1 #LyX 1.6.0rc3 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
9924 \begin_layout Standard
9925 You can directly insert accents like é to formulas.
9926 LyX will transform them to the corresponding accent command.
9931 \begin_layout Plain Layout
9937 it is better to insert a quotation mark before the vowel.
9938 These two characters are then treated by LaTeX as
9942 character when the formula part with the umlaut is marked as German.
9950 \begin_inset Quotes eld
9954 \begin_inset Quotes erd
9957 umlauts are created as demonstrated in the following example:
9960 \begin_layout Standard
9961 \begin_inset VSpace -2mm
9967 \begin_layout Standard
9969 \begin_inset Tabular
9970 <lyxtabular version="3" rows="3" columns="2">
9972 <column alignment="center" valignment="top" width="0">
9973 <column alignment="center" valignment="top" width="0">
9975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9978 \begin_layout Plain Layout
9984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9987 \begin_layout Plain Layout
9989 \begin_inset Note Note
9992 \begin_layout Plain Layout
10000 \begin_inset space \thinspace{}
10003 pt space are only used as spacer.
10015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10018 \begin_layout Plain Layout
10021 \begin_inset Quotes grd
10029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10032 \begin_layout Plain Layout
10033 \begin_inset space \hspace{}
10040 \begin_inset Formula $"i$
10050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10053 \begin_layout Plain Layout
10060 \begin_layout Plain Layout
10074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10077 \begin_layout Plain Layout
10078 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10094 \begin_layout Standard
10095 Another advantage to
10101 is that umlauts can directly be converted to mathematical text because
10102 the accent commands above are
10108 in mathematical text
10111 To convert an accented character to mathematical text, only the character
10112 under the accent may be converted.
10113 This applies also for all other conversions, e.
10114 \begin_inset space \thinspace{}
10118 \begin_inset space ~
10124 \begin_layout Standard
10125 In mathematical text, umlauts and other accented characters can directly
10129 \begin_layout Subsection
10130 Accents for Operators
10134 \begin_layout Plain Layout
10135 Accents ! for operators
10143 \begin_layout Standard
10154 \begin_layout Plain Layout
10172 \begin_layout Plain Layout
10180 characters can be placed above or below an operator, respectively, to accent
10192 \begin_layout Plain Layout
10200 characters can be set before and behind an operator.
10201 The command scheme is:
10204 \begin_layout Standard
10220 \begin_layout Standard
10227 must always be before the operator that should be accented.
10228 You can accent with several characters and even with other operators and
10236 for example only characters behind an operator, write nothing between the
10237 first braces but don't omit the braces.
10240 \begin_layout Standard
10241 For example the command
10246 \begin_inset Formula $\to$
10256 \begin_inset Formula $\to$
10265 \begin_layout Plain Layout
10281 \begin_inset Formula \[
10282 \sideset{}{'}\sum_{k=1}^{n}\]
10289 \begin_layout Standard
10298 \begin_layout Plain Layout
10313 \begin_layout Plain Layout
10325 \begin_inset Formula $\uparrow$
10333 \begin_inset Formula \[
10334 \overset{a}{\maltese}\]
10338 As seen in the last example, with
10350 also symbols and characters can be accented; with
10356 this is not possible.
10359 \begin_layout Subsection
10360 Accents for several Characters
10364 \begin_layout Plain Layout
10365 Accents ! for several characters
10373 \begin_layout Standard
10374 \begin_inset space \hfill{}
10378 \begin_inset Tabular
10379 <lyxtabular version="3" rows="5" columns="2">
10381 <column alignment="center" valignment="top" width="0pt">
10382 <column alignment="center" valignment="top" width="0pt">
10384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10387 \begin_layout Plain Layout
10393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10396 \begin_layout Plain Layout
10398 \begin_inset Note Note
10401 \begin_layout Plain Layout
10408 is only used as spacer.
10420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10423 \begin_layout Plain Layout
10430 \begin_layout Plain Layout
10444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10447 \begin_layout Plain Layout
10448 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10458 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10461 \begin_layout Plain Layout
10468 \begin_layout Plain Layout
10482 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10485 \begin_layout Plain Layout
10486 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10496 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10499 \begin_layout Plain Layout
10506 \begin_layout Plain Layout
10520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10523 \begin_layout Plain Layout
10524 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10537 \begin_layout Plain Layout
10540 underleftrightarrow
10544 \begin_layout Plain Layout
10558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10561 \begin_layout Plain Layout
10562 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10576 \begin_inset space \hfill{}
10580 \begin_inset Tabular
10581 <lyxtabular version="3" rows="5" columns="2">
10583 <column alignment="center" valignment="top" width="0pt">
10584 <column alignment="center" valignment="top" width="0pt">
10586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10589 \begin_layout Plain Layout
10595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10598 \begin_layout Plain Layout
10606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10609 \begin_layout Plain Layout
10616 \begin_layout Plain Layout
10630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10633 \begin_layout Plain Layout
10634 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10647 \begin_layout Plain Layout
10654 \begin_layout Plain Layout
10668 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10671 \begin_layout Plain Layout
10672 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10685 \begin_layout Plain Layout
10692 \begin_layout Plain Layout
10706 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10709 \begin_layout Plain Layout
10710 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10720 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10723 \begin_layout Plain Layout
10730 \begin_layout Plain Layout
10744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10747 \begin_layout Plain Layout
10748 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10762 \begin_inset space \hfill{}
10768 \begin_layout Standard
10769 \begin_inset VSpace medskip
10772 With these commands as many characters as you like can be accented.
10785 will only be set in the output with a length of three characters, as shown
10786 in the following example:
10787 \begin_inset Formula \[
10788 \widetilde{A+B=C-D}\]
10795 \begin_layout Standard
10806 \begin_layout Plain Layout
10824 \begin_layout Plain Layout
10832 described in the previous subsection it is also possible to accent several
10842 \begin_layout Plain Layout
10852 \begin_inset Formula $\downarrow$
10858 \begin_inset Formula \[
10859 \underset{***}{A=B}\]
10866 \begin_layout Section
10868 \begin_inset CommandInset label
10878 \begin_layout Plain Layout
10887 \begin_layout Subsection
10889 \begin_inset CommandInset label
10891 name "sub:Predefined-Space"
10899 \begin_layout Plain Layout
10900 Space ! horizontal ! predefined
10908 \begin_layout Standard
10909 Sometimes it is necessary to insert horizontal space to a formula.
10910 This is done by inserting a protected space (shortcut
10916 \begin_inset Quotes eld
10926 \begin_layout Plain Layout
10939 \begin_inset Quotes erd
10942 appears and by pressing
10946 several times one can select one of eight different space sizes.
10947 The spaces can also be inserted using the math toolbar button
10948 \begin_inset Graphics
10949 filename ../images/math/space.png
10954 or special commands.
10955 Independent from the inserted command, one can select the size again by
10963 \begin_layout Standard
10966 \begin_inset VSpace -5mm
10970 \begin_inset Tabular
10971 <lyxtabular version="3" rows="3" columns="7">
10973 <column alignment="center" valignment="middle" width="6.8cm">
10974 <column alignment="center" valignment="top" width="0">
10975 <column alignment="center" valignment="top" width="0">
10976 <column alignment="center" valignment="top" width="0">
10977 <column alignment="center" valignment="top" width="0">
10978 <column alignment="center" valignment="top" width="0">
10979 <column alignment="center" valignment="top" width="0">
10981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10984 \begin_layout Plain Layout
10990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10993 \begin_layout Plain Layout
11001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11004 \begin_layout Plain Layout
11012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11015 \begin_layout Plain Layout
11023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11026 \begin_layout Plain Layout
11034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11037 \begin_layout Plain Layout
11045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11048 \begin_layout Plain Layout
11058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11061 \begin_layout Plain Layout
11066 keystrokes after inserting the protected space
11071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11074 \begin_layout Plain Layout
11080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11083 \begin_layout Plain Layout
11089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11092 \begin_layout Plain Layout
11098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11101 \begin_layout Plain Layout
11107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11110 \begin_layout Plain Layout
11116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11119 \begin_layout Plain Layout
11127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11130 \begin_layout Plain Layout
11136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11139 \begin_layout Plain Layout
11140 \begin_inset Formula $A\, B$
11148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11151 \begin_layout Plain Layout
11152 \begin_inset Formula $A\: B$
11160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11163 \begin_layout Plain Layout
11164 \begin_inset Formula $A\; B$
11172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11175 \begin_layout Plain Layout
11176 \begin_inset Formula $A\quad B$
11184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11187 \begin_layout Plain Layout
11188 \begin_inset Formula $A\qquad B$
11196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11199 \begin_layout Plain Layout
11200 \begin_inset Formula $A\! B$
11216 \begin_layout Standard
11217 The last size seem to produce no space.
11218 It is displayed red in LyX contrary to the other sizes, because it is a
11220 There are two more negative spaces:
11223 \begin_layout Standard
11225 \begin_inset Tabular
11226 <lyxtabular version="3" rows="3" columns="3">
11228 <column alignment="center" valignment="middle" width="6.8cm">
11229 <column alignment="center" valignment="top" width="0pt">
11230 <column alignment="center" valignment="top" width="0pt">
11232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11235 \begin_layout Plain Layout
11241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11244 \begin_layout Plain Layout
11252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11255 \begin_layout Plain Layout
11265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11268 \begin_layout Plain Layout
11273 keystrokes after inserting the protected space
11278 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11281 \begin_layout Plain Layout
11287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11290 \begin_layout Plain Layout
11298 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11301 \begin_layout Plain Layout
11307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11310 \begin_layout Plain Layout
11311 \begin_inset Formula $A\negmedspace B$
11319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11322 \begin_layout Plain Layout
11323 \begin_inset Formula $A\negthickspace B$
11339 \begin_layout Standard
11340 Negative spaces can lead to characters overlapping each other.
11341 Thus they can be used to enforce ligatures, what is e.
11342 \begin_inset space \thinspace{}
11346 \begin_inset space ~
11349 useful for summation operators:
11352 \begin_layout Standard
11354 \begin_inset Tabular
11355 <lyxtabular version="3" rows="3" columns="2">
11357 <column alignment="center" valignment="top" width="0">
11358 <column alignment="center" valignment="top" width="0">
11360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11363 \begin_layout Plain Layout
11369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11372 \begin_layout Plain Layout
11374 \begin_inset Note Note
11377 \begin_layout Plain Layout
11384 is only used as spacer.
11396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11399 \begin_layout Plain Layout
11408 \begin_layout Plain Layout
11422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11425 \begin_layout Plain Layout
11426 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11439 \begin_layout Plain Layout
11450 \begin_layout Plain Layout
11464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11467 \begin_layout Plain Layout
11468 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11484 \begin_layout Standard
11485 Relations like for example equal signs, are always surrounded by space.
11486 To suppress this, the equal sign is placed into a TeX-brace.
11487 The following example demonstrates this:
11490 \begin_layout Standard
11492 \begin_inset Tabular
11493 <lyxtabular version="3" rows="2" columns="2">
11495 <column alignment="center" valignment="top" width="0pt">
11496 <column alignment="center" valignment="top" width="0pt">
11498 <cell alignment="center" valignment="top" usebox="none">
11501 \begin_layout Plain Layout
11507 <cell alignment="center" valignment="top" usebox="none">
11510 \begin_layout Plain Layout
11511 \begin_inset Formula $A=B$
11521 <cell alignment="center" valignment="top" usebox="none">
11524 \begin_layout Plain Layout
11525 \begin_inset Note Note
11528 \begin_layout Plain Layout
11535 is only used as spacer.
11541 \begin_inset Formula $\raisebox{5mm}{}$
11544 equation without space
11549 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11552 \begin_layout Plain Layout
11553 \begin_inset Formula $A{=}B$
11569 \begin_layout Standard
11571 The command for the last formula is:
11576 \begin_inset Formula $\to$
11582 \begin_layout Standard
11583 \begin_inset VSpace bigskip
11586 Spaces are needed for physical units, because the space between the value
11587 and the unit is the smallest one and not a normal space.
11588 For units in text, the smallest space is inserted via the menu
11590 Insert\SpecialChar \menuseparator
11591 Formatting\SpecialChar \menuseparator
11593 \begin_inset space ~
11605 \begin_layout Standard
11606 An example to visualize the difference:
11609 \begin_layout Standard
11610 \begin_inset Tabular
11611 <lyxtabular version="3" rows="2" columns="2">
11613 <column alignment="left" valignment="top" width="0">
11614 <column alignment="left" valignment="top" width="0">
11616 <cell alignment="center" valignment="top" usebox="none">
11619 \begin_layout Plain Layout
11621 \begin_inset Formula $\cdot$
11629 <cell alignment="center" valignment="top" usebox="none">
11632 \begin_layout Plain Layout
11633 space between value and unit
11640 <cell alignment="center" valignment="top" usebox="none">
11643 \begin_layout Plain Layout
11645 \begin_inset space \thinspace{}
11649 \begin_inset Formula $\cdot$
11657 <cell alignment="center" valignment="top" usebox="none">
11660 \begin_layout Plain Layout
11661 smallest space between value and unit
11674 \begin_layout Subsection
11679 \begin_layout Plain Layout
11692 \begin_layout Plain Layout
11693 for vertical space in formulas see
11694 \begin_inset CommandInset ref
11696 reference "sub:Line-Separation"
11709 \begin_layout Plain Layout
11717 \begin_inset Note Note
11720 \begin_layout Plain Layout
11723 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11726 \begin_layout Plain Layout
11729 texorpdfstring is in section
11730 \begin_inset CommandInset ref
11732 reference "sub:Formulas-in-Section"
11742 \begin_inset CommandInset label
11744 name "sub:Variable-Space"
11752 \begin_layout Plain Layout
11753 Space ! horizontal ! variable
11761 \begin_layout Standard
11762 Space with a defined length can be inserted in LyX with the command
11763 \begin_inset Newline newline
11776 \begin_layout Plain Layout
11785 For the length all units listed in
11786 \begin_inset CommandInset ref
11788 reference "tab:Available-units"
11792 are allowed, except of the unit
11793 \begin_inset Quotes eld
11797 \begin_inset Quotes erd
11801 The length may also be negative.
11802 To insert so many space that the formula uses all available space, the
11813 \begin_layout Plain Layout
11824 \begin_layout Standard
11825 \begin_inset VSpace -1mm
11831 \begin_layout Standard
11833 \begin_inset Tabular
11834 <lyxtabular version="3" rows="4" columns="2">
11836 <column alignment="center" valignment="top" width="0">
11837 <column alignment="center" valignment="top" width="0">
11839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11842 \begin_layout Plain Layout
11848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11851 \begin_layout Plain Layout
11859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11862 \begin_layout Plain Layout
11866 \begin_inset Formula $\to$
11876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11879 \begin_layout Plain Layout
11880 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11893 \begin_layout Plain Layout
11897 \begin_inset Formula $\to$
11907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11910 \begin_layout Plain Layout
11911 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11924 \begin_layout Plain Layout
11931 \begin_layout Plain Layout
11945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11948 \begin_layout Plain Layout
11949 \begin_inset Formula $A=A\hfill B=B$
11965 \begin_layout Standard
11966 In the last example the available space is given by the longest column entry
11968 In an inline formula the space depends on the length of the line in which
11976 Thus, when the line uses the full width, no space will be created.
11983 only has an effect on displayed formulas when the formula style
11988 (Formula styles are explained in
11989 \begin_inset CommandInset ref
11991 reference "sec:Formula-Styles"
11998 \begin_layout Standard
12005 , there are the commands
12017 that fill the space with a pattern, see
12018 \begin_inset CommandInset ref
12020 reference "sub:Ellipses"
12027 \begin_layout Standard
12028 For text, variable space can be inserted via the menu
12030 Insert\SpecialChar \menuseparator
12031 Formatting\SpecialChar \menuseparator
12033 \begin_inset space ~
12038 , what is not possible in formulas:
12041 \begin_layout Standard
12042 This is a line with
12043 \begin_inset space \hspace{}
12048 \begin_inset space \thinspace{}
12054 \begin_layout Standard
12055 This is a line with
12056 \begin_inset space \hfill{}
12062 \begin_layout Subsection
12063 Space besides inline Formulas
12067 \begin_layout Plain Layout
12068 Space ! besides inline formulas
12076 \begin_layout Standard
12077 The space that surrounds inline formulas can be adjusted with the length
12086 \begin_layout Plain Layout
12097 The value of a length is set with the command
12105 \begin_layout Plain Layout
12115 that has the following scheme:
12118 \begin_layout Standard
12123 setlength{length name}{value}
12126 \begin_layout Standard
12134 \begin_inset space \thinspace{}
12140 \begin_layout Standard
12150 \begin_layout Standard
12151 is inserted in TeX-mode.
12153 \begin_inset space \thinspace{}
12156 mm space will now be set around all inline formulas:
12160 \begin_layout Plain Layout
12174 \begin_layout Standard
12175 This is a line with an inline formula
12176 \begin_inset Formula $A=B$
12180 \begin_inset space \thinspace{}
12183 mm surrounding space.
12187 \begin_layout Plain Layout
12201 \begin_layout Standard
12202 To return to the predefined value,
12208 is set to the value 0
12209 \begin_inset space \thinspace{}
12215 \begin_layout Section
12220 \begin_layout Plain Layout
12230 \begin_layout Plain Layout
12235 \begin_layout Plain Layout
12246 \begin_layout Plain Layout
12261 \begin_layout Standard
12262 Boxes for text are described in chapter
12269 \begin_inset space ~
12277 \begin_layout Subsection
12279 \begin_inset CommandInset label
12281 name "sub:Boxes-with-Frame"
12289 \begin_layout Plain Layout
12298 \begin_layout Standard
12299 It is possible to frame formulas or parts of it with the commands
12309 \begin_layout Plain Layout
12327 \begin_layout Plain Layout
12338 \begin_layout Standard
12339 When one of these commands is inserted to a formula, a blue box appears
12340 within a frame to enter formula parts.
12347 an additional formula has to be created by
12355 \begin_layout Plain Layout
12356 Due to a bug in LyX it is not possible to create a new formula with
12361 \begin_inset CommandInset href
12363 name "LyX-bug #1435"
12364 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12373 , because the box content will otherwise be treated as mathematical text.
12380 is used, a new formula is automatically created inside the frame.
12383 \begin_layout Standard
12390 is not suitable to frame displayed formulas, because the formula will always
12391 be set in the size of the text.
12398 is in contrary not suitable to frame inline formulas, because the formula
12399 will always be set in the size of a displayed formula.
12402 \begin_layout Standard
12409 there is the command
12419 \begin_layout Plain Layout
12427 where additionally the frame width and the alignment can be specified.
12434 is used in the following scheme:
12437 \begin_layout Standard
12442 framebox[frame width][position]{box content}
12445 \begin_layout Standard
12446 The position can either be
12463 right aligns the formula in the box.
12464 When no position is given, the formula will be centered.
12465 \begin_inset Newline newline
12468 Is no width given, also no position can be given.
12469 In this case the frame width is adjusted to the box content like for
12478 \begin_layout Standard
12485 is inserted, a box appears containing three blue boxes.
12486 The first two boxes are surrounded by brackets and denote the two optional
12488 The third box is for formula parts like for
12497 \begin_layout Standard
12499 \begin_inset Note Note
12502 \begin_layout Plain Layout
12503 The table has been set into a minipage to make the footnote appearing.
12504 Otherwise the footnote text would not be displayed.
12510 \begin_inset Box Frameless
12519 height_special "totalheight"
12522 \begin_layout Plain Layout
12524 \begin_inset Tabular
12525 <lyxtabular version="3" rows="5" columns="2">
12527 <column alignment="center" valignment="top" width="0">
12528 <column alignment="center" valignment="top" width="0">
12530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12533 \begin_layout Plain Layout
12538 \begin_layout Plain Layout
12539 Due to a bug in LyX it is not possible to create a new formula with
12544 \begin_inset CommandInset href
12546 name "LyX-bug #1435"
12547 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12564 \begin_layout Plain Layout
12566 \begin_inset Note Note
12569 \begin_layout Plain Layout
12576 is only used as spacer.
12588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12591 \begin_layout Plain Layout
12598 \begin_layout Plain Layout
12617 \begin_layout Plain Layout
12631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12634 \begin_layout Plain Layout
12635 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12648 \begin_layout Plain Layout
12655 \begin_layout Plain Layout
12670 \begin_layout Plain Layout
12684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12687 \begin_layout Plain Layout
12688 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12701 \begin_layout Plain Layout
12708 \begin_layout Plain Layout
12722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12725 \begin_layout Plain Layout
12726 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12739 \begin_layout Plain Layout
12746 \begin_layout Plain Layout
12756 \begin_inset Formula $\to$
12760 \begin_inset Formula $\to$
12773 \begin_layout Plain Layout
12783 \begin_inset Formula $\downarrow$
12791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12794 \begin_layout Plain Layout
12795 \begin_inset Formula $\raisebox{6mm}{}$
12799 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12803 \begin_inset Formula $\raisebox{-4mm}{}$
12824 \begin_layout Standard
12825 The frame thickness can also be adjusted.
12826 To do this the following commands have to be inserted in TeX-mode before
12830 \begin_layout Standard
12840 \begin_inset Quotes eld
12844 \begin_inset Quotes erd
12858 \begin_inset Quotes eld
12862 \begin_inset Quotes erd
12868 \begin_layout Standard
12869 \begin_inset Quotes eld
12873 \begin_inset Quotes erd
12876 specifies the minimal distance between the frame and the first character
12878 An example for this is the following framed formula:
12882 \begin_layout Plain Layout
12894 \begin_inset Formula \[
12899 Before this formula the commands
12902 \begin_layout Standard
12924 \begin_layout Standard
12925 were inserted in TeX-mode.
12926 The given values are used for all following boxes.
12929 \begin_layout Standard
12930 To return to the standard frame size, the command
12933 \begin_layout Standard
12958 \begin_layout Plain Layout
12972 \begin_layout Standard
12973 is inserted in TeX-mode before the next formula.
12976 \begin_layout Subsection
12977 Boxes without Frame
12978 \begin_inset CommandInset label
12980 name "sub:Boxes-without-Frame"
12988 \begin_layout Plain Layout
12989 Boxes ! without frame
12997 \begin_layout Standard
12998 For boxes without a frame there are the following box commands:
13008 \begin_layout Plain Layout
13026 \begin_layout Plain Layout
13044 \begin_layout Plain Layout
13055 \begin_layout Standard
13062 a box can be super- or subscripted.
13063 But in contrary to normal super- and subscripting, the characters in the
13064 box keep their font size.
13071 is used in the following scheme:
13074 \begin_layout Standard
13079 raisebox{height}{box content}
13082 \begin_layout Standard
13083 When the box should contain a formula, an extra formula is needed like for
13093 \begin_layout Standard
13095 \begin_inset Tabular
13096 <lyxtabular version="3" rows="4" columns="2">
13098 <column alignment="center" valignment="top" width="0">
13099 <column alignment="center" valignment="top" width="0">
13101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13104 \begin_layout Plain Layout
13110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13113 \begin_layout Plain Layout
13121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13124 \begin_layout Plain Layout
13128 \begin_inset Formula $\to$
13134 \begin_inset Formula $\to$
13142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13145 \begin_layout Plain Layout
13146 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13159 \begin_layout Plain Layout
13163 \begin_inset Formula $\to$
13169 \begin_inset Formula $\to$
13177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13180 \begin_layout Plain Layout
13181 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13194 \begin_layout Plain Layout
13198 \begin_inset Formula $\to$
13213 \begin_layout Plain Layout
13227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13230 \begin_layout Plain Layout
13234 \begin_layout Plain Layout
13258 \begin_layout Standard
13259 The last formula can currently only be created using TeX-mode because LyX
13260 inserts a box instead of the needed extra formula.
13264 \begin_layout Plain Layout
13266 \begin_inset CommandInset href
13268 name "LyX-bug #1435"
13269 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13281 \begin_layout Standard
13306 , with the difference that there is no frame.
13309 \begin_layout Subsection
13311 \begin_inset CommandInset label
13313 name "sub:Colored-Boxes"
13321 \begin_layout Plain Layout
13330 \begin_layout Standard
13331 To be able to use all commands explained in this section, the LaTeX-package
13340 \begin_layout Plain Layout
13345 is part of every LaTeX standard installation.
13354 \begin_layout Plain Layout
13360 has to be loaded in the LaTeX-preamble with the line
13364 \begin_layout Plain Layout
13365 When text is colored somewhere in the document with a predefined color,
13366 LyX loads the LaTeX-package
13371 Thus it is possible that the package is loaded twice, but this doesn't
13378 \begin_inset Note Note
13381 \begin_layout Plain Layout
13382 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13391 \begin_layout Standard
13399 \begin_layout Standard
13400 \begin_inset VSpace medskip
13403 To color boxes, the command
13413 \begin_layout Plain Layout
13421 is used in the following scheme:
13424 \begin_layout Standard
13429 colorbox{color}{box content}
13432 \begin_layout Standard
13433 The box content can also be a box and a
13439 can also be part of another box (see the 2nd and 3rd example).
13440 When the box should contain a formula, an extra formula has to be created,
13451 \begin_layout Plain Layout
13452 This also applies for the command
13460 \begin_inset CommandInset href
13462 name "LyX-bug #1435"
13463 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13475 \begin_layout Standard
13476 One of the following predefined colors can be chosen:
13479 \begin_layout Standard
13513 \begin_layout Standard
13515 \begin_inset Tabular
13516 <lyxtabular version="3" rows="4" columns="2">
13518 <column alignment="center" valignment="top" width="0">
13519 <column alignment="center" valignment="top" width="0">
13521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13524 \begin_layout Plain Layout
13530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13533 \begin_layout Plain Layout
13535 \begin_inset Note Note
13538 \begin_layout Plain Layout
13545 is only used as spacer.
13557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13560 \begin_layout Plain Layout
13564 \begin_inset Formula $\to$
13574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13577 \begin_layout Plain Layout
13578 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13591 \begin_layout Plain Layout
13595 \begin_inset Formula $\to$
13606 \begin_layout Plain Layout
13620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13623 \begin_layout Plain Layout
13624 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13637 \begin_layout Plain Layout
13644 \begin_layout Plain Layout
13656 \begin_inset Formula $\to$
13666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13669 \begin_layout Plain Layout
13670 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13686 \begin_layout Standard
13693 only colors the box but not the characters in the box.
13694 To color all characters, the whole formula is highlighted and the wanted
13695 color is chosen in the
13698 \begin_inset space ~
13704 The dialog can be called with the toolbar button
13705 \begin_inset Graphics
13706 filename ../images/dialog-show_character.png
13713 Edit\SpecialChar \menuseparator
13715 \begin_inset space ~
13718 Style\SpecialChar \menuseparator
13722 The formula number has then the same color as the formula.
13723 When the formula number should get another color than the formula characters,
13724 the color must be changed within the formula.
13727 \begin_layout Standard
13731 \begin_layout Standard
13734 \begin_inset Formula \begin{equation}
13735 \int A=B\label{eq:red}\end{equation}
13742 \begin_inset Formula \begin{equation}
13743 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13750 \begin_layout Standard
13752 \begin_inset CommandInset ref
13758 is completely colored red.
13759 \begin_inset Newline newline
13763 \begin_inset CommandInset ref
13765 reference "eq:redgreen"
13769 was first completely colored green to set the color for the formula number.
13770 Subsequently the formula characters were colored red.
13773 \begin_layout Standard
13774 \begin_inset VSpace bigskip
13777 To color the frame different than the rest of the box, the command
13787 \begin_layout Plain Layout
13795 is used in the following scheme:
13798 \begin_layout Standard
13803 fcolorbox{frame color}{color}{box content}
13806 \begin_layout Standard
13813 is an extension of the command
13820 The frame width is set, like for
13843 \begin_layout Plain Layout
13855 \begin_inset Formula \[
13856 \fcolorbox{cyan}{magenta}{A=B}\]
13864 \begin_layout Plain Layout
13878 \begin_layout Standard
13879 This formula was created with the command
13880 \begin_inset Newline newline
13888 \begin_inset Formula $\to$
13894 \begin_inset Formula $\to$
13904 \begin_layout Standard
13905 \begin_inset VSpace bigskip
13908 To use other colors than the predefined ones, they have to be defined first.
13911 \begin_layout Standard
13912 One can for example define the color
13913 \begin_inset Quotes eld
13921 \begin_inset Quotes erd
13924 with the LaTeX-preamble line:
13927 \begin_layout Standard
13932 definecolor{darkgreen}{cmyk}{0.5,
13950 \begin_layout Plain Layout
13961 \begin_layout Standard
13966 is the color space that denotes the colors
13983 The four comma separated numbers are the portion factor for the corresponding
13984 colors of the color space.
13985 The factors can be in the range of 0
13986 \begin_inset space \thinspace{}
13990 \begin_inset space \thinspace{}
13998 also the color space
14002 can be used for definitions.
14019 , so that there are in this case three portion factors for the corresponding
14021 Furthermore there is the color space
14025 with one portion factor for the gray value.
14028 \begin_layout Standard
14029 As example a framed box with the new defined color
14033 where the characters have been colored
14038 \begin_inset Formula \begin{equation}
14039 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14046 \begin_layout Standard
14047 Self-defined colors can also be used for text with the help of the command
14058 \begin_layout Plain Layout
14067 \begin_layout Standard
14071 \begin_layout Plain Layout
14075 textcolor{darkgreen}{
14081 \begin_inset Quotes eld
14085 \begin_inset Quotes erd
14092 \begin_layout Plain Layout
14102 \begin_layout Standard
14113 \begin_layout Plain Layout
14121 is used in the scheme
14125 textcolor{color}{characters to color}
14130 \begin_layout Subsection
14132 \begin_inset CommandInset label
14134 name "sub:Paragraph-Boxes"
14142 \begin_layout Plain Layout
14143 Boxes ! as paragraph
14151 \begin_layout Standard
14152 A box that can contain several lines and paragraphs, a so called paragraph
14153 box (parbox), can be created with the menu
14155 Insert\SpecialChar \menuseparator
14158 or the toolbar button
14159 \begin_inset Graphics
14160 filename ../images/box-insert.png
14168 \begin_layout Standard
14169 The following example shows a framed parbox in a line:
14172 \begin_layout Standard
14173 \begin_inset VSpace medskip
14177 \begin_inset Box Boxed
14186 height_special "totalheight"
14189 \begin_layout Plain Layout
14190 This is a paragraph box.
14192 \begin_inset space \thinspace{}
14195 cm long and can also contain formulas:
14196 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14207 \begin_layout Standard
14208 \begin_inset VSpace medskip
14214 \begin_layout Standard
14215 Such a box is created by right-clicking on the gray box inset.
14216 A dialog pops up showing the box properties.
14230 \begin_inset space \thinspace{}
14235 Vertical Box Alignment
14240 \begin_layout Standard
14241 \begin_inset VSpace medskip
14244 In LaTeX a parbox is created with the command
14254 \begin_layout Plain Layout
14262 that has the following scheme:
14265 \begin_layout Standard
14270 parbox[position]{width}{box content}
14273 \begin_layout Standard
14287 for bottom means that the box is aligned within the surrounding text with
14293 for top this is done with the first line.
14294 When no position is given, the box will be vertically centered, see section
14302 \begin_inset space ~
14307 manual for examples.
14310 \begin_layout Standard
14311 \begin_inset VSpace bigskip
14314 To frame formulas completely, including the formula number, the formula
14315 must be set into a parbox.
14316 To do this, the command
14330 is inserted in TeX-mode before the formula.
14339 \begin_layout Plain Layout
14349 is hereby the line width set for the document.
14350 Because the frame is outside the parbox, 2
14351 \begin_inset space \thinspace{}
14354 times the frame separation and the frame thickness must be subtracted from
14356 As this is not automatically done by LyX due to a bug
14360 \begin_layout Plain Layout
14361 \begin_inset CommandInset href
14363 name "LyX-bug #4483"
14364 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14373 , TeX-mode has to be used.
14374 To be able to multiply and subtract in arguments, the LaTeX-package
14382 \begin_layout Plain Layout
14387 is part of every LaTeX standard installation.
14396 \begin_layout Plain Layout
14402 must be loaded in the LaTeX-preamble with the line
14405 \begin_layout Standard
14413 \begin_layout Standard
14414 Behind the formula both boxes are closed by entering
14419 Here is an example:
14423 \begin_layout Plain Layout
14437 \begin_layout Standard
14441 \begin_layout Plain Layout
14459 \begin_inset Formula \begin{equation}
14460 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14468 \begin_layout Plain Layout
14479 \begin_layout Plain Layout
14493 \begin_layout Standard
14494 \begin_inset VSpace medskip
14497 As a parbox is used as argument of
14503 , there is in this case no difference between
14518 \begin_layout Standard
14519 \begin_inset VSpace bigskip
14522 Paragraph boxes are very useful to comment formulas directly.
14529 is used in combination with the command
14543 \begin_inset CommandInset ref
14545 reference "sub:User-defined-Numbering"
14552 \begin_layout Standard
14553 An example of a formula commented with
14562 \begin_layout Standard
14566 \begin_layout Plain Layout
14579 This is a description.
14580 It is distinctly separated from the formula and multiline.
14584 \begin_layout Plain Layout
14596 \begin_layout Standard
14597 Such a formula must be inserted completely in TeX-mode because LyX does
14598 not yet support the command
14605 The formula is created with the following command sequence:
14608 \begin_layout Standard
14621 is inserted in TeX-mode.
14625 \begin_layout Plain Layout
14626 When the formula style
14638 can also be replaced by
14645 (formula styles see
14646 \begin_inset CommandInset ref
14648 reference "sec:Formula-Styles"
14657 Then the description follows as normal text, and finally
14663 is inserted in TeX-mode.
14676 hereby create a displayed formula.
14679 \begin_layout Standard
14686 can be seen in this example that was
14687 \begin_inset Quotes eld
14691 \begin_inset Quotes erd
14694 using the mathematical textmode:
14695 \begin_inset Formula \[
14696 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14703 \begin_layout Section
14708 \begin_layout Plain Layout
14717 \begin_layout Subsection
14719 \begin_inset CommandInset label
14721 name "sub:Big-Operators"
14729 \begin_layout Plain Layout
14739 \begin_layout Plain Layout
14749 \begin_layout Plain Layout
14758 \begin_layout Standard
14759 To be able to use all integral operators listed here, the option
14761 Use esint package automatically
14763 must be set in the document settings under
14766 \begin_inset space ~
14774 \begin_layout Standard
14775 \begin_inset space \hfill{}
14779 \begin_inset Tabular
14780 <lyxtabular version="3" rows="11" columns="2">
14782 <column alignment="center" valignment="top" width="0pt">
14783 <column alignment="center" valignment="top" width="0pt">
14785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14788 \begin_layout Plain Layout
14794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14797 \begin_layout Plain Layout
14805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14808 \begin_layout Plain Layout
14815 \begin_layout Plain Layout
14828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14831 \begin_layout Plain Layout
14832 \begin_inset Formula $\sum$
14842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14845 \begin_layout Plain Layout
14852 \begin_layout Plain Layout
14865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14868 \begin_layout Plain Layout
14869 \begin_inset Formula $\int$
14879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14882 \begin_layout Plain Layout
14890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14893 \begin_layout Plain Layout
14894 \begin_inset Formula $\intop$
14904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14907 \begin_layout Plain Layout
14915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14918 \begin_layout Plain Layout
14919 \begin_inset Formula $\oint$
14929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14932 \begin_layout Plain Layout
14940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14943 \begin_layout Plain Layout
14944 \begin_inset Formula $\ointop$
14954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14957 \begin_layout Plain Layout
14965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14968 \begin_layout Plain Layout
14969 \begin_inset Formula $\ointctrclockwise$
14979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14982 \begin_layout Plain Layout
14990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14993 \begin_layout Plain Layout
14994 \begin_inset Formula $\ointclockwise$
15004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15007 \begin_layout Plain Layout
15015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15018 \begin_layout Plain Layout
15019 \begin_inset Formula $\sqint$
15029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15032 \begin_layout Plain Layout
15040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15043 \begin_layout Plain Layout
15044 \begin_inset Formula $\bigcap$
15054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15057 \begin_layout Plain Layout
15065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15068 \begin_layout Plain Layout
15069 \begin_inset Formula $\bigcup$
15083 \begin_inset space \hfill{}
15087 \begin_inset Tabular
15088 <lyxtabular version="3" rows="10" columns="2">
15090 <column alignment="center" valignment="top" width="0pt">
15091 <column alignment="center" valignment="top" width="0pt">
15093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15096 \begin_layout Plain Layout
15102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15105 \begin_layout Plain Layout
15113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15116 \begin_layout Plain Layout
15123 \begin_layout Plain Layout
15136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15139 \begin_layout Plain Layout
15140 \begin_inset Formula $\prod$
15150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15153 \begin_layout Plain Layout
15161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15164 \begin_layout Plain Layout
15165 \begin_inset Formula $\coprod$
15175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15178 \begin_layout Plain Layout
15186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15189 \begin_layout Plain Layout
15190 \begin_inset Formula $\bigodot$
15200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15203 \begin_layout Plain Layout
15211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15214 \begin_layout Plain Layout
15215 \begin_inset Formula $\bigotimes$
15225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15228 \begin_layout Plain Layout
15236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15239 \begin_layout Plain Layout
15240 \begin_inset Formula $\bigoplus$
15250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15253 \begin_layout Plain Layout
15261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15264 \begin_layout Plain Layout
15265 \begin_inset Formula $\bigwedge$
15275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15278 \begin_layout Plain Layout
15286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15289 \begin_layout Plain Layout
15290 \begin_inset Formula $\bigvee$
15300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15303 \begin_layout Plain Layout
15311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15314 \begin_layout Plain Layout
15315 \begin_inset Formula $\bigsqcup$
15325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15328 \begin_layout Plain Layout
15336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15339 \begin_layout Plain Layout
15340 \begin_inset Formula $\biguplus$
15354 \begin_inset space \hfill{}
15360 \begin_layout Standard
15361 All big operators can also be inserted via the math toolbar button
15362 \begin_inset Graphics
15363 filename ../images/math/intop.png
15371 \begin_layout Standard
15372 The operators are called big because they are bigger than the sometimes
15373 equal looking binary operators.
15374 All big operators can have limits as described in the next subsection.
15377 \begin_layout Standard
15403 \begin_inset space ~
15406 in the style the operator limits are displayed, see
15407 \begin_inset CommandInset ref
15409 reference "sub:Operator-Limits"
15417 \begin_layout Subsubsection*
15418 Advices for Integrals
15421 \begin_layout Standard
15426 in an integral is an operator, that therefore has to be set upright.
15427 This is done by highlighting the
15431 and using the keyboard shortcut
15434 \begin_inset space ~
15443 \begin_layout Plain Layout
15449 \begin_inset CommandInset ref
15451 reference "sub:Font-Styles"
15461 Finally the smallest space is inserted before the
15465 , as this is usual for operators.
15469 \begin_layout Standard
15471 \begin_inset Formula $\int A(x)dx$
15475 \begin_inset Newline newline
15482 \begin_layout Plain Layout
15492 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15498 \begin_layout Standard
15499 For multiple integrals there are the following commands:
15500 \begin_inset VSpace medskip
15506 \begin_layout Standard
15507 \begin_inset space \hfill{}
15511 \begin_inset Tabular
15512 <lyxtabular version="3" rows="4" columns="2">
15514 <column alignment="center" valignment="top" width="0">
15515 <column alignment="center" valignment="top" width="0">
15517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15520 \begin_layout Plain Layout
15526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15529 \begin_layout Plain Layout
15531 \begin_inset Note Note
15534 \begin_layout Plain Layout
15541 is only used as spacer.
15553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15556 \begin_layout Plain Layout
15564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15567 \begin_layout Plain Layout
15568 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15581 \begin_layout Plain Layout
15589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15592 \begin_layout Plain Layout
15593 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15606 \begin_layout Plain Layout
15614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15617 \begin_layout Plain Layout
15618 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15632 \begin_inset space \hfill{}
15636 \begin_inset Tabular
15637 <lyxtabular version="3" rows="4" columns="2">
15639 <column alignment="center" valignment="top" width="0">
15640 <column alignment="center" valignment="top" width="0">
15642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15645 \begin_layout Plain Layout
15651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15654 \begin_layout Plain Layout
15662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15665 \begin_layout Plain Layout
15673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15676 \begin_layout Plain Layout
15677 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15690 \begin_layout Plain Layout
15698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15701 \begin_layout Plain Layout
15702 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15715 \begin_layout Plain Layout
15723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15726 \begin_layout Plain Layout
15727 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15741 \begin_inset space \hfill{}
15747 \begin_layout Subsection
15749 \begin_inset CommandInset label
15751 name "sub:Operator-Limits"
15759 \begin_layout Plain Layout
15768 \begin_layout Standard
15769 Limits are created by super- and subscripts:
15772 \begin_layout Standard
15774 \begin_inset Tabular
15775 <lyxtabular version="3" rows="2" columns="2">
15777 <column alignment="center" valignment="top" width="0pt">
15778 <column alignment="center" valignment="top" width="0pt">
15780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15783 \begin_layout Plain Layout
15789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15792 \begin_layout Plain Layout
15794 \begin_inset Note Note
15797 \begin_layout Plain Layout
15804 is only used as spacer.
15816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15819 \begin_layout Plain Layout
15828 \begin_layout Plain Layout
15838 \begin_inset Formula $\to$
15842 \begin_inset Formula $\to$
15850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15853 \begin_layout Plain Layout
15854 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15870 \begin_layout Standard
15871 Limits of inline formulas are set right beside the operator.
15872 Limits in displayed formulas are set above or below the operator, except
15873 of integral limits.
15876 \begin_layout Standard
15877 To force that the limits are set beside the operator, the cursor is set
15878 directly behind the operator and the limits type is changed with the menu
15881 Edit\SpecialChar \menuseparator
15882 Math\SpecialChar \menuseparator
15894 \begin_inset space ~
15903 \begin_layout Standard
15904 The default limits type is this:
15905 \begin_inset Formula \[
15906 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15910 This is how it looks when the limits type was changed to
15917 \begin_inset Formula \[
15918 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15922 For integrals, except of
15934 , the limits are by default set beside the operator.
15935 But for multiple integrals the limits are often set below the operator.
15936 In the following example the limits type was therefore set to
15940 and so set below the integrals:
15941 \begin_inset Formula \begin{equation}
15942 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15949 \begin_layout Standard
15950 \begin_inset VSpace medskip
15953 To specify conditions for limits, the commands
15963 \begin_layout Plain Layout
15981 \begin_layout Plain Layout
15990 To create for example this expression
15991 \begin_inset Formula \begin{equation}
15992 \sum_{\begin{subarray}{c}
15994 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16001 \begin_layout Standard
16002 the following has to be done:
16003 \begin_inset Newline newline
16018 \begin_layout Plain Layout
16030 One is now in a blue box under the summation operator and insert there
16039 \begin_layout Plain Layout
16051 The blue box is now within a purple box and now several lines can be written
16053 A new line is created by inserting a line break (
16059 \begin_inset Newline newline
16064 0<k<1000 Ctrl-Return
16065 \begin_inset Newline newline
16070 is typed in, a new box appears below for the new line.
16073 \begin_layout Standard
16074 The alignment of the lines can be changed to left aligned with the
16084 Edit\SpecialChar \menuseparator
16088 To get right alignment,
16096 \begin_layout Plain Layout
16107 is inserted at the beginning of the line.
16110 \begin_layout Standard
16123 with the difference that the lines are always centered.
16126 \begin_layout Standard
16127 \begin_inset VSpace bigskip
16131 \begin_inset CommandInset ref
16133 reference "eq:substack"
16137 there can be too much space beside an operator, because the characters
16138 following the operator are set beside the limits.
16141 \begin_layout Standard
16142 To avoid this, the following macro can be used in the LaTeX-preamble:
16145 \begin_layout Standard
16159 \begin_inset Newline newline
16171 \begin_inset Newline newline
16178 mathclapinternal #1#2{
16182 mathsurround =0pt #1{#2}$}}
16185 \begin_layout Standard
16186 This defines the command
16196 \begin_layout Plain Layout
16204 that sets the width of the limit to 0
16205 \begin_inset space \thinspace{}
16209 The command scheme is
16212 \begin_layout Standard
16220 \begin_layout Standard
16221 where the limit can consist of several conditions.
16224 \begin_layout Standard
16226 \begin_inset CommandInset ref
16228 reference "eq:substack"
16232 , one uses the command
16235 \begin_layout Standard
16248 \begin_layout Plain Layout
16257 0<k<1000 Ctrl-Enter
16260 \begin_layout Standard
16261 to create the lower limit.
16262 The summand is now directly behind the summation operator:
16263 \begin_inset Formula \[
16264 \sum_{\mathclap{\substack{0<k<1000\\
16265 \\k\,\in\,\mathbb{N}}
16273 \begin_layout Standard
16274 \begin_inset VSpace bigskip
16277 How to use one limit for several operators is described in
16278 \begin_inset CommandInset ref
16280 reference "sub:Self-defined-Operators"
16287 \begin_layout Standard
16288 \begin_inset Newpage newpage
16294 \begin_layout Subsection
16296 \begin_inset CommandInset label
16298 name "sub:Binary-Operators"
16306 \begin_layout Plain Layout
16315 \begin_layout Standard
16316 Binary operators are surrounded by space when there is a character before
16318 \begin_inset VSpace medskip
16324 \begin_layout Standard
16325 \begin_inset space \hfill{}
16329 \begin_inset Tabular
16330 <lyxtabular version="3" rows="13" columns="2">
16332 <column alignment="center" valignment="top" width="0pt">
16333 <column alignment="center" valignment="top" width="0pt">
16335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16338 \begin_layout Plain Layout
16340 \begin_inset Note Note
16343 \begin_layout Plain Layout
16350 is only used as spacer.
16360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16363 \begin_layout Plain Layout
16371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16374 \begin_layout Plain Layout
16380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16383 \begin_layout Plain Layout
16384 \begin_inset Formula $+$
16394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16397 \begin_layout Plain Layout
16403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16406 \begin_layout Plain Layout
16407 \begin_inset Formula $-$
16417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16420 \begin_layout Plain Layout
16428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16431 \begin_layout Plain Layout
16432 \begin_inset Formula $\pm$
16442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16445 \begin_layout Plain Layout
16453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16456 \begin_layout Plain Layout
16457 \begin_inset Formula $\mp$
16467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16470 \begin_layout Plain Layout
16478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16481 \begin_layout Plain Layout
16482 \begin_inset Formula $\cdot$
16492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16495 \begin_layout Plain Layout
16503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16506 \begin_layout Plain Layout
16507 \begin_inset Formula $\times$
16517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16520 \begin_layout Plain Layout
16528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16531 \begin_layout Plain Layout
16532 \begin_inset Formula $\div$
16542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16545 \begin_layout Plain Layout
16549 \begin_layout Plain Layout
16562 \begin_layout Plain Layout
16574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16577 \begin_layout Plain Layout
16578 \begin_inset Formula $*$
16588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16591 \begin_layout Plain Layout
16599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16602 \begin_layout Plain Layout
16603 \begin_inset Formula $\star$
16613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16616 \begin_layout Plain Layout
16624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16627 \begin_layout Plain Layout
16628 \begin_inset Formula $\circ$
16638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16641 \begin_layout Plain Layout
16649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16652 \begin_layout Plain Layout
16653 \begin_inset Formula $\diamond$
16663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16666 \begin_layout Plain Layout
16674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16677 \begin_layout Plain Layout
16678 \begin_inset Formula $\bullet$
16692 \begin_inset space \hfill{}
16696 \begin_inset Tabular
16697 <lyxtabular version="3" rows="13" columns="2">
16699 <column alignment="center" valignment="top" width="0pt">
16700 <column alignment="center" valignment="top" width="0pt">
16702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16705 \begin_layout Plain Layout
16711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16714 \begin_layout Plain Layout
16722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16725 \begin_layout Plain Layout
16733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16736 \begin_layout Plain Layout
16737 \begin_inset Formula $\nabla$
16747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16750 \begin_layout Plain Layout
16758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16761 \begin_layout Plain Layout
16762 \begin_inset Formula $\bigtriangledown$
16772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16775 \begin_layout Plain Layout
16783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16786 \begin_layout Plain Layout
16787 \begin_inset Formula $\bigtriangleup$
16797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16800 \begin_layout Plain Layout
16808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16811 \begin_layout Plain Layout
16812 \begin_inset Formula $\Box$
16822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16825 \begin_layout Plain Layout
16833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16836 \begin_layout Plain Layout
16837 \begin_inset Formula $\cap$
16847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16850 \begin_layout Plain Layout
16858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16861 \begin_layout Plain Layout
16862 \begin_inset Formula $\cup$
16872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16875 \begin_layout Plain Layout
16883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16886 \begin_layout Plain Layout
16887 \begin_inset Formula $\dagger$
16897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16900 \begin_layout Plain Layout
16908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16911 \begin_layout Plain Layout
16912 \begin_inset Formula $\ddagger$
16922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16925 \begin_layout Plain Layout
16933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16936 \begin_layout Plain Layout
16937 \begin_inset Formula $\wr$
16947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16950 \begin_layout Plain Layout
16958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16961 \begin_layout Plain Layout
16962 \begin_inset Formula $\bigcirc$
16972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16975 \begin_layout Plain Layout
16983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16986 \begin_layout Plain Layout
16987 \begin_inset Formula $\wedge$
16997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17000 \begin_layout Plain Layout
17008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17011 \begin_layout Plain Layout
17012 \begin_inset Formula $\vee$
17026 \begin_inset space \hfill{}
17030 \begin_inset Tabular
17031 <lyxtabular version="3" rows="13" columns="2">
17033 <column alignment="center" valignment="top" width="0pt">
17034 <column alignment="center" valignment="top" width="0pt">
17036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17039 \begin_layout Plain Layout
17045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17048 \begin_layout Plain Layout
17056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17059 \begin_layout Plain Layout
17067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17070 \begin_layout Plain Layout
17071 \begin_inset Formula $\oplus$
17081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17084 \begin_layout Plain Layout
17092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17095 \begin_layout Plain Layout
17096 \begin_inset Formula $\ominus$
17106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17109 \begin_layout Plain Layout
17117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17120 \begin_layout Plain Layout
17121 \begin_inset Formula $\otimes$
17131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17134 \begin_layout Plain Layout
17142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17145 \begin_layout Plain Layout
17146 \begin_inset Formula $\oslash$
17156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17159 \begin_layout Plain Layout
17167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17170 \begin_layout Plain Layout
17171 \begin_inset Formula $\odot$
17181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17184 \begin_layout Plain Layout
17192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17195 \begin_layout Plain Layout
17196 \begin_inset Formula $\amalg$
17206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17209 \begin_layout Plain Layout
17217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17220 \begin_layout Plain Layout
17221 \begin_inset Formula $\uplus$
17231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17234 \begin_layout Plain Layout
17242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17245 \begin_layout Plain Layout
17246 \begin_inset Formula $\setminus$
17256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17259 \begin_layout Plain Layout
17267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17270 \begin_layout Plain Layout
17271 \begin_inset Formula $\sqcap$
17281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17284 \begin_layout Plain Layout
17292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17295 \begin_layout Plain Layout
17296 \begin_inset Formula $\sqcup$
17306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17309 \begin_layout Plain Layout
17317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17320 \begin_layout Plain Layout
17321 \begin_inset Formula $\triangleleft$
17331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17334 \begin_layout Plain Layout
17342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17345 \begin_layout Plain Layout
17346 \begin_inset Formula $\triangleright$
17360 \begin_inset space \hfill{}
17366 \begin_layout Standard
17367 All binary operators can also be inserted via the math toolbar button
17368 \begin_inset Graphics
17369 filename ../images/math/pm.png
17377 \begin_layout Standard
17378 To typeset the Laplace operator also
17395 \begin_inset Formula $\nabla^{2}$
17398 ) can be used instead of
17407 \begin_layout Standard
17414 Insert\SpecialChar \menuseparator
17426 \begin_layout Subsection
17427 Self-defined Operators
17428 \begin_inset CommandInset label
17430 name "sub:Self-defined-Operators"
17438 \begin_layout Plain Layout
17439 Operators ! self-defined
17447 \begin_layout Standard
17448 With the help of the command
17452 DeclareMathOperator
17458 \begin_layout Plain Layout
17463 DeclareMathOperator
17468 custom operators can be defined in the LaTeX-preamble.
17469 Its command scheme is:
17472 \begin_layout Standard
17477 DeclareMathOperator{new command}{display}
17480 \begin_layout Standard
17481 Display can be characters or symbols that define how the operator looks
17483 To define a big operator a * is set behind the command.
17484 All self-defined big operators can have limits as described in
17485 \begin_inset CommandInset ref
17487 reference "sub:Operator-Limits"
17494 \begin_layout Standard
17495 For example the LaTeX-preamble line
17498 \begin_layout Standard
17503 DeclareMathOperator*{
17510 \begin_layout Standard
17511 defines the command
17517 , that inserts a big operator consisting of the lozenge symbol from
17518 \begin_inset CommandInset ref
17520 reference "sub:Miscellaneous-Symbols"
17525 \begin_inset Formula \[
17526 \Lozenge_{n=1}^{\infty}\]
17530 The command for this formula is:
17541 \begin_inset Formula $\to$
17547 \begin_layout Standard
17548 \begin_inset VSpace bigskip
17551 When self-defined operators are not used several times in the document,
17552 they can also be defined with the commands
17562 \begin_layout Plain Layout
17580 \begin_layout Plain Layout
17588 , which have the following scheme:
17591 \begin_layout Standard
17605 \begin_layout Standard
17612 defines big operators,
17621 \begin_layout Standard
17629 \begin_inset space \thinspace{}
17633 \begin_inset space ~
17636 be used to use one limit for several operators:
17639 \begin_layout Standard
17640 \begin_inset Formula \[
17641 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17648 \begin_layout Standard
17649 The command for the formula above is:
17650 \begin_inset Newline newline
17669 \begin_layout Plain Layout
17681 \begin_inset Formula $\to$
17690 \begin_layout Plain Layout
17704 \begin_layout Section
17709 \begin_layout Plain Layout
17718 \begin_layout Subsection
17720 \begin_inset CommandInset label
17722 name "sub:Font-Styles"
17730 \begin_layout Plain Layout
17739 \begin_layout Standard
17740 Latin letters in formulas can be set in one of the following font styles:
17741 \begin_inset VSpace -2mm
17747 \begin_layout Standard
17749 \begin_inset Tabular
17750 <lyxtabular version="3" rows="6" columns="3">
17752 <column alignment="center" valignment="top" width="0">
17753 <column alignment="center" valignment="top" width="0">
17754 <column alignment="center" valignment="top" width="0">
17756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17759 \begin_layout Plain Layout
17765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17768 \begin_layout Plain Layout
17774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17777 \begin_layout Plain Layout
17785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17788 \begin_layout Plain Layout
17797 \begin_layout Plain Layout
17813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17816 \begin_layout Plain Layout
17817 \begin_inset Formula $\mathbb{ABC}$
17825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17828 \begin_layout Plain Layout
17836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17839 \begin_layout Plain Layout
17848 \begin_layout Plain Layout
17864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17867 \begin_layout Plain Layout
17868 \begin_inset Formula $\mathbf{AbC}$
17876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17879 \begin_layout Plain Layout
17887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17890 \begin_layout Plain Layout
17899 \begin_layout Plain Layout
17915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17918 \begin_layout Plain Layout
17919 \begin_inset Formula $\boldsymbol{AbC}$
17927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17930 \begin_layout Plain Layout
17931 Alt-c b or Ctrl-Alt-b
17938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17941 \begin_layout Plain Layout
17950 \begin_layout Plain Layout
17966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17969 \begin_layout Plain Layout
17970 \begin_inset Formula $\mathcal{ABC}$
17978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17981 \begin_layout Plain Layout
17989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17992 \begin_layout Plain Layout
18001 \begin_layout Plain Layout
18017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18020 \begin_layout Plain Layout
18021 \begin_inset Formula $\mathfrak{AbC}$
18029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18032 \begin_layout Plain Layout
18046 \begin_layout Standard
18048 \begin_inset Tabular
18049 <lyxtabular version="3" rows="5" columns="3">
18051 <column alignment="center" valignment="top" width="0">
18052 <column alignment="center" valignment="top" width="0">
18053 <column alignment="center" valignment="top" width="0">
18055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18058 \begin_layout Plain Layout
18064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18067 \begin_layout Plain Layout
18073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18076 \begin_layout Plain Layout
18084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18087 \begin_layout Plain Layout
18096 \begin_layout Plain Layout
18112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18115 \begin_layout Plain Layout
18116 \begin_inset Formula $\mathit{AbC}$
18124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18127 \begin_layout Plain Layout
18135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18138 \begin_layout Plain Layout
18147 \begin_layout Plain Layout
18163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18166 \begin_layout Plain Layout
18167 \begin_inset Formula $\mathrm{AbC}$
18175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18178 \begin_layout Plain Layout
18186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18189 \begin_layout Plain Layout
18198 \begin_layout Plain Layout
18214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18217 \begin_layout Plain Layout
18218 \begin_inset Formula $\mathsf{AbC}$
18226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18229 \begin_layout Plain Layout
18237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18240 \begin_layout Plain Layout
18249 \begin_layout Plain Layout
18265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18268 \begin_layout Plain Layout
18269 \begin_inset Formula $\mathtt{AbC}$
18277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18280 \begin_layout Plain Layout
18294 \begin_layout Standard
18295 \begin_inset Note Greyedout
18298 \begin_layout Plain Layout
18315 can only be used for big letters.
18323 \begin_layout Standard
18324 Predefined is the style
18333 \begin_layout Standard
18334 The style commands work also for letters in mathematical constructs:
18335 \begin_inset Formula \[
18336 \mathfrak{A=\frac{b}{C}}\]
18343 \begin_layout Standard
18344 Characters in mathematical text don't appear in a math font style but in
18345 the text font style
18352 That their style can't be set correctly via the text style dialog is a
18357 \begin_layout Plain Layout
18358 \begin_inset CommandInset href
18360 name "LyX-bug #4091"
18361 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18373 \begin_layout Standard
18374 Instead of the style commands the dialog
18376 Edit\SpecialChar \menuseparator
18377 Math\SpecialChar \menuseparator
18380 or the toolbar button
18381 \begin_inset Graphics
18382 filename ../images/math/font.png
18390 \begin_layout Subsection
18392 \begin_inset CommandInset label
18394 name "sub:Bold-Formulas"
18402 \begin_layout Plain Layout
18411 \begin_layout Standard
18412 To make a complete formula bold, the command
18418 from the previous subsection cannot be used, because it doesn't work for
18419 small Greek letters.
18420 Furthermore it prints Latin letters always upright, like in the following
18424 \begin_layout Standard
18425 \begin_inset Formula \[
18426 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18433 \begin_layout Standard
18434 To display the formula correctly, the command
18441 \begin_inset Formula \[
18442 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18446 It is also possible to set the formula in a
18448 boldmath environment
18451 This environment is created by inserting the command
18459 \begin_layout Plain Layout
18470 To end the environment, the command
18478 \begin_layout Plain Layout
18488 is inserted in TeX-mode.
18492 \begin_layout Plain Layout
18502 \begin_inset Formula \[
18503 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18511 \begin_layout Plain Layout
18523 \begin_layout Subsection
18528 \begin_layout Plain Layout
18537 \begin_layout Standard
18538 Formulas can be colored like normal text: Highlight a formula or a formula
18544 Here is a formula in magenta:
18545 \begin_inset Formula \[
18546 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18553 \begin_layout Standard
18554 You can also define your own colors as described in
18555 \begin_inset CommandInset ref
18557 reference "sub:Colored-Boxes"
18562 They can be used with the TeX code command
18572 \begin_layout Plain Layout
18583 \begin_layout Standard
18588 textcolor{color}{characters or formula}
18591 \begin_layout Standard
18592 The following example was colored completely dark green and partly red:
18595 \begin_layout Standard
18599 \begin_layout Plain Layout
18603 textcolor{darkgreen}{
18609 \begin_inset Formula \[
18610 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18618 \begin_layout Plain Layout
18628 \begin_layout Standard
18629 Due to a bug in LyX only complete formulas can be colored with self-defined
18634 \begin_layout Plain Layout
18635 \begin_inset CommandInset href
18637 name "LyX-bug #5269"
18638 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18650 \begin_layout Subsection
18652 \begin_inset CommandInset label
18654 name "sub:Font-Sizes"
18662 \begin_layout Plain Layout
18671 \begin_layout Standard
18672 For characters in formulas there are, analog to characters in text, the
18673 following size commands:
18676 \begin_layout Standard
18720 \begin_inset Newline newline
18742 \begin_layout Standard
18743 The size produced by the commands depends on the document font size, that
18744 corresponds with the command
18751 The other commands produce smaller or larger sizes than
18758 The font size can however not exceed a certain value.
18759 Is for example the document font size 12
18760 \begin_inset space \thinspace{}
18769 switches to the same size as
18779 \begin_layout Standard
18780 A size command is inserted in TeX-mode before the formula and sets the size
18781 for all following formula and text characters.
18782 To switch back to the initial size, the command
18788 is inserted behind the formula in TeX-mode.
18791 \begin_layout Standard
18792 Within a formula the size can only be changed for symbols or letters in
18794 To do this, the size command is inserted in mathematical text.
18795 All following characters until the end of the mathematical text or until
18796 another size command will have the selected size.
18798 \begin_inset VSpace -2mm
18804 \begin_layout Standard
18808 \begin_layout Plain Layout
18818 \begin_inset Formula \[
18819 A=\frac{B}{c}\cdot\maltese\]
18824 \begin_inset Formula \[
18825 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18833 \begin_layout Plain Layout
18845 \begin_layout Standard
18846 \begin_inset VSpace medskip
18849 Before both formulas the command
18856 The command for the second formula is:
18857 \begin_inset Newline newline
18868 \begin_layout Plain Layout
18883 \begin_layout Plain Layout
18898 \begin_layout Plain Layout
18913 \begin_layout Plain Layout
18923 \begin_inset Formula $\to$
18927 \begin_inset Formula $\to$
18931 \begin_inset Newline newline
18935 \begin_inset space \hspace*{}
18949 \begin_layout Plain Layout
18964 \begin_layout Plain Layout
18979 \begin_layout Plain Layout
18991 \begin_layout Standard
18992 If a symbol cannot be displayed in different sizes, it will always be displayed
18993 in the default size.
18996 \begin_layout Section
19001 \begin_layout Plain Layout
19010 \begin_layout Standard
19011 All Greek letters can also be inserted via the toolbar button
19012 \begin_inset Graphics
19013 filename ../images/math/alpha.png
19021 \begin_layout Subsection
19026 \begin_layout Plain Layout
19027 Greek letters ! small
19035 \begin_layout Standard
19036 \begin_inset space \hfill{}
19040 \begin_inset Tabular
19041 <lyxtabular version="3" rows="11" columns="2">
19043 <column alignment="center" valignment="top" width="0pt">
19044 <column alignment="center" valignment="top" width="0pt">
19046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19049 \begin_layout Plain Layout
19055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19058 \begin_layout Plain Layout
19066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19069 \begin_layout Plain Layout
19077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19080 \begin_layout Plain Layout
19081 \begin_inset Formula $\alpha$
19091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19094 \begin_layout Plain Layout
19102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19105 \begin_layout Plain Layout
19106 \begin_inset Formula $\beta$
19116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19119 \begin_layout Plain Layout
19127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19130 \begin_layout Plain Layout
19131 \begin_inset Formula $\gamma$
19141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19144 \begin_layout Plain Layout
19152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19155 \begin_layout Plain Layout
19156 \begin_inset Formula $\delta$
19166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19169 \begin_layout Plain Layout
19177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19180 \begin_layout Plain Layout
19181 \begin_inset Formula $\epsilon$
19191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19194 \begin_layout Plain Layout
19202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19205 \begin_layout Plain Layout
19206 \begin_inset Formula $\varepsilon$
19216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19219 \begin_layout Plain Layout
19227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19230 \begin_layout Plain Layout
19231 \begin_inset Formula $\zeta$
19241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19244 \begin_layout Plain Layout
19252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19255 \begin_layout Plain Layout
19256 \begin_inset Formula $\eta$
19266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19269 \begin_layout Plain Layout
19277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19280 \begin_layout Plain Layout
19281 \begin_inset Formula $\theta$
19291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19294 \begin_layout Plain Layout
19302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19305 \begin_layout Plain Layout
19306 \begin_inset Formula $\vartheta$
19320 \begin_inset space \hfill{}
19324 \begin_inset Tabular
19325 <lyxtabular version="3" rows="12" columns="2">
19327 <column alignment="center" valignment="top" width="0pt">
19328 <column alignment="center" valignment="top" width="0pt">
19330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19333 \begin_layout Plain Layout
19339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19342 \begin_layout Plain Layout
19350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19353 \begin_layout Plain Layout
19361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19364 \begin_layout Plain Layout
19365 \begin_inset Formula $\iota$
19375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19378 \begin_layout Plain Layout
19386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19389 \begin_layout Plain Layout
19390 \begin_inset Formula $\kappa$
19400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19403 \begin_layout Plain Layout
19411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19414 \begin_layout Plain Layout
19415 \begin_inset Formula $\varkappa$
19425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19428 \begin_layout Plain Layout
19436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19439 \begin_layout Plain Layout
19440 \begin_inset Formula $\lambda$
19450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19453 \begin_layout Plain Layout
19461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19464 \begin_layout Plain Layout
19465 \begin_inset Formula $\mu$
19475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19478 \begin_layout Plain Layout
19486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19489 \begin_layout Plain Layout
19490 \begin_inset Formula $\nu$
19500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19503 \begin_layout Plain Layout
19511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19514 \begin_layout Plain Layout
19515 \begin_inset Formula $\xi$
19525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19528 \begin_layout Plain Layout
19534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19537 \begin_layout Plain Layout
19538 \begin_inset Formula $o$
19548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19551 \begin_layout Plain Layout
19559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19562 \begin_layout Plain Layout
19563 \begin_inset Formula $\pi$
19573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19576 \begin_layout Plain Layout
19584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19587 \begin_layout Plain Layout
19588 \begin_inset Formula $\varpi$
19598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19601 \begin_layout Plain Layout
19609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19612 \begin_layout Plain Layout
19613 \begin_inset Formula $\rho$
19627 \begin_inset space \hfill{}
19631 \begin_inset Tabular
19632 <lyxtabular version="3" rows="11" columns="2">
19634 <column alignment="center" valignment="top" width="0pt">
19635 <column alignment="center" valignment="top" width="0pt">
19637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19640 \begin_layout Plain Layout
19646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19649 \begin_layout Plain Layout
19657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19660 \begin_layout Plain Layout
19668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19671 \begin_layout Plain Layout
19672 \begin_inset Formula $\varrho$
19682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19685 \begin_layout Plain Layout
19693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19696 \begin_layout Plain Layout
19697 \begin_inset Formula $\sigma$
19707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19710 \begin_layout Plain Layout
19718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19721 \begin_layout Plain Layout
19722 \begin_inset Formula $\varsigma$
19732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19735 \begin_layout Plain Layout
19743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19746 \begin_layout Plain Layout
19747 \begin_inset Formula $\tau$
19757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19760 \begin_layout Plain Layout
19768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19771 \begin_layout Plain Layout
19772 \begin_inset Formula $\upsilon$
19782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19785 \begin_layout Plain Layout
19793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19796 \begin_layout Plain Layout
19797 \begin_inset Formula $\phi$
19807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19810 \begin_layout Plain Layout
19818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19821 \begin_layout Plain Layout
19822 \begin_inset Formula $\varphi$
19832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19835 \begin_layout Plain Layout
19843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19846 \begin_layout Plain Layout
19847 \begin_inset Formula $\chi$
19857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19860 \begin_layout Plain Layout
19868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19871 \begin_layout Plain Layout
19872 \begin_inset Formula $\psi$
19882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19885 \begin_layout Plain Layout
19893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19896 \begin_layout Plain Layout
19897 \begin_inset Formula $\omega$
19911 \begin_inset space \hfill{}
19917 \begin_layout Standard
19918 \begin_inset VSpace medskip
19924 \begin_layout Standard
19925 How to create upright Greek letters is explained in
19926 \begin_inset CommandInset ref
19928 reference "sub:Upright-small-Greek"
19935 \begin_layout Subsection
19940 \begin_layout Plain Layout
19941 Greek letters ! big
19949 \begin_layout Standard
19950 \begin_inset space \hfill{}
19954 \begin_inset Tabular
19955 <lyxtabular version="3" rows="7" columns="2">
19957 <column alignment="center" valignment="top" width="0pt">
19958 <column alignment="center" valignment="top" width="0pt">
19960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19963 \begin_layout Plain Layout
19969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19972 \begin_layout Plain Layout
19980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19983 \begin_layout Plain Layout
19991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19994 \begin_layout Plain Layout
19995 \begin_inset Formula $\Gamma$
20005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20008 \begin_layout Plain Layout
20016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20019 \begin_layout Plain Layout
20020 \begin_inset Formula $\Delta$
20030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20033 \begin_layout Plain Layout
20041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20044 \begin_layout Plain Layout
20045 \begin_inset Formula $\Theta$
20055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20058 \begin_layout Plain Layout
20066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20069 \begin_layout Plain Layout
20070 \begin_inset Formula $\Lambda$
20080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20083 \begin_layout Plain Layout
20091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20094 \begin_layout Plain Layout
20095 \begin_inset Formula $\Xi$
20105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20108 \begin_layout Plain Layout
20116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20119 \begin_layout Plain Layout
20120 \begin_inset Formula $\Pi$
20134 \begin_inset space \hfill{}
20138 \begin_inset Tabular
20139 <lyxtabular version="3" rows="6" columns="2">
20141 <column alignment="center" valignment="top" width="0pt">
20142 <column alignment="center" valignment="top" width="0pt">
20144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20147 \begin_layout Plain Layout
20153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20156 \begin_layout Plain Layout
20164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20167 \begin_layout Plain Layout
20175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20178 \begin_layout Plain Layout
20179 \begin_inset Formula $\Sigma$
20189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20192 \begin_layout Plain Layout
20200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20203 \begin_layout Plain Layout
20204 \begin_inset Formula $\Upsilon$
20214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20217 \begin_layout Plain Layout
20225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20228 \begin_layout Plain Layout
20229 \begin_inset Formula $\Phi$
20239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20242 \begin_layout Plain Layout
20250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20253 \begin_layout Plain Layout
20254 \begin_inset Formula $\Psi$
20264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20267 \begin_layout Plain Layout
20275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20278 \begin_layout Plain Layout
20279 \begin_inset Formula $\Omega$
20293 \begin_inset space \hfill{}
20299 \begin_layout Standard
20300 \begin_inset VSpace medskip
20303 That the big Greek letters appear upright is caused by a design bug when
20305 To get correct italic big letters, begin every command with
20310 For example the command
20317 \begin_inset Formula $\varGamma$
20323 \begin_layout Subsection
20328 \begin_layout Plain Layout
20329 Greek letters ! bold
20337 \begin_layout Standard
20338 Greek letters cannot be set with different font styles like Latin letters.
20339 They can only be made bold with the command
20349 \begin_layout Plain Layout
20360 \begin_layout Standard
20362 \begin_inset Tabular
20363 <lyxtabular version="3" rows="3" columns="2">
20365 <column alignment="center" valignment="top" width="0">
20366 <column alignment="center" valignment="top" width="0">
20368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20371 \begin_layout Plain Layout
20377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20380 \begin_layout Plain Layout
20388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20391 \begin_layout Plain Layout
20403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20406 \begin_layout Plain Layout
20407 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20420 \begin_layout Plain Layout
20432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20435 \begin_layout Plain Layout
20436 \begin_inset Formula $\theta\boldsymbol{\theta}$
20452 \begin_layout Section
20457 \begin_layout Plain Layout
20470 \begin_layout Plain Layout
20471 A list with all symbols of most of the LaTeX-packages can be found in
20472 \begin_inset CommandInset citation
20487 \begin_layout Plain Layout
20495 \begin_inset Note Note
20498 \begin_layout Plain Layout
20501 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20504 \begin_layout Plain Layout
20507 texorpdfstring is in section
20508 \begin_inset CommandInset ref
20510 reference "sub:Formulas-in-Section"
20523 \begin_layout Plain Layout
20532 \begin_layout Standard
20533 Many of the symbols listed in this section can also be inserted via the
20535 \begin_inset Graphics
20536 filename ../images/math/nabla.png
20542 \begin_inset Graphics
20543 filename ../images/math/digamma.png
20551 \begin_layout Subsection
20552 Mathematical Symbols
20553 \begin_inset CommandInset label
20555 name "sub:Mathematical-Symbols"
20563 \begin_layout Plain Layout
20564 Symbols ! mathematical
20572 \begin_layout Standard
20573 \begin_inset space \hfill{}
20577 \begin_inset Tabular
20578 <lyxtabular version="3" rows="10" columns="2">
20580 <column alignment="center" valignment="top" width="0pt">
20581 <column alignment="center" valignment="top" width="0pt">
20583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20586 \begin_layout Plain Layout
20592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20595 \begin_layout Plain Layout
20603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20606 \begin_layout Plain Layout
20614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20617 \begin_layout Plain Layout
20618 \begin_inset Formula $\neg$
20628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20631 \begin_layout Plain Layout
20639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20642 \begin_layout Plain Layout
20643 \begin_inset Formula $\Im$
20653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20656 \begin_layout Plain Layout
20664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20667 \begin_layout Plain Layout
20668 \begin_inset Formula $\Re$
20678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20681 \begin_layout Plain Layout
20689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20692 \begin_layout Plain Layout
20693 \begin_inset Formula $\aleph$
20703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20706 \begin_layout Plain Layout
20714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20717 \begin_layout Plain Layout
20718 \begin_inset Formula $\partial$
20728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20731 \begin_layout Plain Layout
20739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20742 \begin_layout Plain Layout
20743 \begin_inset Formula $\infty$
20753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20756 \begin_layout Plain Layout
20764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20767 \begin_layout Plain Layout
20768 \begin_inset Formula $\wp$
20778 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20781 \begin_layout Plain Layout
20789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20792 \begin_layout Plain Layout
20793 \begin_inset Formula $\imath$
20803 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20806 \begin_layout Plain Layout
20814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20817 \begin_layout Plain Layout
20818 \begin_inset Formula $\jmath$
20832 \begin_inset space \hfill{}
20836 \begin_inset Tabular
20837 <lyxtabular version="3" rows="10" columns="2">
20839 <column alignment="center" valignment="top" width="0pt">
20840 <column alignment="center" valignment="top" width="0pt">
20842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20845 \begin_layout Plain Layout
20851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20854 \begin_layout Plain Layout
20856 \begin_inset Note Note
20859 \begin_layout Plain Layout
20866 is only used as spacer.
20878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20881 \begin_layout Plain Layout
20889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20892 \begin_layout Plain Layout
20893 \begin_inset Formula $\forall$
20903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20906 \begin_layout Plain Layout
20914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20917 \begin_layout Plain Layout
20918 \begin_inset Formula $\exists$
20928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20931 \begin_layout Plain Layout
20939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20942 \begin_layout Plain Layout
20943 \begin_inset Formula $\nexists$
20953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20956 \begin_layout Plain Layout
20964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20967 \begin_layout Plain Layout
20968 \begin_inset Formula $\emptyset$
20978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20981 \begin_layout Plain Layout
20989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20992 \begin_layout Plain Layout
20993 \begin_inset Formula $\varnothing$
21003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21006 \begin_layout Plain Layout
21014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21017 \begin_layout Plain Layout
21018 \begin_inset Formula $\dag$
21028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21031 \begin_layout Plain Layout
21039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21042 \begin_layout Plain Layout
21043 \begin_inset Formula $\ddag$
21053 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21056 \begin_layout Plain Layout
21064 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21067 \begin_layout Plain Layout
21071 \begin_layout Plain Layout
21081 \begin_inset Formula $\complement$
21088 \begin_layout Plain Layout
21102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21105 \begin_layout Plain Layout
21113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21116 \begin_layout Plain Layout
21117 \begin_inset Formula $\Bbbk$
21131 \begin_inset space \hfill{}
21135 \begin_inset Tabular
21136 <lyxtabular version="3" rows="10" columns="2">
21138 <column alignment="center" valignment="top" width="0pt">
21139 <column alignment="center" valignment="top" width="0pt">
21141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21144 \begin_layout Plain Layout
21150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21153 \begin_layout Plain Layout
21161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21164 \begin_layout Plain Layout
21172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21175 \begin_layout Plain Layout
21176 \begin_inset Formula $\prime$
21186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21189 \begin_layout Plain Layout
21197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21200 \begin_layout Plain Layout
21201 \begin_inset Formula $\backprime$
21211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21214 \begin_layout Plain Layout
21222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21225 \begin_layout Plain Layout
21226 \begin_inset Formula $\mho$
21236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21239 \begin_layout Plain Layout
21247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21250 \begin_layout Plain Layout
21251 \begin_inset Formula $\triangle$
21261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21264 \begin_layout Plain Layout
21272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21275 \begin_layout Plain Layout
21276 \begin_inset Formula $\angle$
21286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21289 \begin_layout Plain Layout
21297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21300 \begin_layout Plain Layout
21301 \begin_inset Formula $\measuredangle$
21311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21314 \begin_layout Plain Layout
21322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21325 \begin_layout Plain Layout
21326 \begin_inset Formula $\sphericalangle$
21336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21339 \begin_layout Plain Layout
21347 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21350 \begin_layout Plain Layout
21351 \begin_inset Formula $\top$
21361 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21364 \begin_layout Plain Layout
21372 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21375 \begin_layout Plain Layout
21376 \begin_inset Formula $\bot$
21390 \begin_inset space \hfill{}
21396 \begin_layout Subsection
21397 Miscellaneous Symbols
21398 \begin_inset CommandInset label
21400 name "sub:Miscellaneous-Symbols"
21408 \begin_layout Plain Layout
21409 Symbols ! miscellaneous
21417 \begin_layout Standard
21420 \begin_inset Tabular
21421 <lyxtabular version="3" rows="10" columns="2">
21423 <column alignment="center" valignment="top" width="0pt">
21424 <column alignment="center" valignment="top" width="0pt">
21426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21429 \begin_layout Plain Layout
21435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21438 \begin_layout Plain Layout
21446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21449 \begin_layout Plain Layout
21457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21460 \begin_layout Plain Layout
21461 \begin_inset Formula $\flat$
21471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21474 \begin_layout Plain Layout
21482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21485 \begin_layout Plain Layout
21486 \begin_inset Formula $\natural$
21496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21499 \begin_layout Plain Layout
21507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21510 \begin_layout Plain Layout
21511 \begin_inset Formula $\sharp$
21521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21524 \begin_layout Plain Layout
21532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21535 \begin_layout Plain Layout
21536 \begin_inset Formula $\surd$
21546 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21549 \begin_layout Plain Layout
21557 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21560 \begin_layout Plain Layout
21561 \begin_inset Formula $\checkmark$
21571 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21574 \begin_layout Plain Layout
21582 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21585 \begin_layout Plain Layout
21586 \begin_inset Formula $\yen$
21596 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21599 \begin_layout Plain Layout
21607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21610 \begin_layout Plain Layout
21611 \begin_inset Formula $\pounds$
21621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21624 \begin_layout Plain Layout
21630 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21633 \begin_layout Plain Layout
21634 \begin_inset Formula $\$$
21644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21647 \begin_layout Plain Layout
21653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21656 \begin_layout Plain Layout
21657 \begin_inset Formula $§$
21671 \begin_inset Tabular
21672 <lyxtabular version="3" rows="10" columns="2">
21674 <column alignment="center" valignment="top" width="0">
21675 <column alignment="center" valignment="top" width="0">
21677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21680 \begin_layout Plain Layout
21686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21689 \begin_layout Plain Layout
21697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21700 \begin_layout Plain Layout
21708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21711 \begin_layout Plain Layout
21712 \begin_inset Formula $\hbar$
21722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21725 \begin_layout Plain Layout
21733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21736 \begin_layout Plain Layout
21737 \begin_inset Formula $\hslash$
21747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21750 \begin_layout Plain Layout
21758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21761 \begin_layout Plain Layout
21762 \begin_inset Formula $\clubsuit$
21772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21775 \begin_layout Plain Layout
21783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21786 \begin_layout Plain Layout
21787 \begin_inset Formula $\spadesuit$
21797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21800 \begin_layout Plain Layout
21808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21811 \begin_layout Plain Layout
21812 \begin_inset Formula $\bigstar$
21822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21825 \begin_layout Plain Layout
21833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21836 \begin_layout Plain Layout
21837 \begin_inset Formula $\blacklozenge$
21847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21850 \begin_layout Plain Layout
21858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21861 \begin_layout Plain Layout
21862 \begin_inset Formula $\blacktriangle$
21872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21875 \begin_layout Plain Layout
21883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21886 \begin_layout Plain Layout
21887 \begin_inset Formula $\blacktriangledown$
21897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21900 \begin_layout Plain Layout
21908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21911 \begin_layout Plain Layout
21912 \begin_inset Formula $\bullet$
21926 \begin_inset Tabular
21927 <lyxtabular version="3" rows="10" columns="2">
21929 <column alignment="center" valignment="top" width="0pt">
21930 <column alignment="center" valignment="top" width="0pt">
21932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21935 \begin_layout Plain Layout
21941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21944 \begin_layout Plain Layout
21952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21955 \begin_layout Plain Layout
21963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21966 \begin_layout Plain Layout
21967 \begin_inset Formula $\diamondsuit$
21977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21980 \begin_layout Plain Layout
21988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21991 \begin_layout Plain Layout
21992 \begin_inset Formula $\Diamond$
22002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22005 \begin_layout Plain Layout
22013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22016 \begin_layout Plain Layout
22017 \begin_inset Formula $\heartsuit$
22027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22030 \begin_layout Plain Layout
22038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22041 \begin_layout Plain Layout
22042 \begin_inset Formula $\P$
22052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22055 \begin_layout Plain Layout
22063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22066 \begin_layout Plain Layout
22067 \begin_inset Formula $\copyright$
22077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22080 \begin_layout Plain Layout
22088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22091 \begin_layout Plain Layout
22092 \begin_inset Formula $\circledR$
22102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22105 \begin_layout Plain Layout
22113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22116 \begin_layout Plain Layout
22117 \begin_inset Formula $\maltese$
22127 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22130 \begin_layout Plain Layout
22138 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22141 \begin_layout Plain Layout
22142 \begin_inset Formula $\diagup$
22152 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22155 \begin_layout Plain Layout
22163 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22166 \begin_layout Plain Layout
22167 \begin_inset Formula $\diagdown$
22183 \begin_layout Standard
22184 \begin_inset VSpace medskip
22187 More symbols are listed in
22188 \begin_inset CommandInset ref
22190 reference "sub:Miscellaneous-special-Characters"
22197 \begin_layout Standard
22198 Some symbols can be displayed in different sizes, see
22199 \begin_inset CommandInset ref
22201 reference "sub:Font-Sizes"
22208 \begin_layout Subsection
22213 \begin_layout Plain Layout
22214 Symbols ! Euro-symbol
22223 \begin_layout Plain Layout
22230 \begin_layout Plain Layout
22247 \begin_layout Standard
22248 To use the Euro symbol in formulas, the LaTeX-package
22256 \begin_layout Plain Layout
22262 must be installed and loaded with the LaTeX-preamble line
22265 \begin_layout Standard
22270 usepackage[gennarrow]{eurosym}
22273 \begin_layout Standard
22274 The Euro symbol can now be inserted with the command
22284 \begin_layout Plain Layout
22295 \begin_layout Standard
22296 The Euro symbol can directly be inserted with the € key in mathematical
22297 text, without having
22312 can also be inserted in TeX-mode.
22313 The official currency symbol can then be inserted with the command
22323 \begin_layout Plain Layout
22331 , that is only available in TeX-mode.
22334 \begin_layout Standard
22338 \begin_layout Plain Layout
22348 \begin_inset Note Note
22351 \begin_layout Plain Layout
22352 The following table will only be displayed when the LaTeX-package
22364 \begin_layout Standard
22365 An overview about the different Euro symbols:
22368 \begin_layout Standard
22370 \begin_inset Tabular
22371 <lyxtabular version="3" rows="4" columns="3">
22373 <column alignment="center" valignment="top" width="0pt">
22374 <column alignment="center" valignment="top" width="0pt">
22375 <column alignment="center" valignment="top" width="0pt">
22377 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22380 \begin_layout Plain Layout
22386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22389 \begin_layout Plain Layout
22395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22398 \begin_layout Plain Layout
22406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22409 \begin_layout Plain Layout
22415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22418 \begin_layout Plain Layout
22426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22429 \begin_layout Plain Layout
22430 \begin_inset Formula $\euro$
22440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22443 \begin_layout Plain Layout
22449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22452 \begin_layout Plain Layout
22458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22461 \begin_layout Plain Layout
22462 \begin_inset Formula $\mbox{€}$
22472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22475 \begin_layout Plain Layout
22481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22484 \begin_layout Plain Layout
22492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22495 \begin_layout Plain Layout
22499 \begin_layout Plain Layout
22521 \begin_layout Standard
22525 \begin_layout Plain Layout
22535 \begin_inset Note Note
22538 \begin_layout Plain Layout
22539 The following will be displayed when the LaTeX-package
22551 \begin_layout Standard
22552 You need to install the LaTeX-package
22556 to see the rest of this subsection in the output.
22559 \begin_layout Standard
22563 \begin_layout Plain Layout
22575 \begin_layout Section
22577 \begin_inset CommandInset label
22579 name "sec:Relations"
22587 \begin_layout Plain Layout
22597 \begin_layout Plain Layout
22602 \begin_layout Plain Layout
22613 \begin_layout Plain Layout
22628 \begin_layout Standard
22629 All relations can also be inserted via the toolbar button
22630 \begin_inset Graphics
22631 filename ../images/math/leq.png
22639 \begin_layout Standard
22640 \begin_inset space \hfill{}
22644 \begin_inset Tabular
22645 <lyxtabular version="3" rows="17" columns="2">
22647 <column alignment="center" valignment="top" width="0pt">
22648 <column alignment="center" valignment="top" width="0pt">
22650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22653 \begin_layout Plain Layout
22659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22662 \begin_layout Plain Layout
22670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22673 \begin_layout Plain Layout
22679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22682 \begin_layout Plain Layout
22683 \begin_inset Formula $<$
22693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22696 \begin_layout Plain Layout
22704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22707 \begin_layout Plain Layout
22708 \begin_inset Formula $\le$
22718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22721 \begin_layout Plain Layout
22729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22732 \begin_layout Plain Layout
22733 \begin_inset Formula $\ll$
22743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22746 \begin_layout Plain Layout
22754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22757 \begin_layout Plain Layout
22758 \begin_inset Formula $\prec$
22768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22771 \begin_layout Plain Layout
22779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22782 \begin_layout Plain Layout
22783 \begin_inset Formula $\preceq$
22793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22796 \begin_layout Plain Layout
22804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22807 \begin_layout Plain Layout
22808 \begin_inset Formula $\subset$
22818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22821 \begin_layout Plain Layout
22829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22832 \begin_layout Plain Layout
22833 \begin_inset Formula $\subseteq$
22843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22846 \begin_layout Plain Layout
22854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22857 \begin_layout Plain Layout
22858 \begin_inset Formula $\sqsubseteq$
22868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22871 \begin_layout Plain Layout
22879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22882 \begin_layout Plain Layout
22883 \begin_inset Formula $\in$
22893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22896 \begin_layout Plain Layout
22904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22907 \begin_layout Plain Layout
22908 \begin_inset Formula $\vdash$
22918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22921 \begin_layout Plain Layout
22929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22932 \begin_layout Plain Layout
22933 \begin_inset Formula $\smile$
22943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22946 \begin_layout Plain Layout
22954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22957 \begin_layout Plain Layout
22958 \begin_inset Formula $\lhd$
22968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22971 \begin_layout Plain Layout
22979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22982 \begin_layout Plain Layout
22983 \begin_inset Formula $\unlhd$
22993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22996 \begin_layout Plain Layout
23004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23007 \begin_layout Plain Layout
23008 \begin_inset Formula $\gtrless$
23018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23021 \begin_layout Plain Layout
23029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23032 \begin_layout Plain Layout
23033 \begin_inset Formula $\mid$
23043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23046 \begin_layout Plain Layout
23054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23057 \begin_layout Plain Layout
23058 \begin_inset Formula $\nmid$
23072 \begin_inset space \hfill{}
23076 \begin_inset Tabular
23077 <lyxtabular version="3" rows="17" columns="2">
23079 <column alignment="center" valignment="top" width="0pt">
23080 <column alignment="center" valignment="top" width="0pt">
23082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23085 \begin_layout Plain Layout
23091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23094 \begin_layout Plain Layout
23102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23105 \begin_layout Plain Layout
23111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23114 \begin_layout Plain Layout
23115 \begin_inset Formula $=$
23125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23128 \begin_layout Plain Layout
23136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23139 \begin_layout Plain Layout
23140 \begin_inset Formula $\not=$
23150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23153 \begin_layout Plain Layout
23161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23164 \begin_layout Plain Layout
23165 \begin_inset Formula $\equiv$
23175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23178 \begin_layout Plain Layout
23186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23189 \begin_layout Plain Layout
23190 \begin_inset Formula $\sim$
23200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23203 \begin_layout Plain Layout
23211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23214 \begin_layout Plain Layout
23215 \begin_inset Formula $\simeq$
23225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23228 \begin_layout Plain Layout
23236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23239 \begin_layout Plain Layout
23240 \begin_inset Formula $\approx$
23250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23253 \begin_layout Plain Layout
23261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23264 \begin_layout Plain Layout
23265 \begin_inset Formula $\cong$
23275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23278 \begin_layout Plain Layout
23286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23289 \begin_layout Plain Layout
23290 \begin_inset Formula $\bowtie$
23300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23303 \begin_layout Plain Layout
23311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23314 \begin_layout Plain Layout
23315 \begin_inset Formula $\notin$
23325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23328 \begin_layout Plain Layout
23336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23339 \begin_layout Plain Layout
23340 \begin_inset Formula $\perp$
23350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23353 \begin_layout Plain Layout
23361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23364 \begin_layout Plain Layout
23365 \begin_inset Formula $\propto$
23375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23378 \begin_layout Plain Layout
23386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23389 \begin_layout Plain Layout
23390 \begin_inset Formula $\asymp$
23400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23403 \begin_layout Plain Layout
23411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23414 \begin_layout Plain Layout
23415 \begin_inset Formula $\doteq$
23425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23428 \begin_layout Plain Layout
23436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23439 \begin_layout Plain Layout
23440 \begin_inset Formula $\circeq$
23450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23453 \begin_layout Plain Layout
23461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23464 \begin_layout Plain Layout
23465 \begin_inset Formula $\models$
23475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23478 \begin_layout Plain Layout
23486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23489 \begin_layout Plain Layout
23490 \begin_inset Formula $\widehat{=}$
23504 \begin_inset space \hfill{}
23508 \begin_inset Tabular
23509 <lyxtabular version="3" rows="17" columns="2">
23511 <column alignment="center" valignment="top" width="0pt">
23512 <column alignment="center" valignment="top" width="0pt">
23514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23517 \begin_layout Plain Layout
23523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23526 \begin_layout Plain Layout
23534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23537 \begin_layout Plain Layout
23543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23546 \begin_layout Plain Layout
23547 \begin_inset Formula $>$
23557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23560 \begin_layout Plain Layout
23568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23571 \begin_layout Plain Layout
23572 \begin_inset Formula $\ge$
23582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23585 \begin_layout Plain Layout
23593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23596 \begin_layout Plain Layout
23597 \begin_inset Formula $\gg$
23607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23610 \begin_layout Plain Layout
23618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23621 \begin_layout Plain Layout
23622 \begin_inset Formula $\succ$
23632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23635 \begin_layout Plain Layout
23643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23646 \begin_layout Plain Layout
23647 \begin_inset Formula $\succeq$
23657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23660 \begin_layout Plain Layout
23668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23671 \begin_layout Plain Layout
23672 \begin_inset Formula $\supset$
23682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23685 \begin_layout Plain Layout
23693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23696 \begin_layout Plain Layout
23697 \begin_inset Formula $\supseteq$
23707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23710 \begin_layout Plain Layout
23718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23721 \begin_layout Plain Layout
23722 \begin_inset Formula $\sqsupseteq$
23732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23735 \begin_layout Plain Layout
23743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23746 \begin_layout Plain Layout
23747 \begin_inset Formula $\ni$
23757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23760 \begin_layout Plain Layout
23768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23771 \begin_layout Plain Layout
23772 \begin_inset Formula $\dashv$
23782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23785 \begin_layout Plain Layout
23793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23796 \begin_layout Plain Layout
23797 \begin_inset Formula $\frown$
23807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23810 \begin_layout Plain Layout
23818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23821 \begin_layout Plain Layout
23822 \begin_inset Formula $\rhd$
23832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23835 \begin_layout Plain Layout
23843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23846 \begin_layout Plain Layout
23847 \begin_inset Formula $\unrhd$
23857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23860 \begin_layout Plain Layout
23868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23871 \begin_layout Plain Layout
23872 \begin_inset Formula $\lessgtr$
23882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23885 \begin_layout Plain Layout
23893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23896 \begin_layout Plain Layout
23897 \begin_inset Formula $\parallel$
23907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23910 \begin_layout Plain Layout
23918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23921 \begin_layout Plain Layout
23922 \begin_inset Formula $\nparallel$
23936 \begin_inset space \hfill{}
23942 \begin_layout Standard
23943 \begin_inset VSpace medskip
23958 are bigger than the equal looking operators
23973 \begin_layout Standard
23974 Relations are, in contrary to symbols, always surrounded by space.
23977 \begin_layout Standard
23978 Relations with labels can be created with the command
23988 \begin_layout Plain Layout
23999 \begin_layout Standard
24001 \begin_inset Tabular
24002 <lyxtabular version="3" rows="2" columns="2">
24004 <column alignment="center" valignment="top" width="0">
24005 <column alignment="center" valignment="top" width="0">
24007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24010 \begin_layout Plain Layout
24016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24019 \begin_layout Plain Layout
24021 \begin_inset Note Note
24024 \begin_layout Plain Layout
24031 is only used as spacer.
24043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24046 \begin_layout Plain Layout
24053 \begin_layout Plain Layout
24070 \begin_layout Plain Layout
24080 \begin_inset Formula $\downarrow$
24089 \begin_layout Plain Layout
24102 \begin_layout Plain Layout
24116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24119 \begin_layout Plain Layout
24120 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24136 \begin_layout Section
24140 \begin_layout Subsection
24141 Predefined Functions
24142 \begin_inset CommandInset label
24144 name "sub:Predefined-Functions"
24152 \begin_layout Plain Layout
24153 Functions ! predefined
24161 \begin_layout Standard
24162 In general, variables are set
24166 in mathematical expressions, but not function names, because
24167 \begin_inset Formula $sin$
24170 could be misunderstood as
24171 \begin_inset Formula $s\cdot i\cdot n$
24175 Therefore there are predefined functions, that are additionally a bit separated
24177 They are inserted as commands starting with a backslash before their name.
24180 \begin_layout Standard
24182 \begin_inset Tabular
24183 <lyxtabular version="3" rows="2" columns="4">
24185 <column alignment="center" valignment="top" width="0pt">
24186 <column alignment="center" valignment="top" width="0pt">
24187 <column alignment="center" valignment="top" width="0pt">
24188 <column alignment="center" valignment="top" width="0pt">
24190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24193 \begin_layout Plain Layout
24199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24202 \begin_layout Plain Layout
24208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24211 \begin_layout Plain Layout
24217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24220 \begin_layout Plain Layout
24228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24231 \begin_layout Plain Layout
24237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24240 \begin_layout Plain Layout
24241 \begin_inset Formula $Asin(x)+B$
24249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24252 \begin_layout Plain Layout
24260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24263 \begin_layout Plain Layout
24264 \begin_inset Formula $A\sin(x)+B$
24280 \begin_layout Standard
24281 The following functions are predefined:
24284 \begin_layout Standard
24285 \begin_inset VSpace -2mm
24291 \begin_layout Standard
24293 \begin_inset Tabular
24294 <lyxtabular version="3" rows="9" columns="4">
24296 <column alignment="center" valignment="top" width="0pt">
24297 <column alignment="center" valignment="top" width="0pt">
24298 <column alignment="center" valignment="top" width="0pt">
24299 <column alignment="center" valignment="top" width="0pt">
24301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24304 \begin_layout Plain Layout
24310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24313 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24322 \begin_layout Plain Layout
24328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24331 \begin_layout Plain Layout
24339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24342 \begin_layout Plain Layout
24350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24353 \begin_layout Plain Layout
24361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24364 \begin_layout Plain Layout
24372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24375 \begin_layout Plain Layout
24385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24388 \begin_layout Plain Layout
24396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24399 \begin_layout Plain Layout
24407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24410 \begin_layout Plain Layout
24418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24421 \begin_layout Plain Layout
24431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24434 \begin_layout Plain Layout
24442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24445 \begin_layout Plain Layout
24453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24456 \begin_layout Plain Layout
24464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24467 \begin_layout Plain Layout
24477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24480 \begin_layout Plain Layout
24488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24491 \begin_layout Plain Layout
24499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24502 \begin_layout Plain Layout
24510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24513 \begin_layout Plain Layout
24523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24526 \begin_layout Plain Layout
24534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24537 \begin_layout Plain Layout
24545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24548 \begin_layout Plain Layout
24556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24559 \begin_layout Plain Layout
24569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24572 \begin_layout Plain Layout
24580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24583 \begin_layout Plain Layout
24591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24594 \begin_layout Plain Layout
24602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24605 \begin_layout Plain Layout
24615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24618 \begin_layout Plain Layout
24626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24629 \begin_layout Plain Layout
24637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24640 \begin_layout Plain Layout
24648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24651 \begin_layout Plain Layout
24661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24664 \begin_layout Plain Layout
24672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24675 \begin_layout Plain Layout
24683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24686 \begin_layout Plain Layout
24694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24697 \begin_layout Plain Layout
24713 \begin_layout Standard
24714 They can also be inserted with the math toolbar button
24715 \begin_inset Graphics
24716 filename ../images/math/functions.png
24724 \begin_layout Subsection
24725 Self-defined Functions
24729 \begin_layout Plain Layout
24730 Functions ! self-defined
24738 \begin_layout Standard
24739 To use a function that is not predefined, like for example the sign function
24740 sgn(x), there are two possibilities:
24743 \begin_layout Itemize
24744 Define the function by inserting the following line to the LaTeX-preamble
24748 \begin_layout Plain Layout
24753 DeclareMathOperator
24756 \begin_inset CommandInset ref
24758 reference "sub:Self-defined-Operators"
24768 \begin_inset Newline newline
24772 \begin_inset VSpace -3mm
24776 \begin_inset Newline newline
24783 DeclareMathOperator{
24791 \begin_layout Plain Layout
24796 DeclareMathOperator
24802 \begin_inset Newline newline
24806 \begin_inset VSpace -2mm
24810 \begin_inset Newline newline
24813 Now the new defined function can be called with the command
24822 \begin_layout Itemize
24823 Write the the formula as usual, mark the formula name, in our example the
24828 , and change it to mathematical text.
24829 At last a space is inserted between prefactor and function.
24832 \begin_layout Standard
24833 The result is the same with both methods as with a predefined function
24837 \begin_layout Plain Layout
24838 In LyX self-defined functions are displayed red, predefined ones black.
24846 \begin_layout Standard
24848 \begin_inset Tabular
24849 <lyxtabular version="3" rows="3" columns="2">
24851 <column alignment="center" valignment="top" width="0pt">
24852 <column alignment="center" valignment="top" width="0pt">
24854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24857 \begin_layout Plain Layout
24863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24866 \begin_layout Plain Layout
24874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24877 \begin_layout Plain Layout
24885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24888 \begin_layout Plain Layout
24889 \begin_inset Formula $A\sgn(x)+B$
24899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24902 \begin_layout Plain Layout
24906 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24917 \begin_layout Plain Layout
24918 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24934 \begin_layout Standard
24935 The first method is more suitable when the self-defined function should
24936 be used several times.
24939 \begin_layout Subsection
24944 \begin_layout Plain Layout
24953 \begin_layout Standard
24954 For limits there are defined besides
24964 \begin_layout Plain Layout
24984 furthermore the following functions:
24987 \begin_layout Standard
24989 \begin_inset Tabular
24990 <lyxtabular version="3" rows="5" columns="2">
24992 <column alignment="center" valignment="top" width="0">
24993 <column alignment="center" valignment="top" width="0">
24995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24998 \begin_layout Plain Layout
25004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25007 \begin_layout Plain Layout
25009 \begin_inset Note Note
25012 \begin_layout Plain Layout
25019 is only used as spacer.
25031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25034 \begin_layout Plain Layout
25042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25045 \begin_layout Plain Layout
25046 \begin_inset Formula $\varliminf$
25056 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25059 \begin_layout Plain Layout
25067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25070 \begin_layout Plain Layout
25071 \begin_inset Formula $\varlimsup$
25081 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25084 \begin_layout Plain Layout
25092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25095 \begin_layout Plain Layout
25096 \begin_inset Formula $\varprojlim$
25106 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25109 \begin_layout Plain Layout
25117 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25120 \begin_layout Plain Layout
25121 \begin_inset Formula $\varinjlim$
25125 \begin_inset Formula $\raisebox{-2.5mm}{}$
25141 \begin_layout Standard
25142 \begin_inset VSpace medskip
25145 The limit is created by inserting a subscript.
25146 It is set right beside the function in an inline formula:
25149 \begin_layout Standard
25151 \begin_inset Tabular
25152 <lyxtabular version="3" rows="2" columns="2">
25154 <column alignment="center" valignment="top" width="0pt">
25155 <column alignment="center" valignment="top" width="0pt">
25157 <cell alignment="center" valignment="top" usebox="none">
25160 \begin_layout Plain Layout
25166 <cell alignment="center" valignment="top" usebox="none">
25169 \begin_layout Plain Layout
25170 \begin_inset space \hspace{}
25175 \begin_inset Note Note
25178 \begin_layout Plain Layout
25191 are used here as spacer.
25203 <cell alignment="center" valignment="top" usebox="none">
25206 \begin_layout Plain Layout
25215 \begin_layout Plain Layout
25228 \begin_layout Plain Layout
25242 <cell alignment="center" valignment="top" usebox="none">
25245 \begin_layout Plain Layout
25246 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25262 \begin_layout Standard
25263 In a displayed formula the limit is set below the formula, as usual:
25264 \begin_inset Formula \[
25272 \begin_layout Subsection
25277 \begin_layout Plain Layout
25278 Functions ! modulo-
25286 \begin_layout Standard
25287 The modulo-function is special, because it exists in four variants.
25290 \begin_layout Standard
25291 The variants in a displayed formula:
25292 \begin_inset Formula \begin{align*}
25293 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25294 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25295 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25296 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25297 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25304 \begin_layout Standard
25305 In an inline formula less space is set before the function names for all
25309 \begin_layout Section
25314 \begin_layout Plain Layout
25323 \begin_layout Subsection
25324 Special Characters in Mathematical Text
25327 \begin_layout Standard
25328 The following commands can only be used in mathematical text or in TeX-mode:
25331 \begin_layout Standard
25332 \begin_inset space \hfill{}
25336 \begin_inset Tabular
25337 <lyxtabular version="3" rows="8" columns="2">
25339 <column alignment="block" valignment="top" width="0">
25340 <column alignment="block" valignment="top" width="0">
25342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25345 \begin_layout Plain Layout
25351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25354 \begin_layout Plain Layout
25362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25365 \begin_layout Plain Layout
25373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25376 \begin_layout Plain Layout
25377 \begin_inset Formula $\textrm{œ}$
25387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25390 \begin_layout Plain Layout
25398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25401 \begin_layout Plain Layout
25402 \begin_inset Formula $\textrm{Œ}$
25412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25415 \begin_layout Plain Layout
25423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25426 \begin_layout Plain Layout
25427 \begin_inset Formula $\textrm{æ}$
25437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25440 \begin_layout Plain Layout
25448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25451 \begin_layout Plain Layout
25452 \begin_inset Formula $\textrm{Æ}$
25462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25465 \begin_layout Plain Layout
25473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25476 \begin_layout Plain Layout
25477 \begin_inset Formula $\textrm{\aa}$
25487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25490 \begin_layout Plain Layout
25497 \begin_layout Plain Layout
25504 \begin_layout Plain Layout
25525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25528 \begin_layout Plain Layout
25529 \begin_inset Formula $\textrm{Å}$
25539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25542 \begin_layout Plain Layout
25550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25553 \begin_layout Plain Layout
25554 \begin_inset Formula $\textrm{ı}$
25568 \begin_inset space \hfill{}
25572 \begin_inset Tabular
25573 <lyxtabular version="3" rows="8" columns="2">
25575 <column alignment="block" valignment="top" width="0">
25576 <column alignment="center" valignment="top" width="0">
25578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25581 \begin_layout Plain Layout
25583 \begin_inset Note Note
25586 \begin_layout Plain Layout
25593 is used for separation, because otherwise the output will be ¡ and ¿ respective
25604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25607 \begin_layout Plain Layout
25615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25618 \begin_layout Plain Layout
25626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25629 \begin_layout Plain Layout
25630 \begin_inset Formula $\textrm{ø}$
25640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25643 \begin_layout Plain Layout
25651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25654 \begin_layout Plain Layout
25655 \begin_inset Formula $\textrm{Ø}$
25665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25668 \begin_layout Plain Layout
25676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25679 \begin_layout Plain Layout
25680 \begin_inset Formula $\textrm{ł}$
25690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25693 \begin_layout Plain Layout
25701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25704 \begin_layout Plain Layout
25705 \begin_inset Formula $\textrm{Ł}$
25715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25718 \begin_layout Plain Layout
25720 \begin_inset space \hspace{}
25728 \begin_layout Plain Layout
25742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25745 \begin_layout Plain Layout
25746 \begin_inset Formula $\textrm{!`}$
25756 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25759 \begin_layout Plain Layout
25761 \begin_inset space \hspace{}
25769 \begin_layout Plain Layout
25783 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25786 \begin_layout Plain Layout
25787 \begin_inset Formula $\textrm{?`}$
25797 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25800 \begin_layout Plain Layout
25808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25811 \begin_layout Plain Layout
25812 \begin_inset Formula $\textrm{ȷ}$
25826 \begin_inset space \hfill{}
25832 \begin_layout Standard
25834 \begin_inset Formula $\textrm{\textrm{Å}}$
25838 \begin_inset Formula $\textrm{\textrm{Ø}}$
25841 can also be inserted via the math toolbar button
25842 \begin_inset Graphics
25843 filename ../images/math/digamma.png
25851 \begin_layout Standard
25852 An exception are the commands
25855 \begin_inset space \hspace{}
25864 \begin_inset space \hspace{}
25870 , because they can be inserted in LyX directly to text.
25873 \begin_layout Subsection
25875 \begin_inset CommandInset label
25877 name "sub:Accents-in-Text"
25885 \begin_layout Plain Layout
25894 \begin_layout Standard
25895 With the following commands all letters can be accented.
25896 The commands must be inserted in TeX-mode.
25899 \begin_layout Standard
25900 \begin_inset space \hfill{}
25904 \begin_inset Tabular
25905 <lyxtabular version="3" rows="8" columns="2">
25907 <column alignment="block" valignment="top" width="0">
25908 <column alignment="block" valignment="top" width="0">
25910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25913 \begin_layout Plain Layout
25919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25922 \begin_layout Plain Layout
25930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25933 \begin_layout Plain Layout
25937 \begin_inset Quotes grd
25945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25948 \begin_layout Plain Layout
25952 \begin_layout Plain Layout
25968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25971 \begin_layout Plain Layout
25979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25982 \begin_layout Plain Layout
25986 \begin_layout Plain Layout
26002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26005 \begin_layout Plain Layout
26012 \begin_layout Plain Layout
26026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26029 \begin_layout Plain Layout
26033 \begin_layout Plain Layout
26049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26052 \begin_layout Plain Layout
26060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26063 \begin_layout Plain Layout
26067 \begin_layout Plain Layout
26083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26086 \begin_layout Plain Layout
26093 \begin_layout Plain Layout
26107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26110 \begin_layout Plain Layout
26114 \begin_layout Plain Layout
26130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26133 \begin_layout Plain Layout
26140 \begin_layout Plain Layout
26154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26157 \begin_layout Plain Layout
26161 \begin_layout Plain Layout
26177 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26180 \begin_layout Plain Layout
26187 \begin_layout Plain Layout
26201 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26204 \begin_layout Plain Layout
26208 \begin_layout Plain Layout
26228 \begin_inset space \hfill{}
26232 \begin_inset Tabular
26233 <lyxtabular version="3" rows="8" columns="2">
26235 <column alignment="block" valignment="top" width="0">
26236 <column alignment="center" valignment="top" width="0">
26238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26241 \begin_layout Plain Layout
26247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26250 \begin_layout Plain Layout
26258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26261 \begin_layout Plain Layout
26268 \begin_layout Plain Layout
26282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26285 \begin_layout Plain Layout
26289 \begin_layout Plain Layout
26305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26308 \begin_layout Plain Layout
26316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26319 \begin_layout Plain Layout
26323 \begin_layout Plain Layout
26339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26342 \begin_layout Plain Layout
26349 \begin_layout Plain Layout
26360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26363 \begin_layout Plain Layout
26367 \begin_layout Plain Layout
26383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26386 \begin_layout Plain Layout
26394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26397 \begin_layout Plain Layout
26401 \begin_layout Plain Layout
26417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26420 \begin_layout Plain Layout
26427 \begin_layout Plain Layout
26441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26444 \begin_layout Plain Layout
26448 \begin_layout Plain Layout
26464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26467 \begin_layout Plain Layout
26474 \begin_layout Plain Layout
26488 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26491 \begin_layout Plain Layout
26495 \begin_layout Plain Layout
26511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26514 \begin_layout Plain Layout
26521 \begin_layout Plain Layout
26535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26538 \begin_layout Plain Layout
26542 \begin_layout Plain Layout
26562 \begin_inset space \hfill{}
26568 \begin_layout Standard
26569 \begin_inset VSpace medskip
26578 also two different characters can be accented.
26587 \begin_layout Plain Layout
26602 \begin_layout Plain Layout
26614 \begin_layout Standard
26627 can in combination with vowels directly be inserted with the keyboard without
26629 The same applies for the tilde
26633 \begin_layout Plain Layout
26634 This only applies for keyboards where the tilde is defined as accent.
26643 in combination with
26658 \begin_layout Standard
26701 , and accents inserted directly with the keyboard are also available in
26703 For the other accents there are special math commands to be used in formulas,
26705 \begin_inset CommandInset ref
26707 reference "sub:Accents-for-one"
26714 \begin_layout Standard
26715 \begin_inset VSpace bigskip
26718 Furthermore, with the command
26728 \begin_layout Plain Layout
26736 all numbers and letters can be set into a circle, quasi accented with a
26737 circle, similar to the the copyright symbol.
26740 \begin_layout Standard
26742 \begin_inset Tabular
26743 <lyxtabular version="3" rows="3" columns="2">
26745 <column alignment="center" valignment="top" width="0">
26746 <column alignment="center" valignment="top" width="0">
26748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26751 \begin_layout Plain Layout
26757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26760 \begin_layout Plain Layout
26762 \begin_inset Note Note
26765 \begin_layout Plain Layout
26772 is only used as spacer.
26784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26787 \begin_layout Plain Layout
26795 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26798 \begin_layout Plain Layout
26802 \begin_layout Plain Layout
26818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26821 \begin_layout Plain Layout
26832 raisebox{-1.5pt}{W}}
26837 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26840 \begin_layout Plain Layout
26841 \begin_inset Formula $\raisebox{4.5mm}{}$
26848 \begin_layout Plain Layout
26866 \begin_inset Formula $\raisebox{-2mm}{}$
26882 \begin_layout Standard
26883 One has to take care that the character fits in the circle.
26894 \begin_layout Plain Layout
26896 \begin_inset CommandInset ref
26898 reference "sub:Font-Sizes"
26907 specifies thereby the size of the circle.
26918 \begin_layout Plain Layout
26920 \begin_inset CommandInset ref
26922 reference "sub:Boxes-without-Frame"
26931 the character can be centered.
26934 \begin_layout Subsection
26939 \begin_layout Plain Layout
26948 \begin_layout Standard
26949 Minuscule numbers are created with the command
26959 \begin_layout Plain Layout
26968 The command can be used in formulas and in TeX-mode.
26969 The command scheme is:
26972 \begin_layout Standard
26977 oldstylenums{number}
26980 \begin_layout Standard
26985 oldstylenums{0123456789
26988 \begin_inset Formula $\oldstylenums{0123456789}$
26994 \begin_layout Subsection
26995 Miscellaneous special Characters
26996 \begin_inset CommandInset label
26998 name "sub:Miscellaneous-special-Characters"
27006 \begin_layout Plain Layout
27007 Special characters ! miscellaneous
27015 \begin_layout Standard
27016 The following characters can only be inserted to formulas by using commands:
27019 \begin_layout Standard
27021 \begin_inset Tabular
27022 <lyxtabular version="3" rows="4" columns="2">
27024 <column alignment="center" valignment="top" width="0">
27025 <column alignment="center" valignment="top" width="0">
27027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27030 \begin_layout Plain Layout
27036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27039 \begin_layout Plain Layout
27047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27050 \begin_layout Plain Layout
27057 \begin_layout Plain Layout
27071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27074 \begin_layout Plain Layout
27075 \begin_inset Formula $\mathcircumflex$
27085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27088 \begin_layout Plain Layout
27096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27099 \begin_layout Plain Layout
27100 \begin_inset Formula $\_$
27110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27113 \begin_layout Plain Layout
27118 \begin_layout Plain Layout
27133 \begin_layout Plain Layout
27146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27149 \begin_layout Plain Layout
27150 \begin_inset Formula $^{\circ}$
27166 \begin_layout Standard
27167 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27168 contains the following line
27172 \begin_layout Plain Layout
27173 More about this is described in
27174 \begin_inset CommandInset ref
27176 reference "sub:Text-Characters-in"
27188 \begin_layout Standard
27193 DeclareInputtext{176}{
27206 \begin_layout Section
27208 \begin_inset CommandInset label
27210 name "sec:Formula-Styles"
27218 \begin_layout Plain Layout
27227 \begin_layout Itemize
27228 There are two different alignment styles:
27232 \begin_layout Description
27233 Centered is the predefined standard
27236 \begin_layout Description
27237 Indented for this the option
27241 must be inserted in the menu
27243 Document\SpecialChar \menuseparator
27249 \begin_inset space ~
27255 \begin_layout Standard
27260 is used, the indentation can be adjusted with the length
27270 \begin_layout Plain Layout
27279 Should the distance be 15
27280 \begin_inset space \thinspace{}
27283 mm, the following command line is inserted in the LaTeX-preamble
27286 \begin_layout Standard
27296 \begin_layout Standard
27297 When no length is specified, the predefined value of 30
27298 \begin_inset space \thinspace{}
27305 \begin_layout Itemize
27306 And two different numbering styles:
27310 \begin_layout Description
27311 Right is the predefined standard
27314 \begin_layout Description
27315 Left for this the option
27319 must be inserted in the menu
27321 Document\SpecialChar \menuseparator
27327 \begin_inset space ~
27334 \begin_layout Standard
27343 can also be used together.
27344 In this case both options are inserted, separated by a comma.
27347 \begin_layout Standard
27348 The chosen styles are used for all displayed formulas of the document.
27349 When both, centered and indented formulas should be created in a document,
27355 The indented formulas are then set in a flalign environment, see
27356 \begin_inset CommandInset ref
27358 reference "sub:Flalign-Environment"
27365 \begin_layout Section
27367 \begin_inset CommandInset label
27369 name "sec:Multiline-Formulas"
27377 \begin_layout Plain Layout
27378 Formula ! multiline
27386 \begin_layout Subsection
27390 \begin_layout Standard
27391 In LyX multiline formulas are created by pressing
27398 This creates either an
27400 eqnarray environment
27402 that is described in
27403 \begin_inset CommandInset ref
27405 reference "sub:Eqnarray-Environment"
27409 or, when the option
27411 Use AMS math package
27413 in the document settings is selected, an
27417 that is described in
27418 \begin_inset CommandInset ref
27420 reference "sub:Standard-align-Environment"
27427 \begin_layout Standard
27428 There are other multiline formula environments that can be created via the
27431 Insert\SpecialChar \menuseparator
27435 These environments are described in the following sections.
27438 \begin_layout Standard
27439 In all multiline formula environments a new line is created by pressing
27445 To add or delete lines, the math toolbar buttons
27446 \begin_inset Graphics
27447 filename ../images/tabular-feature_append-row.png
27453 \begin_inset Graphics
27454 filename ../images/tabular-feature_delete-row.png
27459 , respectively, or the menu
27461 Edit\SpecialChar \menuseparator
27467 \begin_layout Subsubsection
27469 \begin_inset CommandInset label
27471 name "sub:Line-Separation"
27479 \begin_layout Plain Layout
27480 Formula ! multiline ! Line separation
27488 \begin_layout Standard
27489 There is sometimes not enough space in multiline formulas between the lines:
27490 \begin_inset Formula \begin{eqnarray*}
27491 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}\\
27492 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*}
27499 \begin_layout Standard
27500 In LaTeX additional line space is specified as optional argument of the
27502 This is not yet possible in LyX
27506 \begin_layout Plain Layout
27508 \begin_inset CommandInset href
27510 name "LyX-bug #1505"
27511 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27520 , therefore the whole formula must be inserted in TeX-mode.
27521 To add in our example space, the command
27529 is inserted at the end of the first line.
27534 \begin_layout Plain Layout
27541 \begin_layout Plain Layout
27543 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27546 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27553 \begin_layout Plain Layout
27557 left(B^{2}+x_{0}^{2}
27565 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27570 \begin_layout Plain Layout
27582 \begin_layout Standard
27583 \begin_inset VSpace bigskip
27586 To set the the line separation for all lines in a formula, the length
27596 \begin_layout Plain Layout
27606 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27617 \begin_inset space \thinspace{}
27622 \begin_inset space \thinspace{}
27625 mm additional line separation as in the previous example, the command
27628 \begin_layout Standard
27638 \begin_layout Standard
27639 is inserted in TeX-mode before the formula.
27640 This requires that the LaTeX-package
27648 \begin_layout Plain Layout
27653 is part of every LaTeX standard installation.
27662 \begin_layout Plain Layout
27668 was loaded in LaTeX-preamble with the line
27671 \begin_layout Standard
27679 \begin_layout Standard
27684 \begin_layout Plain Layout
27696 \begin_inset Formula \begin{eqnarray*}
27697 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}\\
27698 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*}
27705 \begin_layout Standard
27709 \begin_layout Plain Layout
27720 To get back to the predefined distance,
27726 is set to the value 3
27727 \begin_inset space \thinspace{}
27733 \begin_layout Subsubsection
27735 \begin_inset CommandInset label
27737 name "sub:Column-Separation"
27745 \begin_layout Plain Layout
27746 Formula ! multiline ! Column separation
27754 \begin_layout Standard
27755 Multiline formulas form a matrix.
27756 A formula in the eqnarray environment is for example a matrix with three
27758 By changing the column separation in this environment, the space beside
27759 the relation sign can be changed.
27762 \begin_layout Standard
27763 The column separation is specified with the length
27773 \begin_layout Plain Layout
27782 \begin_inset Newline newline
27785 column separation = 2
27786 \begin_inset space \thinspace{}
27796 \begin_inset Newline newline
27802 \begin_layout Standard
27812 \begin_layout Standard
27813 inserted in TeX-mode, sets for all following formulas a column separation
27815 \begin_inset space \thinspace{}
27819 To get back to the predefined distance,
27826 \begin_inset space \thinspace{}
27832 \begin_layout Standard
27834 \begin_inset space \thinspace{}
27837 cm column separation:
27841 \begin_layout Plain Layout
27853 \begin_inset Formula \begin{eqnarray*}
27855 C & \ne & A\end{eqnarray*}
27859 A formula with the predefined column separation for matrices of 10
27860 \begin_inset space \thinspace{}
27867 \begin_layout Plain Layout
27879 \begin_inset Formula \begin{eqnarray*}
27881 C & \ne & A\end{eqnarray*}
27888 \begin_layout Subsubsection
27893 \begin_layout Plain Layout
27902 \begin_layout Standard
27903 Long formulas can be typeset using these methods:
27906 \begin_layout Itemize
27907 When one side of the equation is much shorther than the line width, this
27908 one is chosen for the left side and the right side is typeset over two
27913 \begin_layout Plain Layout
27923 \begin_inset Formula \begin{eqnarray}
27924 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 \\
27925 & & -\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}
27933 \begin_layout Plain Layout
27943 \begin_inset Newline newline
27946 The minus sign at the beginning of the second line does normally not appear
27947 as operator because it is the first character of the line.
27948 Thus it would not be surrounded by space and could not be distinguished
27949 from the fraction bar.
27950 To avoid this, space was inserted behind the minus sign with the command
27961 \begin_layout Plain Layout
27969 \begin_inset CommandInset ref
27971 reference "sub:Variable-Space"
27984 \begin_layout Plain Layout
27995 \begin_layout Itemize
27996 When both sides of the equation are too long, the command
28006 \begin_layout Plain Layout
28015 It is inserted to the first column of the first line and effects that all
28016 further insertions overwrite the following columns:
28020 \begin_layout Plain Layout
28030 \begin_inset Formula \begin{eqnarray}
28031 \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 \\
28032 & & -\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 \\
28033 & & =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}
28041 \begin_layout Plain Layout
28051 \begin_inset Newline newline
28054 After the insertion of
28060 , the cursor is in a purple box that is a bit shifted to the left from the
28062 In this the formula is inserted.
28066 \begin_layout Plain Layout
28076 \begin_inset Newline newline
28079 The content of the further lines is inserted to the second or another formula
28081 The greater the column number where it was inserted, the larger the indentation.
28085 \begin_layout Plain Layout
28095 \begin_inset Newline newline
28099 \begin_inset Note Greyedout
28102 \begin_layout Plain Layout
28103 Note the following when using
28112 \begin_layout Itemize
28113 The formula doesn't use the full page width.
28115 \begin_inset space \thinspace{}
28119 \begin_inset space ~
28123 \begin_inset Formula $-B^{2}$
28126 is added to the first line in the above example, it would have been outside
28128 To better use the width, negative space can be inserted at the beginning
28132 \begin_layout Itemize
28133 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28138 \begin_layout Plain Layout
28139 \begin_inset CommandInset href
28141 name "LyX-bug #1429"
28142 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28151 One can only set the cursor at the beginning of the line and move it with
28160 \begin_layout Itemize
28161 Other methods to set long formulas are offered by the environments described
28163 \begin_inset CommandInset ref
28165 reference "sub:Multline-Environment"
28170 \begin_inset CommandInset ref
28172 reference "sub:Multiline-Formula-Parts"
28179 \begin_layout Subsubsection
28181 \begin_inset CommandInset label
28183 name "sub:Multiline-Brackets"
28191 \begin_layout Plain Layout
28192 Brackets ! for multiline expressions
28200 \begin_layout Standard
28201 For brackets spanning multiple lines the following problem occurs:
28202 \begin_inset Formula \begin{eqnarray*}
28203 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28204 & & \left.\cdots+B-D\right]\end{eqnarray*}
28211 \begin_layout Standard
28212 The closing bracket is smaller than the opening bracket because brackets
28213 with variable size may not span multiple lines.
28216 \begin_layout Standard
28217 To set the bracket size for the second line correctly, the first line is
28228 \begin_layout Plain Layout
28236 and the second line with
28244 \begin_layout Plain Layout
28258 \begin_inset CommandInset ref
28260 reference "sub:Automatic-Bracket-Size"
28275 \begin_layout Plain Layout
28301 \begin_layout Plain Layout
28320 \begin_layout Plain Layout
28339 \begin_layout Plain Layout
28351 \begin_inset Formula $\downarrow$
28360 \begin_layout Plain Layout
28368 is inserted, because the multiplication operator with its limits is the
28369 largest symbol in the first line and this should be the size for the bracket
28370 in the second line.
28373 \begin_layout Standard
28374 The result is this:
28375 \begin_inset Formula \begin{eqnarray*}
28376 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28377 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28384 \begin_layout Subsection
28388 \begin_layout Standard
28389 Align environments can be used for every kind of multiline formulas.
28390 They are specially useful to set several formulas side by side.
28393 \begin_layout Standard
28394 Align environments consist of columns.
28395 The odd columns are right aligned, the even ones left aligned.
28396 Every line in an Align environment can be numbered.
28399 \begin_layout Standard
28400 Align environments are created via the menu
28402 Insert\SpecialChar \menuseparator
28408 Edit\SpecialChar \menuseparator
28409 Math\SpecialChar \menuseparator
28410 Change Formula Type
28412 already existing formulas can be converted to Align environments.
28415 \begin_layout Standard
28416 To add or delete columns, the math toolbar buttons
28417 \begin_inset Graphics
28418 filename ../images/tabular-feature_append-column.png
28424 \begin_inset Graphics
28425 filename ../images/tabular-feature_delete-column.png
28430 , respectively, or the menu
28432 Edit\SpecialChar \menuseparator
28438 \begin_layout Subsubsection
28439 Standard align Environment
28440 \begin_inset CommandInset label
28442 name "sub:Standard-align-Environment"
28450 \begin_layout Plain Layout
28451 Formula ! multiline ! align environment
28459 \begin_layout Standard
28460 This Align environment is created by presssing
28464 in a formula or by the menu
28466 Insert\SpecialChar \menuseparator
28467 Math\SpecialChar \menuseparator
28468 AMS align Environment
28473 \begin_layout Standard
28474 An example for two formulas set side by side, that are created with a four
28475 column align environment:
28476 \begin_inset Formula \begin{align*}
28477 A & =\sin(B) & C & =D\\
28478 C & \ne A & B & \ne D\end{align*}
28482 As it can be seen, the formulas in this environment are placed so as if
28491 \begin_layout Plain Layout
28499 \begin_inset CommandInset ref
28501 reference "sub:Variable-Space"
28512 before the first and after every even column.
28513 When the formula style
28519 \begin_layout Plain Layout
28521 \begin_inset CommandInset ref
28523 reference "sec:Formula-Styles"
28534 is used, the formula is set without the
28540 before the first column.
28543 \begin_layout Subsubsection
28544 Alignat Environment
28548 \begin_layout Plain Layout
28549 Formula ! multiline ! alignat environment
28557 \begin_layout Standard
28558 The alignat environment has no predefined column separation.
28559 It can be inserted manually with the spaces that are described
28560 \begin_inset CommandInset ref
28562 reference "sub:Space"
28569 \begin_layout Standard
28570 The above example in the alignat environment where 1
28571 \begin_inset space \thinspace{}
28574 cm space was inserted at the beginning of the second formula:
28575 \begin_inset Formula \begin{alignat*}{2}
28576 A & =\sin(B) & \hspace{1cm}C & =D\\
28577 C & \ne A & B & \ne D\end{alignat*}
28581 Because the column separation can be set separately for every column, this
28582 environment is especially suitable to set three and more formulas side
28586 \begin_layout Subsubsection
28587 Flalign Environment
28588 \begin_inset CommandInset label
28590 name "sub:Flalign-Environment"
28598 \begin_layout Plain Layout
28599 Formula ! multiline ! flalign environment
28607 \begin_layout Standard
28608 In this environment the first two columns are always set as much as possible
28609 to the left and the last two ones to the right.
28611 \begin_inset Formula \begin{flalign*}
28612 A & =1 & B & =2 & C & =3\\
28613 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28620 \begin_layout Standard
28621 By creating a flalign environment with an odd number of columns where an
28622 empty TeX-brace is inserted to the last column, several formulas in a document
28623 can be set to the left, although the formula style
28628 As example the indented formula
28629 \begin_inset CommandInset ref
28631 reference "eq:VolInt"
28636 \begin_inset Formula \begin{flalign}
28637 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28641 The first two columns contain the formula.
28642 To indent it as with the formula style
28647 \begin_inset space \thinspace{}
28650 pt space was inserted at the beginning of the first column.
28653 \begin_layout Subsection
28654 Eqnarray Environment
28655 \begin_inset CommandInset label
28657 name "sub:Eqnarray-Environment"
28665 \begin_layout Plain Layout
28666 Formula ! multiline ! eqnarray environment
28674 \begin_layout Standard
28675 When this environment has been created, three blue boxes appear.
28676 The content of the first box is right aligned, the content of the last
28678 The content of the middle box appears centered and a bit smaller, because
28679 it is designed to insert there only relation characters.
28680 \begin_inset Formula \begin{eqnarray*}
28681 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28683 A & = & A\end{eqnarray*}
28690 \begin_layout Subsection
28695 \begin_layout Plain Layout
28696 Formula ! multiline ! gather environment
28704 \begin_layout Standard
28705 This environment consists of only one centered column.
28706 Every line can be numbered.
28707 \begin_inset Formula \begin{gather}
28709 X=\textrm{-}1\end{gather}
28716 \begin_layout Subsection
28717 Multline Environment
28718 \begin_inset CommandInset label
28720 name "sub:Multline-Environment"
28728 \begin_layout Plain Layout
28729 Formula ! multiline ! multline environment
28737 \begin_layout Standard
28738 The multline environment consists, like the gather environment, of only
28740 But the first line is left aligned, the last one right aligned.
28741 All other lines are centered.
28742 Therefore this environment is suitable for long formulas.
28744 \begin_inset CommandInset ref
28746 reference "eq:lefteqn"
28750 in the multline environment:
28751 \begin_inset Formula \begin{multline}
28752 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}\\
28753 -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}\\
28754 =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}
28761 \begin_layout Standard
28762 In the output only the last (first) line of a multline environment appears
28763 numbered when the document numbering is right (left).
28767 \begin_layout Plain Layout
28768 numbering styles see
28769 \begin_inset CommandInset ref
28771 reference "sec:Formula-Styles"
28783 \begin_layout Standard
28792 \begin_layout Plain Layout
28810 \begin_layout Plain Layout
28820 a centered line can be right or left aligned, respectively.
28821 The commands are used as follows:
28824 \begin_layout Standard
28829 shoveright{line content}
28835 shoveleft{line content}
28838 \begin_layout Standard
28839 \begin_inset VSpace medskip
28850 \begin_layout Plain Layout
28860 specifies the distance of the first line from the left page margin.
28861 Predefined is the length 0
28862 \begin_inset space \thinspace{}
28868 \begin_layout Standard
28869 As example the above formula where the command
28872 \begin_layout Standard
28882 \begin_layout Standard
28883 was inserted in TeX-mode before:
28887 \begin_layout Plain Layout
28899 \begin_inset Formula \begin{multline}
28900 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}\\
28901 \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}}\\
28902 =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}
28910 \begin_layout Plain Layout
28921 The second line was left aligned using
28930 \begin_layout Subsection
28931 Multiline Formula Parts
28932 \begin_inset CommandInset label
28934 name "sub:Multiline-Formula-Parts"
28942 \begin_layout Plain Layout
28943 Formula ! multiline ! formula parts
28951 \begin_layout Standard
28952 To display only parts of a formula with multiple lines, one of the following
28953 environments are used:
28970 They can be inserted via the menu
28972 Insert\SpecialChar \menuseparator
28975 or by using the commands described in this section.
28978 \begin_layout Standard
28979 The first three have the same properties as the corresponding multiline
28980 formula environments, but it is possible to set further formula parts beside
28983 \begin_inset Formula \[
28984 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28985 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28986 \right\} \textrm{Uncertainty relations}\]
28993 \begin_layout Standard
28994 To get this formula, a displayed formula is created where the command
29002 \begin_layout Plain Layout
29013 A purple box appears around the blue formula box where now columns and
29014 lines can be added.
29015 Outside the multiline environment other formula parts can be set, like
29019 \begin_layout Standard
29020 The aligned environment is also suitable for long formulas whose lines are
29021 horizontally aligned.
29022 Using aligned in a displayed formula has the advantage that the formula
29023 number is vertically centered behind the lines.
29025 \begin_inset CommandInset ref
29027 reference "eq:kurzlang"
29031 in the aligned environment:
29032 \begin_inset Formula \begin{equation}
29033 \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}|}\\
29034 & -\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}
29042 \begin_layout Standard
29043 To use the environments
29065 \begin_layout Plain Layout
29083 \begin_layout Plain Layout
29101 \begin_layout Plain Layout
29109 are inserted, respectively.
29110 The split environment has the same properties as the aligned environment
29111 but it can only have two columns.
29114 \begin_layout Subsection
29115 Text in multiline Formulas
29116 \begin_inset CommandInset label
29118 name "sub:Text-in-multiline"
29126 \begin_layout Plain Layout
29136 \begin_layout Plain Layout
29137 Formula ! multiline ! text
29145 \begin_layout Standard
29146 In the Align environments, and the multline and gather environment, text
29147 can be inserted that will appear in a separate line and doesn't affect
29148 the column alignment.
29149 To do this, the command
29157 \begin_layout Plain Layout
29167 is used in the following scheme:
29170 \begin_layout Standard
29178 \begin_layout Standard
29179 The text should not be longer than a line because it cannot be hyphenated.
29180 As LyX doesn't yet support
29186 directly, the text is written as mathematical text.
29193 must hereby be at the beginning of a line and appears in the output above
29195 An example where the text was inserted at the beginning of the second line:
29196 \begin_inset Formula \begin{align}
29197 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29198 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29205 \begin_layout Section
29210 \begin_layout Plain Layout
29220 \begin_layout Plain Layout
29221 Formula ! numbering|see
29225 \begin_layout Plain Layout
29236 \begin_layout Plain Layout
29251 \begin_layout Subsection
29255 \begin_layout Standard
29256 Numbered formulas can be created with the menu
29258 Insert\SpecialChar \menuseparator
29259 Math\SpecialChar \menuseparator
29261 \begin_inset space ~
29269 \begin_inset space ~
29275 Existing formulas can be numbered with the menu
29277 Edit\SpecialChar \menuseparator
29278 Math\SpecialChar \menuseparator
29280 \begin_inset space ~
29288 \begin_inset space ~
29294 The formula number is displayed in LyX behind the formula as number sign
29296 The number sign is replaced in the output by the formula number.
29299 \begin_layout Standard
29300 When numbering is turned on in multiline formulas, all lines will be numbered.
29301 But the numbering can be controlled with the menu
29303 Edit\SpecialChar \menuseparator
29304 Math\SpecialChar \menuseparator
29306 \begin_inset space ~
29310 \begin_inset space ~
29314 \begin_inset space ~
29322 \begin_inset space ~
29330 \begin_layout Standard
29331 Except of inline formulas, all formulas can be numbered with two different
29333 \begin_inset CommandInset ref
29335 reference "sec:Formula-Styles"
29342 \begin_layout Subsection
29347 \begin_layout Plain Layout
29348 Cross-references ! to formulas
29356 \begin_layout Standard
29357 All labeled formulas can be cross-referenced.
29358 A label is added by the menu
29360 Insert\SpecialChar \menuseparator
29363 or the toolbar button
29364 \begin_inset Graphics
29365 filename ../images/label-insert.png
29371 The cursor must hereby be inside a displayed formula.
29372 A dialog pops up displaying the prefix
29377 The label is inserted there behind the prefix.
29378 The predefined prefix means
29379 \begin_inset Quotes eld
29383 \begin_inset Quotes erd
29386 and makes it easier to find labels in large documents because it marks
29387 it as formula label to divide it from e.
29388 \begin_inset space \thinspace{}
29392 \begin_inset space ~
29396 To change a label, the menu
29398 Insert\SpecialChar \menuseparator
29404 \begin_layout Standard
29405 The name of the label is displayed in LyX within two parentheses behind
29407 A formula with a label is always numbered.
29410 \begin_layout Standard
29411 Cross-references are inserted via the menu
29413 Insert\SpecialChar \menuseparator
29416 or with the toolbar button
29417 \begin_inset Graphics
29418 filename ../images/dialog-show-new-inset_ref.png
29424 A formula cross-reference appears in the output as formula number.
29425 When in the cross-reference dialog window the format
29429 is chosen, the cross-reference appears in the output as formula number
29431 \begin_inset Newline newline
29434 By right-clicking on a cross-reference in LyX, one jumps to the formula
29435 that is referenced.
29438 \begin_layout Standard
29439 Here are as examples cross-references to formulas of the following subsections:
29440 \begin_inset Note Note
29443 \begin_layout Plain Layout
29444 Note the different cross-reference types.
29452 \begin_layout Standard
29454 \begin_inset CommandInset ref
29461 \begin_inset CommandInset ref
29469 \begin_inset CommandInset ref
29475 ) big Latin letters are used for the numbering in contrary to (
29476 \begin_inset CommandInset ref
29485 \begin_layout Standard
29486 \begin_inset VSpace medskip
29489 When the argument of
29497 \begin_layout Plain Layout
29505 \begin_inset CommandInset ref
29507 reference "sub:User-defined-Numbering"
29518 contains a box like in
29519 \begin_inset CommandInset ref
29521 reference "sub:Paragraph-Boxes"
29525 , the formula cannot be referenced.
29528 \begin_layout Subsection
29533 \begin_layout Plain Layout
29534 Formula numbering ! subnumbering
29542 \begin_layout Standard
29543 With the help of the commands
29547 begin{subequations}
29555 formulas can be subnumbered.
29556 Both commands are inserted in TeX-mode.
29559 \begin_layout Standard
29561 \begin_inset Formula \begin{equation}
29562 A=C-B\label{eq:a}\end{equation}
29570 \begin_layout Plain Layout
29574 addtocounter{equation}{-1}
29583 \begin_layout Plain Layout
29587 begin{subequations}
29593 \begin_inset VSpace -5mm
29597 \begin_inset Formula \begin{equation}
29598 B=C-A\label{eq:b}\end{equation}
29603 \begin_inset Formula \begin{equation}
29604 C=A+B\label{eq:c}\end{equation}
29611 \begin_layout Standard
29615 \begin_layout Plain Layout
29627 \begin_layout Standard
29628 To create the example, the following is done:
29631 \begin_layout Enumerate
29632 first formula is inserted
29635 \begin_layout Enumerate
29640 addtocounter{equation}{-1}
29642 begin{subequations}
29646 \begin_layout Plain Layout
29655 \begin_inset Newline newline
29660 is inserted after the first formula
29663 \begin_layout Enumerate
29664 second formula is inserted
29667 \begin_layout Enumerate
29668 third formula is inserted
29671 \begin_layout Enumerate
29678 is inserted after the third formula
29681 \begin_layout Standard
29682 Every formula between the commands
29694 is subnumbered as a, b,
29695 \begin_inset Newline linebreak
29698 c, \SpecialChar \ldots{}
29699 For multiline formulas every line will be subnumbered.
29700 All subnumbered formulas are treated as
29705 But as every numbered formula increases the counter
29709 by one, the command
29715 is needed to decrease it.
29716 Otherwise the formulas
29717 \begin_inset CommandInset ref
29724 \begin_inset CommandInset ref
29731 \begin_inset CommandInset ref
29737 would be numbered as
29738 \begin_inset CommandInset ref
29745 \begin_inset CommandInset ref
29752 \begin_inset CommandInset ref
29761 \begin_layout Standard
29762 By inserting the commands in TeX-mode, a space is created between the first
29765 \begin_inset space \thinspace{}
29768 mm vertical space is inserted after the command
29772 begin{subequations}
29775 When the formula style
29781 \begin_layout Plain Layout
29783 \begin_inset CommandInset ref
29785 reference "sec:Formula-Styles"
29797 \begin_inset space \thinspace{}
29800 mm space is inserted instead.
29803 \begin_layout Standard
29804 Here is an example for a multiline formula where the numbering was turned
29805 off for the second line:
29809 \begin_layout Plain Layout
29813 begin{subequations}
29819 \begin_inset Formula \begin{eqnarray}
29820 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29821 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29822 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29830 \begin_layout Plain Layout
29842 \begin_layout Subsection
29843 User-defined Numbering
29844 \begin_inset CommandInset label
29846 name "sub:User-defined-Numbering"
29854 \begin_layout Plain Layout
29855 Formula numbering ! user-defined
29863 \begin_layout Standard
29867 \begin_layout Plain Layout
29868 Formula numbering ! self-defined delimiters
29873 With the standard numbering parentheses are set around the formula number.
29874 To replace the parentheses for example by vertical bars, the following
29875 line is added to the LaTeX-preamble:
29878 \begin_layout Standard
29890 \begin_inset Note Note
29893 \begin_layout Plain Layout
29894 This macro is already declared in the LaTeX-preamble for testing.
29895 To activate it, remove the percent sign at the beginning.
29903 \begin_layout Standard
29904 To use other characters, the vertical bars besides the
29908 are replaced by one ore more characters.
29909 To get only the formula number the vertical bars are omitted.
29912 \begin_layout Standard
29913 \begin_inset VSpace bigskip
29916 When there should be an expression of your choice instead of the consecutive
29917 formula number in parentheses behind the formula, the command
29927 \begin_layout Plain Layout
29936 \begin_inset Formula \begin{equation}
29937 A+B=C\tag{something}\label{eq:tag}\end{equation}
29941 In this example the command
29949 \begin_layout Plain Layout
29960 was inserted to the formula.
29963 \begin_layout Standard
29972 \begin_layout Plain Layout
29983 is inserted instead, the star prevents the parentheses around the expression:
29984 \begin_inset Formula \[
29985 A+B=C\tag*{something}\]
29992 \begin_layout Standard
29993 \begin_inset VSpace bigskip
29996 To restart the formula numbering with new document parts or sections, the
29997 following command is used:
30000 \begin_layout Standard
30005 @addtoreset{equation}{part}
30011 \begin_layout Plain Layout
30016 \begin_layout Plain Layout
30027 \begin_layout Plain Layout
30040 \begin_layout Plain Layout
30051 \begin_layout Plain Layout
30064 \begin_inset Newline newline
30068 \begin_inset Newline newline
30075 @addtoreset{equation}{section}
30078 \begin_layout Standard
30079 To be able to use these commands in TeX-mode, the
30080 \begin_inset Quotes eld
30084 \begin_inset Quotes erd
30087 character has to be made
30088 \begin_inset Quotes eld
30092 \begin_inset Quotes erd
30095 for LaTeX using the command
30109 So the command sequence in TeX-mode is:
30112 \begin_layout Standard
30118 \begin_inset Newline newline
30123 @addtoreset{equation}{section}
30124 \begin_inset Newline newline
30132 \begin_layout Standard
30133 In the LaTeX-preamble
30145 can be omitted as they are automatically internally inserted by LyX.
30148 \begin_layout Standard
30163 \begin_layout Plain Layout
30168 is part of the LaTeX-package
30176 \begin_layout Plain Layout
30177 Packages ! carlisle
30182 that is part of every LaTeX standard installation.
30191 \begin_layout Plain Layout
30192 Packages ! remreset
30197 has to be loaded in the LaTeX-preamble with the line
30200 \begin_layout Standard
30205 usepackage{remreset}
30208 \begin_layout Standard
30219 \begin_layout Plain Layout
30224 \begin_layout Plain Layout
30235 \begin_layout Plain Layout
30248 \begin_layout Plain Layout
30259 \begin_layout Plain Layout
30271 can be used with the same scheme as
30280 \begin_layout Standard
30281 \begin_inset VSpace bigskip
30284 Sometimes formulas should be numbered in the following form:
30287 \begin_layout Standard
30290 (section number.formula number)
30293 \begin_layout Standard
30294 The formula number should start with every section with
30295 \begin_inset Quotes eld
30299 \begin_inset Quotes erd
30305 \begin_layout Standard
30306 For this case there is the command
30316 \begin_layout Plain Layout
30324 , which is used with the following scheme:
30327 \begin_layout Standard
30332 numberwithin{counter}{sectioning}
30335 \begin_layout Standard
30336 Counter denotes what kind of numbering is affected, sectioning denotes what
30337 number is before the dot.
30340 \begin_layout Standard
30341 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30344 \begin_layout Standard
30349 numberwithin{equation}{section}
30352 \begin_layout Standard
30353 This is the result:
30357 \begin_layout Plain Layout
30361 numberwithin{equation}{section}
30367 \begin_inset Formula \begin{equation}
30368 A+B=C\end{equation}
30375 \begin_layout Standard
30377 \begin_inset space \thinspace{}
30381 \begin_inset space ~
30384 tables so that the number of the part is the sectioning,
30385 \begin_inset Newline newline
30392 numberwithin{table}{part}
30397 \begin_layout Standard
30398 To go back to the standard numbering or to prevent this kind of numbering
30399 when it is defined by the document class, the following command is inserted
30400 as TeX-Code or to the LaTeX-preamble:
30403 \begin_layout Standard
30416 \begin_layout Plain Layout
30430 \begin_layout Plain Layout
30446 \begin_inset Newline newline
30454 \begin_inset Newline newline
30466 \begin_layout Standard
30473 uses internally the command
30479 , described above, that also needs to be reverted.
30483 \begin_layout Plain Layout
30490 \begin_layout Plain Layout
30494 @removefromreset{equation}{section}
30497 \begin_layout Plain Layout
30509 \begin_layout Subsection
30510 Numbering with Roman Numbers and Letters
30514 \begin_layout Plain Layout
30515 Formula numbering ! with letters
30524 \begin_layout Plain Layout
30525 Formula numbering ! with Roman numbers
30533 \begin_layout Standard
30534 Formulas can also be numbered with Roman numbers and Latin letters.
30535 To number for example with small Roman numbers, the command
30538 \begin_layout Standard
30550 \begin_layout Standard
30551 is inserted before the formula in TeX-mode.
30562 \begin_layout Plain Layout
30570 redefines the predefined command
30586 \begin_layout Plain Layout
30593 has the same scheme like the command
30599 that is described in
30600 \begin_inset CommandInset ref
30602 reference "sec:User-defined-Commands"
30616 is the formula counter.
30623 is used as prefix for a counter, the value of the counter is output as
30625 When a formula is numbered, LaTeX sets internally the command
30631 behind the formula.
30640 \begin_layout Plain Layout
30650 outputs the counter as small Roman number.
30653 \begin_layout Standard
30654 All formulas behind the command
30664 are now numbered Roman.
30665 To switch to numbering with big Roman numbers, the command is inserted
30682 \begin_layout Plain Layout
30694 \begin_inset Quotes eld
30698 \begin_inset Quotes erd
30701 with small Latin letters there is the command
30711 \begin_layout Plain Layout
30719 , for big ones there is the command
30729 \begin_layout Plain Layout
30742 \begin_layout Standard
30743 \begin_inset Note Greyedout
30746 \begin_layout Plain Layout
30751 Only maximal 26 formulas can be numbered with Latin letters in one document.
30759 \begin_layout Standard
30763 \begin_layout Plain Layout
30779 \begin_layout Standard
30780 \begin_inset Formula \begin{equation}
30781 A=\textrm{small roman}\label{eq:rom}\end{equation}
30789 \begin_layout Plain Layout
30803 \begin_inset Formula \begin{equation}
30804 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30812 \begin_layout Plain Layout
30826 \begin_inset Formula \begin{equation}
30827 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30835 \begin_layout Plain Layout
30849 \begin_inset Formula \begin{equation}
30850 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30857 \begin_layout Standard
30858 To switch back to the default numbering, insert the command:
30861 \begin_layout Standard
30874 \begin_layout Plain Layout
30885 \begin_layout Standard
30889 \begin_layout Plain Layout
30903 \begin_inset Formula \begin{equation}
30904 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30911 \begin_layout Standard
30912 \begin_inset VSpace medskip
30915 As you see, formulas are numbered serially independent from the numbering
30917 When then numbering should start with
30918 \begin_inset Quotes eld
30922 \begin_inset Quotes erd
30925 when the style is changed, new equation counters have to be defined.
30926 A description about this can be found in the file
30927 \begin_inset CommandInset href
30929 target "Formula-numbering.lyx"
30936 \begin_layout Section
30937 User-defined Commands
30938 \begin_inset CommandInset label
30940 name "sec:User-defined-Commands"
30948 \begin_layout Plain Layout
30949 User-defined commands
30957 \begin_layout Standard
30958 Many LaTeX-commands are too long to be used frequently.
30959 But it is possible to define with the command
30969 \begin_layout Plain Layout
30977 new shorter commands.
30980 \begin_layout Standard
30981 The command scheme of
30990 \begin_layout Standard
30995 newcommand{new command name}[number of arguments][optional
31000 \begin_inset Newline newline
31007 \begin_layout Plain Layout
31022 \begin_layout Plain Layout
31029 {command definition}
31032 \begin_layout Standard
31033 \begin_inset Note Greyedout
31036 \begin_layout Plain Layout
31041 Assure that the name of the new command is not already used in your document
31042 or by LaTeX-packages that you use.
31043 When you for example define the command
31055 , you get an error message because
31061 is already defined as command for
31062 \begin_inset Quotes eld
31066 \begin_inset Formula $\le$
31070 \begin_inset Quotes erd
31081 \begin_layout Standard
31082 \begin_inset Note Greyedout
31085 \begin_layout Plain Layout
31090 The names of user-defined commands may only consist of Latin letters.
31098 \begin_layout Standard
31099 The number of arguments is an integer in the range 0
31100 \begin_inset space \thinspace{}
31104 \begin_inset space \thinspace{}
31107 9 and specifies how many arguments the new command should have.
31108 With the optional value a value for an optional argument can be predefined.
31109 When this is done, the
31117 rgument of the new command is automatically an optional one.
31120 \begin_layout Standard
31121 Here are some examples:
31124 \begin_layout Itemize
31125 To define the command
31137 , the LaTeX-preamble line is:
31141 \begin_layout Plain Layout
31153 \begin_inset Newline newline
31165 \begin_layout Itemize
31166 To define the command
31178 , the argument (that should be underlined) must be taken into account.
31179 For this the preamble line is:
31183 \begin_layout Plain Layout
31195 \begin_inset Newline newline
31210 \begin_layout Plain Layout
31222 \begin_inset Newline newline
31231 acts as argument placeholder, the
31235 behind it denotes that it is the placeholder for the first argument.
31238 \begin_layout Itemize
31246 \begin_inset space \thinspace{}
31250 \begin_inset space ~
31263 \begin_layout Plain Layout
31275 \begin_inset Newline newline
31284 framebox#1#2{$#3$}}
31290 \begin_layout Plain Layout
31302 \begin_inset Newline newline
31307 The two Dollar signs creates the extra formula needed for
31314 \begin_inset CommandInset ref
31316 reference "sub:Boxes-with-Frame"
31323 \begin_layout Itemize
31324 To create a new command for
31330 where the color for the box needn't to be specified, the argument for the
31331 color is defined optional:
31335 \begin_layout Plain Layout
31347 \begin_inset Newline newline
31356 fcolorbox{#2}{#1}{$#3$}}
31362 \begin_layout Plain Layout
31372 \begin_inset Newline newline
31375 When the color is not specified when using
31381 , the predefined color
31388 \begin_layout Standard
31389 A test of the new defined commands:
31392 \begin_layout Standard
31394 \begin_inset Tabular
31395 <lyxtabular version="3" rows="6" columns="2">
31397 <column alignment="center" valignment="top" width="0">
31398 <column alignment="center" valignment="top" width="0">
31400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31403 \begin_layout Plain Layout
31409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31412 \begin_layout Plain Layout
31414 \begin_inset Note Note
31417 \begin_layout Plain Layout
31424 is only used as spacer.
31436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31439 \begin_layout Plain Layout
31446 \begin_layout Plain Layout
31460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31463 \begin_layout Plain Layout
31464 \begin_inset Formula $A\gr B$
31474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31477 \begin_layout Plain Layout
31485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31488 \begin_layout Plain Layout
31489 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31502 \begin_layout Plain Layout
31506 \begin_inset Formula $\to$
31512 \begin_inset Formula $\to$
31523 \begin_layout Plain Layout
31537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31540 \begin_layout Plain Layout
31541 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31554 \begin_layout Plain Layout
31558 \begin_inset Formula $\to$
31569 \begin_layout Plain Layout
31583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31586 \begin_layout Plain Layout
31587 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31600 \begin_layout Plain Layout
31606 \begin_inset Formula $\to$
31617 \begin_layout Plain Layout
31631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31634 \begin_layout Plain Layout
31635 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31651 \begin_layout Section
31655 \begin_layout Standard
31656 LyX supports two types of commutative diagrams:
31664 that are explained in the following.
31667 \begin_layout Subsection
31672 \begin_layout Plain Layout
31681 \begin_layout Standard
31682 Diagrams of this type visualize relations by vertical and horizontal lines
31684 \begin_inset Formula \[
31685 \begin{CD}A@>>>B@>>>C\\
31687 F@<<<E@<<<D\end{CD}\]
31694 \begin_layout Standard
31695 To get them, the command
31703 \begin_layout Plain Layout
31713 is inserted to a formula.
31714 A blue box appears with two dashed lines where further commands can be
31720 a new line is created.
31721 Horizontal relations are inserted in odd, vertical in even formula lines.
31724 \begin_layout Standard
31725 To create the relations there are the following commands:
31728 \begin_layout Itemize
31733 creates a left arrow,
31744 \begin_layout Itemize
31749 creates an up arrow,
31757 a vertical equal sign
31760 \begin_layout Itemize
31766 is a placeholder for non-existent relations
31769 \begin_layout Standard
31770 All arrows can be labeled as follows:
31773 \begin_layout Itemize
31774 Is text inserted between the first and second < or >, resp., it is placed
31776 When it is inserted between the second and third one, it appears under
31780 \begin_layout Itemize
31781 When text for vertical arrows is inserted between the first and second A
31782 or V, resp., it is placed left beside the arrow.
31783 When it is inserted between the second and third one, it appears right
31785 If the text contains an A or V, these letters must be set into a TeX-brace.
31788 \begin_layout Standard
31789 As example a diagram with all possible relations:
31792 \begin_layout Standard
31793 \begin_inset Formula \[
31794 \begin{CD}A@>j>>B@>>k>C@=F\\
31796 D@<<j<E@>k>>F@=C\end{CD}\]
31803 \begin_layout Standard
31804 The command for this is:
31805 \begin_inset Newline newline
31816 \begin_layout Plain Layout
31825 A@>j>>B@>>k>C@=F Ctrl-Enter
31826 \begin_inset Newline newline
31833 \begin_layout Plain Layout
31848 \begin_layout Plain Layout
31861 \begin_layout Plain Layout
31873 \begin_inset Formula $\to$
31879 \begin_inset Newline newline
31886 \begin_layout Plain Layout
31901 \begin_layout Plain Layout
31914 \begin_layout Plain Layout
31924 \begin_layout Subsection
31929 \begin_layout Plain Layout
31930 Diagrams ! xymatrix
31938 \begin_layout Standard
31939 To be able to use xymatrices, the LaTeX-package
31944 A xymatrix is created by inserting the command
31951 Then you are able to add new matrix columns and rows like for normal matrices,
31953 \begin_inset CommandInset ref
31955 reference "sec:Matrices"
31962 \begin_layout Standard
31963 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31965 All possibilities to create commutative diagrams and decorations are explained
31966 in detail in this manual:
31967 \begin_inset CommandInset href
31969 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31976 \begin_layout Standard
31977 \begin_inset Newpage newpage
31983 \begin_layout Section
31988 \begin_layout Plain Layout
32001 \begin_layout Plain Layout
32002 Other useful math tips can be found in
32003 \begin_inset CommandInset citation
32018 \begin_layout Plain Layout
32026 \begin_inset Note Note
32029 \begin_layout Plain Layout
32032 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
32035 \begin_layout Plain Layout
32038 texorpdfstring is in section
32039 \begin_inset CommandInset ref
32041 reference "sub:Formulas-in-Section"
32054 \begin_layout Plain Layout
32064 \begin_layout Plain Layout
32069 \begin_layout Plain Layout
32076 Chemical characters
32080 \begin_layout Plain Layout
32095 \begin_layout Subsection
32096 Chemical Symbols and Equations
32097 \begin_inset CommandInset label
32099 name "sub:Chemical-Symbols-and"
32107 \begin_layout Plain Layout
32108 Chemical characters ! Symbols
32117 \begin_layout Plain Layout
32127 \begin_layout Plain Layout
32136 \begin_layout Standard
32137 An example text from chemistry:
32140 \begin_layout Quote
32142 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32145 -ion reacts with two
32146 \begin_inset Formula $\mathrm{Na^{+}}$
32149 -ions to sodium sulfate
32150 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32154 The chemical equation for this is:
32155 \begin_inset Formula \[
32156 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32163 \begin_layout Standard
32164 This chemical equation can directly be created as formula.
32165 To avoid that the symbols appear italic, everything is highlighted and
32166 changed by the shortcut
32169 \begin_inset space ~
32174 to the upright font style.
32178 \begin_layout Plain Layout
32184 \begin_inset CommandInset ref
32186 reference "sub:Font-Styles"
32198 \begin_layout Subsection
32203 \begin_layout Plain Layout
32212 \begin_layout Standard
32213 Negative numbers often look ugly in formulas because the minus sign before
32214 the number is set with the same length as the minus operator sign.
32215 When writing the negative number in normal text, the minus sign appears
32219 \begin_layout Standard
32220 Thus, the problem disappears when converting the minus sign to mathematical
32224 \begin_layout Standard
32225 An example to visualize the problem:
32228 \begin_layout Standard
32230 \begin_inset Tabular
32231 <lyxtabular version="3" rows="3" columns="2">
32233 <column alignment="right" valignment="top" width="0">
32234 <column alignment="left" valignment="top" width="0">
32236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32239 \begin_layout Plain Layout
32245 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32248 \begin_layout Plain Layout
32256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32259 \begin_layout Plain Layout
32265 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32268 \begin_layout Plain Layout
32269 \begin_inset Formula $x=-2$
32279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32282 \begin_layout Plain Layout
32288 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32291 \begin_layout Plain Layout
32292 \begin_inset Formula $x=\textrm{-}2$
32308 \begin_layout Subsection
32309 Comma as decimal Separator
32313 \begin_layout Plain Layout
32322 \begin_layout Standard
32323 In LaTeX a comma inside a formula is used, according to the English convention,
32324 as number group separator.
32325 So there will be space added behind all commas in formulas.
32328 \begin_layout Standard
32329 To avoid this, the comma is highlighted and changed to mathematical text
32333 \begin_inset space ~
32341 \begin_layout Standard
32342 To use all formula commas in the document as decimal separator, the file
32351 \begin_layout Plain Layout
32356 is part of the LaTeX-package
32364 \begin_layout Plain Layout
32369 \begin_layout Plain Layout
32392 \begin_layout Plain Layout
32398 is loaded with the LaTeX-preamble line
32401 \begin_layout Standard
32409 \begin_layout Subsection
32411 \begin_inset CommandInset label
32413 name "sub:Physical-Vectors"
32421 \begin_layout Plain Layout
32430 \begin_layout Standard
32431 Predefined vectors are offered by the LaTeX-package
32439 \begin_layout Plain Layout
32444 should be part of every LaTeX standard installation.
32453 \begin_layout Plain Layout
32459 that is loaded with the LaTeX-preamble line
32462 \begin_layout Standard
32470 \begin_layout Standard
32474 \begin_layout Plain Layout
32484 \begin_inset Note Note
32487 \begin_layout Plain Layout
32488 The following table will only be displayed when the LaTeX-package
32497 The following commands are defined:
32500 \begin_layout Standard
32502 \begin_inset Tabular
32503 <lyxtabular version="3" rows="4" columns="2">
32505 <column alignment="center" valignment="top" width="0">
32506 <column alignment="center" valignment="top" width="0">
32508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32511 \begin_layout Plain Layout
32517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32520 \begin_layout Plain Layout
32528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32531 \begin_layout Plain Layout
32541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32544 \begin_layout Plain Layout
32545 \begin_inset Formula $\Bra{\psi}$
32555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32558 \begin_layout Plain Layout
32568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32571 \begin_layout Plain Layout
32572 \begin_inset Formula $\Ket{\psi}$
32582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32585 \begin_layout Plain Layout
32597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32600 \begin_layout Plain Layout
32601 \begin_inset Formula $\Braket{\psi|\phi}$
32617 \begin_layout Standard
32624 assures that all vertical bars are set in the size of the surrounding brackets:
32625 \begin_inset Formula \[
32626 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32634 \begin_layout Plain Layout
32644 \begin_inset Note Note
32647 \begin_layout Plain Layout
32648 The following will be displayed when the LaTeX-package
32660 \begin_layout Standard
32661 You need to install the LaTeX-package
32665 to see the rest of this subsection in the output.
32668 \begin_layout Standard
32672 \begin_layout Plain Layout
32684 \begin_layout Standard
32691 can also be achieved using the command
32697 , that is described in
32698 \begin_inset CommandInset ref
32700 reference "sub:Automatic-Bracket-Size"
32707 \begin_layout Subsection
32708 Self-defined Fractions
32709 \begin_inset CommandInset label
32711 name "sub:Self-defined-Fractions"
32719 \begin_layout Plain Layout
32720 Fractions ! self-defined
32728 \begin_layout Standard
32729 To define custom commands for fractions, the command
32739 \begin_layout Plain Layout
32747 is used in the following scheme:
32750 \begin_layout Standard
32763 bracket}{fraction bar thickness}{style}
32764 \begin_inset Newline newline
32771 \begin_layout Plain Layout
32786 \begin_layout Plain Layout
32793 {numerator}{denominator}
32796 \begin_layout Standard
32797 The style is a number in the range of 0
32798 \begin_inset space \thinspace{}
32802 \begin_inset space \thinspace{}
32808 \begin_layout Standard
32810 \begin_inset Tabular
32811 <lyxtabular version="3" rows="5" columns="2">
32813 <column alignment="center" valignment="top" width="0">
32814 <column alignment="center" valignment="top" width="0">
32816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32819 \begin_layout Plain Layout
32825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32828 \begin_layout Plain Layout
32836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32839 \begin_layout Plain Layout
32845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32848 \begin_layout Plain Layout
32849 display style formula
32856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32859 \begin_layout Plain Layout
32865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32868 \begin_layout Plain Layout
32876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32879 \begin_layout Plain Layout
32885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32888 \begin_layout Plain Layout
32896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32899 \begin_layout Plain Layout
32905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32908 \begin_layout Plain Layout
32922 \begin_layout Standard
32923 When no style is given, the size is adjusted to the surrounding environment
32924 like for the command
32933 \begin_layout Standard
32934 When no fraction bar thickness is given, the predefined value of 0.4
32935 \begin_inset space \thinspace{}
32941 \begin_layout Standard
32942 \begin_inset VSpace medskip
32945 For example, the commands
32958 \begin_inset CommandInset ref
32960 reference "sub:Fractions"
32964 are defined with the commands
32967 \begin_layout Standard
32976 genfrac{}{}{}{0}{#1}{#2}}
32979 \begin_layout Standard
32983 \begin_layout Standard
32992 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32995 \begin_layout Standard
32996 \begin_inset VSpace medskip
32999 To define a fraction where the fraction bar thickness can be given as optional
33000 argument, the following line is inserted to the LaTeX-preamble:
33003 \begin_layout Standard
33012 genfrac{}{}{#1}{}{#2}{#3}}
33015 \begin_layout Standard
33017 \begin_inset Formula \begin{align*}
33018 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33019 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
33023 As one can see, the distance of the numerator and the denominator to the
33024 fraction bar is round about three times the bar thickness.
33027 \begin_layout Subsection
33032 \begin_layout Plain Layout
33041 \begin_layout Standard
33042 To cancel formulas or formula parts, the LaTeX-package
33050 \begin_layout Plain Layout
33055 is part of every LaTeX standard installation.
33064 \begin_layout Plain Layout
33070 has to be loaded with the LaTeX-preamble line
33073 \begin_layout Standard
33078 usepackage[samesize]{cancel}
33081 \begin_layout Standard
33082 There are four ways to cancel formulas:
33085 \begin_layout Standard
33087 \begin_inset Tabular
33088 <lyxtabular version="3" rows="5" columns="2">
33090 <column alignment="center" valignment="top" width="0">
33091 <column alignment="center" valignment="top" width="0">
33093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33096 \begin_layout Plain Layout
33102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33105 \begin_layout Plain Layout
33107 \begin_inset Note Note
33110 \begin_layout Plain Layout
33123 are used here as spacer.
33135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33138 \begin_layout Plain Layout
33147 \begin_layout Plain Layout
33161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33164 \begin_layout Plain Layout
33165 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33178 \begin_layout Plain Layout
33187 \begin_layout Plain Layout
33201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33204 \begin_layout Plain Layout
33205 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33218 \begin_layout Plain Layout
33227 \begin_layout Plain Layout
33241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33244 \begin_layout Plain Layout
33245 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33258 \begin_layout Plain Layout
33262 \begin_inset Formula $\to$
33273 \begin_layout Plain Layout
33287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33290 \begin_layout Plain Layout
33291 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33307 \begin_layout Standard
33314 is especially suitable to visualize the reduction of fractions within formulas:
33315 \begin_inset Formula \[
33316 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33323 \begin_layout Subsection
33324 Formulas in Section Headings
33325 \begin_inset CommandInset label
33327 name "sub:Formulas-in-Section"
33335 \begin_layout Plain Layout
33336 Formula ! in section headings
33344 \begin_layout Standard
33345 When formulas are used in section headings, the following has to be taken
33349 \begin_layout Standard
33350 \begin_inset Note Greyedout
33353 \begin_layout Plain Layout
33362 \begin_layout Plain Layout
33363 Packages ! hyperref
33368 support is enabled in the document settings dialog under
33371 \begin_inset space ~
33376 , PDF-bookmarks are created for every section heading in the table of contents.
33377 If a section heading contains formulas, they are incorrectly displayed
33378 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33387 \begin_layout Standard
33388 Both problems can be solved by inserting at the end of the section heading
33389 a short title with the menu
33391 Insert\SpecialChar \menuseparator
33393 \begin_inset space ~
33399 Short titles are used as alternative for multiline section headings to
33400 keep the table of contents clearly arranged.
33401 Only the short title appears in the table of contents and therefore also
33402 in the PDF-bookmark.
33405 \begin_layout Standard
33406 When formulas should be used in the table of contents but
33410 is used, one can use the following command in TeX-mode:
33413 \begin_layout Standard
33418 texorpdfstring{part}{alternative}
33422 \begin_layout Plain Layout
33433 \begin_layout Standard
33434 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33435 This can be characters, formulas, footnotes, but also cross-references.
33436 The alternative is used instead of the part for the bookmark.
33439 \begin_layout Standard
33440 Here are two example headings:
33441 \begin_inset VSpace -3mm
33448 \begin_layout Plain Layout
33460 \begin_layout Subsubsection
33461 Heading without formula in table of contents
33462 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33466 \begin_inset OptArg
33469 \begin_layout Plain Layout
33470 Heading without formula in table of contents
33478 \begin_layout Subsubsection
33479 Heading with formula in table of contents
33483 \begin_layout Plain Layout
33493 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33500 \begin_layout Plain Layout
33510 \begin_layout Standard
33514 \begin_layout Plain Layout
33523 In the first heading a short title was used, in the second one
33532 \begin_layout Standard
33533 To get the same formatting as for the other headings, the complete heading
33542 \begin_layout Plain Layout
33544 \begin_inset CommandInset ref
33546 reference "sub:Bold-Formulas"
33558 \begin_layout Subsection
33559 Formulas in multi-column Text
33563 \begin_layout Plain Layout
33564 Formula ! in multi-column text
33572 \begin_layout Standard
33573 Formulas in multi-column text are often too wide to fit into a column and
33574 thus need to be set over the whole page width.
33575 This is done by using the LaTeX-package
33583 \begin_layout Plain Layout
33588 is part of every LaTeX standard installation.
33597 \begin_layout Plain Layout
33598 Packages ! multicol
33603 , that is loaded with the LaTeX-preamble line
33606 \begin_layout Standard
33611 usepackage{multicol}
33614 \begin_layout Standard
33615 \begin_inset Note Greyedout
33618 \begin_layout Plain Layout
33619 Note herby that the setting
33622 \begin_inset space ~
33629 Document\SpecialChar \menuseparator
33635 \begin_inset space ~
33655 \begin_layout Standard
33656 Before the multi-column text the command
33659 \begin_layout Standard
33664 begin{multicols}{column number}
33667 \begin_layout Standard
33668 is written in TeX-mode.
33669 The column number is a number in the range of 2
33670 \begin_inset space \thinspace{}
33674 \begin_inset space \thinspace{}
33678 Before the formula the multi-column text is ended by inserting the command
33681 \begin_layout Standard
33689 \begin_layout Standard
33693 \begin_layout Standard
33694 Due to the command some space is automatically added before the formula.
33696 \begin_inset space \thinspace{}
33699 mm vertical space is inserted before the formula.
33700 When the formula style
33706 \begin_layout Plain Layout
33708 \begin_inset CommandInset ref
33710 reference "sec:Formula-Styles"
33722 \begin_inset space \thinspace{}
33725 mm space is inserted instead.
33728 \begin_layout Standard
33729 As example a multi-column text with a displayed formula:
33732 \begin_layout Standard
33736 \begin_layout Plain Layout
33740 begin{multicols}{2}
33745 Das Spektrum wird fouriertransformiert.
33746 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33747 , Lösungsmittel) zu trennen.
33748 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33749 nun das Aussehen des Ausgangssignals.
33750 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33751 über alle Phasen integrieren muss.
33753 \begin_inset Formula $S$
33756 unser normiertes Ausgangssignal and
33757 \begin_inset Formula $P$
33760 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33764 \begin_layout Plain Layout
33774 \begin_inset VSpace -6mm
33778 \begin_inset Formula \begin{equation}
33779 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33787 \begin_layout Plain Layout
33791 begin{multicols}{2}
33797 \begin_inset Formula $S_{0}$
33800 das Signal ohne Gradient ist and the Normierungsbedingung
33801 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33805 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33807 \begin_inset Formula $\nicefrac{\pi}{2}$
33811 \begin_inset space \thinspace{}
33814 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33815 das Signal zusätzlich abschwächt.
33816 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33818 \begin_inset Formula $T_{2}$
33824 \begin_layout Standard
33828 \begin_layout Plain Layout
33840 \begin_layout Subsection
33841 Formulas with Description of Variables
33845 \begin_layout Plain Layout
33846 Formula ! with description of variables
33854 \begin_layout Standard
33855 To describe variables within a formula, like in formula
33856 \begin_inset CommandInset ref
33858 reference "eq:within"
33867 \begin_inset Formula $n$
33871 \begin_inset space ~
33874 matrix is used with left aligned columns for the
33875 \begin_inset Formula $n$
33882 \begin_layout Plain Layout
33884 \begin_inset CommandInset ref
33886 reference "sec:Matrices"
33895 To set the description in a smaller size, before the matrix e.
33896 \begin_inset space \thinspace{}
33900 \begin_inset space ~
33913 \begin_layout Plain Layout
33915 \begin_inset CommandInset ref
33917 reference "sub:Font-Sizes"
33929 \begin_layout Standard
33930 When the formula style
33936 \begin_layout Plain Layout
33938 \begin_inset CommandInset ref
33940 reference "sec:Formula-Styles"
33961 \begin_layout Plain Layout
33968 only works in formulas with the style
33973 \begin_inset CommandInset ref
33975 reference "sub:Variable-Space"
33984 is inserted before and after the matrix to have the same separation of
33985 the matrix from the equation and the side margin.
33988 \begin_layout Standard
33989 When the formula style
33993 is used, the method described in
33994 \begin_inset CommandInset ref
33996 reference "sub:Flalign-Environment"
34000 is used to indent formulas.
34002 \begin_inset CommandInset ref
34004 reference "eq:within"
34008 consists of five columns whereas in the first two columns contain the equation,
34009 the third the matrix, and the last one an empty TeX-brace.
34010 \begin_inset Formula \begin{flalign}
34011 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
34012 \rho & \textrm{density}\\
34013 V & \textrm{volume}\\
34014 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
34021 \begin_layout Subsection
34022 Upright small Greek Letters
34023 \begin_inset CommandInset label
34025 name "sub:Upright-small-Greek"
34033 \begin_layout Plain Layout
34034 Greek letters ! upright
34042 \begin_layout Standard
34043 Most of the math fonts only provide italic small Greek letters.
34044 But for symbols of elementary particles like pions and neutrinos, upright
34045 Greek letters are needed.
34054 \begin_layout Plain Layout
34059 is part of the LaTeX-package
34067 \begin_layout Plain Layout
34072 \begin_layout Plain Layout
34095 \begin_layout Plain Layout
34101 that is loaded with the LaTeX-preamble line
34104 \begin_layout Standard
34109 usepackage{upgreek}
34112 \begin_layout Standard
34118 \begin_layout Plain Layout
34128 \begin_inset Note Note
34131 \begin_layout Plain Layout
34132 The following table will only be displayed when the LaTeX-package
34141 They are created when the command for a small Greek letters is started
34147 For example the command
34154 \begin_inset Formula $\uptau$
34160 \begin_layout Standard
34161 With these commands reactions of elementary particles can be typeset:
34162 \begin_inset Formula \[
34163 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34170 \begin_layout Standard
34171 The upright letters are more bold and wider than the italic ones.
34172 They should therefore not be used for units like
34173 \begin_inset Quotes eld
34177 \begin_inset Quotes erd
34183 \begin_layout Standard
34187 \begin_layout Plain Layout
34197 \begin_inset Note Note
34200 \begin_layout Plain Layout
34201 The following will be displayed when the LaTeX-package
34213 \begin_layout Standard
34214 You need to install the LaTeX-package
34218 to see the rest of this subsection in the output.
34221 \begin_layout Standard
34225 \begin_layout Plain Layout
34237 \begin_layout Subsection
34238 Text Characters in Formulas
34239 \begin_inset CommandInset label
34241 name "sub:Text-Characters-in"
34249 \begin_layout Plain Layout
34258 \begin_layout Standard
34259 In some cases you might want to insert text characters directly into formulas.
34260 When for example the centered dot · is often used in formulas like
34261 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34264 , one would have to insert the command
34274 \begin_layout Plain Layout
34276 \begin_inset CommandInset ref
34278 reference "sub:Binary-Operators"
34287 all the time, because this character is defined in all encodings as text
34289 But the encoding can be changed by this LaTeX-preamble line:
34292 \begin_layout Standard
34297 Declare Inputtext{183}{
34307 f\SpecialChar \textcompwordmark{}
34311 \begin_layout Standard
34312 The character encoding (menu
34314 Document\SpecialChar \menuseparator
34315 Settings\SpecialChar \menuseparator
34318 ) specifies what character appears when a keyboard key is pressed.
34319 When the key for the character '·' is pressed, internally the command
34326 But this command is not available in a formula so that you would get LaTeX-erro
34328 With the changed encoding the right command is chosen automatically, depending
34329 on if the character was inserted into a formula or not.
34332 \begin_layout Standard
34333 The encoding of several characters is saved in definition files.
34334 Fore example the encoding
34338 is defined in the file
34342 that is in the installation folder of LaTeX.
34343 Encodings should only be changed via the LaTeX-preamble and not in the
34345 Otherwise own documents could not be edited by other LyX users working
34346 on other computers.
34349 \begin_layout Standard
34350 \begin_inset VSpace medskip
34353 Besides the centered dot, in this document the degree sign ° is defined
34354 with the following LaTeX-preamble line so that it can directly be inserted
34358 \begin_layout Standard
34363 DeclareInputtext{176}{
34373 f\SpecialChar \textcompwordmark{}
34377 \begin_layout Standard
34378 \begin_inset Newpage newpage
34384 \begin_layout Section
34390 \begin_layout Plain Layout
34399 \begin_layout Standard
34400 This section is a summary of the most important typographic rules, listed
34405 \begin_layout Plain Layout
34406 This collection was partly taken from the German semi-official dictionary
34408 \begin_inset Quotes eld
34412 \begin_inset Quotes erd
34416 \begin_inset CommandInset citation
34422 that lists some of the ISO rules.
34430 \begin_layout Itemize
34439 \begin_layout Plain Layout
34440 done with font styles, see
34441 \begin_inset CommandInset ref
34443 reference "sub:Font-Styles"
34453 \begin_inset space \thinspace{}
34457 \begin_inset Newline newline
34460 Between the value and the unit is the smallest space, see
34461 \begin_inset CommandInset ref
34463 reference "sub:Predefined-Space"
34468 \begin_inset Newline newline
34471 This convention is automatically fulfilled when the command
34478 When it is entered to a formula, two boxes appear.
34479 In the first one the value is inserted, in the second one the unit, and
34481 \begin_inset Formula $\unit[30]{km/h}$
34485 \begin_inset space \thinspace{}
34495 is not a real LaTeX command but the command
34501 , therefore you cannot use it in TeX code.
34504 \begin_layout Itemize
34505 Percent and perthousand signs are set like physical units:
34506 \begin_inset Newline newline
34510 \begin_inset space \thinspace{}
34516 \begin_layout Itemize
34517 The degree sign follows directly on the value: 15°, but not when it is used
34519 \begin_inset space \thinspace{}
34525 \begin_layout Itemize
34526 In numbers with more than four digits the smallest space is inserted before
34527 every third digit to group them:
34537 \begin_inset space \thinspace{}
34541 \begin_inset space \thinspace{}
34547 \begin_layout Itemize
34548 For dimensions like 120×90×40
34549 \begin_inset space \thinspace{}
34552 cm the multiplication sign
34553 \begin_inset Quotes eld
34557 \begin_inset Quotes erd
34561 It is available with the LaTeX-command
34567 , but can also directly be inserted with some keyboard definitions.
34570 \begin_layout Itemize
34571 Functions with names consisting of several letters are set upright to avoid
34573 \begin_inset CommandInset ref
34575 reference "sub:Predefined-Functions"
34582 \begin_layout Itemize
34583 Indices consisting of several letters, are set upright:
34584 \begin_inset Formula $E_{\mathrm{kin}}$
34588 \begin_inset Newline newline
34591 Components of matrices are set italic:
34592 \begin_inset Formula $\hat{H}_{kl}$
34598 \begin_layout Itemize
34599 The differentiation/integration operator 'd', the Euler's number 'e', and
34600 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34604 \begin_layout Standard
34605 \begin_inset Newpage newpage
34611 \begin_layout Section
34616 \begin_layout Plain Layout
34625 \begin_layout Standard
34626 Some characters and symbols can be created with several commands.
34627 Here is a list of the synonym commands:
34630 \begin_layout Standard
34631 \begin_inset VSpace bigskip
34635 \begin_inset space \hfill{}
34639 \begin_inset Tabular
34640 <lyxtabular version="3" rows="12" columns="2">
34642 <column alignment="center" valignment="top" width="0pt">
34643 <column alignment="center" valignment="top" width="0pt">
34645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34648 \begin_layout Plain Layout
34654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34657 \begin_layout Plain Layout
34659 \begin_inset Note Note
34662 \begin_layout Plain Layout
34669 is only used as spacer.
34681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34684 \begin_layout Plain Layout
34692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34695 \begin_layout Plain Layout
34699 \begin_layout Plain Layout
34712 \begin_layout Plain Layout
34726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34729 \begin_layout Plain Layout
34737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34740 \begin_layout Plain Layout
34750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34753 \begin_layout Plain Layout
34761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34764 \begin_layout Plain Layout
34774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34777 \begin_layout Plain Layout
34785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34788 \begin_layout Plain Layout
34796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34799 \begin_layout Plain Layout
34807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34810 \begin_layout Plain Layout
34818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34821 \begin_layout Plain Layout
34829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34832 \begin_layout Plain Layout
34842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34845 \begin_layout Plain Layout
34853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34856 \begin_layout Plain Layout
34866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34869 \begin_layout Plain Layout
34877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34880 \begin_layout Plain Layout
34890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34893 \begin_layout Plain Layout
34901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34904 \begin_layout Plain Layout
34914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34917 \begin_layout Plain Layout
34925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34928 \begin_layout Plain Layout
34936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34939 \begin_layout Plain Layout
34947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34950 \begin_layout Plain Layout
34962 \begin_inset space \hfill{}
34966 \begin_inset Tabular
34967 <lyxtabular version="3" rows="12" columns="2">
34969 <column alignment="center" valignment="top" width="0pt">
34970 <column alignment="center" valignment="top" width="0pt">
34972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34975 \begin_layout Plain Layout
34981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34984 \begin_layout Plain Layout
34992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34995 \begin_layout Plain Layout
35003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35006 \begin_layout Plain Layout
35018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35021 \begin_layout Plain Layout
35029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35032 \begin_layout Plain Layout
35042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35045 \begin_layout Plain Layout
35053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35056 \begin_layout Plain Layout
35066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35069 \begin_layout Plain Layout
35077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35080 \begin_layout Plain Layout
35088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35091 \begin_layout Plain Layout
35099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35102 \begin_layout Plain Layout
35110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35113 \begin_layout Plain Layout
35121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35124 \begin_layout Plain Layout
35134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35137 \begin_layout Plain Layout
35145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35148 \begin_layout Plain Layout
35158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35161 \begin_layout Plain Layout
35169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35172 \begin_layout Plain Layout
35182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35185 \begin_layout Plain Layout
35193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35196 \begin_layout Plain Layout
35206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35209 \begin_layout Plain Layout
35217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35220 \begin_layout Plain Layout
35230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35233 \begin_layout Plain Layout
35241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35244 \begin_layout Plain Layout
35258 \begin_inset space \hfill{}
35264 \begin_layout Standard
35265 \begin_inset Newpage newpage
35271 \begin_layout Bibliography
35272 \begin_inset CommandInset bibitem
35273 LatexCommand bibitem
35285 The LaTeX Companion
35288 Addison Wesley, 2004
35291 \begin_layout Bibliography
35292 \begin_inset CommandInset bibitem
35293 LatexCommand bibitem
35299 \begin_inset CommandInset href
35302 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35306 of LaTeX's math abilities
35309 \begin_layout Bibliography
35310 \begin_inset CommandInset bibitem
35311 LatexCommand bibitem
35316 LaTeX tips and tricks-
35317 \begin_inset CommandInset href
35320 target "http://tug.org/TeXnik/"
35327 \begin_layout Bibliography
35328 \begin_inset CommandInset bibitem
35329 LatexCommand bibitem
35335 \begin_inset CommandInset href
35338 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35346 \begin_layout Plain Layout
35358 \begin_layout Bibliography
35359 \begin_inset CommandInset bibitem
35360 LatexCommand bibitem
35366 \begin_inset CommandInset href
35369 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35373 of all symbols available with LaTeX-packages
35376 \begin_layout Bibliography
35377 \begin_inset CommandInset bibitem
35378 LatexCommand bibitem
35384 \begin_inset CommandInset href
35386 name "Documentation"
35387 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35391 of the LaTeX-package
35399 \begin_layout Plain Layout
35400 Packages ! hyperref
35408 \begin_layout Bibliography
35409 \begin_inset CommandInset bibitem
35410 LatexCommand bibitem
35416 \begin_inset CommandInset href
35419 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35430 \begin_inset CommandInset ref
35432 reference "sub:Operator-Limits"
35440 \begin_layout Plain Layout
35451 \begin_layout Bibliography
35452 \begin_inset CommandInset bibitem
35453 LatexCommand bibitem
35464 Auflage, Duden 2001
35467 \begin_layout Subsubsection*
35468 \begin_inset CommandInset index_print
35469 LatexCommand printindex