841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16844 \begin_layout Plain Layout
16852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16855 \begin_layout Plain Layout
16856 \begin_inset Formula $\cup$
16866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16869 \begin_layout Plain Layout
16877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16880 \begin_layout Plain Layout
16881 \begin_inset Formula $\dagger$
16891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16894 \begin_layout Plain Layout
16902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16905 \begin_layout Plain Layout
16906 \begin_inset Formula $\ddagger$
16916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16919 \begin_layout Plain Layout
16927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16930 \begin_layout Plain Layout
16931 \begin_inset Formula $\wr$
16941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16944 \begin_layout Plain Layout
16952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16955 \begin_layout Plain Layout
16956 \begin_inset Formula $\bigcirc$
16966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16969 \begin_layout Plain Layout
16977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16980 \begin_layout Plain Layout
16981 \begin_inset Formula $\wedge$
16991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16994 \begin_layout Plain Layout
17002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17005 \begin_layout Plain Layout
17006 \begin_inset Formula $\vee$
17020 \begin_inset space \hfill{}
17024 \begin_inset Tabular
17025 <lyxtabular version="3" rows="13" columns="2">
17027 <column alignment="center" valignment="top" width="0pt">
17028 <column alignment="center" valignment="top" width="0pt">
17030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17033 \begin_layout Plain Layout
17039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17042 \begin_layout Plain Layout
17050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17053 \begin_layout Plain Layout
17061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17064 \begin_layout Plain Layout
17065 \begin_inset Formula $\oplus$
17075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17078 \begin_layout Plain Layout
17086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17089 \begin_layout Plain Layout
17090 \begin_inset Formula $\ominus$
17100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17103 \begin_layout Plain Layout
17111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17114 \begin_layout Plain Layout
17115 \begin_inset Formula $\otimes$
17125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17128 \begin_layout Plain Layout
17136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17139 \begin_layout Plain Layout
17140 \begin_inset Formula $\oslash$
17150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17153 \begin_layout Plain Layout
17161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17164 \begin_layout Plain Layout
17165 \begin_inset Formula $\odot$
17175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17178 \begin_layout Plain Layout
17186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17189 \begin_layout Plain Layout
17190 \begin_inset Formula $\amalg$
17200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17203 \begin_layout Plain Layout
17211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17214 \begin_layout Plain Layout
17215 \begin_inset Formula $\uplus$
17225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17228 \begin_layout Plain Layout
17236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17239 \begin_layout Plain Layout
17240 \begin_inset Formula $\setminus$
17250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17253 \begin_layout Plain Layout
17261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17264 \begin_layout Plain Layout
17265 \begin_inset Formula $\sqcap$
17275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17278 \begin_layout Plain Layout
17286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17289 \begin_layout Plain Layout
17290 \begin_inset Formula $\sqcup$
17300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17303 \begin_layout Plain Layout
17311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17314 \begin_layout Plain Layout
17315 \begin_inset Formula $\triangleleft$
17325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17328 \begin_layout Plain Layout
17336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17339 \begin_layout Plain Layout
17340 \begin_inset Formula $\triangleright$
17354 \begin_inset space \hfill{}
17360 \begin_layout Standard
17361 All binary operators can also be inserted via the math toolbar button
17362 \begin_inset Graphics
17363 filename ../images/math/pm.png
17371 \begin_layout Standard
17372 To typeset the Laplace operator also
17389 \begin_inset Formula $\nabla^{2}$
17392 ) can be used instead of
17401 \begin_layout Standard
17408 Insert\SpecialChar \menuseparator
17420 \begin_layout Subsection
17421 Self-defined Operators
17422 \begin_inset CommandInset label
17424 name "sub:Self-defined-Operators"
17432 \begin_layout Plain Layout
17433 Operators ! self-defined
17441 \begin_layout Standard
17442 With the help of the command
17446 DeclareMathOperator
17452 \begin_layout Plain Layout
17457 DeclareMathOperator
17462 custom operators can be defined in the LaTeX-preamble.
17463 Its command scheme is:
17466 \begin_layout Standard
17471 DeclareMathOperator{new command}{display}
17474 \begin_layout Standard
17475 Display can be characters or symbols that define how the operator looks
17477 To define a big operator a * is set behind the command.
17478 All self-defined big operators can have limits as described in
17479 \begin_inset CommandInset ref
17481 reference "sub:Operator-Limits"
17488 \begin_layout Standard
17489 For example the LaTeX-preamble line
17492 \begin_layout Standard
17497 DeclareMathOperator*{
17504 \begin_layout Standard
17505 defines the command
17511 , that inserts a big operator consisting of the lozenge symbol from
17512 \begin_inset CommandInset ref
17514 reference "sub:Miscellaneous-Symbols"
17519 \begin_inset Formula \[
17520 \Lozenge_{n=1}^{\infty}\]
17524 The command for this formula is:
17535 \begin_inset Formula $\to$
17541 \begin_layout Standard
17542 \begin_inset VSpace bigskip
17545 When self-defined operators are not used several times in the document,
17546 they can also be defined with the commands
17556 \begin_layout Plain Layout
17574 \begin_layout Plain Layout
17582 , which have the following scheme:
17585 \begin_layout Standard
17599 \begin_layout Standard
17606 defines big operators,
17615 \begin_layout Standard
17623 \begin_inset space \thinspace{}
17627 \begin_inset space ~
17630 be used to use one limit for several operators:
17633 \begin_layout Standard
17634 \begin_inset Formula \[
17635 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17642 \begin_layout Standard
17643 The command for the formula above is:
17644 \begin_inset Newline newline
17663 \begin_layout Plain Layout
17675 \begin_inset Formula $\to$
17684 \begin_layout Plain Layout
17698 \begin_layout Section
17703 \begin_layout Plain Layout
17712 \begin_layout Subsection
17714 \begin_inset CommandInset label
17716 name "sub:Font-Styles"
17724 \begin_layout Plain Layout
17733 \begin_layout Standard
17734 Latin letters in formulas can be set in one of the following font styles:
17735 \begin_inset VSpace -2mm
17741 \begin_layout Standard
17743 \begin_inset Tabular
17744 <lyxtabular version="3" rows="6" columns="3">
17746 <column alignment="center" valignment="top" width="0">
17747 <column alignment="center" valignment="top" width="0">
17748 <column alignment="center" valignment="top" width="0">
17750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17753 \begin_layout Plain Layout
17759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17762 \begin_layout Plain Layout
17768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17771 \begin_layout Plain Layout
17779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17782 \begin_layout Plain Layout
17791 \begin_layout Plain Layout
17807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17810 \begin_layout Plain Layout
17811 \begin_inset Formula $\mathbb{ABC}$
17819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17822 \begin_layout Plain Layout
17830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17833 \begin_layout Plain Layout
17842 \begin_layout Plain Layout
17858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17861 \begin_layout Plain Layout
17862 \begin_inset Formula $\mathbf{AbC}$
17870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17873 \begin_layout Plain Layout
17881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17884 \begin_layout Plain Layout
17893 \begin_layout Plain Layout
17909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17912 \begin_layout Plain Layout
17913 \begin_inset Formula $\boldsymbol{AbC}$
17921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17924 \begin_layout Plain Layout
17925 Alt-c b or Ctrl-Alt-b
17932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17935 \begin_layout Plain Layout
17944 \begin_layout Plain Layout
17960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17963 \begin_layout Plain Layout
17964 \begin_inset Formula $\mathcal{ABC}$
17972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17975 \begin_layout Plain Layout
17983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17986 \begin_layout Plain Layout
17995 \begin_layout Plain Layout
18011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18014 \begin_layout Plain Layout
18015 \begin_inset Formula $\mathfrak{AbC}$
18023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18026 \begin_layout Plain Layout
18040 \begin_layout Standard
18042 \begin_inset Tabular
18043 <lyxtabular version="3" rows="5" columns="3">
18045 <column alignment="center" valignment="top" width="0">
18046 <column alignment="center" valignment="top" width="0">
18047 <column alignment="center" valignment="top" width="0">
18049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18052 \begin_layout Plain Layout
18058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18061 \begin_layout Plain Layout
18067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18070 \begin_layout Plain Layout
18078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18081 \begin_layout Plain Layout
18090 \begin_layout Plain Layout
18106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18109 \begin_layout Plain Layout
18110 \begin_inset Formula $\mathit{AbC}$
18118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18121 \begin_layout Plain Layout
18129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18132 \begin_layout Plain Layout
18141 \begin_layout Plain Layout
18157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18160 \begin_layout Plain Layout
18161 \begin_inset Formula $\mathrm{AbC}$
18169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18172 \begin_layout Plain Layout
18180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18183 \begin_layout Plain Layout
18192 \begin_layout Plain Layout
18208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18211 \begin_layout Plain Layout
18212 \begin_inset Formula $\mathsf{AbC}$
18220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18223 \begin_layout Plain Layout
18231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18234 \begin_layout Plain Layout
18243 \begin_layout Plain Layout
18259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18262 \begin_layout Plain Layout
18263 \begin_inset Formula $\mathtt{AbC}$
18271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18274 \begin_layout Plain Layout
18288 \begin_layout Standard
18289 \begin_inset Note Greyedout
18292 \begin_layout Plain Layout
18309 can only be used for big letters.
18317 \begin_layout Standard
18318 Predefined is the style
18327 \begin_layout Standard
18328 The style commands work also for letters in mathematical constructs:
18329 \begin_inset Formula \[
18330 \mathfrak{A=\frac{b}{C}}\]
18337 \begin_layout Standard
18338 Characters in mathematical text don't appear in a math font style but in
18339 the text font style
18346 That their style can't be set correctly via the text style dialog is a
18351 \begin_layout Plain Layout
18352 \begin_inset CommandInset href
18354 name "LyX-bug #4091"
18355 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18367 \begin_layout Standard
18368 Instead of the style commands the dialog
18370 Edit\SpecialChar \menuseparator
18371 Math\SpecialChar \menuseparator
18374 or the toolbar button
18375 \begin_inset Graphics
18376 filename ../images/math/font.png
18384 \begin_layout Subsection
18386 \begin_inset CommandInset label
18388 name "sub:Bold-Formulas"
18396 \begin_layout Plain Layout
18405 \begin_layout Standard
18406 To make a complete formula bold, the command
18412 from the previous subsection cannot be used, because it doesn't work for
18413 small Greek letters.
18414 Furthermore it prints Latin letters always upright, like in the following
18418 \begin_layout Standard
18419 \begin_inset Formula \[
18420 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18427 \begin_layout Standard
18428 To display the formula correctly, the command
18435 \begin_inset Formula \[
18436 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18440 It is also possible to set the formula in a
18442 boldmath environment
18445 This environment is created by inserting the command
18453 \begin_layout Plain Layout
18464 To end the environment, the command
18472 \begin_layout Plain Layout
18482 is inserted in TeX-mode.
18486 \begin_layout Plain Layout
18496 \begin_inset Formula \[
18497 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18505 \begin_layout Plain Layout
18517 \begin_layout Subsection
18522 \begin_layout Plain Layout
18531 \begin_layout Standard
18532 Formulas can be colored like normal text: Highlight a formula or a formula
18538 Here is a formula in magenta:
18539 \begin_inset Formula \[
18540 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18547 \begin_layout Standard
18548 You can also define your own colors as described in
18549 \begin_inset CommandInset ref
18551 reference "sub:Colored-Boxes"
18556 They can be used with the TeX code command
18566 \begin_layout Plain Layout
18577 \begin_layout Standard
18582 textcolor{color}{characters or formula}
18585 \begin_layout Standard
18586 The following example was colored completely dark green and partly red:
18589 \begin_layout Standard
18593 \begin_layout Plain Layout
18597 textcolor{darkgreen}{
18603 \begin_inset Formula \[
18604 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18612 \begin_layout Plain Layout
18622 \begin_layout Standard
18623 Due to a bug in LyX only complete formulas can be colored with self-defined
18628 \begin_layout Plain Layout
18629 \begin_inset CommandInset href
18631 name "LyX-bug #5269"
18632 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18644 \begin_layout Subsection
18646 \begin_inset CommandInset label
18648 name "sub:Font-Sizes"
18656 \begin_layout Plain Layout
18665 \begin_layout Standard
18666 For characters in formulas there are, analog to characters in text, the
18667 following size commands:
18670 \begin_layout Standard
18714 \begin_inset Newline newline
18736 \begin_layout Standard
18737 The size produced by the commands depends on the document font size, that
18738 corresponds with the command
18745 The other commands produce smaller or larger sizes than
18752 The font size can however not exceed a certain value.
18753 Is for example the document font size 12
18754 \begin_inset space \thinspace{}
18763 switches to the same size as
18773 \begin_layout Standard
18774 A size command is inserted in TeX-mode before the formula and sets the size
18775 for all following formula and text characters.
18776 To switch back to the initial size, the command
18782 is inserted behind the formula in TeX-mode.
18785 \begin_layout Standard
18786 Within a formula the size can only be changed for symbols or letters in
18788 To do this, the size command is inserted in mathematical text.
18789 All following characters until the end of the mathematical text or until
18790 another size command will have the selected size.
18792 \begin_inset VSpace -2mm
18798 \begin_layout Standard
18802 \begin_layout Plain Layout
18812 \begin_inset Formula \[
18813 A=\frac{B}{c}\cdot\maltese\]
18818 \begin_inset Formula \[
18819 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18827 \begin_layout Plain Layout
18839 \begin_layout Standard
18840 \begin_inset VSpace medskip
18843 Before both formulas the command
18850 The command for the second formula is:
18851 \begin_inset Newline newline
18862 \begin_layout Plain Layout
18877 \begin_layout Plain Layout
18892 \begin_layout Plain Layout
18907 \begin_layout Plain Layout
18917 \begin_inset Formula $\to$
18921 \begin_inset Formula $\to$
18925 \begin_inset Newline newline
18929 \begin_inset space \hspace*{}
18943 \begin_layout Plain Layout
18958 \begin_layout Plain Layout
18973 \begin_layout Plain Layout
18985 \begin_layout Standard
18986 If a symbol cannot be displayed in different sizes, it will always be displayed
18987 in the default size.
18990 \begin_layout Section
18995 \begin_layout Plain Layout
19004 \begin_layout Standard
19005 All Greek letters can also be inserted via the toolbar button
19006 \begin_inset Graphics
19007 filename ../images/math/alpha.png
19015 \begin_layout Subsection
19020 \begin_layout Plain Layout
19021 Greek letters ! small
19029 \begin_layout Standard
19030 \begin_inset space \hfill{}
19034 \begin_inset Tabular
19035 <lyxtabular version="3" rows="11" columns="2">
19037 <column alignment="center" valignment="top" width="0pt">
19038 <column alignment="center" valignment="top" width="0pt">
19040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19043 \begin_layout Plain Layout
19049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19052 \begin_layout Plain Layout
19060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19063 \begin_layout Plain Layout
19071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19074 \begin_layout Plain Layout
19075 \begin_inset Formula $\alpha$
19085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19088 \begin_layout Plain Layout
19096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19099 \begin_layout Plain Layout
19100 \begin_inset Formula $\beta$
19110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19113 \begin_layout Plain Layout
19121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19124 \begin_layout Plain Layout
19125 \begin_inset Formula $\gamma$
19135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19138 \begin_layout Plain Layout
19146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19149 \begin_layout Plain Layout
19150 \begin_inset Formula $\delta$
19160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19163 \begin_layout Plain Layout
19171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19174 \begin_layout Plain Layout
19175 \begin_inset Formula $\epsilon$
19185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19188 \begin_layout Plain Layout
19196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19199 \begin_layout Plain Layout
19200 \begin_inset Formula $\varepsilon$
19210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19213 \begin_layout Plain Layout
19221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19224 \begin_layout Plain Layout
19225 \begin_inset Formula $\zeta$
19235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19238 \begin_layout Plain Layout
19246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19249 \begin_layout Plain Layout
19250 \begin_inset Formula $\eta$
19260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19263 \begin_layout Plain Layout
19271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19274 \begin_layout Plain Layout
19275 \begin_inset Formula $\theta$
19285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19288 \begin_layout Plain Layout
19296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19299 \begin_layout Plain Layout
19300 \begin_inset Formula $\vartheta$
19314 \begin_inset space \hfill{}
19318 \begin_inset Tabular
19319 <lyxtabular version="3" rows="12" columns="2">
19321 <column alignment="center" valignment="top" width="0pt">
19322 <column alignment="center" valignment="top" width="0pt">
19324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19327 \begin_layout Plain Layout
19333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19336 \begin_layout Plain Layout
19344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19347 \begin_layout Plain Layout
19355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19358 \begin_layout Plain Layout
19359 \begin_inset Formula $\iota$
19369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19372 \begin_layout Plain Layout
19380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19383 \begin_layout Plain Layout
19384 \begin_inset Formula $\kappa$
19394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19397 \begin_layout Plain Layout
19405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19408 \begin_layout Plain Layout
19409 \begin_inset Formula $\varkappa$
19419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19422 \begin_layout Plain Layout
19430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19433 \begin_layout Plain Layout
19434 \begin_inset Formula $\lambda$
19444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19447 \begin_layout Plain Layout
19455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19458 \begin_layout Plain Layout
19459 \begin_inset Formula $\mu$
19469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19472 \begin_layout Plain Layout
19480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19483 \begin_layout Plain Layout
19484 \begin_inset Formula $\nu$
19494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19497 \begin_layout Plain Layout
19505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19508 \begin_layout Plain Layout
19509 \begin_inset Formula $\xi$
19519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19522 \begin_layout Plain Layout
19528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19531 \begin_layout Plain Layout
19532 \begin_inset Formula $o$
19542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19545 \begin_layout Plain Layout
19553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19556 \begin_layout Plain Layout
19557 \begin_inset Formula $\pi$
19567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19570 \begin_layout Plain Layout
19578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19581 \begin_layout Plain Layout
19582 \begin_inset Formula $\varpi$
19592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19595 \begin_layout Plain Layout
19603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19606 \begin_layout Plain Layout
19607 \begin_inset Formula $\rho$
19621 \begin_inset space \hfill{}
19625 \begin_inset Tabular
19626 <lyxtabular version="3" rows="11" columns="2">
19628 <column alignment="center" valignment="top" width="0pt">
19629 <column alignment="center" valignment="top" width="0pt">
19631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19634 \begin_layout Plain Layout
19640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19643 \begin_layout Plain Layout
19651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19654 \begin_layout Plain Layout
19662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19665 \begin_layout Plain Layout
19666 \begin_inset Formula $\varrho$
19676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19679 \begin_layout Plain Layout
19687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19690 \begin_layout Plain Layout
19691 \begin_inset Formula $\sigma$
19701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19704 \begin_layout Plain Layout
19712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19715 \begin_layout Plain Layout
19716 \begin_inset Formula $\varsigma$
19726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19729 \begin_layout Plain Layout
19737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19740 \begin_layout Plain Layout
19741 \begin_inset Formula $\tau$
19751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19754 \begin_layout Plain Layout
19762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19765 \begin_layout Plain Layout
19766 \begin_inset Formula $\upsilon$
19776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19779 \begin_layout Plain Layout
19787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19790 \begin_layout Plain Layout
19791 \begin_inset Formula $\phi$
19801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19804 \begin_layout Plain Layout
19812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19815 \begin_layout Plain Layout
19816 \begin_inset Formula $\varphi$
19826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19829 \begin_layout Plain Layout
19837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19840 \begin_layout Plain Layout
19841 \begin_inset Formula $\chi$
19851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19854 \begin_layout Plain Layout
19862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19865 \begin_layout Plain Layout
19866 \begin_inset Formula $\psi$
19876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19879 \begin_layout Plain Layout
19887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19890 \begin_layout Plain Layout
19891 \begin_inset Formula $\omega$
19905 \begin_inset space \hfill{}
19911 \begin_layout Standard
19912 \begin_inset VSpace medskip
19918 \begin_layout Standard
19919 How to create upright Greek letters is explained in
19920 \begin_inset CommandInset ref
19922 reference "sub:Upright-small-Greek"
19929 \begin_layout Subsection
19934 \begin_layout Plain Layout
19935 Greek letters ! big
19943 \begin_layout Standard
19944 \begin_inset space \hfill{}
19948 \begin_inset Tabular
19949 <lyxtabular version="3" rows="7" columns="2">
19951 <column alignment="center" valignment="top" width="0pt">
19952 <column alignment="center" valignment="top" width="0pt">
19954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19957 \begin_layout Plain Layout
19963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19966 \begin_layout Plain Layout
19974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19977 \begin_layout Plain Layout
19985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19988 \begin_layout Plain Layout
19989 \begin_inset Formula $\Gamma$
19999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20002 \begin_layout Plain Layout
20010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20013 \begin_layout Plain Layout
20014 \begin_inset Formula $\Delta$
20024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20027 \begin_layout Plain Layout
20035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20038 \begin_layout Plain Layout
20039 \begin_inset Formula $\Theta$
20049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20052 \begin_layout Plain Layout
20060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20063 \begin_layout Plain Layout
20064 \begin_inset Formula $\Lambda$
20074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20077 \begin_layout Plain Layout
20085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20088 \begin_layout Plain Layout
20089 \begin_inset Formula $\Xi$
20099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20102 \begin_layout Plain Layout
20110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20113 \begin_layout Plain Layout
20114 \begin_inset Formula $\Pi$
20128 \begin_inset space \hfill{}
20132 \begin_inset Tabular
20133 <lyxtabular version="3" rows="6" columns="2">
20135 <column alignment="center" valignment="top" width="0pt">
20136 <column alignment="center" valignment="top" width="0pt">
20138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20141 \begin_layout Plain Layout
20147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20150 \begin_layout Plain Layout
20158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20161 \begin_layout Plain Layout
20169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20172 \begin_layout Plain Layout
20173 \begin_inset Formula $\Sigma$
20183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20186 \begin_layout Plain Layout
20194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20197 \begin_layout Plain Layout
20198 \begin_inset Formula $\Upsilon$
20208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20211 \begin_layout Plain Layout
20219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20222 \begin_layout Plain Layout
20223 \begin_inset Formula $\Phi$
20233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20236 \begin_layout Plain Layout
20244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20247 \begin_layout Plain Layout
20248 \begin_inset Formula $\Psi$
20258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20261 \begin_layout Plain Layout
20269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20272 \begin_layout Plain Layout
20273 \begin_inset Formula $\Omega$
20287 \begin_inset space \hfill{}
20293 \begin_layout Standard
20294 \begin_inset VSpace medskip
20297 That the big Greek letters appear upright is caused by a design bug when
20299 To get correct italic big letters, begin every command with
20304 For example the command
20311 \begin_inset Formula $\varGamma$
20317 \begin_layout Subsection
20322 \begin_layout Plain Layout
20323 Greek letters ! bold
20331 \begin_layout Standard
20332 Greek letters cannot be set with different font styles like Latin letters.
20333 They can only be made bold with the command
20343 \begin_layout Plain Layout
20354 \begin_layout Standard
20356 \begin_inset Tabular
20357 <lyxtabular version="3" rows="3" columns="2">
20359 <column alignment="center" valignment="top" width="0">
20360 <column alignment="center" valignment="top" width="0">
20362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20365 \begin_layout Plain Layout
20371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20374 \begin_layout Plain Layout
20382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20385 \begin_layout Plain Layout
20397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20400 \begin_layout Plain Layout
20401 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20414 \begin_layout Plain Layout
20426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20429 \begin_layout Plain Layout
20430 \begin_inset Formula $\theta\boldsymbol{\theta}$
20446 \begin_layout Section
20451 \begin_layout Plain Layout
20464 \begin_layout Plain Layout
20465 A list with all symbols of most of the LaTeX-packages can be found in
20466 \begin_inset CommandInset citation
20481 \begin_layout Plain Layout
20489 \begin_inset Note Note
20492 \begin_layout Plain Layout
20495 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20498 \begin_layout Plain Layout
20501 texorpdfstring is in section
20502 \begin_inset CommandInset ref
20504 reference "sub:Formulas-in-Section"
20517 \begin_layout Plain Layout
20526 \begin_layout Standard
20527 Many of the symbols listed in this section can also be inserted via the
20529 \begin_inset Graphics
20530 filename ../images/math/nabla.png
20536 \begin_inset Graphics
20537 filename ../images/math/digamma.png
20545 \begin_layout Subsection
20546 Mathematical Symbols
20547 \begin_inset CommandInset label
20549 name "sub:Mathematical-Symbols"
20557 \begin_layout Plain Layout
20558 Symbols ! mathematical
20566 \begin_layout Standard
20567 \begin_inset space \hfill{}
20571 \begin_inset Tabular
20572 <lyxtabular version="3" rows="10" columns="2">
20574 <column alignment="center" valignment="top" width="0pt">
20575 <column alignment="center" valignment="top" width="0pt">
20577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20580 \begin_layout Plain Layout
20586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20589 \begin_layout Plain Layout
20597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20600 \begin_layout Plain Layout
20608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20611 \begin_layout Plain Layout
20612 \begin_inset Formula $\neg$
20622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20625 \begin_layout Plain Layout
20633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20636 \begin_layout Plain Layout
20637 \begin_inset Formula $\Im$
20647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20650 \begin_layout Plain Layout
20658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20661 \begin_layout Plain Layout
20662 \begin_inset Formula $\Re$
20672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20675 \begin_layout Plain Layout
20683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20686 \begin_layout Plain Layout
20687 \begin_inset Formula $\aleph$
20697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20700 \begin_layout Plain Layout
20708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20711 \begin_layout Plain Layout
20712 \begin_inset Formula $\partial$
20722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20725 \begin_layout Plain Layout
20733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20736 \begin_layout Plain Layout
20737 \begin_inset Formula $\infty$
20747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20750 \begin_layout Plain Layout
20758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20761 \begin_layout Plain Layout
20762 \begin_inset Formula $\wp$
20772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20775 \begin_layout Plain Layout
20783 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20786 \begin_layout Plain Layout
20787 \begin_inset Formula $\imath$
20797 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20800 \begin_layout Plain Layout
20808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20811 \begin_layout Plain Layout
20812 \begin_inset Formula $\jmath$
20826 \begin_inset space \hfill{}
20830 \begin_inset Tabular
20831 <lyxtabular version="3" rows="10" columns="2">
20833 <column alignment="center" valignment="top" width="0pt">
20834 <column alignment="center" valignment="top" width="0pt">
20836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20839 \begin_layout Plain Layout
20845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20848 \begin_layout Plain Layout
20850 \begin_inset Note Note
20853 \begin_layout Plain Layout
20860 is only used as spacer.
20872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20875 \begin_layout Plain Layout
20883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20886 \begin_layout Plain Layout
20887 \begin_inset Formula $\forall$
20897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20900 \begin_layout Plain Layout
20908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20911 \begin_layout Plain Layout
20912 \begin_inset Formula $\exists$
20922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20925 \begin_layout Plain Layout
20933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20936 \begin_layout Plain Layout
20937 \begin_inset Formula $\nexists$
20947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20950 \begin_layout Plain Layout
20958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20961 \begin_layout Plain Layout
20962 \begin_inset Formula $\emptyset$
20972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20975 \begin_layout Plain Layout
20983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20986 \begin_layout Plain Layout
20987 \begin_inset Formula $\varnothing$
20997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21000 \begin_layout Plain Layout
21008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21011 \begin_layout Plain Layout
21012 \begin_inset Formula $\dag$
21022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21025 \begin_layout Plain Layout
21033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21036 \begin_layout Plain Layout
21037 \begin_inset Formula $\ddag$
21047 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21050 \begin_layout Plain Layout
21058 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21061 \begin_layout Plain Layout
21065 \begin_layout Plain Layout
21075 \begin_inset Formula $\complement$
21082 \begin_layout Plain Layout
21096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21099 \begin_layout Plain Layout
21107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21110 \begin_layout Plain Layout
21111 \begin_inset Formula $\Bbbk$
21125 \begin_inset space \hfill{}
21129 \begin_inset Tabular
21130 <lyxtabular version="3" rows="10" columns="2">
21132 <column alignment="center" valignment="top" width="0pt">
21133 <column alignment="center" valignment="top" width="0pt">
21135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21138 \begin_layout Plain Layout
21144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21147 \begin_layout Plain Layout
21155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21158 \begin_layout Plain Layout
21166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21169 \begin_layout Plain Layout
21170 \begin_inset Formula $\prime$
21180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21183 \begin_layout Plain Layout
21191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21194 \begin_layout Plain Layout
21195 \begin_inset Formula $\backprime$
21205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21208 \begin_layout Plain Layout
21216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21219 \begin_layout Plain Layout
21220 \begin_inset Formula $\mho$
21230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21233 \begin_layout Plain Layout
21241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21244 \begin_layout Plain Layout
21245 \begin_inset Formula $\triangle$
21255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21258 \begin_layout Plain Layout
21266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21269 \begin_layout Plain Layout
21270 \begin_inset Formula $\angle$
21280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21283 \begin_layout Plain Layout
21291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21294 \begin_layout Plain Layout
21295 \begin_inset Formula $\measuredangle$
21305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21308 \begin_layout Plain Layout
21316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21319 \begin_layout Plain Layout
21320 \begin_inset Formula $\sphericalangle$
21330 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21333 \begin_layout Plain Layout
21341 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21344 \begin_layout Plain Layout
21345 \begin_inset Formula $\top$
21355 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21358 \begin_layout Plain Layout
21366 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21369 \begin_layout Plain Layout
21370 \begin_inset Formula $\bot$
21384 \begin_inset space \hfill{}
21390 \begin_layout Subsection
21391 Miscellaneous Symbols
21392 \begin_inset CommandInset label
21394 name "sub:Miscellaneous-Symbols"
21402 \begin_layout Plain Layout
21403 Symbols ! miscellaneous
21411 \begin_layout Standard
21414 \begin_inset Tabular
21415 <lyxtabular version="3" rows="10" columns="2">
21417 <column alignment="center" valignment="top" width="0pt">
21418 <column alignment="center" valignment="top" width="0pt">
21420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21423 \begin_layout Plain Layout
21429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21432 \begin_layout Plain Layout
21440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21443 \begin_layout Plain Layout
21451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21454 \begin_layout Plain Layout
21455 \begin_inset Formula $\flat$
21465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21468 \begin_layout Plain Layout
21476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21479 \begin_layout Plain Layout
21480 \begin_inset Formula $\natural$
21490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21493 \begin_layout Plain Layout
21501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21504 \begin_layout Plain Layout
21505 \begin_inset Formula $\sharp$
21515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21518 \begin_layout Plain Layout
21526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21529 \begin_layout Plain Layout
21530 \begin_inset Formula $\surd$
21540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21543 \begin_layout Plain Layout
21551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21554 \begin_layout Plain Layout
21555 \begin_inset Formula $\checkmark$
21565 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21568 \begin_layout Plain Layout
21576 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21579 \begin_layout Plain Layout
21580 \begin_inset Formula $\yen$
21590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21593 \begin_layout Plain Layout
21601 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21604 \begin_layout Plain Layout
21605 \begin_inset Formula $\pounds$
21615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21618 \begin_layout Plain Layout
21624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21627 \begin_layout Plain Layout
21628 \begin_inset Formula $\$$
21638 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21641 \begin_layout Plain Layout
21647 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21650 \begin_layout Plain Layout
21651 \begin_inset Formula $§$
21665 \begin_inset Tabular
21666 <lyxtabular version="3" rows="10" columns="2">
21668 <column alignment="center" valignment="top" width="0">
21669 <column alignment="center" valignment="top" width="0">
21671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21674 \begin_layout Plain Layout
21680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21683 \begin_layout Plain Layout
21691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21694 \begin_layout Plain Layout
21702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21705 \begin_layout Plain Layout
21706 \begin_inset Formula $\hbar$
21716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21719 \begin_layout Plain Layout
21727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21730 \begin_layout Plain Layout
21731 \begin_inset Formula $\hslash$
21741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21744 \begin_layout Plain Layout
21752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21755 \begin_layout Plain Layout
21756 \begin_inset Formula $\clubsuit$
21766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21769 \begin_layout Plain Layout
21777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21780 \begin_layout Plain Layout
21781 \begin_inset Formula $\spadesuit$
21791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21794 \begin_layout Plain Layout
21802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21805 \begin_layout Plain Layout
21806 \begin_inset Formula $\bigstar$
21816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21819 \begin_layout Plain Layout
21827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21830 \begin_layout Plain Layout
21831 \begin_inset Formula $\blacklozenge$
21841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21844 \begin_layout Plain Layout
21852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21855 \begin_layout Plain Layout
21856 \begin_inset Formula $\blacktriangle$
21866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21869 \begin_layout Plain Layout
21877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21880 \begin_layout Plain Layout
21881 \begin_inset Formula $\blacktriangledown$
21891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21894 \begin_layout Plain Layout
21902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21905 \begin_layout Plain Layout
21906 \begin_inset Formula $\bullet$
21920 \begin_inset Tabular
21921 <lyxtabular version="3" rows="10" columns="2">
21923 <column alignment="center" valignment="top" width="0pt">
21924 <column alignment="center" valignment="top" width="0pt">
21926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21929 \begin_layout Plain Layout
21935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21938 \begin_layout Plain Layout
21946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21949 \begin_layout Plain Layout
21957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21960 \begin_layout Plain Layout
21961 \begin_inset Formula $\diamondsuit$
21971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21974 \begin_layout Plain Layout
21982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21985 \begin_layout Plain Layout
21986 \begin_inset Formula $\Diamond$
21996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21999 \begin_layout Plain Layout
22007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22010 \begin_layout Plain Layout
22011 \begin_inset Formula $\heartsuit$
22021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22024 \begin_layout Plain Layout
22032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22035 \begin_layout Plain Layout
22036 \begin_inset Formula $\P$
22046 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22049 \begin_layout Plain Layout
22057 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22060 \begin_layout Plain Layout
22061 \begin_inset Formula $\copyright$
22071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22074 \begin_layout Plain Layout
22082 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22085 \begin_layout Plain Layout
22086 \begin_inset Formula $\circledR$
22096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22099 \begin_layout Plain Layout
22107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22110 \begin_layout Plain Layout
22111 \begin_inset Formula $\maltese$
22121 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22124 \begin_layout Plain Layout
22132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22135 \begin_layout Plain Layout
22136 \begin_inset Formula $\diagup$
22146 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22149 \begin_layout Plain Layout
22157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22160 \begin_layout Plain Layout
22161 \begin_inset Formula $\diagdown$
22177 \begin_layout Standard
22178 \begin_inset VSpace medskip
22181 More symbols are listed in
22182 \begin_inset CommandInset ref
22184 reference "sub:Miscellaneous-special-Characters"
22191 \begin_layout Standard
22192 Some symbols can be displayed in different sizes, see
22193 \begin_inset CommandInset ref
22195 reference "sub:Font-Sizes"
22202 \begin_layout Subsection
22207 \begin_layout Plain Layout
22208 Symbols ! Euro-symbol
22217 \begin_layout Plain Layout
22224 \begin_layout Plain Layout
22241 \begin_layout Standard
22242 To use the Euro symbol in formulas, the LaTeX-package
22250 \begin_layout Plain Layout
22256 must be installed and loaded with the LaTeX-preamble line
22259 \begin_layout Standard
22264 usepackage[gennarrow]{eurosym}
22267 \begin_layout Standard
22268 The Euro symbol can now be inserted with the command
22278 \begin_layout Plain Layout
22289 \begin_layout Standard
22290 The Euro symbol can directly be inserted with the € key in mathematical
22291 text, without having
22306 can also be inserted in TeX-mode.
22307 The official currency symbol can then be inserted with the command
22317 \begin_layout Plain Layout
22325 , that is only available in TeX-mode.
22328 \begin_layout Standard
22332 \begin_layout Plain Layout
22342 \begin_inset Note Note
22345 \begin_layout Plain Layout
22346 The following table will only be displayed when the LaTeX-package
22358 \begin_layout Standard
22359 An overview about the different Euro symbols:
22362 \begin_layout Standard
22364 \begin_inset Tabular
22365 <lyxtabular version="3" rows="4" columns="3">
22367 <column alignment="center" valignment="top" width="0pt">
22368 <column alignment="center" valignment="top" width="0pt">
22369 <column alignment="center" valignment="top" width="0pt">
22371 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22374 \begin_layout Plain Layout
22380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22383 \begin_layout Plain Layout
22389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22392 \begin_layout Plain Layout
22400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22403 \begin_layout Plain Layout
22409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22412 \begin_layout Plain Layout
22420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22423 \begin_layout Plain Layout
22424 \begin_inset Formula $\euro$
22434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22437 \begin_layout Plain Layout
22443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22446 \begin_layout Plain Layout
22452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22455 \begin_layout Plain Layout
22456 \begin_inset Formula $\mbox{€}$
22466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22469 \begin_layout Plain Layout
22475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22478 \begin_layout Plain Layout
22486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22489 \begin_layout Plain Layout
22493 \begin_layout Plain Layout
22515 \begin_layout Standard
22519 \begin_layout Plain Layout
22529 \begin_inset Note Note
22532 \begin_layout Plain Layout
22533 The following will be displayed when the LaTeX-package
22545 \begin_layout Standard
22546 You need to install the LaTeX-package
22550 to see the rest of this subsection in the output.
22553 \begin_layout Standard
22557 \begin_layout Plain Layout
22569 \begin_layout Section
22571 \begin_inset CommandInset label
22573 name "sec:Relations"
22581 \begin_layout Plain Layout
22591 \begin_layout Plain Layout
22596 \begin_layout Plain Layout
22607 \begin_layout Plain Layout
22622 \begin_layout Standard
22623 All relations can also be inserted via the toolbar button
22624 \begin_inset Graphics
22625 filename ../images/math/leq.png
22633 \begin_layout Standard
22634 \begin_inset space \hfill{}
22638 \begin_inset Tabular
22639 <lyxtabular version="3" rows="17" columns="2">
22641 <column alignment="center" valignment="top" width="0pt">
22642 <column alignment="center" valignment="top" width="0pt">
22644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22647 \begin_layout Plain Layout
22653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22656 \begin_layout Plain Layout
22664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22667 \begin_layout Plain Layout
22673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22676 \begin_layout Plain Layout
22677 \begin_inset Formula $<$
22687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22690 \begin_layout Plain Layout
22698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22701 \begin_layout Plain Layout
22702 \begin_inset Formula $\le$
22712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22715 \begin_layout Plain Layout
22723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22726 \begin_layout Plain Layout
22727 \begin_inset Formula $\ll$
22737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22740 \begin_layout Plain Layout
22748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22751 \begin_layout Plain Layout
22752 \begin_inset Formula $\prec$
22762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22765 \begin_layout Plain Layout
22773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22776 \begin_layout Plain Layout
22777 \begin_inset Formula $\preceq$
22787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22790 \begin_layout Plain Layout
22798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22801 \begin_layout Plain Layout
22802 \begin_inset Formula $\subset$
22812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22815 \begin_layout Plain Layout
22823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22826 \begin_layout Plain Layout
22827 \begin_inset Formula $\subseteq$
22837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22840 \begin_layout Plain Layout
22848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22851 \begin_layout Plain Layout
22852 \begin_inset Formula $\sqsubseteq$
22862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22865 \begin_layout Plain Layout
22873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22876 \begin_layout Plain Layout
22877 \begin_inset Formula $\in$
22887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22890 \begin_layout Plain Layout
22898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22901 \begin_layout Plain Layout
22902 \begin_inset Formula $\vdash$
22912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22915 \begin_layout Plain Layout
22923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22926 \begin_layout Plain Layout
22927 \begin_inset Formula $\smile$
22937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22940 \begin_layout Plain Layout
22948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22951 \begin_layout Plain Layout
22952 \begin_inset Formula $\lhd$
22962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22965 \begin_layout Plain Layout
22973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22976 \begin_layout Plain Layout
22977 \begin_inset Formula $\unlhd$
22987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22990 \begin_layout Plain Layout
22998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23001 \begin_layout Plain Layout
23002 \begin_inset Formula $\gtrless$
23012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23015 \begin_layout Plain Layout
23023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23026 \begin_layout Plain Layout
23027 \begin_inset Formula $\mid$
23037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23040 \begin_layout Plain Layout
23048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23051 \begin_layout Plain Layout
23052 \begin_inset Formula $\nmid$
23066 \begin_inset space \hfill{}
23070 \begin_inset Tabular
23071 <lyxtabular version="3" rows="17" columns="2">
23073 <column alignment="center" valignment="top" width="0pt">
23074 <column alignment="center" valignment="top" width="0pt">
23076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23079 \begin_layout Plain Layout
23085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23088 \begin_layout Plain Layout
23096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23099 \begin_layout Plain Layout
23105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23108 \begin_layout Plain Layout
23109 \begin_inset Formula $=$
23119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23122 \begin_layout Plain Layout
23130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23133 \begin_layout Plain Layout
23134 \begin_inset Formula $\not=$
23144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23147 \begin_layout Plain Layout
23155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23158 \begin_layout Plain Layout
23159 \begin_inset Formula $\equiv$
23169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23172 \begin_layout Plain Layout
23180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23183 \begin_layout Plain Layout
23184 \begin_inset Formula $\sim$
23194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23197 \begin_layout Plain Layout
23205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23208 \begin_layout Plain Layout
23209 \begin_inset Formula $\simeq$
23219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23222 \begin_layout Plain Layout
23230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23233 \begin_layout Plain Layout
23234 \begin_inset Formula $\approx$
23244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23247 \begin_layout Plain Layout
23255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23258 \begin_layout Plain Layout
23259 \begin_inset Formula $\cong$
23269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23272 \begin_layout Plain Layout
23280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23283 \begin_layout Plain Layout
23284 \begin_inset Formula $\bowtie$
23294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23297 \begin_layout Plain Layout
23305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23308 \begin_layout Plain Layout
23309 \begin_inset Formula $\notin$
23319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23322 \begin_layout Plain Layout
23330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23333 \begin_layout Plain Layout
23334 \begin_inset Formula $\perp$
23344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23347 \begin_layout Plain Layout
23355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23358 \begin_layout Plain Layout
23359 \begin_inset Formula $\propto$
23369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23372 \begin_layout Plain Layout
23380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23383 \begin_layout Plain Layout
23384 \begin_inset Formula $\asymp$
23394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23397 \begin_layout Plain Layout
23405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23408 \begin_layout Plain Layout
23409 \begin_inset Formula $\doteq$
23419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23422 \begin_layout Plain Layout
23430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23433 \begin_layout Plain Layout
23434 \begin_inset Formula $\circeq$
23444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23447 \begin_layout Plain Layout
23455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23458 \begin_layout Plain Layout
23459 \begin_inset Formula $\models$
23469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23472 \begin_layout Plain Layout
23480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23483 \begin_layout Plain Layout
23484 \begin_inset Formula $\widehat{=}$
23498 \begin_inset space \hfill{}
23502 \begin_inset Tabular
23503 <lyxtabular version="3" rows="17" columns="2">
23505 <column alignment="center" valignment="top" width="0pt">
23506 <column alignment="center" valignment="top" width="0pt">
23508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23511 \begin_layout Plain Layout
23517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23520 \begin_layout Plain Layout
23528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23531 \begin_layout Plain Layout
23537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23540 \begin_layout Plain Layout
23541 \begin_inset Formula $>$
23551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23554 \begin_layout Plain Layout
23562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23565 \begin_layout Plain Layout
23566 \begin_inset Formula $\ge$
23576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23579 \begin_layout Plain Layout
23587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23590 \begin_layout Plain Layout
23591 \begin_inset Formula $\gg$
23601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23604 \begin_layout Plain Layout
23612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23615 \begin_layout Plain Layout
23616 \begin_inset Formula $\succ$
23626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23629 \begin_layout Plain Layout
23637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23640 \begin_layout Plain Layout
23641 \begin_inset Formula $\succeq$
23651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23654 \begin_layout Plain Layout
23662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23665 \begin_layout Plain Layout
23666 \begin_inset Formula $\supset$
23676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23679 \begin_layout Plain Layout
23687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23690 \begin_layout Plain Layout
23691 \begin_inset Formula $\supseteq$
23701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23704 \begin_layout Plain Layout
23712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23715 \begin_layout Plain Layout
23716 \begin_inset Formula $\sqsupseteq$
23726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23729 \begin_layout Plain Layout
23737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23740 \begin_layout Plain Layout
23741 \begin_inset Formula $\ni$
23751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23754 \begin_layout Plain Layout
23762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23765 \begin_layout Plain Layout
23766 \begin_inset Formula $\dashv$
23776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23779 \begin_layout Plain Layout
23787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23790 \begin_layout Plain Layout
23791 \begin_inset Formula $\frown$
23801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23804 \begin_layout Plain Layout
23812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23815 \begin_layout Plain Layout
23816 \begin_inset Formula $\rhd$
23826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23829 \begin_layout Plain Layout
23837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23840 \begin_layout Plain Layout
23841 \begin_inset Formula $\unrhd$
23851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23854 \begin_layout Plain Layout
23862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23865 \begin_layout Plain Layout
23866 \begin_inset Formula $\lessgtr$
23876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23879 \begin_layout Plain Layout
23887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23890 \begin_layout Plain Layout
23891 \begin_inset Formula $\parallel$
23901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23904 \begin_layout Plain Layout
23912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23915 \begin_layout Plain Layout
23916 \begin_inset Formula $\nparallel$
23930 \begin_inset space \hfill{}
23936 \begin_layout Standard
23937 \begin_inset VSpace medskip
23952 are bigger than the equal looking operators
23967 \begin_layout Standard
23968 Relations are, in contrary to symbols, always surrounded by space.
23971 \begin_layout Standard
23972 Relations with labels can be created with the command
23982 \begin_layout Plain Layout
23993 \begin_layout Standard
23995 \begin_inset Tabular
23996 <lyxtabular version="3" rows="2" columns="2">
23998 <column alignment="center" valignment="top" width="0">
23999 <column alignment="center" valignment="top" width="0">
24001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24004 \begin_layout Plain Layout
24010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24013 \begin_layout Plain Layout
24015 \begin_inset Note Note
24018 \begin_layout Plain Layout
24025 is only used as spacer.
24037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24040 \begin_layout Plain Layout
24047 \begin_layout Plain Layout
24064 \begin_layout Plain Layout
24074 \begin_inset Formula $\downarrow$
24083 \begin_layout Plain Layout
24096 \begin_layout Plain Layout
24110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24113 \begin_layout Plain Layout
24114 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24130 \begin_layout Section
24134 \begin_layout Subsection
24135 Predefined Functions
24136 \begin_inset CommandInset label
24138 name "sub:Predefined-Functions"
24146 \begin_layout Plain Layout
24147 Functions ! predefined
24155 \begin_layout Standard
24156 In general, variables are set
24160 in mathematical expressions, but not function names, because
24161 \begin_inset Formula $sin$
24164 could be misunderstood as
24165 \begin_inset Formula $s\cdot i\cdot n$
24169 Therefore there are predefined functions, that are additionally a bit separated
24171 They are inserted as commands starting with a backslash before their name.
24174 \begin_layout Standard
24176 \begin_inset Tabular
24177 <lyxtabular version="3" rows="2" columns="4">
24179 <column alignment="center" valignment="top" width="0pt">
24180 <column alignment="center" valignment="top" width="0pt">
24181 <column alignment="center" valignment="top" width="0pt">
24182 <column alignment="center" valignment="top" width="0pt">
24184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24187 \begin_layout Plain Layout
24193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24196 \begin_layout Plain Layout
24202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24205 \begin_layout Plain Layout
24211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24214 \begin_layout Plain Layout
24222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24225 \begin_layout Plain Layout
24231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24234 \begin_layout Plain Layout
24235 \begin_inset Formula $Asin(x)+B$
24243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24246 \begin_layout Plain Layout
24254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24257 \begin_layout Plain Layout
24258 \begin_inset Formula $A\sin(x)+B$
24274 \begin_layout Standard
24275 The following functions are predefined:
24278 \begin_layout Standard
24279 \begin_inset VSpace -2mm
24285 \begin_layout Standard
24287 \begin_inset Tabular
24288 <lyxtabular version="3" rows="9" columns="4">
24290 <column alignment="center" valignment="top" width="0pt">
24291 <column alignment="center" valignment="top" width="0pt">
24292 <column alignment="center" valignment="top" width="0pt">
24293 <column alignment="center" valignment="top" width="0pt">
24295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24298 \begin_layout Plain Layout
24304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24307 \begin_layout Plain Layout
24313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24316 \begin_layout Plain Layout
24322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24325 \begin_layout Plain Layout
24333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24336 \begin_layout Plain Layout
24344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24347 \begin_layout Plain Layout
24355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24358 \begin_layout Plain Layout
24366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24369 \begin_layout Plain Layout
24379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24382 \begin_layout Plain Layout
24390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24393 \begin_layout Plain Layout
24401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24404 \begin_layout Plain Layout
24412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24415 \begin_layout Plain Layout
24425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24428 \begin_layout Plain Layout
24436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24439 \begin_layout Plain Layout
24447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24450 \begin_layout Plain Layout
24458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24461 \begin_layout Plain Layout
24471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24474 \begin_layout Plain Layout
24482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24485 \begin_layout Plain Layout
24493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24496 \begin_layout Plain Layout
24504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24507 \begin_layout Plain Layout
24517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24520 \begin_layout Plain Layout
24528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24531 \begin_layout Plain Layout
24539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24542 \begin_layout Plain Layout
24550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24553 \begin_layout Plain Layout
24563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24566 \begin_layout Plain Layout
24574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24577 \begin_layout Plain Layout
24585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24588 \begin_layout Plain Layout
24596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24599 \begin_layout Plain Layout
24609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24612 \begin_layout Plain Layout
24620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24623 \begin_layout Plain Layout
24631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24634 \begin_layout Plain Layout
24642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24645 \begin_layout Plain Layout
24655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24658 \begin_layout Plain Layout
24666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24669 \begin_layout Plain Layout
24677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24680 \begin_layout Plain Layout
24688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24691 \begin_layout Plain Layout
24707 \begin_layout Standard
24708 They can also be inserted with the math toolbar button
24709 \begin_inset Graphics
24710 filename ../images/math/functions.png
24718 \begin_layout Subsection
24719 Self-defined Functions
24723 \begin_layout Plain Layout
24724 Functions ! self-defined
24732 \begin_layout Standard
24733 To use a function that is not predefined, like for example the sign function
24734 sgn(x), there are two possibilities:
24737 \begin_layout Itemize
24738 Define the function by inserting the following line to the LaTeX-preamble
24742 \begin_layout Plain Layout
24747 DeclareMathOperator
24750 \begin_inset CommandInset ref
24752 reference "sub:Self-defined-Operators"
24762 \begin_inset Newline newline
24766 \begin_inset VSpace -3mm
24770 \begin_inset Newline newline
24777 DeclareMathOperator{
24785 \begin_layout Plain Layout
24790 DeclareMathOperator
24796 \begin_inset Newline newline
24800 \begin_inset VSpace -2mm
24804 \begin_inset Newline newline
24807 Now the new defined function can be called with the command
24816 \begin_layout Itemize
24817 Write the the formula as usual, mark the formula name, in our example the
24822 , and change it to mathematical text.
24823 At last a space is inserted between prefactor and function.
24826 \begin_layout Standard
24827 The result is the same with both methods as with a predefined function
24831 \begin_layout Plain Layout
24832 In LyX self-defined functions are displayed red, predefined ones black.
24840 \begin_layout Standard
24842 \begin_inset Tabular
24843 <lyxtabular version="3" rows="3" columns="2">
24845 <column alignment="center" valignment="top" width="0pt">
24846 <column alignment="center" valignment="top" width="0pt">
24848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24851 \begin_layout Plain Layout
24857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24860 \begin_layout Plain Layout
24868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24871 \begin_layout Plain Layout
24879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24882 \begin_layout Plain Layout
24883 \begin_inset Formula $A\sgn(x)+B$
24893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24896 \begin_layout Plain Layout
24900 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24911 \begin_layout Plain Layout
24912 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24928 \begin_layout Standard
24929 The first method is more suitable when the self-defined function should
24930 be used several times.
24933 \begin_layout Subsection
24938 \begin_layout Plain Layout
24947 \begin_layout Standard
24948 For limits there are defined besides
24958 \begin_layout Plain Layout
24978 furthermore the following functions:
24981 \begin_layout Standard
24983 \begin_inset Tabular
24984 <lyxtabular version="3" rows="5" columns="2">
24986 <column alignment="center" valignment="top" width="0">
24987 <column alignment="center" valignment="top" width="0">
24989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24992 \begin_layout Plain Layout
24998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25001 \begin_layout Plain Layout
25003 \begin_inset Note Note
25006 \begin_layout Plain Layout
25013 is only used as spacer.
25025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25028 \begin_layout Plain Layout
25036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25039 \begin_layout Plain Layout
25040 \begin_inset Formula $\varliminf$
25050 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25053 \begin_layout Plain Layout
25061 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25064 \begin_layout Plain Layout
25065 \begin_inset Formula $\varlimsup$
25075 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25078 \begin_layout Plain Layout
25086 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25089 \begin_layout Plain Layout
25090 \begin_inset Formula $\varprojlim$
25100 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25103 \begin_layout Plain Layout
25111 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25114 \begin_layout Plain Layout
25115 \begin_inset Formula $\varinjlim$
25119 \begin_inset Formula $\raisebox{-2.5mm}{}$
25135 \begin_layout Standard
25136 \begin_inset VSpace medskip
25139 The limit is created by inserting a subscript.
25140 It is set right beside the function in an inline formula:
25143 \begin_layout Standard
25145 \begin_inset Tabular
25146 <lyxtabular version="3" rows="2" columns="2">
25148 <column alignment="center" valignment="top" width="0pt">
25149 <column alignment="center" valignment="top" width="0pt">
25151 <cell alignment="center" valignment="top" usebox="none">
25154 \begin_layout Plain Layout
25160 <cell alignment="center" valignment="top" usebox="none">
25163 \begin_layout Plain Layout
25164 \begin_inset space \hspace{}
25169 \begin_inset Note Note
25172 \begin_layout Plain Layout
25185 are used here as spacer.
25197 <cell alignment="center" valignment="top" usebox="none">
25200 \begin_layout Plain Layout
25209 \begin_layout Plain Layout
25222 \begin_layout Plain Layout
25236 <cell alignment="center" valignment="top" usebox="none">
25239 \begin_layout Plain Layout
25240 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25256 \begin_layout Standard
25257 In a displayed formula the limit is set below the formula, as usual:
25258 \begin_inset Formula \[
25266 \begin_layout Subsection
25271 \begin_layout Plain Layout
25272 Functions ! modulo-
25280 \begin_layout Standard
25281 The modulo-function is special, because it exists in four variants.
25284 \begin_layout Standard
25285 The variants in a displayed formula:
25286 \begin_inset Formula \begin{align*}
25287 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25288 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25289 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25290 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25291 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25298 \begin_layout Standard
25299 In an inline formula less space is set before the function names for all
25303 \begin_layout Section
25308 \begin_layout Plain Layout
25317 \begin_layout Subsection
25318 Special Characters in Mathematical Text
25321 \begin_layout Standard
25322 The following commands can only be used in mathematical text or in TeX-mode:
25325 \begin_layout Standard
25326 \begin_inset space \hfill{}
25330 \begin_inset Tabular
25331 <lyxtabular version="3" rows="8" columns="2">
25333 <column alignment="block" valignment="top" width="0">
25334 <column alignment="block" valignment="top" width="0">
25336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25339 \begin_layout Plain Layout
25345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25348 \begin_layout Plain Layout
25356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25359 \begin_layout Plain Layout
25367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25370 \begin_layout Plain Layout
25371 \begin_inset Formula $\textrm{œ}$
25381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25384 \begin_layout Plain Layout
25392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25395 \begin_layout Plain Layout
25396 \begin_inset Formula $\textrm{Œ}$
25406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25409 \begin_layout Plain Layout
25417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25420 \begin_layout Plain Layout
25421 \begin_inset Formula $\textrm{æ}$
25431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25434 \begin_layout Plain Layout
25442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25445 \begin_layout Plain Layout
25446 \begin_inset Formula $\textrm{Æ}$
25456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25459 \begin_layout Plain Layout
25467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25470 \begin_layout Plain Layout
25471 \begin_inset Formula $\textrm{\aa}$
25481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25484 \begin_layout Plain Layout
25491 \begin_layout Plain Layout
25498 \begin_layout Plain Layout
25519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25522 \begin_layout Plain Layout
25523 \begin_inset Formula $\textrm{Å}$
25533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25536 \begin_layout Plain Layout
25544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25547 \begin_layout Plain Layout
25548 \begin_inset Formula $\textrm{ı}$
25562 \begin_inset space \hfill{}
25566 \begin_inset Tabular
25567 <lyxtabular version="3" rows="8" columns="2">
25569 <column alignment="block" valignment="top" width="0">
25570 <column alignment="center" valignment="top" width="0">
25572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25575 \begin_layout Plain Layout
25577 \begin_inset Note Note
25580 \begin_layout Plain Layout
25587 is used for separation, because otherwise the output will be ¡ and ¿ respective
25598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25601 \begin_layout Plain Layout
25609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25612 \begin_layout Plain Layout
25620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25623 \begin_layout Plain Layout
25624 \begin_inset Formula $\textrm{ø}$
25634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25637 \begin_layout Plain Layout
25645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25648 \begin_layout Plain Layout
25649 \begin_inset Formula $\textrm{Ø}$
25659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25662 \begin_layout Plain Layout
25670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25673 \begin_layout Plain Layout
25674 \begin_inset Formula $\textrm{ł}$
25684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25687 \begin_layout Plain Layout
25695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25698 \begin_layout Plain Layout
25699 \begin_inset Formula $\textrm{Ł}$
25709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25712 \begin_layout Plain Layout
25714 \begin_inset space \hspace{}
25722 \begin_layout Plain Layout
25736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25739 \begin_layout Plain Layout
25740 \begin_inset Formula $\textrm{!`}$
25750 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25753 \begin_layout Plain Layout
25755 \begin_inset space \hspace{}
25763 \begin_layout Plain Layout
25777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25780 \begin_layout Plain Layout
25781 \begin_inset Formula $\textrm{?`}$
25791 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25794 \begin_layout Plain Layout
25802 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25805 \begin_layout Plain Layout
25806 \begin_inset Formula $\textrm{ȷ}$
25820 \begin_inset space \hfill{}
25826 \begin_layout Standard
25828 \begin_inset Formula $\textrm{\textrm{Å}}$
25832 \begin_inset Formula $\textrm{\textrm{Ø}}$
25835 can also be inserted via the math toolbar button
25836 \begin_inset Graphics
25837 filename ../images/math/digamma.png
25845 \begin_layout Standard
25846 An exception are the commands
25849 \begin_inset space \hspace{}
25858 \begin_inset space \hspace{}
25864 , because they can be inserted in LyX directly to text.
25867 \begin_layout Subsection
25869 \begin_inset CommandInset label
25871 name "sub:Accents-in-Text"
25879 \begin_layout Plain Layout
25888 \begin_layout Standard
25889 With the following commands all letters can be accented.
25890 The commands must be inserted in TeX-mode.
25893 \begin_layout Standard
25894 \begin_inset space \hfill{}
25898 \begin_inset Tabular
25899 <lyxtabular version="3" rows="8" columns="2">
25901 <column alignment="block" valignment="top" width="0">
25902 <column alignment="block" valignment="top" width="0">
25904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25907 \begin_layout Plain Layout
25913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25916 \begin_layout Plain Layout
25924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25927 \begin_layout Plain Layout
25931 \begin_inset Quotes grd
25939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25942 \begin_layout Plain Layout
25946 \begin_layout Plain Layout
25962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25965 \begin_layout Plain Layout
25973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25976 \begin_layout Plain Layout
25980 \begin_layout Plain Layout
25996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25999 \begin_layout Plain Layout
26006 \begin_layout Plain Layout
26020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26023 \begin_layout Plain Layout
26027 \begin_layout Plain Layout
26043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26046 \begin_layout Plain Layout
26054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26057 \begin_layout Plain Layout
26061 \begin_layout Plain Layout
26077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26080 \begin_layout Plain Layout
26087 \begin_layout Plain Layout
26101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26104 \begin_layout Plain Layout
26108 \begin_layout Plain Layout
26124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26127 \begin_layout Plain Layout
26134 \begin_layout Plain Layout
26148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26151 \begin_layout Plain Layout
26155 \begin_layout Plain Layout
26171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26174 \begin_layout Plain Layout
26181 \begin_layout Plain Layout
26195 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26198 \begin_layout Plain Layout
26202 \begin_layout Plain Layout
26222 \begin_inset space \hfill{}
26226 \begin_inset Tabular
26227 <lyxtabular version="3" rows="8" columns="2">
26229 <column alignment="block" valignment="top" width="0">
26230 <column alignment="center" valignment="top" width="0">
26232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26235 \begin_layout Plain Layout
26241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26244 \begin_layout Plain Layout
26252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26255 \begin_layout Plain Layout
26262 \begin_layout Plain Layout
26276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26279 \begin_layout Plain Layout
26283 \begin_layout Plain Layout
26299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26302 \begin_layout Plain Layout
26310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26313 \begin_layout Plain Layout
26317 \begin_layout Plain Layout
26333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26336 \begin_layout Plain Layout
26343 \begin_layout Plain Layout
26354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26357 \begin_layout Plain Layout
26361 \begin_layout Plain Layout
26377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26380 \begin_layout Plain Layout
26388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26391 \begin_layout Plain Layout
26395 \begin_layout Plain Layout
26411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26414 \begin_layout Plain Layout
26421 \begin_layout Plain Layout
26435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26438 \begin_layout Plain Layout
26442 \begin_layout Plain Layout
26458 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26461 \begin_layout Plain Layout
26468 \begin_layout Plain Layout
26482 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26485 \begin_layout Plain Layout
26489 \begin_layout Plain Layout
26505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26508 \begin_layout Plain Layout
26515 \begin_layout Plain Layout
26529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26532 \begin_layout Plain Layout
26536 \begin_layout Plain Layout
26556 \begin_inset space \hfill{}
26562 \begin_layout Standard
26563 \begin_inset VSpace medskip
26572 also two different characters can be accented.
26581 \begin_layout Plain Layout
26596 \begin_layout Plain Layout
26608 \begin_layout Standard
26621 can in combination with vowels directly be inserted with the keyboard without
26623 The same applies for the tilde
26627 \begin_layout Plain Layout
26628 This only applies for keyboards where the tilde is defined as accent.
26637 in combination with
26652 \begin_layout Standard
26695 , and accents inserted directly with the keyboard are also available in
26697 For the other accents there are special math commands to be used in formulas,
26699 \begin_inset CommandInset ref
26701 reference "sub:Accents-for-one"
26708 \begin_layout Standard
26709 \begin_inset VSpace bigskip
26712 Furthermore, with the command
26722 \begin_layout Plain Layout
26730 all numbers and letters can be set into a circle, quasi accented with a
26731 circle, similar to the the copyright symbol.
26734 \begin_layout Standard
26736 \begin_inset Tabular
26737 <lyxtabular version="3" rows="3" columns="2">
26739 <column alignment="center" valignment="top" width="0">
26740 <column alignment="center" valignment="top" width="0">
26742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26745 \begin_layout Plain Layout
26751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26754 \begin_layout Plain Layout
26756 \begin_inset Note Note
26759 \begin_layout Plain Layout
26766 is only used as spacer.
26778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26781 \begin_layout Plain Layout
26789 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26792 \begin_layout Plain Layout
26796 \begin_layout Plain Layout
26812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26815 \begin_layout Plain Layout
26826 raisebox{-1.5pt}{W}}
26831 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26834 \begin_layout Plain Layout
26835 \begin_inset Formula $\raisebox{4.5mm}{}$
26842 \begin_layout Plain Layout
26860 \begin_inset Formula $\raisebox{-2mm}{}$
26876 \begin_layout Standard
26877 One has to take care that the character fits in the circle.
26888 \begin_layout Plain Layout
26890 \begin_inset CommandInset ref
26892 reference "sub:Font-Sizes"
26901 specifies thereby the size of the circle.
26912 \begin_layout Plain Layout
26914 \begin_inset CommandInset ref
26916 reference "sub:Boxes-without-Frame"
26925 the character can be centered.
26928 \begin_layout Subsection
26933 \begin_layout Plain Layout
26942 \begin_layout Standard
26943 Minuscule numbers are created with the command
26953 \begin_layout Plain Layout
26962 The command can be used in formulas and in TeX-mode.
26963 The command scheme is:
26966 \begin_layout Standard
26971 oldstylenums{number}
26974 \begin_layout Standard
26979 oldstylenums{0123456789
26982 \begin_inset Formula $\oldstylenums{0123456789}$
26988 \begin_layout Subsection
26989 Miscellaneous special Characters
26990 \begin_inset CommandInset label
26992 name "sub:Miscellaneous-special-Characters"
27000 \begin_layout Plain Layout
27001 Special characters ! miscellaneous
27009 \begin_layout Standard
27010 The following characters can only be inserted to formulas by using commands:
27013 \begin_layout Standard
27015 \begin_inset Tabular
27016 <lyxtabular version="3" rows="4" columns="2">
27018 <column alignment="center" valignment="top" width="0">
27019 <column alignment="center" valignment="top" width="0">
27021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27024 \begin_layout Plain Layout
27030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27033 \begin_layout Plain Layout
27041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27044 \begin_layout Plain Layout
27051 \begin_layout Plain Layout
27065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27068 \begin_layout Plain Layout
27069 \begin_inset Formula $\mathcircumflex$
27079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27082 \begin_layout Plain Layout
27090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27093 \begin_layout Plain Layout
27094 \begin_inset Formula $\_$
27104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27107 \begin_layout Plain Layout
27112 \begin_layout Plain Layout
27127 \begin_layout Plain Layout
27140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27143 \begin_layout Plain Layout
27144 \begin_inset Formula $^{\circ}$
27160 \begin_layout Standard
27161 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27162 contains the following line
27166 \begin_layout Plain Layout
27167 More about this is described in
27168 \begin_inset CommandInset ref
27170 reference "sub:Text-Characters-in"
27182 \begin_layout Standard
27187 DeclareInputtext{176}{
27200 \begin_layout Section
27202 \begin_inset CommandInset label
27204 name "sec:Formula-Styles"
27212 \begin_layout Plain Layout
27221 \begin_layout Itemize
27222 There are two different alignment styles:
27226 \begin_layout Description
27227 Centered is the predefined standard
27230 \begin_layout Description
27231 Indented for this the option
27235 must be inserted in the menu
27237 Document\SpecialChar \menuseparator
27243 \begin_inset space ~
27249 \begin_layout Standard
27254 is used, the indentation can be adjusted with the length
27264 \begin_layout Plain Layout
27273 Should the distance be 15
27274 \begin_inset space \thinspace{}
27277 mm, the following command line is inserted in the LaTeX-preamble
27280 \begin_layout Standard
27290 \begin_layout Standard
27291 When no length is specified, the predefined value of 30
27292 \begin_inset space \thinspace{}
27299 \begin_layout Itemize
27300 And two different numbering styles:
27304 \begin_layout Description
27305 Right is the predefined standard
27308 \begin_layout Description
27309 Left for this the option
27313 must be inserted in the menu
27315 Document\SpecialChar \menuseparator
27321 \begin_inset space ~
27328 \begin_layout Standard
27337 can also be used together.
27338 In this case both options are inserted, separated by a comma.
27341 \begin_layout Standard
27342 The chosen styles are used for all displayed formulas of the document.
27343 When both, centered and indented formulas should be created in a document,
27349 The indented formulas are then set in a flalign environment, see
27350 \begin_inset CommandInset ref
27352 reference "sub:Flalign-Environment"
27359 \begin_layout Section
27361 \begin_inset CommandInset label
27363 name "sec:Multiline-Formulas"
27371 \begin_layout Plain Layout
27372 Formula ! multiline
27380 \begin_layout Subsection
27384 \begin_layout Standard
27385 In LyX multiline formulas are created by pressing
27392 This creates either an
27394 eqnarray environment
27396 that is described in
27397 \begin_inset CommandInset ref
27399 reference "sub:Eqnarray-Environment"
27403 or, when the option
27405 Use AMS math package
27407 in the document settings is selected, an
27411 that is described in
27412 \begin_inset CommandInset ref
27414 reference "sub:Standard-align-Environment"
27421 \begin_layout Standard
27422 There are other multiline formula environments that can be created via the
27425 Insert\SpecialChar \menuseparator
27429 These environments are described in the following sections.
27432 \begin_layout Standard
27433 In all multiline formula environments a new line is created by pressing
27439 To add or delete lines, the math toolbar buttons
27440 \begin_inset Graphics
27441 filename ../images/tabular-feature_append-row.png
27447 \begin_inset Graphics
27448 filename ../images/tabular-feature_delete-row.png
27453 , respectively, or the menu
27455 Edit\SpecialChar \menuseparator
27461 \begin_layout Subsubsection
27463 \begin_inset CommandInset label
27465 name "sub:Line-Separation"
27473 \begin_layout Plain Layout
27474 Formula ! multiline ! Line separation
27482 \begin_layout Standard
27483 There is sometimes not enough space in multiline formulas between the lines:
27484 \begin_inset Formula \begin{eqnarray*}
27485 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}\\
27486 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*}
27493 \begin_layout Standard
27494 In LaTeX additional line space is specified as optional argument of the
27496 This is not yet possible in LyX
27500 \begin_layout Plain Layout
27502 \begin_inset CommandInset href
27504 name "LyX-bug #1505"
27505 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27514 , therefore the whole formula must be inserted in TeX-mode.
27515 To add in our example space, the command
27523 is inserted at the end of the first line.
27528 \begin_layout Plain Layout
27535 \begin_layout Plain Layout
27537 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27540 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27547 \begin_layout Plain Layout
27551 left(B^{2}+x_{0}^{2}
27559 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27564 \begin_layout Plain Layout
27576 \begin_layout Standard
27577 \begin_inset VSpace bigskip
27580 To set the the line separation for all lines in a formula, the length
27590 \begin_layout Plain Layout
27600 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27611 \begin_inset space \thinspace{}
27616 \begin_inset space \thinspace{}
27619 mm additional line separation as in the previous example, the command
27622 \begin_layout Standard
27632 \begin_layout Standard
27633 is inserted in TeX-mode before the formula.
27634 This requires that the LaTeX-package
27642 \begin_layout Plain Layout
27647 is part of every LaTeX standard installation.
27656 \begin_layout Plain Layout
27662 was loaded in LaTeX-preamble with the line
27665 \begin_layout Standard
27673 \begin_layout Standard
27678 \begin_layout Plain Layout
27690 \begin_inset Formula \begin{eqnarray*}
27691 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}\\
27692 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*}
27699 \begin_layout Standard
27703 \begin_layout Plain Layout
27714 To get back to the predefined distance,
27720 is set to the value 3
27721 \begin_inset space \thinspace{}
27727 \begin_layout Subsubsection
27729 \begin_inset CommandInset label
27731 name "sub:Column-Separation"
27739 \begin_layout Plain Layout
27740 Formula ! multiline ! Column separation
27748 \begin_layout Standard
27749 Multiline formulas form a matrix.
27750 A formula in the eqnarray environment is for example a matrix with three
27752 By changing the column separation in this environment, the space beside
27753 the relation sign can be changed.
27756 \begin_layout Standard
27757 The column separation is specified with the length
27767 \begin_layout Plain Layout
27776 \begin_inset Newline newline
27779 column separation = 2
27780 \begin_inset space \thinspace{}
27790 \begin_inset Newline newline
27796 \begin_layout Standard
27806 \begin_layout Standard
27807 inserted in TeX-mode, sets for all following formulas a column separation
27809 \begin_inset space \thinspace{}
27813 To get back to the predefined distance,
27820 \begin_inset space \thinspace{}
27826 \begin_layout Standard
27828 \begin_inset space \thinspace{}
27831 cm column separation:
27835 \begin_layout Plain Layout
27847 \begin_inset Formula \begin{eqnarray*}
27849 C & \ne & A\end{eqnarray*}
27853 A formula with the predefined column separation for matrices of 10
27854 \begin_inset space \thinspace{}
27861 \begin_layout Plain Layout
27873 \begin_inset Formula \begin{eqnarray*}
27875 C & \ne & A\end{eqnarray*}
27882 \begin_layout Subsubsection
27887 \begin_layout Plain Layout
27896 \begin_layout Standard
27897 Long formulas can be typeset using these methods:
27900 \begin_layout Itemize
27901 When one side of the equation is much shorther than the line width, this
27902 one is chosen for the left side and the right side is typeset over two
27907 \begin_layout Plain Layout
27917 \begin_inset Formula \begin{eqnarray}
27918 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 \\
27919 & & -\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}
27927 \begin_layout Plain Layout
27937 \begin_inset Newline newline
27940 The minus sign at the beginning of the second line does normally not appear
27941 as operator because it is the first character of the line.
27942 Thus it would not be surrounded by space and could not be distinguished
27943 from the fraction bar.
27944 To avoid this, space was inserted behind the minus sign with the command
27955 \begin_layout Plain Layout
27963 \begin_inset CommandInset ref
27965 reference "sub:Variable-Space"
27978 \begin_layout Plain Layout
27989 \begin_layout Itemize
27990 When both sides of the equation are too long, the command
28000 \begin_layout Plain Layout
28009 It is inserted to the first column of the first line and effects that all
28010 further insertions overwrite the following columns:
28014 \begin_layout Plain Layout
28024 \begin_inset Formula \begin{eqnarray}
28025 \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 \\
28026 & & -\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 \\
28027 & & =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}
28035 \begin_layout Plain Layout
28045 \begin_inset Newline newline
28048 After the insertion of
28054 , the cursor is in a purple box that is a bit shifted to the left from the
28056 In this the formula is inserted.
28060 \begin_layout Plain Layout
28070 \begin_inset Newline newline
28073 The content of the further lines is inserted to the second or another formula
28075 The greater the column number where it was inserted, the larger the indentation.
28079 \begin_layout Plain Layout
28089 \begin_inset Newline newline
28093 \begin_inset Note Greyedout
28096 \begin_layout Plain Layout
28097 Note the following when using
28106 \begin_layout Itemize
28107 The formula doesn't use the full page width.
28109 \begin_inset space \thinspace{}
28113 \begin_inset space ~
28117 \begin_inset Formula $-B^{2}$
28120 is added to the first line in the above example, it would have been outside
28122 To better use the width, negative space can be inserted at the beginning
28126 \begin_layout Itemize
28127 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28132 \begin_layout Plain Layout
28133 \begin_inset CommandInset href
28135 name "LyX-bug #1429"
28136 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28145 One can only set the cursor at the beginning of the line and move it with
28154 \begin_layout Itemize
28155 Other methods to set long formulas are offered by the environments described
28157 \begin_inset CommandInset ref
28159 reference "sub:Multline-Environment"
28164 \begin_inset CommandInset ref
28166 reference "sub:Multiline-Formula-Parts"
28173 \begin_layout Subsubsection
28175 \begin_inset CommandInset label
28177 name "sub:Multiline-Brackets"
28185 \begin_layout Plain Layout
28186 Brackets ! for multiline expressions
28194 \begin_layout Standard
28195 For brackets spanning multiple lines the following problem occurs:
28196 \begin_inset Formula \begin{eqnarray*}
28197 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28198 & & \left.\cdots+B-D\right]\end{eqnarray*}
28205 \begin_layout Standard
28206 The closing bracket is smaller than the opening bracket because brackets
28207 with variable size may not span multiple lines.
28210 \begin_layout Standard
28211 To set the bracket size for the second line correctly, the first line is
28222 \begin_layout Plain Layout
28230 and the second line with
28238 \begin_layout Plain Layout
28252 \begin_inset CommandInset ref
28254 reference "sub:Automatic-Bracket-Size"
28269 \begin_layout Plain Layout
28295 \begin_layout Plain Layout
28314 \begin_layout Plain Layout
28333 \begin_layout Plain Layout
28345 \begin_inset Formula $\downarrow$
28354 \begin_layout Plain Layout
28362 is inserted, because the multiplication operator with its limits is the
28363 largest symbol in the first line and this should be the size for the bracket
28364 in the second line.
28367 \begin_layout Standard
28368 The result is this:
28369 \begin_inset Formula \begin{eqnarray*}
28370 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28371 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28378 \begin_layout Subsection
28382 \begin_layout Standard
28383 Align environments can be used for every kind of multiline formulas.
28384 They are specially useful to set several formulas side by side.
28387 \begin_layout Standard
28388 Align environments consist of columns.
28389 The odd columns are right aligned, the even ones left aligned.
28390 Every line in an Align environment can be numbered.
28393 \begin_layout Standard
28394 Align environments are created via the menu
28396 Insert\SpecialChar \menuseparator
28402 Edit\SpecialChar \menuseparator
28403 Math\SpecialChar \menuseparator
28404 Change Formula Type
28406 already existing formulas can be converted to Align environments.
28409 \begin_layout Standard
28410 To add or delete columns, the math toolbar buttons
28411 \begin_inset Graphics
28412 filename ../images/tabular-feature_append-column.png
28418 \begin_inset Graphics
28419 filename ../images/tabular-feature_delete-column.png
28424 , respectively, or the menu
28426 Edit\SpecialChar \menuseparator
28432 \begin_layout Subsubsection
28433 Standard align Environment
28434 \begin_inset CommandInset label
28436 name "sub:Standard-align-Environment"
28444 \begin_layout Plain Layout
28445 Formula ! multiline ! align environment
28453 \begin_layout Standard
28454 This Align environment is created by presssing
28458 in a formula or by the menu
28460 Insert\SpecialChar \menuseparator
28461 Math\SpecialChar \menuseparator
28462 AMS align Environment
28467 \begin_layout Standard
28468 An example for two formulas set side by side, that are created with a four
28469 column align environment:
28470 \begin_inset Formula \begin{align*}
28471 A & =\sin(B) & C & =D\\
28472 C & \ne A & B & \ne D\end{align*}
28476 As it can be seen, the formulas in this environment are placed so as if
28485 \begin_layout Plain Layout
28493 \begin_inset CommandInset ref
28495 reference "sub:Variable-Space"
28506 before the first and after every even column.
28507 When the formula style
28513 \begin_layout Plain Layout
28515 \begin_inset CommandInset ref
28517 reference "sec:Formula-Styles"
28528 is used, the formula is set without the
28534 before the first column.
28537 \begin_layout Subsubsection
28538 Alignat Environment
28542 \begin_layout Plain Layout
28543 Formula ! multiline ! alignat environment
28551 \begin_layout Standard
28552 The alignat environment has no predefined column separation.
28553 It can be inserted manually with the spaces that are described
28554 \begin_inset CommandInset ref
28556 reference "sub:Space"
28563 \begin_layout Standard
28564 The above example in the alignat environment where 1
28565 \begin_inset space \thinspace{}
28568 cm space was inserted at the beginning of the second formula:
28569 \begin_inset Formula \begin{alignat*}{2}
28570 A & =\sin(B) & \hspace{1cm}C & =D\\
28571 C & \ne A & B & \ne D\end{alignat*}
28575 Because the column separation can be set separately for every column, this
28576 environment is especially suitable to set three and more formulas side
28580 \begin_layout Subsubsection
28581 Flalign Environment
28582 \begin_inset CommandInset label
28584 name "sub:Flalign-Environment"
28592 \begin_layout Plain Layout
28593 Formula ! multiline ! flalign environment
28601 \begin_layout Standard
28602 In this environment the first two columns are always set as much as possible
28603 to the left and the last two ones to the right.
28605 \begin_inset Formula \begin{flalign*}
28606 A & =1 & B & =2 & C & =3\\
28607 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28614 \begin_layout Standard
28615 By creating a flalign environment with an odd number of columns where an
28616 empty TeX-brace is inserted to the last column, several formulas in a document
28617 can be set to the left, although the formula style
28622 As example the indented formula
28623 \begin_inset CommandInset ref
28625 reference "eq:VolInt"
28630 \begin_inset Formula \begin{flalign}
28631 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28635 The first two columns contain the formula.
28636 To indent it as with the formula style
28641 \begin_inset space \thinspace{}
28644 pt space was inserted at the beginning of the first column.
28647 \begin_layout Subsection
28648 Eqnarray Environment
28649 \begin_inset CommandInset label
28651 name "sub:Eqnarray-Environment"
28659 \begin_layout Plain Layout
28660 Formula ! multiline ! eqnarray environment
28668 \begin_layout Standard
28669 When this environment has been created, three blue boxes appear.
28670 The content of the first box is right aligned, the content of the last
28672 The content of the middle box appears centered and a bit smaller, because
28673 it is designed to insert there only relation characters.
28674 \begin_inset Formula \begin{eqnarray*}
28675 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28677 A & = & A\end{eqnarray*}
28684 \begin_layout Subsection
28689 \begin_layout Plain Layout
28690 Formula ! multiline ! gather environment
28698 \begin_layout Standard
28699 This environment consists of only one centered column.
28700 Every line can be numbered.
28701 \begin_inset Formula \begin{gather}
28703 X=\textrm{-}1\end{gather}
28710 \begin_layout Subsection
28711 Multline Environment
28712 \begin_inset CommandInset label
28714 name "sub:Multline-Environment"
28722 \begin_layout Plain Layout
28723 Formula ! multiline ! multline environment
28731 \begin_layout Standard
28732 The multline environment consists, like the gather environment, of only
28734 But the first line is left aligned, the last one right aligned.
28735 All other lines are centered.
28736 Therefore this environment is suitable for long formulas.
28738 \begin_inset CommandInset ref
28740 reference "eq:lefteqn"
28744 in the multline environment:
28745 \begin_inset Formula \begin{multline}
28746 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}\\
28747 -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}\\
28748 =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}
28755 \begin_layout Standard
28756 In the output only the last (first) line of a multline environment appears
28757 numbered when the document numbering is right (left).
28761 \begin_layout Plain Layout
28762 numbering styles see
28763 \begin_inset CommandInset ref
28765 reference "sec:Formula-Styles"
28777 \begin_layout Standard
28786 \begin_layout Plain Layout
28804 \begin_layout Plain Layout
28814 a centered line can be right or left aligned, respectively.
28815 The commands are used as follows:
28818 \begin_layout Standard
28823 shoveright{line content}
28829 shoveleft{line content}
28832 \begin_layout Standard
28833 \begin_inset VSpace medskip
28844 \begin_layout Plain Layout
28854 specifies the distance of the first line from the left page margin.
28855 Predefined is the length 0
28856 \begin_inset space \thinspace{}
28862 \begin_layout Standard
28863 As example the above formula where the command
28866 \begin_layout Standard
28876 \begin_layout Standard
28877 was inserted in TeX-mode before:
28881 \begin_layout Plain Layout
28893 \begin_inset Formula \begin{multline}
28894 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}\\
28895 \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}}\\
28896 =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}
28904 \begin_layout Plain Layout
28915 The second line was left aligned using
28924 \begin_layout Subsection
28925 Multiline Formula Parts
28926 \begin_inset CommandInset label
28928 name "sub:Multiline-Formula-Parts"
28936 \begin_layout Plain Layout
28937 Formula ! multiline ! formula parts
28945 \begin_layout Standard
28946 To display only parts of a formula with multiple lines, one of the following
28947 environments are used:
28964 They can be inserted via the menu
28966 Insert\SpecialChar \menuseparator
28969 or by using the commands described in this section.
28972 \begin_layout Standard
28973 The first three have the same properties as the corresponding multiline
28974 formula environments, but it is possible to set further formula parts beside
28977 \begin_inset Formula \[
28978 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28979 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28980 \right\} \textrm{Uncertainty relations}\]
28987 \begin_layout Standard
28988 To get this formula, a displayed formula is created where the command
28996 \begin_layout Plain Layout
29007 A purple box appears around the blue formula box where now columns and
29008 lines can be added.
29009 Outside the multiline environment other formula parts can be set, like
29013 \begin_layout Standard
29014 The aligned environment is also suitable for long formulas whose lines are
29015 horizontally aligned.
29016 Using aligned in a displayed formula has the advantage that the formula
29017 number is vertically centered behind the lines.
29019 \begin_inset CommandInset ref
29021 reference "eq:kurzlang"
29025 in the aligned environment:
29026 \begin_inset Formula \begin{equation}
29027 \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}|}\\
29028 & -\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}
29036 \begin_layout Standard
29037 To use the environments
29059 \begin_layout Plain Layout
29077 \begin_layout Plain Layout
29095 \begin_layout Plain Layout
29103 are inserted, respectively.
29104 The split environment has the same properties as the aligned environment
29105 but it can only have two columns.
29108 \begin_layout Subsection
29109 Text in multiline Formulas
29110 \begin_inset CommandInset label
29112 name "sub:Text-in-multiline"
29120 \begin_layout Plain Layout
29130 \begin_layout Plain Layout
29131 Formula ! multiline ! text
29139 \begin_layout Standard
29140 In the Align environments, and the multline and gather environment, text
29141 can be inserted that will appear in a separate line and doesn't affect
29142 the column alignment.
29143 To do this, the command
29151 \begin_layout Plain Layout
29161 is used in the following scheme:
29164 \begin_layout Standard
29172 \begin_layout Standard
29173 The text should not be longer than a line because it cannot be hyphenated.
29174 As LyX doesn't yet support
29180 directly, the text is written as mathematical text.
29187 must hereby be at the beginning of a line and appears in the output above
29189 An example where the text was inserted at the beginning of the second line:
29190 \begin_inset Formula \begin{align}
29191 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29192 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29199 \begin_layout Section
29204 \begin_layout Plain Layout
29214 \begin_layout Plain Layout
29215 Formula ! numbering|see
29219 \begin_layout Plain Layout
29230 \begin_layout Plain Layout
29245 \begin_layout Subsection
29249 \begin_layout Standard
29250 Numbered formulas can be created with the menu
29252 Insert\SpecialChar \menuseparator
29253 Math\SpecialChar \menuseparator
29255 \begin_inset space ~
29263 \begin_inset space ~
29269 Existing formulas can be numbered with the menu
29271 Edit\SpecialChar \menuseparator
29272 Math\SpecialChar \menuseparator
29274 \begin_inset space ~
29282 \begin_inset space ~
29288 The formula number is displayed in LyX behind the formula as number sign
29290 The number sign is replaced in the output by the formula number.
29293 \begin_layout Standard
29294 When numbering is turned on in multiline formulas, all lines will be numbered.
29295 But the numbering can be controlled with the menu
29297 Edit\SpecialChar \menuseparator
29298 Math\SpecialChar \menuseparator
29300 \begin_inset space ~
29304 \begin_inset space ~
29308 \begin_inset space ~
29316 \begin_inset space ~
29324 \begin_layout Standard
29325 Except of inline formulas, all formulas can be numbered with two different
29327 \begin_inset CommandInset ref
29329 reference "sec:Formula-Styles"
29336 \begin_layout Subsection
29341 \begin_layout Plain Layout
29342 Cross-references ! to formulas
29350 \begin_layout Standard
29351 All labeled formulas can be cross-referenced.
29352 A label is added by the menu
29354 Insert\SpecialChar \menuseparator
29357 or the toolbar button
29358 \begin_inset Graphics
29359 filename ../images/label-insert.png
29365 The cursor must hereby be inside a displayed formula.
29366 A dialog pops up displaying the prefix
29371 The label is inserted there behind the prefix.
29372 The predefined prefix means
29373 \begin_inset Quotes eld
29377 \begin_inset Quotes erd
29380 and makes it easier to find labels in large documents because it marks
29381 it as formula label to divide it from e.
29382 \begin_inset space \thinspace{}
29386 \begin_inset space ~
29390 To change a label, the menu
29392 Insert\SpecialChar \menuseparator
29398 \begin_layout Standard
29399 The name of the label is displayed in LyX within two parentheses behind
29401 A formula with a label is always numbered.
29404 \begin_layout Standard
29405 Cross-references are inserted via the menu
29407 Insert\SpecialChar \menuseparator
29410 or with the toolbar button
29411 \begin_inset Graphics
29412 filename ../images/dialog-show-new-inset_ref.png
29418 A formula cross-reference appears in the output as formula number.
29419 When in the cross-reference dialog window the format
29423 is chosen, the cross-reference appears in the output as formula number
29425 \begin_inset Newline newline
29428 By right-clicking on a cross-reference in LyX, one jumps to the formula
29429 that is referenced.
29432 \begin_layout Standard
29433 Here are as examples cross-references to formulas of the following subsections:
29434 \begin_inset Note Note
29437 \begin_layout Plain Layout
29438 Note the different cross-reference types.
29446 \begin_layout Standard
29448 \begin_inset CommandInset ref
29455 \begin_inset CommandInset ref
29463 \begin_inset CommandInset ref
29469 ) big Latin letters are used for the numbering in contrary to (
29470 \begin_inset CommandInset ref
29479 \begin_layout Standard
29480 \begin_inset VSpace medskip
29483 When the argument of
29491 \begin_layout Plain Layout
29499 \begin_inset CommandInset ref
29501 reference "sub:User-defined-Numbering"
29512 contains a box like in
29513 \begin_inset CommandInset ref
29515 reference "sub:Paragraph-Boxes"
29519 , the formula cannot be referenced.
29522 \begin_layout Subsection
29527 \begin_layout Plain Layout
29528 Formula numbering ! subnumbering
29536 \begin_layout Standard
29537 With the help of the commands
29541 begin{subequations}
29549 formulas can be subnumbered.
29550 Both commands are inserted in TeX-mode.
29553 \begin_layout Standard
29555 \begin_inset Formula \begin{equation}
29556 A=C-B\label{eq:a}\end{equation}
29564 \begin_layout Plain Layout
29568 addtocounter{equation}{-1}
29577 \begin_layout Plain Layout
29581 begin{subequations}
29587 \begin_inset VSpace -5mm
29591 \begin_inset Formula \begin{equation}
29592 B=C-A\label{eq:b}\end{equation}
29597 \begin_inset Formula \begin{equation}
29598 C=A+B\label{eq:c}\end{equation}
29605 \begin_layout Standard
29609 \begin_layout Plain Layout
29621 \begin_layout Standard
29622 To create the example, the following is done:
29625 \begin_layout Enumerate
29626 first formula is inserted
29629 \begin_layout Enumerate
29634 addtocounter{equation}{-1}
29636 begin{subequations}
29640 \begin_layout Plain Layout
29649 \begin_inset Newline newline
29654 is inserted after the first formula
29657 \begin_layout Enumerate
29658 second formula is inserted
29661 \begin_layout Enumerate
29662 third formula is inserted
29665 \begin_layout Enumerate
29672 is inserted after the third formula
29675 \begin_layout Standard
29676 Every formula between the commands
29688 is subnumbered as a, b,
29689 \begin_inset Newline linebreak
29692 c, \SpecialChar \ldots{}
29693 For multiline formulas every line will be subnumbered.
29694 All subnumbered formulas are treated as
29699 But as every numbered formula increases the counter
29703 by one, the command
29709 is needed to decrease it.
29710 Otherwise the formulas
29711 \begin_inset CommandInset ref
29718 \begin_inset CommandInset ref
29725 \begin_inset CommandInset ref
29731 would be numbered as
29732 \begin_inset CommandInset ref
29739 \begin_inset CommandInset ref
29746 \begin_inset CommandInset ref
29755 \begin_layout Standard
29756 By inserting the commands in TeX-mode, a space is created between the first
29759 \begin_inset space \thinspace{}
29762 mm vertical space is inserted after the command
29766 begin{subequations}
29769 When the formula style
29775 \begin_layout Plain Layout
29777 \begin_inset CommandInset ref
29779 reference "sec:Formula-Styles"
29791 \begin_inset space \thinspace{}
29794 mm space is inserted instead.
29797 \begin_layout Standard
29798 Here is an example for a multiline formula where the numbering was turned
29799 off for the second line:
29803 \begin_layout Plain Layout
29807 begin{subequations}
29813 \begin_inset Formula \begin{eqnarray}
29814 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29815 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29816 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29824 \begin_layout Plain Layout
29836 \begin_layout Subsection
29837 User-defined Numbering
29838 \begin_inset CommandInset label
29840 name "sub:User-defined-Numbering"
29848 \begin_layout Plain Layout
29849 Formula numbering ! user-defined
29857 \begin_layout Standard
29861 \begin_layout Plain Layout
29862 Formula numbering ! self-defined delimiters
29867 With the standard numbering parentheses are set around the formula number.
29868 To replace the parentheses for example by vertical bars, the following
29869 line is added to the LaTeX-preamble:
29872 \begin_layout Standard
29884 \begin_inset Note Note
29887 \begin_layout Plain Layout
29888 This macro is already declared in the LaTeX-preamble for testing.
29889 To activate it, remove the percent sign at the beginning.
29897 \begin_layout Standard
29898 To use other characters, the vertical bars besides the
29902 are replaced by one ore more characters.
29903 To get only the formula number the vertical bars are omitted.
29906 \begin_layout Standard
29907 \begin_inset VSpace bigskip
29910 When there should be an expression of your choice instead of the consecutive
29911 formula number in parentheses behind the formula, the command
29921 \begin_layout Plain Layout
29930 \begin_inset Formula \begin{equation}
29931 A+B=C\tag{something}\label{eq:tag}\end{equation}
29935 In this example the command
29943 \begin_layout Plain Layout
29954 was inserted to the formula.
29957 \begin_layout Standard
29966 \begin_layout Plain Layout
29977 is inserted instead, the star prevents the parentheses around the expression:
29978 \begin_inset Formula \[
29979 A+B=C\tag*{something}\]
29986 \begin_layout Standard
29987 \begin_inset VSpace bigskip
29990 To restart the formula numbering with new document parts or sections, the
29991 following command is used:
29994 \begin_layout Standard
29999 @addtoreset{equation}{part}
30005 \begin_layout Plain Layout
30010 \begin_layout Plain Layout
30021 \begin_layout Plain Layout
30034 \begin_layout Plain Layout
30045 \begin_layout Plain Layout
30058 \begin_inset Newline newline
30062 \begin_inset Newline newline
30069 @addtoreset{equation}{section}
30072 \begin_layout Standard
30073 To be able to use these commands in TeX-mode, the
30074 \begin_inset Quotes eld
30078 \begin_inset Quotes erd
30081 character has to be made
30082 \begin_inset Quotes eld
30086 \begin_inset Quotes erd
30089 for LaTeX using the command
30103 So the command sequence in TeX-mode is:
30106 \begin_layout Standard
30112 \begin_inset Newline newline
30117 @addtoreset{equation}{section}
30118 \begin_inset Newline newline
30126 \begin_layout Standard
30127 In the LaTeX-preamble
30139 can be omitted as they are automatically internally inserted by LyX.
30142 \begin_layout Standard
30157 \begin_layout Plain Layout
30162 is part of the LaTeX-package
30170 \begin_layout Plain Layout
30171 Packages ! carlisle
30176 that is part of every LaTeX standard installation.
30185 \begin_layout Plain Layout
30186 Packages ! remreset
30191 has to be loaded in the LaTeX-preamble with the line
30194 \begin_layout Standard
30199 usepackage{remreset}
30202 \begin_layout Standard
30213 \begin_layout Plain Layout
30218 \begin_layout Plain Layout
30229 \begin_layout Plain Layout
30242 \begin_layout Plain Layout
30253 \begin_layout Plain Layout
30265 can be used with the same scheme as
30274 \begin_layout Standard
30275 \begin_inset VSpace bigskip
30278 Sometimes formulas should be numbered in the following form:
30281 \begin_layout Standard
30284 (section number.formula number)
30287 \begin_layout Standard
30288 The formula number should start with every section with
30289 \begin_inset Quotes eld
30293 \begin_inset Quotes erd
30299 \begin_layout Standard
30300 For this case there is the command
30310 \begin_layout Plain Layout
30318 , which is used with the following scheme:
30321 \begin_layout Standard
30326 numberwithin{counter}{sectioning}
30329 \begin_layout Standard
30330 Counter denotes what kind of numbering is affected, sectioning denotes what
30331 number is before the dot.
30334 \begin_layout Standard
30335 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30338 \begin_layout Standard
30343 numberwithin{equation}{section}
30346 \begin_layout Standard
30347 This is the result:
30351 \begin_layout Plain Layout
30355 numberwithin{equation}{section}
30361 \begin_inset Formula \begin{equation}
30362 A+B=C\end{equation}
30369 \begin_layout Standard
30371 \begin_inset space \thinspace{}
30375 \begin_inset space ~
30378 tables so that the number of the part is the sectioning,
30379 \begin_inset Newline newline
30386 numberwithin{table}{part}
30391 \begin_layout Standard
30392 To go back to the standard numbering or to prevent this kind of numbering
30393 when it is defined by the document class, the following command is inserted
30394 as TeX-Code or to the LaTeX-preamble:
30397 \begin_layout Standard
30410 \begin_layout Plain Layout
30424 \begin_layout Plain Layout
30440 \begin_inset Newline newline
30448 \begin_inset Newline newline
30460 \begin_layout Standard
30467 uses internally the command
30473 , described above, that also needs to be reverted.
30477 \begin_layout Plain Layout
30484 \begin_layout Plain Layout
30488 @removefromreset{equation}{section}
30491 \begin_layout Plain Layout
30503 \begin_layout Subsection
30504 Numbering with Roman Numbers and Letters
30508 \begin_layout Plain Layout
30509 Formula numbering ! with letters
30518 \begin_layout Plain Layout
30519 Formula numbering ! with Roman numbers
30527 \begin_layout Standard
30528 Formulas can also be numbered with Roman numbers and Latin letters.
30529 To number for example with small Roman numbers, the command
30532 \begin_layout Standard
30544 \begin_layout Standard
30545 is inserted before the formula in TeX-mode.
30556 \begin_layout Plain Layout
30564 redefines the predefined command
30580 \begin_layout Plain Layout
30587 has the same scheme like the command
30593 that is described in
30594 \begin_inset CommandInset ref
30596 reference "sec:User-defined-Commands"
30610 is the formula counter.
30617 is used as prefix for a counter, the value of the counter is output as
30619 When a formula is numbered, LaTeX sets internally the command
30625 behind the formula.
30634 \begin_layout Plain Layout
30644 outputs the counter as small Roman number.
30647 \begin_layout Standard
30648 All formulas behind the command
30658 are now numbered Roman.
30659 To switch to numbering with big Roman numbers, the command is inserted
30676 \begin_layout Plain Layout
30688 \begin_inset Quotes eld
30692 \begin_inset Quotes erd
30695 with small Latin letters there is the command
30705 \begin_layout Plain Layout
30713 , for big ones there is the command
30723 \begin_layout Plain Layout
30736 \begin_layout Standard
30737 \begin_inset Note Greyedout
30740 \begin_layout Plain Layout
30745 Only maximal 26 formulas can be numbered with Latin letters in one document.
30753 \begin_layout Standard
30757 \begin_layout Plain Layout
30773 \begin_layout Standard
30774 \begin_inset Formula \begin{equation}
30775 A=\textrm{small roman}\label{eq:rom}\end{equation}
30783 \begin_layout Plain Layout
30797 \begin_inset Formula \begin{equation}
30798 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30806 \begin_layout Plain Layout
30820 \begin_inset Formula \begin{equation}
30821 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30829 \begin_layout Plain Layout
30843 \begin_inset Formula \begin{equation}
30844 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30851 \begin_layout Standard
30852 To switch back to the default numbering, insert the command:
30855 \begin_layout Standard
30868 \begin_layout Plain Layout
30879 \begin_layout Standard
30883 \begin_layout Plain Layout
30897 \begin_inset Formula \begin{equation}
30898 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30905 \begin_layout Standard
30906 \begin_inset VSpace medskip
30909 As you see, formulas are numbered serially independent from the numbering
30911 When then numbering should start with
30912 \begin_inset Quotes eld
30916 \begin_inset Quotes erd
30919 when the style is changed, new equation counters have to be defined.
30920 A description about this can be found in the file
30921 \begin_inset CommandInset href
30923 target "Formula-numbering.lyx"
30930 \begin_layout Section
30931 User-defined Commands
30932 \begin_inset CommandInset label
30934 name "sec:User-defined-Commands"
30942 \begin_layout Plain Layout
30943 User-defined commands
30951 \begin_layout Standard
30952 Many LaTeX-commands are too long to be used frequently.
30953 But it is possible to define with the command
30963 \begin_layout Plain Layout
30971 new shorter commands.
30974 \begin_layout Standard
30975 The command scheme of
30984 \begin_layout Standard
30989 newcommand{new command name}[number of arguments][optional
30994 \begin_inset Newline newline
31001 \begin_layout Plain Layout
31016 \begin_layout Plain Layout
31023 {command definition}
31026 \begin_layout Standard
31027 \begin_inset Note Greyedout
31030 \begin_layout Plain Layout
31035 Assure that the name of the new command is not already used in your document
31036 or by LaTeX-packages that you use.
31037 When you for example define the command
31049 , you get an error message because
31055 is already defined as command for
31056 \begin_inset Quotes eld
31060 \begin_inset Formula $\le$
31064 \begin_inset Quotes erd
31075 \begin_layout Standard
31076 \begin_inset Note Greyedout
31079 \begin_layout Plain Layout
31084 The names of user-defined commands may only consist of Latin letters.
31092 \begin_layout Standard
31093 The number of arguments is an integer in the range 0
31094 \begin_inset space \thinspace{}
31098 \begin_inset space \thinspace{}
31101 9 and specifies how many arguments the new command should have.
31102 With the optional value a value for an optional argument can be predefined.
31103 When this is done, the
31111 rgument of the new command is automatically an optional one.
31114 \begin_layout Standard
31115 Here are some examples:
31118 \begin_layout Itemize
31119 To define the command
31131 , the LaTeX-preamble line is:
31135 \begin_layout Plain Layout
31147 \begin_inset Newline newline
31159 \begin_layout Itemize
31160 To define the command
31172 , the argument (that should be underlined) must be taken into account.
31173 For this the preamble line is:
31177 \begin_layout Plain Layout
31189 \begin_inset Newline newline
31204 \begin_layout Plain Layout
31216 \begin_inset Newline newline
31225 acts as argument placeholder, the
31229 behind it denotes that it is the placeholder for the first argument.
31232 \begin_layout Itemize
31240 \begin_inset space \thinspace{}
31244 \begin_inset space ~
31257 \begin_layout Plain Layout
31269 \begin_inset Newline newline
31278 framebox#1#2{$#3$}}
31284 \begin_layout Plain Layout
31296 \begin_inset Newline newline
31301 The two Dollar signs creates the extra formula needed for
31308 \begin_inset CommandInset ref
31310 reference "sub:Boxes-with-Frame"
31317 \begin_layout Itemize
31318 To create a new command for
31324 where the color for the box needn't to be specified, the argument for the
31325 color is defined optional:
31329 \begin_layout Plain Layout
31341 \begin_inset Newline newline
31350 fcolorbox{#2}{#1}{$#3$}}
31356 \begin_layout Plain Layout
31366 \begin_inset Newline newline
31369 When the color is not specified when using
31375 , the predefined color
31382 \begin_layout Standard
31383 A test of the new defined commands:
31386 \begin_layout Standard
31388 \begin_inset Tabular
31389 <lyxtabular version="3" rows="6" columns="2">
31391 <column alignment="center" valignment="top" width="0">
31392 <column alignment="center" valignment="top" width="0">
31394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31397 \begin_layout Plain Layout
31403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31406 \begin_layout Plain Layout
31408 \begin_inset Note Note
31411 \begin_layout Plain Layout
31418 is only used as spacer.
31430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31433 \begin_layout Plain Layout
31440 \begin_layout Plain Layout
31454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31457 \begin_layout Plain Layout
31458 \begin_inset Formula $A\gr B$
31468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31471 \begin_layout Plain Layout
31479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31482 \begin_layout Plain Layout
31483 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31496 \begin_layout Plain Layout
31500 \begin_inset Formula $\to$
31506 \begin_inset Formula $\to$
31517 \begin_layout Plain Layout
31531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31534 \begin_layout Plain Layout
31535 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31548 \begin_layout Plain Layout
31552 \begin_inset Formula $\to$
31563 \begin_layout Plain Layout
31577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31580 \begin_layout Plain Layout
31581 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31594 \begin_layout Plain Layout
31600 \begin_inset Formula $\to$
31611 \begin_layout Plain Layout
31625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31628 \begin_layout Plain Layout
31629 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31645 \begin_layout Section
31649 \begin_layout Standard
31650 LyX supports two types of commutative diagrams:
31658 that are explained in the following.
31661 \begin_layout Subsection
31666 \begin_layout Plain Layout
31675 \begin_layout Standard
31676 Diagrams of this type visualize relations by vertical and horizontal lines
31678 \begin_inset Formula \[
31679 \begin{CD}A@>>>B@>>>C\\
31681 F@<<<E@<<<D\end{CD}\]
31688 \begin_layout Standard
31689 To get them, the command
31697 \begin_layout Plain Layout
31707 is inserted to a formula.
31708 A blue box appears with two dashed lines where further commands can be
31714 a new line is created.
31715 Horizontal relations are inserted in odd, vertical in even formula lines.
31718 \begin_layout Standard
31719 To create the relations there are the following commands:
31722 \begin_layout Itemize
31727 creates a left arrow,
31738 \begin_layout Itemize
31743 creates an up arrow,
31751 a vertical equal sign
31754 \begin_layout Itemize
31760 is a placeholder for non-existent relations
31763 \begin_layout Standard
31764 All arrows can be labeled as follows:
31767 \begin_layout Itemize
31768 Is text inserted between the first and second < or >, resp., it is placed
31770 When it is inserted between the second and third one, it appears under
31774 \begin_layout Itemize
31775 When text for vertical arrows is inserted between the first and second A
31776 or V, resp., it is placed left beside the arrow.
31777 When it is inserted between the second and third one, it appears right
31779 If the text contains an A or V, these letters must be set into a TeX-brace.
31782 \begin_layout Standard
31783 As example a diagram with all possible relations:
31786 \begin_layout Standard
31787 \begin_inset Formula \[
31788 \begin{CD}A@>j>>B@>>k>C@=F\\
31790 D@<<j<E@>k>>F@=C\end{CD}\]
31797 \begin_layout Standard
31798 The command for this is:
31799 \begin_inset Newline newline
31810 \begin_layout Plain Layout
31819 A@>j>>B@>>k>C@=F Ctrl-Enter
31820 \begin_inset Newline newline
31827 \begin_layout Plain Layout
31842 \begin_layout Plain Layout
31855 \begin_layout Plain Layout
31867 \begin_inset Formula $\to$
31873 \begin_inset Newline newline
31880 \begin_layout Plain Layout
31895 \begin_layout Plain Layout
31908 \begin_layout Plain Layout
31918 \begin_layout Subsection
31923 \begin_layout Plain Layout
31924 Diagrams ! xymatrix
31932 \begin_layout Standard
31933 To be able to use xymatrices, the LaTeX-package
31938 A xymatrix is created by inserting the command
31945 Then you are able to add new matrix columns and rows like for normal matrices,
31947 \begin_inset CommandInset ref
31949 reference "sec:Matrices"
31956 \begin_layout Standard
31957 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31959 All possibilities to create commutative diagrams and decorations are explained
31960 in detail in this manual:
31961 \begin_inset CommandInset href
31963 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31970 \begin_layout Standard
31971 \begin_inset Newpage newpage
31977 \begin_layout Section
31982 \begin_layout Plain Layout
31995 \begin_layout Plain Layout
31996 Other useful math tips can be found in
31997 \begin_inset CommandInset citation
32012 \begin_layout Plain Layout
32020 \begin_inset Note Note
32023 \begin_layout Plain Layout
32026 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
32029 \begin_layout Plain Layout
32032 texorpdfstring is in section
32033 \begin_inset CommandInset ref
32035 reference "sub:Formulas-in-Section"
32048 \begin_layout Plain Layout
32058 \begin_layout Plain Layout
32063 \begin_layout Plain Layout
32070 Chemical characters
32074 \begin_layout Plain Layout
32089 \begin_layout Subsection
32090 Chemical Symbols and Equations
32091 \begin_inset CommandInset label
32093 name "sub:Chemical-Symbols-and"
32101 \begin_layout Plain Layout
32102 Chemical characters ! Symbols
32111 \begin_layout Plain Layout
32121 \begin_layout Plain Layout
32130 \begin_layout Standard
32131 An example text from chemistry:
32134 \begin_layout Quote
32136 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32139 -ion reacts with two
32140 \begin_inset Formula $\mathrm{Na^{+}}$
32143 -ions to sodium sulfate
32144 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32148 The chemical equation for this is:
32149 \begin_inset Formula \[
32150 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32157 \begin_layout Standard
32158 This chemical equation can directly be created as formula.
32159 To avoid that the symbols appear italic, everything is highlighted and
32160 changed by the shortcut
32163 \begin_inset space ~
32168 to the upright font style.
32172 \begin_layout Plain Layout
32178 \begin_inset CommandInset ref
32180 reference "sub:Font-Styles"
32192 \begin_layout Subsection
32197 \begin_layout Plain Layout
32206 \begin_layout Standard
32207 Negative numbers often look ugly in formulas because the minus sign before
32208 the number is set with the same length as the minus operator sign.
32209 When writing the negative number in normal text, the minus sign appears
32213 \begin_layout Standard
32214 Thus, the problem disappears when converting the minus sign to mathematical
32218 \begin_layout Standard
32219 An example to visualize the problem:
32222 \begin_layout Standard
32224 \begin_inset Tabular
32225 <lyxtabular version="3" rows="3" columns="2">
32227 <column alignment="right" valignment="top" width="0">
32228 <column alignment="left" valignment="top" width="0">
32230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32233 \begin_layout Plain Layout
32239 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32242 \begin_layout Plain Layout
32250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32253 \begin_layout Plain Layout
32259 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32262 \begin_layout Plain Layout
32263 \begin_inset Formula $x=-2$
32273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32276 \begin_layout Plain Layout
32282 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32285 \begin_layout Plain Layout
32286 \begin_inset Formula $x=\textrm{-}2$
32302 \begin_layout Subsection
32303 Comma as decimal Separator
32307 \begin_layout Plain Layout
32316 \begin_layout Standard
32317 In LaTeX a comma inside a formula is used, according to the English convention,
32318 as number group separator.
32319 So there will be space added behind all commas in formulas.
32322 \begin_layout Standard
32323 To avoid this, the comma is highlighted and changed to mathematical text
32327 \begin_inset space ~
32335 \begin_layout Standard
32336 To use all formula commas in the document as decimal separator, the file
32345 \begin_layout Plain Layout
32350 is part of the LaTeX-package
32358 \begin_layout Plain Layout
32363 \begin_layout Plain Layout
32386 \begin_layout Plain Layout
32392 is loaded with the LaTeX-preamble line
32395 \begin_layout Standard
32403 \begin_layout Subsection
32405 \begin_inset CommandInset label
32407 name "sub:Physical-Vectors"
32415 \begin_layout Plain Layout
32424 \begin_layout Standard
32425 Predefined vectors are offered by the LaTeX-package
32433 \begin_layout Plain Layout
32438 should be part of every LaTeX standard installation.
32447 \begin_layout Plain Layout
32453 that is loaded with the LaTeX-preamble line
32456 \begin_layout Standard
32464 \begin_layout Standard
32468 \begin_layout Plain Layout
32478 \begin_inset Note Note
32481 \begin_layout Plain Layout
32482 The following table will only be displayed when the LaTeX-package
32491 The following commands are defined:
32494 \begin_layout Standard
32496 \begin_inset Tabular
32497 <lyxtabular version="3" rows="4" columns="2">
32499 <column alignment="center" valignment="top" width="0">
32500 <column alignment="center" valignment="top" width="0">
32502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32505 \begin_layout Plain Layout
32511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32514 \begin_layout Plain Layout
32522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32525 \begin_layout Plain Layout
32535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32538 \begin_layout Plain Layout
32539 \begin_inset Formula $\Bra{\psi}$
32549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32552 \begin_layout Plain Layout
32562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32565 \begin_layout Plain Layout
32566 \begin_inset Formula $\Ket{\psi}$
32576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32579 \begin_layout Plain Layout
32591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32594 \begin_layout Plain Layout
32595 \begin_inset Formula $\Braket{\psi|\phi}$
32611 \begin_layout Standard
32618 assures that all vertical bars are set in the size of the surrounding brackets:
32619 \begin_inset Formula \[
32620 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32628 \begin_layout Plain Layout
32638 \begin_inset Note Note
32641 \begin_layout Plain Layout
32642 The following will be displayed when the LaTeX-package
32654 \begin_layout Standard
32655 You need to install the LaTeX-package
32659 to see the rest of this subsection in the output.
32662 \begin_layout Standard
32666 \begin_layout Plain Layout
32678 \begin_layout Standard
32685 can also be achieved using the command
32691 , that is described in
32692 \begin_inset CommandInset ref
32694 reference "sub:Automatic-Bracket-Size"
32701 \begin_layout Subsection
32702 Self-defined Fractions
32703 \begin_inset CommandInset label
32705 name "sub:Self-defined-Fractions"
32713 \begin_layout Plain Layout
32714 Fractions ! self-defined
32722 \begin_layout Standard
32723 To define custom commands for fractions, the command
32733 \begin_layout Plain Layout
32741 is used in the following scheme:
32744 \begin_layout Standard
32757 bracket}{fraction bar thickness}{style}
32758 \begin_inset Newline newline
32765 \begin_layout Plain Layout
32780 \begin_layout Plain Layout
32787 {numerator}{denominator}
32790 \begin_layout Standard
32791 The style is a number in the range of 0
32792 \begin_inset space \thinspace{}
32796 \begin_inset space \thinspace{}
32802 \begin_layout Standard
32804 \begin_inset Tabular
32805 <lyxtabular version="3" rows="5" columns="2">
32807 <column alignment="center" valignment="top" width="0">
32808 <column alignment="center" valignment="top" width="0">
32810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32813 \begin_layout Plain Layout
32819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32822 \begin_layout Plain Layout
32830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32833 \begin_layout Plain Layout
32839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32842 \begin_layout Plain Layout
32843 display style formula
32850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32853 \begin_layout Plain Layout
32859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32862 \begin_layout Plain Layout
32870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32873 \begin_layout Plain Layout
32879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32882 \begin_layout Plain Layout
32890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32893 \begin_layout Plain Layout
32899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32902 \begin_layout Plain Layout
32916 \begin_layout Standard
32917 When no style is given, the size is adjusted to the surrounding environment
32918 like for the command
32927 \begin_layout Standard
32928 When no fraction bar thickness is given, the predefined value of 0.4
32929 \begin_inset space \thinspace{}
32935 \begin_layout Standard
32936 \begin_inset VSpace medskip
32939 For example, the commands
32952 \begin_inset CommandInset ref
32954 reference "sub:Fractions"
32958 are defined with the commands
32961 \begin_layout Standard
32970 genfrac{}{}{}{0}{#1}{#2}}
32973 \begin_layout Standard
32977 \begin_layout Standard
32986 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32989 \begin_layout Standard
32990 \begin_inset VSpace medskip
32993 To define a fraction where the fraction bar thickness can be given as optional
32994 argument, the following line is inserted to the LaTeX-preamble:
32997 \begin_layout Standard
33006 genfrac{}{}{#1}{}{#2}{#3}}
33009 \begin_layout Standard
33011 \begin_inset Formula \begin{align*}
33012 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33013 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
33017 As one can see, the distance of the numerator and the denominator to the
33018 fraction bar is round about three times the bar thickness.
33021 \begin_layout Subsection
33026 \begin_layout Plain Layout
33035 \begin_layout Standard
33036 To cancel formulas or formula parts, the LaTeX-package
33044 \begin_layout Plain Layout
33049 is part of every LaTeX standard installation.
33058 \begin_layout Plain Layout
33064 has to be loaded with the LaTeX-preamble line
33067 \begin_layout Standard
33072 usepackage[samesize]{cancel}
33075 \begin_layout Standard
33076 There are four ways to cancel formulas:
33079 \begin_layout Standard
33081 \begin_inset Tabular
33082 <lyxtabular version="3" rows="5" columns="2">
33084 <column alignment="center" valignment="top" width="0">
33085 <column alignment="center" valignment="top" width="0">
33087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33090 \begin_layout Plain Layout
33096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33099 \begin_layout Plain Layout
33101 \begin_inset Note Note
33104 \begin_layout Plain Layout
33117 are used here as spacer.
33129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33132 \begin_layout Plain Layout
33141 \begin_layout Plain Layout
33155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33158 \begin_layout Plain Layout
33159 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33172 \begin_layout Plain Layout
33181 \begin_layout Plain Layout
33195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33198 \begin_layout Plain Layout
33199 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33212 \begin_layout Plain Layout
33221 \begin_layout Plain Layout
33235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33238 \begin_layout Plain Layout
33239 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33252 \begin_layout Plain Layout
33256 \begin_inset Formula $\to$
33267 \begin_layout Plain Layout
33281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33284 \begin_layout Plain Layout
33285 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33301 \begin_layout Standard
33308 is especially suitable to visualize the reduction of fractions within formulas:
33309 \begin_inset Formula \[
33310 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33317 \begin_layout Subsection
33318 Formulas in Section Headings
33319 \begin_inset CommandInset label
33321 name "sub:Formulas-in-Section"
33329 \begin_layout Plain Layout
33330 Formula ! in section headings
33338 \begin_layout Standard
33339 When formulas are used in section headings, the following has to be taken
33343 \begin_layout Standard
33344 \begin_inset Note Greyedout
33347 \begin_layout Plain Layout
33356 \begin_layout Plain Layout
33357 Packages ! hyperref
33362 support is enabled in the document settings dialog under
33365 \begin_inset space ~
33370 , PDF-bookmarks are created for every section heading in the table of contents.
33371 If a section heading contains formulas, they are incorrectly displayed
33372 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33381 \begin_layout Standard
33382 Both problems can be solved by inserting at the end of the section heading
33383 a short title with the menu
33385 Insert\SpecialChar \menuseparator
33387 \begin_inset space ~
33393 Short titles are used as alternative for multiline section headings to
33394 keep the table of contents clearly arranged.
33395 Only the short title appears in the table of contents and therefore also
33396 in the PDF-bookmark.
33399 \begin_layout Standard
33400 When formulas should be used in the table of contents but
33404 is used, one can use the following command in TeX-mode:
33407 \begin_layout Standard
33412 texorpdfstring{part}{alternative}
33416 \begin_layout Plain Layout
33427 \begin_layout Standard
33428 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33429 This can be characters, formulas, footnotes, but also cross-references.
33430 The alternative is used instead of the part for the bookmark.
33433 \begin_layout Standard
33434 Here are two example headings:
33435 \begin_inset VSpace -3mm
33442 \begin_layout Plain Layout
33454 \begin_layout Subsubsection
33455 Heading without formula in table of contents
33456 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33460 \begin_inset OptArg
33463 \begin_layout Plain Layout
33464 Heading without formula in table of contents
33472 \begin_layout Subsubsection
33473 Heading with formula in table of contents
33477 \begin_layout Plain Layout
33487 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33494 \begin_layout Plain Layout
33504 \begin_layout Standard
33508 \begin_layout Plain Layout
33517 In the first heading a short title was used, in the second one
33526 \begin_layout Standard
33527 To get the same formatting as for the other headings, the complete heading
33536 \begin_layout Plain Layout
33538 \begin_inset CommandInset ref
33540 reference "sub:Bold-Formulas"
33552 \begin_layout Subsection
33553 Formulas in multi-column Text
33557 \begin_layout Plain Layout
33558 Formula ! in multi-column text
33566 \begin_layout Standard
33567 Formulas in multi-column text are often too wide to fit into a column and
33568 thus need to be set over the whole page width.
33569 This is done by using the LaTeX-package
33577 \begin_layout Plain Layout
33582 is part of every LaTeX standard installation.
33591 \begin_layout Plain Layout
33592 Packages ! multicol
33597 , that is loaded with the LaTeX-preamble line
33600 \begin_layout Standard
33605 usepackage{multicol}
33608 \begin_layout Standard
33609 \begin_inset Note Greyedout
33612 \begin_layout Plain Layout
33613 Note herby that the setting
33616 \begin_inset space ~
33623 Document\SpecialChar \menuseparator
33629 \begin_inset space ~
33649 \begin_layout Standard
33650 Before the multi-column text the command
33653 \begin_layout Standard
33658 begin{multicols}{column number}
33661 \begin_layout Standard
33662 is written in TeX-mode.
33663 The column number is a number in the range of 2
33664 \begin_inset space \thinspace{}
33668 \begin_inset space \thinspace{}
33672 Before the formula the multi-column text is ended by inserting the command
33675 \begin_layout Standard
33683 \begin_layout Standard
33687 \begin_layout Standard
33688 Due to the command some space is automatically added before the formula.
33690 \begin_inset space \thinspace{}
33693 mm vertical space is inserted before the formula.
33694 When the formula style
33700 \begin_layout Plain Layout
33702 \begin_inset CommandInset ref
33704 reference "sec:Formula-Styles"
33716 \begin_inset space \thinspace{}
33719 mm space is inserted instead.
33722 \begin_layout Standard
33723 As example a multi-column text with a displayed formula:
33726 \begin_layout Standard
33730 \begin_layout Plain Layout
33734 begin{multicols}{2}
33739 Das Spektrum wird fouriertransformiert.
33740 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33741 , Lösungsmittel) zu trennen.
33742 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33743 nun das Aussehen des Ausgangssignals.
33744 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33745 über alle Phasen integrieren muss.
33747 \begin_inset Formula $S$
33750 unser normiertes Ausgangssignal and
33751 \begin_inset Formula $P$
33754 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33758 \begin_layout Plain Layout
33768 \begin_inset VSpace -6mm
33772 \begin_inset Formula \begin{equation}
33773 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33781 \begin_layout Plain Layout
33785 begin{multicols}{2}
33791 \begin_inset Formula $S_{0}$
33794 das Signal ohne Gradient ist and the Normierungsbedingung
33795 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33799 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33801 \begin_inset Formula $\nicefrac{\pi}{2}$
33805 \begin_inset space \thinspace{}
33808 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33809 das Signal zusätzlich abschwächt.
33810 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33812 \begin_inset Formula $T_{2}$
33818 \begin_layout Standard
33822 \begin_layout Plain Layout
33834 \begin_layout Subsection
33835 Formulas with Description of Variables
33839 \begin_layout Plain Layout
33840 Formula ! with description of variables
33848 \begin_layout Standard
33849 To describe variables within a formula, like in formula
33850 \begin_inset CommandInset ref
33852 reference "eq:within"
33861 \begin_inset Formula $n$
33865 \begin_inset space ~
33868 matrix is used with left aligned columns for the
33869 \begin_inset Formula $n$
33876 \begin_layout Plain Layout
33878 \begin_inset CommandInset ref
33880 reference "sec:Matrices"
33889 To set the description in a smaller size, before the matrix e.
33890 \begin_inset space \thinspace{}
33894 \begin_inset space ~
33907 \begin_layout Plain Layout
33909 \begin_inset CommandInset ref
33911 reference "sub:Font-Sizes"
33923 \begin_layout Standard
33924 When the formula style
33930 \begin_layout Plain Layout
33932 \begin_inset CommandInset ref
33934 reference "sec:Formula-Styles"
33955 \begin_layout Plain Layout
33962 only works in formulas with the style
33967 \begin_inset CommandInset ref
33969 reference "sub:Variable-Space"
33978 is inserted before and after the matrix to have the same separation of
33979 the matrix from the equation and the side margin.
33982 \begin_layout Standard
33983 When the formula style
33987 is used, the method described in
33988 \begin_inset CommandInset ref
33990 reference "sub:Flalign-Environment"
33994 is used to indent formulas.
33996 \begin_inset CommandInset ref
33998 reference "eq:within"
34002 consists of five columns whereas in the first two columns contain the equation,
34003 the third the matrix, and the last one an empty TeX-brace.
34004 \begin_inset Formula \begin{flalign}
34005 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
34006 \rho & \textrm{density}\\
34007 V & \textrm{volume}\\
34008 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
34015 \begin_layout Subsection
34016 Upright small Greek Letters
34017 \begin_inset CommandInset label
34019 name "sub:Upright-small-Greek"
34027 \begin_layout Plain Layout
34028 Greek letters ! upright
34036 \begin_layout Standard
34037 Most of the math fonts only provide italic small Greek letters.
34038 But for symbols of elementary particles like pions and neutrinos, upright
34039 Greek letters are needed.
34048 \begin_layout Plain Layout
34053 is part of the LaTeX-package
34061 \begin_layout Plain Layout
34066 \begin_layout Plain Layout
34089 \begin_layout Plain Layout
34095 that is loaded with the LaTeX-preamble line
34098 \begin_layout Standard
34103 usepackage{upgreek}
34106 \begin_layout Standard
34112 \begin_layout Plain Layout
34122 \begin_inset Note Note
34125 \begin_layout Plain Layout
34126 The following table will only be displayed when the LaTeX-package
34135 They are created when the command for a small Greek letters is started
34141 For example the command
34148 \begin_inset Formula $\uptau$
34154 \begin_layout Standard
34155 With these commands reactions of elementary particles can be typeset:
34156 \begin_inset Formula \[
34157 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34164 \begin_layout Standard
34165 The upright letters are more bold and wider than the italic ones.
34166 They should therefore not be used for units like
34167 \begin_inset Quotes eld
34171 \begin_inset Quotes erd
34177 \begin_layout Standard
34181 \begin_layout Plain Layout
34191 \begin_inset Note Note
34194 \begin_layout Plain Layout
34195 The following will be displayed when the LaTeX-package
34207 \begin_layout Standard
34208 You need to install the LaTeX-package
34212 to see the rest of this subsection in the output.
34215 \begin_layout Standard
34219 \begin_layout Plain Layout
34231 \begin_layout Subsection
34232 Text Characters in Formulas
34233 \begin_inset CommandInset label
34235 name "sub:Text-Characters-in"
34243 \begin_layout Plain Layout
34252 \begin_layout Standard
34253 In some cases you might want to insert text characters directly into formulas.
34254 When for example the centered dot · is often used in formulas like
34255 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34258 , one would have to insert the command
34268 \begin_layout Plain Layout
34270 \begin_inset CommandInset ref
34272 reference "sub:Binary-Operators"
34281 all the time, because this character is defined in all encodings as text
34283 But the encoding can be changed by this LaTeX-preamble line:
34286 \begin_layout Standard
34291 Declare Inputtext{183}{
34301 f\SpecialChar \textcompwordmark{}
34305 \begin_layout Standard
34306 The character encoding (menu
34308 Document\SpecialChar \menuseparator
34309 Settings\SpecialChar \menuseparator
34312 ) specifies what character appears when a keyboard key is pressed.
34313 When the key for the character '·' is pressed, internally the command
34320 But this command is not available in a formula so that you would get LaTeX-erro
34322 With the changed encoding the right command is chosen automatically, depending
34323 on if the character was inserted into a formula or not.
34326 \begin_layout Standard
34327 The encoding of several characters is saved in definition files.
34328 Fore example the encoding
34332 is defined in the file
34336 that is in the installation folder of LaTeX.
34337 Encodings should only be changed via the LaTeX-preamble and not in the
34339 Otherwise own documents could not be edited by other LyX users working
34340 on other computers.
34343 \begin_layout Standard
34344 \begin_inset VSpace medskip
34347 Besides the centered dot, in this document the degree sign ° is defined
34348 with the following LaTeX-preamble line so that it can directly be inserted
34352 \begin_layout Standard
34357 DeclareInputtext{176}{
34367 f\SpecialChar \textcompwordmark{}
34371 \begin_layout Standard
34372 \begin_inset Newpage newpage
34378 \begin_layout Section
34384 \begin_layout Plain Layout
34393 \begin_layout Standard
34394 This section is a summary of the most important typographic rules, listed
34399 \begin_layout Plain Layout
34400 This collection was partly taken from the German semi-official dictionary
34402 \begin_inset Quotes eld
34406 \begin_inset Quotes erd
34410 \begin_inset CommandInset citation
34416 that lists some of the ISO rules.
34424 \begin_layout Itemize
34433 \begin_layout Plain Layout
34434 done with font styles, see
34435 \begin_inset CommandInset ref
34437 reference "sub:Font-Styles"
34447 \begin_inset space \thinspace{}
34451 \begin_inset Newline newline
34454 Between the value and the unit is the smallest space, see
34455 \begin_inset CommandInset ref
34457 reference "sub:Predefined-Space"
34462 \begin_inset Newline newline
34465 This convention is automatically fulfilled when the command
34472 When it is entered to a formula, two boxes appear.
34473 In the first one the value is inserted, in the second one the unit, and
34475 \begin_inset Formula $\unit[30]{km/h}$
34479 \begin_inset space \thinspace{}
34489 is not a real LaTeX command but the command
34495 , therefore you cannot use it in TeX code.
34498 \begin_layout Itemize
34499 Percent and perthousand signs are set like physical units:
34500 \begin_inset Newline newline
34504 \begin_inset space \thinspace{}
34510 \begin_layout Itemize
34511 The degree sign follows directly on the value: 15°, but not when it is used
34513 \begin_inset space \thinspace{}
34519 \begin_layout Itemize
34520 In numbers with more than four digits the smallest space is inserted before
34521 every third digit to group them:
34531 \begin_inset space \thinspace{}
34535 \begin_inset space \thinspace{}
34541 \begin_layout Itemize
34542 For dimensions like 120×90×40
34543 \begin_inset space \thinspace{}
34546 cm the multiplication sign
34547 \begin_inset Quotes eld
34551 \begin_inset Quotes erd
34555 It is available with the LaTeX-command
34561 , but can also directly be inserted with some keyboard definitions.
34564 \begin_layout Itemize
34565 Functions with names consisting of several letters are set upright to avoid
34567 \begin_inset CommandInset ref
34569 reference "sub:Predefined-Functions"
34576 \begin_layout Itemize
34577 Indices consisting of several letters, are set upright:
34578 \begin_inset Formula $E_{\mathrm{kin}}$
34582 \begin_inset Newline newline
34585 Components of matrices are set italic:
34586 \begin_inset Formula $\hat{H}_{kl}$
34592 \begin_layout Itemize
34593 The differentiation/integration operator 'd', the Euler's number 'e', and
34594 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34598 \begin_layout Standard
34599 \begin_inset Newpage newpage
34605 \begin_layout Section
34610 \begin_layout Plain Layout
34619 \begin_layout Standard
34620 Some characters and symbols can be created with several commands.
34621 Here is a list of the synonym commands:
34624 \begin_layout Standard
34625 \begin_inset VSpace bigskip
34629 \begin_inset space \hfill{}
34633 \begin_inset Tabular
34634 <lyxtabular version="3" rows="12" columns="2">
34636 <column alignment="center" valignment="top" width="0pt">
34637 <column alignment="center" valignment="top" width="0pt">
34639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34642 \begin_layout Plain Layout
34648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34651 \begin_layout Plain Layout
34653 \begin_inset Note Note
34656 \begin_layout Plain Layout
34663 is only used as spacer.
34675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34678 \begin_layout Plain Layout
34686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34689 \begin_layout Plain Layout
34693 \begin_layout Plain Layout
34706 \begin_layout Plain Layout
34720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34723 \begin_layout Plain Layout
34731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34734 \begin_layout Plain Layout
34744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34747 \begin_layout Plain Layout
34755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34758 \begin_layout Plain Layout
34768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34771 \begin_layout Plain Layout
34779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34782 \begin_layout Plain Layout
34790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34793 \begin_layout Plain Layout
34801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34804 \begin_layout Plain Layout
34812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34815 \begin_layout Plain Layout
34823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34826 \begin_layout Plain Layout
34836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34839 \begin_layout Plain Layout
34847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34850 \begin_layout Plain Layout
34860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34863 \begin_layout Plain Layout
34871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34874 \begin_layout Plain Layout
34884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34887 \begin_layout Plain Layout
34895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34898 \begin_layout Plain Layout
34908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34911 \begin_layout Plain Layout
34919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34922 \begin_layout Plain Layout
34930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34933 \begin_layout Plain Layout
34941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34944 \begin_layout Plain Layout
34956 \begin_inset space \hfill{}
34960 \begin_inset Tabular
34961 <lyxtabular version="3" rows="12" columns="2">
34963 <column alignment="center" valignment="top" width="0pt">
34964 <column alignment="center" valignment="top" width="0pt">
34966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34969 \begin_layout Plain Layout
34975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34978 \begin_layout Plain Layout
34986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34989 \begin_layout Plain Layout
34997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35000 \begin_layout Plain Layout
35012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35015 \begin_layout Plain Layout
35023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35026 \begin_layout Plain Layout
35036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35039 \begin_layout Plain Layout
35047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35050 \begin_layout Plain Layout
35060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35063 \begin_layout Plain Layout
35071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35074 \begin_layout Plain Layout
35082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35085 \begin_layout Plain Layout
35093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35096 \begin_layout Plain Layout
35104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35107 \begin_layout Plain Layout
35115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35118 \begin_layout Plain Layout
35128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35131 \begin_layout Plain Layout
35139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35142 \begin_layout Plain Layout
35152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35155 \begin_layout Plain Layout
35163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35166 \begin_layout Plain Layout
35176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35179 \begin_layout Plain Layout
35187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35190 \begin_layout Plain Layout
35200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35203 \begin_layout Plain Layout
35211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35214 \begin_layout Plain Layout
35224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35227 \begin_layout Plain Layout
35235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35238 \begin_layout Plain Layout
35252 \begin_inset space \hfill{}
35258 \begin_layout Standard
35259 \begin_inset Newpage newpage
35265 \begin_layout Bibliography
35266 \begin_inset CommandInset bibitem
35267 LatexCommand bibitem
35279 The LaTeX Companion
35282 Addison Wesley, 2004
35285 \begin_layout Bibliography
35286 \begin_inset CommandInset bibitem
35287 LatexCommand bibitem
35293 \begin_inset CommandInset href
35296 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35300 of LaTeX's math abilities
35303 \begin_layout Bibliography
35304 \begin_inset CommandInset bibitem
35305 LatexCommand bibitem
35310 LaTeX tips and tricks-
35311 \begin_inset CommandInset href
35314 target "http://tug.org/TeXnik/"
35321 \begin_layout Bibliography
35322 \begin_inset CommandInset bibitem
35323 LatexCommand bibitem
35329 \begin_inset CommandInset href
35332 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35340 \begin_layout Plain Layout
35352 \begin_layout Bibliography
35353 \begin_inset CommandInset bibitem
35354 LatexCommand bibitem
35360 \begin_inset CommandInset href
35363 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35367 of all symbols available with LaTeX-packages
35370 \begin_layout Bibliography
35371 \begin_inset CommandInset bibitem
35372 LatexCommand bibitem
35378 \begin_inset CommandInset href
35380 name "Documentation"
35381 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35385 of the LaTeX-package
35393 \begin_layout Plain Layout
35394 Packages ! hyperref
35402 \begin_layout Bibliography
35403 \begin_inset CommandInset bibitem
35404 LatexCommand bibitem
35410 \begin_inset CommandInset href
35413 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35424 \begin_inset CommandInset ref
35426 reference "sub:Operator-Limits"
35434 \begin_layout Plain Layout
35445 \begin_layout Bibliography
35446 \begin_inset CommandInset bibitem
35447 LatexCommand bibitem
35458 Auflage, Duden 2001
35461 \begin_layout Subsubsection*
35462 \begin_inset CommandInset index_print
35463 LatexCommand printindex