1 #LyX 1.6.1svn 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
146 \use_default_options false
151 \font_typewriter default
152 \font_default_family default
162 \pdf_title "LyX's Math Manual"
163 \pdf_author "LyX Team, Uwe Stöhr"
164 \pdf_subject "LyX-documentation about math"
165 \pdf_keywords "LyX, Mathed"
167 \pdf_bookmarksnumbered true
168 \pdf_bookmarksopen true
169 \pdf_bookmarksopenlevel 1
170 \pdf_breaklinks 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, use one of the shortcuts
472 or the toolbar button
473 \begin_inset Graphics
474 filename ../images/math-mode.png
480 \begin_inset Newline newline
483 To create a display style formula
487 \begin_layout Plain Layout
488 Formula ! display style
493 that will appear bigger and in an own paragraph, use one of these shortcuts:
503 \begin_layout Standard
504 To change a display style formula to an inline formula, set the cursor into
505 the formula and use one of the shortcuts
513 Edit\SpecialChar \menuseparator
514 Math\SpecialChar \menuseparator
518 The same way is used to change an inline formula to a display style formula.
521 \begin_layout Standard
522 To display parts of an inline formula in the size of a display style formula,
531 \begin_layout Plain Layout
542 Then a new blue box appears in which the desired formula part is inserted.
545 \begin_layout Standard
546 Only inline formulas are allowed inside tables.
549 \begin_layout Standard
554 can be turned on in the menu
556 View\SpecialChar \menuseparator
560 When you click there on
561 \begin_inset Quotes eld
565 \begin_inset Quotes erd
568 the toolbar will be shown permanently at the bottom; this state is visualized
573 menu with a checkmark.
574 When you click in this state again on
575 \begin_inset Quotes eld
579 \begin_inset Quotes erd
590 is only shown when the cursor is within a formula; this state is visualized
591 by the renaming of the menu entry from
592 \begin_inset Quotes eld
596 \begin_inset Quotes erd
600 \begin_inset Quotes eld
608 \begin_inset Quotes erd
614 \begin_layout Standard
619 \begin_layout Plain Layout
625 is invoked by pressing the toolbar button
626 \begin_inset Graphics
627 filename ../images/ert-insert.png
634 Insert\SpecialChar \menuseparator
639 \begin_layout Plain Layout
655 \begin_inset Note Note
658 \begin_layout Plain Layout
659 In LyX there are three
660 \begin_inset Quotes eld
664 \begin_inset Quotes erd
667 that appear in the output with sub- and superscript letters: TeX, LaTeX,
671 \begin_layout Plain Layout
672 To avoid that these names are recognized as proper names, a TeX-brace pair
681 \begin_layout Standard
682 To change the LaTeX-preamble
686 \begin_layout Plain Layout
694 Document\SpecialChar \menuseparator
695 Settings\SpecialChar \menuseparator
700 \begin_layout Plain Layout
716 \begin_layout Standard
717 To edit matrices, case differentiations, and multiline formulas subsequently,
720 Edit\SpecialChar \menuseparator
725 Edit\SpecialChar \menuseparator
727 \begin_inset space \thinspace{}
731 \begin_inset space \thinspace{}
741 When lines and columns are swapped via the menu, the column or line where
742 the cursor is in is exchanged with the column to the right or the line
744 Is the cursor in the last column or row, the exchange is done with the
745 column to the left or the line above.
748 \begin_layout Standard
749 To write text in formulas
753 \begin_layout Plain Layout
754 For multiline formulas the command
761 \begin_inset CommandInset ref
763 reference "sub:Text-in-multiline"
780 \begin_layout Plain Layout
790 \begin_layout Plain Layout
797 This mode is invoked with the the shortcut
803 or by the insertion of the command
811 \begin_layout Plain Layout
822 The text appears black in LyX and can therefore be distinguished from the
823 other formula parts that appear blue.
824 In the output mathematical text is set upright, in contrary to other formula
828 \begin_layout Subsection*
832 \begin_layout Standard
833 Most of the LaTeX-commands for math constructs have the following scheme:
836 \begin_layout Standard
852 \begin_layout Standard
853 A command starts always with a backslash
854 \begin_inset Quotes gld
864 \begin_inset Quotes grd
868 To omit optional arguments, also omit the associated brackets.
869 The braces around the required arguments are named in this document as
874 \begin_layout Plain Layout
881 If you add in a formula a left brace to a command name, LyX creates automatical
883 In all other cases TeX-braces are created in formulas with the command
891 TeX-braces appear red in LyX, in contrary to normal braces that appear
893 In TeX-mode no command is needed to get TeX-braces.
894 TeX-braces don't appear in the output.
897 \begin_layout Standard
898 When commands without arguments, like commands for symbols are entered in
899 TeX-mode, a space character must
903 be behind the command to end it.
904 This space doesn't appear in the output.
905 When the space should appear in the output, the space must be followed
906 by a protected space in normal text.
909 \begin_layout Standard
910 A protected space is inserted with
913 arg "space-insert protected"
919 \begin_layout Subsection*
920 \begin_inset Newpage newpage
926 \begin_layout Itemize
931 \begin_layout Plain Layout
932 This visible space character can be created with the command
942 \begin_layout Plain Layout
950 , inserted in TeX-mode.
959 \begin_layout Plain Layout
972 denotes a space character to be input.
975 \begin_layout Itemize
977 \begin_inset Formula $\to$
980 denotes the usage of the corresponding arrow key on the keyboard.
983 \begin_layout Subsection*
987 \begin_layout Standard
989 \begin_inset Float table
995 \begin_layout Plain Layout
999 \begin_layout Plain Layout
1000 \begin_inset CommandInset label
1002 name "tab:Available-units"
1014 \begin_layout Plain Layout
1016 \begin_inset Tabular
1017 <lyxtabular version="3" rows="13" columns="2">
1019 <column alignment="center" valignment="top" width="0">
1020 <column alignment="center" valignment="top" width="0">
1022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1025 \begin_layout Plain Layout
1031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1034 \begin_layout Plain Layout
1042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1045 \begin_layout Plain Layout
1051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1054 \begin_layout Plain Layout
1062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1065 \begin_layout Plain Layout
1071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1074 \begin_layout Plain Layout
1082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1085 \begin_layout Plain Layout
1091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1094 \begin_layout Plain Layout
1096 \begin_inset space \thinspace{}
1100 \begin_inset space \thinspace{}
1110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1113 \begin_layout Plain Layout
1119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1122 \begin_layout Plain Layout
1124 \begin_inset space \thinspace{}
1128 \begin_inset space \thinspace{}
1138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1141 \begin_layout Plain Layout
1147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1150 \begin_layout Plain Layout
1152 \begin_inset space \thinspace{}
1156 \begin_inset space \thinspace{}
1166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1169 \begin_layout Plain Layout
1175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1178 \begin_layout Plain Layout
1180 \begin_inset space \thinspace{}
1184 \begin_inset space \thinspace{}
1194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1197 \begin_layout Plain Layout
1203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1206 \begin_layout Plain Layout
1208 \begin_inset space \thinspace{}
1212 \begin_inset space \thinspace{}
1222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1225 \begin_layout Plain Layout
1231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1234 \begin_layout Plain Layout
1236 \begin_inset space \thinspace{}
1240 \begin_inset Formula $\approx$
1244 \begin_inset space \thinspace{}
1254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1257 \begin_layout Plain Layout
1263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1266 \begin_layout Plain Layout
1268 \begin_inset space \thinspace{}
1272 \begin_inset space \thinspace{}
1282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1285 \begin_layout Plain Layout
1291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1294 \begin_layout Plain Layout
1298 \begin_inset Quotes eld
1304 \begin_inset Quotes erd
1314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1317 \begin_layout Plain Layout
1323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1326 \begin_layout Plain Layout
1328 \begin_inset Quotes eld
1336 \begin_inset Quotes erd
1346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1349 \begin_layout Plain Layout
1355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1358 \begin_layout Plain Layout
1360 \begin_inset space \thinspace{}
1364 \begin_inset Formula $\nicefrac{1}{18}$
1368 \begin_inset space \thinspace{}
1389 \begin_layout Standard
1390 \begin_inset Newpage newpage
1396 \begin_layout Section
1400 \begin_layout Subsection
1405 \begin_layout Plain Layout
1415 \begin_layout Plain Layout
1425 \begin_layout Plain Layout
1430 \begin_layout Plain Layout
1441 \begin_layout Plain Layout
1457 \begin_layout Plain Layout
1462 \begin_layout Plain Layout
1473 \begin_layout Plain Layout
1488 \begin_layout Standard
1489 Indices are created with an underscore
1490 \begin_inset Quotes eld
1494 \begin_inset Quotes erd
1497 or via the math toolbar button
1498 \begin_inset Graphics
1499 filename ../images/math-subscript.png
1504 , exponents with a caret
1505 \begin_inset Quotes eld
1509 \begin_inset Quotes erd
1512 or via the math toolbar button
1513 \begin_inset Graphics
1514 filename ../images/math-superscript.png
1522 \begin_layout Standard
1524 \begin_inset Tabular
1525 <lyxtabular version="3" rows="4" columns="2">
1527 <column alignment="center" valignment="top" width="0pt">
1528 <column alignment="center" valignment="top" width="0pt">
1530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1533 \begin_layout Plain Layout
1539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1542 \begin_layout Plain Layout
1544 \begin_inset Note Note
1547 \begin_layout Plain Layout
1554 is only used as spacer.
1566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1569 \begin_layout Plain Layout
1575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1578 \begin_layout Plain Layout
1579 \begin_inset Formula $B_{V}$
1589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1592 \begin_layout Plain Layout
1598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1601 \begin_layout Plain Layout
1602 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1615 \begin_layout Plain Layout
1620 \begin_layout Plain Layout
1634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1637 \begin_layout Plain Layout
1638 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1654 \begin_layout Standard
1655 As the caret is in some languages an accent, vowels will be accentuated
1656 in this case and not set as exponents
1660 \begin_layout Plain Layout
1661 Depending on the used keyboard settings this can also happen for other character
1668 To get in this case exponents, press
1672 after the caret as in the last example.
1675 \begin_layout Subsection
1677 \begin_inset CommandInset label
1679 name "sub:Fractions"
1687 \begin_layout Plain Layout
1696 \begin_layout Standard
1697 Fractions are generated with the command
1707 \begin_layout Plain Layout
1715 or via the math toolbar button
1716 \begin_inset Graphics
1717 filename ../images/math/frac.png
1723 The font size is adjusted automatically, depending on whether the fraction
1724 is in an inline or display style formula.
1725 With the math toolbar button
1726 \begin_inset Graphics
1727 filename ../images/math/frac-square.png
1732 you can select different fraction types.
1735 \begin_layout Standard
1744 \begin_layout Plain Layout
1754 a fraction can be created that has in any case the size of a display style
1764 \begin_layout Plain Layout
1774 the fraction appears always with the size of an inline formula.
1778 \begin_layout Standard
1779 A line with the fraction
1780 \begin_inset Formula $\frac{1}{2}$
1783 that was created with the command
1792 \begin_layout Standard
1793 A line with the fraction
1794 \begin_inset Formula $\dfrac{1}{2}$
1797 that was created with the command
1806 \begin_layout Standard
1808 \begin_inset Tabular
1809 <lyxtabular version="3" rows="4" columns="2">
1811 <column alignment="center" valignment="top" width="0pt">
1812 <column alignment="center" valignment="top" width="0pt">
1814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1817 \begin_layout Plain Layout
1823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1826 \begin_layout Plain Layout
1828 \begin_inset Note Note
1831 \begin_layout Plain Layout
1838 is only used as spacer.
1850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1853 \begin_layout Plain Layout
1860 \begin_layout Plain Layout
1870 \begin_inset Formula $\downarrow$
1878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1881 \begin_layout Plain Layout
1882 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1895 \begin_layout Plain Layout
1902 \begin_layout Plain Layout
1912 \begin_inset Formula $\downarrow$
1920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1923 \begin_layout Plain Layout
1924 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1937 \begin_layout Plain Layout
1944 \begin_layout Plain Layout
1957 \begin_layout Plain Layout
1972 \begin_layout Plain Layout
1982 \begin_inset Formula $\downarrow$
1986 \begin_inset Formula $\downarrow\downarrow$
1994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1997 \begin_layout Plain Layout
1998 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2014 \begin_layout Standard
2015 \begin_inset VSpace bigskip
2019 \begin_inset Newpage newpage
2022 For nested fractions the command
2032 \begin_layout Plain Layout
2042 \begin_inset VSpace -3mm
2048 \begin_layout Standard
2049 \begin_inset Formula \begin{align*}
2050 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2051 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2058 \begin_layout Standard
2059 The command for the example above is:
2062 \begin_layout Standard
2068 \begin_inset Formula $\to$
2078 \begin_inset Formula $\to$
2084 \begin_inset Formula $\to\to$
2092 \begin_layout Standard
2093 \begin_inset VSpace medskip
2099 \begin_layout Standard
2106 sets the fraction always in the size of a displayed formula, also when
2107 it is part of another fraction.
2114 has the following command scheme:
2117 \begin_layout Standard
2122 cfrac[numerator position]{numerator}{denominator}
2125 \begin_layout Standard
2126 The numerator position can be
2139 l or r aligns the numerator to the left or right, resp.
2140 \begin_inset space ~
2143 with the fraction stroke.
2148 or no position is given, the numerator appears centered.
2149 These fractions demonstrate the different alignments:
2150 \begin_inset Newline newline
2156 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2160 \begin_inset Formula $\cfrac{A}{B+C}$
2164 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2170 \begin_layout Standard
2171 \begin_inset VSpace medskip
2174 It is often advantageous to combine
2187 \begin_inset Formula \[
2188 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2195 \begin_layout Standard
2196 For inline fractions with a sloped fraction stroke you can use the command
2207 \begin_layout Plain Layout
2216 \begin_inset Formula $\nicefrac{5}{31}$
2229 \begin_layout Plain Layout
2238 \begin_inset Formula $\unitfrac{5}{31}$
2241 There is furthermore the command
2247 that offers to write a fraction in combination with a number:
2248 \begin_inset Formula $\unitfrac[2]{1}{3}$
2252 \begin_inset Newline newline
2261 is not a real LaTeX command but the command
2262 \begin_inset Newline newline
2269 unitfrac[number]{numerator}{denominator}
2271 , therefore you cannot use it in TeX code.
2274 \begin_layout Standard
2275 How to define own fractions where the fraction stroke can be changed, is
2277 \begin_inset CommandInset ref
2279 reference "sub:Self-defined-Fractions"
2286 \begin_layout Subsection
2291 \begin_layout Plain Layout
2300 \begin_layout Standard
2301 Square roots are created with
2311 \begin_layout Plain Layout
2319 or the math toolbar button
2320 \begin_inset Graphics
2321 filename ../images/math/sqrt.png
2326 , all other roots with the command
2336 \begin_layout Plain Layout
2344 or with the math toolbar button
2345 \begin_inset Graphics
2346 filename ../images/math/root.png
2354 \begin_layout Standard
2356 \begin_inset Tabular
2357 <lyxtabular version="3" rows="3" columns="2">
2359 <column alignment="center" valignment="top" width="0pt">
2360 <column alignment="center" valignment="top" width="0pt">
2362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2365 \begin_layout Plain Layout
2371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2374 \begin_layout Plain Layout
2376 \begin_inset Note Note
2379 \begin_layout Plain Layout
2386 is only used as spacer.
2398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2401 \begin_layout Plain Layout
2408 \begin_layout Plain Layout
2422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2425 \begin_layout Plain Layout
2426 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2436 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2439 \begin_layout Plain Layout
2446 \begin_layout Plain Layout
2456 \begin_inset Formula $\downarrow$
2464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2467 \begin_layout Plain Layout
2468 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2484 \begin_layout Standard
2485 A square root can also be created with
2491 when the root index field is left empty.
2494 \begin_layout Standard
2495 With certain indices the distance to the root is too small, like in this
2497 \begin_inset Formula $\sqrt[\beta]{B}$
2501 \begin_inset Newline newline
2505 \begin_inset Formula $\beta$
2509 To avoid this, the commands
2519 \begin_layout Plain Layout
2537 \begin_layout Plain Layout
2545 are used with the following scheme:
2548 \begin_layout Standard
2562 \begin_layout Standard
2563 Distance is the number of Big Points (unit bp;
2564 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2567 ), that the index should be moved to the left or top, resp..
2568 The commands are written to the index.
2569 This way the command
2570 \begin_inset Newline newline
2580 \begin_inset Formula $\to$
2586 \begin_inset Formula $\to$
2595 \begin_layout Plain Layout
2605 \begin_inset Formula $\to$
2609 \begin_inset Newline newline
2614 produces a correct typeset formula:
2615 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2621 \begin_layout Subsection
2622 Binomial Coefficients
2626 \begin_layout Plain Layout
2627 Binomial coefficients
2635 \begin_layout Standard
2636 Binomial coefficients are inserted with the command
2646 \begin_layout Plain Layout
2654 or with the submenu of the math toolbar button
2655 \begin_inset Graphics
2656 filename ../images/math/frac-square.png
2662 Analog to fractions (
2682 \begin_layout Plain Layout
2702 \begin_layout Plain Layout
2711 For other brackets around binomial coeficients there are the commands
2721 \begin_layout Plain Layout
2739 \begin_layout Plain Layout
2750 \begin_layout Standard
2752 \begin_inset Tabular
2753 <lyxtabular version="3" rows="6" columns="2">
2755 <column alignment="center" valignment="top" width="0pt">
2756 <column alignment="center" valignment="top" width="0pt">
2758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2761 \begin_layout Plain Layout
2767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2770 \begin_layout Plain Layout
2772 \begin_inset Note Note
2775 \begin_layout Plain Layout
2782 is only used as spacer.
2794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2797 \begin_layout Plain Layout
2804 \begin_layout Plain Layout
2814 \begin_inset Formula $\downarrow$
2822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2825 \begin_layout Plain Layout
2826 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2839 \begin_layout Plain Layout
2846 \begin_layout Plain Layout
2856 \begin_inset Formula $\downarrow$
2864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2867 \begin_layout Plain Layout
2868 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2881 \begin_layout Plain Layout
2888 \begin_layout Plain Layout
2898 \begin_inset Formula $\downarrow$
2906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2909 \begin_layout Plain Layout
2910 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2923 \begin_layout Plain Layout
2930 \begin_layout Plain Layout
2940 \begin_inset Formula $\downarrow$
2948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2951 \begin_layout Plain Layout
2952 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2965 \begin_layout Plain Layout
2972 \begin_layout Plain Layout
2982 \begin_inset Formula $\downarrow$
2990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2993 \begin_layout Plain Layout
2994 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3010 \begin_layout Subsection
3011 Case Differentiations
3015 \begin_layout Plain Layout
3016 Case differentiations
3024 \begin_layout Standard
3026 \begin_inset Tabular
3027 <lyxtabular version="3" rows="3" columns="2">
3029 <column alignment="center" valignment="top" width="0pt">
3030 <column alignment="center" valignment="top" width="0pt">
3032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3035 \begin_layout Plain Layout
3041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3044 \begin_layout Plain Layout
3052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3055 \begin_layout Plain Layout
3062 \begin_layout Plain Layout
3072 \begin_inset Formula $\to$
3079 \begin_layout Plain Layout
3092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3095 \begin_layout Plain Layout
3096 \begin_inset Formula $\begin{cases}
3107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3110 \begin_layout Plain Layout
3117 \begin_layout Plain Layout
3129 arg "newline-insert newline"
3137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3140 \begin_layout Plain Layout
3141 \begin_inset Formula $\begin{cases}
3142 A & \textrm{for }x>0\\
3143 B & \textrm{for }x=0\end{cases}$
3159 \begin_layout Standard
3166 or the usage of the math toolbar button
3167 \begin_inset Graphics
3168 filename ../images/math/cases.png
3173 you can create new lines with the shortcut
3176 arg "newline-insert newline"
3179 or the table toolbar button
3180 \begin_inset Graphics
3181 filename ../images/tabular-feature_append-row.png
3189 \begin_layout Standard
3196 is also available via the menu
3198 Insert\SpecialChar \menuseparator
3199 Math\SpecialChar \menuseparator
3205 \begin_layout Subsection
3210 \begin_layout Plain Layout
3219 \begin_layout Standard
3230 \begin_layout Plain Layout
3238 every character can be displayed canceled.
3239 The characters are quasi accentuated by a slash.
3242 \begin_layout Standard
3244 \begin_inset Tabular
3245 <lyxtabular version="3" rows="4" columns="2">
3247 <column alignment="center" valignment="top" width="0pt">
3248 <column alignment="center" valignment="top" width="0pt">
3250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3253 \begin_layout Plain Layout
3259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3262 \begin_layout Plain Layout
3270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3273 \begin_layout Plain Layout
3281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3284 \begin_layout Plain Layout
3285 \begin_inset Formula $\not=$
3295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3298 \begin_layout Plain Layout
3308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3311 \begin_layout Plain Layout
3312 \begin_inset Formula $\not\le$
3322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3325 \begin_layout Plain Layout
3335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3338 \begin_layout Plain Layout
3339 \begin_inset Formula $\not\parallel$
3355 \begin_layout Standard
3356 The last example shows, that not all negations look good.
3357 Therefore there are for some negations special commands (see
3358 \begin_inset CommandInset ref
3360 reference "sub:Mathematical-Symbols"
3365 \begin_inset CommandInset ref
3367 reference "sec:Relations"
3374 \begin_layout Subsection
3376 \begin_inset CommandInset label
3378 name "sub:Placeholders"
3386 \begin_layout Plain Layout
3396 \begin_layout Plain Layout
3397 Chemical characters ! Isotopes
3406 \begin_layout Plain Layout
3411 \begin_layout Plain Layout
3422 \begin_layout Plain Layout
3437 \begin_layout Standard
3439 \begin_inset space \thinspace{}
3443 \begin_inset space \space{}
3450 \begin_layout Plain Layout
3451 More about chemical symbols is written in
3452 \begin_inset CommandInset ref
3454 reference "sub:Chemical-Symbols-and"
3463 the following problem occurs:
3466 \begin_layout Standard
3468 \begin_inset Tabular
3469 <lyxtabular version="3" rows="2" columns="2">
3471 <column alignment="center" valignment="top" width="0pt">
3472 <column alignment="center" valignment="top" width="0pt">
3474 <cell alignment="center" valignment="top" usebox="none">
3477 \begin_layout Plain Layout
3478 Indices created with sub- and superscripts:
3483 <cell alignment="center" valignment="top" usebox="none">
3486 \begin_layout Plain Layout
3487 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3497 <cell alignment="center" valignment="top" usebox="none">
3500 \begin_layout Plain Layout
3506 <cell alignment="center" valignment="top" usebox="none">
3509 \begin_layout Plain Layout
3510 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3524 \begin_inset Note Note
3527 \begin_layout Plain Layout
3534 is only used as spacer.
3542 \begin_layout Standard
3543 The shorter index is by default placed below or above the first character
3544 of the longer index.
3545 To avoid this there is the command
3555 \begin_layout Plain Layout
3563 or the math toolbar button
3564 \begin_inset space \thinspace{}
3571 \begin_layout Plain Layout
3572 can be found in the submenu of the toolbar button
3573 \begin_inset Graphics
3574 filename ../images/math/space.png
3585 \begin_inset Graphics
3586 filename ../images/math/phantom.png
3591 that creates one or more phantom characters.
3598 a small blue box appears that is superposed with two red arrows.
3599 The arrows indicate that the complete width and height of the box content
3600 will be created as placeholder.
3601 Phantom characters are accordingly placeholders with the size of the characters.
3604 \begin_layout Standard
3606 \begin_inset Tabular
3607 <lyxtabular version="3" rows="4" columns="2">
3609 <column alignment="center" valignment="top" width="0">
3610 <column alignment="center" valignment="top" width="0">
3612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3615 \begin_layout Plain Layout
3621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3624 \begin_layout Plain Layout
3626 \begin_inset Note Note
3629 \begin_layout Plain Layout
3636 is only used as spacer.
3648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3651 \begin_layout Plain Layout
3656 \begin_layout Plain Layout
3671 \begin_layout Plain Layout
3681 \begin_inset Formula $\to$
3688 \begin_layout Plain Layout
3702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3705 \begin_layout Plain Layout
3706 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3719 \begin_layout Plain Layout
3724 \begin_layout Plain Layout
3739 \begin_layout Plain Layout
3749 \begin_inset Formula $\to$
3756 \begin_layout Plain Layout
3770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3773 \begin_layout Plain Layout
3774 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3787 \begin_layout Plain Layout
3794 \begin_layout Plain Layout
3809 \begin_layout Plain Layout
3819 \begin_inset Formula $\to$
3826 \begin_layout Plain Layout
3840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3843 \begin_layout Plain Layout
3844 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3860 \begin_layout Standard
3861 Furthermore there are the commands
3871 \begin_layout Plain Layout
3880 \begin_inset space ~
3884 \begin_inset Graphics
3885 filename ../images/math/vphantom.png
3900 \begin_layout Plain Layout
3909 \begin_inset space ~
3913 \begin_inset Graphics
3914 filename ../images/math/hphantom.png
3926 creates only space for the maximal height of the characters in the box
3927 but not for its width.
3934 creates only space for the width of the box content.
3935 Therefore the boxes of both commands have only one red arrow.
3938 \begin_layout Standard
3949 \begin_layout Plain Layout
3964 space for the height of the integral sign,
3968 \begin_layout Plain Layout
3975 creates an integral sign, see
3976 \begin_inset CommandInset ref
3978 reference "sub:Big-Operators"
3987 because this is the larger character.
3988 An example application is in
3989 \begin_inset CommandInset ref
3991 reference "sub:Multiline-Brackets"
3998 \begin_layout Subsection
4003 \begin_layout Plain Layout
4013 \begin_layout Plain Layout
4014 Formula ! underlined
4022 \begin_layout Standard
4024 \begin_inset Tabular
4025 <lyxtabular version="3" rows="4" columns="2">
4027 <column alignment="center" valignment="top" width="0pt">
4028 <column alignment="center" valignment="top" width="0pt">
4030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4033 \begin_layout Plain Layout
4039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4042 \begin_layout Plain Layout
4044 \begin_inset Note Note
4047 \begin_layout Plain Layout
4054 is only used as spacer.
4066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4069 \begin_layout Plain Layout
4076 \begin_layout Plain Layout
4089 \begin_layout Plain Layout
4102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4105 \begin_layout Plain Layout
4106 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4119 \begin_layout Plain Layout
4126 \begin_layout Plain Layout
4139 \begin_layout Plain Layout
4152 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4155 \begin_layout Plain Layout
4156 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4169 \begin_layout Plain Layout
4176 \begin_layout Plain Layout
4191 \begin_layout Plain Layout
4205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4208 \begin_layout Plain Layout
4209 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4225 \begin_layout Standard
4226 In the last example it doesn't matter if first
4241 \begin_layout Standard
4242 To double underline e.
4243 \begin_inset space \thinspace{}
4247 \begin_inset space \space{}
4259 \begin_layout Standard
4260 It is possible to place up to 6 lines above or below characters.
4263 \begin_layout Standard
4264 \begin_inset VSpace bigskip
4267 Custom lines can be created using the command
4277 \begin_layout Plain Layout
4285 which has the following scheme:
4288 \begin_layout Standard
4293 rule[vertical offset]{length}{thickness}
4296 \begin_layout Standard
4297 The optional vertical offset shifts the line upwards (or downwards, when
4298 the value is negative).
4300 \begin_inset CommandInset ref
4302 reference "tab:Available-units"
4306 can be used for the values.
4307 Here are two example lines created with the commands
4308 \begin_inset Newline newline
4315 rule[-2ex]{3cm}{2pt}
4326 \begin_layout Standard
4328 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4334 \begin_layout Standard
4341 can also be used for text when it is inserted in TeX-mode.
4344 \begin_layout Subsection
4346 \begin_inset CommandInset label
4356 \begin_layout Plain Layout
4365 \begin_layout Standard
4366 There are different types of ellipses available.
4370 \begin_layout Plain Layout
4371 In the math toolbar in the submenu of the button
4372 \begin_inset Graphics
4373 filename ../images/math/ldots.png
4383 For listings dots at the baseline are used (
4393 \begin_layout Plain Layout
4401 ), while for operations dots are needed that are on the same height as the
4412 \begin_layout Plain Layout
4421 When using the command
4431 \begin_layout Plain Layout
4439 , LaTeX decides on the basis of the next character what type is used.
4442 \begin_layout Standard
4444 \begin_inset Tabular
4445 <lyxtabular version="3" rows="8" columns="2">
4447 <column alignment="center" valignment="top" width="0pt">
4448 <column alignment="center" valignment="top" width="0pt">
4450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4453 \begin_layout Plain Layout
4459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4462 \begin_layout Plain Layout
4470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4473 \begin_layout Plain Layout
4478 \begin_layout Plain Layout
4493 \begin_layout Plain Layout
4507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4510 \begin_layout Plain Layout
4511 \begin_inset Formula $A_{1},\dots,A_{n}$
4521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4524 \begin_layout Plain Layout
4529 \begin_layout Plain Layout
4544 \begin_layout Plain Layout
4558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4561 \begin_layout Plain Layout
4562 \begin_inset Formula $A_{1}+\dots+A_{n}$
4572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4575 \begin_layout Plain Layout
4580 \begin_layout Plain Layout
4595 \begin_layout Plain Layout
4609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4612 \begin_layout Plain Layout
4613 \begin_inset Formula $A_{1},\ldots,A_{n}$
4623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4626 \begin_layout Plain Layout
4631 \begin_layout Plain Layout
4646 \begin_layout Plain Layout
4660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4663 \begin_layout Plain Layout
4664 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4677 \begin_layout Plain Layout
4685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4688 \begin_layout Plain Layout
4689 \begin_inset Formula $\vdots$
4699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4702 \begin_layout Plain Layout
4710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4713 \begin_layout Plain Layout
4714 \begin_inset Formula $\ddots$
4724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4727 \begin_layout Plain Layout
4729 \begin_inset space \thinspace{}
4732 matrix with the different dots
4737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4740 \begin_layout Plain Layout
4741 \begin_inset Formula $\begin{array}{ccc}
4742 A_{11} & \cdots & A_{1m}\\
4743 \vdots & \ddots & \vdots\\
4744 A_{n1} & \cdots & A_{nm}\end{array}$
4760 \begin_layout Standard
4761 The ellipses available in menu
4763 Insert\SpecialChar \menuseparator
4765 \begin_inset space ~
4779 \begin_layout Standard
4780 \begin_inset VSpace medskip
4783 Specially for matrices there are ellipses that span over several columns.
4784 They are created with the command
4794 \begin_layout Plain Layout
4802 , that has the following scheme:
4805 \begin_layout Standard
4810 hdotsfor[distance]{number of columns}
4813 \begin_layout Standard
4814 The number of columns specifies how many columns should be spanned.
4815 Distance is a factor for the distance between the dots.
4818 \begin_layout Standard
4819 In the following matrix the command
4825 was inserted in the first box of the second line, to get an ellipsis with
4826 a dot distance twice as long as with the command
4833 \begin_inset Formula \[
4834 \left(\begin{array}{cccc}
4837 q & w & e & r\end{array}\right)\]
4841 Note that the matrix fields that should be spanned must be empty, otherwise
4842 you get LaTeX-errors.
4845 \begin_layout Standard
4846 \begin_inset VSpace bigskip
4849 Furthermore you can fill with the command
4859 \begin_layout Plain Layout
4867 the rest of a line with dots.
4868 The effect of these commands is the same like with
4875 \begin_inset CommandInset ref
4877 reference "sub:Variable-Space"
4884 \begin_layout Standard
4885 For example the command
4893 \begin_layout Plain Layout
4907 \begin_layout Standard
4908 \begin_inset Formula $A\dotfill B$
4914 \begin_layout Standard
4921 there is for a line the command
4931 \begin_layout Plain Layout
4942 \begin_layout Standard
4943 \begin_inset Formula $A\hrulefill B$
4949 \begin_layout Standard
4950 To use the commands for text, they have to be inserted in TeX-mode.
4953 \begin_layout Section
4955 \begin_inset CommandInset label
4965 \begin_layout Plain Layout
4974 \begin_layout Standard
4975 Matrices can be inserted via the math toolbar button
4976 \begin_inset Graphics
4977 filename ../images/dialog-show_mathmatrix.png
4984 Insert\SpecialChar \menuseparator
4985 Math\SpecialChar \menuseparator
4989 You will be asked for the number of matrix columns and rows, and the alignment.
4990 The vertical alignment is hereby only of importance for matrices in inline
4994 \begin_layout Standard
4995 The first matrix is top
4996 \begin_inset Formula $\begin{array}[t]{cccc}
4999 C & F & I & L\end{array}$
5003 \begin_inset Formula $\begin{array}{cccc}
5006 C & F & I & L\end{array}$
5009 , and the third bottom
5010 \begin_inset Formula $\begin{array}[b]{cccc}
5013 C & F & I & L\end{array}$
5019 \begin_layout Standard
5020 The horizontal alignment specifies how the column entries should be aligned.
5021 It is set by entering a letter for every column.
5026 denotes left aligned,
5035 To create for example a 4
5040 \begin_inset space ~
5043 matrix where the first column is left aligned, the second and third are
5044 centered, and the last one is right aligned, one enters for the horizontal
5050 Normally are in a matrix all columns centered, therefore the default is
5051 for every column is a
5058 \begin_layout Standard
5059 Horizontal alignment:
5062 \begin_layout Standard
5068 \begin_inset Formula $\begin{array}{lll}
5071 C & F & 10000\end{array}$
5079 \begin_inset Formula $\begin{array}{ccc}
5082 C & F & 10000\end{array}$
5090 \begin_inset Formula $\begin{array}{rrr}
5093 C & F & 10000\end{array}$
5099 \begin_layout Standard
5100 To add or delete rows and columns subsequently, the math toolbar buttons
5102 \begin_inset Graphics
5103 filename ../images/tabular-feature_append-row.png
5109 \begin_inset Graphics
5110 filename ../images/tabular-feature_delete-row.png
5116 \begin_inset space \thinspace{}
5121 Edit\SpecialChar \menuseparator
5125 New rows can also be created with
5128 arg "newline-insert newline"
5134 \begin_layout Standard
5135 \begin_inset VSpace bigskip
5138 Parentheses around a matrix can can either be created with the commands
5149 \begin_layout Plain Layout
5167 \begin_layout Plain Layout
5178 \begin_inset space ~
5184 \begin_inset CommandInset ref
5186 reference "sub:Automatic-Bracket-Size"
5190 , or by using the following commands:
5191 \begin_inset VSpace medskip
5197 \begin_layout Standard
5198 \begin_inset space \hfill{}
5202 \begin_inset Tabular
5203 <lyxtabular version="3" rows="4" columns="2">
5205 <column alignment="center" valignment="top" width="0">
5206 <column alignment="center" valignment="top" width="0">
5208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5211 \begin_layout Plain Layout
5217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5220 \begin_layout Plain Layout
5222 \begin_inset Note Note
5225 \begin_layout Plain Layout
5232 is only used as spacer.
5244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5247 \begin_layout Plain Layout
5254 \begin_layout Plain Layout
5268 \begin_inset space \thinspace{}
5276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5279 \begin_layout Plain Layout
5280 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5281 0 & \textrm{-}\mathrm{i}\\
5282 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5295 \begin_layout Plain Layout
5302 \begin_layout Plain Layout
5316 \begin_inset space \thinspace{}
5324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5327 \begin_layout Plain Layout
5328 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5329 0 & \textrm{-}\mathrm{i}\\
5330 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5343 \begin_layout Plain Layout
5350 \begin_layout Plain Layout
5364 \begin_inset space \thinspace{}
5372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5375 \begin_layout Plain Layout
5376 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5377 0 & \textrm{-}\mathrm{i}\\
5378 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5392 \begin_inset space \hfill{}
5396 \begin_inset Tabular
5397 <lyxtabular version="3" rows="4" columns="2">
5399 <column alignment="center" valignment="top" width="0">
5400 <column alignment="center" valignment="top" width="0">
5402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5405 \begin_layout Plain Layout
5411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5414 \begin_layout Plain Layout
5422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5425 \begin_layout Plain Layout
5432 \begin_layout Plain Layout
5446 \begin_inset space \thinspace{}
5454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5457 \begin_layout Plain Layout
5458 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5459 0 & \textrm{-}\mathrm{i}\\
5460 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5473 \begin_layout Plain Layout
5480 \begin_layout Plain Layout
5494 \begin_inset space \thinspace{}
5502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5505 \begin_layout Plain Layout
5506 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5507 0 & \textrm{-}\mathrm{i}\\
5508 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5521 \begin_layout Plain Layout
5528 \begin_layout Plain Layout
5542 \begin_inset space \thinspace{}
5550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5553 \begin_layout Plain Layout
5554 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5555 0 & \textrm{-}\mathrm{i}\\
5556 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5570 \begin_inset space \hfill{}
5576 \begin_layout Standard
5577 \begin_inset VSpace medskip
5581 \begin_inset space \thinspace{}
5585 \begin_inset space \space{}
5594 is inserted, a blue box appears between two vertical lines where the matrix
5598 \begin_layout Standard
5599 \begin_inset VSpace bigskip
5602 As all multiline formulas are matrices, the length
5612 \begin_layout Plain Layout
5620 that is described in
5621 \begin_inset CommandInset ref
5623 reference "sub:Column-Separation"
5627 can also be used to change the column separation of matrices.
5630 \begin_layout Standard
5631 To change the row separation, the command
5641 \begin_layout Plain Layout
5650 It is used as follows:
5653 \begin_layout Standard
5660 arraystretch}{stretch factor}
5664 \begin_layout Plain Layout
5675 \begin_layout Standard
5682 assigns the stretch factor to the predefined command
5690 \begin_inset space \thinspace{}
5694 \begin_inset space \space{}
5697 the row separation, use the factor 2.
5698 This is then used for all following matrices.
5699 To go back to the original separation, assign the factor 1 to
5708 \begin_layout Standard
5709 To set matrices into a text line, the command
5719 \begin_layout Plain Layout
5728 When it is inserted a blue box with two dashed lines appears.
5729 In this box the matrix is inserted.
5732 \begin_layout Standard
5734 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5735 C & D\end{smallmatrix}\right)$
5741 \begin_layout Section
5742 Brackets and Delimiters
5746 \begin_layout Plain Layout
5756 \begin_layout Plain Layout
5765 \begin_layout Subsection
5766 Vertical Brackets and Delimiters
5770 \begin_layout Plain Layout
5779 \begin_layout Standard
5780 \begin_inset space \hfill{}
5784 \begin_inset Tabular
5785 <lyxtabular version="3" rows="9" columns="2">
5787 <column alignment="center" valignment="top" width="0pt">
5788 <column alignment="center" valignment="top" width="0pt">
5790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5793 \begin_layout Plain Layout
5799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5802 \begin_layout Plain Layout
5810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5813 \begin_layout Plain Layout
5819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5822 \begin_layout Plain Layout
5823 \begin_inset Formula $($
5833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5836 \begin_layout Plain Layout
5842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5845 \begin_layout Plain Layout
5846 \begin_inset Formula $\{$
5856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5859 \begin_layout Plain Layout
5865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5868 \begin_layout Plain Layout
5869 \begin_inset Formula $[$
5879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5882 \begin_layout Plain Layout
5890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5893 \begin_layout Plain Layout
5894 \begin_inset Formula $\langle$
5904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5907 \begin_layout Plain Layout
5915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5918 \begin_layout Plain Layout
5919 \begin_inset Formula $\lceil$
5929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5932 \begin_layout Plain Layout
5940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5943 \begin_layout Plain Layout
5944 \begin_inset Formula $\lfloor$
5954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5957 \begin_layout Plain Layout
5963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5966 \begin_layout Plain Layout
5967 \begin_inset Formula $/$
5977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5980 \begin_layout Plain Layout
5986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5989 \begin_layout Plain Layout
5990 \begin_inset Formula $|$
6004 \begin_inset space \hfill{}
6008 \begin_inset Tabular
6009 <lyxtabular version="3" rows="9" columns="2">
6011 <column alignment="center" valignment="top" width="0pt">
6012 <column alignment="center" valignment="top" width="0pt">
6014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6017 \begin_layout Plain Layout
6023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6026 \begin_layout Plain Layout
6034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6037 \begin_layout Plain Layout
6043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6046 \begin_layout Plain Layout
6047 \begin_inset Formula $)$
6057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6060 \begin_layout Plain Layout
6066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6069 \begin_layout Plain Layout
6070 \begin_inset Formula $\}$
6080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6083 \begin_layout Plain Layout
6089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6092 \begin_layout Plain Layout
6093 \begin_inset Formula $]$
6103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6106 \begin_layout Plain Layout
6114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6117 \begin_layout Plain Layout
6118 \begin_inset Formula $\rangle$
6128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6131 \begin_layout Plain Layout
6139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6142 \begin_layout Plain Layout
6143 \begin_inset Formula $\rceil$
6153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6156 \begin_layout Plain Layout
6164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6167 \begin_layout Plain Layout
6168 \begin_inset Formula $\rfloor$
6178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6181 \begin_layout Plain Layout
6191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6194 \begin_layout Plain Layout
6195 \begin_inset Formula $\backslash$
6205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6208 \begin_layout Plain Layout
6216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6219 \begin_layout Plain Layout
6220 \begin_inset Formula $\|$
6234 \begin_inset space \hfill{}
6240 \begin_layout Standard
6243 \begin_inset Note Greyedout
6246 \begin_layout Plain Layout
6251 In TeX-mode the command
6261 \begin_layout Plain Layout
6269 must be used for the backslash, because the command
6277 produces there a line break.
6285 \begin_layout Standard
6286 For all characters listed above the size can be adjusted with the commands
6287 described in the following two subsections.
6288 When using these commands, the characters < and > can directly be used
6289 instead of the commands
6304 \begin_layout Subsubsection
6306 \begin_inset CommandInset label
6308 name "sub:Manual-Bracket-Size"
6316 \begin_layout Plain Layout
6317 Bracket size ! manual
6325 \begin_layout Standard
6326 The bracket size can be specified manually by the LaTeX-commands
6336 \begin_layout Plain Layout
6369 denotes the smallest and
6375 the largest bracket size.
6378 \begin_layout Standard
6379 These commands are used to emphasize levels of brackets:
6382 \begin_layout Standard
6384 \begin_inset Tabular
6385 <lyxtabular version="3" rows="2" columns="2">
6387 <column alignment="center" valignment="top" width="0pt">
6388 <column alignment="center" valignment="top" width="0pt">
6390 <cell alignment="center" valignment="top" usebox="none">
6393 \begin_layout Plain Layout
6394 all brackets in the same size:
6399 <cell alignment="center" valignment="top" usebox="none">
6402 \begin_layout Plain Layout
6403 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6413 <cell alignment="center" valignment="top" usebox="none">
6416 \begin_layout Plain Layout
6422 <cell alignment="center" valignment="top" usebox="none">
6425 \begin_layout Plain Layout
6426 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6440 \begin_inset Note Note
6443 \begin_layout Plain Layout
6450 is only used as spacer.
6458 \begin_layout Standard
6459 For the second formula the command
6469 \begin_layout Plain Layout
6483 \begin_layout Standard
6484 Here is an overview about all bracket sizes:
6487 \begin_layout Standard
6507 \begin_layout Plain Layout
6524 \begin_layout Plain Layout
6537 \begin_layout Plain Layout
6553 \begin_layout Standard
6555 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6561 \begin_layout Standard
6568 -commands there is the variant
6578 \begin_layout Plain Layout
6586 that adds a bit more space between the bracket and its content, and the
6603 \begin_layout Plain Layout
6613 , that don't add additional space.
6618 at the end of the command
6624 is for a left bracket; for a right bracket this will be replaced by an
6630 A left or right bracket can each be an opening or closing bracket.
6633 \begin_layout Standard
6634 In the following table is a comparison of the variants:
6637 \begin_layout Standard
6639 \begin_inset Tabular
6640 <lyxtabular version="3" rows="5" columns="2">
6642 <column alignment="center" valignment="middle" width="0">
6643 <column alignment="center" valignment="middle" width="0">
6645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6648 \begin_layout Plain Layout
6654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6657 \begin_layout Plain Layout
6659 \begin_inset Note Note
6662 \begin_layout Plain Layout
6669 is only used as spacer.
6681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6684 \begin_layout Plain Layout
6699 \begin_layout Plain Layout
6717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6720 \begin_layout Plain Layout
6721 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6734 \begin_layout Plain Layout
6749 \begin_layout Plain Layout
6767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6770 \begin_layout Plain Layout
6771 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6784 \begin_layout Plain Layout
6799 \begin_layout Plain Layout
6817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6820 \begin_layout Plain Layout
6821 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6834 \begin_layout Plain Layout
6846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6849 \begin_layout Plain Layout
6850 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6866 \begin_layout Subsubsection
6867 Automatic Bracket Size
6868 \begin_inset CommandInset label
6870 name "sub:Automatic-Bracket-Size"
6878 \begin_layout Plain Layout
6879 Bracket size ! automatic
6887 \begin_layout Standard
6888 Brackets with variable size can be inserted with the commands
6898 \begin_layout Plain Layout
6916 \begin_layout Plain Layout
6924 or via the math toolbar button
6925 \begin_inset Graphics
6926 filename ../images/dialog-show_mathdelimiter.png
6944 the wanted bracket must be inserted.
6945 The bracket size will then automatically be calculated for the output.
6948 \begin_layout Standard
6950 normal bracket: The command
6960 \begin_layout Plain Layout
6970 \begin_inset Formula $\downarrow$
6977 \begin_layout Plain Layout
6989 \begin_inset Formula \[
6997 \begin_layout Standard
6999 multiline bracket: The command
7011 \begin_layout Plain Layout
7021 \begin_inset Formula $\downarrow$
7028 \begin_layout Plain Layout
7042 \begin_inset Formula \[
7043 \ln\left(\frac{A}{C}\right)\]
7050 \begin_layout Standard
7066 \begin_inset space ~
7072 This has the advantage that you can see in LyX immediately the real bracket
7073 size and that the matching right bracket will be created too.
7074 \begin_inset Newline newline
7077 The command for the last example would then be:
7091 \begin_layout Plain Layout
7101 \begin_inset Formula $\downarrow$
7107 \begin_layout Standard
7108 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7109 For example the command
7119 \begin_layout Plain Layout
7129 \begin_inset Formula $\downarrow$
7136 \begin_layout Plain Layout
7152 \begin_inset Formula \[
7153 \left.\frac{A}{B}\right\} \]
7171 will be converted by LyX to brackets in the right size when the document
7172 is reloaded and an omitted bracket will appear as dashed line.
7175 \begin_layout Standard
7176 \begin_inset VSpace bigskip
7179 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7190 \begin_layout Plain Layout
7198 is additionally available for all brackets and limits.
7199 With this command the height of the following character is adapted to the
7200 one of the surrounding brackets, what is e.
7201 \begin_inset space \thinspace{}
7205 \begin_inset space \space{}
7208 needed for physical vectors:
7209 \begin_inset Formula \[
7210 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7214 For physical vectors there is a special LaTeX-package, described in
7215 \begin_inset CommandInset ref
7217 reference "sub:Physical-Vectors"
7224 \begin_layout Subsection
7229 \begin_layout Plain Layout
7230 Brackets ! horizontal
7238 \begin_layout Standard
7240 \begin_inset Tabular
7241 <lyxtabular version="3" rows="4" columns="2">
7243 <column alignment="center" valignment="top" width="0pt">
7244 <column alignment="center" valignment="top" width="0pt">
7246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7249 \begin_layout Plain Layout
7251 \begin_inset Note Note
7254 \begin_layout Plain Layout
7261 is only used as spacer.
7271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7274 \begin_layout Plain Layout
7282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7285 \begin_layout Plain Layout
7289 \begin_layout Plain Layout
7304 \begin_layout Plain Layout
7317 \begin_layout Plain Layout
7330 \begin_layout Plain Layout
7343 \begin_layout Plain Layout
7354 \begin_layout Plain Layout
7367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7370 \begin_layout Plain Layout
7371 \begin_inset Formula $\overbrace{A+B}^{3}$
7381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7384 \begin_layout Plain Layout
7388 \begin_layout Plain Layout
7403 \begin_layout Plain Layout
7416 \begin_layout Plain Layout
7429 \begin_layout Plain Layout
7440 \begin_layout Plain Layout
7453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7456 \begin_layout Plain Layout
7457 \begin_inset Formula $\underbrace{A+B}_{5}$
7467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7470 \begin_layout Plain Layout
7477 \begin_layout Plain Layout
7492 \begin_layout Plain Layout
7505 \begin_layout Plain Layout
7518 \begin_layout Plain Layout
7531 \begin_layout Plain Layout
7544 \begin_layout Plain Layout
7557 \begin_layout Plain Layout
7571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7574 \begin_layout Plain Layout
7575 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7591 \begin_layout Standard
7592 In the last example it doesn't matter if
7604 is inserted at first.
7607 \begin_layout Standard
7608 \begin_inset VSpace bigskip
7611 When brackets are needed that overlap each other, multiline formulas, as
7613 \begin_inset CommandInset ref
7615 reference "sec:Multiline-Formulas"
7620 \begin_inset Formula \begin{eqnarray*}
7621 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7622 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7626 In the first row the formula is inserted together with the first brace.
7627 It is hereby important that the space command
7631 \begin_layout Plain Layout
7632 Space commands are explained in
7633 \begin_inset CommandInset ref
7635 reference "sub:Predefined-Space"
7650 is inserted before the first
7651 \begin_inset Formula $d$
7654 , because the brace that ends behind the
7655 \begin_inset Formula $q$
7658 prevents that the following
7659 \begin_inset Quotes eld
7663 \begin_inset Quotes erd
7666 is surrounded by space.
7670 \begin_layout Plain Layout
7671 because a bracket is not handled as character, see
7672 \begin_inset CommandInset ref
7674 reference "sub:Binary-Operators"
7683 In the second row the second brace is inserted.
7684 As it should begin before the
7685 \begin_inset Formula $b$
7700 \begin_layout Plain Layout
7708 \begin_inset CommandInset ref
7710 reference "sub:Placeholders"
7719 This space is needed because the
7720 \begin_inset Quotes eld
7724 \begin_inset Quotes erd
7727 is also surrounded by space in the formula.
7728 The brace is placed under the command
7737 \begin_layout Standard
7738 It gets more complicated when brackets overlap each other, like in the following
7743 \begin_layout Plain Layout
7755 \begin_inset Formula \begin{eqnarray*}
7756 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7757 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7765 \begin_layout Plain Layout
7776 The first formula row is the same as the second row of the previous example,
7777 with the difference that the brace is above.
7778 The second row contains the formula together with the second brace.
7779 To avoid that there is space between the upper brace in the first row and
7780 the formula, the row spacing need to be reduced.
7781 This is not easily possible due to a bug in LyX
7785 \begin_layout Plain Layout
7786 \begin_inset CommandInset href
7788 name "LyX-bug #1505"
7789 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7799 As solution for the problem, the global formula row separation
7809 \begin_layout Plain Layout
7817 must be changed to -6
7818 \begin_inset space \thinspace{}
7821 pt before the formula with the command
7836 is set back after the formula to the standard value of 3
7837 \begin_inset space \thinspace{}
7840 pt using the same command.
7841 More about the row separation in formulas is explained in
7842 \begin_inset CommandInset ref
7844 reference "sub:Line-Separation"
7851 \begin_layout Section
7856 \begin_layout Plain Layout
7865 \begin_layout Standard
7866 Arrows can be inserted via the math toolbar button
7867 \begin_inset Graphics
7868 filename ../images/math/leftarrow.png
7873 or the commands listed in the following subsections.
7876 \begin_layout Standard
7877 \begin_inset Newpage newpage
7883 \begin_layout Subsection
7888 \begin_layout Plain Layout
7897 \begin_layout Standard
7898 \begin_inset space \hfill{}
7902 \begin_inset Tabular
7903 <lyxtabular version="3" rows="8" columns="2">
7905 <column alignment="center" valignment="top" width="0pt">
7906 <column alignment="center" valignment="top" width="0pt">
7908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7911 \begin_layout Plain Layout
7917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7920 \begin_layout Plain Layout
7928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7931 \begin_layout Plain Layout
7939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7942 \begin_layout Plain Layout
7943 \begin_inset Formula $\gets$
7953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7956 \begin_layout Plain Layout
7964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7967 \begin_layout Plain Layout
7968 \begin_inset Formula $\Leftarrow$
7978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7981 \begin_layout Plain Layout
7989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7992 \begin_layout Plain Layout
7993 \begin_inset Formula $\longleftarrow$
8003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8006 \begin_layout Plain Layout
8014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8017 \begin_layout Plain Layout
8018 \begin_inset Formula $\Longleftarrow$
8028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8031 \begin_layout Plain Layout
8039 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8042 \begin_layout Plain Layout
8043 \begin_inset Formula $\leftharpoonup$
8053 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8056 \begin_layout Plain Layout
8064 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8067 \begin_layout Plain Layout
8068 \begin_inset Formula $\leftharpoondown$
8078 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8081 \begin_layout Plain Layout
8089 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8092 \begin_layout Plain Layout
8093 \begin_inset Formula $\hookleftarrow$
8107 \begin_inset space \hfill{}
8111 \begin_inset Tabular
8112 <lyxtabular version="3" rows="8" columns="2">
8114 <column alignment="center" valignment="top" width="0pt">
8115 <column alignment="center" valignment="top" width="0pt">
8117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8120 \begin_layout Plain Layout
8126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8129 \begin_layout Plain Layout
8137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8140 \begin_layout Plain Layout
8148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8151 \begin_layout Plain Layout
8152 \begin_inset Formula $\to$
8162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8165 \begin_layout Plain Layout
8173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8176 \begin_layout Plain Layout
8177 \begin_inset Formula $\Rightarrow$
8187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8190 \begin_layout Plain Layout
8198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8201 \begin_layout Plain Layout
8202 \begin_inset Formula $\longrightarrow$
8212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8215 \begin_layout Plain Layout
8223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8226 \begin_layout Plain Layout
8227 \begin_inset Formula $\Longrightarrow$
8237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8240 \begin_layout Plain Layout
8248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8251 \begin_layout Plain Layout
8252 \begin_inset Formula $\rightharpoonup$
8262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8265 \begin_layout Plain Layout
8273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8276 \begin_layout Plain Layout
8277 \begin_inset Formula $\rightharpoondown$
8287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8290 \begin_layout Plain Layout
8298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8301 \begin_layout Plain Layout
8302 \begin_inset Formula $\hookrightarrow$
8316 \begin_inset space \hfill{}
8322 \begin_layout Standard
8323 \begin_inset space \hfill{}
8327 \begin_inset Tabular
8328 <lyxtabular version="3" rows="6" columns="2">
8330 <column alignment="center" valignment="top" width="0pt">
8331 <column alignment="center" valignment="top" width="0pt">
8333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8336 \begin_layout Plain Layout
8342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8345 \begin_layout Plain Layout
8353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8356 \begin_layout Plain Layout
8364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8367 \begin_layout Plain Layout
8368 \begin_inset Formula $\leftrightarrow$
8378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8381 \begin_layout Plain Layout
8389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8392 \begin_layout Plain Layout
8393 \begin_inset Formula $\Leftrightarrow$
8403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8406 \begin_layout Plain Layout
8414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8417 \begin_layout Plain Layout
8418 \begin_inset Formula $\longleftrightarrow$
8428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8431 \begin_layout Plain Layout
8439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8442 \begin_layout Plain Layout
8443 \begin_inset Formula $\Longleftrightarrow$
8453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8456 \begin_layout Plain Layout
8464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8467 \begin_layout Plain Layout
8468 \begin_inset Formula $\rightleftharpoons$
8482 \begin_inset space \hspace{}
8487 \begin_inset space \hfill{}
8491 \begin_inset Tabular
8492 <lyxtabular version="3" rows="5" columns="2">
8494 <column alignment="center" valignment="top" width="0pt">
8495 <column alignment="center" valignment="top" width="0pt">
8497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8500 \begin_layout Plain Layout
8506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8509 \begin_layout Plain Layout
8517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8520 \begin_layout Plain Layout
8528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8531 \begin_layout Plain Layout
8532 \begin_inset Formula $\mapsto$
8542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8545 \begin_layout Plain Layout
8553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8556 \begin_layout Plain Layout
8557 \begin_inset Formula $\longmapsto$
8567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8570 \begin_layout Plain Layout
8578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8581 \begin_layout Plain Layout
8582 \begin_inset Formula $\leadsto$
8592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8595 \begin_layout Plain Layout
8603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8606 \begin_layout Plain Layout
8607 \begin_inset Formula $\dasharrow$
8621 \begin_inset space \hfill{}
8627 \begin_layout Standard
8628 \begin_inset VSpace medskip
8631 Arrows used as accent like e.
8632 \begin_inset space \thinspace{}
8636 \begin_inset space \space{}
8639 vector arrows are listed in
8640 \begin_inset CommandInset ref
8642 reference "sec:Accents"
8649 \begin_layout Standard
8650 \begin_inset VSpace bigskip
8653 Furthermore there are the labeled arrows
8657 \begin_layout Plain Layout
8673 \begin_layout Plain Layout
8691 \begin_layout Plain Layout
8698 \begin_layout Plain Layout
8713 When inserting one of these commands in a formula, an arrow with two blue
8714 boxes appear where the label can be inserted.
8715 The length of the arrow adapts to the label width.
8718 \begin_layout Standard
8720 \begin_inset Tabular
8721 <lyxtabular version="3" rows="3" columns="2">
8723 <column alignment="center" valignment="top" width="0pt">
8724 <column alignment="center" valignment="top" width="0pt">
8726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8729 \begin_layout Plain Layout
8735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8738 \begin_layout Plain Layout
8740 \begin_inset Note Note
8743 \begin_layout Plain Layout
8750 is only used as spacer.
8762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8765 \begin_layout Plain Layout
8772 \begin_layout Plain Layout
8782 \begin_inset Formula $\downarrow$
8786 \begin_inset Formula $\to$
8794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8797 \begin_layout Plain Layout
8798 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8811 \begin_layout Plain Layout
8818 \begin_layout Plain Layout
8828 \begin_inset Formula $\downarrow$
8832 \begin_inset Formula $\to$
8840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8843 \begin_layout Plain Layout
8844 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8860 \begin_layout Subsection
8861 Vertical and diagonal Arrows
8865 \begin_layout Plain Layout
8875 \begin_layout Plain Layout
8884 \begin_layout Standard
8885 \begin_inset space \hfill{}
8889 \begin_inset Tabular
8890 <lyxtabular version="3" rows="7" columns="2">
8892 <column alignment="center" valignment="top" width="0pt">
8893 <column alignment="center" valignment="top" width="0pt">
8895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8898 \begin_layout Plain Layout
8904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8907 \begin_layout Plain Layout
8915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8918 \begin_layout Plain Layout
8926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8929 \begin_layout Plain Layout
8930 \begin_inset Formula $\uparrow$
8940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8943 \begin_layout Plain Layout
8951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8954 \begin_layout Plain Layout
8955 \begin_inset Formula $\Uparrow$
8965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8968 \begin_layout Plain Layout
8976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8979 \begin_layout Plain Layout
8980 \begin_inset Formula $\updownarrow$
8990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8993 \begin_layout Plain Layout
9001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9004 \begin_layout Plain Layout
9005 \begin_inset Formula $\Updownarrow$
9015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9018 \begin_layout Plain Layout
9026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9029 \begin_layout Plain Layout
9030 \begin_inset Formula $\Downarrow$
9040 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9043 \begin_layout Plain Layout
9051 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9054 \begin_layout Plain Layout
9055 \begin_inset Formula $\downarrow$
9069 \begin_inset space \hfill{}
9073 \begin_inset Tabular
9074 <lyxtabular version="3" rows="5" columns="2">
9076 <column alignment="center" valignment="top" width="0pt">
9077 <column alignment="center" valignment="top" width="0pt">
9079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9082 \begin_layout Plain Layout
9088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9091 \begin_layout Plain Layout
9099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9102 \begin_layout Plain Layout
9110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9113 \begin_layout Plain Layout
9114 \begin_inset Formula $\nearrow$
9124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9127 \begin_layout Plain Layout
9135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9138 \begin_layout Plain Layout
9139 \begin_inset Formula $\searrow$
9149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9152 \begin_layout Plain Layout
9160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9163 \begin_layout Plain Layout
9164 \begin_inset Formula $\swarrow$
9174 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9177 \begin_layout Plain Layout
9185 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9188 \begin_layout Plain Layout
9189 \begin_inset Formula $\nwarrow$
9203 \begin_inset space \hfill{}
9209 \begin_layout Standard
9210 \begin_inset VSpace medskip
9213 Vertical arrows can be used also as delimiter together with the commands
9215 \begin_inset CommandInset ref
9217 reference "sub:Manual-Bracket-Size"
9222 \begin_inset CommandInset ref
9224 reference "sub:Automatic-Bracket-Size"
9231 \begin_layout Standard
9232 \begin_inset Newpage newpage
9238 \begin_layout Section
9240 \begin_inset CommandInset label
9250 \begin_layout Plain Layout
9259 \begin_layout Standard
9260 Accents can be inserted via the math toolbar button
9261 \begin_inset Graphics
9262 filename ../images/math/hat.png
9267 or the commands listed in the following subsections.
9270 \begin_layout Subsection
9271 Accents for one Character
9275 \begin_layout Plain Layout
9288 \begin_layout Plain Layout
9290 \begin_inset CommandInset ref
9292 reference "sub:Accents-in-Text"
9305 \begin_layout Plain Layout
9313 \begin_inset Note Note
9316 \begin_layout Plain Layout
9319 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9322 \begin_layout Plain Layout
9325 texorpdfstring is in section
9326 \begin_inset CommandInset ref
9328 reference "sub:Formulas-in-Section"
9338 \begin_inset CommandInset label
9340 name "sub:Accents-for-one"
9348 \begin_layout Plain Layout
9349 Accents ! for one character
9357 \begin_layout Standard
9358 \begin_inset space \hfill{}
9362 \begin_inset Tabular
9363 <lyxtabular version="3" rows="8" columns="2">
9365 <column alignment="center" valignment="top" width="0pt">
9366 <column alignment="center" valignment="top" width="0pt">
9368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9371 \begin_layout Plain Layout
9377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9380 \begin_layout Plain Layout
9382 \begin_inset Note Note
9385 \begin_layout Plain Layout
9392 is only used as spacer.
9404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9407 \begin_layout Plain Layout
9414 \begin_layout Plain Layout
9428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9431 \begin_layout Plain Layout
9432 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9442 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9445 \begin_layout Plain Layout
9452 \begin_layout Plain Layout
9466 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9469 \begin_layout Plain Layout
9470 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9480 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9483 \begin_layout Plain Layout
9490 \begin_layout Plain Layout
9504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9507 \begin_layout Plain Layout
9508 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9521 \begin_layout Plain Layout
9529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9532 \begin_layout Plain Layout
9533 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9543 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9546 \begin_layout Plain Layout
9553 \begin_layout Plain Layout
9566 \begin_layout Plain Layout
9577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9580 \begin_layout Plain Layout
9581 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9594 \begin_layout Plain Layout
9601 \begin_layout Plain Layout
9615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9618 \begin_layout Plain Layout
9619 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9629 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9632 \begin_layout Plain Layout
9639 \begin_layout Plain Layout
9653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9656 \begin_layout Plain Layout
9657 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9671 \begin_inset space \hfill{}
9675 \begin_inset Tabular
9676 <lyxtabular version="3" rows="7" columns="2">
9678 <column alignment="center" valignment="top" width="0pt">
9679 <column alignment="center" valignment="top" width="0pt">
9681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9684 \begin_layout Plain Layout
9690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9693 \begin_layout Plain Layout
9701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9704 \begin_layout Plain Layout
9711 \begin_layout Plain Layout
9725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9728 \begin_layout Plain Layout
9729 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9742 \begin_layout Plain Layout
9749 \begin_layout Plain Layout
9763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9766 \begin_layout Plain Layout
9767 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9780 \begin_layout Plain Layout
9787 \begin_layout Plain Layout
9801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9804 \begin_layout Plain Layout
9805 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9818 \begin_layout Plain Layout
9825 \begin_layout Plain Layout
9839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9842 \begin_layout Plain Layout
9843 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9853 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9856 \begin_layout Plain Layout
9863 \begin_layout Plain Layout
9877 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9880 \begin_layout Plain Layout
9881 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9891 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9894 \begin_layout Plain Layout
9901 \begin_layout Plain Layout
9915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9918 \begin_layout Plain Layout
9919 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9933 \begin_inset space \hfill{}
9939 \begin_layout Standard
9940 \begin_inset VSpace bigskip
9946 \begin_layout Standard
9947 You can directly insert accents like é to formulas.
9948 LyX will transform them to the corresponding accent command.
9953 \begin_layout Plain Layout
9959 it is better to insert a quotation mark before the vowel.
9960 These two characters are then treated by LaTeX as
9964 character when the formula part with the umlaut is marked as German.
9972 \begin_inset Quotes eld
9976 \begin_inset Quotes erd
9979 umlauts are created as demonstrated in the following example:
9982 \begin_layout Standard
9983 \begin_inset VSpace -2mm
9989 \begin_layout Standard
9991 \begin_inset Tabular
9992 <lyxtabular version="3" rows="3" columns="2">
9994 <column alignment="center" valignment="top" width="0">
9995 <column alignment="center" valignment="top" width="0">
9997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10000 \begin_layout Plain Layout
10006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10009 \begin_layout Plain Layout
10011 \begin_inset Note Note
10014 \begin_layout Plain Layout
10022 \begin_inset space \thinspace{}
10025 pt space are only used as spacer.
10037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10040 \begin_layout Plain Layout
10043 \begin_inset Quotes grd
10051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10054 \begin_layout Plain Layout
10055 \begin_inset space \hspace{}
10062 \begin_inset Formula $"i$
10072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10075 \begin_layout Plain Layout
10082 \begin_layout Plain Layout
10096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10099 \begin_layout Plain Layout
10100 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10116 \begin_layout Standard
10117 Another advantage to
10123 is that umlauts can directly be converted to mathematical text because
10124 the accent commands above are
10130 in mathematical text
10133 To convert an accented character to mathematical text, only the character
10134 under the accent may be converted.
10135 This applies also for all other conversions, e.
10136 \begin_inset space \thinspace{}
10140 \begin_inset space \space{}
10146 \begin_layout Standard
10147 In mathematical text, umlauts and other accented characters can directly
10151 \begin_layout Subsection
10152 Accents for Operators
10156 \begin_layout Plain Layout
10157 Accents ! for operators
10165 \begin_layout Standard
10176 \begin_layout Plain Layout
10194 \begin_layout Plain Layout
10202 characters can be placed above or below an operator, respectively, to accent
10214 \begin_layout Plain Layout
10222 characters can be set before and behind an operator.
10223 The command scheme is:
10226 \begin_layout Standard
10242 \begin_layout Standard
10249 must always be before the operator that should be accented.
10250 You can accent with several characters and even with other operators and
10258 for example only characters behind an operator, write nothing between the
10259 first braces but don't omit the braces.
10262 \begin_layout Standard
10263 For example the command
10268 \begin_inset Formula $\to$
10278 \begin_inset Formula $\to$
10287 \begin_layout Plain Layout
10303 \begin_inset Formula \[
10304 \sideset{}{'}\sum_{k=1}^{n}\]
10311 \begin_layout Standard
10320 \begin_layout Plain Layout
10335 \begin_layout Plain Layout
10347 \begin_inset Formula $\uparrow$
10355 \begin_inset Formula \[
10356 \overset{a}{\maltese}\]
10360 As seen in the last example, with
10372 also symbols and characters can be accented; with
10378 this is not possible.
10381 \begin_layout Subsection
10382 Accents for several Characters
10386 \begin_layout Plain Layout
10387 Accents ! for several characters
10395 \begin_layout Standard
10396 \begin_inset space \hfill{}
10400 \begin_inset Tabular
10401 <lyxtabular version="3" rows="5" columns="2">
10403 <column alignment="center" valignment="top" width="0pt">
10404 <column alignment="center" valignment="top" width="0pt">
10406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10409 \begin_layout Plain Layout
10415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10418 \begin_layout Plain Layout
10420 \begin_inset Note Note
10423 \begin_layout Plain Layout
10430 is only used as spacer.
10442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10445 \begin_layout Plain Layout
10452 \begin_layout Plain Layout
10466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10469 \begin_layout Plain Layout
10470 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10480 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10483 \begin_layout Plain Layout
10490 \begin_layout Plain Layout
10504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10507 \begin_layout Plain Layout
10508 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10521 \begin_layout Plain Layout
10528 \begin_layout Plain Layout
10542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10545 \begin_layout Plain Layout
10546 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10556 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10559 \begin_layout Plain Layout
10562 underleftrightarrow
10566 \begin_layout Plain Layout
10580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10583 \begin_layout Plain Layout
10584 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10598 \begin_inset space \hfill{}
10602 \begin_inset Tabular
10603 <lyxtabular version="3" rows="5" columns="2">
10605 <column alignment="center" valignment="top" width="0pt">
10606 <column alignment="center" valignment="top" width="0pt">
10608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10611 \begin_layout Plain Layout
10617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10620 \begin_layout Plain Layout
10628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10631 \begin_layout Plain Layout
10638 \begin_layout Plain Layout
10652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10655 \begin_layout Plain Layout
10656 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10666 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10669 \begin_layout Plain Layout
10676 \begin_layout Plain Layout
10690 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10693 \begin_layout Plain Layout
10694 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10707 \begin_layout Plain Layout
10714 \begin_layout Plain Layout
10728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10731 \begin_layout Plain Layout
10732 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10745 \begin_layout Plain Layout
10752 \begin_layout Plain Layout
10766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10769 \begin_layout Plain Layout
10770 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10784 \begin_inset space \hfill{}
10790 \begin_layout Standard
10791 \begin_inset VSpace medskip
10794 With these commands as many characters as you like can be accented.
10807 will only be set in the output with a length of three characters, as shown
10808 in the following example:
10809 \begin_inset Formula \[
10810 \widetilde{A+B=C-D}\]
10817 \begin_layout Standard
10828 \begin_layout Plain Layout
10846 \begin_layout Plain Layout
10854 described in the previous subsection it is also possible to accent several
10864 \begin_layout Plain Layout
10874 \begin_inset Formula $\downarrow$
10880 \begin_inset Formula \[
10881 \underset{***}{A=B}\]
10888 \begin_layout Section
10890 \begin_inset CommandInset label
10900 \begin_layout Plain Layout
10909 \begin_layout Subsection
10911 \begin_inset CommandInset label
10913 name "sub:Predefined-Space"
10921 \begin_layout Plain Layout
10922 Space ! horizontal ! predefined
10930 \begin_layout Standard
10931 Sometimes it is necessary to insert horizontal space to a formula.
10932 This is done by inserting a protected space (shortcut
10935 arg "space-insert protected"
10940 \begin_inset Quotes eld
10950 \begin_layout Plain Layout
10963 \begin_inset Quotes erd
10966 appears and by pressing
10970 several times one can select one of eight different space sizes.
10971 The spaces can also be inserted using the math toolbar button
10972 \begin_inset Graphics
10973 filename ../images/math/space.png
10978 or special commands.
10979 Independent from the inserted command, one can select the size again by
10987 \begin_layout Standard
10990 \begin_inset VSpace -5mm
10994 \begin_inset Tabular
10995 <lyxtabular version="3" rows="3" columns="7">
10997 <column alignment="center" valignment="middle" width="6.8cm">
10998 <column alignment="center" valignment="top" width="0">
10999 <column alignment="center" valignment="top" width="0">
11000 <column alignment="center" valignment="top" width="0">
11001 <column alignment="center" valignment="top" width="0">
11002 <column alignment="center" valignment="top" width="0">
11003 <column alignment="center" valignment="top" width="0">
11005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11008 \begin_layout Plain Layout
11014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11017 \begin_layout Plain Layout
11025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11028 \begin_layout Plain Layout
11036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11039 \begin_layout Plain Layout
11047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11050 \begin_layout Plain Layout
11058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11061 \begin_layout Plain Layout
11069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11072 \begin_layout Plain Layout
11082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11085 \begin_layout Plain Layout
11090 keystrokes after inserting the protected space
11095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11098 \begin_layout Plain Layout
11104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11107 \begin_layout Plain Layout
11113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11116 \begin_layout Plain Layout
11122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11125 \begin_layout Plain Layout
11131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11134 \begin_layout Plain Layout
11140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11143 \begin_layout Plain Layout
11151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11154 \begin_layout Plain Layout
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 $A\: B$
11184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11187 \begin_layout Plain Layout
11188 \begin_inset Formula $A\; B$
11196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11199 \begin_layout Plain Layout
11200 \begin_inset Formula $A\quad B$
11208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11211 \begin_layout Plain Layout
11212 \begin_inset Formula $A\qquad B$
11220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11223 \begin_layout Plain Layout
11224 \begin_inset Formula $A\! B$
11240 \begin_layout Standard
11241 The last size seem to produce no space.
11242 It is displayed red in LyX contrary to the other sizes, because it is a
11244 There are two more negative spaces:
11247 \begin_layout Standard
11249 \begin_inset Tabular
11250 <lyxtabular version="3" rows="3" columns="3">
11252 <column alignment="center" valignment="middle" width="6.8cm">
11253 <column alignment="center" valignment="top" width="0pt">
11254 <column alignment="center" valignment="top" width="0pt">
11256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11259 \begin_layout Plain Layout
11265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11268 \begin_layout Plain Layout
11276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11279 \begin_layout Plain Layout
11289 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11292 \begin_layout Plain Layout
11297 keystrokes after inserting the protected space
11302 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11305 \begin_layout Plain Layout
11311 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11314 \begin_layout Plain Layout
11322 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11325 \begin_layout Plain Layout
11331 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11334 \begin_layout Plain Layout
11335 \begin_inset Formula $A\negmedspace B$
11343 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11346 \begin_layout Plain Layout
11347 \begin_inset Formula $A\negthickspace B$
11363 \begin_layout Standard
11364 Negative spaces can lead to characters overlapping each other.
11365 Thus they can be used to enforce ligatures, what is e.
11366 \begin_inset space \thinspace{}
11370 \begin_inset space \space{}
11373 useful for summation operators:
11376 \begin_layout Standard
11378 \begin_inset Tabular
11379 <lyxtabular version="3" rows="3" columns="2">
11381 <column alignment="center" valignment="top" width="0">
11382 <column alignment="center" valignment="top" width="0">
11384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11387 \begin_layout Plain Layout
11393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11396 \begin_layout Plain Layout
11398 \begin_inset Note Note
11401 \begin_layout Plain Layout
11408 is only used as spacer.
11420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11423 \begin_layout Plain Layout
11432 \begin_layout Plain Layout
11446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11449 \begin_layout Plain Layout
11450 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11463 \begin_layout Plain Layout
11474 \begin_layout Plain Layout
11488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11491 \begin_layout Plain Layout
11492 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11508 \begin_layout Standard
11509 Relations like for example equal signs, are always surrounded by space.
11510 To suppress this, the equal sign is placed into a TeX-brace.
11511 The following example demonstrates this:
11514 \begin_layout Standard
11516 \begin_inset Tabular
11517 <lyxtabular version="3" rows="2" columns="2">
11519 <column alignment="center" valignment="top" width="0pt">
11520 <column alignment="center" valignment="top" width="0pt">
11522 <cell alignment="center" valignment="top" usebox="none">
11525 \begin_layout Plain Layout
11531 <cell alignment="center" valignment="top" usebox="none">
11534 \begin_layout Plain Layout
11535 \begin_inset Formula $A=B$
11545 <cell alignment="center" valignment="top" usebox="none">
11548 \begin_layout Plain Layout
11549 \begin_inset Note Note
11552 \begin_layout Plain Layout
11559 is only used as spacer.
11565 \begin_inset Formula $\raisebox{5mm}{}$
11568 equation without space
11573 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11576 \begin_layout Plain Layout
11577 \begin_inset Formula $A{=}B$
11593 \begin_layout Standard
11595 The command for the last formula is:
11600 \begin_inset Formula $\to$
11606 \begin_layout Standard
11607 \begin_inset VSpace bigskip
11610 Spaces are needed for physical units, because the space between the value
11611 and the unit is the smallest one and not a normal space.
11612 For units in text, the smallest space is inserted via the menu
11614 Insert\SpecialChar \menuseparator
11615 Formatting\SpecialChar \menuseparator
11617 \begin_inset space ~
11625 arg "space-insert thin"
11631 \begin_layout Standard
11632 An example to visualize the difference:
11635 \begin_layout Standard
11636 \begin_inset Tabular
11637 <lyxtabular version="3" rows="2" columns="2">
11639 <column alignment="left" valignment="top" width="0">
11640 <column alignment="left" valignment="top" width="0">
11642 <cell alignment="center" valignment="top" usebox="none">
11645 \begin_layout Plain Layout
11647 \begin_inset Formula $\cdot$
11655 <cell alignment="center" valignment="top" usebox="none">
11658 \begin_layout Plain Layout
11659 space between value and unit
11666 <cell alignment="center" valignment="top" usebox="none">
11669 \begin_layout Plain Layout
11671 \begin_inset space \thinspace{}
11675 \begin_inset Formula $\cdot$
11683 <cell alignment="center" valignment="top" usebox="none">
11686 \begin_layout Plain Layout
11687 smallest space between value and unit
11700 \begin_layout Subsection
11705 \begin_layout Plain Layout
11718 \begin_layout Plain Layout
11719 for vertical space in formulas see
11720 \begin_inset CommandInset ref
11722 reference "sub:Line-Separation"
11735 \begin_layout Plain Layout
11743 \begin_inset Note Note
11746 \begin_layout Plain Layout
11749 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11752 \begin_layout Plain Layout
11755 texorpdfstring is in section
11756 \begin_inset CommandInset ref
11758 reference "sub:Formulas-in-Section"
11768 \begin_inset CommandInset label
11770 name "sub:Variable-Space"
11778 \begin_layout Plain Layout
11779 Space ! horizontal ! variable
11787 \begin_layout Standard
11788 Space with a defined length can be inserted in LyX with the command
11789 \begin_inset Newline newline
11802 \begin_layout Plain Layout
11811 For the length all units listed in
11812 \begin_inset CommandInset ref
11814 reference "tab:Available-units"
11818 are allowed, except of the unit
11819 \begin_inset Quotes eld
11823 \begin_inset Quotes erd
11827 The length may also be negative.
11828 To insert so many space that the formula uses all available space, the
11839 \begin_layout Plain Layout
11850 \begin_layout Standard
11851 \begin_inset VSpace -1mm
11857 \begin_layout Standard
11859 \begin_inset Tabular
11860 <lyxtabular version="3" rows="4" columns="2">
11862 <column alignment="center" valignment="top" width="0">
11863 <column alignment="center" valignment="top" width="0">
11865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11868 \begin_layout Plain Layout
11874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11877 \begin_layout Plain Layout
11885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11888 \begin_layout Plain Layout
11892 \begin_inset Formula $\to$
11902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11905 \begin_layout Plain Layout
11906 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11919 \begin_layout Plain Layout
11923 \begin_inset Formula $\to$
11933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11936 \begin_layout Plain Layout
11937 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11950 \begin_layout Plain Layout
11957 \begin_layout Plain Layout
11971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11974 \begin_layout Plain Layout
11975 \begin_inset Formula $A=A\hfill B=B$
11991 \begin_layout Standard
11992 In the last example the available space is given by the longest column entry
11994 In an inline formula the space depends on the length of the line in which
12002 Thus, when the line uses the full width, no space will be created.
12009 only has an effect on displayed formulas when the formula style
12014 (Formula styles are explained in
12015 \begin_inset CommandInset ref
12017 reference "sec:Formula-Styles"
12024 \begin_layout Standard
12031 , there are the commands
12043 that fill the space with a pattern, see
12044 \begin_inset CommandInset ref
12046 reference "sub:Ellipses"
12053 \begin_layout Standard
12054 For text, variable space can be inserted via the menu
12056 Insert\SpecialChar \menuseparator
12057 Formatting\SpecialChar \menuseparator
12059 \begin_inset space ~
12064 , what is not possible in formulas:
12067 \begin_layout Standard
12068 This is a line with
12069 \begin_inset space \hspace{}
12074 \begin_inset space \thinspace{}
12080 \begin_layout Standard
12081 This is a line with
12082 \begin_inset space \hfill{}
12088 \begin_layout Subsection
12089 Space besides inline Formulas
12093 \begin_layout Plain Layout
12094 Space ! besides inline formulas
12102 \begin_layout Standard
12103 The space that surrounds inline formulas can be adjusted with the length
12112 \begin_layout Plain Layout
12123 The value of a length is set with the command
12131 \begin_layout Plain Layout
12141 that has the following scheme:
12144 \begin_layout Standard
12149 setlength{length name}{value}
12152 \begin_layout Standard
12160 \begin_inset space \thinspace{}
12166 \begin_layout Standard
12176 \begin_layout Standard
12177 is inserted in TeX-mode.
12179 \begin_inset space \thinspace{}
12182 mm space will now be set around all inline formulas:
12186 \begin_layout Plain Layout
12200 \begin_layout Standard
12201 This is a line with an inline formula
12202 \begin_inset Formula $A=B$
12206 \begin_inset space \thinspace{}
12209 mm surrounding space.
12213 \begin_layout Plain Layout
12227 \begin_layout Standard
12228 To return to the predefined value,
12234 is set to the value 0
12235 \begin_inset space \thinspace{}
12241 \begin_layout Section
12246 \begin_layout Plain Layout
12256 \begin_layout Plain Layout
12261 \begin_layout Plain Layout
12272 \begin_layout Plain Layout
12287 \begin_layout Standard
12288 Boxes for text are described in chapter
12295 \begin_inset space ~
12303 \begin_layout Subsection
12305 \begin_inset CommandInset label
12307 name "sub:Boxes-with-Frame"
12315 \begin_layout Plain Layout
12324 \begin_layout Standard
12325 It is possible to frame formulas or parts of it with the commands
12335 \begin_layout Plain Layout
12353 \begin_layout Plain Layout
12364 \begin_layout Standard
12365 When one of these commands is inserted to a formula, a blue box appears
12366 within a frame to enter formula parts.
12373 an additional formula has to be created by
12381 \begin_layout Plain Layout
12382 Due to a bug in LyX it is not possible to create a new formula with
12387 \begin_inset CommandInset href
12389 name "LyX-bug #1435"
12390 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12399 , because the box content will otherwise be treated as mathematical text.
12406 is used, a new formula is automatically created inside the frame.
12409 \begin_layout Standard
12416 is not suitable to frame displayed formulas, because the formula will always
12417 be set in the size of the text.
12424 is in contrary not suitable to frame inline formulas, because the formula
12425 will always be set in the size of a displayed formula.
12428 \begin_layout Standard
12435 there is the command
12445 \begin_layout Plain Layout
12453 where additionally the frame width and the alignment can be specified.
12460 is used in the following scheme:
12463 \begin_layout Standard
12468 framebox[frame width][position]{box content}
12471 \begin_layout Standard
12472 The position can either be
12489 right aligns the formula in the box.
12490 When no position is given, the formula will be centered.
12491 \begin_inset Newline newline
12494 Is no width given, also no position can be given.
12495 In this case the frame width is adjusted to the box content like for
12504 \begin_layout Standard
12511 is inserted, a box appears containing three blue boxes.
12512 The first two boxes are surrounded by brackets and denote the two optional
12514 The third box is for formula parts like for
12523 \begin_layout Standard
12525 \begin_inset Note Note
12528 \begin_layout Plain Layout
12529 The table has been set into a minipage to make the footnote appearing.
12530 Otherwise the footnote text would not be displayed.
12536 \begin_inset Box Frameless
12545 height_special "totalheight"
12548 \begin_layout Plain Layout
12550 \begin_inset Tabular
12551 <lyxtabular version="3" rows="5" columns="2">
12553 <column alignment="center" valignment="top" width="0">
12554 <column alignment="center" valignment="top" width="0">
12556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12559 \begin_layout Plain Layout
12564 \begin_layout Plain Layout
12565 Due to a bug in LyX it is not possible to create a new formula with
12570 \begin_inset CommandInset href
12572 name "LyX-bug #1435"
12573 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12590 \begin_layout Plain Layout
12592 \begin_inset Note Note
12595 \begin_layout Plain Layout
12602 is only used as spacer.
12614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12617 \begin_layout Plain Layout
12624 \begin_layout Plain Layout
12643 \begin_layout Plain Layout
12657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12660 \begin_layout Plain Layout
12661 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12674 \begin_layout Plain Layout
12681 \begin_layout Plain Layout
12696 \begin_layout Plain Layout
12710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12713 \begin_layout Plain Layout
12714 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12727 \begin_layout Plain Layout
12734 \begin_layout Plain Layout
12748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12751 \begin_layout Plain Layout
12752 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12765 \begin_layout Plain Layout
12772 \begin_layout Plain Layout
12782 \begin_inset Formula $\to$
12786 \begin_inset Formula $\to$
12799 \begin_layout Plain Layout
12809 \begin_inset Formula $\downarrow$
12817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12820 \begin_layout Plain Layout
12821 \begin_inset Formula $\raisebox{6mm}{}$
12825 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12829 \begin_inset Formula $\raisebox{-4mm}{}$
12850 \begin_layout Standard
12851 The frame thickness can also be adjusted.
12852 To do this the following commands have to be inserted in TeX-mode before
12856 \begin_layout Standard
12866 \begin_inset Quotes eld
12870 \begin_inset Quotes erd
12884 \begin_inset Quotes eld
12888 \begin_inset Quotes erd
12894 \begin_layout Standard
12895 \begin_inset Quotes eld
12899 \begin_inset Quotes erd
12902 specifies the minimal distance between the frame and the first character
12904 An example for this is the following framed formula:
12908 \begin_layout Plain Layout
12920 \begin_inset Formula \[
12925 Before this formula the commands
12928 \begin_layout Standard
12950 \begin_layout Standard
12951 were inserted in TeX-mode.
12952 The given values are used for all following boxes.
12955 \begin_layout Standard
12956 To return to the standard frame size, the command
12959 \begin_layout Standard
12984 \begin_layout Plain Layout
12998 \begin_layout Standard
12999 is inserted in TeX-mode before the next formula.
13002 \begin_layout Subsection
13003 Boxes without Frame
13004 \begin_inset CommandInset label
13006 name "sub:Boxes-without-Frame"
13014 \begin_layout Plain Layout
13015 Boxes ! without frame
13023 \begin_layout Standard
13024 For boxes without a frame there are the following box commands:
13034 \begin_layout Plain Layout
13052 \begin_layout Plain Layout
13070 \begin_layout Plain Layout
13081 \begin_layout Standard
13088 a box can be super- or subscripted.
13089 But in contrary to normal super- and subscripting, the characters in the
13090 box keep their font size.
13097 is used in the following scheme:
13100 \begin_layout Standard
13105 raisebox{height}{box content}
13108 \begin_layout Standard
13109 When the box should contain a formula, an extra formula is needed like for
13119 \begin_layout Standard
13121 \begin_inset Tabular
13122 <lyxtabular version="3" rows="4" columns="2">
13124 <column alignment="center" valignment="top" width="0">
13125 <column alignment="center" valignment="top" width="0">
13127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13130 \begin_layout Plain Layout
13136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13139 \begin_layout Plain Layout
13147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13150 \begin_layout Plain Layout
13154 \begin_inset Formula $\to$
13160 \begin_inset Formula $\to$
13168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13171 \begin_layout Plain Layout
13172 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13185 \begin_layout Plain Layout
13189 \begin_inset Formula $\to$
13195 \begin_inset Formula $\to$
13203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13206 \begin_layout Plain Layout
13207 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13220 \begin_layout Plain Layout
13224 \begin_inset Formula $\to$
13239 \begin_layout Plain Layout
13253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13256 \begin_layout Plain Layout
13260 \begin_layout Plain Layout
13284 \begin_layout Standard
13285 The last formula can currently only be created using TeX-mode because LyX
13286 inserts a box instead of the needed extra formula.
13290 \begin_layout Plain Layout
13292 \begin_inset CommandInset href
13294 name "LyX-bug #1435"
13295 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13307 \begin_layout Standard
13332 , with the difference that there is no frame.
13335 \begin_layout Subsection
13337 \begin_inset CommandInset label
13339 name "sub:Colored-Boxes"
13347 \begin_layout Plain Layout
13356 \begin_layout Standard
13357 To be able to use all commands explained in this section, the LaTeX-package
13366 \begin_layout Plain Layout
13371 is part of every LaTeX standard installation.
13380 \begin_layout Plain Layout
13386 has to be loaded in the LaTeX-preamble with the line
13390 \begin_layout Plain Layout
13391 When text is colored somewhere in the document with a predefined color,
13392 LyX loads the LaTeX-package
13397 Thus it is possible that the package is loaded twice, but this doesn't
13404 \begin_inset Note Note
13407 \begin_layout Plain Layout
13408 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13417 \begin_layout Standard
13425 \begin_layout Standard
13426 \begin_inset VSpace medskip
13429 To color boxes, the command
13439 \begin_layout Plain Layout
13447 is used in the following scheme:
13450 \begin_layout Standard
13455 colorbox{color}{box content}
13458 \begin_layout Standard
13459 The box content can also be a box and a
13465 can also be part of another box (see the 2nd and 3rd example).
13466 When the box should contain a formula, an extra formula has to be created,
13477 \begin_layout Plain Layout
13478 This also applies for the command
13486 \begin_inset CommandInset href
13488 name "LyX-bug #1435"
13489 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13501 \begin_layout Standard
13502 One of the following predefined colors can be chosen:
13505 \begin_layout Standard
13539 \begin_layout Standard
13541 \begin_inset Tabular
13542 <lyxtabular version="3" rows="4" columns="2">
13544 <column alignment="center" valignment="top" width="0">
13545 <column alignment="center" valignment="top" width="0">
13547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13550 \begin_layout Plain Layout
13556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13559 \begin_layout Plain Layout
13561 \begin_inset Note Note
13564 \begin_layout Plain Layout
13571 is only used as spacer.
13583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13586 \begin_layout Plain Layout
13590 \begin_inset Formula $\to$
13600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13603 \begin_layout Plain Layout
13604 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13617 \begin_layout Plain Layout
13621 \begin_inset Formula $\to$
13632 \begin_layout Plain Layout
13646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13649 \begin_layout Plain Layout
13650 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13663 \begin_layout Plain Layout
13670 \begin_layout Plain Layout
13682 \begin_inset Formula $\to$
13692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13695 \begin_layout Plain Layout
13696 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13712 \begin_layout Standard
13719 only colors the box but not the characters in the box.
13720 To color all characters, the whole formula is highlighted and the wanted
13721 color is chosen in the
13724 \begin_inset space ~
13730 The dialog can be called with the toolbar button
13731 \begin_inset Graphics
13732 filename ../images/dialog-show_character.png
13739 Edit\SpecialChar \menuseparator
13741 \begin_inset space ~
13744 Style\SpecialChar \menuseparator
13748 The formula number has then the same color as the formula.
13749 When the formula number should get another color than the formula characters,
13750 the color must be changed within the formula.
13753 \begin_layout Standard
13757 \begin_layout Standard
13760 \begin_inset Formula \begin{equation}
13761 \int A=B\label{eq:red}\end{equation}
13768 \begin_inset Formula \begin{equation}
13769 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13776 \begin_layout Standard
13778 \begin_inset CommandInset ref
13784 is completely colored red.
13785 \begin_inset Newline newline
13789 \begin_inset CommandInset ref
13791 reference "eq:redgreen"
13795 was first completely colored green to set the color for the formula number.
13796 Subsequently the formula characters were colored red.
13799 \begin_layout Standard
13800 \begin_inset VSpace bigskip
13803 To color the frame different than the rest of the box, the command
13813 \begin_layout Plain Layout
13821 is used in the following scheme:
13824 \begin_layout Standard
13829 fcolorbox{frame color}{color}{box content}
13832 \begin_layout Standard
13839 is an extension of the command
13846 The frame width is set, like for
13869 \begin_layout Plain Layout
13881 \begin_inset Formula \[
13882 \fcolorbox{cyan}{magenta}{A=B}\]
13890 \begin_layout Plain Layout
13904 \begin_layout Standard
13905 This formula was created with the command
13906 \begin_inset Newline newline
13914 \begin_inset Formula $\to$
13920 \begin_inset Formula $\to$
13930 \begin_layout Standard
13931 \begin_inset VSpace bigskip
13934 To use other colors than the predefined ones, they have to be defined first.
13937 \begin_layout Standard
13938 One can for example define the color
13939 \begin_inset Quotes eld
13947 \begin_inset Quotes erd
13950 with the LaTeX-preamble line:
13953 \begin_layout Standard
13958 definecolor{darkgreen}{cmyk}{0.5,
13976 \begin_layout Plain Layout
13987 \begin_layout Standard
13992 is the color space that denotes the colors
14009 The four comma separated numbers are the portion factor for the corresponding
14010 colors of the color space.
14011 The factors can be in the range of 0
14012 \begin_inset space \thinspace{}
14016 \begin_inset space \thinspace{}
14024 also the color space
14028 can be used for definitions.
14045 , so that there are in this case three portion factors for the corresponding
14047 Furthermore there is the color space
14051 with one portion factor for the gray value.
14054 \begin_layout Standard
14055 As example a framed box with the new defined color
14059 where the characters have been colored
14064 \begin_inset Formula \begin{equation}
14065 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14072 \begin_layout Standard
14073 Self-defined colors can also be used for text with the help of the command
14084 \begin_layout Plain Layout
14093 \begin_layout Standard
14097 \begin_layout Plain Layout
14101 textcolor{darkgreen}{
14107 \begin_inset Quotes eld
14111 \begin_inset Quotes erd
14118 \begin_layout Plain Layout
14128 \begin_layout Standard
14139 \begin_layout Plain Layout
14147 is used in the scheme
14151 textcolor{color}{characters to color}
14156 \begin_layout Subsection
14158 \begin_inset CommandInset label
14160 name "sub:Paragraph-Boxes"
14168 \begin_layout Plain Layout
14169 Boxes ! as paragraph
14177 \begin_layout Standard
14178 A box that can contain several lines and paragraphs, a so called paragraph
14179 box (parbox), can be created with the menu
14181 Insert\SpecialChar \menuseparator
14184 or the toolbar button
14185 \begin_inset Graphics
14186 filename ../images/box-insert.png
14194 \begin_layout Standard
14195 The following example shows a framed parbox in a line:
14198 \begin_layout Standard
14199 \begin_inset VSpace medskip
14203 \begin_inset Box Boxed
14212 height_special "totalheight"
14215 \begin_layout Plain Layout
14216 This is a paragraph box.
14218 \begin_inset space \thinspace{}
14221 cm long and can also contain formulas:
14222 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14233 \begin_layout Standard
14234 \begin_inset VSpace medskip
14240 \begin_layout Standard
14241 Such a box is created by right-clicking on the gray box inset.
14242 A dialog pops up showing the box properties.
14256 \begin_inset space \thinspace{}
14261 Vertical Box Alignment
14266 \begin_layout Standard
14267 \begin_inset VSpace medskip
14270 In LaTeX a parbox is created with the command
14280 \begin_layout Plain Layout
14288 that has the following scheme:
14291 \begin_layout Standard
14296 parbox[position]{width}{box content}
14299 \begin_layout Standard
14313 for bottom means that the box is aligned within the surrounding text with
14319 for top this is done with the first line.
14320 When no position is given, the box will be vertically centered, see section
14328 \begin_inset space ~
14333 manual for examples.
14336 \begin_layout Standard
14337 \begin_inset VSpace bigskip
14340 To frame formulas completely, including the formula number, the formula
14341 must be set into a parbox.
14342 To do this, the command
14356 is inserted in TeX-mode before the formula.
14365 \begin_layout Plain Layout
14375 is hereby the line width set for the document.
14376 Because the frame is outside the parbox, 2
14377 \begin_inset space \thinspace{}
14380 times the frame separation and the frame thickness must be subtracted from
14382 As this is not automatically done by LyX due to a bug
14386 \begin_layout Plain Layout
14387 \begin_inset CommandInset href
14389 name "LyX-bug #4483"
14390 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14399 , TeX-mode has to be used.
14400 To be able to multiply and subtract in arguments, the LaTeX-package
14408 \begin_layout Plain Layout
14413 is part of every LaTeX standard installation.
14422 \begin_layout Plain Layout
14428 must be loaded in the LaTeX-preamble with the line
14431 \begin_layout Standard
14439 \begin_layout Standard
14440 Behind the formula both boxes are closed by entering
14445 Here is an example:
14449 \begin_layout Plain Layout
14463 \begin_layout Standard
14467 \begin_layout Plain Layout
14485 \begin_inset Formula \begin{equation}
14486 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14494 \begin_layout Plain Layout
14505 \begin_layout Plain Layout
14519 \begin_layout Standard
14520 \begin_inset VSpace medskip
14523 As a parbox is used as argument of
14529 , there is in this case no difference between
14544 \begin_layout Standard
14545 \begin_inset VSpace bigskip
14548 Paragraph boxes are very useful to comment formulas directly.
14555 is used in combination with the command
14569 \begin_inset CommandInset ref
14571 reference "sub:User-defined-Numbering"
14578 \begin_layout Standard
14579 An example of a formula commented with
14588 \begin_layout Standard
14592 \begin_layout Plain Layout
14605 This is a description.
14606 It is distinctly separated from the formula and multiline.
14610 \begin_layout Plain Layout
14622 \begin_layout Standard
14623 Such a formula must be inserted completely in TeX-mode because LyX does
14624 not yet support the command
14631 The formula is created with the following command sequence:
14634 \begin_layout Standard
14647 is inserted in TeX-mode.
14651 \begin_layout Plain Layout
14652 When the formula style
14664 can also be replaced by
14671 (formula styles see
14672 \begin_inset CommandInset ref
14674 reference "sec:Formula-Styles"
14683 Then the description follows as normal text, and finally
14689 is inserted in TeX-mode.
14702 hereby create a displayed formula.
14705 \begin_layout Standard
14712 can be seen in this example that was
14713 \begin_inset Quotes eld
14717 \begin_inset Quotes erd
14720 using the mathematical textmode:
14721 \begin_inset Formula \[
14722 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14729 \begin_layout Section
14734 \begin_layout Plain Layout
14743 \begin_layout Subsection
14745 \begin_inset CommandInset label
14747 name "sub:Big-Operators"
14755 \begin_layout Plain Layout
14765 \begin_layout Plain Layout
14775 \begin_layout Plain Layout
14784 \begin_layout Standard
14785 To be able to use all integral operators listed here, the option
14787 Use esint package automatically
14789 must be set in the document settings under
14792 \begin_inset space ~
14800 \begin_layout Standard
14801 \begin_inset space \hfill{}
14805 \begin_inset Tabular
14806 <lyxtabular version="3" rows="11" columns="2">
14808 <column alignment="center" valignment="top" width="0pt">
14809 <column alignment="center" valignment="top" width="0pt">
14811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14814 \begin_layout Plain Layout
14820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14823 \begin_layout Plain Layout
14831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14834 \begin_layout Plain Layout
14841 \begin_layout Plain Layout
14854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14857 \begin_layout Plain Layout
14858 \begin_inset Formula $\sum$
14868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14871 \begin_layout Plain Layout
14878 \begin_layout Plain Layout
14891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14894 \begin_layout Plain Layout
14895 \begin_inset Formula $\int$
14905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14908 \begin_layout Plain Layout
14916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14919 \begin_layout Plain Layout
14920 \begin_inset Formula $\intop$
14930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14933 \begin_layout Plain Layout
14941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14944 \begin_layout Plain Layout
14945 \begin_inset Formula $\oint$
14955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14958 \begin_layout Plain Layout
14966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14969 \begin_layout Plain Layout
14970 \begin_inset Formula $\ointop$
14980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14983 \begin_layout Plain Layout
14991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14994 \begin_layout Plain Layout
14995 \begin_inset Formula $\ointctrclockwise$
15005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15008 \begin_layout Plain Layout
15016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15019 \begin_layout Plain Layout
15020 \begin_inset Formula $\ointclockwise$
15030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15033 \begin_layout Plain Layout
15041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15044 \begin_layout Plain Layout
15045 \begin_inset Formula $\sqint$
15055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15058 \begin_layout Plain Layout
15066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15069 \begin_layout Plain Layout
15070 \begin_inset Formula $\bigcap$
15080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15083 \begin_layout Plain Layout
15091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15094 \begin_layout Plain Layout
15095 \begin_inset Formula $\bigcup$
15109 \begin_inset space \hfill{}
15113 \begin_inset Tabular
15114 <lyxtabular version="3" rows="10" columns="2">
15116 <column alignment="center" valignment="top" width="0pt">
15117 <column alignment="center" valignment="top" width="0pt">
15119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15122 \begin_layout Plain Layout
15128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15131 \begin_layout Plain Layout
15139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15142 \begin_layout Plain Layout
15149 \begin_layout Plain Layout
15162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15165 \begin_layout Plain Layout
15166 \begin_inset Formula $\prod$
15176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15179 \begin_layout Plain Layout
15187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15190 \begin_layout Plain Layout
15191 \begin_inset Formula $\coprod$
15201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15204 \begin_layout Plain Layout
15212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15215 \begin_layout Plain Layout
15216 \begin_inset Formula $\bigodot$
15226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15229 \begin_layout Plain Layout
15237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15240 \begin_layout Plain Layout
15241 \begin_inset Formula $\bigotimes$
15251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15254 \begin_layout Plain Layout
15262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15265 \begin_layout Plain Layout
15266 \begin_inset Formula $\bigoplus$
15276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15279 \begin_layout Plain Layout
15287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15290 \begin_layout Plain Layout
15291 \begin_inset Formula $\bigwedge$
15301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15304 \begin_layout Plain Layout
15312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15315 \begin_layout Plain Layout
15316 \begin_inset Formula $\bigvee$
15326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15329 \begin_layout Plain Layout
15337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15340 \begin_layout Plain Layout
15341 \begin_inset Formula $\bigsqcup$
15351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15354 \begin_layout Plain Layout
15362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15365 \begin_layout Plain Layout
15366 \begin_inset Formula $\biguplus$
15380 \begin_inset space \hfill{}
15386 \begin_layout Standard
15387 All big operators can also be inserted via the math toolbar button
15388 \begin_inset Graphics
15389 filename ../images/math/intop.png
15397 \begin_layout Standard
15398 The operators are called big because they are bigger than the sometimes
15399 equal looking binary operators.
15400 All big operators can have limits as described in the next subsection.
15403 \begin_layout Standard
15429 \begin_inset space ~
15432 in the style the operator limits are displayed, see
15433 \begin_inset CommandInset ref
15435 reference "sub:Operator-Limits"
15443 \begin_layout Subsubsection*
15444 Advices for Integrals
15447 \begin_layout Standard
15452 in an integral is an operator, that therefore has to be set upright.
15453 This is done by highlighting the
15457 and using the keyboard shortcut
15467 \begin_layout Plain Layout
15473 \begin_inset CommandInset ref
15475 reference "sub:Font-Styles"
15485 Finally the smallest space is inserted before the
15489 , as this is usual for operators.
15493 \begin_layout Standard
15495 \begin_inset Formula $\int A(x)dx$
15499 \begin_inset Newline newline
15506 \begin_layout Plain Layout
15516 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15522 \begin_layout Standard
15523 For multiple integrals there are the following commands:
15524 \begin_inset VSpace medskip
15530 \begin_layout Standard
15531 \begin_inset space \hfill{}
15535 \begin_inset Tabular
15536 <lyxtabular version="3" rows="4" columns="2">
15538 <column alignment="center" valignment="top" width="0">
15539 <column alignment="center" valignment="top" width="0">
15541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15544 \begin_layout Plain Layout
15550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15553 \begin_layout Plain Layout
15555 \begin_inset Note Note
15558 \begin_layout Plain Layout
15565 is only used as spacer.
15577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15580 \begin_layout Plain Layout
15588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15591 \begin_layout Plain Layout
15592 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15605 \begin_layout Plain Layout
15613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15616 \begin_layout Plain Layout
15617 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15630 \begin_layout Plain Layout
15638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15641 \begin_layout Plain Layout
15642 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15656 \begin_inset space \hfill{}
15660 \begin_inset Tabular
15661 <lyxtabular version="3" rows="4" columns="2">
15663 <column alignment="center" valignment="top" width="0">
15664 <column alignment="center" valignment="top" width="0">
15666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15669 \begin_layout Plain Layout
15675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15678 \begin_layout Plain Layout
15686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15689 \begin_layout Plain Layout
15697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15700 \begin_layout Plain Layout
15701 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15714 \begin_layout Plain Layout
15722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15725 \begin_layout Plain Layout
15726 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15739 \begin_layout Plain Layout
15747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15750 \begin_layout Plain Layout
15751 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15765 \begin_inset space \hfill{}
15771 \begin_layout Subsection
15773 \begin_inset CommandInset label
15775 name "sub:Operator-Limits"
15783 \begin_layout Plain Layout
15792 \begin_layout Standard
15793 Limits are created by super- and subscripts:
15796 \begin_layout Standard
15798 \begin_inset Tabular
15799 <lyxtabular version="3" rows="2" columns="2">
15801 <column alignment="center" valignment="top" width="0pt">
15802 <column alignment="center" valignment="top" width="0pt">
15804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15807 \begin_layout Plain Layout
15813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15816 \begin_layout Plain Layout
15818 \begin_inset Note Note
15821 \begin_layout Plain Layout
15828 is only used as spacer.
15840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15843 \begin_layout Plain Layout
15852 \begin_layout Plain Layout
15862 \begin_inset Formula $\to$
15866 \begin_inset Formula $\to$
15874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15877 \begin_layout Plain Layout
15878 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15894 \begin_layout Standard
15895 Limits of inline formulas are set right beside the operator.
15896 Limits in displayed formulas are set above or below the operator, except
15897 of integral limits.
15900 \begin_layout Standard
15901 To force that the limits are set beside the operator, the cursor is set
15902 directly behind the operator and the limits type is changed with the menu
15905 Edit\SpecialChar \menuseparator
15906 Math\SpecialChar \menuseparator
15925 \begin_layout Standard
15926 The default limits type is this:
15927 \begin_inset Formula \[
15928 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15932 This is how it looks when the limits type was changed to
15939 \begin_inset Formula \[
15940 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15944 For integrals, except of
15956 , the limits are by default set beside the operator.
15957 But for multiple integrals the limits are often set below the operator.
15958 In the following example the limits type was therefore set to
15962 and so set below the integrals:
15963 \begin_inset Formula \begin{equation}
15964 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15971 \begin_layout Standard
15972 \begin_inset VSpace medskip
15975 To specify conditions for limits, the commands
15985 \begin_layout Plain Layout
16003 \begin_layout Plain Layout
16012 To create for example this expression
16013 \begin_inset Formula \begin{equation}
16014 \sum_{\begin{subarray}{c}
16016 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16023 \begin_layout Standard
16024 the following has to be done:
16025 \begin_inset Newline newline
16040 \begin_layout Plain Layout
16052 One is now in a blue box under the summation operator and insert there
16061 \begin_layout Plain Layout
16073 The blue box is now within a purple box and now several lines can be written
16075 A new line is created by inserting a line break (
16078 arg "newline-insert newline"
16083 \begin_inset Newline newline
16088 0<k<1000 Ctrl+Return
16089 \begin_inset Newline newline
16094 is typed in, a new box appears below for the new line.
16097 \begin_layout Standard
16098 The alignment of the lines can be changed to left aligned with the
16108 Edit\SpecialChar \menuseparator
16112 To get right alignment,
16120 \begin_layout Plain Layout
16131 is inserted at the beginning of the line.
16134 \begin_layout Standard
16147 with the difference that the lines are always centered.
16150 \begin_layout Standard
16151 \begin_inset VSpace bigskip
16155 \begin_inset CommandInset ref
16157 reference "eq:substack"
16161 there can be too much space beside an operator, because the characters
16162 following the operator are set beside the limits.
16165 \begin_layout Standard
16166 To avoid this, the following macro can be used in the LaTeX-preamble:
16169 \begin_layout Standard
16183 \begin_inset Newline newline
16195 \begin_inset Newline newline
16202 mathclapinternal #1#2{
16206 mathsurround =0pt #1{#2}$}}
16209 \begin_layout Standard
16210 This defines the command
16220 \begin_layout Plain Layout
16228 that sets the width of the limit to 0
16229 \begin_inset space \thinspace{}
16233 The command scheme is
16236 \begin_layout Standard
16244 \begin_layout Standard
16245 where the limit can consist of several conditions.
16248 \begin_layout Standard
16250 \begin_inset CommandInset ref
16252 reference "eq:substack"
16256 , one uses the command
16259 \begin_layout Standard
16272 \begin_layout Plain Layout
16281 0<k<1000 Ctrl+Return
16284 \begin_layout Standard
16285 to create the lower limit.
16286 The summand is now directly behind the summation operator:
16287 \begin_inset Formula \[
16288 \sum_{\mathclap{\substack{0<k<1000\\
16289 \\k\,\in\,\mathbb{N}}
16297 \begin_layout Standard
16298 \begin_inset VSpace bigskip
16301 How to use one limit for several operators is described in
16302 \begin_inset CommandInset ref
16304 reference "sub:Self-defined-Operators"
16311 \begin_layout Standard
16312 \begin_inset Newpage newpage
16318 \begin_layout Subsection
16320 \begin_inset CommandInset label
16322 name "sub:Binary-Operators"
16330 \begin_layout Plain Layout
16339 \begin_layout Standard
16340 Binary operators are surrounded by space when there is a character before
16342 \begin_inset VSpace medskip
16348 \begin_layout Standard
16349 \begin_inset space \hfill{}
16353 \begin_inset Tabular
16354 <lyxtabular version="3" rows="13" columns="2">
16356 <column alignment="center" valignment="top" width="0pt">
16357 <column alignment="center" valignment="top" width="0pt">
16359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16362 \begin_layout Plain Layout
16364 \begin_inset Note Note
16367 \begin_layout Plain Layout
16374 is only used as spacer.
16384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16387 \begin_layout Plain Layout
16395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16398 \begin_layout Plain Layout
16404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16407 \begin_layout Plain Layout
16408 \begin_inset Formula $+$
16418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16421 \begin_layout Plain Layout
16427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16430 \begin_layout Plain Layout
16431 \begin_inset Formula $-$
16441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16444 \begin_layout Plain Layout
16452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16455 \begin_layout Plain Layout
16456 \begin_inset Formula $\pm$
16466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16469 \begin_layout Plain Layout
16477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16480 \begin_layout Plain Layout
16481 \begin_inset Formula $\mp$
16491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16494 \begin_layout Plain Layout
16502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16505 \begin_layout Plain Layout
16506 \begin_inset Formula $\cdot$
16516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16519 \begin_layout Plain Layout
16527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16530 \begin_layout Plain Layout
16531 \begin_inset Formula $\times$
16541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16544 \begin_layout Plain Layout
16552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16555 \begin_layout Plain Layout
16556 \begin_inset Formula $\div$
16566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16569 \begin_layout Plain Layout
16573 \begin_layout Plain Layout
16586 \begin_layout Plain Layout
16598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16601 \begin_layout Plain Layout
16602 \begin_inset Formula $*$
16612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16615 \begin_layout Plain Layout
16623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16626 \begin_layout Plain Layout
16627 \begin_inset Formula $\star$
16637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16640 \begin_layout Plain Layout
16648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16651 \begin_layout Plain Layout
16652 \begin_inset Formula $\circ$
16662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16665 \begin_layout Plain Layout
16673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16676 \begin_layout Plain Layout
16677 \begin_inset Formula $\diamond$
16687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16690 \begin_layout Plain Layout
16698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16701 \begin_layout Plain Layout
16702 \begin_inset Formula $\bullet$
16716 \begin_inset space \hfill{}
16720 \begin_inset Tabular
16721 <lyxtabular version="3" rows="13" columns="2">
16723 <column alignment="center" valignment="top" width="0pt">
16724 <column alignment="center" valignment="top" width="0pt">
16726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16729 \begin_layout Plain Layout
16735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16738 \begin_layout Plain Layout
16746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16749 \begin_layout Plain Layout
16757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16760 \begin_layout Plain Layout
16761 \begin_inset Formula $\nabla$
16771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16774 \begin_layout Plain Layout
16782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16785 \begin_layout Plain Layout
16786 \begin_inset Formula $\bigtriangledown$
16796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16799 \begin_layout Plain Layout
16807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16810 \begin_layout Plain Layout
16811 \begin_inset Formula $\bigtriangleup$
16821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16824 \begin_layout Plain Layout
16832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16835 \begin_layout Plain Layout
16836 \begin_inset Formula $\Box$
16846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16849 \begin_layout Plain Layout
16857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16860 \begin_layout Plain Layout
16861 \begin_inset Formula $\cap$
16871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16874 \begin_layout Plain Layout
16882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16885 \begin_layout Plain Layout
16886 \begin_inset Formula $\cup$
16896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16899 \begin_layout Plain Layout
16907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16910 \begin_layout Plain Layout
16911 \begin_inset Formula $\dagger$
16921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16924 \begin_layout Plain Layout
16932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16935 \begin_layout Plain Layout
16936 \begin_inset Formula $\ddagger$
16946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16949 \begin_layout Plain Layout
16957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16960 \begin_layout Plain Layout
16961 \begin_inset Formula $\wr$
16971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16974 \begin_layout Plain Layout
16982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16985 \begin_layout Plain Layout
16986 \begin_inset Formula $\bigcirc$
16996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16999 \begin_layout Plain Layout
17007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17010 \begin_layout Plain Layout
17011 \begin_inset Formula $\wedge$
17021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17024 \begin_layout Plain Layout
17032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17035 \begin_layout Plain Layout
17036 \begin_inset Formula $\vee$
17050 \begin_inset space \hfill{}
17054 \begin_inset Tabular
17055 <lyxtabular version="3" rows="13" columns="2">
17057 <column alignment="center" valignment="top" width="0pt">
17058 <column alignment="center" valignment="top" width="0pt">
17060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17063 \begin_layout Plain Layout
17069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17072 \begin_layout Plain Layout
17080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17083 \begin_layout Plain Layout
17091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17094 \begin_layout Plain Layout
17095 \begin_inset Formula $\oplus$
17105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17108 \begin_layout Plain Layout
17116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17119 \begin_layout Plain Layout
17120 \begin_inset Formula $\ominus$
17130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17133 \begin_layout Plain Layout
17141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17144 \begin_layout Plain Layout
17145 \begin_inset Formula $\otimes$
17155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17158 \begin_layout Plain Layout
17166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17169 \begin_layout Plain Layout
17170 \begin_inset Formula $\oslash$
17180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17183 \begin_layout Plain Layout
17191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17194 \begin_layout Plain Layout
17195 \begin_inset Formula $\odot$
17205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17208 \begin_layout Plain Layout
17216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17219 \begin_layout Plain Layout
17220 \begin_inset Formula $\amalg$
17230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17233 \begin_layout Plain Layout
17241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17244 \begin_layout Plain Layout
17245 \begin_inset Formula $\uplus$
17255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17258 \begin_layout Plain Layout
17266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17269 \begin_layout Plain Layout
17270 \begin_inset Formula $\setminus$
17280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17283 \begin_layout Plain Layout
17291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17294 \begin_layout Plain Layout
17295 \begin_inset Formula $\sqcap$
17305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17308 \begin_layout Plain Layout
17316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17319 \begin_layout Plain Layout
17320 \begin_inset Formula $\sqcup$
17330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17333 \begin_layout Plain Layout
17341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17344 \begin_layout Plain Layout
17345 \begin_inset Formula $\triangleleft$
17355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17358 \begin_layout Plain Layout
17366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17369 \begin_layout Plain Layout
17370 \begin_inset Formula $\triangleright$
17384 \begin_inset space \hfill{}
17390 \begin_layout Standard
17391 All binary operators can also be inserted via the math toolbar button
17392 \begin_inset Graphics
17393 filename ../images/math/pm.png
17401 \begin_layout Standard
17402 To typeset the Laplace operator also
17419 \begin_inset Formula $\nabla^{2}$
17422 ) can be used instead of
17431 \begin_layout Standard
17438 Insert\SpecialChar \menuseparator
17450 \begin_layout Subsection
17451 Self-defined Operators
17452 \begin_inset CommandInset label
17454 name "sub:Self-defined-Operators"
17462 \begin_layout Plain Layout
17463 Operators ! self-defined
17471 \begin_layout Standard
17472 With the help of the command
17476 DeclareMathOperator
17482 \begin_layout Plain Layout
17487 DeclareMathOperator
17492 custom operators can be defined in the LaTeX-preamble.
17493 Its command scheme is:
17496 \begin_layout Standard
17501 DeclareMathOperator{new command}{display}
17504 \begin_layout Standard
17505 Display can be characters or symbols that define how the operator looks
17507 To define a big operator a * is set behind the command.
17508 All self-defined big operators can have limits as described in
17509 \begin_inset CommandInset ref
17511 reference "sub:Operator-Limits"
17518 \begin_layout Standard
17519 For example the LaTeX-preamble line
17522 \begin_layout Standard
17527 DeclareMathOperator*{
17534 \begin_layout Standard
17535 defines the command
17541 , that inserts a big operator consisting of the lozenge symbol from
17542 \begin_inset CommandInset ref
17544 reference "sub:Miscellaneous-Symbols"
17549 \begin_inset Formula \[
17550 \Lozenge_{n=1}^{\infty}\]
17554 The command for this formula is:
17565 \begin_inset Formula $\to$
17571 \begin_layout Standard
17572 \begin_inset VSpace bigskip
17575 When self-defined operators are not used several times in the document,
17576 they can also be defined with the commands
17586 \begin_layout Plain Layout
17604 \begin_layout Plain Layout
17612 , which have the following scheme:
17615 \begin_layout Standard
17629 \begin_layout Standard
17636 defines big operators,
17645 \begin_layout Standard
17653 \begin_inset space \thinspace{}
17657 \begin_inset space \space{}
17660 be used to use one limit for several operators:
17663 \begin_layout Standard
17664 \begin_inset Formula \[
17665 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17672 \begin_layout Standard
17673 The command for the formula above is:
17674 \begin_inset Newline newline
17693 \begin_layout Plain Layout
17705 \begin_inset Formula $\to$
17714 \begin_layout Plain Layout
17728 \begin_layout Section
17733 \begin_layout Plain Layout
17742 \begin_layout Subsection
17744 \begin_inset CommandInset label
17746 name "sub:Font-Styles"
17754 \begin_layout Plain Layout
17763 \begin_layout Standard
17764 Latin letters in formulas can be set in one of the following font styles:
17765 \begin_inset VSpace -2mm
17771 \begin_layout Standard
17773 \begin_inset Tabular
17774 <lyxtabular version="3" rows="6" columns="3">
17776 <column alignment="center" valignment="top" width="0">
17777 <column alignment="center" valignment="top" width="0">
17778 <column alignment="center" valignment="top" width="0">
17780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17783 \begin_layout Plain Layout
17789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17792 \begin_layout Plain Layout
17798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17801 \begin_layout Plain Layout
17809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17812 \begin_layout Plain Layout
17821 \begin_layout Plain Layout
17837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17840 \begin_layout Plain Layout
17841 \begin_inset Formula $\mathbb{ABC}$
17849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17852 \begin_layout Plain Layout
17865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17868 \begin_layout Plain Layout
17877 \begin_layout Plain Layout
17893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17896 \begin_layout Plain Layout
17897 \begin_inset Formula $\mathbf{AbC}$
17905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17908 \begin_layout Plain Layout
17921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17924 \begin_layout Plain Layout
17933 \begin_layout Plain Layout
17949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17952 \begin_layout Plain Layout
17953 \begin_inset Formula $\boldsymbol{AbC}$
17961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17964 \begin_layout Plain Layout
17967 arg "font-boldsymbol"
17977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17980 \begin_layout Plain Layout
17989 \begin_layout Plain Layout
18005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18008 \begin_layout Plain Layout
18009 \begin_inset Formula $\mathcal{ABC}$
18017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18020 \begin_layout Plain Layout
18033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18036 \begin_layout Plain Layout
18045 \begin_layout Plain Layout
18061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18064 \begin_layout Plain Layout
18065 \begin_inset Formula $\mathfrak{AbC}$
18073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18076 \begin_layout Plain Layout
18090 \begin_layout Standard
18092 \begin_inset Tabular
18093 <lyxtabular version="3" rows="5" columns="3">
18095 <column alignment="center" valignment="top" width="0">
18096 <column alignment="center" valignment="top" width="0">
18097 <column alignment="center" valignment="top" width="0">
18099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18102 \begin_layout Plain Layout
18108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18111 \begin_layout Plain Layout
18117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18120 \begin_layout Plain Layout
18128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18131 \begin_layout Plain Layout
18140 \begin_layout Plain Layout
18156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18159 \begin_layout Plain Layout
18160 \begin_inset Formula $\mathit{AbC}$
18168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18171 \begin_layout Plain Layout
18179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18182 \begin_layout Plain Layout
18191 \begin_layout Plain Layout
18207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18210 \begin_layout Plain Layout
18211 \begin_inset Formula $\mathrm{AbC}$
18219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18222 \begin_layout Plain Layout
18235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18238 \begin_layout Plain Layout
18247 \begin_layout Plain Layout
18263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18266 \begin_layout Plain Layout
18267 \begin_inset Formula $\mathsf{AbC}$
18275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18278 \begin_layout Plain Layout
18291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18294 \begin_layout Plain Layout
18303 \begin_layout Plain Layout
18319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18322 \begin_layout Plain Layout
18323 \begin_inset Formula $\mathtt{AbC}$
18331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18334 \begin_layout Plain Layout
18337 arg "font-typewriter"
18353 \begin_layout Standard
18354 \begin_inset Note Greyedout
18357 \begin_layout Plain Layout
18374 can only be used for big letters.
18382 \begin_layout Standard
18383 Predefined is the style
18392 \begin_layout Standard
18393 The style commands work also for letters in mathematical constructs:
18394 \begin_inset Formula \[
18395 \mathfrak{A=\frac{b}{C}}\]
18402 \begin_layout Standard
18403 Characters in mathematical text don't appear in a math font style but in
18404 the text font style
18411 That their style can't be set correctly via the text style dialog is a
18416 \begin_layout Plain Layout
18417 \begin_inset CommandInset href
18419 name "LyX-bug #4091"
18420 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18432 \begin_layout Standard
18433 Instead of the style commands the dialog
18435 Edit\SpecialChar \menuseparator
18436 Math\SpecialChar \menuseparator
18439 or the toolbar button
18440 \begin_inset Graphics
18441 filename ../images/math/font.png
18449 \begin_layout Subsection
18451 \begin_inset CommandInset label
18453 name "sub:Bold-Formulas"
18461 \begin_layout Plain Layout
18470 \begin_layout Standard
18471 To make a complete formula bold, the command
18477 from the previous subsection cannot be used, because it doesn't work for
18478 small Greek letters.
18479 Furthermore it prints Latin letters always upright, like in the following
18483 \begin_layout Standard
18484 \begin_inset Formula \[
18485 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18492 \begin_layout Standard
18493 To display the formula correctly, the command
18500 \begin_inset Formula \[
18501 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18505 It is also possible to set the formula in a
18507 boldmath environment
18510 This environment is created by inserting the command
18518 \begin_layout Plain Layout
18529 To end the environment, the command
18537 \begin_layout Plain Layout
18547 is inserted in TeX-mode.
18551 \begin_layout Plain Layout
18561 \begin_inset Formula \[
18562 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18570 \begin_layout Plain Layout
18582 \begin_layout Subsection
18587 \begin_layout Plain Layout
18596 \begin_layout Standard
18597 Formulas can be colored like normal text: Highlight a formula or a formula
18603 Here is a formula in magenta:
18604 \begin_inset Formula \[
18605 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18612 \begin_layout Standard
18613 You can also define your own colors as described in
18614 \begin_inset CommandInset ref
18616 reference "sub:Colored-Boxes"
18621 They can be used with the TeX code command
18631 \begin_layout Plain Layout
18642 \begin_layout Standard
18647 textcolor{color}{characters or formula}
18650 \begin_layout Standard
18651 The following example was colored completely dark green and partly red:
18654 \begin_layout Standard
18658 \begin_layout Plain Layout
18662 textcolor{darkgreen}{
18668 \begin_inset Formula \[
18669 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18677 \begin_layout Plain Layout
18687 \begin_layout Standard
18688 Due to a bug in LyX only complete formulas can be colored with self-defined
18693 \begin_layout Plain Layout
18694 \begin_inset CommandInset href
18696 name "LyX-bug #5269"
18697 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18709 \begin_layout Subsection
18711 \begin_inset CommandInset label
18713 name "sub:Font-Sizes"
18721 \begin_layout Plain Layout
18730 \begin_layout Standard
18731 For characters in formulas there are, analog to characters in text, the
18732 following size commands:
18735 \begin_layout Standard
18779 \begin_inset Newline newline
18801 \begin_layout Standard
18802 The size produced by the commands depends on the document font size, that
18803 corresponds with the command
18810 The other commands produce smaller or larger sizes than
18817 The font size can however not exceed a certain value.
18818 Is for example the document font size 12
18819 \begin_inset space \thinspace{}
18828 switches to the same size as
18838 \begin_layout Standard
18839 A size command is inserted in TeX-mode before the formula and sets the size
18840 for all following formula and text characters.
18841 To switch back to the initial size, the command
18847 is inserted behind the formula in TeX-mode.
18850 \begin_layout Standard
18851 Within a formula the size can only be changed for symbols or letters in
18853 To do this, the size command is inserted in mathematical text.
18854 All following characters until the end of the mathematical text or until
18855 another size command will have the selected size.
18857 \begin_inset VSpace -2mm
18863 \begin_layout Standard
18867 \begin_layout Plain Layout
18877 \begin_inset Formula \[
18878 A=\frac{B}{c}\cdot\maltese\]
18883 \begin_inset Formula \[
18884 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18892 \begin_layout Plain Layout
18904 \begin_layout Standard
18905 \begin_inset VSpace medskip
18908 Before both formulas the command
18915 The command for the second formula is:
18916 \begin_inset Newline newline
18927 \begin_layout Plain Layout
18942 \begin_layout Plain Layout
18957 \begin_layout Plain Layout
18972 \begin_layout Plain Layout
18982 \begin_inset Formula $\to$
18986 \begin_inset Formula $\to$
18990 \begin_inset Newline newline
18994 \begin_inset space \hspace*{}
19008 \begin_layout Plain Layout
19023 \begin_layout Plain Layout
19038 \begin_layout Plain Layout
19050 \begin_layout Standard
19051 If a symbol cannot be displayed in different sizes, it will always be displayed
19052 in the default size.
19055 \begin_layout Section
19060 \begin_layout Plain Layout
19069 \begin_layout Standard
19070 All Greek letters can also be inserted via the toolbar button
19071 \begin_inset Graphics
19072 filename ../images/math/alpha.png
19080 \begin_layout Subsection
19085 \begin_layout Plain Layout
19086 Greek letters ! small
19094 \begin_layout Standard
19095 \begin_inset space \hfill{}
19099 \begin_inset Tabular
19100 <lyxtabular version="3" rows="11" columns="2">
19102 <column alignment="center" valignment="top" width="0pt">
19103 <column alignment="center" valignment="top" width="0pt">
19105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19108 \begin_layout Plain Layout
19114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19117 \begin_layout Plain Layout
19125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19128 \begin_layout Plain Layout
19136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19139 \begin_layout Plain Layout
19140 \begin_inset Formula $\alpha$
19150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19153 \begin_layout Plain Layout
19161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19164 \begin_layout Plain Layout
19165 \begin_inset Formula $\beta$
19175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19178 \begin_layout Plain Layout
19186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19189 \begin_layout Plain Layout
19190 \begin_inset Formula $\gamma$
19200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19203 \begin_layout Plain Layout
19211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19214 \begin_layout Plain Layout
19215 \begin_inset Formula $\delta$
19225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19228 \begin_layout Plain Layout
19236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19239 \begin_layout Plain Layout
19240 \begin_inset Formula $\epsilon$
19250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19253 \begin_layout Plain Layout
19261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19264 \begin_layout Plain Layout
19265 \begin_inset Formula $\varepsilon$
19275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19278 \begin_layout Plain Layout
19286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19289 \begin_layout Plain Layout
19290 \begin_inset Formula $\zeta$
19300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19303 \begin_layout Plain Layout
19311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19314 \begin_layout Plain Layout
19315 \begin_inset Formula $\eta$
19325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19328 \begin_layout Plain Layout
19336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19339 \begin_layout Plain Layout
19340 \begin_inset Formula $\theta$
19350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19353 \begin_layout Plain Layout
19361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19364 \begin_layout Plain Layout
19365 \begin_inset Formula $\vartheta$
19379 \begin_inset space \hfill{}
19383 \begin_inset Tabular
19384 <lyxtabular version="3" rows="12" columns="2">
19386 <column alignment="center" valignment="top" width="0pt">
19387 <column alignment="center" valignment="top" width="0pt">
19389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19392 \begin_layout Plain Layout
19398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19401 \begin_layout Plain Layout
19409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19412 \begin_layout Plain Layout
19420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19423 \begin_layout Plain Layout
19424 \begin_inset Formula $\iota$
19434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19437 \begin_layout Plain Layout
19445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19448 \begin_layout Plain Layout
19449 \begin_inset Formula $\kappa$
19459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19462 \begin_layout Plain Layout
19470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19473 \begin_layout Plain Layout
19474 \begin_inset Formula $\varkappa$
19484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19487 \begin_layout Plain Layout
19495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19498 \begin_layout Plain Layout
19499 \begin_inset Formula $\lambda$
19509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19512 \begin_layout Plain Layout
19520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19523 \begin_layout Plain Layout
19524 \begin_inset Formula $\mu$
19534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19537 \begin_layout Plain Layout
19545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19548 \begin_layout Plain Layout
19549 \begin_inset Formula $\nu$
19559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19562 \begin_layout Plain Layout
19570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19573 \begin_layout Plain Layout
19574 \begin_inset Formula $\xi$
19584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19587 \begin_layout Plain Layout
19593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19596 \begin_layout Plain Layout
19597 \begin_inset Formula $o$
19607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19610 \begin_layout Plain Layout
19618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19621 \begin_layout Plain Layout
19622 \begin_inset Formula $\pi$
19632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19635 \begin_layout Plain Layout
19643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19646 \begin_layout Plain Layout
19647 \begin_inset Formula $\varpi$
19657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19660 \begin_layout Plain Layout
19668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19671 \begin_layout Plain Layout
19672 \begin_inset Formula $\rho$
19686 \begin_inset space \hfill{}
19690 \begin_inset Tabular
19691 <lyxtabular version="3" rows="11" columns="2">
19693 <column alignment="center" valignment="top" width="0pt">
19694 <column alignment="center" valignment="top" width="0pt">
19696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19699 \begin_layout Plain Layout
19705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19708 \begin_layout Plain Layout
19716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19719 \begin_layout Plain Layout
19727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19730 \begin_layout Plain Layout
19731 \begin_inset Formula $\varrho$
19741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19744 \begin_layout Plain Layout
19752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19755 \begin_layout Plain Layout
19756 \begin_inset Formula $\sigma$
19766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19769 \begin_layout Plain Layout
19777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19780 \begin_layout Plain Layout
19781 \begin_inset Formula $\varsigma$
19791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19794 \begin_layout Plain Layout
19802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19805 \begin_layout Plain Layout
19806 \begin_inset Formula $\tau$
19816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19819 \begin_layout Plain Layout
19827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19830 \begin_layout Plain Layout
19831 \begin_inset Formula $\upsilon$
19841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19844 \begin_layout Plain Layout
19852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19855 \begin_layout Plain Layout
19856 \begin_inset Formula $\phi$
19866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19869 \begin_layout Plain Layout
19877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19880 \begin_layout Plain Layout
19881 \begin_inset Formula $\varphi$
19891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19894 \begin_layout Plain Layout
19902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19905 \begin_layout Plain Layout
19906 \begin_inset Formula $\chi$
19916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19919 \begin_layout Plain Layout
19927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19930 \begin_layout Plain Layout
19931 \begin_inset Formula $\psi$
19941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19944 \begin_layout Plain Layout
19952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19955 \begin_layout Plain Layout
19956 \begin_inset Formula $\omega$
19970 \begin_inset space \hfill{}
19976 \begin_layout Standard
19977 \begin_inset VSpace medskip
19983 \begin_layout Standard
19984 How to create upright Greek letters is explained in
19985 \begin_inset CommandInset ref
19987 reference "sub:Upright-small-Greek"
19994 \begin_layout Subsection
19999 \begin_layout Plain Layout
20000 Greek letters ! big
20008 \begin_layout Standard
20009 \begin_inset space \hfill{}
20013 \begin_inset Tabular
20014 <lyxtabular version="3" rows="7" columns="2">
20016 <column alignment="center" valignment="top" width="0pt">
20017 <column alignment="center" valignment="top" width="0pt">
20019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20022 \begin_layout Plain Layout
20028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20031 \begin_layout Plain Layout
20039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20042 \begin_layout Plain Layout
20050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20053 \begin_layout Plain Layout
20054 \begin_inset Formula $\Gamma$
20064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20067 \begin_layout Plain Layout
20075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20078 \begin_layout Plain Layout
20079 \begin_inset Formula $\Delta$
20089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20092 \begin_layout Plain Layout
20100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20103 \begin_layout Plain Layout
20104 \begin_inset Formula $\Theta$
20114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20117 \begin_layout Plain Layout
20125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20128 \begin_layout Plain Layout
20129 \begin_inset Formula $\Lambda$
20139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20142 \begin_layout Plain Layout
20150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20153 \begin_layout Plain Layout
20154 \begin_inset Formula $\Xi$
20164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20167 \begin_layout Plain Layout
20175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20178 \begin_layout Plain Layout
20179 \begin_inset Formula $\Pi$
20193 \begin_inset space \hfill{}
20197 \begin_inset Tabular
20198 <lyxtabular version="3" rows="6" columns="2">
20200 <column alignment="center" valignment="top" width="0pt">
20201 <column alignment="center" valignment="top" width="0pt">
20203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20206 \begin_layout Plain Layout
20212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20215 \begin_layout Plain Layout
20223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20226 \begin_layout Plain Layout
20234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20237 \begin_layout Plain Layout
20238 \begin_inset Formula $\Sigma$
20248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20251 \begin_layout Plain Layout
20259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20262 \begin_layout Plain Layout
20263 \begin_inset Formula $\Upsilon$
20273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20276 \begin_layout Plain Layout
20284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20287 \begin_layout Plain Layout
20288 \begin_inset Formula $\Phi$
20298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20301 \begin_layout Plain Layout
20309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20312 \begin_layout Plain Layout
20313 \begin_inset Formula $\Psi$
20323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20326 \begin_layout Plain Layout
20334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20337 \begin_layout Plain Layout
20338 \begin_inset Formula $\Omega$
20352 \begin_inset space \hfill{}
20358 \begin_layout Standard
20359 \begin_inset VSpace medskip
20362 That the big Greek letters appear upright is caused by a design bug when
20364 To get correct italic big letters, begin every command with
20369 For example the command
20376 \begin_inset Formula $\varGamma$
20382 \begin_layout Subsection
20387 \begin_layout Plain Layout
20388 Greek letters ! bold
20396 \begin_layout Standard
20397 Greek letters cannot be set with different font styles like Latin letters.
20398 They can only be made bold with the command
20408 \begin_layout Plain Layout
20419 \begin_layout Standard
20421 \begin_inset Tabular
20422 <lyxtabular version="3" rows="3" columns="2">
20424 <column alignment="center" valignment="top" width="0">
20425 <column alignment="center" valignment="top" width="0">
20427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20430 \begin_layout Plain Layout
20436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20439 \begin_layout Plain Layout
20447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20450 \begin_layout Plain Layout
20462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20465 \begin_layout Plain Layout
20466 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20479 \begin_layout Plain Layout
20491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20494 \begin_layout Plain Layout
20495 \begin_inset Formula $\theta\boldsymbol{\theta}$
20511 \begin_layout Section
20516 \begin_layout Plain Layout
20529 \begin_layout Plain Layout
20530 A list with all symbols of most of the LaTeX-packages can be found in
20531 \begin_inset CommandInset citation
20546 \begin_layout Plain Layout
20554 \begin_inset Note Note
20557 \begin_layout Plain Layout
20560 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20563 \begin_layout Plain Layout
20566 texorpdfstring is in section
20567 \begin_inset CommandInset ref
20569 reference "sub:Formulas-in-Section"
20582 \begin_layout Plain Layout
20591 \begin_layout Standard
20592 Many of the symbols listed in this section can also be inserted via the
20594 \begin_inset Graphics
20595 filename ../images/math/nabla.png
20601 \begin_inset Graphics
20602 filename ../images/math/digamma.png
20610 \begin_layout Subsection
20611 Mathematical Symbols
20612 \begin_inset CommandInset label
20614 name "sub:Mathematical-Symbols"
20622 \begin_layout Plain Layout
20623 Symbols ! mathematical
20631 \begin_layout Standard
20632 \begin_inset space \hfill{}
20636 \begin_inset Tabular
20637 <lyxtabular version="3" rows="10" columns="2">
20639 <column alignment="center" valignment="top" width="0pt">
20640 <column alignment="center" valignment="top" width="0pt">
20642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20645 \begin_layout Plain Layout
20651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20654 \begin_layout Plain Layout
20662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20665 \begin_layout Plain Layout
20673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20676 \begin_layout Plain Layout
20677 \begin_inset Formula $\neg$
20687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20690 \begin_layout Plain Layout
20698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20701 \begin_layout Plain Layout
20702 \begin_inset Formula $\Im$
20712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20715 \begin_layout Plain Layout
20723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20726 \begin_layout Plain Layout
20727 \begin_inset Formula $\Re$
20737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20740 \begin_layout Plain Layout
20748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20751 \begin_layout Plain Layout
20752 \begin_inset Formula $\aleph$
20762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20765 \begin_layout Plain Layout
20773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20776 \begin_layout Plain Layout
20777 \begin_inset Formula $\partial$
20787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20790 \begin_layout Plain Layout
20798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20801 \begin_layout Plain Layout
20802 \begin_inset Formula $\infty$
20812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20815 \begin_layout Plain Layout
20823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20826 \begin_layout Plain Layout
20827 \begin_inset Formula $\wp$
20837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20840 \begin_layout Plain Layout
20848 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20851 \begin_layout Plain Layout
20852 \begin_inset Formula $\imath$
20862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20865 \begin_layout Plain Layout
20873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20876 \begin_layout Plain Layout
20877 \begin_inset Formula $\jmath$
20891 \begin_inset space \hfill{}
20895 \begin_inset Tabular
20896 <lyxtabular version="3" rows="10" columns="2">
20898 <column alignment="center" valignment="top" width="0pt">
20899 <column alignment="center" valignment="top" width="0pt">
20901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20904 \begin_layout Plain Layout
20910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20913 \begin_layout Plain Layout
20915 \begin_inset Note Note
20918 \begin_layout Plain Layout
20925 is only used as spacer.
20937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20940 \begin_layout Plain Layout
20948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20951 \begin_layout Plain Layout
20952 \begin_inset Formula $\forall$
20962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20965 \begin_layout Plain Layout
20973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20976 \begin_layout Plain Layout
20977 \begin_inset Formula $\exists$
20987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20990 \begin_layout Plain Layout
20998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21001 \begin_layout Plain Layout
21002 \begin_inset Formula $\nexists$
21012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21015 \begin_layout Plain Layout
21023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21026 \begin_layout Plain Layout
21027 \begin_inset Formula $\emptyset$
21037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21040 \begin_layout Plain Layout
21048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21051 \begin_layout Plain Layout
21052 \begin_inset Formula $\varnothing$
21062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21065 \begin_layout Plain Layout
21073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21076 \begin_layout Plain Layout
21077 \begin_inset Formula $\dag$
21087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21090 \begin_layout Plain Layout
21098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21101 \begin_layout Plain Layout
21102 \begin_inset Formula $\ddag$
21112 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21115 \begin_layout Plain Layout
21123 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21126 \begin_layout Plain Layout
21130 \begin_layout Plain Layout
21140 \begin_inset Formula $\complement$
21147 \begin_layout Plain Layout
21161 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21164 \begin_layout Plain Layout
21172 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21175 \begin_layout Plain Layout
21176 \begin_inset Formula $\Bbbk$
21190 \begin_inset space \hfill{}
21194 \begin_inset Tabular
21195 <lyxtabular version="3" rows="10" columns="2">
21197 <column alignment="center" valignment="top" width="0pt">
21198 <column alignment="center" valignment="top" width="0pt">
21200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21203 \begin_layout Plain Layout
21209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21212 \begin_layout Plain Layout
21220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21223 \begin_layout Plain Layout
21231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21234 \begin_layout Plain Layout
21235 \begin_inset Formula $\prime$
21245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21248 \begin_layout Plain Layout
21256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21259 \begin_layout Plain Layout
21260 \begin_inset Formula $\backprime$
21270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21273 \begin_layout Plain Layout
21281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21284 \begin_layout Plain Layout
21285 \begin_inset Formula $\mho$
21295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21298 \begin_layout Plain Layout
21306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21309 \begin_layout Plain Layout
21310 \begin_inset Formula $\triangle$
21320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21323 \begin_layout Plain Layout
21331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21334 \begin_layout Plain Layout
21335 \begin_inset Formula $\angle$
21345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21348 \begin_layout Plain Layout
21356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21359 \begin_layout Plain Layout
21360 \begin_inset Formula $\measuredangle$
21370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21373 \begin_layout Plain Layout
21381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21384 \begin_layout Plain Layout
21385 \begin_inset Formula $\sphericalangle$
21395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21398 \begin_layout Plain Layout
21406 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21409 \begin_layout Plain Layout
21410 \begin_inset Formula $\top$
21420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21423 \begin_layout Plain Layout
21431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21434 \begin_layout Plain Layout
21435 \begin_inset Formula $\bot$
21449 \begin_inset space \hfill{}
21455 \begin_layout Subsection
21456 Miscellaneous Symbols
21457 \begin_inset CommandInset label
21459 name "sub:Miscellaneous-Symbols"
21467 \begin_layout Plain Layout
21468 Symbols ! miscellaneous
21476 \begin_layout Standard
21479 \begin_inset Tabular
21480 <lyxtabular version="3" rows="10" columns="2">
21482 <column alignment="center" valignment="top" width="0pt">
21483 <column alignment="center" valignment="top" width="0pt">
21485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21488 \begin_layout Plain Layout
21494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21497 \begin_layout Plain Layout
21505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21508 \begin_layout Plain Layout
21516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21519 \begin_layout Plain Layout
21520 \begin_inset Formula $\flat$
21530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21533 \begin_layout Plain Layout
21541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21544 \begin_layout Plain Layout
21545 \begin_inset Formula $\natural$
21555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21558 \begin_layout Plain Layout
21566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21569 \begin_layout Plain Layout
21570 \begin_inset Formula $\sharp$
21580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21583 \begin_layout Plain Layout
21591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21594 \begin_layout Plain Layout
21595 \begin_inset Formula $\surd$
21605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21608 \begin_layout Plain Layout
21616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21619 \begin_layout Plain Layout
21620 \begin_inset Formula $\checkmark$
21630 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21633 \begin_layout Plain Layout
21641 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21644 \begin_layout Plain Layout
21645 \begin_inset Formula $\yen$
21655 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21658 \begin_layout Plain Layout
21666 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21669 \begin_layout Plain Layout
21670 \begin_inset Formula $\pounds$
21680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21683 \begin_layout Plain Layout
21689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21692 \begin_layout Plain Layout
21693 \begin_inset Formula $\$$
21703 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21706 \begin_layout Plain Layout
21712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21715 \begin_layout Plain Layout
21716 \begin_inset Formula $§$
21730 \begin_inset Tabular
21731 <lyxtabular version="3" rows="10" columns="2">
21733 <column alignment="center" valignment="top" width="0">
21734 <column alignment="center" valignment="top" width="0">
21736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21739 \begin_layout Plain Layout
21745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21748 \begin_layout Plain Layout
21756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21759 \begin_layout Plain Layout
21767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21770 \begin_layout Plain Layout
21771 \begin_inset Formula $\hbar$
21781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21784 \begin_layout Plain Layout
21792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21795 \begin_layout Plain Layout
21796 \begin_inset Formula $\hslash$
21806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21809 \begin_layout Plain Layout
21817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21820 \begin_layout Plain Layout
21821 \begin_inset Formula $\clubsuit$
21831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21834 \begin_layout Plain Layout
21842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21845 \begin_layout Plain Layout
21846 \begin_inset Formula $\spadesuit$
21856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21859 \begin_layout Plain Layout
21867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21870 \begin_layout Plain Layout
21871 \begin_inset Formula $\bigstar$
21881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21884 \begin_layout Plain Layout
21892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21895 \begin_layout Plain Layout
21896 \begin_inset Formula $\blacklozenge$
21906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21909 \begin_layout Plain Layout
21917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21920 \begin_layout Plain Layout
21921 \begin_inset Formula $\blacktriangle$
21931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21934 \begin_layout Plain Layout
21942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21945 \begin_layout Plain Layout
21946 \begin_inset Formula $\blacktriangledown$
21956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21959 \begin_layout Plain Layout
21967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21970 \begin_layout Plain Layout
21971 \begin_inset Formula $\bullet$
21985 \begin_inset Tabular
21986 <lyxtabular version="3" rows="10" columns="2">
21988 <column alignment="center" valignment="top" width="0pt">
21989 <column alignment="center" valignment="top" width="0pt">
21991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21994 \begin_layout Plain Layout
22000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22003 \begin_layout Plain Layout
22011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22014 \begin_layout Plain Layout
22022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22025 \begin_layout Plain Layout
22026 \begin_inset Formula $\diamondsuit$
22036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22039 \begin_layout Plain Layout
22047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22050 \begin_layout Plain Layout
22051 \begin_inset Formula $\Diamond$
22061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22064 \begin_layout Plain Layout
22072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22075 \begin_layout Plain Layout
22076 \begin_inset Formula $\heartsuit$
22086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22089 \begin_layout Plain Layout
22097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22100 \begin_layout Plain Layout
22101 \begin_inset Formula $\P$
22111 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22114 \begin_layout Plain Layout
22122 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22125 \begin_layout Plain Layout
22126 \begin_inset Formula $\copyright$
22136 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22139 \begin_layout Plain Layout
22147 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22150 \begin_layout Plain Layout
22151 \begin_inset Formula $\circledR$
22161 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22164 \begin_layout Plain Layout
22172 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22175 \begin_layout Plain Layout
22176 \begin_inset Formula $\maltese$
22186 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22189 \begin_layout Plain Layout
22197 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22200 \begin_layout Plain Layout
22201 \begin_inset Formula $\diagup$
22211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22214 \begin_layout Plain Layout
22222 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22225 \begin_layout Plain Layout
22226 \begin_inset Formula $\diagdown$
22242 \begin_layout Standard
22243 \begin_inset VSpace medskip
22246 More symbols are listed in
22247 \begin_inset CommandInset ref
22249 reference "sub:Miscellaneous-special-Characters"
22256 \begin_layout Standard
22257 Some symbols can be displayed in different sizes, see
22258 \begin_inset CommandInset ref
22260 reference "sub:Font-Sizes"
22267 \begin_layout Subsection
22272 \begin_layout Plain Layout
22273 Symbols ! Euro-symbol
22282 \begin_layout Plain Layout
22289 \begin_layout Plain Layout
22306 \begin_layout Standard
22307 To use the Euro symbol in formulas, the LaTeX-package
22315 \begin_layout Plain Layout
22321 must be installed and loaded with the LaTeX-preamble line
22324 \begin_layout Standard
22329 usepackage[gennarrow]{eurosym}
22332 \begin_layout Standard
22333 The Euro symbol can now be inserted with the command
22343 \begin_layout Plain Layout
22354 \begin_layout Standard
22355 The Euro symbol can directly be inserted with the € key in mathematical
22356 text, without having
22371 can also be inserted in TeX-mode.
22372 The official currency symbol can then be inserted with the command
22382 \begin_layout Plain Layout
22390 , that is only available in TeX-mode.
22393 \begin_layout Standard
22397 \begin_layout Plain Layout
22407 \begin_inset Note Note
22410 \begin_layout Plain Layout
22411 The following table will only be displayed when the LaTeX-package
22423 \begin_layout Standard
22424 An overview about the different Euro symbols:
22427 \begin_layout Standard
22429 \begin_inset Tabular
22430 <lyxtabular version="3" rows="4" columns="3">
22432 <column alignment="center" valignment="top" width="0pt">
22433 <column alignment="center" valignment="top" width="0pt">
22434 <column alignment="center" valignment="top" width="0pt">
22436 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22439 \begin_layout Plain Layout
22445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22448 \begin_layout Plain Layout
22454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22457 \begin_layout Plain Layout
22465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22468 \begin_layout Plain Layout
22474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22477 \begin_layout Plain Layout
22485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22488 \begin_layout Plain Layout
22489 \begin_inset Formula $\euro$
22499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22502 \begin_layout Plain Layout
22508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22511 \begin_layout Plain Layout
22517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22520 \begin_layout Plain Layout
22521 \begin_inset Formula $\mbox{€}$
22531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22534 \begin_layout Plain Layout
22540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22543 \begin_layout Plain Layout
22551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22554 \begin_layout Plain Layout
22558 \begin_layout Plain Layout
22580 \begin_layout Standard
22584 \begin_layout Plain Layout
22594 \begin_inset Note Note
22597 \begin_layout Plain Layout
22598 The following will be displayed when the LaTeX-package
22610 \begin_layout Standard
22611 You need to install the LaTeX-package
22615 to see the rest of this subsection in the output.
22618 \begin_layout Standard
22622 \begin_layout Plain Layout
22634 \begin_layout Section
22636 \begin_inset CommandInset label
22638 name "sec:Relations"
22646 \begin_layout Plain Layout
22656 \begin_layout Plain Layout
22661 \begin_layout Plain Layout
22672 \begin_layout Plain Layout
22687 \begin_layout Standard
22688 All relations can also be inserted via the toolbar button
22689 \begin_inset Graphics
22690 filename ../images/math/leq.png
22698 \begin_layout Standard
22699 \begin_inset space \hfill{}
22703 \begin_inset Tabular
22704 <lyxtabular version="3" rows="17" columns="2">
22706 <column alignment="center" valignment="top" width="0pt">
22707 <column alignment="center" valignment="top" width="0pt">
22709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22712 \begin_layout Plain Layout
22718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22721 \begin_layout Plain Layout
22729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22732 \begin_layout Plain Layout
22738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22741 \begin_layout Plain Layout
22742 \begin_inset Formula $<$
22752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22755 \begin_layout Plain Layout
22763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22766 \begin_layout Plain Layout
22767 \begin_inset Formula $\le$
22777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22780 \begin_layout Plain Layout
22788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22791 \begin_layout Plain Layout
22792 \begin_inset Formula $\ll$
22802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22805 \begin_layout Plain Layout
22813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22816 \begin_layout Plain Layout
22817 \begin_inset Formula $\prec$
22827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22830 \begin_layout Plain Layout
22838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22841 \begin_layout Plain Layout
22842 \begin_inset Formula $\preceq$
22852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22855 \begin_layout Plain Layout
22863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22866 \begin_layout Plain Layout
22867 \begin_inset Formula $\subset$
22877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22880 \begin_layout Plain Layout
22888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22891 \begin_layout Plain Layout
22892 \begin_inset Formula $\subseteq$
22902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22905 \begin_layout Plain Layout
22913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22916 \begin_layout Plain Layout
22917 \begin_inset Formula $\sqsubseteq$
22927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22930 \begin_layout Plain Layout
22938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22941 \begin_layout Plain Layout
22942 \begin_inset Formula $\in$
22952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22955 \begin_layout Plain Layout
22963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22966 \begin_layout Plain Layout
22967 \begin_inset Formula $\vdash$
22977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22980 \begin_layout Plain Layout
22988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22991 \begin_layout Plain Layout
22992 \begin_inset Formula $\smile$
23002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23005 \begin_layout Plain Layout
23013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23016 \begin_layout Plain Layout
23017 \begin_inset Formula $\lhd$
23027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23030 \begin_layout Plain Layout
23038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23041 \begin_layout Plain Layout
23042 \begin_inset Formula $\unlhd$
23052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23055 \begin_layout Plain Layout
23063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23066 \begin_layout Plain Layout
23067 \begin_inset Formula $\gtrless$
23077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23080 \begin_layout Plain Layout
23088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23091 \begin_layout Plain Layout
23092 \begin_inset Formula $\mid$
23102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23105 \begin_layout Plain Layout
23113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23116 \begin_layout Plain Layout
23117 \begin_inset Formula $\nmid$
23131 \begin_inset space \hfill{}
23135 \begin_inset Tabular
23136 <lyxtabular version="3" rows="17" columns="2">
23138 <column alignment="center" valignment="top" width="0pt">
23139 <column alignment="center" valignment="top" width="0pt">
23141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23144 \begin_layout Plain Layout
23150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23153 \begin_layout Plain Layout
23161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23164 \begin_layout Plain Layout
23170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23173 \begin_layout Plain Layout
23174 \begin_inset Formula $=$
23184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23187 \begin_layout Plain Layout
23195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23198 \begin_layout Plain Layout
23199 \begin_inset Formula $\not=$
23209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23212 \begin_layout Plain Layout
23220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23223 \begin_layout Plain Layout
23224 \begin_inset Formula $\equiv$
23234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23237 \begin_layout Plain Layout
23245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23248 \begin_layout Plain Layout
23249 \begin_inset Formula $\sim$
23259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23262 \begin_layout Plain Layout
23270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23273 \begin_layout Plain Layout
23274 \begin_inset Formula $\simeq$
23284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23287 \begin_layout Plain Layout
23295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23298 \begin_layout Plain Layout
23299 \begin_inset Formula $\approx$
23309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23312 \begin_layout Plain Layout
23320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23323 \begin_layout Plain Layout
23324 \begin_inset Formula $\cong$
23334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23337 \begin_layout Plain Layout
23345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23348 \begin_layout Plain Layout
23349 \begin_inset Formula $\bowtie$
23359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23362 \begin_layout Plain Layout
23370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23373 \begin_layout Plain Layout
23374 \begin_inset Formula $\notin$
23384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23387 \begin_layout Plain Layout
23395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23398 \begin_layout Plain Layout
23399 \begin_inset Formula $\perp$
23409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23412 \begin_layout Plain Layout
23420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23423 \begin_layout Plain Layout
23424 \begin_inset Formula $\propto$
23434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23437 \begin_layout Plain Layout
23445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23448 \begin_layout Plain Layout
23449 \begin_inset Formula $\asymp$
23459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23462 \begin_layout Plain Layout
23470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23473 \begin_layout Plain Layout
23474 \begin_inset Formula $\doteq$
23484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23487 \begin_layout Plain Layout
23495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23498 \begin_layout Plain Layout
23499 \begin_inset Formula $\circeq$
23509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23512 \begin_layout Plain Layout
23520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23523 \begin_layout Plain Layout
23524 \begin_inset Formula $\models$
23534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23537 \begin_layout Plain Layout
23545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23548 \begin_layout Plain Layout
23549 \begin_inset Formula $\widehat{=}$
23563 \begin_inset space \hfill{}
23567 \begin_inset Tabular
23568 <lyxtabular version="3" rows="17" columns="2">
23570 <column alignment="center" valignment="top" width="0pt">
23571 <column alignment="center" valignment="top" width="0pt">
23573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23576 \begin_layout Plain Layout
23582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23585 \begin_layout Plain Layout
23593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23596 \begin_layout Plain Layout
23602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23605 \begin_layout Plain Layout
23606 \begin_inset Formula $>$
23616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23619 \begin_layout Plain Layout
23627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23630 \begin_layout Plain Layout
23631 \begin_inset Formula $\ge$
23641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23644 \begin_layout Plain Layout
23652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23655 \begin_layout Plain Layout
23656 \begin_inset Formula $\gg$
23666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23669 \begin_layout Plain Layout
23677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23680 \begin_layout Plain Layout
23681 \begin_inset Formula $\succ$
23691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23694 \begin_layout Plain Layout
23702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23705 \begin_layout Plain Layout
23706 \begin_inset Formula $\succeq$
23716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23719 \begin_layout Plain Layout
23727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23730 \begin_layout Plain Layout
23731 \begin_inset Formula $\supset$
23741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23744 \begin_layout Plain Layout
23752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23755 \begin_layout Plain Layout
23756 \begin_inset Formula $\supseteq$
23766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23769 \begin_layout Plain Layout
23777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23780 \begin_layout Plain Layout
23781 \begin_inset Formula $\sqsupseteq$
23791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23794 \begin_layout Plain Layout
23802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23805 \begin_layout Plain Layout
23806 \begin_inset Formula $\ni$
23816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23819 \begin_layout Plain Layout
23827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23830 \begin_layout Plain Layout
23831 \begin_inset Formula $\dashv$
23841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23844 \begin_layout Plain Layout
23852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23855 \begin_layout Plain Layout
23856 \begin_inset Formula $\frown$
23866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23869 \begin_layout Plain Layout
23877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23880 \begin_layout Plain Layout
23881 \begin_inset Formula $\rhd$
23891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23894 \begin_layout Plain Layout
23902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23905 \begin_layout Plain Layout
23906 \begin_inset Formula $\unrhd$
23916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23919 \begin_layout Plain Layout
23927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23930 \begin_layout Plain Layout
23931 \begin_inset Formula $\lessgtr$
23941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23944 \begin_layout Plain Layout
23952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23955 \begin_layout Plain Layout
23956 \begin_inset Formula $\parallel$
23966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23969 \begin_layout Plain Layout
23977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23980 \begin_layout Plain Layout
23981 \begin_inset Formula $\nparallel$
23995 \begin_inset space \hfill{}
24001 \begin_layout Standard
24002 \begin_inset VSpace medskip
24017 are bigger than the equal looking operators
24032 \begin_layout Standard
24033 Relations are, in contrary to symbols, always surrounded by space.
24036 \begin_layout Standard
24037 Relations with labels can be created with the command
24047 \begin_layout Plain Layout
24058 \begin_layout Standard
24060 \begin_inset Tabular
24061 <lyxtabular version="3" rows="2" columns="2">
24063 <column alignment="center" valignment="top" width="0">
24064 <column alignment="center" valignment="top" width="0">
24066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24069 \begin_layout Plain Layout
24075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24078 \begin_layout Plain Layout
24080 \begin_inset Note Note
24083 \begin_layout Plain Layout
24090 is only used as spacer.
24102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24105 \begin_layout Plain Layout
24112 \begin_layout Plain Layout
24129 \begin_layout Plain Layout
24139 \begin_inset Formula $\downarrow$
24148 \begin_layout Plain Layout
24161 \begin_layout Plain Layout
24175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24178 \begin_layout Plain Layout
24179 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24195 \begin_layout Section
24199 \begin_layout Subsection
24200 Predefined Functions
24201 \begin_inset CommandInset label
24203 name "sub:Predefined-Functions"
24211 \begin_layout Plain Layout
24212 Functions ! predefined
24220 \begin_layout Standard
24221 In general, variables are set
24225 in mathematical expressions, but not function names, because
24226 \begin_inset Formula $sin$
24229 could be misunderstood as
24230 \begin_inset Formula $s\cdot i\cdot n$
24234 Therefore there are predefined functions, that are additionally a bit separated
24236 They are inserted as commands starting with a backslash before their name.
24239 \begin_layout Standard
24241 \begin_inset Tabular
24242 <lyxtabular version="3" rows="2" columns="4">
24244 <column alignment="center" valignment="top" width="0pt">
24245 <column alignment="center" valignment="top" width="0pt">
24246 <column alignment="center" valignment="top" width="0pt">
24247 <column alignment="center" valignment="top" width="0pt">
24249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24252 \begin_layout Plain Layout
24258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24261 \begin_layout Plain Layout
24267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24270 \begin_layout Plain Layout
24276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24279 \begin_layout Plain Layout
24287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24290 \begin_layout Plain Layout
24296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24299 \begin_layout Plain Layout
24300 \begin_inset Formula $Asin(x)+B$
24308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24311 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24322 \begin_layout Plain Layout
24323 \begin_inset Formula $A\sin(x)+B$
24339 \begin_layout Standard
24340 The following functions are predefined:
24343 \begin_layout Standard
24344 \begin_inset VSpace -2mm
24350 \begin_layout Standard
24352 \begin_inset Tabular
24353 <lyxtabular version="3" rows="9" columns="4">
24355 <column alignment="center" valignment="top" width="0pt">
24356 <column alignment="center" valignment="top" width="0pt">
24357 <column alignment="center" valignment="top" width="0pt">
24358 <column alignment="center" valignment="top" width="0pt">
24360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24363 \begin_layout Plain Layout
24369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24372 \begin_layout Plain Layout
24378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24381 \begin_layout Plain Layout
24387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24390 \begin_layout Plain Layout
24398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24401 \begin_layout Plain Layout
24409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24412 \begin_layout Plain Layout
24420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24423 \begin_layout Plain Layout
24431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24434 \begin_layout Plain Layout
24444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24447 \begin_layout Plain Layout
24455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24458 \begin_layout Plain Layout
24466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24469 \begin_layout Plain Layout
24477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24480 \begin_layout Plain Layout
24490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24493 \begin_layout Plain Layout
24501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24504 \begin_layout Plain Layout
24512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24515 \begin_layout Plain Layout
24523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24526 \begin_layout Plain Layout
24536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24539 \begin_layout Plain Layout
24547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24550 \begin_layout Plain Layout
24558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24561 \begin_layout Plain Layout
24569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24572 \begin_layout Plain Layout
24582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24585 \begin_layout Plain Layout
24593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24596 \begin_layout Plain Layout
24604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24607 \begin_layout Plain Layout
24615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24618 \begin_layout Plain Layout
24628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24631 \begin_layout Plain Layout
24639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24642 \begin_layout Plain Layout
24650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24653 \begin_layout Plain Layout
24661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24664 \begin_layout Plain Layout
24674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24677 \begin_layout Plain Layout
24685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24688 \begin_layout Plain Layout
24696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24699 \begin_layout Plain Layout
24707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24710 \begin_layout Plain Layout
24720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24723 \begin_layout Plain Layout
24731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24734 \begin_layout Plain Layout
24742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24745 \begin_layout Plain Layout
24753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24756 \begin_layout Plain Layout
24772 \begin_layout Standard
24773 They can also be inserted with the math toolbar button
24774 \begin_inset Graphics
24775 filename ../images/math/functions.png
24783 \begin_layout Subsection
24784 Self-defined Functions
24788 \begin_layout Plain Layout
24789 Functions ! self-defined
24797 \begin_layout Standard
24798 To use a function that is not predefined, like for example the sign function
24799 sgn(x), there are two possibilities:
24802 \begin_layout Itemize
24803 Define the function by inserting the following line to the LaTeX-preamble
24807 \begin_layout Plain Layout
24812 DeclareMathOperator
24815 \begin_inset CommandInset ref
24817 reference "sub:Self-defined-Operators"
24827 \begin_inset Newline newline
24831 \begin_inset VSpace -3mm
24835 \begin_inset Newline newline
24842 DeclareMathOperator{
24850 \begin_layout Plain Layout
24855 DeclareMathOperator
24861 \begin_inset Newline newline
24865 \begin_inset VSpace -2mm
24869 \begin_inset Newline newline
24872 Now the new defined function can be called with the command
24881 \begin_layout Itemize
24882 Write the the formula as usual, mark the formula name, in our example the
24887 , and change it to mathematical text.
24888 At last a space is inserted between prefactor and function.
24891 \begin_layout Standard
24892 The result is the same with both methods as with a predefined function
24896 \begin_layout Plain Layout
24897 In LyX self-defined functions are displayed red, predefined ones black.
24905 \begin_layout Standard
24907 \begin_inset Tabular
24908 <lyxtabular version="3" rows="3" columns="2">
24910 <column alignment="center" valignment="top" width="0pt">
24911 <column alignment="center" valignment="top" width="0pt">
24913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24916 \begin_layout Plain Layout
24922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24925 \begin_layout Plain Layout
24933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24936 \begin_layout Plain Layout
24944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24947 \begin_layout Plain Layout
24948 \begin_inset Formula $A\sgn(x)+B$
24958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24961 \begin_layout Plain Layout
24965 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24976 \begin_layout Plain Layout
24977 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24993 \begin_layout Standard
24994 The first method is more suitable when the self-defined function should
24995 be used several times.
24998 \begin_layout Subsection
25003 \begin_layout Plain Layout
25012 \begin_layout Standard
25013 For limits there are defined besides
25023 \begin_layout Plain Layout
25043 furthermore the following functions:
25046 \begin_layout Standard
25048 \begin_inset Tabular
25049 <lyxtabular version="3" rows="5" columns="2">
25051 <column alignment="center" valignment="top" width="0">
25052 <column alignment="center" valignment="top" width="0">
25054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25057 \begin_layout Plain Layout
25063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25066 \begin_layout Plain Layout
25068 \begin_inset Note Note
25071 \begin_layout Plain Layout
25078 is only used as spacer.
25090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25093 \begin_layout Plain Layout
25101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25104 \begin_layout Plain Layout
25105 \begin_inset Formula $\varliminf$
25115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25118 \begin_layout Plain Layout
25126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25129 \begin_layout Plain Layout
25130 \begin_inset Formula $\varlimsup$
25140 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25143 \begin_layout Plain Layout
25151 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25154 \begin_layout Plain Layout
25155 \begin_inset Formula $\varprojlim$
25165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25168 \begin_layout Plain Layout
25176 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25179 \begin_layout Plain Layout
25180 \begin_inset Formula $\varinjlim$
25184 \begin_inset Formula $\raisebox{-2.5mm}{}$
25200 \begin_layout Standard
25201 \begin_inset VSpace medskip
25204 The limit is created by inserting a subscript.
25205 It is set right beside the function in an inline formula:
25208 \begin_layout Standard
25210 \begin_inset Tabular
25211 <lyxtabular version="3" rows="2" columns="2">
25213 <column alignment="center" valignment="top" width="0pt">
25214 <column alignment="center" valignment="top" width="0pt">
25216 <cell alignment="center" valignment="top" usebox="none">
25219 \begin_layout Plain Layout
25225 <cell alignment="center" valignment="top" usebox="none">
25228 \begin_layout Plain Layout
25229 \begin_inset space \hspace{}
25234 \begin_inset Note Note
25237 \begin_layout Plain Layout
25250 are used here as spacer.
25262 <cell alignment="center" valignment="top" usebox="none">
25265 \begin_layout Plain Layout
25274 \begin_layout Plain Layout
25287 \begin_layout Plain Layout
25301 <cell alignment="center" valignment="top" usebox="none">
25304 \begin_layout Plain Layout
25305 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25321 \begin_layout Standard
25322 In a displayed formula the limit is set below the formula, as usual:
25323 \begin_inset Formula \[
25331 \begin_layout Subsection
25336 \begin_layout Plain Layout
25337 Functions ! modulo-
25345 \begin_layout Standard
25346 The modulo-function is special, because it exists in four variants.
25349 \begin_layout Standard
25350 The variants in a displayed formula:
25351 \begin_inset Formula \begin{align*}
25352 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25353 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25354 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25355 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25356 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25363 \begin_layout Standard
25364 In an inline formula less space is set before the function names for all
25368 \begin_layout Section
25373 \begin_layout Plain Layout
25382 \begin_layout Subsection
25383 Special Characters in Mathematical Text
25386 \begin_layout Standard
25387 The following commands can only be used in mathematical text or in TeX-mode:
25390 \begin_layout Standard
25391 \begin_inset space \hfill{}
25395 \begin_inset Tabular
25396 <lyxtabular version="3" rows="8" columns="2">
25398 <column alignment="block" valignment="top" width="0">
25399 <column alignment="block" valignment="top" width="0">
25401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25404 \begin_layout Plain Layout
25410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25413 \begin_layout Plain Layout
25421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25424 \begin_layout Plain Layout
25432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25435 \begin_layout Plain Layout
25436 \begin_inset Formula $\textrm{œ}$
25446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25449 \begin_layout Plain Layout
25457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25460 \begin_layout Plain Layout
25461 \begin_inset Formula $\textrm{Œ}$
25471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25474 \begin_layout Plain Layout
25482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25485 \begin_layout Plain Layout
25486 \begin_inset Formula $\textrm{æ}$
25496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25499 \begin_layout Plain Layout
25507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25510 \begin_layout Plain Layout
25511 \begin_inset Formula $\textrm{Æ}$
25521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25524 \begin_layout Plain Layout
25532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25535 \begin_layout Plain Layout
25536 \begin_inset Formula $\textrm{\aa}$
25546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25549 \begin_layout Plain Layout
25556 \begin_layout Plain Layout
25563 \begin_layout Plain Layout
25584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25587 \begin_layout Plain Layout
25588 \begin_inset Formula $\textrm{Å}$
25598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25601 \begin_layout Plain Layout
25609 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25612 \begin_layout Plain Layout
25613 \begin_inset Formula $\textrm{ı}$
25627 \begin_inset space \hfill{}
25631 \begin_inset Tabular
25632 <lyxtabular version="3" rows="8" columns="2">
25634 <column alignment="block" valignment="top" width="0">
25635 <column alignment="center" valignment="top" width="0">
25637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25640 \begin_layout Plain Layout
25642 \begin_inset Note Note
25645 \begin_layout Plain Layout
25652 is used for separation, because otherwise the output will be ¡ and ¿ respective
25663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25666 \begin_layout Plain Layout
25674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25677 \begin_layout Plain Layout
25685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25688 \begin_layout Plain Layout
25689 \begin_inset Formula $\textrm{ø}$
25699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25702 \begin_layout Plain Layout
25710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25713 \begin_layout Plain Layout
25714 \begin_inset Formula $\textrm{Ø}$
25724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25727 \begin_layout Plain Layout
25735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25738 \begin_layout Plain Layout
25739 \begin_inset Formula $\textrm{ł}$
25749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25752 \begin_layout Plain Layout
25760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25763 \begin_layout Plain Layout
25764 \begin_inset Formula $\textrm{Ł}$
25774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25777 \begin_layout Plain Layout
25779 \begin_inset space \hspace{}
25787 \begin_layout Plain Layout
25801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25804 \begin_layout Plain Layout
25805 \begin_inset Formula $\textrm{!`}$
25815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25818 \begin_layout Plain Layout
25820 \begin_inset space \hspace{}
25828 \begin_layout Plain Layout
25842 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25845 \begin_layout Plain Layout
25846 \begin_inset Formula $\textrm{?`}$
25856 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25859 \begin_layout Plain Layout
25867 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25870 \begin_layout Plain Layout
25871 \begin_inset Formula $\textrm{ȷ}$
25885 \begin_inset space \hfill{}
25891 \begin_layout Standard
25893 \begin_inset Formula $\textrm{\textrm{Å}}$
25897 \begin_inset Formula $\textrm{\textrm{Ø}}$
25900 can also be inserted via the math toolbar button
25901 \begin_inset Graphics
25902 filename ../images/math/digamma.png
25910 \begin_layout Standard
25911 An exception are the commands
25914 \begin_inset space \hspace{}
25923 \begin_inset space \hspace{}
25929 , because they can be inserted in LyX directly to text.
25932 \begin_layout Subsection
25934 \begin_inset CommandInset label
25936 name "sub:Accents-in-Text"
25944 \begin_layout Plain Layout
25953 \begin_layout Standard
25954 With the following commands all letters can be accented.
25955 The commands must be inserted in TeX-mode.
25958 \begin_layout Standard
25959 \begin_inset space \hfill{}
25963 \begin_inset Tabular
25964 <lyxtabular version="3" rows="8" columns="2">
25966 <column alignment="block" valignment="top" width="0">
25967 <column alignment="block" valignment="top" width="0">
25969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25972 \begin_layout Plain Layout
25978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25981 \begin_layout Plain Layout
25989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25992 \begin_layout Plain Layout
25996 \begin_inset Quotes grd
26004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26007 \begin_layout Plain Layout
26011 \begin_layout Plain Layout
26027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26030 \begin_layout Plain Layout
26038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26041 \begin_layout Plain Layout
26045 \begin_layout Plain Layout
26061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26064 \begin_layout Plain Layout
26071 \begin_layout Plain Layout
26085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26088 \begin_layout Plain Layout
26092 \begin_layout Plain Layout
26108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26111 \begin_layout Plain Layout
26119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26122 \begin_layout Plain Layout
26126 \begin_layout Plain Layout
26142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26145 \begin_layout Plain Layout
26152 \begin_layout Plain Layout
26166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26169 \begin_layout Plain Layout
26173 \begin_layout Plain Layout
26189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26192 \begin_layout Plain Layout
26199 \begin_layout Plain Layout
26213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26216 \begin_layout Plain Layout
26220 \begin_layout Plain Layout
26236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26239 \begin_layout Plain Layout
26246 \begin_layout Plain Layout
26260 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26263 \begin_layout Plain Layout
26267 \begin_layout Plain Layout
26287 \begin_inset space \hfill{}
26291 \begin_inset Tabular
26292 <lyxtabular version="3" rows="8" columns="2">
26294 <column alignment="block" valignment="top" width="0">
26295 <column alignment="center" valignment="top" width="0">
26297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26300 \begin_layout Plain Layout
26306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26309 \begin_layout Plain Layout
26317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26320 \begin_layout Plain Layout
26327 \begin_layout Plain Layout
26341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26344 \begin_layout Plain Layout
26348 \begin_layout Plain Layout
26364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26367 \begin_layout Plain Layout
26375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26378 \begin_layout Plain Layout
26382 \begin_layout Plain Layout
26398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26401 \begin_layout Plain Layout
26408 \begin_layout Plain Layout
26419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26422 \begin_layout Plain Layout
26426 \begin_layout Plain Layout
26442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26445 \begin_layout Plain Layout
26453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26456 \begin_layout Plain Layout
26460 \begin_layout Plain Layout
26476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26479 \begin_layout Plain Layout
26486 \begin_layout Plain Layout
26500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26503 \begin_layout Plain Layout
26507 \begin_layout Plain Layout
26523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26526 \begin_layout Plain Layout
26533 \begin_layout Plain Layout
26547 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26550 \begin_layout Plain Layout
26554 \begin_layout Plain Layout
26570 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26573 \begin_layout Plain Layout
26580 \begin_layout Plain Layout
26594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26597 \begin_layout Plain Layout
26601 \begin_layout Plain Layout
26621 \begin_inset space \hfill{}
26627 \begin_layout Standard
26628 \begin_inset VSpace medskip
26637 also two different characters can be accented.
26646 \begin_layout Plain Layout
26661 \begin_layout Plain Layout
26673 \begin_layout Standard
26686 can in combination with vowels directly be inserted with the keyboard without
26688 The same applies for the tilde
26692 \begin_layout Plain Layout
26693 This only applies for keyboards where the tilde is defined as accent.
26702 in combination with
26717 \begin_layout Standard
26760 , and accents inserted directly with the keyboard are also available in
26762 For the other accents there are special math commands to be used in formulas,
26764 \begin_inset CommandInset ref
26766 reference "sub:Accents-for-one"
26773 \begin_layout Standard
26774 \begin_inset VSpace bigskip
26777 Furthermore, with the command
26787 \begin_layout Plain Layout
26795 all numbers and letters can be set into a circle, quasi accented with a
26796 circle, similar to the the copyright symbol.
26799 \begin_layout Standard
26801 \begin_inset Tabular
26802 <lyxtabular version="3" rows="3" columns="2">
26804 <column alignment="center" valignment="top" width="0">
26805 <column alignment="center" valignment="top" width="0">
26807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26810 \begin_layout Plain Layout
26816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26819 \begin_layout Plain Layout
26821 \begin_inset Note Note
26824 \begin_layout Plain Layout
26831 is only used as spacer.
26843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26846 \begin_layout Plain Layout
26854 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26857 \begin_layout Plain Layout
26861 \begin_layout Plain Layout
26877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26880 \begin_layout Plain Layout
26891 raisebox{-1.5pt}{W}}
26896 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26899 \begin_layout Plain Layout
26900 \begin_inset Formula $\raisebox{4.5mm}{}$
26907 \begin_layout Plain Layout
26925 \begin_inset Formula $\raisebox{-2mm}{}$
26941 \begin_layout Standard
26942 One has to take care that the character fits in the circle.
26953 \begin_layout Plain Layout
26955 \begin_inset CommandInset ref
26957 reference "sub:Font-Sizes"
26966 specifies thereby the size of the circle.
26977 \begin_layout Plain Layout
26979 \begin_inset CommandInset ref
26981 reference "sub:Boxes-without-Frame"
26990 the character can be centered.
26993 \begin_layout Subsection
26998 \begin_layout Plain Layout
27007 \begin_layout Standard
27008 Minuscule numbers are created with the command
27018 \begin_layout Plain Layout
27027 The command can be used in formulas and in TeX-mode.
27028 The command scheme is:
27031 \begin_layout Standard
27036 oldstylenums{number}
27039 \begin_layout Standard
27044 oldstylenums{0123456789
27047 \begin_inset Formula $\oldstylenums{0123456789}$
27053 \begin_layout Subsection
27054 Miscellaneous special Characters
27055 \begin_inset CommandInset label
27057 name "sub:Miscellaneous-special-Characters"
27065 \begin_layout Plain Layout
27066 Special characters ! miscellaneous
27074 \begin_layout Standard
27075 The following characters can only be inserted to formulas by using commands:
27078 \begin_layout Standard
27080 \begin_inset Tabular
27081 <lyxtabular version="3" rows="4" columns="2">
27083 <column alignment="center" valignment="top" width="0">
27084 <column alignment="center" valignment="top" width="0">
27086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27089 \begin_layout Plain Layout
27095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27098 \begin_layout Plain Layout
27106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27109 \begin_layout Plain Layout
27116 \begin_layout Plain Layout
27130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27133 \begin_layout Plain Layout
27134 \begin_inset Formula $\mathcircumflex$
27144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27147 \begin_layout Plain Layout
27155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27158 \begin_layout Plain Layout
27159 \begin_inset Formula $\_$
27169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27172 \begin_layout Plain Layout
27177 \begin_layout Plain Layout
27192 \begin_layout Plain Layout
27205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27208 \begin_layout Plain Layout
27209 \begin_inset Formula $^{\circ}$
27225 \begin_layout Standard
27226 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27227 contains the following line
27231 \begin_layout Plain Layout
27232 More about this is described in
27233 \begin_inset CommandInset ref
27235 reference "sub:Text-Characters-in"
27247 \begin_layout Standard
27252 DeclareInputtext{176}{
27265 \begin_layout Section
27267 \begin_inset CommandInset label
27269 name "sec:Formula-Styles"
27277 \begin_layout Plain Layout
27286 \begin_layout Itemize
27287 There are two different alignment styles:
27291 \begin_layout Description
27292 Centered is the predefined standard
27295 \begin_layout Description
27296 Indented for this the option
27300 must be inserted in the menu
27302 Document\SpecialChar \menuseparator
27308 \begin_inset space ~
27314 \begin_layout Standard
27319 is used, the indentation can be adjusted with the length
27329 \begin_layout Plain Layout
27338 Should the distance be 15
27339 \begin_inset space \thinspace{}
27342 mm, the following command line is inserted in the LaTeX-preamble
27345 \begin_layout Standard
27355 \begin_layout Standard
27356 When no length is specified, the predefined value of 30
27357 \begin_inset space \thinspace{}
27364 \begin_layout Itemize
27365 And two different numbering styles:
27369 \begin_layout Description
27370 Right is the predefined standard
27373 \begin_layout Description
27374 Left for this the option
27378 must be inserted in the menu
27380 Document\SpecialChar \menuseparator
27386 \begin_inset space ~
27393 \begin_layout Standard
27402 can also be used together.
27403 In this case both options are inserted, separated by a comma.
27406 \begin_layout Standard
27407 The chosen styles are used for all displayed formulas of the document.
27408 When both, centered and indented formulas should be created in a document,
27414 The indented formulas are then set in a flalign environment, see
27415 \begin_inset CommandInset ref
27417 reference "sub:Flalign-Environment"
27424 \begin_layout Section
27426 \begin_inset CommandInset label
27428 name "sec:Multiline-Formulas"
27436 \begin_layout Plain Layout
27437 Formula ! multiline
27445 \begin_layout Subsection
27449 \begin_layout Standard
27450 In LyX multiline formulas are created by pressing
27455 arg "newline-insert newline"
27461 This creates either an
27463 eqnarray environment
27465 that is described in
27466 \begin_inset CommandInset ref
27468 reference "sub:Eqnarray-Environment"
27472 or, when the option
27474 Use AMS math package
27476 in the document settings is selected, an
27480 that is described in
27481 \begin_inset CommandInset ref
27483 reference "sub:Standard-align-Environment"
27490 \begin_layout Standard
27491 There are other multiline formula environments that can be created via the
27494 Insert\SpecialChar \menuseparator
27498 These environments are described in the following sections.
27501 \begin_layout Standard
27502 In all multiline formula environments a new line is created by pressing
27506 arg "newline-insert newline"
27510 To add or delete lines, the math toolbar buttons
27511 \begin_inset Graphics
27512 filename ../images/tabular-feature_append-row.png
27518 \begin_inset Graphics
27519 filename ../images/tabular-feature_delete-row.png
27524 , respectively, or the menu
27526 Edit\SpecialChar \menuseparator
27532 \begin_layout Subsubsection
27534 \begin_inset CommandInset label
27536 name "sub:Line-Separation"
27544 \begin_layout Plain Layout
27545 Formula ! multiline ! Line separation
27553 \begin_layout Standard
27554 There is sometimes not enough space in multiline formulas between the lines:
27555 \begin_inset Formula \begin{eqnarray*}
27556 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}\\
27557 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*}
27564 \begin_layout Standard
27565 In LaTeX additional line space is specified as optional argument of the
27567 This is not yet possible in LyX
27571 \begin_layout Plain Layout
27573 \begin_inset CommandInset href
27575 name "LyX-bug #1505"
27576 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27585 , therefore the whole formula must be inserted in TeX-mode.
27586 To add in our example space, the command
27594 is inserted at the end of the first line.
27599 \begin_layout Plain Layout
27606 \begin_layout Plain Layout
27608 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27611 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27618 \begin_layout Plain Layout
27622 left(B^{2}+x_{0}^{2}
27630 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27635 \begin_layout Plain Layout
27647 \begin_layout Standard
27648 \begin_inset VSpace bigskip
27651 To set the the line separation for all lines in a formula, the length
27661 \begin_layout Plain Layout
27671 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27682 \begin_inset space \thinspace{}
27687 \begin_inset space \thinspace{}
27690 mm additional line separation as in the previous example, the command
27693 \begin_layout Standard
27703 \begin_layout Standard
27704 is inserted in TeX-mode before the formula.
27705 This requires that the LaTeX-package
27713 \begin_layout Plain Layout
27718 is part of every LaTeX standard installation.
27727 \begin_layout Plain Layout
27733 was loaded in LaTeX-preamble with the line
27736 \begin_layout Standard
27744 \begin_layout Standard
27749 \begin_layout Plain Layout
27761 \begin_inset Formula \begin{eqnarray*}
27762 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}\\
27763 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*}
27770 \begin_layout Standard
27774 \begin_layout Plain Layout
27785 To get back to the predefined distance,
27791 is set to the value 3
27792 \begin_inset space \thinspace{}
27798 \begin_layout Subsubsection
27800 \begin_inset CommandInset label
27802 name "sub:Column-Separation"
27810 \begin_layout Plain Layout
27811 Formula ! multiline ! Column separation
27819 \begin_layout Standard
27820 Multiline formulas form a matrix.
27821 A formula in the eqnarray environment is for example a matrix with three
27823 By changing the column separation in this environment, the space beside
27824 the relation sign can be changed.
27827 \begin_layout Standard
27828 The column separation is specified with the length
27838 \begin_layout Plain Layout
27847 \begin_inset Newline newline
27850 column separation = 2
27851 \begin_inset space \thinspace{}
27861 \begin_inset Newline newline
27867 \begin_layout Standard
27877 \begin_layout Standard
27878 inserted in TeX-mode, sets for all following formulas a column separation
27880 \begin_inset space \thinspace{}
27884 To get back to the predefined distance,
27891 \begin_inset space \thinspace{}
27897 \begin_layout Standard
27899 \begin_inset space \thinspace{}
27902 cm column separation:
27906 \begin_layout Plain Layout
27918 \begin_inset Formula \begin{eqnarray*}
27920 C & \ne & A\end{eqnarray*}
27924 A formula with the predefined column separation for matrices of 10
27925 \begin_inset space \thinspace{}
27932 \begin_layout Plain Layout
27944 \begin_inset Formula \begin{eqnarray*}
27946 C & \ne & A\end{eqnarray*}
27953 \begin_layout Subsubsection
27958 \begin_layout Plain Layout
27967 \begin_layout Standard
27968 Long formulas can be typeset using these methods:
27971 \begin_layout Itemize
27972 When one side of the equation is much shorther than the line width, this
27973 one is chosen for the left side and the right side is typeset over two
27978 \begin_layout Plain Layout
27988 \begin_inset Formula \begin{eqnarray}
27989 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 \\
27990 & & -\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:shortlong}\end{eqnarray}
27998 \begin_layout Plain Layout
28008 \begin_inset Newline newline
28011 The minus sign at the beginning of the second line does normally not appear
28012 as operator because it is the first character of the line.
28013 Thus it would not be surrounded by space and could not be distinguished
28014 from the fraction bar.
28015 To avoid this, space was inserted behind the minus sign with the command
28026 \begin_layout Plain Layout
28034 \begin_inset CommandInset ref
28036 reference "sub:Variable-Space"
28049 \begin_layout Plain Layout
28060 \begin_layout Itemize
28061 When both sides of the equation are too long, the command
28071 \begin_layout Plain Layout
28080 It is inserted to the first column of the first line and effects that all
28081 further insertions overwrite the following columns:
28085 \begin_layout Plain Layout
28095 \begin_inset Formula \begin{eqnarray}
28096 \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 \\
28097 & & -\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 \\
28098 & & =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}
28106 \begin_layout Plain Layout
28116 \begin_inset Newline newline
28119 After the insertion of
28125 , the cursor is in a purple box that is a bit shifted to the left from the
28127 In this the formula is inserted.
28131 \begin_layout Plain Layout
28141 \begin_inset Newline newline
28144 The content of the further lines is inserted to the second or another formula
28146 The greater the column number where it was inserted, the larger the indentation.
28150 \begin_layout Plain Layout
28160 \begin_inset Newline newline
28164 \begin_inset Note Greyedout
28167 \begin_layout Plain Layout
28168 Note the following when using
28177 \begin_layout Itemize
28178 The formula doesn't use the full page width.
28180 \begin_inset space \thinspace{}
28184 \begin_inset space \space{}
28188 \begin_inset Formula $-B^{2}$
28191 is added to the first line in the above example, it would have been outside
28193 To better use the width, negative space can be inserted at the beginning
28197 \begin_layout Itemize
28198 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28203 \begin_layout Plain Layout
28204 \begin_inset CommandInset href
28206 name "LyX-bug #1429"
28207 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28216 One can only set the cursor at the beginning of the line and move it with
28225 \begin_layout Itemize
28226 Other methods to set long formulas are offered by the environments described
28228 \begin_inset CommandInset ref
28230 reference "sub:Multline-Environment"
28235 \begin_inset CommandInset ref
28237 reference "sub:Multiline-Formula-Parts"
28244 \begin_layout Subsubsection
28246 \begin_inset CommandInset label
28248 name "sub:Multiline-Brackets"
28256 \begin_layout Plain Layout
28257 Brackets ! for multiline expressions
28265 \begin_layout Standard
28266 For brackets spanning multiple lines the following problem occurs:
28267 \begin_inset Formula \begin{eqnarray*}
28268 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28269 & & \left.\cdots+B-D\right]\end{eqnarray*}
28276 \begin_layout Standard
28277 The closing bracket is smaller than the opening bracket because brackets
28278 with variable size may not span multiple lines.
28281 \begin_layout Standard
28282 To set the bracket size for the second line correctly, the first line is
28293 \begin_layout Plain Layout
28301 and the second line with
28309 \begin_layout Plain Layout
28323 \begin_inset CommandInset ref
28325 reference "sub:Automatic-Bracket-Size"
28340 \begin_layout Plain Layout
28366 \begin_layout Plain Layout
28385 \begin_layout Plain Layout
28404 \begin_layout Plain Layout
28416 \begin_inset Formula $\downarrow$
28425 \begin_layout Plain Layout
28433 is inserted, because the multiplication operator with its limits is the
28434 largest symbol in the first line and this should be the size for the bracket
28435 in the second line.
28438 \begin_layout Standard
28439 The result is this:
28440 \begin_inset Formula \begin{eqnarray*}
28441 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28442 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28449 \begin_layout Subsection
28453 \begin_layout Standard
28454 Align environments can be used for every kind of multiline formulas.
28455 They are specially useful to set several formulas side by side.
28458 \begin_layout Standard
28459 Align environments consist of columns.
28460 The odd columns are right aligned, the even ones left aligned.
28461 Every line in an Align environment can be numbered.
28464 \begin_layout Standard
28465 Align environments are created via the menu
28467 Insert\SpecialChar \menuseparator
28473 Edit\SpecialChar \menuseparator
28474 Math\SpecialChar \menuseparator
28475 Change Formula Type
28477 already existing formulas can be converted to Align environments.
28480 \begin_layout Standard
28481 To add or delete columns, the math toolbar buttons
28482 \begin_inset Graphics
28483 filename ../images/tabular-feature_append-column.png
28489 \begin_inset Graphics
28490 filename ../images/tabular-feature_delete-column.png
28495 , respectively, or the menu
28497 Edit\SpecialChar \menuseparator
28503 \begin_layout Subsubsection
28504 Standard align Environment
28505 \begin_inset CommandInset label
28507 name "sub:Standard-align-Environment"
28515 \begin_layout Plain Layout
28516 Formula ! multiline ! align environment
28524 \begin_layout Standard
28525 This Align environment is created by presssing
28528 arg "newline-insert newline"
28531 in a formula or by the menu
28533 Insert\SpecialChar \menuseparator
28534 Math\SpecialChar \menuseparator
28535 AMS align Environment
28540 \begin_layout Standard
28541 An example for two formulas set side by side, that are created with a four
28542 column align environment:
28543 \begin_inset Formula \begin{align*}
28544 A & =\sin(B) & C & =D\\
28545 C & \ne A & B & \ne D\end{align*}
28549 As it can be seen, the formulas in this environment are placed so as if
28558 \begin_layout Plain Layout
28566 \begin_inset CommandInset ref
28568 reference "sub:Variable-Space"
28579 before the first and after every even column.
28580 When the formula style
28586 \begin_layout Plain Layout
28588 \begin_inset CommandInset ref
28590 reference "sec:Formula-Styles"
28601 is used, the formula is set without the
28607 before the first column.
28610 \begin_layout Subsubsection
28611 Alignat Environment
28615 \begin_layout Plain Layout
28616 Formula ! multiline ! alignat environment
28624 \begin_layout Standard
28625 The alignat environment has no predefined column separation.
28626 It can be inserted manually with the spaces that are described
28627 \begin_inset CommandInset ref
28629 reference "sub:Space"
28636 \begin_layout Standard
28637 The above example in the alignat environment where 1
28638 \begin_inset space \thinspace{}
28641 cm space was inserted at the beginning of the second formula:
28642 \begin_inset Formula \begin{alignat*}{2}
28643 A & =\sin(B) & \hspace{1cm}C & =D\\
28644 C & \ne A & B & \ne D\end{alignat*}
28648 Because the column separation can be set separately for every column, this
28649 environment is especially suitable to set three and more formulas side
28653 \begin_layout Subsubsection
28654 Flalign Environment
28655 \begin_inset CommandInset label
28657 name "sub:Flalign-Environment"
28665 \begin_layout Plain Layout
28666 Formula ! multiline ! flalign environment
28674 \begin_layout Standard
28675 In this environment the first two columns are always set as much as possible
28676 to the left and the last two ones to the right.
28678 \begin_inset Formula \begin{flalign*}
28679 A & =1 & B & =2 & C & =3\\
28680 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28687 \begin_layout Standard
28688 By creating a flalign environment with an odd number of columns where an
28689 empty TeX-brace is inserted to the last column, several formulas in a document
28690 can be set to the left, although the formula style
28695 As example the indented formula
28696 \begin_inset CommandInset ref
28698 reference "eq:VolInt"
28703 \begin_inset Formula \begin{flalign}
28704 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28708 The first two columns contain the formula.
28709 To indent it as with the formula style
28714 \begin_inset space \thinspace{}
28717 pt space was inserted at the beginning of the first column.
28720 \begin_layout Subsection
28721 Eqnarray Environment
28722 \begin_inset CommandInset label
28724 name "sub:Eqnarray-Environment"
28732 \begin_layout Plain Layout
28733 Formula ! multiline ! eqnarray environment
28741 \begin_layout Standard
28742 When this environment has been created, three blue boxes appear.
28743 The content of the first box is right aligned, the content of the last
28745 The content of the middle box appears centered and a bit smaller, because
28746 it is designed to insert there only relation characters.
28747 \begin_inset Formula \begin{eqnarray*}
28748 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28750 A & = & A\end{eqnarray*}
28757 \begin_layout Subsection
28762 \begin_layout Plain Layout
28763 Formula ! multiline ! gather environment
28771 \begin_layout Standard
28772 This environment consists of only one centered column.
28773 Every line can be numbered.
28774 \begin_inset Formula \begin{gather}
28776 X=\textrm{-}1\end{gather}
28783 \begin_layout Subsection
28784 Multline Environment
28785 \begin_inset CommandInset label
28787 name "sub:Multline-Environment"
28795 \begin_layout Plain Layout
28796 Formula ! multiline ! multline environment
28804 \begin_layout Standard
28805 The multline environment consists, like the gather environment, of only
28807 But the first line is left aligned, the last one right aligned.
28808 All other lines are centered.
28809 Therefore this environment is suitable for long formulas.
28811 \begin_inset CommandInset ref
28813 reference "eq:lefteqn"
28817 in the multline environment:
28818 \begin_inset Formula \begin{multline}
28819 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}\\
28820 -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}\\
28821 =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}
28828 \begin_layout Standard
28829 In the output only the last (first) line of a multline environment appears
28830 numbered when the document numbering is right (left).
28834 \begin_layout Plain Layout
28835 numbering styles see
28836 \begin_inset CommandInset ref
28838 reference "sec:Formula-Styles"
28850 \begin_layout Standard
28859 \begin_layout Plain Layout
28877 \begin_layout Plain Layout
28887 a centered line can be right or left aligned, respectively.
28888 The commands are used as follows:
28891 \begin_layout Standard
28896 shoveright{line content}
28902 shoveleft{line content}
28905 \begin_layout Standard
28906 \begin_inset VSpace medskip
28917 \begin_layout Plain Layout
28927 specifies the distance of the first line from the left page margin.
28928 Predefined is the length 0
28929 \begin_inset space \thinspace{}
28935 \begin_layout Standard
28936 As example the above formula where the command
28939 \begin_layout Standard
28949 \begin_layout Standard
28950 was inserted in TeX-mode before:
28954 \begin_layout Plain Layout
28966 \begin_inset Formula \begin{multline}
28967 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}\\
28968 \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}}\\
28969 =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}
28977 \begin_layout Plain Layout
28988 The second line was left aligned using
28997 \begin_layout Subsection
28998 Multiline Formula Parts
28999 \begin_inset CommandInset label
29001 name "sub:Multiline-Formula-Parts"
29009 \begin_layout Plain Layout
29010 Formula ! multiline ! formula parts
29018 \begin_layout Standard
29019 To display only parts of a formula with multiple lines, one of the following
29020 environments are used:
29037 They can be inserted via the menu
29039 Insert\SpecialChar \menuseparator
29042 or by using the commands described in this section.
29045 \begin_layout Standard
29046 The first three have the same properties as the corresponding multiline
29047 formula environments, but it is possible to set further formula parts beside
29050 \begin_inset Formula \[
29051 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29052 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29053 \right\} \textrm{Uncertainty relations}\]
29060 \begin_layout Standard
29061 To get this formula, a displayed formula is created where the command
29069 \begin_layout Plain Layout
29080 A purple box appears around the blue formula box where now columns and
29081 lines can be added.
29082 Outside the multiline environment other formula parts can be set, like
29086 \begin_layout Standard
29087 The aligned environment is also suitable for long formulas whose lines are
29088 horizontally aligned.
29089 Using aligned in a displayed formula has the advantage that the formula
29090 number is vertically centered behind the lines.
29092 \begin_inset CommandInset ref
29094 reference "eq:shortlong"
29098 in the aligned environment:
29099 \begin_inset Formula \begin{equation}
29100 \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}|}\\
29101 & -\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}
29109 \begin_layout Standard
29110 To use the environments
29132 \begin_layout Plain Layout
29150 \begin_layout Plain Layout
29168 \begin_layout Plain Layout
29176 are inserted, respectively.
29177 The split environment has the same properties as the aligned environment
29178 but it can only have two columns.
29181 \begin_layout Subsection
29182 Text in multiline Formulas
29183 \begin_inset CommandInset label
29185 name "sub:Text-in-multiline"
29193 \begin_layout Plain Layout
29203 \begin_layout Plain Layout
29204 Formula ! multiline ! text
29212 \begin_layout Standard
29213 In the Align environments, and the multline and gather environment, text
29214 can be inserted that will appear in a separate line and doesn't affect
29215 the column alignment.
29216 To do this, the command
29224 \begin_layout Plain Layout
29234 is used in the following scheme:
29237 \begin_layout Standard
29245 \begin_layout Standard
29246 The text should not be longer than a line because it cannot be hyphenated.
29247 As LyX doesn't yet support
29253 directly, the text is written as mathematical text.
29260 must hereby be at the beginning of a line and appears in the output above
29262 An example where the text was inserted at the beginning of the second line:
29263 \begin_inset Formula \begin{align}
29264 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29265 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29272 \begin_layout Section
29277 \begin_layout Plain Layout
29287 \begin_layout Plain Layout
29288 Formula ! numbering|see
29292 \begin_layout Plain Layout
29303 \begin_layout Plain Layout
29318 \begin_layout Subsection
29322 \begin_layout Standard
29323 Numbered formulas can be created with the menu
29325 Insert\SpecialChar \menuseparator
29326 Math\SpecialChar \menuseparator
29328 \begin_inset space ~
29336 \begin_inset space ~
29342 Existing formulas can be numbered with the menu
29344 Edit\SpecialChar \menuseparator
29345 Math\SpecialChar \menuseparator
29347 \begin_inset space ~
29355 arg "math-number-toggle"
29359 The formula number is displayed in LyX behind the formula as number sign
29361 The number sign is replaced in the output by the formula number.
29364 \begin_layout Standard
29365 When numbering is turned on in multiline formulas, all lines will be numbered.
29366 But the numbering can be controlled with the menu
29368 Edit\SpecialChar \menuseparator
29369 Math\SpecialChar \menuseparator
29371 \begin_inset space ~
29375 \begin_inset space ~
29379 \begin_inset space ~
29387 arg "math-number-line-toggle"
29393 \begin_layout Standard
29394 Except of inline formulas, all formulas can be numbered with two different
29396 \begin_inset CommandInset ref
29398 reference "sec:Formula-Styles"
29405 \begin_layout Subsection
29410 \begin_layout Plain Layout
29411 Cross-references ! to formulas
29419 \begin_layout Standard
29420 All labeled formulas can be cross-referenced.
29421 A label is added by the menu
29423 Insert\SpecialChar \menuseparator
29426 or the toolbar button
29427 \begin_inset Graphics
29428 filename ../images/label-insert.png
29434 The cursor must hereby be inside a displayed formula.
29435 A dialog pops up displaying the prefix
29440 The label is inserted there behind the prefix.
29441 The predefined prefix means
29442 \begin_inset Quotes eld
29446 \begin_inset Quotes erd
29449 and makes it easier to find labels in large documents because it marks
29450 it as formula label to divide it from e.
29451 \begin_inset space \thinspace{}
29455 \begin_inset space \space{}
29459 To change a label, the menu
29461 Insert\SpecialChar \menuseparator
29467 \begin_layout Standard
29468 The name of the label is displayed in LyX within two parentheses behind
29470 A formula with a label is always numbered.
29473 \begin_layout Standard
29474 Cross-references are inserted via the menu
29476 Insert\SpecialChar \menuseparator
29479 or with the toolbar button
29480 \begin_inset Graphics
29481 filename ../images/dialog-show-new-inset_ref.png
29487 A formula cross-reference appears in the output as formula number.
29488 When in the cross-reference dialog window the format
29492 is chosen, the cross-reference appears in the output as formula number
29494 \begin_inset Newline newline
29497 By right-clicking on a cross-reference in LyX, one jumps to the formula
29498 that is referenced.
29501 \begin_layout Standard
29502 Here are as examples cross-references to formulas of the following subsections:
29503 \begin_inset Note Note
29506 \begin_layout Plain Layout
29507 Note the different cross-reference types.
29515 \begin_layout Standard
29517 \begin_inset CommandInset ref
29524 \begin_inset CommandInset ref
29532 \begin_inset CommandInset ref
29538 ) big Latin letters are used for the numbering in contrary to (
29539 \begin_inset CommandInset ref
29548 \begin_layout Standard
29549 \begin_inset VSpace medskip
29552 When the argument of
29560 \begin_layout Plain Layout
29568 \begin_inset CommandInset ref
29570 reference "sub:User-defined-Numbering"
29581 contains a box like in
29582 \begin_inset CommandInset ref
29584 reference "sub:Paragraph-Boxes"
29588 , the formula cannot be referenced.
29591 \begin_layout Subsection
29596 \begin_layout Plain Layout
29597 Formula numbering ! subnumbering
29605 \begin_layout Standard
29606 With the help of the commands
29610 begin{subequations}
29618 formulas can be subnumbered.
29619 Both commands are inserted in TeX-mode.
29622 \begin_layout Standard
29624 \begin_inset Formula \begin{equation}
29625 A=C-B\label{eq:a}\end{equation}
29633 \begin_layout Plain Layout
29637 addtocounter{equation}{-1}
29646 \begin_layout Plain Layout
29650 begin{subequations}
29656 \begin_inset VSpace -5mm
29660 \begin_inset Formula \begin{equation}
29661 B=C-A\label{eq:b}\end{equation}
29666 \begin_inset Formula \begin{equation}
29667 C=A+B\label{eq:c}\end{equation}
29674 \begin_layout Standard
29678 \begin_layout Plain Layout
29690 \begin_layout Standard
29691 To create the example, the following is done:
29694 \begin_layout Enumerate
29695 first formula is inserted
29698 \begin_layout Enumerate
29703 addtocounter{equation}{-1}
29705 begin{subequations}
29709 \begin_layout Plain Layout
29718 \begin_inset Newline newline
29723 is inserted after the first formula
29726 \begin_layout Enumerate
29727 second formula is inserted
29730 \begin_layout Enumerate
29731 third formula is inserted
29734 \begin_layout Enumerate
29741 is inserted after the third formula
29744 \begin_layout Standard
29745 Every formula between the commands
29757 is subnumbered as a, b,
29758 \begin_inset Newline linebreak
29761 c, \SpecialChar \ldots{}
29762 For multiline formulas every line will be subnumbered.
29763 All subnumbered formulas are treated as
29768 But as every numbered formula increases the counter
29772 by one, the command
29778 is needed to decrease it.
29779 Otherwise the formulas
29780 \begin_inset CommandInset ref
29787 \begin_inset CommandInset ref
29794 \begin_inset CommandInset ref
29800 would be numbered as
29801 \begin_inset CommandInset ref
29808 \begin_inset CommandInset ref
29815 \begin_inset CommandInset ref
29824 \begin_layout Standard
29825 By inserting the commands in TeX-mode, a space is created between the first
29828 \begin_inset space \thinspace{}
29831 mm vertical space is inserted after the command
29835 begin{subequations}
29838 When the formula style
29844 \begin_layout Plain Layout
29846 \begin_inset CommandInset ref
29848 reference "sec:Formula-Styles"
29860 \begin_inset space \thinspace{}
29863 mm space is inserted instead.
29866 \begin_layout Standard
29867 Here is an example for a multiline formula where the numbering was turned
29868 off for the second line:
29872 \begin_layout Plain Layout
29876 begin{subequations}
29882 \begin_inset Formula \begin{eqnarray}
29883 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29884 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29885 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29893 \begin_layout Plain Layout
29905 \begin_layout Subsection
29906 User-defined Numbering
29907 \begin_inset CommandInset label
29909 name "sub:User-defined-Numbering"
29917 \begin_layout Plain Layout
29918 Formula numbering ! user-defined
29926 \begin_layout Standard
29930 \begin_layout Plain Layout
29931 Formula numbering ! self-defined delimiters
29936 With the standard numbering parentheses are set around the formula number.
29937 To replace the parentheses for example by vertical bars, the following
29938 line is added to the LaTeX-preamble:
29941 \begin_layout Standard
29953 \begin_inset Note Note
29956 \begin_layout Plain Layout
29957 This macro is already declared in the LaTeX-preamble for testing.
29958 To activate it, remove the percent sign at the beginning.
29966 \begin_layout Standard
29967 To use other characters, the vertical bars besides the
29971 are replaced by one ore more characters.
29972 To get only the formula number the vertical bars are omitted.
29975 \begin_layout Standard
29976 \begin_inset VSpace bigskip
29979 When there should be an expression of your choice instead of the consecutive
29980 formula number in parentheses behind the formula, the command
29990 \begin_layout Plain Layout
29999 \begin_inset Formula \begin{equation}
30000 A+B=C\tag{something}\label{eq:tag}\end{equation}
30004 In this example the command
30012 \begin_layout Plain Layout
30023 was inserted to the formula.
30026 \begin_layout Standard
30035 \begin_layout Plain Layout
30046 is inserted instead, the star prevents the parentheses around the expression:
30047 \begin_inset Formula \[
30048 A+B=C\tag*{something}\]
30055 \begin_layout Standard
30056 \begin_inset VSpace bigskip
30059 To restart the formula numbering with new document parts or sections, the
30060 following command is used:
30063 \begin_layout Standard
30068 @addtoreset{equation}{part}
30074 \begin_layout Plain Layout
30079 \begin_layout Plain Layout
30090 \begin_layout Plain Layout
30103 \begin_layout Plain Layout
30114 \begin_layout Plain Layout
30127 \begin_inset Newline newline
30131 \begin_inset Newline newline
30138 @addtoreset{equation}{section}
30141 \begin_layout Standard
30142 To be able to use these commands in TeX-mode, the
30143 \begin_inset Quotes eld
30147 \begin_inset Quotes erd
30150 character has to be made
30151 \begin_inset Quotes eld
30155 \begin_inset Quotes erd
30158 for LaTeX using the command
30172 So the command sequence in TeX-mode is:
30175 \begin_layout Standard
30181 \begin_inset Newline newline
30186 @addtoreset{equation}{section}
30187 \begin_inset Newline newline
30195 \begin_layout Standard
30196 In the LaTeX-preamble
30208 can be omitted as they are automatically internally inserted by LyX.
30211 \begin_layout Standard
30226 \begin_layout Plain Layout
30231 is part of the LaTeX-package
30239 \begin_layout Plain Layout
30240 Packages ! carlisle
30245 that is part of every LaTeX standard installation.
30254 \begin_layout Plain Layout
30255 Packages ! remreset
30260 has to be loaded in the LaTeX-preamble with the line
30263 \begin_layout Standard
30268 usepackage{remreset}
30271 \begin_layout Standard
30282 \begin_layout Plain Layout
30287 \begin_layout Plain Layout
30298 \begin_layout Plain Layout
30311 \begin_layout Plain Layout
30322 \begin_layout Plain Layout
30334 can be used with the same scheme as
30343 \begin_layout Standard
30344 \begin_inset VSpace bigskip
30347 Sometimes formulas should be numbered in the following form:
30350 \begin_layout Standard
30353 (section number.formula number)
30356 \begin_layout Standard
30357 The formula number should start with every section with
30358 \begin_inset Quotes eld
30362 \begin_inset Quotes erd
30368 \begin_layout Standard
30369 For this case there is the command
30379 \begin_layout Plain Layout
30387 , which is used with the following scheme:
30390 \begin_layout Standard
30395 numberwithin{counter}{sectioning}
30398 \begin_layout Standard
30399 Counter denotes what kind of numbering is affected, sectioning denotes what
30400 number is before the dot.
30403 \begin_layout Standard
30404 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30407 \begin_layout Standard
30412 numberwithin{equation}{section}
30415 \begin_layout Standard
30416 This is the result:
30420 \begin_layout Plain Layout
30424 numberwithin{equation}{section}
30430 \begin_inset Formula \begin{equation}
30431 A+B=C\end{equation}
30438 \begin_layout Standard
30440 \begin_inset space \thinspace{}
30444 \begin_inset space \space{}
30447 tables so that the number of the part is the sectioning,
30448 \begin_inset Newline newline
30455 numberwithin{table}{part}
30460 \begin_layout Standard
30461 To go back to the standard numbering or to prevent this kind of numbering
30462 when it is defined by the document class, the following command is inserted
30463 as TeX-Code or to the LaTeX-preamble:
30466 \begin_layout Standard
30479 \begin_layout Plain Layout
30493 \begin_layout Plain Layout
30509 \begin_inset Newline newline
30517 \begin_inset Newline newline
30529 \begin_layout Standard
30536 uses internally the command
30542 , described above, that also needs to be reverted.
30546 \begin_layout Plain Layout
30553 \begin_layout Plain Layout
30557 @removefromreset{equation}{section}
30560 \begin_layout Plain Layout
30572 \begin_layout Subsection
30573 Numbering with Roman Numbers and Letters
30577 \begin_layout Plain Layout
30578 Formula numbering ! with letters
30587 \begin_layout Plain Layout
30588 Formula numbering ! with Roman numbers
30596 \begin_layout Standard
30597 Formulas can also be numbered with Roman numbers and Latin letters.
30598 To number for example with small Roman numbers, the command
30601 \begin_layout Standard
30613 \begin_layout Standard
30614 is inserted before the formula in TeX-mode.
30625 \begin_layout Plain Layout
30633 redefines the predefined command
30649 \begin_layout Plain Layout
30656 has the same scheme like the command
30662 that is described in
30663 \begin_inset CommandInset ref
30665 reference "sub:The-Command-newcommand"
30678 is the formula counter.
30685 is used as prefix for a counter, the value of the counter is output as
30687 When a formula is numbered, LaTeX sets internally the command
30693 behind the formula.
30702 \begin_layout Plain Layout
30712 outputs the counter as small Roman number.
30715 \begin_layout Standard
30716 All formulas behind the command
30726 are now numbered Roman.
30727 To switch to numbering with big Roman numbers, the command is inserted
30744 \begin_layout Plain Layout
30756 \begin_inset Quotes eld
30760 \begin_inset Quotes erd
30763 with small Latin letters there is the command
30773 \begin_layout Plain Layout
30781 , for big ones there is the command
30791 \begin_layout Plain Layout
30804 \begin_layout Standard
30805 \begin_inset Note Greyedout
30808 \begin_layout Plain Layout
30813 Only maximal 26 formulas can be numbered with Latin letters in one document.
30821 \begin_layout Standard
30825 \begin_layout Plain Layout
30841 \begin_layout Standard
30842 \begin_inset Formula \begin{equation}
30843 A=\textrm{small roman}\label{eq:rom}\end{equation}
30851 \begin_layout Plain Layout
30865 \begin_inset Formula \begin{equation}
30866 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30874 \begin_layout Plain Layout
30888 \begin_inset Formula \begin{equation}
30889 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30897 \begin_layout Plain Layout
30911 \begin_inset Formula \begin{equation}
30912 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30919 \begin_layout Standard
30920 To switch back to the default numbering, insert the command:
30923 \begin_layout Standard
30936 \begin_layout Plain Layout
30947 \begin_layout Standard
30951 \begin_layout Plain Layout
30965 \begin_inset Formula \begin{equation}
30966 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30973 \begin_layout Standard
30974 \begin_inset VSpace medskip
30977 As you see, formulas are numbered serially independent from the numbering
30979 When then numbering should start with
30980 \begin_inset Quotes eld
30984 \begin_inset Quotes erd
30987 when the style is changed, new equation counters have to be defined.
30988 A description about this can be found in the file
30989 \begin_inset CommandInset href
30991 target "Formula-numbering.lyx"
30998 \begin_layout Section
30999 User-defined Commands
31003 \begin_layout Plain Layout
31004 User-defined commands
31012 \begin_layout Standard
31013 \begin_inset Note Greyedout
31016 \begin_layout Plain Layout
31021 The names of user-defined commands and macros may only consist of Latin
31030 \begin_layout Subsection
31034 \begin_inset CommandInset label
31036 name "sub:The-Command-newcommand"
31044 \begin_layout Plain Layout
31045 User-defined commands !
31056 \begin_layout Plain Layout
31067 \begin_layout Standard
31068 Many LaTeX-commands are too long to be used frequently.
31069 But it is possible to define with the command
31075 new shorter commands.
31078 \begin_layout Standard
31079 The command scheme of
31088 \begin_layout Standard
31093 newcommand{new command name}[number of arguments][optional
31098 \begin_inset Newline newline
31105 \begin_layout Plain Layout
31120 \begin_layout Plain Layout
31127 {command definition}
31130 \begin_layout Standard
31131 \begin_inset Note Greyedout
31134 \begin_layout Plain Layout
31139 Assure that the name of the new command is not already used in your document
31140 or by LaTeX-packages that you use.
31141 When you for example define the command
31153 , you get an error message because
31159 is already defined as command for
31160 \begin_inset Quotes eld
31164 \begin_inset Formula $\le$
31168 \begin_inset Quotes erd
31179 \begin_layout Standard
31180 The number of arguments is an integer in the range 0
31181 \begin_inset space \thinspace{}
31185 \begin_inset space \thinspace{}
31188 9 and specifies how many arguments the new command should have.
31189 With the optional value a value for an optional argument can be predefined.
31190 When this is done, the
31198 rgument of the new command is automatically an optional one.
31201 \begin_layout Standard
31202 Here are some examples:
31205 \begin_layout Itemize
31206 To define the command
31218 , the LaTeX-preamble line is:
31222 \begin_layout Plain Layout
31234 \begin_inset Newline newline
31246 \begin_layout Itemize
31247 To define the command
31259 , the argument (that should be underlined) must be taken into account.
31260 For this the preamble line is:
31264 \begin_layout Plain Layout
31276 \begin_inset Newline newline
31291 \begin_layout Plain Layout
31303 \begin_inset Newline newline
31312 acts as argument placeholder, the
31316 behind it denotes that it is the placeholder for the first argument.
31319 \begin_layout Itemize
31327 \begin_inset space \thinspace{}
31331 \begin_inset space \space{}
31344 \begin_layout Plain Layout
31356 \begin_inset Newline newline
31365 framebox#1#2{$#3$}}
31371 \begin_layout Plain Layout
31383 \begin_inset Newline newline
31388 The two Dollar signs creates the extra formula needed for
31395 \begin_inset CommandInset ref
31397 reference "sub:Boxes-with-Frame"
31404 \begin_layout Itemize
31405 To create a new command for
31411 where the color for the box needn't to be specified, the argument for the
31412 color is defined optional:
31416 \begin_layout Plain Layout
31428 \begin_inset Newline newline
31437 fcolorbox{#2}{#1}{$#3$}}
31443 \begin_layout Plain Layout
31453 \begin_inset Newline newline
31456 When the color is not specified when using
31462 , the predefined color
31469 \begin_layout Standard
31470 A test of the new defined commands:
31473 \begin_layout Standard
31475 \begin_inset Tabular
31476 <lyxtabular version="3" rows="6" columns="2">
31478 <column alignment="center" valignment="top" width="0">
31479 <column alignment="center" valignment="top" width="0">
31481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31484 \begin_layout Plain Layout
31490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31493 \begin_layout Plain Layout
31495 \begin_inset Note Note
31498 \begin_layout Plain Layout
31505 is only used as spacer.
31517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31520 \begin_layout Plain Layout
31527 \begin_layout Plain Layout
31541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31544 \begin_layout Plain Layout
31545 \begin_inset Formula $A\gr B$
31555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31558 \begin_layout Plain Layout
31566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31569 \begin_layout Plain Layout
31570 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31583 \begin_layout Plain Layout
31587 \begin_inset Formula $\to$
31593 \begin_inset Formula $\to$
31604 \begin_layout Plain Layout
31618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31621 \begin_layout Plain Layout
31622 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31635 \begin_layout Plain Layout
31639 \begin_inset Formula $\to$
31650 \begin_layout Plain Layout
31664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31667 \begin_layout Plain Layout
31668 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31681 \begin_layout Plain Layout
31687 \begin_inset Formula $\to$
31698 \begin_layout Plain Layout
31712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31715 \begin_layout Plain Layout
31716 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31732 \begin_layout Subsection
31737 \begin_layout Plain Layout
31738 User-defined commands! Math macros
31747 \begin_layout Plain Layout
31756 \begin_layout Standard
31757 User-defined commands are especially convenient for complex expressions.
31758 When you are for example dealing in a document with quadratic equations,
31759 the same solution type occurs several times.
31760 The general form of a quadratic equation is
31761 \begin_inset Formula \[
31762 0=\lambda^{2}+p\lambda+q\]
31766 The general form of the solution is
31767 \begin_inset Formula \[
31768 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
31775 \begin_layout Standard
31776 To define a command for the solution formula where only the three parameters
31778 \begin_inset Formula $\lambda$
31782 \begin_inset Formula $p$
31786 \begin_inset Formula $q$
31789 need to be specified and the index of
31790 \begin_inset Formula $\lambda$
31793 can be given optionally, the LaTeX-preamble line is
31794 \begin_inset Newline newline
31810 \begin_inset Newline newline
31817 \begin_layout Plain Layout
31832 \begin_layout Plain Layout
31843 frac{#3^{2}}{4}-#4}}
31846 \begin_layout Standard
31847 To create with this the solution formula, the command
31848 \begin_inset Newline newline
31858 \begin_inset Formula $\to$
31864 \begin_inset Formula $\to$
31871 is inserted to a formula
31876 \begin_layout Standard
31877 The definition of the new command is unintuitive because one has to know
31878 the schemes of all used LaTeX commands, e.
31879 \begin_inset space \thinspace{}
31883 \begin_inset space \space{}
31886 that a fraction is inserted in LaTeX as
31890 frac{numerator}{denominator}
31893 Furthermore one can easily forget a brace in the definition and cannot
31894 see in LyX what the new command is doing.
31895 To avoid these problems LyX offers the possibility to use math macros instead
31905 \begin_layout Standard
31906 A math macro is created by using the menu
31908 Insert\SpecialChar \menuseparator
31909 Math\SpecialChar \menuseparator
31912 or the toolbar button
31913 \begin_inset Graphics
31914 filename ../images/math-macro_newmacroname_newcommand.png
31920 The math macro toolbar appears together with the following box where the
31922 \begin_inset Newline newline
31926 \begin_inset space \hspace*{\fill}
31930 \begin_inset Graphics
31931 filename clipart/macrobox.png
31938 \begin_inset space \hspace*{\fill}
31942 \begin_inset Newline newline
31946 \begin_inset FormulaMacro
31947 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
31952 newmacroname is the default name of the macro that should be changed to
31953 something sensible.
31954 The wanted formula is inserted in the first blue box.
31955 An argument placeholder is inserted with the command
31962 \begin_inset space \thinspace{}
31966 \begin_inset space \space{}
31975 or by using the macro toolbar button
31976 \begin_inset Graphics
31977 filename ../images/math-macro-add-param.png
31983 Argument placeholders are displayed red.
31984 Maximum 9 arguments are possible.
31985 Optional arguments are created with the toolbar button
31986 \begin_inset Graphics
31987 filename ../images/math-macro-add-optional-param.png
31993 The first non-optional argument can be transformed to an optional one with
31995 \begin_inset Graphics
31996 filename ../images/math-macro-make-optional.png
32002 In the second blue box the appearance of the macro in LyX can be defined.
32003 Normally you want to see it as it is defined, so the box is kept empty.
32004 But when you have created a macro that needs lot of space on the screen,
32005 you can insert in the box for example
32006 \begin_inset Newline newline
32036 \begin_inset Newline newline
32041 For the macro only the arguments with the macro name in front of them will
32042 then be displayed in LyX, leading to a better overview.
32043 The formula appears in the output as defined in the first box.
32044 \begin_inset Newline newline
32047 The appearance of macros in formulas can furthermore be changed for single
32048 macros by setting the cursor in the macro and using the menu
32050 View\SpecialChar \menuseparator
32052 \begin_inset space ~
32056 \begin_inset space ~
32064 \begin_layout Standard
32065 To use a macro, the macro name is inserted as command to a formula, in our
32073 Our macro looks in LyX like this:
32074 \begin_inset Newline newline
32078 \begin_inset space \hspace*{\fill}
32082 \begin_inset Graphics
32083 filename clipart/macrouse.png
32090 \begin_inset space \hspace*{\fill}
32094 \begin_inset Newline newline
32097 Here is our macro example with the arguments
32098 \begin_inset Formula $x$
32102 \begin_inset Formula $\ln(x)$
32106 \begin_inset Formula $B$
32112 \begin_layout Standard
32113 \begin_inset Formula \[
32121 \begin_layout Standard
32122 A math macro is transformed internally to a
32128 command when exporting the document.
32135 command is not placed in the LaTeX-preamble, therefore macros can only
32136 be used in formulas that are in the document below the macro definition
32140 \begin_layout Standard
32141 Math macros can also be directly be created from a
32148 When writing for example the command
32151 \begin_inset Newline newline
32160 xleftarrow[#2]{#1}}
32161 \begin_inset Newline newline
32166 in LyX as normal text, highlighting it completely and using then the shortcut
32171 , the command will be transformed to a math macro.
32172 Using this method you need to be careful that the
32178 command is typed correctly, otherwise you get a faulty macro leading to
32182 \begin_layout Standard
32183 Math macros currently yet have the problem that further formulas in macro
32184 definitions are handled wrongly.
32185 Therefore the example
32192 \begin_inset CommandInset ref
32194 reference "sub:The-Command-newcommand"
32198 cannot be created as macro.
32201 \begin_layout Standard
32202 When the cursor is in a macro definition box, you will see the macro toolbar
32206 \begin_layout Standard
32207 \begin_inset VSpace defskip
32213 \begin_layout Standard
32214 \begin_inset Graphics
32215 filename clipart/MacroToolbar.png
32223 \begin_layout Plain Layout
32232 \begin_layout Standard
32233 \begin_inset VSpace defskip
32239 \begin_layout Standard
32240 The macro toolbar contains from left to right the following buttons:
32243 \begin_layout Standard
32244 \begin_inset VSpace defskip
32250 \begin_layout Standard
32251 \begin_inset Tabular
32252 <lyxtabular version="3" rows="9" columns="2">
32253 <features islongtable="true">
32254 <column alignment="left" valignment="top" width="0">
32255 <column alignment="left" valignment="top" width="85col%">
32256 <row interlinespace="2.5mm">
32257 <cell alignment="center" valignment="top" usebox="none">
32260 \begin_layout Plain Layout
32261 \begin_inset Graphics
32262 filename ../images/math-macro-remove-param.png
32263 BoundingBox 0bp 5bp 20bp 25bp
32264 rotateOrigin center
32273 <cell alignment="center" valignment="top" usebox="none">
32276 \begin_layout Plain Layout
32279 Edit\SpecialChar \menuseparator
32280 Math\SpecialChar \menuseparator
32282 \begin_inset space ~
32285 Definition\SpecialChar \menuseparator
32292 <row interlinespace="2.5mm">
32293 <cell alignment="center" valignment="top" usebox="none">
32296 \begin_layout Plain Layout
32297 \begin_inset Graphics
32298 filename ../images/math-macro-add-param.png
32299 BoundingBox 0bp 5bp 20bp 25bp
32300 rotateOrigin center
32309 <cell alignment="center" valignment="top" usebox="none">
32312 \begin_layout Plain Layout
32315 Edit\SpecialChar \menuseparator
32316 Math\SpecialChar \menuseparator
32318 \begin_inset space ~
32321 Definition\SpecialChar \menuseparator
32322 Remove Last Argument
32328 <row interlinespace="2.5mm">
32329 <cell alignment="center" valignment="top" usebox="none">
32332 \begin_layout Plain Layout
32333 \begin_inset Graphics
32334 filename ../images/math-macro-make-optional.png
32335 BoundingBox 0bp 5bp 20bp 25bp
32336 rotateOrigin center
32345 <cell alignment="center" valignment="top" usebox="none">
32348 \begin_layout Plain Layout
32351 Edit\SpecialChar \menuseparator
32352 Math\SpecialChar \menuseparator
32354 \begin_inset space ~
32357 Definition\SpecialChar \menuseparator
32358 Make First Non-Optional into
32359 \begin_inset Newline newline
32366 \begin_layout Plain Layout
32375 Edit\SpecialChar \menuseparator
32376 Math\SpecialChar \menuseparator
32378 \begin_inset space ~
32381 Definition\SpecialChar \menuseparator
32386 \begin_layout Plain Layout
32399 <row interlinespace="2.5mm">
32400 <cell alignment="center" valignment="top" usebox="none">
32403 \begin_layout Plain Layout
32404 \begin_inset Graphics
32405 filename ../images/math-macro-make-nonoptional.png
32406 BoundingBox 0bp 5bp 20bp 25bp
32407 rotateOrigin center
32416 <cell alignment="center" valignment="top" usebox="none">
32419 \begin_layout Plain Layout
32422 Edit\SpecialChar \menuseparator
32423 Math\SpecialChar \menuseparator
32425 \begin_inset space ~
32428 Definition\SpecialChar \menuseparator
32429 Make Last Optional into
32430 \begin_inset Newline newline
32437 \begin_layout Plain Layout
32446 Edit\SpecialChar \menuseparator
32447 Math\SpecialChar \menuseparator
32449 \begin_inset space ~
32452 Definition\SpecialChar \menuseparator
32457 \begin_layout Plain Layout
32464 Non-Optional Argument
32470 <row interlinespace="2.5mm">
32471 <cell alignment="center" valignment="top" usebox="none">
32474 \begin_layout Plain Layout
32475 \begin_inset Graphics
32476 filename ../images/math-macro-remove-optional-param.png
32477 BoundingBox 0bp 5bp 20bp 25bp
32478 rotateOrigin center
32487 <cell alignment="center" valignment="top" usebox="none">
32490 \begin_layout Plain Layout
32493 Edit\SpecialChar \menuseparator
32494 Math\SpecialChar \menuseparator
32496 \begin_inset space ~
32499 Definition\SpecialChar \menuseparator
32500 Insert Optional Argument
32506 <row interlinespace="2.5mm">
32507 <cell alignment="center" valignment="top" usebox="none">
32510 \begin_layout Plain Layout
32511 \begin_inset Graphics
32512 filename ../images/math-macro-add-optional-param.png
32513 BoundingBox 0bp 5bp 20bp 25bp
32514 rotateOrigin center
32523 <cell alignment="center" valignment="top" usebox="none">
32526 \begin_layout Plain Layout
32529 Edit\SpecialChar \menuseparator
32530 Math\SpecialChar \menuseparator
32532 \begin_inset space ~
32535 Definition\SpecialChar \menuseparator
32536 Remove Optional Argument
32542 <row interlinespace="2.5mm">
32543 <cell alignment="center" valignment="top" usebox="none">
32546 \begin_layout Plain Layout
32547 \begin_inset Graphics
32548 filename ../images/math-macro-remove-greedy-param.png
32549 BoundingBox 0bp 5bp 20bp 25bp
32550 rotateOrigin center
32559 <cell alignment="center" valignment="top" usebox="none">
32562 \begin_layout Plain Layout
32565 Edit\SpecialChar \menuseparator
32566 Math\SpecialChar \menuseparator
32568 \begin_inset space ~
32571 Definition\SpecialChar \menuseparator
32572 Append Argument Eating
32573 \begin_inset Newline newline
32580 \begin_layout Plain Layout
32589 Edit\SpecialChar \menuseparator
32590 Math\SpecialChar \menuseparator
32592 \begin_inset space ~
32595 Definition\SpecialChar \menuseparator
32600 \begin_layout Plain Layout
32613 <row interlinespace="2.5mm">
32614 <cell alignment="center" valignment="top" usebox="none">
32617 \begin_layout Plain Layout
32618 \begin_inset Graphics
32619 filename ../images/math-macro-append-greedy-param.png
32620 BoundingBox 0bp 5bp 20bp 25bp
32621 rotateOrigin center
32630 <cell alignment="center" valignment="top" usebox="none">
32633 \begin_layout Plain Layout
32636 Edit\SpecialChar \menuseparator
32637 Math\SpecialChar \menuseparator
32639 \begin_inset space ~
32642 Definition\SpecialChar \menuseparator
32643 Append Optional Argument
32644 \begin_inset Newline newline
32651 \begin_layout Plain Layout
32660 Edit\SpecialChar \menuseparator
32661 Math\SpecialChar \menuseparator
32663 \begin_inset space ~
32666 Definition\SpecialChar \menuseparator
32671 \begin_layout Plain Layout
32678 Eating From The Right
32684 <row interlinespace="2.5mm">
32685 <cell alignment="center" valignment="top" usebox="none">
32688 \begin_layout Plain Layout
32689 \begin_inset Graphics
32690 filename ../images/math-macro-add-greedy-optional-param.png
32691 BoundingBox 0bp 5bp 20bp 25bp
32692 rotateOrigin center
32701 <cell alignment="center" valignment="top" usebox="none">
32704 \begin_layout Plain Layout
32707 Edit\SpecialChar \menuseparator
32708 Math\SpecialChar \menuseparator
32710 \begin_inset space ~
32713 Definition\SpecialChar \menuseparator
32714 Remove Last Argument
32715 \begin_inset Newline newline
32722 \begin_layout Plain Layout
32731 Edit\SpecialChar \menuseparator
32732 Math\SpecialChar \menuseparator
32734 \begin_inset space ~
32737 Definition\SpecialChar \menuseparator
32742 \begin_layout Plain Layout
32749 Spitting Out To The Right
32762 \begin_layout Standard
32763 \begin_inset Newpage newpage
32769 \begin_layout Section
32773 \begin_layout Standard
32774 LyX supports two types of commutative diagrams:
32782 that are explained in the following.
32785 \begin_layout Subsection
32790 \begin_layout Plain Layout
32799 \begin_layout Standard
32800 Diagrams of this type visualize relations by vertical and horizontal lines
32802 \begin_inset Formula \[
32803 \begin{CD}A@>>>B@>>>C\\
32805 F@<<<E@<<<D\end{CD}\]
32812 \begin_layout Standard
32813 To get them, the command
32821 \begin_layout Plain Layout
32831 is inserted to a formula.
32832 A blue box appears with two dashed lines where further commands can be
32837 arg "newline-insert newline"
32840 a new line is created.
32841 Horizontal relations are inserted in odd, vertical in even formula lines.
32844 \begin_layout Standard
32845 To create the relations there are the following commands:
32848 \begin_layout Itemize
32853 creates a left arrow,
32864 \begin_layout Itemize
32869 creates an up arrow,
32877 a vertical equal sign
32880 \begin_layout Itemize
32886 is a placeholder for non-existent relations
32889 \begin_layout Standard
32890 All arrows can be labeled as follows:
32893 \begin_layout Itemize
32894 Is text inserted between the first and second < or >, resp., it is placed
32896 When it is inserted between the second and third one, it appears under
32900 \begin_layout Itemize
32901 When text for vertical arrows is inserted between the first and second A
32902 or V, resp., it is placed left beside the arrow.
32903 When it is inserted between the second and third one, it appears right
32905 If the text contains an A or V, these letters must be set into a TeX-brace.
32908 \begin_layout Standard
32909 As example a diagram with all possible relations:
32912 \begin_layout Standard
32913 \begin_inset Formula \[
32914 \begin{CD}A@>j>>B@>>k>C@=F\\
32916 D@<<j<E@>k>>F@=C\end{CD}\]
32923 \begin_layout Standard
32924 The command for this is:
32925 \begin_inset Newline newline
32936 \begin_layout Plain Layout
32945 A@>j>>B@>>k>C@=F Ctrl+Return
32946 \begin_inset Newline newline
32953 \begin_layout Plain Layout
32968 \begin_layout Plain Layout
32981 \begin_layout Plain Layout
32993 \begin_inset Formula $\to$
32999 \begin_inset Newline newline
33006 \begin_layout Plain Layout
33021 \begin_layout Plain Layout
33034 \begin_layout Plain Layout
33044 \begin_layout Subsection
33049 \begin_layout Plain Layout
33050 Diagrams ! xymatrix
33058 \begin_layout Standard
33059 To be able to use xymatrices, the LaTeX-package
33064 A xymatrix is created by inserting the command
33071 Then you are able to add new matrix columns and rows like for normal matrices,
33073 \begin_inset CommandInset ref
33075 reference "sec:Matrices"
33082 \begin_layout Standard
33083 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33085 All possibilities to create commutative diagrams and decorations are explained
33090 that you find in the menu
33092 Help\SpecialChar \menuseparator
33094 \begin_inset space ~
33097 Manuals\SpecialChar \menuseparator
33099 \begin_inset space ~
33107 \begin_layout Standard
33108 \begin_inset Newpage newpage
33114 \begin_layout Section
33119 \begin_layout Plain Layout
33132 \begin_layout Plain Layout
33133 Other useful math tips can be found in
33134 \begin_inset CommandInset citation
33149 \begin_layout Plain Layout
33157 \begin_inset Note Note
33160 \begin_layout Plain Layout
33163 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
33166 \begin_layout Plain Layout
33169 texorpdfstring is in section
33170 \begin_inset CommandInset ref
33172 reference "sub:Formulas-in-Section"
33185 \begin_layout Plain Layout
33195 \begin_layout Plain Layout
33200 \begin_layout Plain Layout
33207 Chemical characters
33211 \begin_layout Plain Layout
33226 \begin_layout Subsection
33227 Chemical Symbols and Equations
33228 \begin_inset CommandInset label
33230 name "sub:Chemical-Symbols-and"
33238 \begin_layout Plain Layout
33239 Chemical characters ! Symbols
33248 \begin_layout Plain Layout
33258 \begin_layout Plain Layout
33267 \begin_layout Standard
33268 An example text from chemistry:
33271 \begin_layout Quote
33273 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
33276 -ion reacts with two
33277 \begin_inset Formula $\mathrm{Na^{+}}$
33280 -ions to sodium sulfate
33281 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
33285 The chemical equation for this is:
33286 \begin_inset Formula \[
33287 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
33294 \begin_layout Standard
33295 This chemical equation can directly be created as formula.
33296 To avoid that the symbols appear italic, everything is highlighted and
33297 changed by the shortcut
33303 to the upright font style.
33307 \begin_layout Plain Layout
33313 \begin_inset CommandInset ref
33315 reference "sub:Font-Styles"
33327 \begin_layout Subsection
33332 \begin_layout Plain Layout
33341 \begin_layout Standard
33342 Negative numbers often look ugly in formulas because the minus sign before
33343 the number is set with the same length as the minus operator sign.
33344 When writing the negative number in normal text, the minus sign appears
33348 \begin_layout Standard
33349 Thus, the problem disappears when converting the minus sign to mathematical
33353 \begin_layout Standard
33354 An example to visualize the problem:
33357 \begin_layout Standard
33359 \begin_inset Tabular
33360 <lyxtabular version="3" rows="3" columns="2">
33362 <column alignment="right" valignment="top" width="0">
33363 <column alignment="left" valignment="top" width="0">
33365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33368 \begin_layout Plain Layout
33374 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33377 \begin_layout Plain Layout
33385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33388 \begin_layout Plain Layout
33394 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33397 \begin_layout Plain Layout
33398 \begin_inset Formula $x=-2$
33408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33411 \begin_layout Plain Layout
33417 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33420 \begin_layout Plain Layout
33421 \begin_inset Formula $x=\textrm{-}2$
33437 \begin_layout Subsection
33438 Comma as decimal Separator
33442 \begin_layout Plain Layout
33451 \begin_layout Standard
33452 In LaTeX a comma inside a formula is used, according to the English convention,
33453 as number group separator.
33454 So there will be space added behind all commas in formulas.
33457 \begin_layout Standard
33458 To avoid this, the comma is highlighted and changed to mathematical text
33468 \begin_layout Standard
33469 To use all formula commas in the document as decimal separator, the file
33478 \begin_layout Plain Layout
33483 is part of the LaTeX-package
33491 \begin_layout Plain Layout
33496 \begin_layout Plain Layout
33519 \begin_layout Plain Layout
33525 is loaded with the LaTeX-preamble line
33528 \begin_layout Standard
33536 \begin_layout Subsection
33538 \begin_inset CommandInset label
33540 name "sub:Physical-Vectors"
33548 \begin_layout Plain Layout
33557 \begin_layout Standard
33558 Predefined vectors are offered by the LaTeX-package
33566 \begin_layout Plain Layout
33571 should be part of every LaTeX standard installation.
33580 \begin_layout Plain Layout
33586 that is loaded with the LaTeX-preamble line
33589 \begin_layout Standard
33597 \begin_layout Standard
33601 \begin_layout Plain Layout
33611 \begin_inset Note Note
33614 \begin_layout Plain Layout
33615 The following table will only be displayed when the LaTeX-package
33624 The following commands are defined:
33627 \begin_layout Standard
33629 \begin_inset Tabular
33630 <lyxtabular version="3" rows="4" columns="2">
33632 <column alignment="center" valignment="top" width="0">
33633 <column alignment="center" valignment="top" width="0">
33635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33638 \begin_layout Plain Layout
33644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33647 \begin_layout Plain Layout
33655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33658 \begin_layout Plain Layout
33668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33671 \begin_layout Plain Layout
33672 \begin_inset Formula $\Bra{\psi}$
33682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33685 \begin_layout Plain Layout
33695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33698 \begin_layout Plain Layout
33699 \begin_inset Formula $\Ket{\psi}$
33709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33712 \begin_layout Plain Layout
33724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33727 \begin_layout Plain Layout
33728 \begin_inset Formula $\Braket{\psi|\phi}$
33744 \begin_layout Standard
33751 assures that all vertical bars are set in the size of the surrounding brackets:
33752 \begin_inset Formula \[
33753 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
33761 \begin_layout Plain Layout
33771 \begin_inset Note Note
33774 \begin_layout Plain Layout
33775 The following will be displayed when the LaTeX-package
33787 \begin_layout Standard
33788 You need to install the LaTeX-package
33792 to see the rest of this subsection in the output.
33795 \begin_layout Standard
33799 \begin_layout Plain Layout
33811 \begin_layout Standard
33818 can also be achieved using the command
33824 , that is described in
33825 \begin_inset CommandInset ref
33827 reference "sub:Automatic-Bracket-Size"
33834 \begin_layout Subsection
33835 Self-defined Fractions
33836 \begin_inset CommandInset label
33838 name "sub:Self-defined-Fractions"
33846 \begin_layout Plain Layout
33847 Fractions ! self-defined
33855 \begin_layout Standard
33856 To define custom commands for fractions, the command
33866 \begin_layout Plain Layout
33874 is used in the following scheme:
33877 \begin_layout Standard
33890 bracket}{fraction bar thickness}{style}
33891 \begin_inset Newline newline
33898 \begin_layout Plain Layout
33913 \begin_layout Plain Layout
33920 {numerator}{denominator}
33923 \begin_layout Standard
33924 The style is a number in the range of 0
33925 \begin_inset space \thinspace{}
33929 \begin_inset space \thinspace{}
33935 \begin_layout Standard
33937 \begin_inset Tabular
33938 <lyxtabular version="3" rows="5" columns="2">
33940 <column alignment="center" valignment="top" width="0">
33941 <column alignment="center" valignment="top" width="0">
33943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33946 \begin_layout Plain Layout
33952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33955 \begin_layout Plain Layout
33963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33966 \begin_layout Plain Layout
33972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33975 \begin_layout Plain Layout
33976 display style formula
33983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33986 \begin_layout Plain Layout
33992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33995 \begin_layout Plain Layout
34003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34006 \begin_layout Plain Layout
34012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34015 \begin_layout Plain Layout
34023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34026 \begin_layout Plain Layout
34032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34035 \begin_layout Plain Layout
34049 \begin_layout Standard
34050 When no style is given, the size is adjusted to the surrounding environment
34051 like for the command
34060 \begin_layout Standard
34061 When no fraction bar thickness is given, the predefined value of 0.4
34062 \begin_inset space \thinspace{}
34068 \begin_layout Standard
34069 \begin_inset VSpace medskip
34072 For example, the commands
34085 \begin_inset CommandInset ref
34087 reference "sub:Fractions"
34091 are defined with the commands
34094 \begin_layout Standard
34103 genfrac{}{}{}{0}{#1}{#2}}
34106 \begin_layout Standard
34110 \begin_layout Standard
34119 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34122 \begin_layout Standard
34123 \begin_inset VSpace medskip
34126 To define a fraction where the fraction bar thickness can be given as optional
34127 argument, the following line is inserted to the LaTeX-preamble:
34130 \begin_layout Standard
34139 genfrac{}{}{#1}{}{#2}{#3}}
34142 \begin_layout Standard
34144 \begin_inset Formula \begin{align*}
34145 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34146 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34150 As one can see, the distance of the numerator and the denominator to the
34151 fraction bar is round about three times the bar thickness.
34154 \begin_layout Subsection
34159 \begin_layout Plain Layout
34168 \begin_layout Standard
34169 To cancel formulas or formula parts, the LaTeX-package
34177 \begin_layout Plain Layout
34182 is part of every LaTeX standard installation.
34191 \begin_layout Plain Layout
34197 has to be loaded with the LaTeX-preamble line
34200 \begin_layout Standard
34205 usepackage[samesize]{cancel}
34208 \begin_layout Standard
34209 There are four ways to cancel formulas:
34212 \begin_layout Standard
34214 \begin_inset Tabular
34215 <lyxtabular version="3" rows="5" columns="2">
34217 <column alignment="center" valignment="top" width="0">
34218 <column alignment="center" valignment="top" width="0">
34220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34223 \begin_layout Plain Layout
34229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34232 \begin_layout Plain Layout
34234 \begin_inset Note Note
34237 \begin_layout Plain Layout
34250 are used here as spacer.
34262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34265 \begin_layout Plain Layout
34274 \begin_layout Plain Layout
34288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34291 \begin_layout Plain Layout
34292 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34305 \begin_layout Plain Layout
34314 \begin_layout Plain Layout
34328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34331 \begin_layout Plain Layout
34332 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34345 \begin_layout Plain Layout
34354 \begin_layout Plain Layout
34368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34371 \begin_layout Plain Layout
34372 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34385 \begin_layout Plain Layout
34389 \begin_inset Formula $\to$
34400 \begin_layout Plain Layout
34414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34417 \begin_layout Plain Layout
34418 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34434 \begin_layout Standard
34441 is especially suitable to visualize the reduction of fractions within formulas:
34442 \begin_inset Formula \[
34443 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
34450 \begin_layout Subsection
34451 Formulas in Section Headings
34452 \begin_inset CommandInset label
34454 name "sub:Formulas-in-Section"
34462 \begin_layout Plain Layout
34463 Formula ! in section headings
34471 \begin_layout Standard
34472 When formulas are used in section headings, the following has to be taken
34476 \begin_layout Standard
34477 \begin_inset Note Greyedout
34480 \begin_layout Plain Layout
34489 \begin_layout Plain Layout
34490 Packages ! hyperref
34495 support is enabled in the document settings dialog under
34498 \begin_inset space ~
34503 , PDF-bookmarks are created for every section heading in the table of contents.
34504 If a section heading contains formulas, they are incorrectly displayed
34505 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34514 \begin_layout Standard
34515 Both problems can be solved by inserting at the end of the section heading
34516 a short title with the menu
34518 Insert\SpecialChar \menuseparator
34520 \begin_inset space ~
34526 Short titles are used as alternative for multiline section headings to
34527 keep the table of contents clearly arranged.
34528 Only the short title appears in the table of contents and therefore also
34529 in the PDF-bookmark.
34532 \begin_layout Standard
34533 When formulas should be used in the table of contents but
34537 is used, one can use the following command in TeX-mode:
34540 \begin_layout Standard
34545 texorpdfstring{part}{alternative}
34549 \begin_layout Plain Layout
34560 \begin_layout Standard
34561 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34562 This can be characters, formulas, footnotes, but also cross-references.
34563 The alternative is used instead of the part for the bookmark.
34566 \begin_layout Standard
34567 Here are two example headings:
34568 \begin_inset VSpace -3mm
34575 \begin_layout Plain Layout
34587 \begin_layout Subsubsection
34588 Heading without formula in table of contents
34589 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34593 \begin_inset OptArg
34596 \begin_layout Plain Layout
34597 Heading without formula in table of contents
34605 \begin_layout Subsubsection
34606 Heading with formula in table of contents
34610 \begin_layout Plain Layout
34620 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34627 \begin_layout Plain Layout
34637 \begin_layout Standard
34641 \begin_layout Plain Layout
34650 In the first heading a short title was used, in the second one
34659 \begin_layout Standard
34660 To get the same formatting as for the other headings, the complete heading
34669 \begin_layout Plain Layout
34671 \begin_inset CommandInset ref
34673 reference "sub:Bold-Formulas"
34685 \begin_layout Subsection
34686 Formulas in multi-column Text
34690 \begin_layout Plain Layout
34691 Formula ! in multi-column text
34699 \begin_layout Standard
34700 Formulas in multi-column text are often too wide to fit into a column and
34701 thus need to be set over the whole page width.
34702 This is done by using the LaTeX-package
34710 \begin_layout Plain Layout
34715 is part of every LaTeX standard installation.
34724 \begin_layout Plain Layout
34725 Packages ! multicol
34730 , that is loaded with the LaTeX-preamble line
34733 \begin_layout Standard
34738 usepackage{multicol}
34741 \begin_layout Standard
34742 \begin_inset Note Greyedout
34745 \begin_layout Plain Layout
34746 Note herby that the setting
34749 \begin_inset space ~
34756 Document\SpecialChar \menuseparator
34762 \begin_inset space ~
34782 \begin_layout Standard
34783 Before the multi-column text the command
34786 \begin_layout Standard
34791 begin{multicols}{column number}
34794 \begin_layout Standard
34795 is written in TeX-mode.
34796 The column number is a number in the range of 2
34797 \begin_inset space \thinspace{}
34801 \begin_inset space \thinspace{}
34805 Before the formula the multi-column text is ended by inserting the command
34808 \begin_layout Standard
34816 \begin_layout Standard
34820 \begin_layout Standard
34821 Due to the command some space is automatically added before the formula.
34823 \begin_inset space \thinspace{}
34826 mm vertical space is inserted before the formula.
34827 When the formula style
34833 \begin_layout Plain Layout
34835 \begin_inset CommandInset ref
34837 reference "sec:Formula-Styles"
34849 \begin_inset space \thinspace{}
34852 mm space is inserted instead.
34855 \begin_layout Standard
34856 As example a multi-column text with a displayed formula:
34859 \begin_layout Standard
34863 \begin_layout Plain Layout
34867 begin{multicols}{2}
34872 Das Spektrum wird fouriertransformiert.
34873 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
34874 , Lösungsmittel) zu trennen.
34875 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
34876 nun das Aussehen des Ausgangssignals.
34877 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
34878 über alle Phasen integrieren muss.
34880 \begin_inset Formula $S$
34883 unser normiertes Ausgangssignal and
34884 \begin_inset Formula $P$
34887 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
34891 \begin_layout Plain Layout
34901 \begin_inset VSpace -6mm
34905 \begin_inset Formula \begin{equation}
34906 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
34914 \begin_layout Plain Layout
34918 begin{multicols}{2}
34924 \begin_inset Formula $S_{0}$
34927 das Signal ohne Gradient ist and the Normierungsbedingung
34928 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34932 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
34934 \begin_inset Formula $\nicefrac{\pi}{2}$
34938 \begin_inset space \thinspace{}
34941 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
34942 das Signal zusätzlich abschwächt.
34943 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
34945 \begin_inset Formula $T_{2}$
34951 \begin_layout Standard
34955 \begin_layout Plain Layout
34967 \begin_layout Subsection
34968 Formulas with Description of Variables
34972 \begin_layout Plain Layout
34973 Formula ! with description of variables
34981 \begin_layout Standard
34982 To describe variables within a formula, like in formula
34983 \begin_inset CommandInset ref
34985 reference "eq:within"
34994 \begin_inset Formula $n$
34998 \begin_inset space ~
35001 matrix is used with left aligned columns for the
35002 \begin_inset Formula $n$
35009 \begin_layout Plain Layout
35011 \begin_inset CommandInset ref
35013 reference "sec:Matrices"
35022 To set the description in a smaller size, before the matrix e.
35023 \begin_inset space \thinspace{}
35027 \begin_inset space \space{}
35040 \begin_layout Plain Layout
35042 \begin_inset CommandInset ref
35044 reference "sub:Font-Sizes"
35056 \begin_layout Standard
35057 When the formula style
35063 \begin_layout Plain Layout
35065 \begin_inset CommandInset ref
35067 reference "sec:Formula-Styles"
35088 \begin_layout Plain Layout
35095 only works in formulas with the style
35100 \begin_inset CommandInset ref
35102 reference "sub:Variable-Space"
35111 is inserted before and after the matrix to have the same separation of
35112 the matrix from the equation and the side margin.
35115 \begin_layout Standard
35116 When the formula style
35120 is used, the method described in
35121 \begin_inset CommandInset ref
35123 reference "sub:Flalign-Environment"
35127 is used to indent formulas.
35129 \begin_inset CommandInset ref
35131 reference "eq:within"
35135 consists of five columns whereas in the first two columns contain the equation,
35136 the third the matrix, and the last one an empty TeX-brace.
35137 \begin_inset Formula \begin{flalign}
35138 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35139 \rho & \textrm{density}\\
35140 V & \textrm{volume}\\
35141 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35148 \begin_layout Subsection
35149 Upright small Greek Letters
35150 \begin_inset CommandInset label
35152 name "sub:Upright-small-Greek"
35160 \begin_layout Plain Layout
35161 Greek letters ! upright
35169 \begin_layout Standard
35170 Most of the math fonts only provide italic small Greek letters.
35171 But for symbols of elementary particles like pions and neutrinos, upright
35172 Greek letters are needed.
35181 \begin_layout Plain Layout
35186 is part of the LaTeX-package
35194 \begin_layout Plain Layout
35199 \begin_layout Plain Layout
35222 \begin_layout Plain Layout
35228 that is loaded with the LaTeX-preamble line
35231 \begin_layout Standard
35236 usepackage{upgreek}
35239 \begin_layout Standard
35245 \begin_layout Plain Layout
35255 \begin_inset Note Note
35258 \begin_layout Plain Layout
35259 The following table will only be displayed when the LaTeX-package
35268 They are created when the command for a small Greek letters is started
35274 For example the command
35281 \begin_inset Formula $\uptau$
35287 \begin_layout Standard
35288 With these commands reactions of elementary particles can be typeset:
35289 \begin_inset Formula \[
35290 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
35297 \begin_layout Standard
35298 The upright letters are more bold and wider than the italic ones.
35299 They should therefore not be used for units like
35300 \begin_inset Quotes eld
35304 \begin_inset Quotes erd
35310 \begin_layout Standard
35314 \begin_layout Plain Layout
35324 \begin_inset Note Note
35327 \begin_layout Plain Layout
35328 The following will be displayed when the LaTeX-package
35340 \begin_layout Standard
35341 You need to install the LaTeX-package
35345 to see the rest of this subsection in the output.
35348 \begin_layout Standard
35352 \begin_layout Plain Layout
35364 \begin_layout Subsection
35365 Text Characters in Formulas
35366 \begin_inset CommandInset label
35368 name "sub:Text-Characters-in"
35376 \begin_layout Plain Layout
35385 \begin_layout Standard
35386 In some cases you might want to insert text characters directly into formulas.
35387 When for example the centered dot · is often used in formulas like
35388 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35391 , one would have to insert the command
35401 \begin_layout Plain Layout
35403 \begin_inset CommandInset ref
35405 reference "sub:Binary-Operators"
35414 all the time, because this character is defined in all encodings as text
35416 But the encoding can be changed by this LaTeX-preamble line:
35419 \begin_layout Standard
35424 Declare Inputtext{183}{
35434 f\SpecialChar \textcompwordmark{}
35438 \begin_layout Standard
35439 The character encoding (menu
35441 Document\SpecialChar \menuseparator
35442 Settings\SpecialChar \menuseparator
35445 ) specifies what character appears when a keyboard key is pressed.
35446 When the key for the character '·' is pressed, internally the command
35453 But this command is not available in a formula so that you would get LaTeX-erro
35455 With the changed encoding the right command is chosen automatically, depending
35456 on if the character was inserted into a formula or not.
35459 \begin_layout Standard
35460 The encoding of several characters is saved in definition files.
35461 Fore example the encoding
35465 is defined in the file
35469 that is in the installation folder of LaTeX.
35470 Encodings should only be changed via the LaTeX-preamble and not in the
35472 Otherwise own documents could not be edited by other LyX users working
35473 on other computers.
35476 \begin_layout Standard
35477 \begin_inset VSpace medskip
35480 Besides the centered dot, in this document the degree sign ° is defined
35481 with the following LaTeX-preamble line so that it can directly be inserted
35485 \begin_layout Standard
35490 DeclareInputtext{176}{
35500 f\SpecialChar \textcompwordmark{}
35504 \begin_layout Standard
35505 \begin_inset Newpage newpage
35511 \begin_layout Section
35517 \begin_layout Plain Layout
35526 \begin_layout Standard
35527 This section is a summary of the most important typographic rules, listed
35532 \begin_layout Plain Layout
35533 This collection was partly taken from the German semi-official dictionary
35535 \begin_inset Quotes eld
35539 \begin_inset Quotes erd
35543 \begin_inset CommandInset citation
35549 that lists some of the ISO rules.
35557 \begin_layout Itemize
35566 \begin_layout Plain Layout
35567 done with font styles, see
35568 \begin_inset CommandInset ref
35570 reference "sub:Font-Styles"
35580 \begin_inset space \thinspace{}
35584 \begin_inset Newline newline
35587 Between the value and the unit is the smallest space, see
35588 \begin_inset CommandInset ref
35590 reference "sub:Predefined-Space"
35595 \begin_inset Newline newline
35598 This convention is automatically fulfilled when the command
35605 When it is entered to a formula, two boxes appear.
35606 In the first one the value is inserted, in the second one the unit, and
35608 \begin_inset Formula $\unit[30]{km/h}$
35612 \begin_inset space \thinspace{}
35622 is not a real LaTeX command but the command
35628 , therefore you cannot use it in TeX code.
35631 \begin_layout Itemize
35632 Percent and perthousand signs are set like physical units:
35633 \begin_inset Newline newline
35637 \begin_inset space \thinspace{}
35643 \begin_layout Itemize
35644 The degree sign follows directly on the value: 15°, but not when it is used
35646 \begin_inset space \thinspace{}
35652 \begin_layout Itemize
35653 In numbers with more than four digits the smallest space is inserted before
35654 every third digit to group them:
35664 \begin_inset space \thinspace{}
35668 \begin_inset space \thinspace{}
35674 \begin_layout Itemize
35675 For dimensions like 120×90×40
35676 \begin_inset space \thinspace{}
35679 cm the multiplication sign
35680 \begin_inset Quotes eld
35684 \begin_inset Quotes erd
35688 It is available via the menu
35690 Insert\SpecialChar \menuseparator
35691 Special Character\SpecialChar \menuseparator
35695 With some keyboard definitions it can also be inserted directly.
35698 \begin_layout Itemize
35699 Functions with names consisting of several letters are set upright to avoid
35701 \begin_inset CommandInset ref
35703 reference "sub:Predefined-Functions"
35710 \begin_layout Itemize
35711 Indices consisting of several letters, are set upright:
35712 \begin_inset Formula $E_{\mathrm{kin}}$
35716 \begin_inset Newline newline
35719 Components of matrices are set italic:
35720 \begin_inset Formula $\hat{H}_{kl}$
35726 \begin_layout Itemize
35727 The differentiation/integration operator 'd', the Euler's number 'e', and
35728 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35732 \begin_layout Standard
35733 \begin_inset Newpage newpage
35739 \begin_layout Section
35744 \begin_layout Plain Layout
35753 \begin_layout Standard
35754 Some characters and symbols can be created with several commands.
35755 Here is a list of the synonym commands:
35758 \begin_layout Standard
35759 \begin_inset VSpace bigskip
35763 \begin_inset space \hfill{}
35767 \begin_inset Tabular
35768 <lyxtabular version="3" rows="12" columns="2">
35770 <column alignment="center" valignment="top" width="0pt">
35771 <column alignment="center" valignment="top" width="0pt">
35773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35776 \begin_layout Plain Layout
35782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35785 \begin_layout Plain Layout
35787 \begin_inset Note Note
35790 \begin_layout Plain Layout
35797 is only used as spacer.
35809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35812 \begin_layout Plain Layout
35820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35823 \begin_layout Plain Layout
35827 \begin_layout Plain Layout
35840 \begin_layout Plain Layout
35854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35857 \begin_layout Plain Layout
35865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35868 \begin_layout Plain Layout
35878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35881 \begin_layout Plain Layout
35889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35892 \begin_layout Plain Layout
35902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35905 \begin_layout Plain Layout
35913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35916 \begin_layout Plain Layout
35924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35927 \begin_layout Plain Layout
35935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35938 \begin_layout Plain Layout
35946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35949 \begin_layout Plain Layout
35957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35960 \begin_layout Plain Layout
35970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35973 \begin_layout Plain Layout
35981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35984 \begin_layout Plain Layout
35994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35997 \begin_layout Plain Layout
36005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36008 \begin_layout Plain Layout
36018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36021 \begin_layout Plain Layout
36029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36032 \begin_layout Plain Layout
36042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36045 \begin_layout Plain Layout
36053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36056 \begin_layout Plain Layout
36064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36067 \begin_layout Plain Layout
36075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36078 \begin_layout Plain Layout
36090 \begin_inset space \hfill{}
36094 \begin_inset Tabular
36095 <lyxtabular version="3" rows="12" columns="2">
36097 <column alignment="center" valignment="top" width="0pt">
36098 <column alignment="center" valignment="top" width="0pt">
36100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36103 \begin_layout Plain Layout
36109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36112 \begin_layout Plain Layout
36120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36123 \begin_layout Plain Layout
36131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36134 \begin_layout Plain Layout
36146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36149 \begin_layout Plain Layout
36157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36160 \begin_layout Plain Layout
36170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36173 \begin_layout Plain Layout
36181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36184 \begin_layout Plain Layout
36194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36197 \begin_layout Plain Layout
36205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36208 \begin_layout Plain Layout
36216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36219 \begin_layout Plain Layout
36227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36230 \begin_layout Plain Layout
36238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36241 \begin_layout Plain Layout
36249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36252 \begin_layout Plain Layout
36262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36265 \begin_layout Plain Layout
36273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36276 \begin_layout Plain Layout
36286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36289 \begin_layout Plain Layout
36297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36300 \begin_layout Plain Layout
36310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36313 \begin_layout Plain Layout
36321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36324 \begin_layout Plain Layout
36334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36337 \begin_layout Plain Layout
36345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36348 \begin_layout Plain Layout
36358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36361 \begin_layout Plain Layout
36369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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36386 \begin_inset space \hfill{}
36392 \begin_layout Standard
36393 \begin_inset Newpage newpage
36399 \begin_layout Bibliography
36400 \begin_inset CommandInset bibitem
36401 LatexCommand bibitem
36413 The LaTeX Companion
36416 Addison Wesley, 2004
36419 \begin_layout Bibliography
36420 \begin_inset CommandInset bibitem
36421 LatexCommand bibitem
36427 \begin_inset CommandInset href
36430 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
36434 of LaTeX's math abilities
36437 \begin_layout Bibliography
36438 \begin_inset CommandInset bibitem
36439 LatexCommand bibitem
36444 LaTeX tips and tricks-
36445 \begin_inset CommandInset href
36448 target "http://tug.org/TeXnik/"
36455 \begin_layout Bibliography
36456 \begin_inset CommandInset bibitem
36457 LatexCommand bibitem
36463 \begin_inset CommandInset href
36466 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
36474 \begin_layout Plain Layout
36486 \begin_layout Bibliography
36487 \begin_inset CommandInset bibitem
36488 LatexCommand bibitem
36494 \begin_inset CommandInset href
36497 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
36501 of all symbols available with LaTeX-packages
36504 \begin_layout Bibliography
36505 \begin_inset CommandInset bibitem
36506 LatexCommand bibitem
36512 \begin_inset CommandInset href
36514 name "Documentation"
36515 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
36519 of the LaTeX-package
36527 \begin_layout Plain Layout
36528 Packages ! hyperref
36536 \begin_layout Bibliography
36537 \begin_inset CommandInset bibitem
36538 LatexCommand bibitem
36544 \begin_inset CommandInset href
36547 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
36558 \begin_inset CommandInset ref
36560 reference "sub:Operator-Limits"
36568 \begin_layout Plain Layout
36579 \begin_layout Bibliography
36580 \begin_inset CommandInset bibitem
36581 LatexCommand bibitem
36592 Auflage, Duden 2001
36595 \begin_layout Subsubsection*
36596 \begin_inset CommandInset index_print
36597 LatexCommand printindex