1 #LyX 1.6.0svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 \fi % end if pdflatex is used
27 % Folgendes Problem lösen:
28 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
29 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
30 % die Kapitelnummer geschrieben.
31 % Als Lösung wird mehr Platz zwischen Nummer und
32 % Überschrift eingefügt.
33 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
34 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
36 % To be able to enter the character ° and · directly in LyX,
38 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
39 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
41 % increase link area for cross-references and autoname them,
42 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
44 \settowidth{\abc}{\space}
46 \renewcommand{\equationautorefname}{\hspace{-\abc}}
47 \renewcommand{\sectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
49 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
51 % don't load packages twice
52 % see first footnote in sec. 9.3
53 \@ifundefined{textcolor}{\usepackage{color}}{}
55 % the pages of the TOC are numbered roman
56 % and a PDF-bookmark for the TOC is added
58 \let\myTOC\tableofcontents
59 \renewcommand{\tableofcontents}{%
61 \pdfbookmark[1]{\contentsname}{}
64 \pagenumbering{arabic}}
66 % insert additional vertical space of 1.5 mm between footnotes,
68 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
70 % provides caption formatting
71 \setkomafont{captionlabel}{\bfseries}
77 \usepackage[samesize]{cancel}
79 % enables calculation of values,
82 % for multiple table row and column cells
92 % center multirows (e.g. in sec. 13.3)
93 \renewcommand{\multirowsetup}{\centering}
95 % define a color, used in sec.9.3
96 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
98 % declare operators (see sec. 10.4 and sec. 15.2)
99 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
100 \DeclareMathOperator{\sgn}{sgn}
102 \newcommand{\spce}{\textvisiblespace}
104 % example definitions for sec. 20.1
105 \newcommand{\gr}{\Longrightarrow}
106 \newcommand{\us}[1]{\underline{#1}}
107 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
108 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
109 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
111 % example macro from sec. 19.4
112 %\def\tagform@#1{\maketag@@@{|#1|}}
114 % macro from sec. 10.2
115 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
116 \def\mathclap {\mathpalette \mathclapinternal}
117 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
119 % redefine the greyed out note
120 \renewenvironment{lyxgreyedout}
121 {\textcolor{blue}\bgroup}{\egroup}
123 % ------------------------------------
124 % used to check for needed LaTeX packages
127 % check for package eurosym
128 % used for the Euro symbol
130 \IfFileExists{eurosym.sty}
131 {\usepackage[gennarrow]{eurosym}
132 \setboolean{eurosym}{true}}
133 {\setboolean{eurosym}{false}}
135 % needed in sec. 22.4
136 % check for package braket
138 \IfFileExists{braket.sty}
140 \setboolean{braket}{true}}
141 {\setboolean{braket}{false}}
143 % needed in sec. 22.10
144 % check for package upgreek
146 \IfFileExists{upgreek.sty}
147 {\usepackage{upgreek}
148 \setboolean{upgreek}{true}}
149 {\setboolean{upgreek}{false}}
151 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
156 \font_typewriter default
157 \font_default_family default
167 \pdf_title "LyX's Math Manual"
168 \pdf_author "LyX Team, Uwe Stöhr"
169 \pdf_subject "LyX-documentation about math"
170 \pdf_keywords "LyX, Mathed"
172 \pdf_bookmarksnumbered true
173 \pdf_bookmarksopen true
174 \pdf_bookmarksopenlevel 1
175 \pdf_breaklinks false
179 \pdf_pagebackref false
180 \pdf_pdfusetitle false
181 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
188 \paperorientation portrait
191 \paragraph_separation skip
193 \quotes_language english
196 \paperpagestyle plain
200 \tracking_changes false
201 \output_changes false
209 LyX's detailed Math manual
217 \begin_layout Plain Layout
219 If you have comments or error corrections, please send them to the LyX Documenta
223 \begin_inset CommandInset href
225 name "lyx-docs@lists.lyx.org"
226 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
237 \begin_inset Note Note
240 \begin_layout Plain Layout
247 \begin_inset Newline newline
251 \begin_inset Newline newline
259 \begin_layout Standard
260 \begin_inset CommandInset toc
261 LatexCommand tableofcontents
268 \begin_layout Standard
269 \begin_inset Note Note
272 \begin_layout Plain Layout
273 To export this document to PDF, PS, or DVI the LaTeX-packages
286 If they are not installed you can export the document anyway but the sections
287 where the packages are required won't appear in the output.
290 \begin_layout Plain Layout
291 The latest PDF-version of this document can be found here:
292 \begin_inset Newline newline
297 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
305 \begin_layout Standard
306 \begin_inset Newpage newpage
312 \begin_layout Section
314 \begin_inset CommandInset label
316 name "sec:Introduction"
323 \begin_layout Standard
324 This document explains LyX's math features and is furthermore a collection
325 of LaTeX-commands used for mathematical characters and constructs.
326 The explanations are designed for the usage of commands.
327 It is therefore required that you have read the section
338 \begin_layout Standard
339 Most of the characters and many constructs explained in this manual are
340 also accessible via the menu
344 \SpecialChar \menuseparator
360 But everybody who has to write lots of formulas will notice that it is
361 much faster to use commands instead of the math toolbar.
362 Therefore this manual is focused on commands but also mentions the correspondin
363 g toolbar buttons when available.
366 \begin_layout Standard
367 If not specially mentioned the commands are only available within formulas.
368 To be able to use all commands explained in this document, the option
372 must be used in the document settings (menu
374 Document\SpecialChar \menuseparator
375 Settings\SpecialChar \menuseparator
386 \begin_layout Plain Layout
389 Use AMS math package automatically
395 \begin_layout Plain Layout
404 -math when math constructs are found that are supported by LyX.
412 \begin_layout Standard
413 This document doesn't list all
417 \begin_layout Plain Layout
430 \begin_layout Plain Layout
435 \begin_layout Plain Layout
444 -math commands is in the file
447 \begin_inset CommandInset href
450 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
456 , which is part of every LaTeX standard installation.
461 for lucidity reasons.
464 \begin_layout Section
466 \begin_inset CommandInset label
468 name "sec:General-Instructions"
475 \begin_layout Standard
476 To create an inline formula
480 \begin_layout Plain Layout
486 that is embedded into a text line, press
490 or the toolbar button
491 \begin_inset Graphics
492 filename ../images/math-mode.png
498 \begin_inset Newline newline
501 To create a display style formula
505 \begin_layout Plain Layout
506 Formula ! display style
511 that will appear bigger and in an own paragraph, press
518 \begin_layout Standard
519 To change a display style formula to an inline formula, set the cursor into
520 the formula and press
526 Edit\SpecialChar \menuseparator
527 Math\SpecialChar \menuseparator
531 The same way is used to change an inline formula to a display style formula.
534 \begin_layout Standard
535 To display parts of an inline formula in the size of a display style formula,
544 \begin_layout Plain Layout
555 Then a new blue box appears in which the desired formula part is inserted.
558 \begin_layout Standard
559 Only inline formulas are allowed inside tables.
562 \begin_layout Standard
567 can be turned on in the menu
569 View\SpecialChar \menuseparator
573 When you click there on
574 \begin_inset Quotes eld
578 \begin_inset Quotes erd
581 the toolbar will be shown permanently at the bottom; this state is visualized
586 menu with a checkmark.
587 When you click in this state again on
588 \begin_inset Quotes eld
592 \begin_inset Quotes erd
603 is only shown when the cursor is within a formula; this state is visualized
604 by the renaming of the menu entry from
605 \begin_inset Quotes eld
609 \begin_inset Quotes erd
613 \begin_inset Quotes eld
621 \begin_inset Quotes erd
627 \begin_layout Standard
632 \begin_layout Plain Layout
638 is invoked by pressing the toolbar button
639 \begin_inset Graphics
640 filename ../images/ert-insert.png
647 Insert\SpecialChar \menuseparator
652 \begin_layout Plain Layout
666 \begin_inset Note Note
669 \begin_layout Plain Layout
670 In LyX there are three
671 \begin_inset Quotes eld
675 \begin_inset Quotes erd
678 that appear in the output with sub- and superscript letters: TeX, LaTeX,
682 \begin_layout Plain Layout
683 To avoid that these names are recognized as proper names, a TeX-brace pair
692 \begin_layout Standard
693 To change the LaTeX-preamble
697 \begin_layout Plain Layout
705 Document\SpecialChar \menuseparator
706 Settings\SpecialChar \menuseparator
711 \begin_layout Plain Layout
727 \begin_layout Standard
728 To edit matrices, case differentiations, and multiline formulas subsequently,
731 Edit\SpecialChar \menuseparator
736 Edit\SpecialChar \menuseparator
738 \begin_inset space \thinspace{}
742 \begin_inset space \thinspace{}
752 When lines and columns are swapped via the menu, the column or line where
753 the cursor is in is exchanged with the column to the right or the line
755 Is the cursor in the last column or row, the exchange is done with the
756 column to the left or the line above.
759 \begin_layout Standard
760 To write text in formulas
764 \begin_layout Plain Layout
765 For multiline formulas the command
772 \begin_inset CommandInset ref
774 reference "sub:Text-in-multiline"
791 \begin_layout Plain Layout
801 \begin_layout Plain Layout
808 This mode is invoked with the the shortcut
816 or by the insertion of the command
824 \begin_layout Plain Layout
835 The text appears black in LyX and can therefore be distinguished from the
836 other formula parts that appear blue.
837 In the output mathematical text is set upright, in contrary to other formula
841 \begin_layout Subsection*
845 \begin_layout Standard
846 Most of the LaTeX-commands for math constructs have the following scheme:
849 \begin_layout Standard
865 \begin_layout Standard
866 A command starts always with a backslash
867 \begin_inset Quotes gld
877 \begin_inset Quotes grd
881 To omit optional arguments, also omit the associated brackets.
882 The braces around the required arguments are named in this document as
887 \begin_layout Plain Layout
894 If you add in a formula a left brace to a command name, LyX creates automatical
896 In all other cases TeX-braces are created in formulas with the command
904 TeX-braces appear red in LyX, in contrary to normal braces that appear
906 In TeX-mode no command is needed to get TeX-braces.
907 TeX-braces don't appear in the output.
910 \begin_layout Standard
911 When commands without arguments, like commands for symbols are entered in
912 TeX-mode, a space character must
916 be behind the command to end it.
917 This space doesn't appear in the output.
918 When the space should appear in the output, the space must be followed
919 by a protected space in normal text.
922 \begin_layout Standard
923 A protected space is inserted with
930 \begin_layout Subsection*
931 \begin_inset Newpage newpage
937 \begin_layout Itemize
942 \begin_layout Plain Layout
943 This visible space character can be created with the command
953 \begin_layout Plain Layout
961 , inserted in TeX-mode.
970 \begin_layout Plain Layout
983 denotes a space character to be input.
986 \begin_layout Itemize
988 \begin_inset Formula $\to$
991 denotes the usage of the corresponding arrow key on the keyboard.
994 \begin_layout Subsection*
998 \begin_layout Standard
1000 \begin_inset Float table
1006 \begin_layout Plain Layout
1008 \begin_inset Caption
1010 \begin_layout Plain Layout
1011 \begin_inset CommandInset label
1013 name "tab:Used-units"
1025 \begin_layout Plain Layout
1027 \begin_inset Tabular
1028 <lyxtabular version="3" rows="13" columns="2">
1030 <column alignment="center" valignment="top" width="0">
1031 <column alignment="center" valignment="top" width="0">
1033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1036 \begin_layout Plain Layout
1042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1045 \begin_layout Plain Layout
1053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1056 \begin_layout Plain Layout
1062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1065 \begin_layout Plain Layout
1073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1076 \begin_layout Plain Layout
1082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1085 \begin_layout Plain Layout
1093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1096 \begin_layout Plain Layout
1102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1105 \begin_layout Plain Layout
1107 \begin_inset space \thinspace{}
1111 \begin_inset space \thinspace{}
1121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1124 \begin_layout Plain Layout
1130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1133 \begin_layout Plain Layout
1135 \begin_inset space \thinspace{}
1139 \begin_inset space \thinspace{}
1149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1152 \begin_layout Plain Layout
1158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1161 \begin_layout Plain Layout
1163 \begin_inset space \thinspace{}
1167 \begin_inset space \thinspace{}
1177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1180 \begin_layout Plain Layout
1186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1189 \begin_layout Plain Layout
1191 \begin_inset space \thinspace{}
1195 \begin_inset space \thinspace{}
1205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1208 \begin_layout Plain Layout
1214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1217 \begin_layout Plain Layout
1219 \begin_inset space \thinspace{}
1223 \begin_inset space \thinspace{}
1233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1236 \begin_layout Plain Layout
1242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1245 \begin_layout Plain Layout
1247 \begin_inset space \thinspace{}
1251 \begin_inset Formula $\approx$
1255 \begin_inset space \thinspace{}
1265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1268 \begin_layout Plain Layout
1274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1277 \begin_layout Plain Layout
1279 \begin_inset space \thinspace{}
1283 \begin_inset space \thinspace{}
1293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1296 \begin_layout Plain Layout
1302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1305 \begin_layout Plain Layout
1309 \begin_inset Quotes eld
1315 \begin_inset Quotes erd
1325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1328 \begin_layout Plain Layout
1334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1337 \begin_layout Plain Layout
1339 \begin_inset Quotes eld
1347 \begin_inset Quotes erd
1357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1360 \begin_layout Plain Layout
1366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1369 \begin_layout Plain Layout
1371 \begin_inset space \thinspace{}
1375 \begin_inset Formula $\nicefrac{1}{18}$
1379 \begin_inset space \thinspace{}
1400 \begin_layout Standard
1401 \begin_inset Newpage newpage
1407 \begin_layout Section
1411 \begin_layout Subsection
1416 \begin_layout Plain Layout
1426 \begin_layout Plain Layout
1436 \begin_layout Plain Layout
1441 \begin_layout Plain Layout
1452 \begin_layout Plain Layout
1468 \begin_layout Plain Layout
1473 \begin_layout Plain Layout
1484 \begin_layout Plain Layout
1499 \begin_layout Standard
1500 Indices are created with an underscore
1501 \begin_inset Quotes eld
1505 \begin_inset Quotes erd
1508 or via the math toolbar button
1509 \begin_inset Graphics
1510 filename ../images/math-subscript.png
1515 , exponents with a caret
1516 \begin_inset Quotes eld
1520 \begin_inset Quotes erd
1523 or via the math toolbar button
1524 \begin_inset Graphics
1525 filename ../images/math-superscript.png
1533 \begin_layout Standard
1535 \begin_inset Tabular
1536 <lyxtabular version="3" rows="4" columns="2">
1538 <column alignment="center" valignment="top" width="0pt">
1539 <column alignment="center" valignment="top" width="0pt">
1541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1544 \begin_layout Plain Layout
1550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1553 \begin_layout Plain Layout
1555 \begin_inset Note Note
1558 \begin_layout Plain Layout
1565 is only used as spacer.
1577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1580 \begin_layout Plain Layout
1586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1589 \begin_layout Plain Layout
1590 \begin_inset Formula $B_{V}$
1600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1603 \begin_layout Plain Layout
1609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1612 \begin_layout Plain Layout
1613 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1626 \begin_layout Plain Layout
1631 \begin_layout Plain Layout
1645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1648 \begin_layout Plain Layout
1649 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1665 \begin_layout Standard
1666 As the caret is in some languages an accent, vowels will be accentuated
1667 in this case and not set as exponents
1671 \begin_layout Plain Layout
1672 Depending on the used keyboard settings this can also happen for other character
1679 To get in this case exponents, press
1683 after the caret as in the last example.
1686 \begin_layout Subsection
1688 \begin_inset CommandInset label
1690 name "sub:Fractions"
1698 \begin_layout Plain Layout
1707 \begin_layout Standard
1708 Fractions are generated with the command
1718 \begin_layout Plain Layout
1726 or via the math toolbar button
1727 \begin_inset Graphics
1728 filename ../images/math/frac.png
1734 The font size is adjusted automatically, depending on whether the fraction
1735 is in an inline or display style formula.
1736 With the math toolbar button
1737 \begin_inset Graphics
1738 filename ../images/math/frac-square.png
1743 you can select different fraction types.
1746 \begin_layout Standard
1755 \begin_layout Plain Layout
1765 a fraction can be created that has in any case the size of a display style
1775 \begin_layout Plain Layout
1785 the fraction appears always with the size of an inline formula.
1789 \begin_layout Standard
1790 A line with the fraction
1791 \begin_inset Formula $\frac{1}{2}$
1794 that was created with the command
1803 \begin_layout Standard
1804 A line with the fraction
1805 \begin_inset Formula $\dfrac{1}{2}$
1808 that was created with the command
1817 \begin_layout Standard
1819 \begin_inset Tabular
1820 <lyxtabular version="3" rows="4" columns="2">
1822 <column alignment="center" valignment="top" width="0pt">
1823 <column alignment="center" valignment="top" width="0pt">
1825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1828 \begin_layout Plain Layout
1834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1837 \begin_layout Plain Layout
1839 \begin_inset Note Note
1842 \begin_layout Plain Layout
1849 is only used as spacer.
1861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1864 \begin_layout Plain Layout
1871 \begin_layout Plain Layout
1881 \begin_inset Formula $\downarrow$
1889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1892 \begin_layout Plain Layout
1893 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1906 \begin_layout Plain Layout
1913 \begin_layout Plain Layout
1923 \begin_inset Formula $\downarrow$
1931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1934 \begin_layout Plain Layout
1935 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1948 \begin_layout Plain Layout
1955 \begin_layout Plain Layout
1968 \begin_layout Plain Layout
1983 \begin_layout Plain Layout
1993 \begin_inset Formula $\downarrow$
1997 \begin_inset Formula $\downarrow\downarrow$
2005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2008 \begin_layout Plain Layout
2009 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2025 \begin_layout Standard
2026 \begin_inset VSpace bigskip
2030 \begin_inset Newpage newpage
2033 For nested fractions the command
2043 \begin_layout Plain Layout
2053 \begin_inset VSpace -3mm
2059 \begin_layout Standard
2060 \begin_inset Formula \begin{align*}
2061 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2062 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2069 \begin_layout Standard
2070 The command for the example above is:
2073 \begin_layout Standard
2079 \begin_inset Formula $\to$
2089 \begin_inset Formula $\to$
2095 \begin_inset Formula $\to\to$
2103 \begin_layout Standard
2104 \begin_inset VSpace medskip
2110 \begin_layout Standard
2117 sets the fraction always in the size of a displayed formula, also when
2118 it is part of another fraction.
2125 has the following command scheme:
2128 \begin_layout Standard
2133 cfrac[numerator position]{numerator}{denominator}
2136 \begin_layout Standard
2137 The numerator position can be
2150 l or r aligns the numerator to the left or right, resp.
2151 \begin_inset space ~
2154 with the fraction stroke.
2159 or no position is given, the numerator appears centered.
2160 These fractions demonstrate the different alignments:
2161 \begin_inset Newline newline
2167 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2171 \begin_inset Formula $\cfrac{A}{B+C}$
2175 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2181 \begin_layout Standard
2182 \begin_inset VSpace medskip
2185 It is often advantageous to combine
2198 \begin_inset Formula \[
2199 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2206 \begin_layout Standard
2207 For inline fractions with a sloped fraction stroke you can use the command
2218 \begin_layout Plain Layout
2227 \begin_inset Formula $\nicefrac{5}{31}$
2240 \begin_layout Plain Layout
2249 \begin_inset Formula $\unitfrac{5}{31}$
2252 There is furthermore the command
2258 that offers to write a fraction in combination with a number:
2259 \begin_inset Formula $\unitfrac[2]{1}{3}$
2263 \begin_inset Newline newline
2272 is not a real LaTeX command but the command
2273 \begin_inset Newline newline
2280 unitfrac[number]{numerator}{denominator}
2282 , therefore you cannot use it in TeX code.
2285 \begin_layout Standard
2286 How to define own fractions where the fraction stroke can be changed, is
2288 \begin_inset CommandInset ref
2290 reference "sub:Self-defined-Fractions"
2297 \begin_layout Subsection
2302 \begin_layout Plain Layout
2311 \begin_layout Standard
2312 Square roots are created with
2322 \begin_layout Plain Layout
2330 or the math toolbar button
2331 \begin_inset Graphics
2332 filename ../images/math/sqrt.png
2337 , all other roots with the command
2347 \begin_layout Plain Layout
2355 or with the math toolbar button
2356 \begin_inset Graphics
2357 filename ../images/math/root.png
2365 \begin_layout Standard
2367 \begin_inset Tabular
2368 <lyxtabular version="3" rows="3" columns="2">
2370 <column alignment="center" valignment="top" width="0pt">
2371 <column alignment="center" valignment="top" width="0pt">
2373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2376 \begin_layout Plain Layout
2382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2385 \begin_layout Plain Layout
2387 \begin_inset Note Note
2390 \begin_layout Plain Layout
2397 is only used as spacer.
2409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2412 \begin_layout Plain Layout
2419 \begin_layout Plain Layout
2433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2436 \begin_layout Plain Layout
2437 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2447 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2450 \begin_layout Plain Layout
2457 \begin_layout Plain Layout
2467 \begin_inset Formula $\downarrow$
2475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2478 \begin_layout Plain Layout
2479 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2495 \begin_layout Standard
2496 A square root can also be created with
2502 when the root index field is left empty.
2505 \begin_layout Standard
2506 With certain indices the distance to the root is too small, like in this
2508 \begin_inset Formula $\sqrt[\beta]{B}$
2512 \begin_inset Newline newline
2516 \begin_inset Formula $\beta$
2520 To avoid this, the commands
2530 \begin_layout Plain Layout
2548 \begin_layout Plain Layout
2556 are used with the following scheme:
2559 \begin_layout Standard
2573 \begin_layout Standard
2574 Distance is the number of Big Points (unit bp;
2575 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2578 ), that the index should be moved to the left or top, resp..
2579 The commands are written to the index.
2580 This way the command
2581 \begin_inset Newline newline
2591 \begin_inset Formula $\to$
2597 \begin_inset Formula $\to$
2606 \begin_layout Plain Layout
2616 \begin_inset Formula $\to$
2620 \begin_inset Newline newline
2625 produces a correct typeset formula:
2626 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2632 \begin_layout Subsection
2633 Binomial coefficients
2637 \begin_layout Plain Layout
2638 Binomial coefficient s
2646 \begin_layout Standard
2647 Binomial coefficients are inserted with the command
2657 \begin_layout Plain Layout
2665 or with the submenu of the math toolbar button
2666 \begin_inset Graphics
2667 filename ../images/math/frac-square.png
2673 Analog to fractions (
2693 \begin_layout Plain Layout
2713 \begin_layout Plain Layout
2722 For other brackets around binomial coeficients there are the commands
2732 \begin_layout Plain Layout
2750 \begin_layout Plain Layout
2761 \begin_layout Standard
2763 \begin_inset Tabular
2764 <lyxtabular version="3" rows="6" columns="2">
2766 <column alignment="center" valignment="top" width="0pt">
2767 <column alignment="center" valignment="top" width="0pt">
2769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2772 \begin_layout Plain Layout
2778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2781 \begin_layout Plain Layout
2783 \begin_inset Note Note
2786 \begin_layout Plain Layout
2793 is only used as spacer.
2805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2808 \begin_layout Plain Layout
2815 \begin_layout Plain Layout
2825 \begin_inset Formula $\downarrow$
2833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2836 \begin_layout Plain Layout
2837 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2850 \begin_layout Plain Layout
2857 \begin_layout Plain Layout
2867 \begin_inset Formula $\downarrow$
2875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2878 \begin_layout Plain Layout
2879 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2892 \begin_layout Plain Layout
2899 \begin_layout Plain Layout
2909 \begin_inset Formula $\downarrow$
2917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2920 \begin_layout Plain Layout
2921 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2934 \begin_layout Plain Layout
2941 \begin_layout Plain Layout
2951 \begin_inset Formula $\downarrow$
2959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2962 \begin_layout Plain Layout
2963 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2976 \begin_layout Plain Layout
2983 \begin_layout Plain Layout
2993 \begin_inset Formula $\downarrow$
3001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3004 \begin_layout Plain Layout
3005 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3021 \begin_layout Subsection
3022 Case differentiations
3026 \begin_layout Plain Layout
3027 Case differentiations
3035 \begin_layout Standard
3037 \begin_inset Tabular
3038 <lyxtabular version="3" rows="3" columns="2">
3040 <column alignment="center" valignment="top" width="0pt">
3041 <column alignment="center" valignment="top" width="0pt">
3043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3046 \begin_layout Plain Layout
3052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3055 \begin_layout Plain Layout
3063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3066 \begin_layout Plain Layout
3073 \begin_layout Plain Layout
3083 \begin_inset Formula $\to$
3090 \begin_layout Plain Layout
3103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3106 \begin_layout Plain Layout
3107 \begin_inset Formula $\begin{cases}
3118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3121 \begin_layout Plain Layout
3128 \begin_layout Plain Layout
3142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3145 \begin_layout Plain Layout
3146 \begin_inset Formula $\begin{cases}
3147 A & \textrm{for }x>0\\
3148 B & \textrm{for }x=0\end{cases}$
3164 \begin_layout Standard
3171 or the usage of the math toolbar button
3172 \begin_inset Graphics
3173 filename ../images/math/cases.png
3178 you can create new lines with the shortcut
3182 or the table toolbar button
3183 \begin_inset Graphics
3184 filename ../images/tabular-feature_append-row.png
3192 \begin_layout Standard
3199 is also available via the menu
3201 Insert\SpecialChar \menuseparator
3202 Math\SpecialChar \menuseparator
3208 \begin_layout Subsection
3213 \begin_layout Plain Layout
3222 \begin_layout Standard
3233 \begin_layout Plain Layout
3241 every character can be displayed canceled.
3242 The characters are quasi accentuated by a slash.
3245 \begin_layout Standard
3247 \begin_inset Tabular
3248 <lyxtabular version="3" rows="4" columns="2">
3250 <column alignment="center" valignment="top" width="0pt">
3251 <column alignment="center" valignment="top" width="0pt">
3253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3256 \begin_layout Plain Layout
3262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3265 \begin_layout Plain Layout
3273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3276 \begin_layout Plain Layout
3284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3287 \begin_layout Plain Layout
3288 \begin_inset Formula $\not=$
3298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3301 \begin_layout Plain Layout
3311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3314 \begin_layout Plain Layout
3315 \begin_inset Formula $\not\le$
3325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3328 \begin_layout Plain Layout
3338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3341 \begin_layout Plain Layout
3342 \begin_inset Formula $\not\parallel$
3358 \begin_layout Standard
3359 The last example shows, that not all negations look good.
3360 Therefore there are for some negations special commands (see
3361 \begin_inset CommandInset ref
3363 reference "sub:Mathematical-Symbols"
3368 \begin_inset CommandInset ref
3370 reference "sec:Relations"
3377 \begin_layout Subsection
3379 \begin_inset CommandInset label
3381 name "sub:Placeholders"
3389 \begin_layout Plain Layout
3399 \begin_layout Plain Layout
3400 Chemical characters ! Isotopes
3409 \begin_layout Plain Layout
3414 \begin_layout Plain Layout
3425 \begin_layout Plain Layout
3440 \begin_layout Standard
3442 \begin_inset space \thinspace{}
3446 \begin_inset space ~
3453 \begin_layout Plain Layout
3454 More about chemical symbols is written in
3455 \begin_inset CommandInset ref
3457 reference "sub:Chemical-Symbols-and"
3466 the following problem occurs:
3469 \begin_layout Standard
3471 \begin_inset Tabular
3472 <lyxtabular version="3" rows="2" columns="2">
3474 <column alignment="center" valignment="top" width="0pt">
3475 <column alignment="center" valignment="top" width="0pt">
3477 <cell alignment="center" valignment="top" usebox="none">
3480 \begin_layout Plain Layout
3481 Indices created with sub- and superscripts:
3486 <cell alignment="center" valignment="top" usebox="none">
3489 \begin_layout Plain Layout
3490 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3500 <cell alignment="center" valignment="top" usebox="none">
3503 \begin_layout Plain Layout
3509 <cell alignment="center" valignment="top" usebox="none">
3512 \begin_layout Plain Layout
3513 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3527 \begin_inset Note Note
3530 \begin_layout Plain Layout
3537 is only used as spacer.
3545 \begin_layout Standard
3546 The shorter index is by default placed below or above the first character
3547 of the longer index.
3548 To avoid this there is the command
3558 \begin_layout Plain Layout
3566 or the math toolbar button
3567 \begin_inset space \thinspace{}
3574 \begin_layout Plain Layout
3575 can be found in the submenu of the toolbar button
3576 \begin_inset Graphics
3577 filename ../images/math/space.png
3588 \begin_inset Graphics
3589 filename ../images/math/phantom.png
3594 that creates one or more phantom characters.
3601 a small blue box appears that is superposed with two red arrows.
3602 The arrows indicate that the complete width and height of the box content
3603 will be created as placeholder.
3604 Phantom characters are accordingly placeholders with the size of the characters.
3607 \begin_layout Standard
3609 \begin_inset Tabular
3610 <lyxtabular version="3" rows="4" columns="2">
3612 <column alignment="center" valignment="top" width="0">
3613 <column alignment="center" valignment="top" width="0">
3615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3618 \begin_layout Plain Layout
3624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3627 \begin_layout Plain Layout
3629 \begin_inset Note Note
3632 \begin_layout Plain Layout
3639 is only used as spacer.
3651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3654 \begin_layout Plain Layout
3659 \begin_layout Plain Layout
3674 \begin_layout Plain Layout
3684 \begin_inset Formula $\to$
3691 \begin_layout Plain Layout
3705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3708 \begin_layout Plain Layout
3709 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3722 \begin_layout Plain Layout
3727 \begin_layout Plain Layout
3742 \begin_layout Plain Layout
3752 \begin_inset Formula $\to$
3759 \begin_layout Plain Layout
3773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3776 \begin_layout Plain Layout
3777 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3790 \begin_layout Plain Layout
3797 \begin_layout Plain Layout
3812 \begin_layout Plain Layout
3822 \begin_inset Formula $\to$
3829 \begin_layout Plain Layout
3843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3846 \begin_layout Plain Layout
3847 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3863 \begin_layout Standard
3864 Furthermore there are the commands
3874 \begin_layout Plain Layout
3883 \begin_inset space ~
3887 \begin_inset Graphics
3888 filename ../images/math/vphantom.png
3903 \begin_layout Plain Layout
3912 \begin_inset space ~
3916 \begin_inset Graphics
3917 filename ../images/math/hphantom.png
3929 creates only space for the maximal height of the characters in the box
3930 but not for its width.
3937 creates only space for the width of the box content.
3938 Therefore the boxes of both commands have only one red arrow.
3941 \begin_layout Standard
3952 \begin_layout Plain Layout
3967 space for the height of the integral sign,
3971 \begin_layout Plain Layout
3978 creates an integral sign, see
3979 \begin_inset CommandInset ref
3981 reference "sub:Big-Operators"
3990 because this is the larger character.
3991 An example application is in
3992 \begin_inset CommandInset ref
3994 reference "sub:Multiline-Brackets"
4001 \begin_layout Subsection
4006 \begin_layout Plain Layout
4016 \begin_layout Plain Layout
4017 Formula ! underlined
4025 \begin_layout Standard
4027 \begin_inset Tabular
4028 <lyxtabular version="3" rows="4" columns="2">
4030 <column alignment="center" valignment="top" width="0pt">
4031 <column alignment="center" valignment="top" width="0pt">
4033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4036 \begin_layout Plain Layout
4042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4045 \begin_layout Plain Layout
4047 \begin_inset Note Note
4050 \begin_layout Plain Layout
4057 is only used as spacer.
4069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4072 \begin_layout Plain Layout
4079 \begin_layout Plain Layout
4092 \begin_layout Plain Layout
4105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4108 \begin_layout Plain Layout
4109 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4119 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4122 \begin_layout Plain Layout
4129 \begin_layout Plain Layout
4142 \begin_layout Plain Layout
4155 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4158 \begin_layout Plain Layout
4159 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4172 \begin_layout Plain Layout
4179 \begin_layout Plain Layout
4194 \begin_layout Plain Layout
4208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4211 \begin_layout Plain Layout
4212 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4228 \begin_layout Standard
4229 In the last example it doesn't matter if first
4244 \begin_layout Standard
4245 To double underline e.
4246 \begin_inset space \thinspace{}
4259 \begin_layout Standard
4260 It is possible to place up to 6 lines above or below characters.
4263 \begin_layout Subsection
4265 \begin_inset CommandInset label
4275 \begin_layout Plain Layout
4284 \begin_layout Standard
4285 There are different types of ellipses available.
4289 \begin_layout Plain Layout
4290 In the math toolbar in the submenu of the button
4291 \begin_inset Graphics
4292 filename ../images/math/ldots.png
4302 For listings dots at the baseline are used (
4312 \begin_layout Plain Layout
4320 ), while for operations dots are needed that are on the same height as the
4331 \begin_layout Plain Layout
4340 When using the command
4350 \begin_layout Plain Layout
4358 , LaTeX decides on the basis of the next character what type is used.
4361 \begin_layout Standard
4363 \begin_inset Tabular
4364 <lyxtabular version="3" rows="8" columns="2">
4366 <column alignment="center" valignment="top" width="0pt">
4367 <column alignment="center" valignment="top" width="0pt">
4369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4372 \begin_layout Plain Layout
4378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4381 \begin_layout Plain Layout
4389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4392 \begin_layout Plain Layout
4397 \begin_layout Plain Layout
4412 \begin_layout Plain Layout
4426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4429 \begin_layout Plain Layout
4430 \begin_inset Formula $A_{1},\dots,A_{n}$
4440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4443 \begin_layout Plain Layout
4448 \begin_layout Plain Layout
4463 \begin_layout Plain Layout
4477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4480 \begin_layout Plain Layout
4481 \begin_inset Formula $A_{1}+\dots+A_{n}$
4491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4494 \begin_layout Plain Layout
4499 \begin_layout Plain Layout
4514 \begin_layout Plain Layout
4528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4531 \begin_layout Plain Layout
4532 \begin_inset Formula $A_{1},\ldots,A_{n}$
4542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4545 \begin_layout Plain Layout
4550 \begin_layout Plain Layout
4565 \begin_layout Plain Layout
4579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4582 \begin_layout Plain Layout
4583 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4596 \begin_layout Plain Layout
4604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4607 \begin_layout Plain Layout
4608 \begin_inset Formula $\vdots$
4618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4621 \begin_layout Plain Layout
4629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4632 \begin_layout Plain Layout
4633 \begin_inset Formula $\ddots$
4643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4646 \begin_layout Plain Layout
4648 \begin_inset space \thinspace{}
4651 matrix with the different dots
4656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4659 \begin_layout Plain Layout
4660 \begin_inset Formula $\begin{array}{ccc}
4661 A_{11} & \cdots & A_{1m}\\
4662 \vdots & \ddots & \vdots\\
4663 A_{n1} & \cdots & A_{nm}\end{array}$
4679 \begin_layout Standard
4680 The ellipses available in menu
4682 Insert\SpecialChar \menuseparator
4684 \begin_inset space ~
4698 \begin_layout Standard
4699 \begin_inset VSpace medskip
4702 Specially for matrices there are ellipses that span over several columns.
4703 They are created with the command
4713 \begin_layout Plain Layout
4721 , that has the following scheme:
4724 \begin_layout Standard
4729 hdotsfor[distance]{number of columns}
4732 \begin_layout Standard
4733 The number of columns specifies how many columns should be spanned.
4734 Distance is a factor for the distance between the dots.
4737 \begin_layout Standard
4738 In the following matrix the command
4744 was inserted in the first box of the second line, to get an ellipsis with
4745 a dot distance twice as long as with the command
4752 \begin_inset Formula \[
4753 \left(\begin{array}{cccc}
4756 q & w & e & r\end{array}\right)\]
4760 Note that the matrix fields that should be spanned must be empty, otherwise
4761 you get LaTeX-errors.
4764 \begin_layout Standard
4765 \begin_inset VSpace bigskip
4768 Furthermore you can fill with the command
4778 \begin_layout Plain Layout
4786 the rest of a line with dots.
4787 The effect of these commands is the same like with
4794 \begin_inset CommandInset ref
4796 reference "sub:Variable-Space"
4803 \begin_layout Standard
4804 For example the command
4812 \begin_layout Plain Layout
4826 \begin_layout Standard
4827 \begin_inset Formula $A\dotfill B$
4833 \begin_layout Standard
4840 there is for a line the command
4850 \begin_layout Plain Layout
4861 \begin_layout Standard
4862 \begin_inset Formula $A\hrulefill B$
4868 \begin_layout Standard
4869 To use the commands for text, they have to be inserted in TeX-mode.
4872 \begin_layout Section
4874 \begin_inset CommandInset label
4884 \begin_layout Plain Layout
4893 \begin_layout Standard
4894 Matrices can be inserted via the math toolbar button
4895 \begin_inset Graphics
4896 filename ../images/dialog-show_mathmatrix.png
4903 Insert\SpecialChar \menuseparator
4904 Math\SpecialChar \menuseparator
4908 You will be asked for the number of matrix columns and rows, and the alignment.
4909 The vertical alignment is hereby only of importance for matrices in inline
4913 \begin_layout Standard
4914 The first matrix is top
4915 \begin_inset Formula $\begin{array}[t]{cccc}
4918 C & F & I & L\end{array}$
4922 \begin_inset Formula $\begin{array}{cccc}
4925 C & F & I & L\end{array}$
4928 , and the third bottom
4929 \begin_inset Formula $\begin{array}[b]{cccc}
4932 C & F & I & L\end{array}$
4938 \begin_layout Standard
4939 The horizontal alignment specifies how the column entries should be aligned.
4940 It is set by entering a letter for every column.
4945 denotes left aligned,
4954 To create for example a 4
4959 \begin_inset space ~
4962 matrix where the first column is left aligned, the second and third are
4963 centered, and the last one is right aligned, one enters for the horizontal
4969 Normally are in a matrix all columns centered, therefore the default is
4970 for every column is a
4977 \begin_layout Standard
4978 Horizontal alignment:
4981 \begin_layout Standard
4987 \begin_inset Formula $\begin{array}{lll}
4990 C & F & 10000\end{array}$
4998 \begin_inset Formula $\begin{array}{ccc}
5001 C & F & 10000\end{array}$
5009 \begin_inset Formula $\begin{array}{rrr}
5012 C & F & 10000\end{array}$
5018 \begin_layout Standard
5019 To add or delete rows and columns subsequently, the math toolbar buttons
5021 \begin_inset Graphics
5022 filename ../images/tabular-feature_append-row.png
5028 \begin_inset Graphics
5029 filename ../images/tabular-feature_delete-row.png
5035 \begin_inset space \thinspace{}
5040 Edit\SpecialChar \menuseparator
5044 New rows can also be created with
5051 \begin_layout Standard
5052 \begin_inset VSpace bigskip
5055 Parentheses around a matrix can can either be created with the commands
5066 \begin_layout Plain Layout
5084 \begin_layout Plain Layout
5095 \begin_inset space ~
5101 \begin_inset CommandInset ref
5103 reference "sub:Automatic-Bracket-Size"
5107 , or by using the following commands:
5108 \begin_inset VSpace medskip
5114 \begin_layout Standard
5115 \begin_inset space \hfill{}
5119 \begin_inset Tabular
5120 <lyxtabular version="3" rows="4" columns="2">
5122 <column alignment="center" valignment="top" width="0">
5123 <column alignment="center" valignment="top" width="0">
5125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5128 \begin_layout Plain Layout
5134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5137 \begin_layout Plain Layout
5139 \begin_inset Note Note
5142 \begin_layout Plain Layout
5149 is only used as spacer.
5161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5164 \begin_layout Plain Layout
5171 \begin_layout Plain Layout
5185 \begin_inset space \thinspace{}
5193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5196 \begin_layout Plain Layout
5197 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5198 0 & \textrm{-}\mathrm{i}\\
5199 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5212 \begin_layout Plain Layout
5219 \begin_layout Plain Layout
5233 \begin_inset space \thinspace{}
5241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5244 \begin_layout Plain Layout
5245 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5246 0 & \textrm{-}\mathrm{i}\\
5247 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5260 \begin_layout Plain Layout
5267 \begin_layout Plain Layout
5281 \begin_inset space \thinspace{}
5289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5292 \begin_layout Plain Layout
5293 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5294 0 & \textrm{-}\mathrm{i}\\
5295 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5309 \begin_inset space \hfill{}
5313 \begin_inset Tabular
5314 <lyxtabular version="3" rows="4" columns="2">
5316 <column alignment="center" valignment="top" width="0">
5317 <column alignment="center" valignment="top" width="0">
5319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5322 \begin_layout Plain Layout
5328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5331 \begin_layout Plain Layout
5339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5342 \begin_layout Plain Layout
5349 \begin_layout Plain Layout
5363 \begin_inset space \thinspace{}
5371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5374 \begin_layout Plain Layout
5375 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5376 0 & \textrm{-}\mathrm{i}\\
5377 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5390 \begin_layout Plain Layout
5397 \begin_layout Plain Layout
5411 \begin_inset space \thinspace{}
5419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5422 \begin_layout Plain Layout
5423 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5424 0 & \textrm{-}\mathrm{i}\\
5425 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5438 \begin_layout Plain Layout
5445 \begin_layout Plain Layout
5459 \begin_inset space \thinspace{}
5467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5470 \begin_layout Plain Layout
5471 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5472 0 & \textrm{-}\mathrm{i}\\
5473 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5487 \begin_inset space \hfill{}
5493 \begin_layout Standard
5494 \begin_inset VSpace medskip
5498 \begin_inset space \thinspace{}
5502 \begin_inset space ~
5511 is inserted, a blue box appears between two vertical lines where the matrix
5515 \begin_layout Standard
5516 \begin_inset VSpace bigskip
5519 As all multiline formulas are matrices, the length
5529 \begin_layout Plain Layout
5537 that is described in
5538 \begin_inset CommandInset ref
5540 reference "sub:Column-Separation"
5544 can also be used to change the column separation of matrices.
5547 \begin_layout Standard
5548 To change the row separation, the command
5558 \begin_layout Plain Layout
5567 It is used as follows:
5570 \begin_layout Standard
5577 arraystretch}{stretch factor}
5581 \begin_layout Plain Layout
5592 \begin_layout Standard
5599 assigns the stretch factor to the predefined command
5607 \begin_inset space \thinspace{}
5611 \begin_inset space ~
5614 the row separation, use the factor 2.
5615 This is then used for all following matrices.
5616 To go back to the original separation, assign the factor 1 to
5625 \begin_layout Standard
5626 To set matrices into a text line, the command
5636 \begin_layout Plain Layout
5645 When it is inserted a blue box with two dashed lines appears.
5646 In this box the matrix is inserted.
5649 \begin_layout Standard
5651 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5652 C & D\end{smallmatrix}\right)$
5658 \begin_layout Section
5659 Brackets and Delimiters
5663 \begin_layout Plain Layout
5673 \begin_layout Plain Layout
5682 \begin_layout Subsection
5683 Vertical Brackets and Delimiters
5687 \begin_layout Plain Layout
5696 \begin_layout Standard
5697 \begin_inset space \hfill{}
5701 \begin_inset Tabular
5702 <lyxtabular version="3" rows="9" columns="2">
5704 <column alignment="center" valignment="top" width="0pt">
5705 <column alignment="center" valignment="top" width="0pt">
5707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5710 \begin_layout Plain Layout
5716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5719 \begin_layout Plain Layout
5727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5730 \begin_layout Plain Layout
5736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5739 \begin_layout Plain Layout
5740 \begin_inset Formula $($
5750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5753 \begin_layout Plain Layout
5759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5762 \begin_layout Plain Layout
5763 \begin_inset Formula $\{$
5773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5776 \begin_layout Plain Layout
5782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5785 \begin_layout Plain Layout
5786 \begin_inset Formula $[$
5796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5799 \begin_layout Plain Layout
5807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5810 \begin_layout Plain Layout
5811 \begin_inset Formula $\langle$
5821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5824 \begin_layout Plain Layout
5832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5835 \begin_layout Plain Layout
5836 \begin_inset Formula $\lceil$
5846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5849 \begin_layout Plain Layout
5857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5860 \begin_layout Plain Layout
5861 \begin_inset Formula $\lfloor$
5871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5874 \begin_layout Plain Layout
5880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5883 \begin_layout Plain Layout
5884 \begin_inset Formula $/$
5894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5897 \begin_layout Plain Layout
5903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5906 \begin_layout Plain Layout
5907 \begin_inset Formula $|$
5921 \begin_inset space \hfill{}
5925 \begin_inset Tabular
5926 <lyxtabular version="3" rows="9" columns="2">
5928 <column alignment="center" valignment="top" width="0pt">
5929 <column alignment="center" valignment="top" width="0pt">
5931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5934 \begin_layout Plain Layout
5940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5943 \begin_layout Plain Layout
5951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5954 \begin_layout Plain Layout
5960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5963 \begin_layout Plain Layout
5964 \begin_inset Formula $)$
5974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5977 \begin_layout Plain Layout
5983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5986 \begin_layout Plain Layout
5987 \begin_inset Formula $\}$
5997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6000 \begin_layout Plain Layout
6006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6009 \begin_layout Plain Layout
6010 \begin_inset Formula $]$
6020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6023 \begin_layout Plain Layout
6031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6034 \begin_layout Plain Layout
6035 \begin_inset Formula $\rangle$
6045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6048 \begin_layout Plain Layout
6056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6059 \begin_layout Plain Layout
6060 \begin_inset Formula $\rceil$
6070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6073 \begin_layout Plain Layout
6081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6084 \begin_layout Plain Layout
6085 \begin_inset Formula $\rfloor$
6095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6098 \begin_layout Plain Layout
6108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6111 \begin_layout Plain Layout
6112 \begin_inset Formula $\backslash$
6122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6125 \begin_layout Plain Layout
6133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6136 \begin_layout Plain Layout
6137 \begin_inset Formula $\|$
6151 \begin_inset space \hfill{}
6157 \begin_layout Standard
6160 \begin_inset Note Greyedout
6163 \begin_layout Plain Layout
6168 In TeX-mode the command
6178 \begin_layout Plain Layout
6186 must be used for the backslash, because the command
6194 produces there a line break.
6202 \begin_layout Standard
6203 For all characters listed above the size can be adjusted with the commands
6204 described in the following two subsections.
6205 When using these commands, the characters < and > can directly be used
6206 instead of the commands
6221 \begin_layout Subsubsection
6223 \begin_inset CommandInset label
6225 name "sub:Manual-Bracket-Size"
6233 \begin_layout Plain Layout
6234 Bracket size ! manual
6242 \begin_layout Standard
6243 The bracket size can be specified manually by the LaTeX-commands
6253 \begin_layout Plain Layout
6286 denotes the smallest and
6292 the largest bracket size.
6295 \begin_layout Standard
6296 These commands are used to emphasize levels of brackets:
6299 \begin_layout Standard
6301 \begin_inset Tabular
6302 <lyxtabular version="3" rows="2" columns="2">
6304 <column alignment="center" valignment="top" width="0pt">
6305 <column alignment="center" valignment="top" width="0pt">
6307 <cell alignment="center" valignment="top" usebox="none">
6310 \begin_layout Plain Layout
6311 all brackets in the same size:
6316 <cell alignment="center" valignment="top" usebox="none">
6319 \begin_layout Plain Layout
6320 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6330 <cell alignment="center" valignment="top" usebox="none">
6333 \begin_layout Plain Layout
6339 <cell alignment="center" valignment="top" usebox="none">
6342 \begin_layout Plain Layout
6343 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6357 \begin_inset Note Note
6360 \begin_layout Plain Layout
6367 is only used as spacer.
6375 \begin_layout Standard
6376 For the second formula the command
6386 \begin_layout Plain Layout
6400 \begin_layout Standard
6401 Here is an overview about all bracket sizes:
6404 \begin_layout Standard
6424 \begin_layout Plain Layout
6441 \begin_layout Plain Layout
6454 \begin_layout Plain Layout
6470 \begin_layout Standard
6472 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6478 \begin_layout Standard
6479 \begin_inset Newpage newpage
6488 -commands there is the variant
6498 \begin_layout Plain Layout
6506 that adds a bit more space between the bracket and its content, and the
6523 \begin_layout Plain Layout
6533 , that don't add additional space.
6538 at the end of the command
6544 is for a left bracket; for a right bracket this will be replaced by an
6550 A left or right bracket can each be an opening or closing bracket.
6553 \begin_layout Standard
6554 In the following table is a comparison of the variants:
6557 \begin_layout Standard
6559 \begin_inset Tabular
6560 <lyxtabular version="3" rows="5" columns="2">
6562 <column alignment="center" valignment="middle" width="0">
6563 <column alignment="center" valignment="middle" width="0">
6565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6568 \begin_layout Plain Layout
6574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6577 \begin_layout Plain Layout
6579 \begin_inset Note Note
6582 \begin_layout Plain Layout
6589 is only used as spacer.
6601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6604 \begin_layout Plain Layout
6619 \begin_layout Plain Layout
6637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6640 \begin_layout Plain Layout
6641 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6654 \begin_layout Plain Layout
6669 \begin_layout Plain Layout
6687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6690 \begin_layout Plain Layout
6691 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6704 \begin_layout Plain Layout
6719 \begin_layout Plain Layout
6737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6740 \begin_layout Plain Layout
6741 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6754 \begin_layout Plain Layout
6766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6769 \begin_layout Plain Layout
6770 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6786 \begin_layout Subsubsection
6787 Automatic Bracket Size
6788 \begin_inset CommandInset label
6790 name "sub:Automatic-Bracket-Size"
6798 \begin_layout Plain Layout
6799 Bracket size ! automatic
6807 \begin_layout Standard
6808 Brackets with variable size can be inserted with the commands
6818 \begin_layout Plain Layout
6836 \begin_layout Plain Layout
6844 or via the math toolbar button
6845 \begin_inset Graphics
6846 filename ../images/dialog-show_mathdelimiter.png
6864 the wanted bracket must be inserted.
6865 The bracket size will then automatically be calculated for the output.
6868 \begin_layout Standard
6870 normal bracket: The command
6880 \begin_layout Plain Layout
6890 \begin_inset Formula $\downarrow$
6897 \begin_layout Plain Layout
6909 \begin_inset Formula \[
6917 \begin_layout Standard
6919 multiline bracket: The command
6931 \begin_layout Plain Layout
6941 \begin_inset Formula $\downarrow$
6948 \begin_layout Plain Layout
6962 \begin_inset Formula \[
6963 \ln\left(\frac{A}{C}\right)\]
6970 \begin_layout Standard
6986 \begin_inset space ~
6992 This has the advantage that you can see in LyX immediately the real bracket
6993 size and that the matching right bracket will be created too.
6994 \begin_inset Newline newline
6997 The command for the last example would then be:
7011 \begin_layout Plain Layout
7021 \begin_inset Formula $\downarrow$
7027 \begin_layout Standard
7028 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7029 For example the command
7039 \begin_layout Plain Layout
7049 \begin_inset Formula $\downarrow$
7056 \begin_layout Plain Layout
7072 \begin_inset Formula \[
7073 \left.\frac{A}{B}\right\} \]
7091 will be converted by LyX to brackets in the right size when the document
7092 is reloaded and an omitted bracket will appear as dashed line.
7095 \begin_layout Standard
7096 \begin_inset VSpace bigskip
7099 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7110 \begin_layout Plain Layout
7118 is additionally available for all brackets and limits.
7119 With this command the height of the following character is adapted to the
7120 one of the surrounding brackets, what is e.
7121 \begin_inset space \thinspace{}
7125 \begin_inset space ~
7128 needed for physical vectors:
7129 \begin_inset Formula \[
7130 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7134 For physical vectors there is a special LaTeX-package, described in
7135 \begin_inset CommandInset ref
7137 reference "sub:Physical-Vectors"
7144 \begin_layout Subsection
7149 \begin_layout Plain Layout
7150 Brackets ! horizontal
7158 \begin_layout Standard
7160 \begin_inset Tabular
7161 <lyxtabular version="3" rows="4" columns="2">
7163 <column alignment="center" valignment="top" width="0pt">
7164 <column alignment="center" valignment="top" width="0pt">
7166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7169 \begin_layout Plain Layout
7171 \begin_inset Note Note
7174 \begin_layout Plain Layout
7181 is only used as spacer.
7191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7194 \begin_layout Plain Layout
7202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7205 \begin_layout Plain Layout
7209 \begin_layout Plain Layout
7224 \begin_layout Plain Layout
7237 \begin_layout Plain Layout
7250 \begin_layout Plain Layout
7263 \begin_layout Plain Layout
7274 \begin_layout Plain Layout
7287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7290 \begin_layout Plain Layout
7291 \begin_inset Formula $\overbrace{A+B}^{3}$
7301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7304 \begin_layout Plain Layout
7308 \begin_layout Plain Layout
7323 \begin_layout Plain Layout
7336 \begin_layout Plain Layout
7349 \begin_layout Plain Layout
7360 \begin_layout Plain Layout
7373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7376 \begin_layout Plain Layout
7377 \begin_inset Formula $\underbrace{A+B}_{5}$
7387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7390 \begin_layout Plain Layout
7397 \begin_layout Plain Layout
7412 \begin_layout Plain Layout
7425 \begin_layout Plain Layout
7438 \begin_layout Plain Layout
7451 \begin_layout Plain Layout
7464 \begin_layout Plain Layout
7477 \begin_layout Plain Layout
7491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7494 \begin_layout Plain Layout
7495 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7511 \begin_layout Standard
7512 In the last example it doesn't matter if
7524 is inserted at first.
7527 \begin_layout Standard
7528 \begin_inset VSpace bigskip
7531 When brackets are needed that overlap each other, multiline formulas, as
7533 \begin_inset CommandInset ref
7535 reference "sec:Multiline-Formulas"
7540 \begin_inset Formula \begin{eqnarray*}
7541 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7542 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7546 In the first row the formula is inserted together with the first brace.
7547 It is hereby important that the space command
7551 \begin_layout Plain Layout
7552 Space commands are explained in
7553 \begin_inset CommandInset ref
7555 reference "sub:Predefined-Space"
7570 is inserted before the first
7571 \begin_inset Formula $d$
7574 , because the brace that ends behind the
7575 \begin_inset Formula $q$
7578 prevents that the following
7579 \begin_inset Quotes eld
7583 \begin_inset Quotes erd
7586 is surrounded by space.
7590 \begin_layout Plain Layout
7591 because a bracket is not handled as character, see
7592 \begin_inset CommandInset ref
7594 reference "sub:Binary-Operators"
7603 In the second row the second brace is inserted.
7604 As it should begin before the
7605 \begin_inset Formula $b$
7620 \begin_layout Plain Layout
7628 \begin_inset CommandInset ref
7630 reference "sub:Placeholders"
7639 This space is needed because the
7640 \begin_inset Quotes eld
7644 \begin_inset Quotes erd
7647 is also surrounded by space in the formula.
7648 The brace is placed under the command
7657 \begin_layout Standard
7658 It gets more complicated when brackets overlap each other, like in the following
7663 \begin_layout Plain Layout
7675 \begin_inset Formula \begin{eqnarray*}
7676 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7677 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7685 \begin_layout Plain Layout
7696 The first formula row is the same as the second row of the previous example,
7697 with the difference that the brace is above.
7698 The second row contains the formula together with the second brace.
7699 To avoid that there is space between the upper brace in the first row and
7700 the formula, the row spacing need to be reduced.
7701 This is not easily possible due to a bug in LyX
7705 \begin_layout Plain Layout
7706 \begin_inset CommandInset href
7708 name "LyX-bug #1505"
7709 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7719 As solution for the problem, the global formula row separation
7729 \begin_layout Plain Layout
7737 must be changed to -6
7738 \begin_inset space \thinspace{}
7741 pt before the formula with the command
7756 is set back after the formula to the standard value of 3
7757 \begin_inset space \thinspace{}
7760 pt using the same command.
7761 More about the row separation in formulas is explained in
7762 \begin_inset CommandInset ref
7764 reference "sub:Line-Separation"
7771 \begin_layout Section
7776 \begin_layout Plain Layout
7785 \begin_layout Standard
7786 Arrows can be inserted via the math toolbar button
7787 \begin_inset Graphics
7788 filename ../images/math/leftarrow.png
7793 or the commands listed in the following subsections.
7796 \begin_layout Subsection
7801 \begin_layout Plain Layout
7810 \begin_layout Standard
7811 \begin_inset space \hfill{}
7815 \begin_inset Tabular
7816 <lyxtabular version="3" rows="8" columns="2">
7818 <column alignment="center" valignment="top" width="0pt">
7819 <column alignment="center" valignment="top" width="0pt">
7821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7824 \begin_layout Plain Layout
7830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7833 \begin_layout Plain Layout
7841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7844 \begin_layout Plain Layout
7852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7855 \begin_layout Plain Layout
7856 \begin_inset Formula $\gets$
7866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7869 \begin_layout Plain Layout
7877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7880 \begin_layout Plain Layout
7881 \begin_inset Formula $\Leftarrow$
7891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7894 \begin_layout Plain Layout
7902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7905 \begin_layout Plain Layout
7906 \begin_inset Formula $\longleftarrow$
7916 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7919 \begin_layout Plain Layout
7927 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7930 \begin_layout Plain Layout
7931 \begin_inset Formula $\Longleftarrow$
7941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7944 \begin_layout Plain Layout
7952 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7955 \begin_layout Plain Layout
7956 \begin_inset Formula $\leftharpoonup$
7966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7969 \begin_layout Plain Layout
7977 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7980 \begin_layout Plain Layout
7981 \begin_inset Formula $\leftharpoondown$
7991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7994 \begin_layout Plain Layout
8002 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8005 \begin_layout Plain Layout
8006 \begin_inset Formula $\hookleftarrow$
8020 \begin_inset space \hfill{}
8024 \begin_inset Tabular
8025 <lyxtabular version="3" rows="8" columns="2">
8027 <column alignment="center" valignment="top" width="0pt">
8028 <column alignment="center" valignment="top" width="0pt">
8030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8033 \begin_layout Plain Layout
8039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8042 \begin_layout Plain Layout
8050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8053 \begin_layout Plain Layout
8061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8064 \begin_layout Plain Layout
8065 \begin_inset Formula $\to$
8075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8078 \begin_layout Plain Layout
8086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8089 \begin_layout Plain Layout
8090 \begin_inset Formula $\Rightarrow$
8100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8103 \begin_layout Plain Layout
8111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8114 \begin_layout Plain Layout
8115 \begin_inset Formula $\longrightarrow$
8125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8128 \begin_layout Plain Layout
8136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8139 \begin_layout Plain Layout
8140 \begin_inset Formula $\Longrightarrow$
8150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8153 \begin_layout Plain Layout
8161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8164 \begin_layout Plain Layout
8165 \begin_inset Formula $\rightharpoonup$
8175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8178 \begin_layout Plain Layout
8186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8189 \begin_layout Plain Layout
8190 \begin_inset Formula $\rightharpoondown$
8200 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8203 \begin_layout Plain Layout
8211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8214 \begin_layout Plain Layout
8215 \begin_inset Formula $\hookrightarrow$
8229 \begin_inset space \hfill{}
8235 \begin_layout Standard
8236 \begin_inset space \hfill{}
8240 \begin_inset Tabular
8241 <lyxtabular version="3" rows="6" columns="2">
8243 <column alignment="center" valignment="top" width="0pt">
8244 <column alignment="center" valignment="top" width="0pt">
8246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8249 \begin_layout Plain Layout
8255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8258 \begin_layout Plain Layout
8266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8269 \begin_layout Plain Layout
8277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8280 \begin_layout Plain Layout
8281 \begin_inset Formula $\leftrightarrow$
8291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8294 \begin_layout Plain Layout
8302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8305 \begin_layout Plain Layout
8306 \begin_inset Formula $\Leftrightarrow$
8316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8319 \begin_layout Plain Layout
8327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8330 \begin_layout Plain Layout
8331 \begin_inset Formula $\longleftrightarrow$
8341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8344 \begin_layout Plain Layout
8352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8355 \begin_layout Plain Layout
8356 \begin_inset Formula $\Longleftrightarrow$
8366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8369 \begin_layout Plain Layout
8377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8380 \begin_layout Plain Layout
8381 \begin_inset Formula $\rightleftharpoons$
8395 \begin_inset space \hspace{}
8400 \begin_inset space \hfill{}
8404 \begin_inset Tabular
8405 <lyxtabular version="3" rows="5" columns="2">
8407 <column alignment="center" valignment="top" width="0pt">
8408 <column alignment="center" valignment="top" width="0pt">
8410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8413 \begin_layout Plain Layout
8419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8422 \begin_layout Plain Layout
8430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8433 \begin_layout Plain Layout
8441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8444 \begin_layout Plain Layout
8445 \begin_inset Formula $\mapsto$
8455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8458 \begin_layout Plain Layout
8466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8469 \begin_layout Plain Layout
8470 \begin_inset Formula $\longmapsto$
8480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8483 \begin_layout Plain Layout
8491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8494 \begin_layout Plain Layout
8495 \begin_inset Formula $\leadsto$
8505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8508 \begin_layout Plain Layout
8516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8519 \begin_layout Plain Layout
8520 \begin_inset Formula $\dasharrow$
8534 \begin_inset space \hfill{}
8540 \begin_layout Standard
8541 \begin_inset VSpace medskip
8544 Arrows used as accent like e.
8545 \begin_inset space \thinspace{}
8549 \begin_inset space ~
8552 vector arrows are listed in
8553 \begin_inset CommandInset ref
8555 reference "sec:Accents"
8562 \begin_layout Standard
8563 \begin_inset VSpace bigskip
8566 Furthermore there are the labeled arrows
8570 \begin_layout Plain Layout
8586 \begin_layout Plain Layout
8604 \begin_layout Plain Layout
8611 \begin_layout Plain Layout
8626 When inserting one of these commands in a formula, an arrow with two blue
8627 boxes appear where the label can be inserted.
8628 The length of the arrow adapts to the label width.
8631 \begin_layout Standard
8633 \begin_inset Tabular
8634 <lyxtabular version="3" rows="3" columns="2">
8636 <column alignment="center" valignment="top" width="0pt">
8637 <column alignment="center" valignment="top" width="0pt">
8639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8642 \begin_layout Plain Layout
8648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8651 \begin_layout Plain Layout
8653 \begin_inset Note Note
8656 \begin_layout Plain Layout
8663 is only used as spacer.
8675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8678 \begin_layout Plain Layout
8685 \begin_layout Plain Layout
8695 \begin_inset Formula $\downarrow$
8699 \begin_inset Formula $\to$
8707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8710 \begin_layout Plain Layout
8711 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8724 \begin_layout Plain Layout
8731 \begin_layout Plain Layout
8741 \begin_inset Formula $\downarrow$
8745 \begin_inset Formula $\to$
8753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8756 \begin_layout Plain Layout
8757 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8773 \begin_layout Subsection
8774 Vertical and diagonal Arrows
8778 \begin_layout Plain Layout
8788 \begin_layout Plain Layout
8797 \begin_layout Standard
8798 \begin_inset space \hfill{}
8802 \begin_inset Tabular
8803 <lyxtabular version="3" rows="7" columns="2">
8805 <column alignment="center" valignment="top" width="0pt">
8806 <column alignment="center" valignment="top" width="0pt">
8808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8811 \begin_layout Plain Layout
8817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8820 \begin_layout Plain Layout
8828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8831 \begin_layout Plain Layout
8839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8842 \begin_layout Plain Layout
8843 \begin_inset Formula $\uparrow$
8853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8856 \begin_layout Plain Layout
8864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8867 \begin_layout Plain Layout
8868 \begin_inset Formula $\Uparrow$
8878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8881 \begin_layout Plain Layout
8889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8892 \begin_layout Plain Layout
8893 \begin_inset Formula $\updownarrow$
8903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8906 \begin_layout Plain Layout
8914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8917 \begin_layout Plain Layout
8918 \begin_inset Formula $\Updownarrow$
8928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8931 \begin_layout Plain Layout
8939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8942 \begin_layout Plain Layout
8943 \begin_inset Formula $\Downarrow$
8953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8956 \begin_layout Plain Layout
8964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8967 \begin_layout Plain Layout
8968 \begin_inset Formula $\downarrow$
8982 \begin_inset space \hfill{}
8986 \begin_inset Tabular
8987 <lyxtabular version="3" rows="5" columns="2">
8989 <column alignment="center" valignment="top" width="0pt">
8990 <column alignment="center" valignment="top" width="0pt">
8992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8995 \begin_layout Plain Layout
9001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9004 \begin_layout Plain Layout
9012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9015 \begin_layout Plain Layout
9023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9026 \begin_layout Plain Layout
9027 \begin_inset Formula $\nearrow$
9037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9040 \begin_layout Plain Layout
9048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9051 \begin_layout Plain Layout
9052 \begin_inset Formula $\searrow$
9062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9065 \begin_layout Plain Layout
9073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9076 \begin_layout Plain Layout
9077 \begin_inset Formula $\swarrow$
9087 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9090 \begin_layout Plain Layout
9098 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9101 \begin_layout Plain Layout
9102 \begin_inset Formula $\nwarrow$
9116 \begin_inset space \hfill{}
9122 \begin_layout Standard
9123 \begin_inset VSpace medskip
9126 Vertical arrows can be used also as delimiter together with the commands
9128 \begin_inset CommandInset ref
9130 reference "sub:Manual-Bracket-Size"
9135 \begin_inset CommandInset ref
9137 reference "sub:Automatic-Bracket-Size"
9144 \begin_layout Standard
9145 \begin_inset Newpage newpage
9151 \begin_layout Section
9153 \begin_inset CommandInset label
9163 \begin_layout Plain Layout
9172 \begin_layout Standard
9173 Accents can be inserted via the math toolbar button
9174 \begin_inset Graphics
9175 filename ../images/math/hat.png
9180 or the commands listed in the following subsections.
9183 \begin_layout Subsection
9184 Accents for one Character
9188 \begin_layout Plain Layout
9201 \begin_layout Plain Layout
9203 \begin_inset CommandInset ref
9205 reference "sub:Accents-in-Text"
9218 \begin_layout Plain Layout
9226 \begin_inset Note Note
9229 \begin_layout Plain Layout
9232 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9235 \begin_layout Plain Layout
9238 texorpdfstring is in section
9239 \begin_inset CommandInset ref
9241 reference "sub:Formulas-in-Section"
9251 \begin_inset CommandInset label
9253 name "sub:Accents-for-one"
9261 \begin_layout Plain Layout
9262 Accents ! for one character
9270 \begin_layout Standard
9271 \begin_inset space \hfill{}
9275 \begin_inset Tabular
9276 <lyxtabular version="3" rows="8" columns="2">
9278 <column alignment="center" valignment="top" width="0pt">
9279 <column alignment="center" valignment="top" width="0pt">
9281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9284 \begin_layout Plain Layout
9290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9293 \begin_layout Plain Layout
9295 \begin_inset Note Note
9298 \begin_layout Plain Layout
9305 is only used as spacer.
9317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9320 \begin_layout Plain Layout
9327 \begin_layout Plain Layout
9341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9344 \begin_layout Plain Layout
9345 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9355 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9358 \begin_layout Plain Layout
9365 \begin_layout Plain Layout
9379 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9382 \begin_layout Plain Layout
9383 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9393 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9396 \begin_layout Plain Layout
9403 \begin_layout Plain Layout
9417 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9420 \begin_layout Plain Layout
9421 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9434 \begin_layout Plain Layout
9442 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9445 \begin_layout Plain Layout
9446 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9456 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9459 \begin_layout Plain Layout
9466 \begin_layout Plain Layout
9479 \begin_layout Plain Layout
9490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9493 \begin_layout Plain Layout
9494 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9507 \begin_layout Plain Layout
9514 \begin_layout Plain Layout
9528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9531 \begin_layout Plain Layout
9532 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9545 \begin_layout Plain Layout
9552 \begin_layout Plain Layout
9566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9569 \begin_layout Plain Layout
9570 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9584 \begin_inset space \hfill{}
9588 \begin_inset Tabular
9589 <lyxtabular version="3" rows="7" columns="2">
9591 <column alignment="center" valignment="top" width="0pt">
9592 <column alignment="center" valignment="top" width="0pt">
9594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9597 \begin_layout Plain Layout
9603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9606 \begin_layout Plain Layout
9614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9617 \begin_layout Plain Layout
9624 \begin_layout Plain Layout
9638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9641 \begin_layout Plain Layout
9642 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9655 \begin_layout Plain Layout
9662 \begin_layout Plain Layout
9676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9679 \begin_layout Plain Layout
9680 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9690 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9693 \begin_layout Plain Layout
9700 \begin_layout Plain Layout
9714 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9717 \begin_layout Plain Layout
9718 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9731 \begin_layout Plain Layout
9738 \begin_layout Plain Layout
9752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9755 \begin_layout Plain Layout
9756 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9769 \begin_layout Plain Layout
9776 \begin_layout Plain Layout
9790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9793 \begin_layout Plain Layout
9794 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9807 \begin_layout Plain Layout
9814 \begin_layout Plain Layout
9828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9831 \begin_layout Plain Layout
9832 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9846 \begin_inset space \hfill{}
9852 \begin_layout Standard
9853 \begin_inset VSpace bigskip
9860 \begin_layout Plain Layout
9866 in formulas, a quotation mark is inserted before the vowel.
9867 These two characters are then treated by LaTeX as
9871 character when the formula part with the umlaut is marked as German.
9879 \begin_inset Quotes eld
9883 \begin_inset Quotes erd
9886 umlauts are created as demonstrated in the following example:
9889 \begin_layout Standard
9890 \begin_inset VSpace -2mm
9896 \begin_layout Standard
9898 \begin_inset Tabular
9899 <lyxtabular version="3" rows="3" columns="2">
9901 <column alignment="center" valignment="top" width="0">
9902 <column alignment="center" valignment="top" width="0">
9904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9907 \begin_layout Plain Layout
9913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9916 \begin_layout Plain Layout
9918 \begin_inset Note Note
9921 \begin_layout Plain Layout
9928 is only used as spacer.
9940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9943 \begin_layout Plain Layout
9946 \begin_inset Quotes grd
9954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9957 \begin_layout Plain Layout
9960 \begin_inset Formula $"i$
9970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9973 \begin_layout Plain Layout
9980 \begin_layout Plain Layout
9994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9997 \begin_layout Plain Layout
9998 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10014 \begin_layout Standard
10015 Another advantage to
10021 is that umlauts can directly be converted to mathematical text because
10022 the accent commands above are
10028 in mathematical text
10031 To convert an accented character to mathematical text, only the character
10032 under the accent may be converted.
10033 This applies also for all other conversions, e.
10034 \begin_inset space \thinspace{}
10038 \begin_inset space ~
10044 \begin_layout Standard
10045 In mathematical text, umlauts and other accented characters can directly
10049 \begin_layout Subsection
10050 Accents for Operators
10054 \begin_layout Plain Layout
10055 Accents ! for operators
10063 \begin_layout Standard
10074 \begin_layout Plain Layout
10092 \begin_layout Plain Layout
10100 characters can be placed above or below an operator, respectively, to accent
10112 \begin_layout Plain Layout
10120 characters can be set before and behind an operator.
10121 The command scheme is:
10124 \begin_layout Standard
10140 \begin_layout Standard
10147 must always be before the operator that should be accented.
10148 You can accent with several characters and even with other operators and
10156 for example only characters behind an operator, write nothing between the
10157 first braces but don't omit the braces.
10160 \begin_layout Standard
10161 For example the command
10166 \begin_inset Formula $\to$
10176 \begin_inset Formula $\to$
10185 \begin_layout Plain Layout
10201 \begin_inset Formula \[
10202 \sideset{}{'}\sum_{k=1}^{n}\]
10209 \begin_layout Standard
10218 \begin_layout Plain Layout
10233 \begin_layout Plain Layout
10245 \begin_inset Formula $\uparrow$
10253 \begin_inset Formula \[
10254 \overset{a}{\maltese}\]
10258 As seen in the last example, with
10270 also symbols and characters can be accented; with
10276 this is not possible.
10279 \begin_layout Subsection
10280 Accents for several Characters
10281 \begin_inset CommandInset label
10283 name "sub:Accents-for-several"
10291 \begin_layout Plain Layout
10292 Accents ! for several characters
10300 \begin_layout Standard
10301 \begin_inset space \hfill{}
10305 \begin_inset Tabular
10306 <lyxtabular version="3" rows="5" columns="2">
10308 <column alignment="center" valignment="top" width="0pt">
10309 <column alignment="center" valignment="top" width="0pt">
10311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10314 \begin_layout Plain Layout
10320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10323 \begin_layout Plain Layout
10325 \begin_inset Note Note
10328 \begin_layout Plain Layout
10335 is only used as spacer.
10347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10350 \begin_layout Plain Layout
10357 \begin_layout Plain Layout
10371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10374 \begin_layout Plain Layout
10375 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10385 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10388 \begin_layout Plain Layout
10395 \begin_layout Plain Layout
10409 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10412 \begin_layout Plain Layout
10413 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10423 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10426 \begin_layout Plain Layout
10433 \begin_layout Plain Layout
10447 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10450 \begin_layout Plain Layout
10451 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10464 \begin_layout Plain Layout
10467 underleftrightarrow
10471 \begin_layout Plain Layout
10485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10488 \begin_layout Plain Layout
10489 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10503 \begin_inset space \hfill{}
10507 \begin_inset Tabular
10508 <lyxtabular version="3" rows="5" columns="2">
10510 <column alignment="center" valignment="top" width="0pt">
10511 <column alignment="center" valignment="top" width="0pt">
10513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10516 \begin_layout Plain Layout
10522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10525 \begin_layout Plain Layout
10533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10536 \begin_layout Plain Layout
10543 \begin_layout Plain Layout
10557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10560 \begin_layout Plain Layout
10561 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10571 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10574 \begin_layout Plain Layout
10581 \begin_layout Plain Layout
10595 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10598 \begin_layout Plain Layout
10599 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10609 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10612 \begin_layout Plain Layout
10619 \begin_layout Plain Layout
10633 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10636 \begin_layout Plain Layout
10637 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10647 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10650 \begin_layout Plain Layout
10657 \begin_layout Plain Layout
10671 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10674 \begin_layout Plain Layout
10675 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10689 \begin_inset space \hfill{}
10695 \begin_layout Standard
10696 \begin_inset VSpace medskip
10699 With these commands as many characters as you like can be accented.
10712 will only be set in the output with a length of three characters, as shown
10713 in the following example:
10714 \begin_inset Formula \[
10715 \widetilde{A+B=C-D}\]
10722 \begin_layout Standard
10733 \begin_layout Plain Layout
10751 \begin_layout Plain Layout
10759 described in the previous subsection it is also possible to accent several
10769 \begin_layout Plain Layout
10779 \begin_inset Formula $\downarrow$
10785 \begin_inset Formula \[
10786 \underset{***}{A=B}\]
10793 \begin_layout Section
10795 \begin_inset CommandInset label
10805 \begin_layout Plain Layout
10814 \begin_layout Subsection
10816 \begin_inset CommandInset label
10818 name "sub:Predefined-Space"
10826 \begin_layout Plain Layout
10827 Space ! horizontal ! predefined
10835 \begin_layout Standard
10836 Sometimes it is necessary to insert horizontal space to a formula.
10837 This is done by inserting a protected space (shortcut
10843 \begin_inset Quotes eld
10853 \begin_layout Plain Layout
10866 \begin_inset Quotes erd
10869 appears and by pressing
10873 several times one can select one of eight different space sizes.
10874 The spaces can also be inserted using the math toolbar button
10875 \begin_inset Graphics
10876 filename ../images/math/space.png
10881 or special commands.
10882 Independent from the inserted command, one can select the size again by
10890 \begin_layout Standard
10893 \begin_inset VSpace -5mm
10897 \begin_inset Tabular
10898 <lyxtabular version="3" rows="3" columns="7">
10900 <column alignment="center" valignment="middle" width="6.8cm">
10901 <column alignment="center" valignment="top" width="0">
10902 <column alignment="center" valignment="top" width="0">
10903 <column alignment="center" valignment="top" width="0">
10904 <column alignment="center" valignment="top" width="0">
10905 <column alignment="center" valignment="top" width="0">
10906 <column alignment="center" valignment="top" width="0">
10908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10911 \begin_layout Plain Layout
10917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10920 \begin_layout Plain Layout
10928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10931 \begin_layout Plain Layout
10939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10942 \begin_layout Plain Layout
10950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10953 \begin_layout Plain Layout
10961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10964 \begin_layout Plain Layout
10972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10975 \begin_layout Plain Layout
10985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10988 \begin_layout Plain Layout
10993 keystrokes after inserting the protected space
10998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11001 \begin_layout Plain Layout
11007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11010 \begin_layout Plain Layout
11016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11019 \begin_layout Plain Layout
11025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11028 \begin_layout Plain Layout
11034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11037 \begin_layout Plain Layout
11043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11046 \begin_layout Plain Layout
11054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11057 \begin_layout Plain Layout
11063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11066 \begin_layout Plain Layout
11067 \begin_inset Formula $A\, B$
11075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11078 \begin_layout Plain Layout
11079 \begin_inset Formula $A\: B$
11087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11090 \begin_layout Plain Layout
11091 \begin_inset Formula $A\; B$
11099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11102 \begin_layout Plain Layout
11103 \begin_inset Formula $A\quad B$
11111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11114 \begin_layout Plain Layout
11115 \begin_inset Formula $A\qquad B$
11123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11126 \begin_layout Plain Layout
11127 \begin_inset Formula $A\! B$
11143 \begin_layout Standard
11144 The last size seem to produce no space.
11145 It is displayed red in LyX contrary to the other sizes, because it is a
11147 There are two more negative spaces:
11150 \begin_layout Standard
11152 \begin_inset Tabular
11153 <lyxtabular version="3" rows="3" columns="3">
11155 <column alignment="center" valignment="middle" width="6.8cm">
11156 <column alignment="center" valignment="top" width="0pt">
11157 <column alignment="center" valignment="top" width="0pt">
11159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11162 \begin_layout Plain Layout
11168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11171 \begin_layout Plain Layout
11179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11182 \begin_layout Plain Layout
11192 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11195 \begin_layout Plain Layout
11200 keystrokes after inserting the protected space
11205 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11208 \begin_layout Plain Layout
11214 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11217 \begin_layout Plain Layout
11225 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11228 \begin_layout Plain Layout
11234 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11237 \begin_layout Plain Layout
11238 \begin_inset Formula $A\negmedspace B$
11246 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11249 \begin_layout Plain Layout
11250 \begin_inset Formula $A\negthickspace B$
11266 \begin_layout Standard
11267 Negative spaces can lead to characters overlapping each other.
11268 Thus they can be used to enforce ligatures, what is e.
11269 \begin_inset space \thinspace{}
11273 \begin_inset space ~
11276 useful for summation operators:
11279 \begin_layout Standard
11281 \begin_inset Tabular
11282 <lyxtabular version="3" rows="3" columns="2">
11284 <column alignment="center" valignment="top" width="0">
11285 <column alignment="center" valignment="top" width="0">
11287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11290 \begin_layout Plain Layout
11296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11299 \begin_layout Plain Layout
11301 \begin_inset Note Note
11304 \begin_layout Plain Layout
11311 is only used as spacer.
11323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11326 \begin_layout Plain Layout
11335 \begin_layout Plain Layout
11349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11352 \begin_layout Plain Layout
11353 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11366 \begin_layout Plain Layout
11377 \begin_layout Plain Layout
11391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11394 \begin_layout Plain Layout
11395 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11411 \begin_layout Standard
11412 Relations like for example equal signs, are always surrounded by space.
11413 To suppress this, the equal sign is placed into a TeX-brace.
11414 The following example demonstrates this:
11417 \begin_layout Standard
11419 \begin_inset Tabular
11420 <lyxtabular version="3" rows="2" columns="2">
11422 <column alignment="center" valignment="top" width="0pt">
11423 <column alignment="center" valignment="top" width="0pt">
11425 <cell alignment="center" valignment="top" usebox="none">
11428 \begin_layout Plain Layout
11434 <cell alignment="center" valignment="top" usebox="none">
11437 \begin_layout Plain Layout
11438 \begin_inset Formula $A=B$
11448 <cell alignment="center" valignment="top" usebox="none">
11451 \begin_layout Plain Layout
11452 \begin_inset Note Note
11455 \begin_layout Plain Layout
11462 is only used as spacer.
11468 \begin_inset Formula $\raisebox{5mm}{}$
11471 equation without space
11476 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11479 \begin_layout Plain Layout
11480 \begin_inset Formula $A{=}B$
11496 \begin_layout Standard
11498 The command for the last formula is:
11503 \begin_inset Formula $\to$
11509 \begin_layout Standard
11510 \begin_inset VSpace bigskip
11513 Spaces are needed for physical units, because the space between the value
11514 and the unit is the smallest one and not a normal space.
11515 For units in text, the smallest space is inserted via the menu
11517 Insert\SpecialChar \menuseparator
11518 Formatting\SpecialChar \menuseparator
11520 \begin_inset space ~
11532 \begin_layout Standard
11533 An example to visualize the difference:
11536 \begin_layout Standard
11537 \begin_inset Tabular
11538 <lyxtabular version="3" rows="2" columns="2">
11540 <column alignment="left" valignment="top" width="0">
11541 <column alignment="left" valignment="top" width="0">
11543 <cell alignment="center" valignment="top" usebox="none">
11546 \begin_layout Plain Layout
11548 \begin_inset Formula $\cdot$
11556 <cell alignment="center" valignment="top" usebox="none">
11559 \begin_layout Plain Layout
11560 space between value and unit
11567 <cell alignment="center" valignment="top" usebox="none">
11570 \begin_layout Plain Layout
11572 \begin_inset space \thinspace{}
11576 \begin_inset Formula $\cdot$
11584 <cell alignment="center" valignment="top" usebox="none">
11587 \begin_layout Plain Layout
11588 smallest space between value and unit
11601 \begin_layout Subsection
11606 \begin_layout Plain Layout
11619 \begin_layout Plain Layout
11620 for vertical space in formulas see
11621 \begin_inset CommandInset ref
11623 reference "sub:Line-Separation"
11636 \begin_layout Plain Layout
11644 \begin_inset Note Note
11647 \begin_layout Plain Layout
11650 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11653 \begin_layout Plain Layout
11656 texorpdfstring is in section
11657 \begin_inset CommandInset ref
11659 reference "sub:Formulas-in-Section"
11669 \begin_inset CommandInset label
11671 name "sub:Variable-Space"
11679 \begin_layout Plain Layout
11680 Space ! horizontal ! variable
11688 \begin_layout Standard
11689 Space with a defined length can be inserted in LyX with the command
11690 \begin_inset Newline newline
11703 \begin_layout Plain Layout
11712 For the length all units listed in
11713 \begin_inset CommandInset ref
11715 reference "tab:Used-units"
11719 are allowed, except of the unit
11720 \begin_inset Quotes eld
11724 \begin_inset Quotes erd
11728 The length may also be negative.
11729 To insert so many space that the formula uses all available space, the
11740 \begin_layout Plain Layout
11751 \begin_layout Standard
11752 \begin_inset VSpace -1mm
11758 \begin_layout Standard
11760 \begin_inset Tabular
11761 <lyxtabular version="3" rows="4" columns="2">
11763 <column alignment="center" valignment="top" width="0">
11764 <column alignment="center" valignment="top" width="0">
11766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11769 \begin_layout Plain Layout
11775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11778 \begin_layout Plain Layout
11786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11789 \begin_layout Plain Layout
11793 \begin_inset Formula $\to$
11803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11806 \begin_layout Plain Layout
11807 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11820 \begin_layout Plain Layout
11824 \begin_inset Formula $\to$
11834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11837 \begin_layout Plain Layout
11838 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11851 \begin_layout Plain Layout
11858 \begin_layout Plain Layout
11872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11875 \begin_layout Plain Layout
11876 \begin_inset Formula $A=A\hfill B=B$
11892 \begin_layout Standard
11893 In the last example the available space is given by the longest column entry
11895 In an inline formula the space depends on the length of the line in which
11903 Thus, when the line uses the full width, no space will be created.
11910 only has an effect on displayed formulas when the formula style
11915 (Formula styles are explained in
11916 \begin_inset CommandInset ref
11918 reference "sec:Formula-Styles"
11925 \begin_layout Standard
11932 , there are the commands
11944 that fill the space with a pattern, see
11945 \begin_inset CommandInset ref
11947 reference "sub:Ellipses"
11954 \begin_layout Standard
11955 For text, variable space can be inserted via the menu
11957 Insert\SpecialChar \menuseparator
11958 Formatting\SpecialChar \menuseparator
11960 \begin_inset space ~
11965 , what is not possible in formulas:
11968 \begin_layout Standard
11969 This is a line with
11970 \begin_inset space \hspace{}
11975 \begin_inset space \thinspace{}
11981 \begin_layout Standard
11982 This is a line with
11983 \begin_inset space \hfill{}
11989 \begin_layout Subsection
11990 Space besides inline Formulas
11994 \begin_layout Plain Layout
11995 Space ! besides inline formulas
12003 \begin_layout Standard
12004 The space that surrounds inline formulas can be adjusted with the length
12013 \begin_layout Plain Layout
12024 The value of a length is set with the command
12032 \begin_layout Plain Layout
12042 that has the following scheme:
12045 \begin_layout Standard
12050 setlength{length name}{value}
12053 \begin_layout Standard
12061 \begin_inset space \thinspace{}
12067 \begin_layout Standard
12077 \begin_layout Standard
12078 is inserted in TeX-mode.
12080 \begin_inset space \thinspace{}
12083 mm space will now be set around all inline formulas:
12087 \begin_layout Plain Layout
12101 \begin_layout Standard
12102 This is a line with an inline formula
12103 \begin_inset Formula $A=B$
12107 \begin_inset space \thinspace{}
12110 mm surrounding space.
12114 \begin_layout Plain Layout
12128 \begin_layout Standard
12129 To return to the predefined value,
12135 is set to the value 0
12136 \begin_inset space \thinspace{}
12142 \begin_layout Section
12147 \begin_layout Plain Layout
12157 \begin_layout Plain Layout
12162 \begin_layout Plain Layout
12173 \begin_layout Plain Layout
12188 \begin_layout Standard
12189 Boxes for text are described in chapter
12196 \begin_inset space ~
12204 \begin_layout Subsection
12206 \begin_inset CommandInset label
12208 name "sub:Boxes-with-Frame"
12216 \begin_layout Plain Layout
12225 \begin_layout Standard
12226 It is possible to frame formulas or parts of it with the commands
12236 \begin_layout Plain Layout
12254 \begin_layout Plain Layout
12265 \begin_layout Standard
12266 When one of these commands is inserted to a formula, a blue box appears
12267 within a frame to enter formula parts.
12274 an additional formula has to be created by
12282 \begin_layout Plain Layout
12283 Due to a bug in LyX it is not possible to create a new formula with
12288 \begin_inset CommandInset href
12290 name "LyX-bug #1435"
12291 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12300 , because the box content will otherwise be treated as mathematical text.
12307 is used, a new formula is automatically created inside the frame.
12310 \begin_layout Standard
12317 is not suitable to frame displayed formulas, because the formula will always
12318 be set in the size of the text.
12325 is in contrary not suitable to frame inline formulas, because the formula
12326 will always be set in the size of a displayed formula.
12329 \begin_layout Standard
12336 there is the command
12346 \begin_layout Plain Layout
12354 where additionally the frame width and the alignment can be specified.
12361 is used in the following scheme:
12364 \begin_layout Standard
12369 framebox[frame width][position]{box content}
12372 \begin_layout Standard
12373 The position can either be
12390 right aligns the formula in the box.
12391 When no position is given, the formula will be centered.
12392 \begin_inset Newline newline
12395 Is no width given, also no position can be given.
12396 In this case the frame width is adjusted to the box content like for
12405 \begin_layout Standard
12412 is inserted, a box appears containing three blue boxes.
12413 The first two boxes are surrounded by brackets and denote the two optional
12415 The third box is for formula parts like for
12424 \begin_layout Standard
12426 \begin_inset Note Note
12429 \begin_layout Plain Layout
12430 The table has been set into a minipage to make the footnote appearing.
12431 Otherwise the footnote text would not be displayed.
12437 \begin_inset Box Frameless
12446 height_special "totalheight"
12449 \begin_layout Plain Layout
12451 \begin_inset Tabular
12452 <lyxtabular version="3" rows="5" columns="2">
12454 <column alignment="center" valignment="top" width="0">
12455 <column alignment="center" valignment="top" width="0">
12457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12460 \begin_layout Plain Layout
12465 \begin_layout Plain Layout
12466 Due to a bug in LyX it is not possible to create a new formula with
12471 \begin_inset CommandInset href
12473 name "LyX-bug #1435"
12474 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12491 \begin_layout Plain Layout
12493 \begin_inset Note Note
12496 \begin_layout Plain Layout
12503 is only used as spacer.
12515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12518 \begin_layout Plain Layout
12525 \begin_layout Plain Layout
12544 \begin_layout Plain Layout
12558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12561 \begin_layout Plain Layout
12562 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
12573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12576 \begin_layout Plain Layout
12583 \begin_layout Plain Layout
12598 \begin_layout Plain Layout
12612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12615 \begin_layout Plain Layout
12616 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12629 \begin_layout Plain Layout
12636 \begin_layout Plain Layout
12650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12653 \begin_layout Plain Layout
12654 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12667 \begin_layout Plain Layout
12674 \begin_layout Plain Layout
12684 \begin_inset Formula $\to$
12688 \begin_inset Formula $\to$
12701 \begin_layout Plain Layout
12711 \begin_inset Formula $\downarrow$
12719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12722 \begin_layout Plain Layout
12723 \begin_inset Formula $\raisebox{6mm}{}$
12727 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12731 \begin_inset Formula $\raisebox{-4mm}{}$
12752 \begin_layout Standard
12753 The frame thickness can also be adjusted.
12754 To do this the following commands have to be inserted in TeX-mode before
12758 \begin_layout Standard
12768 \begin_inset Quotes eld
12772 \begin_inset Quotes erd
12786 \begin_inset Quotes eld
12790 \begin_inset Quotes erd
12796 \begin_layout Standard
12797 \begin_inset Quotes eld
12801 \begin_inset Quotes erd
12804 specifies the minimal distance between the frame and the first character
12806 An example for this is the following framed formula:
12810 \begin_layout Plain Layout
12822 \begin_inset Formula \[
12827 Before this formula the commands
12830 \begin_layout Standard
12852 \begin_layout Standard
12853 were inserted in TeX-mode.
12854 The given values are used for all following boxes.
12857 \begin_layout Standard
12858 To return to the standard frame size, the command
12861 \begin_layout Standard
12886 \begin_layout Plain Layout
12900 \begin_layout Standard
12901 is inserted in TeX-mode before the next formula.
12904 \begin_layout Subsection
12905 Boxes without Frame
12906 \begin_inset CommandInset label
12908 name "sub:Boxes-without-Frame"
12916 \begin_layout Plain Layout
12917 Boxes ! without frame
12925 \begin_layout Standard
12926 For boxes without a frame there are the following box commands:
12936 \begin_layout Plain Layout
12954 \begin_layout Plain Layout
12972 \begin_layout Plain Layout
12983 \begin_layout Standard
12990 a box can be super- or subscripted.
12991 But in contrary to normal super- and subscripting, the characters in the
12992 box keep their font size.
12999 is used in the following scheme:
13002 \begin_layout Standard
13007 raisebox{height}{box content}
13010 \begin_layout Standard
13011 When the box should contain a formula, an extra formula is needed like for
13021 \begin_layout Standard
13023 \begin_inset Tabular
13024 <lyxtabular version="3" rows="4" columns="2">
13026 <column alignment="center" valignment="top" width="0">
13027 <column alignment="center" valignment="top" width="0">
13029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13032 \begin_layout Plain Layout
13038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13041 \begin_layout Plain Layout
13049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13052 \begin_layout Plain Layout
13056 \begin_inset Formula $\to$
13062 \begin_inset Formula $\to$
13070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13073 \begin_layout Plain Layout
13074 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13087 \begin_layout Plain Layout
13091 \begin_inset Formula $\to$
13097 \begin_inset Formula $\to$
13105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13108 \begin_layout Plain Layout
13109 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13122 \begin_layout Plain Layout
13126 \begin_inset Formula $\to$
13141 \begin_layout Plain Layout
13155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13158 \begin_layout Plain Layout
13162 \begin_layout Plain Layout
13186 \begin_layout Standard
13187 The last formula can currently only be created using TeX-mode because LyX
13188 inserts a box instead of the needed extra formula.
13192 \begin_layout Plain Layout
13194 \begin_inset CommandInset href
13196 name "LyX-bug #1435"
13197 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13209 \begin_layout Standard
13234 , with the difference that there is no frame.
13237 \begin_layout Subsection
13239 \begin_inset CommandInset label
13241 name "sub:Colored-Boxes"
13249 \begin_layout Plain Layout
13258 \begin_layout Standard
13259 To be able to use all commands explained in this section, the LaTeX-package
13268 \begin_layout Plain Layout
13273 is part of every LaTeX standard installation.
13282 \begin_layout Plain Layout
13288 has to be loaded in the LaTeX-preamble with the line
13292 \begin_layout Plain Layout
13293 When text is colored somewhere in the document with a predefined color,
13294 LyX loads the LaTeX-package
13299 Thus it is possible that the package is loaded twice, but this doesn't
13306 \begin_inset Note Note
13309 \begin_layout Plain Layout
13310 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13319 \begin_layout Standard
13327 \begin_layout Standard
13328 \begin_inset VSpace medskip
13331 To color boxes, the command
13341 \begin_layout Plain Layout
13349 is used in the following scheme:
13352 \begin_layout Standard
13357 colorbox{color}{box content}
13360 \begin_layout Standard
13361 The box content can also be a box and a
13367 can also be part of another box (see the 2nd and 3rd example).
13368 When the box should contain a formula, an extra formula has to be created,
13379 \begin_layout Plain Layout
13380 This also applies for the command
13388 \begin_inset CommandInset href
13390 name "LyX-bug #1435"
13391 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13403 \begin_layout Standard
13404 One of the following predefined colors can be chosen:
13407 \begin_layout Standard
13441 \begin_layout Standard
13443 \begin_inset Tabular
13444 <lyxtabular version="3" rows="4" columns="2">
13446 <column alignment="center" valignment="top" width="0">
13447 <column alignment="center" valignment="top" width="0">
13449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13452 \begin_layout Plain Layout
13458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13461 \begin_layout Plain Layout
13463 \begin_inset Note Note
13466 \begin_layout Plain Layout
13473 is only used as spacer.
13485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13488 \begin_layout Plain Layout
13492 \begin_inset Formula $\to$
13502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13505 \begin_layout Plain Layout
13506 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13519 \begin_layout Plain Layout
13523 \begin_inset Formula $\to$
13534 \begin_layout Plain Layout
13548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13551 \begin_layout Plain Layout
13552 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13565 \begin_layout Plain Layout
13572 \begin_layout Plain Layout
13584 \begin_inset Formula $\to$
13594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13597 \begin_layout Plain Layout
13598 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13614 \begin_layout Standard
13621 only colors the box but not the characters in the box.
13622 To color all characters, the whole formula is highlighted and the wanted
13623 color is chosen in the
13626 \begin_inset space ~
13632 The dialog can be called with the toolbar button
13633 \begin_inset Graphics
13634 filename ../images/dialog-show_character.png
13641 Edit\SpecialChar \menuseparator
13643 \begin_inset space ~
13646 Style\SpecialChar \menuseparator
13650 The formula number has then the same color as the formula.
13651 When the formula number should get another color than the formula characters,
13652 the color must be changed within the formula.
13655 \begin_layout Standard
13659 \begin_layout Standard
13662 \begin_inset Formula \begin{equation}
13663 \int A=B\label{eq:red}\end{equation}
13670 \begin_inset Formula \begin{equation}
13671 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13678 \begin_layout Standard
13680 \begin_inset CommandInset ref
13686 is completely colored red.
13687 \begin_inset Newline newline
13691 \begin_inset CommandInset ref
13693 reference "eq:redgreen"
13697 was first completely colored green to set the color for the formula number.
13698 Subsequently the formula characters were colored red.
13701 \begin_layout Standard
13702 \begin_inset VSpace bigskip
13705 To color the frame different than the rest of the box, the command
13715 \begin_layout Plain Layout
13723 is used in the following scheme:
13726 \begin_layout Standard
13731 fcolorbox{frame color}{color}{box content}
13734 \begin_layout Standard
13741 is an extension of the command
13748 The frame width is set, like for
13771 \begin_layout Plain Layout
13783 \begin_inset Formula \[
13784 \fcolorbox{cyan}{magenta}{A=B}\]
13792 \begin_layout Plain Layout
13806 \begin_layout Standard
13807 This formula was created with the command
13808 \begin_inset Newline newline
13816 \begin_inset Formula $\to$
13822 \begin_inset Formula $\to$
13832 \begin_layout Standard
13833 \begin_inset VSpace bigskip
13836 To use other colors than the predefined ones, they have to be defined first.
13839 \begin_layout Standard
13840 One can for example define the color
13841 \begin_inset Quotes eld
13849 \begin_inset Quotes erd
13852 with the LaTeX-preamble line:
13855 \begin_layout Standard
13860 definecolor{darkgreen}{cmyk}{0.5,
13878 \begin_layout Plain Layout
13889 \begin_layout Standard
13894 is the color space that denotes the colors
13911 The four comma separated numbers are the portion factor for the corresponding
13912 colors of the color space.
13913 The factors can be in the range of 0
13914 \begin_inset space \thinspace{}
13918 \begin_inset space \thinspace{}
13926 also the color space
13930 can be used for definitions.
13947 , so that there are in this case three portion factors for the corresponding
13949 Furthermore there is the color space
13953 with one portion factor for the gray value.
13956 \begin_layout Standard
13957 As example a framed box with the new defined color
13961 where the characters have been colored
13966 \begin_inset Formula \begin{equation}
13967 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13974 \begin_layout Standard
13975 Self-defined colors can also be used for text with the help of the command
13986 \begin_layout Plain Layout
13995 \begin_layout Standard
13999 \begin_layout Plain Layout
14003 textcolor{darkgreen}{
14009 \begin_inset Quotes eld
14013 \begin_inset Quotes erd
14020 \begin_layout Plain Layout
14030 \begin_layout Standard
14041 \begin_layout Plain Layout
14049 is used in the scheme
14053 textcolor{color}{characters to color}
14058 \begin_layout Subsection
14060 \begin_inset CommandInset label
14062 name "sub:Paragraph-Boxes"
14070 \begin_layout Plain Layout
14071 Boxes ! as paragraph
14079 \begin_layout Standard
14080 A box that can contain several lines and paragraphs, a so called paragraph
14081 box (parbox), can be created with the menu
14083 Insert\SpecialChar \menuseparator
14086 or the toolbar button
14087 \begin_inset Graphics
14088 filename ../images/box-insert.png
14096 \begin_layout Standard
14097 The following example shows a framed parbox in a line:
14100 \begin_layout Standard
14101 \begin_inset VSpace medskip
14105 \begin_inset Box Boxed
14114 height_special "totalheight"
14117 \begin_layout Plain Layout
14118 This is a paragraph box.
14120 \begin_inset space \thinspace{}
14123 cm long and can also contain formulas:
14124 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14135 \begin_layout Standard
14136 \begin_inset VSpace medskip
14142 \begin_layout Standard
14143 Such a box is created by right-clicking on the gray box inset.
14144 A dialog pops up showing the box properties.
14158 \begin_inset space \thinspace{}
14163 Vertical Box Alignment
14168 \begin_layout Standard
14169 \begin_inset VSpace medskip
14172 In LaTeX a parbox is created with the command
14182 \begin_layout Plain Layout
14190 that has the following scheme:
14193 \begin_layout Standard
14198 parbox[position]{width}{box content}
14201 \begin_layout Standard
14215 for bottom means that the box is aligned within the surrounding text with
14221 for top this is done with the first line.
14222 When no position is given, the box will be vertically centered, see section
14230 \begin_inset space ~
14235 manual for examples.
14238 \begin_layout Standard
14239 \begin_inset VSpace bigskip
14242 To frame formulas completely, including the formula number, the formula
14243 must be set into a parbox.
14244 To do this, the command
14258 is inserted in TeX-mode before the formula.
14267 \begin_layout Plain Layout
14277 is hereby the line width set for the document.
14278 Because the frame is outside the parbox, 2
14279 \begin_inset space \thinspace{}
14282 times the frame separation and the frame thickness must be subtracted from
14284 As this is not automatically done by LyX due to a bug
14288 \begin_layout Plain Layout
14289 \begin_inset CommandInset href
14291 name "LyX-bug #4483"
14292 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14301 , TeX-mode has to be used.
14302 To be able to multiply and subtract in arguments, the LaTeX-package
14310 \begin_layout Plain Layout
14315 is part of every LaTeX standard installation.
14324 \begin_layout Plain Layout
14330 must be loaded in the LaTeX-preamble with the line
14333 \begin_layout Standard
14341 \begin_layout Standard
14342 Behind the formula both boxes are closed by entering
14347 Here is an example:
14351 \begin_layout Plain Layout
14365 \begin_layout Standard
14369 \begin_layout Plain Layout
14387 \begin_inset Formula \begin{equation}
14388 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14396 \begin_layout Plain Layout
14407 \begin_layout Plain Layout
14421 \begin_layout Standard
14422 \begin_inset VSpace medskip
14425 As a parbox is used as argument of
14431 , there is in this case no difference between
14446 \begin_layout Standard
14447 \begin_inset VSpace bigskip
14450 Paragraph boxes are very useful to comment formulas directly.
14457 is used in combination with the command
14471 \begin_inset CommandInset ref
14473 reference "sub:User-defined-Numbering"
14480 \begin_layout Standard
14481 An example of a formula commented with
14490 \begin_layout Standard
14494 \begin_layout Plain Layout
14507 This is a description.
14508 It is distinctly separated from the formula and multiline.
14512 \begin_layout Plain Layout
14524 \begin_layout Standard
14525 Such a formula must be inserted completely in TeX-mode because LyX does
14526 not yet support the command
14533 The formula is created with the following command sequence:
14536 \begin_layout Standard
14549 is inserted in TeX-mode.
14553 \begin_layout Plain Layout
14554 When the formula style
14566 can also be replaced by
14573 (formula styles see
14574 \begin_inset CommandInset ref
14576 reference "sec:Formula-Styles"
14585 Then the description follows as normal text, and finally
14591 is inserted in TeX-mode.
14604 hereby create a displayed formula.
14607 \begin_layout Standard
14614 can be seen in this example that was
14615 \begin_inset Quotes eld
14619 \begin_inset Quotes erd
14622 using the mathematical textmode:
14623 \begin_inset Formula \[
14624 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14631 \begin_layout Section
14636 \begin_layout Plain Layout
14645 \begin_layout Subsection
14647 \begin_inset CommandInset label
14649 name "sub:Big-Operators"
14657 \begin_layout Plain Layout
14667 \begin_layout Plain Layout
14677 \begin_layout Plain Layout
14686 \begin_layout Standard
14687 To be able to use all integral operators listed here, the option
14689 Use esint package automatically
14691 must be set in the document settings under
14694 \begin_inset space ~
14702 \begin_layout Standard
14703 \begin_inset space \hfill{}
14707 \begin_inset Tabular
14708 <lyxtabular version="3" rows="11" columns="2">
14710 <column alignment="center" valignment="top" width="0pt">
14711 <column alignment="center" valignment="top" width="0pt">
14713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14716 \begin_layout Plain Layout
14722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14725 \begin_layout Plain Layout
14733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14736 \begin_layout Plain Layout
14743 \begin_layout Plain Layout
14756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14759 \begin_layout Plain Layout
14760 \begin_inset Formula $\sum$
14770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14773 \begin_layout Plain Layout
14780 \begin_layout Plain Layout
14793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14796 \begin_layout Plain Layout
14797 \begin_inset Formula $\int$
14807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14810 \begin_layout Plain Layout
14818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14821 \begin_layout Plain Layout
14822 \begin_inset Formula $\intop$
14832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14835 \begin_layout Plain Layout
14843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14846 \begin_layout Plain Layout
14847 \begin_inset Formula $\oint$
14857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14860 \begin_layout Plain Layout
14868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14871 \begin_layout Plain Layout
14872 \begin_inset Formula $\ointop$
14882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14885 \begin_layout Plain Layout
14893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14896 \begin_layout Plain Layout
14897 \begin_inset Formula $\ointctrclockwise$
14907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14910 \begin_layout Plain Layout
14918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14921 \begin_layout Plain Layout
14922 \begin_inset Formula $\ointclockwise$
14932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14935 \begin_layout Plain Layout
14943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14946 \begin_layout Plain Layout
14947 \begin_inset Formula $\sqint$
14957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14960 \begin_layout Plain Layout
14968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14971 \begin_layout Plain Layout
14972 \begin_inset Formula $\bigcap$
14982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14985 \begin_layout Plain Layout
14993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14996 \begin_layout Plain Layout
14997 \begin_inset Formula $\bigcup$
15011 \begin_inset space \hfill{}
15015 \begin_inset Tabular
15016 <lyxtabular version="3" rows="10" columns="2">
15018 <column alignment="center" valignment="top" width="0pt">
15019 <column alignment="center" valignment="top" width="0pt">
15021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15024 \begin_layout Plain Layout
15030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15033 \begin_layout Plain Layout
15041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15044 \begin_layout Plain Layout
15051 \begin_layout Plain Layout
15064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15067 \begin_layout Plain Layout
15068 \begin_inset Formula $\prod$
15078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15081 \begin_layout Plain Layout
15089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15092 \begin_layout Plain Layout
15093 \begin_inset Formula $\coprod$
15103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15106 \begin_layout Plain Layout
15114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15117 \begin_layout Plain Layout
15118 \begin_inset Formula $\bigodot$
15128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15131 \begin_layout Plain Layout
15139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15142 \begin_layout Plain Layout
15143 \begin_inset Formula $\bigotimes$
15153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15156 \begin_layout Plain Layout
15164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15167 \begin_layout Plain Layout
15168 \begin_inset Formula $\bigoplus$
15178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15181 \begin_layout Plain Layout
15189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15192 \begin_layout Plain Layout
15193 \begin_inset Formula $\bigwedge$
15203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15206 \begin_layout Plain Layout
15214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15217 \begin_layout Plain Layout
15218 \begin_inset Formula $\bigvee$
15228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15231 \begin_layout Plain Layout
15239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15242 \begin_layout Plain Layout
15243 \begin_inset Formula $\bigsqcup$
15253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15256 \begin_layout Plain Layout
15264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15267 \begin_layout Plain Layout
15268 \begin_inset Formula $\biguplus$
15282 \begin_inset space \hfill{}
15288 \begin_layout Standard
15289 All big operators can also be inserted via the math toolbar button
15290 \begin_inset Graphics
15291 filename ../images/math/intop.png
15299 \begin_layout Standard
15300 The operators are called big because they are bigger than the sometimes
15301 equal looking binary operators.
15302 All big operators can have limits as described in the next subsection.
15305 \begin_layout Standard
15331 \begin_inset space ~
15334 in the style the operator limits are displayed, see
15335 \begin_inset CommandInset ref
15337 reference "sub:Operator-Limits"
15345 \begin_layout Subsubsection*
15346 Advices for Integrals
15349 \begin_layout Standard
15354 in an integral is an operator, that therefore has to be set upright.
15355 This is done by highlighting the
15359 and using the keyboard shortcut
15362 \begin_inset space ~
15371 \begin_layout Plain Layout
15377 \begin_inset CommandInset ref
15379 reference "sub:Font-Styles"
15389 Finally the smallest space is inserted before the
15393 , as this is usual for operators.
15397 \begin_layout Standard
15399 \begin_inset Formula $\int A(x)dx$
15403 \begin_inset Newline newline
15410 \begin_layout Plain Layout
15420 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15426 \begin_layout Standard
15427 For multiple integrals there are the following commands:
15428 \begin_inset VSpace medskip
15434 \begin_layout Standard
15435 \begin_inset space \hfill{}
15439 \begin_inset Tabular
15440 <lyxtabular version="3" rows="4" columns="2">
15442 <column alignment="center" valignment="top" width="0">
15443 <column alignment="center" valignment="top" width="0">
15445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15448 \begin_layout Plain Layout
15454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15457 \begin_layout Plain Layout
15459 \begin_inset Note Note
15462 \begin_layout Plain Layout
15469 is only used as spacer.
15481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15484 \begin_layout Plain Layout
15492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15495 \begin_layout Plain Layout
15496 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15509 \begin_layout Plain Layout
15517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15520 \begin_layout Plain Layout
15521 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15534 \begin_layout Plain Layout
15542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15545 \begin_layout Plain Layout
15546 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15560 \begin_inset space \hfill{}
15564 \begin_inset Tabular
15565 <lyxtabular version="3" rows="4" columns="2">
15567 <column alignment="center" valignment="top" width="0">
15568 <column alignment="center" valignment="top" width="0">
15570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15573 \begin_layout Plain Layout
15579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15582 \begin_layout Plain Layout
15590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15593 \begin_layout Plain Layout
15601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15604 \begin_layout Plain Layout
15605 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15618 \begin_layout Plain Layout
15626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15629 \begin_layout Plain Layout
15630 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15643 \begin_layout Plain Layout
15651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15654 \begin_layout Plain Layout
15655 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15669 \begin_inset space \hfill{}
15675 \begin_layout Subsection
15677 \begin_inset CommandInset label
15679 name "sub:Operator-Limits"
15687 \begin_layout Plain Layout
15696 \begin_layout Standard
15697 Limits are created by super- and subscripts:
15700 \begin_layout Standard
15702 \begin_inset Tabular
15703 <lyxtabular version="3" rows="2" columns="2">
15705 <column alignment="center" valignment="top" width="0pt">
15706 <column alignment="center" valignment="top" width="0pt">
15708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15711 \begin_layout Plain Layout
15717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15720 \begin_layout Plain Layout
15722 \begin_inset Note Note
15725 \begin_layout Plain Layout
15732 is only used as spacer.
15744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15747 \begin_layout Plain Layout
15756 \begin_layout Plain Layout
15766 \begin_inset Formula $\to$
15770 \begin_inset Formula $\to$
15778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15781 \begin_layout Plain Layout
15782 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15798 \begin_layout Standard
15799 Limits of inline formulas are set right beside the operator.
15800 Limits in displayed formulas are set above or below the operator, except
15801 of integral limits.
15804 \begin_layout Standard
15805 To force that the limits are set beside the operator, the cursor is set
15806 directly behind the operator and the limits type is changed with the menu
15809 Edit\SpecialChar \menuseparator
15810 Math\SpecialChar \menuseparator
15822 \begin_inset space ~
15831 \begin_layout Standard
15832 The default limits type is this:
15833 \begin_inset Formula \[
15834 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15838 This is how it looks when the limits type was changed to
15845 \begin_inset Formula \[
15846 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15850 For integrals, except of
15862 , the limits are by default set beside the operator.
15863 But for multiple integrals the limits are often set below the operator.
15864 In the following example the limits type was therefore set to
15868 and so set below the integrals:
15869 \begin_inset Formula \begin{equation}
15870 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15877 \begin_layout Standard
15878 \begin_inset VSpace medskip
15881 To specify conditions for limits, the commands
15891 \begin_layout Plain Layout
15909 \begin_layout Plain Layout
15918 To create for example this expression
15919 \begin_inset Formula \begin{equation}
15920 \sum_{\begin{subarray}{c}
15922 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
15929 \begin_layout Standard
15930 the following has to be done:
15931 \begin_inset Newline newline
15946 \begin_layout Plain Layout
15958 One is now in a blue box under the summation operator and insert there
15967 \begin_layout Plain Layout
15979 The blue box is now within a purple box and now several lines can be written
15981 A new line is created by inserting a line break (
15987 \begin_inset Newline newline
15992 0<k<1000 Ctrl-Return
15993 \begin_inset Newline newline
15998 is typed in, a new box appears below for the new line.
16001 \begin_layout Standard
16002 The alignment of the lines can be changed to left aligned with the
16012 Edit\SpecialChar \menuseparator
16016 To get right alignment,
16024 \begin_layout Plain Layout
16035 is inserted at the beginning of the line.
16038 \begin_layout Standard
16051 with the difference that the lines are always centered.
16054 \begin_layout Standard
16055 \begin_inset VSpace bigskip
16059 \begin_inset CommandInset ref
16061 reference "eq:substack"
16065 there can be too much space beside an operator, because the characters
16066 following the operator are set beside the limits.
16069 \begin_layout Standard
16070 To avoid this, the following macro can be used in the LaTeX-preamble:
16073 \begin_layout Standard
16087 \begin_inset Newline newline
16099 \begin_inset Newline newline
16106 mathclapinternal #1#2{
16110 mathsurround =0pt #1{#2}$}}
16113 \begin_layout Standard
16114 This defines the command
16124 \begin_layout Plain Layout
16132 that sets the width of the limit to 0
16133 \begin_inset space \thinspace{}
16137 The command scheme is
16140 \begin_layout Standard
16148 \begin_layout Standard
16149 where the limit can consist of several conditions.
16152 \begin_layout Standard
16154 \begin_inset CommandInset ref
16156 reference "eq:substack"
16160 , one uses the command
16163 \begin_layout Standard
16176 \begin_layout Plain Layout
16185 0<k<1000 Ctrl-Enter
16188 \begin_layout Standard
16189 to create the lower limit.
16190 The summand is now directly behind the summation operator:
16191 \begin_inset Formula \[
16192 \sum_{\mathclap{\substack{0<k<1000\\
16193 \\k\,\in\,\mathbb{N}}
16201 \begin_layout Standard
16202 \begin_inset VSpace bigskip
16205 How to use one limit for several operators is described in
16206 \begin_inset CommandInset ref
16208 reference "sub:Self-defined-Operators"
16215 \begin_layout Subsection
16217 \begin_inset CommandInset label
16219 name "sub:Binary-Operators"
16227 \begin_layout Plain Layout
16236 \begin_layout Standard
16237 Binary operators are surrounded by space when there is a character before
16239 \begin_inset VSpace medskip
16245 \begin_layout Standard
16246 \begin_inset space \hfill{}
16250 \begin_inset Tabular
16251 <lyxtabular version="3" rows="13" columns="2">
16253 <column alignment="center" valignment="top" width="0pt">
16254 <column alignment="center" valignment="top" width="0pt">
16256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16259 \begin_layout Plain Layout
16261 \begin_inset Note Note
16264 \begin_layout Plain Layout
16271 is only used as spacer.
16281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16284 \begin_layout Plain Layout
16292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16295 \begin_layout Plain Layout
16301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16304 \begin_layout Plain Layout
16305 \begin_inset Formula $+$
16315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16318 \begin_layout Plain Layout
16324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16327 \begin_layout Plain Layout
16328 \begin_inset Formula $-$
16338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16341 \begin_layout Plain Layout
16349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16352 \begin_layout Plain Layout
16353 \begin_inset Formula $\pm$
16363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16366 \begin_layout Plain Layout
16374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16377 \begin_layout Plain Layout
16378 \begin_inset Formula $\mp$
16388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16391 \begin_layout Plain Layout
16399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16402 \begin_layout Plain Layout
16403 \begin_inset Formula $\cdot$
16413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16416 \begin_layout Plain Layout
16424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16427 \begin_layout Plain Layout
16428 \begin_inset Formula $\times$
16438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16441 \begin_layout Plain Layout
16449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16452 \begin_layout Plain Layout
16453 \begin_inset Formula $\div$
16463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16466 \begin_layout Plain Layout
16470 \begin_layout Plain Layout
16483 \begin_layout Plain Layout
16495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16498 \begin_layout Plain Layout
16499 \begin_inset Formula $*$
16509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16512 \begin_layout Plain Layout
16520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16523 \begin_layout Plain Layout
16524 \begin_inset Formula $\star$
16534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16537 \begin_layout Plain Layout
16545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16548 \begin_layout Plain Layout
16549 \begin_inset Formula $\circ$
16559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16562 \begin_layout Plain Layout
16570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16573 \begin_layout Plain Layout
16574 \begin_inset Formula $\diamond$
16584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16587 \begin_layout Plain Layout
16595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16598 \begin_layout Plain Layout
16599 \begin_inset Formula $\bullet$
16613 \begin_inset space \hfill{}
16617 \begin_inset Tabular
16618 <lyxtabular version="3" rows="13" columns="2">
16620 <column alignment="center" valignment="top" width="0pt">
16621 <column alignment="center" valignment="top" width="0pt">
16623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16626 \begin_layout Plain Layout
16632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16635 \begin_layout Plain Layout
16643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16646 \begin_layout Plain Layout
16654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16657 \begin_layout Plain Layout
16658 \begin_inset Formula $\nabla$
16668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16671 \begin_layout Plain Layout
16679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16682 \begin_layout Plain Layout
16683 \begin_inset Formula $\bigtriangledown$
16693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16696 \begin_layout Plain Layout
16704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16707 \begin_layout Plain Layout
16708 \begin_inset Formula $\bigtriangleup$
16718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16721 \begin_layout Plain Layout
16729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16732 \begin_layout Plain Layout
16733 \begin_inset Formula $\Box$
16743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16746 \begin_layout Plain Layout
16754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16757 \begin_layout Plain Layout
16758 \begin_inset Formula $\cap$
16768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16771 \begin_layout Plain Layout
16779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16782 \begin_layout Plain Layout
16783 \begin_inset Formula $\cup$
16793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16796 \begin_layout Plain Layout
16804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16807 \begin_layout Plain Layout
16808 \begin_inset Formula $\dagger$
16818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16821 \begin_layout Plain Layout
16829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16832 \begin_layout Plain Layout
16833 \begin_inset Formula $\ddagger$
16843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16846 \begin_layout Plain Layout
16854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16857 \begin_layout Plain Layout
16858 \begin_inset Formula $\wr$
16868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16871 \begin_layout Plain Layout
16879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16882 \begin_layout Plain Layout
16883 \begin_inset Formula $\bigcirc$
16893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16896 \begin_layout Plain Layout
16904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16907 \begin_layout Plain Layout
16908 \begin_inset Formula $\wedge$
16918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16921 \begin_layout Plain Layout
16929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16932 \begin_layout Plain Layout
16933 \begin_inset Formula $\vee$
16947 \begin_inset space \hfill{}
16951 \begin_inset Tabular
16952 <lyxtabular version="3" rows="13" columns="2">
16954 <column alignment="center" valignment="top" width="0pt">
16955 <column alignment="center" valignment="top" width="0pt">
16957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16960 \begin_layout Plain Layout
16966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16969 \begin_layout Plain Layout
16977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16980 \begin_layout Plain Layout
16988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16991 \begin_layout Plain Layout
16992 \begin_inset Formula $\oplus$
17002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17005 \begin_layout Plain Layout
17013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17016 \begin_layout Plain Layout
17017 \begin_inset Formula $\ominus$
17027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17030 \begin_layout Plain Layout
17038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17041 \begin_layout Plain Layout
17042 \begin_inset Formula $\otimes$
17052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17055 \begin_layout Plain Layout
17063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17066 \begin_layout Plain Layout
17067 \begin_inset Formula $\oslash$
17077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17080 \begin_layout Plain Layout
17088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17091 \begin_layout Plain Layout
17092 \begin_inset Formula $\odot$
17102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17105 \begin_layout Plain Layout
17113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17116 \begin_layout Plain Layout
17117 \begin_inset Formula $\amalg$
17127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17130 \begin_layout Plain Layout
17138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17141 \begin_layout Plain Layout
17142 \begin_inset Formula $\uplus$
17152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17155 \begin_layout Plain Layout
17163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17166 \begin_layout Plain Layout
17167 \begin_inset Formula $\setminus$
17177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17180 \begin_layout Plain Layout
17188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17191 \begin_layout Plain Layout
17192 \begin_inset Formula $\sqcap$
17202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17205 \begin_layout Plain Layout
17213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17216 \begin_layout Plain Layout
17217 \begin_inset Formula $\sqcup$
17227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17230 \begin_layout Plain Layout
17238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17241 \begin_layout Plain Layout
17242 \begin_inset Formula $\triangleleft$
17252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17255 \begin_layout Plain Layout
17263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17266 \begin_layout Plain Layout
17267 \begin_inset Formula $\triangleright$
17281 \begin_inset space \hfill{}
17287 \begin_layout Standard
17288 All binary operators can also be inserted via the math toolbar button
17289 \begin_inset Graphics
17290 filename ../images/math/pm.png
17298 \begin_layout Standard
17299 To typeset the Laplace operator also
17316 \begin_inset Formula $\nabla^{2}$
17319 ) can be used instead of
17328 \begin_layout Standard
17335 Insert\SpecialChar \menuseparator
17347 \begin_layout Subsection
17348 Self-defined Operators
17349 \begin_inset CommandInset label
17351 name "sub:Self-defined-Operators"
17359 \begin_layout Plain Layout
17360 Operators ! self-defined
17368 \begin_layout Standard
17369 With the help of the command
17373 DeclareMathOperator
17379 \begin_layout Plain Layout
17384 DeclareMathOperator
17389 custom operators can be defined in the LaTeX-preamble.
17390 Its command scheme is:
17393 \begin_layout Standard
17398 DeclareMathOperator{new command}{display}
17401 \begin_layout Standard
17402 Display can be characters or symbols that define how the operator looks
17404 To define a big operator a * is set behind the command.
17405 All self-defined big operators can have limits as described in
17406 \begin_inset CommandInset ref
17408 reference "sub:Operator-Limits"
17415 \begin_layout Standard
17416 For example the LaTeX-preamble line
17419 \begin_layout Standard
17424 DeclareMathOperator*{
17431 \begin_layout Standard
17432 defines the command
17438 , that inserts a big operator consisting of the lozenge symbol from
17439 \begin_inset CommandInset ref
17441 reference "sub:Miscellaneous-Symbols"
17446 \begin_inset Formula \[
17447 \Lozenge_{n=1}^{\infty}\]
17451 The command for this formula is:
17462 \begin_inset Formula $\to$
17468 \begin_layout Standard
17469 \begin_inset VSpace bigskip
17472 When self-defined operators are not used several times in the document,
17473 they can also be defined with the commands
17483 \begin_layout Plain Layout
17501 \begin_layout Plain Layout
17509 , which have the following scheme:
17512 \begin_layout Standard
17526 \begin_layout Standard
17533 defines big operators,
17542 \begin_layout Standard
17550 \begin_inset space \thinspace{}
17554 \begin_inset space ~
17557 be used to use one limit for several operators:
17560 \begin_layout Standard
17561 \begin_inset Formula \[
17562 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17569 \begin_layout Standard
17570 The command for the formula above is:
17571 \begin_inset Newline newline
17590 \begin_layout Plain Layout
17602 \begin_inset Formula $\to$
17611 \begin_layout Plain Layout
17625 \begin_layout Section
17630 \begin_layout Plain Layout
17639 \begin_layout Subsection
17641 \begin_inset CommandInset label
17643 name "sub:Font-Styles"
17651 \begin_layout Plain Layout
17660 \begin_layout Standard
17661 Latin letters in formulas can be set in one of the following font styles:
17662 \begin_inset VSpace -2mm
17668 \begin_layout Standard
17670 \begin_inset Tabular
17671 <lyxtabular version="3" rows="6" columns="3">
17673 <column alignment="center" valignment="top" width="0">
17674 <column alignment="center" valignment="top" width="0">
17675 <column alignment="center" valignment="top" width="0">
17677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17680 \begin_layout Plain Layout
17686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17689 \begin_layout Plain Layout
17695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17698 \begin_layout Plain Layout
17706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17709 \begin_layout Plain Layout
17718 \begin_layout Plain Layout
17734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17737 \begin_layout Plain Layout
17738 \begin_inset Formula $\mathbb{ABC}$
17746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17749 \begin_layout Plain Layout
17757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17760 \begin_layout Plain Layout
17769 \begin_layout Plain Layout
17785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17788 \begin_layout Plain Layout
17789 \begin_inset Formula $\mathbf{AbC}$
17797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17800 \begin_layout Plain Layout
17808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17811 \begin_layout Plain Layout
17820 \begin_layout Plain Layout
17836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17839 \begin_layout Plain Layout
17840 \begin_inset Formula $\boldsymbol{AbC}$
17848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17851 \begin_layout Plain Layout
17859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17862 \begin_layout Plain Layout
17871 \begin_layout Plain Layout
17887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17890 \begin_layout Plain Layout
17891 \begin_inset Formula $\mathcal{ABC}$
17899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17902 \begin_layout Plain Layout
17910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17913 \begin_layout Plain Layout
17922 \begin_layout Plain Layout
17938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17941 \begin_layout Plain Layout
17942 \begin_inset Formula $\mathfrak{AbC}$
17950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17953 \begin_layout Plain Layout
17967 \begin_layout Standard
17969 \begin_inset Tabular
17970 <lyxtabular version="3" rows="5" columns="3">
17972 <column alignment="center" valignment="top" width="0">
17973 <column alignment="center" valignment="top" width="0">
17974 <column alignment="center" valignment="top" width="0">
17976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17979 \begin_layout Plain Layout
17985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17988 \begin_layout Plain Layout
17994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17997 \begin_layout Plain Layout
18005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18008 \begin_layout Plain Layout
18017 \begin_layout Plain Layout
18033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18036 \begin_layout Plain Layout
18037 \begin_inset Formula $\mathit{AbC}$
18045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18048 \begin_layout Plain Layout
18056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18059 \begin_layout Plain Layout
18068 \begin_layout Plain Layout
18084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18087 \begin_layout Plain Layout
18088 \begin_inset Formula $\mathrm{AbC}$
18096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18099 \begin_layout Plain Layout
18107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18110 \begin_layout Plain Layout
18119 \begin_layout Plain Layout
18135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18138 \begin_layout Plain Layout
18139 \begin_inset Formula $\mathsf{AbC}$
18147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18150 \begin_layout Plain Layout
18158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18161 \begin_layout Plain Layout
18170 \begin_layout Plain Layout
18186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18189 \begin_layout Plain Layout
18190 \begin_inset Formula $\mathtt{AbC}$
18198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18201 \begin_layout Plain Layout
18215 \begin_layout Standard
18216 \begin_inset Note Greyedout
18219 \begin_layout Plain Layout
18236 can only be used for big letters.
18244 \begin_layout Standard
18245 Predefined is the style
18254 \begin_layout Standard
18255 The style commands work also for letters in mathematical constructs:
18256 \begin_inset Formula \[
18257 \mathfrak{A=\frac{b}{C}}\]
18264 \begin_layout Standard
18265 Characters in mathematical text don't appear in a math font style but in
18266 the text font style
18273 That their style can't be set correctly via the text style dialog is a
18278 \begin_layout Plain Layout
18279 \begin_inset CommandInset href
18281 name "LyX-bug #4091"
18282 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18294 \begin_layout Standard
18295 Instead of the style commands the dialog
18297 Edit\SpecialChar \menuseparator
18298 Math\SpecialChar \menuseparator
18301 or the toolbar button
18302 \begin_inset Graphics
18303 filename ../images/math/font.png
18311 \begin_layout Subsection
18313 \begin_inset CommandInset label
18315 name "sub:Bold-Formulas"
18323 \begin_layout Plain Layout
18332 \begin_layout Standard
18333 To make a complete formula bold, the command
18339 from the previous subsection cannot be used, because it doesn't work for
18340 small Greek letters.
18341 Furthermore it prints Latin letters always upright, like in the following
18345 \begin_layout Standard
18346 \begin_inset Formula \[
18347 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18354 \begin_layout Standard
18355 To display the formula correctly, the command
18362 \begin_inset Formula \[
18363 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18367 It is also possible to set the formula in a
18369 boldmath environment
18372 This environment is created by inserting the command
18380 \begin_layout Plain Layout
18391 To end the environment, the command
18399 \begin_layout Plain Layout
18409 is inserted in TeX-mode.
18413 \begin_layout Plain Layout
18423 \begin_inset Formula \[
18424 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18432 \begin_layout Plain Layout
18444 \begin_layout Subsection
18446 \begin_inset CommandInset label
18448 name "sub:Font-Sizes"
18456 \begin_layout Plain Layout
18465 \begin_layout Standard
18466 For characters in formulas there are, analog to characters in text, the
18467 following size commands:
18470 \begin_layout Standard
18514 \begin_inset Newline newline
18536 \begin_layout Standard
18537 The size produced by the commands depends on the document font size, that
18538 corresponds with the command
18545 The other commands produce smaller or larger sizes than
18552 The font size can however not exceed a certain value.
18553 Is for example the document font size 12
18554 \begin_inset space \thinspace{}
18563 switches to the same size as
18573 \begin_layout Standard
18574 A size command is inserted in TeX-mode before the formula and sets the size
18575 for all following formula and text characters.
18576 To switch back to the initial size, the command
18582 is inserted behind the formula in TeX-mode.
18585 \begin_layout Standard
18586 Within a formula the size can only be changed for symbols or letters in
18588 To do this, the size command is inserted in mathematical text.
18589 All following characters until the end of the mathematical text or until
18590 another size command will have the selected size.
18592 \begin_inset VSpace -2mm
18598 \begin_layout Standard
18602 \begin_layout Plain Layout
18612 \begin_inset Formula \[
18613 A=\frac{B}{c}\cdot\maltese\]
18618 \begin_inset Formula \[
18619 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18627 \begin_layout Plain Layout
18639 \begin_layout Standard
18640 \begin_inset VSpace medskip
18643 Before both formulas the command
18650 The command for the second formula is:
18651 \begin_inset Newline newline
18662 \begin_layout Plain Layout
18677 \begin_layout Plain Layout
18692 \begin_layout Plain Layout
18707 \begin_layout Plain Layout
18717 \begin_inset Formula $\to$
18721 \begin_inset Formula $\to$
18725 \begin_inset Newline newline
18729 \begin_inset space \hspace*{}
18743 \begin_layout Plain Layout
18758 \begin_layout Plain Layout
18773 \begin_layout Plain Layout
18785 \begin_layout Standard
18786 If a symbol cannot be displayed in different sizes, it will always be displayed
18787 in the default size.
18790 \begin_layout Section
18795 \begin_layout Plain Layout
18804 \begin_layout Standard
18805 All Greek letters can also be inserted via the toolbar button
18806 \begin_inset Graphics
18807 filename ../images/math/alpha.png
18815 \begin_layout Subsection
18817 \begin_inset CommandInset label
18819 name "sub:Small-Letters"
18827 \begin_layout Plain Layout
18828 Greek letters ! small
18836 \begin_layout Standard
18837 \begin_inset space \hfill{}
18841 \begin_inset Tabular
18842 <lyxtabular version="3" rows="11" columns="2">
18844 <column alignment="center" valignment="top" width="0pt">
18845 <column alignment="center" valignment="top" width="0pt">
18847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18850 \begin_layout Plain Layout
18856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18859 \begin_layout Plain Layout
18867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18870 \begin_layout Plain Layout
18878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18881 \begin_layout Plain Layout
18882 \begin_inset Formula $\alpha$
18892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18895 \begin_layout Plain Layout
18903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18906 \begin_layout Plain Layout
18907 \begin_inset Formula $\beta$
18917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18920 \begin_layout Plain Layout
18928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18931 \begin_layout Plain Layout
18932 \begin_inset Formula $\gamma$
18942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18945 \begin_layout Plain Layout
18953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18956 \begin_layout Plain Layout
18957 \begin_inset Formula $\delta$
18967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18970 \begin_layout Plain Layout
18978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18981 \begin_layout Plain Layout
18982 \begin_inset Formula $\epsilon$
18992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18995 \begin_layout Plain Layout
19003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19006 \begin_layout Plain Layout
19007 \begin_inset Formula $\varepsilon$
19017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19020 \begin_layout Plain Layout
19028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19031 \begin_layout Plain Layout
19032 \begin_inset Formula $\zeta$
19042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19045 \begin_layout Plain Layout
19053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19056 \begin_layout Plain Layout
19057 \begin_inset Formula $\eta$
19067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19070 \begin_layout Plain Layout
19078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19081 \begin_layout Plain Layout
19082 \begin_inset Formula $\theta$
19092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19095 \begin_layout Plain Layout
19103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19106 \begin_layout Plain Layout
19107 \begin_inset Formula $\vartheta$
19121 \begin_inset space \hfill{}
19125 \begin_inset Tabular
19126 <lyxtabular version="3" rows="12" columns="2">
19128 <column alignment="center" valignment="top" width="0pt">
19129 <column alignment="center" valignment="top" width="0pt">
19131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19134 \begin_layout Plain Layout
19140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19143 \begin_layout Plain Layout
19151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19154 \begin_layout Plain Layout
19162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19165 \begin_layout Plain Layout
19166 \begin_inset Formula $\iota$
19176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19179 \begin_layout Plain Layout
19187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19190 \begin_layout Plain Layout
19191 \begin_inset Formula $\kappa$
19201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19204 \begin_layout Plain Layout
19212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19215 \begin_layout Plain Layout
19216 \begin_inset Formula $\varkappa$
19226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19229 \begin_layout Plain Layout
19237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19240 \begin_layout Plain Layout
19241 \begin_inset Formula $\lambda$
19251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19254 \begin_layout Plain Layout
19262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19265 \begin_layout Plain Layout
19266 \begin_inset Formula $\mu$
19276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19279 \begin_layout Plain Layout
19287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19290 \begin_layout Plain Layout
19291 \begin_inset Formula $\nu$
19301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19304 \begin_layout Plain Layout
19312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19315 \begin_layout Plain Layout
19316 \begin_inset Formula $\xi$
19326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19329 \begin_layout Plain Layout
19335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19338 \begin_layout Plain Layout
19339 \begin_inset Formula $o$
19349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19352 \begin_layout Plain Layout
19360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19363 \begin_layout Plain Layout
19364 \begin_inset Formula $\pi$
19374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19377 \begin_layout Plain Layout
19385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19388 \begin_layout Plain Layout
19389 \begin_inset Formula $\varpi$
19399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19402 \begin_layout Plain Layout
19410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19413 \begin_layout Plain Layout
19414 \begin_inset Formula $\rho$
19428 \begin_inset space \hfill{}
19432 \begin_inset Tabular
19433 <lyxtabular version="3" rows="11" columns="2">
19435 <column alignment="center" valignment="top" width="0pt">
19436 <column alignment="center" valignment="top" width="0pt">
19438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19441 \begin_layout Plain Layout
19447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19450 \begin_layout Plain Layout
19458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19461 \begin_layout Plain Layout
19469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19472 \begin_layout Plain Layout
19473 \begin_inset Formula $\varrho$
19483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19486 \begin_layout Plain Layout
19494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19497 \begin_layout Plain Layout
19498 \begin_inset Formula $\sigma$
19508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19511 \begin_layout Plain Layout
19519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19522 \begin_layout Plain Layout
19523 \begin_inset Formula $\varsigma$
19533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19536 \begin_layout Plain Layout
19544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19547 \begin_layout Plain Layout
19548 \begin_inset Formula $\tau$
19558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19561 \begin_layout Plain Layout
19569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19572 \begin_layout Plain Layout
19573 \begin_inset Formula $\upsilon$
19583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19586 \begin_layout Plain Layout
19594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19597 \begin_layout Plain Layout
19598 \begin_inset Formula $\phi$
19608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19611 \begin_layout Plain Layout
19619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19622 \begin_layout Plain Layout
19623 \begin_inset Formula $\varphi$
19633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19636 \begin_layout Plain Layout
19644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19647 \begin_layout Plain Layout
19648 \begin_inset Formula $\chi$
19658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19661 \begin_layout Plain Layout
19669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19672 \begin_layout Plain Layout
19673 \begin_inset Formula $\psi$
19683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19686 \begin_layout Plain Layout
19694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19697 \begin_layout Plain Layout
19698 \begin_inset Formula $\omega$
19712 \begin_inset space \hfill{}
19718 \begin_layout Standard
19719 \begin_inset VSpace medskip
19725 \begin_layout Standard
19726 How to create upright Greek letters is explained in
19727 \begin_inset CommandInset ref
19729 reference "sub:Upright-small-Greek"
19736 \begin_layout Subsection
19741 \begin_layout Plain Layout
19742 Greek letters ! big
19750 \begin_layout Standard
19751 \begin_inset space \hfill{}
19755 \begin_inset Tabular
19756 <lyxtabular version="3" rows="7" columns="2">
19758 <column alignment="center" valignment="top" width="0pt">
19759 <column alignment="center" valignment="top" width="0pt">
19761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19764 \begin_layout Plain Layout
19770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19773 \begin_layout Plain Layout
19781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19784 \begin_layout Plain Layout
19792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19795 \begin_layout Plain Layout
19796 \begin_inset Formula $\Gamma$
19806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19809 \begin_layout Plain Layout
19817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19820 \begin_layout Plain Layout
19821 \begin_inset Formula $\Delta$
19831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19834 \begin_layout Plain Layout
19842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19845 \begin_layout Plain Layout
19846 \begin_inset Formula $\Theta$
19856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19859 \begin_layout Plain Layout
19867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19870 \begin_layout Plain Layout
19871 \begin_inset Formula $\Lambda$
19881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19884 \begin_layout Plain Layout
19892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19895 \begin_layout Plain Layout
19896 \begin_inset Formula $\Xi$
19906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19909 \begin_layout Plain Layout
19917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19920 \begin_layout Plain Layout
19921 \begin_inset Formula $\Pi$
19935 \begin_inset space \hfill{}
19939 \begin_inset Tabular
19940 <lyxtabular version="3" rows="6" columns="2">
19942 <column alignment="center" valignment="top" width="0pt">
19943 <column alignment="center" valignment="top" width="0pt">
19945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19948 \begin_layout Plain Layout
19954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19957 \begin_layout Plain Layout
19965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19968 \begin_layout Plain Layout
19976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19979 \begin_layout Plain Layout
19980 \begin_inset Formula $\Sigma$
19990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19993 \begin_layout Plain Layout
20001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20004 \begin_layout Plain Layout
20005 \begin_inset Formula $\Upsilon$
20015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20018 \begin_layout Plain Layout
20026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20029 \begin_layout Plain Layout
20030 \begin_inset Formula $\Phi$
20040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20043 \begin_layout Plain Layout
20051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20054 \begin_layout Plain Layout
20055 \begin_inset Formula $\Psi$
20065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20068 \begin_layout Plain Layout
20076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20079 \begin_layout Plain Layout
20080 \begin_inset Formula $\Omega$
20094 \begin_inset space \hfill{}
20100 \begin_layout Standard
20101 \begin_inset VSpace medskip
20104 That the big Greek letters appear upright is caused by a design bug when
20106 To get correct italic big letters, begin every command with
20111 For example the command
20118 \begin_inset Formula $\varGamma$
20124 \begin_layout Subsection
20129 \begin_layout Plain Layout
20130 Greek letters ! bold
20138 \begin_layout Standard
20139 Greek letters cannot be set with different font styles like Latin letters.
20140 They can only be made bold with the command
20150 \begin_layout Plain Layout
20161 \begin_layout Standard
20163 \begin_inset Tabular
20164 <lyxtabular version="3" rows="3" columns="2">
20166 <column alignment="center" valignment="top" width="0">
20167 <column alignment="center" valignment="top" width="0">
20169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20172 \begin_layout Plain Layout
20178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20181 \begin_layout Plain Layout
20189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20192 \begin_layout Plain Layout
20204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20207 \begin_layout Plain Layout
20208 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20221 \begin_layout Plain Layout
20233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20236 \begin_layout Plain Layout
20237 \begin_inset Formula $\theta\boldsymbol{\theta}$
20253 \begin_layout Section
20258 \begin_layout Plain Layout
20271 \begin_layout Plain Layout
20272 A list with all symbols of most of the LaTeX-packages can be found in
20273 \begin_inset CommandInset citation
20288 \begin_layout Plain Layout
20296 \begin_inset Note Note
20299 \begin_layout Plain Layout
20302 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20305 \begin_layout Plain Layout
20308 texorpdfstring is in section
20309 \begin_inset CommandInset ref
20311 reference "sub:Formulas-in-Section"
20324 \begin_layout Plain Layout
20333 \begin_layout Standard
20334 Many of the symbols listed in this section can also be inserted via the
20336 \begin_inset Graphics
20337 filename ../images/math/nabla.png
20343 \begin_inset Graphics
20344 filename ../images/math/digamma.png
20352 \begin_layout Subsection
20353 Mathematical Symbols
20354 \begin_inset CommandInset label
20356 name "sub:Mathematical-Symbols"
20364 \begin_layout Plain Layout
20365 Symbols ! mathematical
20373 \begin_layout Standard
20374 \begin_inset space \hfill{}
20378 \begin_inset Tabular
20379 <lyxtabular version="3" rows="10" columns="2">
20381 <column alignment="center" valignment="top" width="0pt">
20382 <column alignment="center" valignment="top" width="0pt">
20384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20387 \begin_layout Plain Layout
20393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20396 \begin_layout Plain Layout
20404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20407 \begin_layout Plain Layout
20415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20418 \begin_layout Plain Layout
20419 \begin_inset Formula $\neg$
20429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20432 \begin_layout Plain Layout
20440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20443 \begin_layout Plain Layout
20444 \begin_inset Formula $\Im$
20454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20457 \begin_layout Plain Layout
20465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20468 \begin_layout Plain Layout
20469 \begin_inset Formula $\Re$
20479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20482 \begin_layout Plain Layout
20490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20493 \begin_layout Plain Layout
20494 \begin_inset Formula $\aleph$
20504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20507 \begin_layout Plain Layout
20515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20518 \begin_layout Plain Layout
20519 \begin_inset Formula $\partial$
20529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20532 \begin_layout Plain Layout
20540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20543 \begin_layout Plain Layout
20544 \begin_inset Formula $\infty$
20554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20557 \begin_layout Plain Layout
20565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20568 \begin_layout Plain Layout
20569 \begin_inset Formula $\wp$
20579 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20582 \begin_layout Plain Layout
20590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20593 \begin_layout Plain Layout
20594 \begin_inset Formula $\imath$
20604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20607 \begin_layout Plain Layout
20615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20618 \begin_layout Plain Layout
20619 \begin_inset Formula $\jmath$
20633 \begin_inset space \hfill{}
20637 \begin_inset Tabular
20638 <lyxtabular version="3" rows="10" columns="2">
20640 <column alignment="center" valignment="top" width="0pt">
20641 <column alignment="center" valignment="top" width="0pt">
20643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20646 \begin_layout Plain Layout
20652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20655 \begin_layout Plain Layout
20657 \begin_inset Note Note
20660 \begin_layout Plain Layout
20667 is only used as spacer.
20679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20682 \begin_layout Plain Layout
20690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20693 \begin_layout Plain Layout
20694 \begin_inset Formula $\forall$
20704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20707 \begin_layout Plain Layout
20715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20718 \begin_layout Plain Layout
20719 \begin_inset Formula $\exists$
20729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20732 \begin_layout Plain Layout
20740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20743 \begin_layout Plain Layout
20744 \begin_inset Formula $\nexists$
20754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20757 \begin_layout Plain Layout
20765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20768 \begin_layout Plain Layout
20769 \begin_inset Formula $\emptyset$
20779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20782 \begin_layout Plain Layout
20790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20793 \begin_layout Plain Layout
20794 \begin_inset Formula $\varnothing$
20804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20807 \begin_layout Plain Layout
20815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20818 \begin_layout Plain Layout
20819 \begin_inset Formula $\dag$
20829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20832 \begin_layout Plain Layout
20840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20843 \begin_layout Plain Layout
20844 \begin_inset Formula $\ddag$
20854 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20857 \begin_layout Plain Layout
20865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20868 \begin_layout Plain Layout
20872 \begin_layout Plain Layout
20882 \begin_inset Formula $\complement$
20889 \begin_layout Plain Layout
20903 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20906 \begin_layout Plain Layout
20914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20917 \begin_layout Plain Layout
20918 \begin_inset Formula $\Bbbk$
20932 \begin_inset space \hfill{}
20936 \begin_inset Tabular
20937 <lyxtabular version="3" rows="10" columns="2">
20939 <column alignment="center" valignment="top" width="0pt">
20940 <column alignment="center" valignment="top" width="0pt">
20942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20945 \begin_layout Plain Layout
20951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20954 \begin_layout Plain Layout
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 $\prime$
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 $\backprime$
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 $\mho$
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 $\triangle$
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 $\angle$
21087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21090 \begin_layout Plain Layout
21098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21101 \begin_layout Plain Layout
21102 \begin_inset Formula $\measuredangle$
21112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21115 \begin_layout Plain Layout
21123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21126 \begin_layout Plain Layout
21127 \begin_inset Formula $\sphericalangle$
21137 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21140 \begin_layout Plain Layout
21148 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21151 \begin_layout Plain Layout
21152 \begin_inset Formula $\top$
21162 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21165 \begin_layout Plain Layout
21173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21176 \begin_layout Plain Layout
21177 \begin_inset Formula $\bot$
21191 \begin_inset space \hfill{}
21197 \begin_layout Standard
21198 \begin_inset Newpage newpage
21204 \begin_layout Subsection
21205 Miscellaneous Symbols
21206 \begin_inset CommandInset label
21208 name "sub:Miscellaneous-Symbols"
21216 \begin_layout Plain Layout
21217 Symbols ! miscellaneous
21225 \begin_layout Standard
21228 \begin_inset Tabular
21229 <lyxtabular version="3" rows="10" columns="2">
21231 <column alignment="center" valignment="top" width="0pt">
21232 <column alignment="center" valignment="top" width="0pt">
21234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21237 \begin_layout Plain Layout
21243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21246 \begin_layout Plain Layout
21254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21257 \begin_layout Plain Layout
21265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21268 \begin_layout Plain Layout
21269 \begin_inset Formula $\flat$
21279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21282 \begin_layout Plain Layout
21290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21293 \begin_layout Plain Layout
21294 \begin_inset Formula $\natural$
21304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21307 \begin_layout Plain Layout
21315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21318 \begin_layout Plain Layout
21319 \begin_inset Formula $\sharp$
21329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21332 \begin_layout Plain Layout
21340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21343 \begin_layout Plain Layout
21344 \begin_inset Formula $\surd$
21354 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21357 \begin_layout Plain Layout
21365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21368 \begin_layout Plain Layout
21369 \begin_inset Formula $\checkmark$
21379 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21382 \begin_layout Plain Layout
21390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21393 \begin_layout Plain Layout
21394 \begin_inset Formula $\yen$
21404 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21407 \begin_layout Plain Layout
21415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21418 \begin_layout Plain Layout
21419 \begin_inset Formula $\pounds$
21429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21432 \begin_layout Plain Layout
21438 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21441 \begin_layout Plain Layout
21442 \begin_inset Formula $\$$
21452 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21455 \begin_layout Plain Layout
21461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21464 \begin_layout Plain Layout
21465 \begin_inset Formula $§$
21479 \begin_inset Tabular
21480 <lyxtabular version="3" rows="10" columns="2">
21482 <column alignment="center" valignment="top" width="0">
21483 <column alignment="center" valignment="top" width="0">
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 $\hbar$
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 $\hslash$
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 $\clubsuit$
21580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21583 \begin_layout Plain Layout
21591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21594 \begin_layout Plain Layout
21595 \begin_inset Formula $\spadesuit$
21605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21608 \begin_layout Plain Layout
21616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21619 \begin_layout Plain Layout
21620 \begin_inset Formula $\bigstar$
21630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21633 \begin_layout Plain Layout
21641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21644 \begin_layout Plain Layout
21645 \begin_inset Formula $\blacklozenge$
21655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21658 \begin_layout Plain Layout
21666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21669 \begin_layout Plain Layout
21670 \begin_inset Formula $\blacktriangle$
21680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21683 \begin_layout Plain Layout
21691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21694 \begin_layout Plain Layout
21695 \begin_inset Formula $\blacktriangledown$
21705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21708 \begin_layout Plain Layout
21716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21719 \begin_layout Plain Layout
21720 \begin_inset Formula $\bullet$
21734 \begin_inset Tabular
21735 <lyxtabular version="3" rows="10" columns="2">
21737 <column alignment="center" valignment="top" width="0pt">
21738 <column alignment="center" valignment="top" width="0pt">
21740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21743 \begin_layout Plain Layout
21749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21752 \begin_layout Plain Layout
21760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21763 \begin_layout Plain Layout
21771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21774 \begin_layout Plain Layout
21775 \begin_inset Formula $\diamondsuit$
21785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21788 \begin_layout Plain Layout
21796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21799 \begin_layout Plain Layout
21800 \begin_inset Formula $\Diamond$
21810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21813 \begin_layout Plain Layout
21821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21824 \begin_layout Plain Layout
21825 \begin_inset Formula $\heartsuit$
21835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21838 \begin_layout Plain Layout
21846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21849 \begin_layout Plain Layout
21850 \begin_inset Formula $\P$
21860 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21863 \begin_layout Plain Layout
21871 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21874 \begin_layout Plain Layout
21875 \begin_inset Formula $\copyright$
21885 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21888 \begin_layout Plain Layout
21896 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21899 \begin_layout Plain Layout
21900 \begin_inset Formula $\circledR$
21910 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21913 \begin_layout Plain Layout
21921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21924 \begin_layout Plain Layout
21925 \begin_inset Formula $\maltese$
21935 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21938 \begin_layout Plain Layout
21946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21949 \begin_layout Plain Layout
21950 \begin_inset Formula $\diagup$
21960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21963 \begin_layout Plain Layout
21971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21974 \begin_layout Plain Layout
21975 \begin_inset Formula $\diagdown$
21991 \begin_layout Standard
21992 \begin_inset VSpace medskip
21995 More symbols are listed in
21996 \begin_inset CommandInset ref
21998 reference "sub:Miscellaneous-Special-Characters"
22005 \begin_layout Standard
22006 Some symbols can be displayed in different sizes, see
22007 \begin_inset CommandInset ref
22009 reference "sub:Font-Sizes"
22016 \begin_layout Subsection
22021 \begin_layout Plain Layout
22022 Symbols ! Euro-symbol
22031 \begin_layout Plain Layout
22035 \begin_layout Plain Layout
22052 \begin_layout Standard
22053 To use the Euro symbol in formulas, the LaTeX-package
22061 \begin_layout Plain Layout
22067 must be installed and loaded with the LaTeX-preamble line
22070 \begin_layout Standard
22075 usepackage[gennarrow]{eurosym}
22078 \begin_layout Standard
22079 The Euro symbol can now be inserted with the command
22089 \begin_layout Plain Layout
22100 \begin_layout Standard
22101 The Euro symbol can directly be inserted with the € key in mathematical
22102 text, without having
22117 can also be inserted in TeX-mode.
22118 The official currency symbol can then be inserted with the command
22128 \begin_layout Plain Layout
22136 , that is only available in TeX-mode.
22139 \begin_layout Standard
22143 \begin_layout Plain Layout
22153 \begin_inset Note Note
22156 \begin_layout Plain Layout
22157 The following table will only be displayed when the LaTeX-package
22169 \begin_layout Standard
22170 An overview about the different Euro symbols:
22173 \begin_layout Standard
22175 \begin_inset Tabular
22176 <lyxtabular version="3" rows="4" columns="3">
22178 <column alignment="center" valignment="top" width="0pt">
22179 <column alignment="center" valignment="top" width="0pt">
22180 <column alignment="center" valignment="top" width="0pt">
22182 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22185 \begin_layout Plain Layout
22191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22194 \begin_layout Plain Layout
22200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22203 \begin_layout Plain Layout
22211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22214 \begin_layout Plain Layout
22220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22223 \begin_layout Plain Layout
22231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22234 \begin_layout Plain Layout
22235 \begin_inset Formula $\euro$
22245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22248 \begin_layout Plain Layout
22254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22257 \begin_layout Plain Layout
22263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22266 \begin_layout Plain Layout
22267 \begin_inset Formula $\mbox{€}$
22277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22280 \begin_layout Plain Layout
22286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22289 \begin_layout Plain Layout
22297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22300 \begin_layout Plain Layout
22304 \begin_layout Plain Layout
22326 \begin_layout Standard
22330 \begin_layout Plain Layout
22340 \begin_inset Note Note
22343 \begin_layout Plain Layout
22344 The following will be displayed when the LaTeX-package
22356 \begin_layout Standard
22357 You need to install the LaTeX-package
22361 to see the rest of this subsection in the output.
22364 \begin_layout Standard
22368 \begin_layout Plain Layout
22380 \begin_layout Section
22382 \begin_inset CommandInset label
22384 name "sec:Relations"
22392 \begin_layout Plain Layout
22402 \begin_layout Plain Layout
22407 \begin_layout Plain Layout
22418 \begin_layout Plain Layout
22433 \begin_layout Standard
22434 All relations can also be inserted via the toolbar button
22435 \begin_inset Graphics
22436 filename ../images/math/leq.png
22444 \begin_layout Standard
22445 \begin_inset space \hfill{}
22449 \begin_inset Tabular
22450 <lyxtabular version="3" rows="17" columns="2">
22452 <column alignment="center" valignment="top" width="0pt">
22453 <column alignment="center" valignment="top" width="0pt">
22455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22458 \begin_layout Plain Layout
22464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22467 \begin_layout Plain Layout
22475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22478 \begin_layout Plain Layout
22484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22487 \begin_layout Plain Layout
22488 \begin_inset Formula $<$
22498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22501 \begin_layout Plain Layout
22509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22512 \begin_layout Plain Layout
22513 \begin_inset Formula $\le$
22523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22526 \begin_layout Plain Layout
22534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22537 \begin_layout Plain Layout
22538 \begin_inset Formula $\ll$
22548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22551 \begin_layout Plain Layout
22559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22562 \begin_layout Plain Layout
22563 \begin_inset Formula $\prec$
22573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22576 \begin_layout Plain Layout
22584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22587 \begin_layout Plain Layout
22588 \begin_inset Formula $\preceq$
22598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22601 \begin_layout Plain Layout
22609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22612 \begin_layout Plain Layout
22613 \begin_inset Formula $\subset$
22623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22626 \begin_layout Plain Layout
22634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22637 \begin_layout Plain Layout
22638 \begin_inset Formula $\subseteq$
22648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22651 \begin_layout Plain Layout
22659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22662 \begin_layout Plain Layout
22663 \begin_inset Formula $\sqsubseteq$
22673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22676 \begin_layout Plain Layout
22684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22687 \begin_layout Plain Layout
22688 \begin_inset Formula $\in$
22698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22701 \begin_layout Plain Layout
22709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22712 \begin_layout Plain Layout
22713 \begin_inset Formula $\vdash$
22723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22726 \begin_layout Plain Layout
22734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22737 \begin_layout Plain Layout
22738 \begin_inset Formula $\smile$
22748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22751 \begin_layout Plain Layout
22759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22762 \begin_layout Plain Layout
22763 \begin_inset Formula $\lhd$
22773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22776 \begin_layout Plain Layout
22784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22787 \begin_layout Plain Layout
22788 \begin_inset Formula $\unlhd$
22798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22801 \begin_layout Plain Layout
22809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22812 \begin_layout Plain Layout
22813 \begin_inset Formula $\gtrless$
22823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22826 \begin_layout Plain Layout
22834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22837 \begin_layout Plain Layout
22838 \begin_inset Formula $\mid$
22848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22851 \begin_layout Plain Layout
22859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22862 \begin_layout Plain Layout
22863 \begin_inset Formula $\nmid$
22877 \begin_inset space \hfill{}
22881 \begin_inset Tabular
22882 <lyxtabular version="3" rows="17" columns="2">
22884 <column alignment="center" valignment="top" width="0pt">
22885 <column alignment="center" valignment="top" width="0pt">
22887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22890 \begin_layout Plain Layout
22896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22899 \begin_layout Plain Layout
22907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22910 \begin_layout Plain Layout
22916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22919 \begin_layout Plain Layout
22920 \begin_inset Formula $=$
22930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22933 \begin_layout Plain Layout
22941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22944 \begin_layout Plain Layout
22945 \begin_inset Formula $\not=$
22955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22958 \begin_layout Plain Layout
22966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22969 \begin_layout Plain Layout
22970 \begin_inset Formula $\equiv$
22980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22983 \begin_layout Plain Layout
22991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22994 \begin_layout Plain Layout
22995 \begin_inset Formula $\sim$
23005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23008 \begin_layout Plain Layout
23016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23019 \begin_layout Plain Layout
23020 \begin_inset Formula $\simeq$
23030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23033 \begin_layout Plain Layout
23041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23044 \begin_layout Plain Layout
23045 \begin_inset Formula $\approx$
23055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23058 \begin_layout Plain Layout
23066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23069 \begin_layout Plain Layout
23070 \begin_inset Formula $\cong$
23080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23083 \begin_layout Plain Layout
23091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23094 \begin_layout Plain Layout
23095 \begin_inset Formula $\bowtie$
23105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23108 \begin_layout Plain Layout
23116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23119 \begin_layout Plain Layout
23120 \begin_inset Formula $\notin$
23130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23133 \begin_layout Plain Layout
23141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23144 \begin_layout Plain Layout
23145 \begin_inset Formula $\perp$
23155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23158 \begin_layout Plain Layout
23166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23169 \begin_layout Plain Layout
23170 \begin_inset Formula $\propto$
23180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23183 \begin_layout Plain Layout
23191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23194 \begin_layout Plain Layout
23195 \begin_inset Formula $\asymp$
23205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23208 \begin_layout Plain Layout
23216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23219 \begin_layout Plain Layout
23220 \begin_inset Formula $\doteq$
23230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23233 \begin_layout Plain Layout
23241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23244 \begin_layout Plain Layout
23245 \begin_inset Formula $\circeq$
23255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23258 \begin_layout Plain Layout
23266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23269 \begin_layout Plain Layout
23270 \begin_inset Formula $\models$
23280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23283 \begin_layout Plain Layout
23291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23294 \begin_layout Plain Layout
23295 \begin_inset Formula $\widehat{=}$
23309 \begin_inset space \hfill{}
23313 \begin_inset Tabular
23314 <lyxtabular version="3" rows="17" columns="2">
23316 <column alignment="center" valignment="top" width="0pt">
23317 <column alignment="center" valignment="top" width="0pt">
23319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23322 \begin_layout Plain Layout
23328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23331 \begin_layout Plain Layout
23339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23342 \begin_layout Plain Layout
23348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23351 \begin_layout Plain Layout
23352 \begin_inset Formula $>$
23362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23365 \begin_layout Plain Layout
23373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23376 \begin_layout Plain Layout
23377 \begin_inset Formula $\ge$
23387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23390 \begin_layout Plain Layout
23398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23401 \begin_layout Plain Layout
23402 \begin_inset Formula $\gg$
23412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23415 \begin_layout Plain Layout
23423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23426 \begin_layout Plain Layout
23427 \begin_inset Formula $\succ$
23437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23440 \begin_layout Plain Layout
23448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23451 \begin_layout Plain Layout
23452 \begin_inset Formula $\succeq$
23462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23465 \begin_layout Plain Layout
23473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23476 \begin_layout Plain Layout
23477 \begin_inset Formula $\supset$
23487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23490 \begin_layout Plain Layout
23498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23501 \begin_layout Plain Layout
23502 \begin_inset Formula $\supseteq$
23512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23515 \begin_layout Plain Layout
23523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23526 \begin_layout Plain Layout
23527 \begin_inset Formula $\sqsupseteq$
23537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23540 \begin_layout Plain Layout
23548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23551 \begin_layout Plain Layout
23552 \begin_inset Formula $\ni$
23562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23565 \begin_layout Plain Layout
23573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23576 \begin_layout Plain Layout
23577 \begin_inset Formula $\dashv$
23587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23590 \begin_layout Plain Layout
23598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23601 \begin_layout Plain Layout
23602 \begin_inset Formula $\frown$
23612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23615 \begin_layout Plain Layout
23623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23626 \begin_layout Plain Layout
23627 \begin_inset Formula $\rhd$
23637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23640 \begin_layout Plain Layout
23648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23651 \begin_layout Plain Layout
23652 \begin_inset Formula $\unrhd$
23662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23665 \begin_layout Plain Layout
23673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23676 \begin_layout Plain Layout
23677 \begin_inset Formula $\lessgtr$
23687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23690 \begin_layout Plain Layout
23698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23701 \begin_layout Plain Layout
23702 \begin_inset Formula $\parallel$
23712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23715 \begin_layout Plain Layout
23723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23726 \begin_layout Plain Layout
23727 \begin_inset Formula $\nparallel$
23741 \begin_inset space \hfill{}
23747 \begin_layout Standard
23748 \begin_inset VSpace medskip
23763 are bigger than the equal looking operators
23778 \begin_layout Standard
23779 Relations are, in contrary to symbols, always surrounded by space.
23782 \begin_layout Standard
23783 Relations with labels can be created with the command
23793 \begin_layout Plain Layout
23804 \begin_layout Standard
23806 \begin_inset Tabular
23807 <lyxtabular version="3" rows="2" columns="2">
23809 <column alignment="center" valignment="top" width="0">
23810 <column alignment="center" valignment="top" width="0">
23812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23815 \begin_layout Plain Layout
23821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23824 \begin_layout Plain Layout
23826 \begin_inset Note Note
23829 \begin_layout Plain Layout
23836 is only used as spacer.
23848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23851 \begin_layout Plain Layout
23858 \begin_layout Plain Layout
23875 \begin_layout Plain Layout
23885 \begin_inset Formula $\downarrow$
23894 \begin_layout Plain Layout
23907 \begin_layout Plain Layout
23921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23924 \begin_layout Plain Layout
23925 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23941 \begin_layout Section
23945 \begin_layout Subsection
23946 Predefined Functions
23947 \begin_inset CommandInset label
23949 name "sub:Predefined-Functions"
23957 \begin_layout Plain Layout
23958 Functions ! predefined
23966 \begin_layout Standard
23967 In general, variables are set
23971 in mathematical expressions, but not function names, because
23972 \begin_inset Formula $sin$
23975 could be misunderstood as
23976 \begin_inset Formula $s\cdot i\cdot n$
23980 Therefore there are predefined functions, that are additionally a bit separated
23982 They are inserted as commands starting with a backslash before their name.
23985 \begin_layout Standard
23987 \begin_inset Tabular
23988 <lyxtabular version="3" rows="2" columns="4">
23990 <column alignment="center" valignment="top" width="0pt">
23991 <column alignment="center" valignment="top" width="0pt">
23992 <column alignment="center" valignment="top" width="0pt">
23993 <column alignment="center" valignment="top" width="0pt">
23995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23998 \begin_layout Plain Layout
24004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24007 \begin_layout Plain Layout
24013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24016 \begin_layout Plain Layout
24022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24025 \begin_layout Plain Layout
24033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24036 \begin_layout Plain Layout
24042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24045 \begin_layout Plain Layout
24046 \begin_inset Formula $Asin(x)+B$
24054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24057 \begin_layout Plain Layout
24065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24068 \begin_layout Plain Layout
24069 \begin_inset Formula $A\sin(x)+B$
24083 \begin_inset Newpage pagebreak
24089 \begin_layout Standard
24090 The following functions are predefined:
24093 \begin_layout Standard
24094 \begin_inset VSpace -2mm
24100 \begin_layout Standard
24102 \begin_inset Tabular
24103 <lyxtabular version="3" rows="9" columns="4">
24105 <column alignment="center" valignment="top" width="0pt">
24106 <column alignment="center" valignment="top" width="0pt">
24107 <column alignment="center" valignment="top" width="0pt">
24108 <column alignment="center" valignment="top" width="0pt">
24110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24113 \begin_layout Plain Layout
24119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24122 \begin_layout Plain Layout
24128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24131 \begin_layout Plain Layout
24137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24140 \begin_layout Plain Layout
24148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24151 \begin_layout Plain Layout
24159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24162 \begin_layout Plain Layout
24170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24173 \begin_layout Plain Layout
24181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24184 \begin_layout Plain Layout
24194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24197 \begin_layout Plain Layout
24205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24208 \begin_layout Plain Layout
24216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24219 \begin_layout Plain Layout
24227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24230 \begin_layout Plain Layout
24240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24243 \begin_layout Plain Layout
24251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24254 \begin_layout Plain Layout
24262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24265 \begin_layout Plain Layout
24273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24276 \begin_layout Plain Layout
24286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24289 \begin_layout Plain Layout
24297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24300 \begin_layout Plain Layout
24308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24311 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24322 \begin_layout Plain Layout
24332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24335 \begin_layout Plain Layout
24343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24346 \begin_layout Plain Layout
24354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24357 \begin_layout Plain Layout
24365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24368 \begin_layout Plain Layout
24378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24381 \begin_layout Plain Layout
24389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24392 \begin_layout Plain Layout
24400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24403 \begin_layout Plain Layout
24411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24414 \begin_layout Plain Layout
24424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24427 \begin_layout Plain Layout
24435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24438 \begin_layout Plain Layout
24446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24449 \begin_layout Plain Layout
24457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24460 \begin_layout Plain Layout
24470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24473 \begin_layout Plain Layout
24481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24484 \begin_layout Plain Layout
24492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24506 \begin_layout Plain Layout
24522 \begin_layout Standard
24523 They can also be inserted with the math toolbar button
24524 \begin_inset Graphics
24525 filename ../images/math/functions.png
24533 \begin_layout Subsection
24534 Self-defined Functions
24538 \begin_layout Plain Layout
24539 Functions ! self-defined
24547 \begin_layout Standard
24548 To use a function that is not predefined, like for example the sign function
24549 sgn(x), there are two possibilities:
24552 \begin_layout Itemize
24553 Define the function by inserting the following line to the LaTeX-preamble
24557 \begin_layout Plain Layout
24562 DeclareMathOperator
24565 \begin_inset CommandInset ref
24567 reference "sub:Self-defined-Operators"
24577 \begin_inset Newline newline
24581 \begin_inset VSpace -3mm
24585 \begin_inset Newline newline
24592 DeclareMathOperator{
24600 \begin_layout Plain Layout
24605 DeclareMathOperator
24611 \begin_inset Newline newline
24615 \begin_inset VSpace -2mm
24619 \begin_inset Newline newline
24622 Now the new defined function can be called with the command
24631 \begin_layout Itemize
24632 Write the the formula as usual, mark the formula name, in our example the
24637 , and change it to mathematical text.
24638 At last a space is inserted between prefactor and function.
24641 \begin_layout Standard
24642 The result is the same with both methods as with a predefined function
24646 \begin_layout Plain Layout
24647 In LyX self-defined functions are displayed red, predefined ones black.
24655 \begin_layout Standard
24657 \begin_inset Tabular
24658 <lyxtabular version="3" rows="3" columns="2">
24660 <column alignment="center" valignment="top" width="0pt">
24661 <column alignment="center" valignment="top" width="0pt">
24663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24666 \begin_layout Plain Layout
24672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24675 \begin_layout Plain Layout
24683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24686 \begin_layout Plain Layout
24694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24697 \begin_layout Plain Layout
24698 \begin_inset Formula $A\sgn(x)+B$
24708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24711 \begin_layout Plain Layout
24715 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24726 \begin_layout Plain Layout
24727 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24743 \begin_layout Standard
24744 The first method is more suitable when the self-defined function should
24745 be used several times.
24748 \begin_layout Subsection
24753 \begin_layout Plain Layout
24762 \begin_layout Standard
24763 For limits there are defined besides
24773 \begin_layout Plain Layout
24793 furthermore the following functions:
24796 \begin_layout Standard
24798 \begin_inset Tabular
24799 <lyxtabular version="3" rows="5" columns="2">
24801 <column alignment="center" valignment="top" width="0">
24802 <column alignment="center" valignment="top" width="0">
24804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24807 \begin_layout Plain Layout
24813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24816 \begin_layout Plain Layout
24818 \begin_inset Note Note
24821 \begin_layout Plain Layout
24828 is only used as spacer.
24840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24843 \begin_layout Plain Layout
24851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24854 \begin_layout Plain Layout
24855 \begin_inset Formula $\varliminf$
24865 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24868 \begin_layout Plain Layout
24876 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24879 \begin_layout Plain Layout
24880 \begin_inset Formula $\varlimsup$
24890 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24893 \begin_layout Plain Layout
24901 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24904 \begin_layout Plain Layout
24905 \begin_inset Formula $\varprojlim$
24915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24918 \begin_layout Plain Layout
24926 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24929 \begin_layout Plain Layout
24930 \begin_inset Formula $\varinjlim$
24934 \begin_inset Formula $\raisebox{-2.5mm}{}$
24950 \begin_layout Standard
24951 \begin_inset VSpace medskip
24954 The limit is created by inserting a subscript.
24955 It is set right beside the function in an inline formula:
24958 \begin_layout Standard
24960 \begin_inset Tabular
24961 <lyxtabular version="3" rows="2" columns="2">
24963 <column alignment="center" valignment="top" width="0pt">
24964 <column alignment="center" valignment="top" width="0pt">
24966 <cell alignment="center" valignment="top" usebox="none">
24969 \begin_layout Plain Layout
24975 <cell alignment="center" valignment="top" usebox="none">
24978 \begin_layout Plain Layout
24979 \begin_inset space \hspace{}
24984 \begin_inset Note Note
24987 \begin_layout Plain Layout
25000 are used here as spacer.
25012 <cell alignment="center" valignment="top" usebox="none">
25015 \begin_layout Plain Layout
25024 \begin_layout Plain Layout
25037 \begin_layout Plain Layout
25051 <cell alignment="center" valignment="top" usebox="none">
25054 \begin_layout Plain Layout
25055 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25071 \begin_layout Standard
25072 In a displayed formula the limit is set below the formula, as usual:
25073 \begin_inset Formula \[
25081 \begin_layout Subsection
25086 \begin_layout Plain Layout
25087 Functions ! modulo-
25095 \begin_layout Standard
25096 The modulo-function is special, because it exists in four variants.
25099 \begin_layout Standard
25100 The variants in a displayed formula:
25101 \begin_inset Formula \begin{align*}
25102 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25103 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25104 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25105 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25106 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25113 \begin_layout Standard
25114 In an inline formula less space is set before the function names for all
25118 \begin_layout Section
25123 \begin_layout Plain Layout
25132 \begin_layout Subsection
25133 Special Characters in Mathematical Text
25136 \begin_layout Standard
25137 The following commands can only be used in mathematical text or in TeX-mode:
25140 \begin_layout Standard
25141 \begin_inset space \hfill{}
25145 \begin_inset Tabular
25146 <lyxtabular version="3" rows="8" columns="2">
25148 <column alignment="block" valignment="top" width="0">
25149 <column alignment="block" valignment="top" width="0">
25151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25154 \begin_layout Plain Layout
25160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25163 \begin_layout Plain Layout
25171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25174 \begin_layout Plain Layout
25182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25185 \begin_layout Plain Layout
25186 \begin_inset Formula $\textrm{œ}$
25196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25199 \begin_layout Plain Layout
25207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25210 \begin_layout Plain Layout
25211 \begin_inset Formula $\textrm{Œ}$
25221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25224 \begin_layout Plain Layout
25232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25235 \begin_layout Plain Layout
25236 \begin_inset Formula $\textrm{æ}$
25246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25249 \begin_layout Plain Layout
25257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25260 \begin_layout Plain Layout
25261 \begin_inset Formula $\textrm{Æ}$
25271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25274 \begin_layout Plain Layout
25282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25285 \begin_layout Plain Layout
25286 \begin_inset Formula $\textrm{\aa}$
25296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25299 \begin_layout Plain Layout
25306 \begin_layout Plain Layout
25310 \begin_layout Plain Layout
25333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25336 \begin_layout Plain Layout
25337 \begin_inset Formula $\textrm{Å}$
25347 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25350 \begin_layout Plain Layout
25358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25361 \begin_layout Plain Layout
25362 \begin_inset Formula $\textrm{ı}$
25376 \begin_inset space \hfill{}
25380 \begin_inset Tabular
25381 <lyxtabular version="3" rows="8" columns="2">
25383 <column alignment="block" valignment="top" width="0">
25384 <column alignment="center" valignment="top" width="0">
25386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25389 \begin_layout Plain Layout
25391 \begin_inset Note Note
25394 \begin_layout Plain Layout
25401 is used for separation, because otherwise the output will be ¡ and ¿ respective
25412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25415 \begin_layout Plain Layout
25423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25426 \begin_layout Plain Layout
25434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25437 \begin_layout Plain Layout
25438 \begin_inset Formula $\textrm{ø}$
25448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25451 \begin_layout Plain Layout
25459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25462 \begin_layout Plain Layout
25463 \begin_inset Formula $\textrm{Ø}$
25473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25476 \begin_layout Plain Layout
25484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25487 \begin_layout Plain Layout
25488 \begin_inset Formula $\textrm{ł}$
25498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25501 \begin_layout Plain Layout
25509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25512 \begin_layout Plain Layout
25513 \begin_inset Formula $\textrm{Ł}$
25523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25526 \begin_layout Plain Layout
25528 \begin_inset space \hspace{}
25536 \begin_layout Plain Layout
25550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25553 \begin_layout Plain Layout
25554 \begin_inset Formula $\textrm{!`}$
25564 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25567 \begin_layout Plain Layout
25569 \begin_inset space \hspace{}
25577 \begin_layout Plain Layout
25591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25594 \begin_layout Plain Layout
25595 \begin_inset Formula $\textrm{?`}$
25605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25608 \begin_layout Plain Layout
25616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25619 \begin_layout Plain Layout
25620 \begin_inset Formula $\textrm{ȷ}$
25634 \begin_inset space \hfill{}
25640 \begin_layout Standard
25642 \begin_inset Formula $\textrm{\textrm{Å}}$
25646 \begin_inset Formula $\textrm{\textrm{Ø}}$
25649 can also be inserted via the math toolbar button
25650 \begin_inset Graphics
25651 filename ../images/math/digamma.png
25659 \begin_layout Standard
25660 An exception are the commands
25663 \begin_inset space \hspace{}
25672 \begin_inset space \hspace{}
25678 , because they can be inserted in LyX directly to text.
25681 \begin_layout Subsection
25683 \begin_inset CommandInset label
25685 name "sub:Accents-in-Text"
25693 \begin_layout Plain Layout
25702 \begin_layout Standard
25703 With the following commands all letters can be accented.
25704 The commands must be inserted in TeX-mode.
25707 \begin_layout Standard
25708 \begin_inset space \hfill{}
25712 \begin_inset Tabular
25713 <lyxtabular version="3" rows="8" columns="2">
25715 <column alignment="block" valignment="top" width="0">
25716 <column alignment="block" valignment="top" width="0">
25718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25721 \begin_layout Plain Layout
25727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25730 \begin_layout Plain Layout
25738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25741 \begin_layout Plain Layout
25745 \begin_inset Quotes grd
25753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25756 \begin_layout Plain Layout
25760 \begin_layout Plain Layout
25776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25779 \begin_layout Plain Layout
25787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25790 \begin_layout Plain Layout
25794 \begin_layout Plain Layout
25810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25813 \begin_layout Plain Layout
25820 \begin_layout Plain Layout
25834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25837 \begin_layout Plain Layout
25841 \begin_layout Plain Layout
25857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25860 \begin_layout Plain Layout
25868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25871 \begin_layout Plain Layout
25875 \begin_layout Plain Layout
25891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25894 \begin_layout Plain Layout
25901 \begin_layout Plain Layout
25915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25918 \begin_layout Plain Layout
25922 \begin_layout Plain Layout
25938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25941 \begin_layout Plain Layout
25948 \begin_layout Plain Layout
25962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25965 \begin_layout Plain Layout
25969 \begin_layout Plain Layout
25985 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25988 \begin_layout Plain Layout
25995 \begin_layout Plain Layout
26009 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26012 \begin_layout Plain Layout
26016 \begin_layout Plain Layout
26036 \begin_inset space \hfill{}
26040 \begin_inset Tabular
26041 <lyxtabular version="3" rows="8" columns="2">
26043 <column alignment="block" valignment="top" width="0">
26044 <column alignment="center" valignment="top" width="0">
26046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26049 \begin_layout Plain Layout
26055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26058 \begin_layout Plain Layout
26066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26069 \begin_layout Plain Layout
26076 \begin_layout Plain Layout
26090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26093 \begin_layout Plain Layout
26097 \begin_layout Plain Layout
26113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26116 \begin_layout Plain Layout
26124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26127 \begin_layout Plain Layout
26131 \begin_layout Plain Layout
26147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26150 \begin_layout Plain Layout
26157 \begin_layout Plain Layout
26168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26171 \begin_layout Plain Layout
26175 \begin_layout Plain Layout
26191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26194 \begin_layout Plain Layout
26202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26205 \begin_layout Plain Layout
26209 \begin_layout Plain Layout
26225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26228 \begin_layout Plain Layout
26235 \begin_layout Plain Layout
26249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26252 \begin_layout Plain Layout
26256 \begin_layout Plain Layout
26272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26275 \begin_layout Plain Layout
26282 \begin_layout Plain Layout
26296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26299 \begin_layout Plain Layout
26303 \begin_layout Plain Layout
26319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26322 \begin_layout Plain Layout
26329 \begin_layout Plain Layout
26343 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26346 \begin_layout Plain Layout
26350 \begin_layout Plain Layout
26370 \begin_inset space \hfill{}
26376 \begin_layout Standard
26377 \begin_inset VSpace medskip
26386 also two different characters can be accented.
26395 \begin_layout Plain Layout
26410 \begin_layout Plain Layout
26422 \begin_layout Standard
26435 can in combination with vowels directly be inserted with the keyboard without
26437 The same applies for the tilde
26441 \begin_layout Plain Layout
26442 This only applies for keyboards where the tilde is defined as accent.
26451 in combination with
26466 \begin_layout Standard
26509 , and accents inserted directly with the keyboard are also available in
26511 For the other accents there are special math commands to be used in formulas,
26513 \begin_inset CommandInset ref
26515 reference "sub:Accents-for-one"
26522 \begin_layout Standard
26523 \begin_inset VSpace bigskip
26526 Furthermore, with the command
26536 \begin_layout Plain Layout
26544 all numbers and letters can be set into a circle, quasi accented with a
26545 circle, similar to the the copyright symbol.
26548 \begin_layout Standard
26550 \begin_inset Tabular
26551 <lyxtabular version="3" rows="3" columns="2">
26553 <column alignment="center" valignment="top" width="0">
26554 <column alignment="center" valignment="top" width="0">
26556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26559 \begin_layout Plain Layout
26565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26568 \begin_layout Plain Layout
26570 \begin_inset Note Note
26573 \begin_layout Plain Layout
26580 is only used as spacer.
26592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26595 \begin_layout Plain Layout
26603 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26606 \begin_layout Plain Layout
26610 \begin_layout Plain Layout
26626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26629 \begin_layout Plain Layout
26640 raisebox{-1.5pt}{W}}
26645 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26648 \begin_layout Plain Layout
26649 \begin_inset Formula $\raisebox{4.5mm}{}$
26656 \begin_layout Plain Layout
26674 \begin_inset Formula $\raisebox{-2mm}{}$
26690 \begin_layout Standard
26691 One has to take care that the character fits in the circle.
26702 \begin_layout Plain Layout
26704 \begin_inset CommandInset ref
26706 reference "sub:Font-Sizes"
26715 specifies thereby the size of the circle.
26726 \begin_layout Plain Layout
26728 \begin_inset CommandInset ref
26730 reference "sub:Boxes-without-Frame"
26739 the character can be centered.
26742 \begin_layout Subsection
26747 \begin_layout Plain Layout
26756 \begin_layout Standard
26757 Minuscule numbers are created with the command
26767 \begin_layout Plain Layout
26776 The command can be used in formulas and in TeX-mode.
26777 The command scheme is:
26780 \begin_layout Standard
26785 oldstylenums{number}
26788 \begin_layout Standard
26793 oldstylenums{0123456789
26796 \begin_inset Formula $\oldstylenums{0123456789}$
26802 \begin_layout Subsection
26803 Miscellaneous Special Characters
26804 \begin_inset CommandInset label
26806 name "sub:Miscellaneous-Special-Characters"
26814 \begin_layout Plain Layout
26815 Special characters ! miscellaneous
26823 \begin_layout Standard
26824 The following characters can only be inserted to formulas by using commands:
26827 \begin_layout Standard
26829 \begin_inset Tabular
26830 <lyxtabular version="3" rows="4" columns="2">
26832 <column alignment="center" valignment="top" width="0">
26833 <column alignment="center" valignment="top" width="0">
26835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26838 \begin_layout Plain Layout
26844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26847 \begin_layout Plain Layout
26855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26858 \begin_layout Plain Layout
26865 \begin_layout Plain Layout
26879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26882 \begin_layout Plain Layout
26883 \begin_inset Formula $\mathcircumflex$
26893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26896 \begin_layout Plain Layout
26904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26907 \begin_layout Plain Layout
26908 \begin_inset Formula $\_$
26918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26921 \begin_layout Plain Layout
26926 \begin_layout Plain Layout
26941 \begin_layout Plain Layout
26952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26955 \begin_layout Plain Layout
26956 \begin_inset Formula $^{\circ}$
26972 \begin_layout Standard
26973 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
26974 contains the following line
26978 \begin_layout Plain Layout
26979 More about this is described in
26980 \begin_inset CommandInset ref
26982 reference "sub:Text-Characters-in"
26994 \begin_layout Standard
26999 DeclareInputtext{176}{
27012 \begin_layout Section
27014 \begin_inset CommandInset label
27016 name "sec:Formula-Styles"
27024 \begin_layout Plain Layout
27033 \begin_layout Itemize
27034 There are two different alignment styles:
27038 \begin_layout Description
27039 Centered is the predefined standard
27042 \begin_layout Description
27043 Indented for this the option
27047 must be inserted in the menu
27049 Document\SpecialChar \menuseparator
27055 \begin_inset space ~
27061 \begin_layout Standard
27066 is used, the indentation can be adjusted with the length
27076 \begin_layout Plain Layout
27085 Should the distance be 15
27086 \begin_inset space \thinspace{}
27089 mm, the following command line is inserted in the LaTeX-preamble
27092 \begin_layout Standard
27102 \begin_layout Standard
27103 When no length is specified, the predefined value of 30
27104 \begin_inset space \thinspace{}
27111 \begin_layout Itemize
27112 And two different numbering styles:
27116 \begin_layout Description
27117 Right is the predefined standard
27120 \begin_layout Description
27121 Left for this the option
27125 must be inserted in the menu
27127 Document\SpecialChar \menuseparator
27133 \begin_inset space ~
27140 \begin_layout Standard
27149 can also be used together.
27150 In this case both options are inserted, separated by a comma.
27153 \begin_layout Standard
27154 The chosen styles are used for all displayed formulas of the document.
27155 When both, centered and indented formulas should be created in a document,
27161 The indented formulas are then set in a flalign environment, see
27162 \begin_inset CommandInset ref
27164 reference "sub:Flalign-Environment"
27171 \begin_layout Section
27173 \begin_inset CommandInset label
27175 name "sec:Multiline-Formulas"
27183 \begin_layout Plain Layout
27184 Formula ! multiline
27192 \begin_layout Subsection
27196 \begin_layout Standard
27197 In LyX multiline formulas are created by pressing
27204 This creates either an
27206 eqnarray environment
27208 that is described in
27209 \begin_inset CommandInset ref
27211 reference "sub:Eqnarray-Environment"
27215 or, when the option
27217 Use AMS math package
27219 in the document settings is selected, an
27223 that is described in
27224 \begin_inset CommandInset ref
27226 reference "sub:Standard-align-Environment"
27233 \begin_layout Standard
27234 There are other multiline formula environments that can be created via the
27237 Insert\SpecialChar \menuseparator
27241 These environments are described in the following sections.
27244 \begin_layout Standard
27245 In all multiline formula environments a new line is created by pressing
27251 To add or delete lines, the math toolbar buttons
27252 \begin_inset Graphics
27253 filename ../images/tabular-feature_append-row.png
27259 \begin_inset Graphics
27260 filename ../images/tabular-feature_delete-row.png
27265 , respectively, or the menu
27267 Edit\SpecialChar \menuseparator
27273 \begin_layout Subsubsection
27275 \begin_inset CommandInset label
27277 name "sub:Line-Separation"
27285 \begin_layout Plain Layout
27286 Formula ! multiline ! Line separation
27294 \begin_layout Standard
27295 There is sometimes not enough space in multiline formulas between the lines:
27296 \begin_inset Formula \begin{eqnarray*}
27297 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}\\
27298 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*}
27305 \begin_layout Standard
27306 In LaTeX additional line space is specified as optional argument of the
27308 This is not yet possible in LyX
27312 \begin_layout Plain Layout
27314 \begin_inset CommandInset href
27316 name "LyX-bug #1505"
27317 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27326 , therefore the whole formula must be inserted in TeX-mode.
27327 To add in our example space, the command
27335 is inserted at the end of the first line.
27340 \begin_layout Plain Layout
27347 \begin_layout Plain Layout
27349 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27352 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27359 \begin_layout Plain Layout
27363 left(B^{2}+x_{0}^{2}
27371 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27376 \begin_layout Plain Layout
27388 \begin_layout Standard
27389 \begin_inset VSpace bigskip
27392 To set the the line separation for all lines in a formula, the length
27402 \begin_layout Plain Layout
27412 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27423 \begin_inset space \thinspace{}
27428 \begin_inset space \thinspace{}
27431 mm additional line separation as in the previous example, the command
27434 \begin_layout Standard
27444 \begin_layout Standard
27445 is inserted in TeX-mode before the formula.
27446 This requires that the LaTeX-package
27454 \begin_layout Plain Layout
27459 is part of every LaTeX standard installation.
27468 \begin_layout Plain Layout
27474 was loaded in LaTeX-preamble with the line
27477 \begin_layout Standard
27485 \begin_layout Standard
27490 \begin_layout Plain Layout
27502 \begin_inset Formula \begin{eqnarray*}
27503 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}\\
27504 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*}
27511 \begin_layout Standard
27515 \begin_layout Plain Layout
27526 To get back to the predefined distance,
27532 is set to the value 3
27533 \begin_inset space \thinspace{}
27539 \begin_layout Subsubsection
27541 \begin_inset CommandInset label
27543 name "sub:Column-Separation"
27551 \begin_layout Plain Layout
27552 Formula ! multiline ! Column separation
27560 \begin_layout Standard
27561 Multiline formulas form a matrix.
27562 A formula in the eqnarray environment is for example a matrix with three
27564 By changing the column separation in this environment, the space beside
27565 the relation sign can be changed.
27568 \begin_layout Standard
27569 The column separation is specified with the length
27579 \begin_layout Plain Layout
27588 \begin_inset Newline newline
27591 column separation = 2
27592 \begin_inset space \thinspace{}
27602 \begin_inset Newline newline
27608 \begin_layout Standard
27618 \begin_layout Standard
27619 inserted in TeX-mode, sets for all following formulas a column separation
27621 \begin_inset space \thinspace{}
27625 To get back to the predefined distance,
27632 \begin_inset space \thinspace{}
27638 \begin_layout Standard
27640 \begin_inset space \thinspace{}
27643 cm column separation:
27647 \begin_layout Plain Layout
27659 \begin_inset Formula \begin{eqnarray*}
27661 C & \ne & A\end{eqnarray*}
27665 A formula with the predefined column separation for matrices of 10
27666 \begin_inset space \thinspace{}
27673 \begin_layout Plain Layout
27685 \begin_inset Formula \begin{eqnarray*}
27687 C & \ne & A\end{eqnarray*}
27694 \begin_layout Subsubsection
27699 \begin_layout Plain Layout
27708 \begin_layout Standard
27709 Long formulas can be typeset using these methods:
27712 \begin_layout Itemize
27713 When one side of the equation is much shorther than the line width, this
27714 one is chosen for the left side and the right side is typeset over two
27719 \begin_layout Plain Layout
27729 \begin_inset Formula \begin{eqnarray}
27730 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 \\
27731 & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:kurzlang}\end{eqnarray}
27739 \begin_layout Plain Layout
27749 \begin_inset Newline newline
27752 The minus sign at the beginning of the second line does normally not appear
27753 as operator because it is the first character of the line.
27754 Thus it would not be surrounded by space and could not be distinguished
27755 from the fraction bar.
27756 To avoid this, space was inserted behind the minus sign with the command
27767 \begin_layout Plain Layout
27775 \begin_inset CommandInset ref
27777 reference "sub:Variable-Space"
27790 \begin_layout Plain Layout
27801 \begin_layout Itemize
27802 When both sides of the equation are too long, the command
27812 \begin_layout Plain Layout
27821 It is inserted to the first column of the first line and effects that all
27822 further insertions overwrite the following columns:
27826 \begin_layout Plain Layout
27836 \begin_inset Formula \begin{eqnarray}
27837 \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 \\
27838 & & -\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 \\
27839 & & =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}
27847 \begin_layout Plain Layout
27857 \begin_inset Newline newline
27860 After the insertion of
27866 , the cursor is in a purple box that is a bit shifted to the left from the
27868 In this the formula is inserted.
27872 \begin_layout Plain Layout
27882 \begin_inset Newline newline
27885 The content of the further lines is inserted to the second or another formula
27887 The greater the column number where it was inserted, the larger the indentation.
27891 \begin_layout Plain Layout
27901 \begin_inset Newline newline
27905 \begin_inset Note Greyedout
27908 \begin_layout Plain Layout
27909 Note the following when using
27918 \begin_layout Itemize
27919 The formula doesn't use the full page width.
27921 \begin_inset space \thinspace{}
27925 \begin_inset space ~
27929 \begin_inset Formula $-B^{2}$
27932 is added to the first line in the above example, it would have been outside
27934 To better use the width, negative space can be inserted at the beginning
27938 \begin_layout Itemize
27939 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27944 \begin_layout Plain Layout
27945 \begin_inset CommandInset href
27947 name "LyX-bug #1429"
27948 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
27957 One can only set the cursor at the beginning of the line and move it with
27966 \begin_layout Itemize
27967 Other methods to set long formulas are offered by the environments described
27969 \begin_inset CommandInset ref
27971 reference "sub:Multline-Environment"
27976 \begin_inset CommandInset ref
27978 reference "sub:Multiline-Formula-Parts"
27985 \begin_layout Subsubsection
27987 \begin_inset CommandInset label
27989 name "sub:Multiline-Brackets"
27997 \begin_layout Plain Layout
27998 Brackets ! for multiline expressions
28006 \begin_layout Standard
28007 For brackets spanning multiple lines the following problem occurs:
28008 \begin_inset Formula \begin{eqnarray*}
28009 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28010 & & \left.\cdots+B-D\right]\end{eqnarray*}
28017 \begin_layout Standard
28018 The closing bracket is smaller than the opening bracket because brackets
28019 with variable size may not span multiple lines.
28022 \begin_layout Standard
28023 To set the bracket size for the second line correctly, the first line is
28034 \begin_layout Plain Layout
28042 and the second line with
28050 \begin_layout Plain Layout
28064 \begin_inset CommandInset ref
28066 reference "sub:Automatic-Bracket-Size"
28081 \begin_layout Plain Layout
28107 \begin_layout Plain Layout
28126 \begin_layout Plain Layout
28145 \begin_layout Plain Layout
28157 \begin_inset Formula $\downarrow$
28166 \begin_layout Plain Layout
28174 is inserted, because the multiplication operator with its limits is the
28175 largest symbol in the first line and this should be the size for the bracket
28176 in the second line.
28179 \begin_layout Standard
28180 The result is this:
28181 \begin_inset Formula \begin{eqnarray*}
28182 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28183 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28190 \begin_layout Subsection
28194 \begin_layout Standard
28195 Align environments can be used for every kind of multiline formulas.
28196 They are specially useful to set several formulas side by side.
28199 \begin_layout Standard
28200 Align environments consist of columns.
28201 The odd columns are right aligned, the even ones left aligned.
28202 Every line in an Align environment can be numbered.
28205 \begin_layout Standard
28206 Align environments are created via the menu
28208 Insert\SpecialChar \menuseparator
28214 Edit\SpecialChar \menuseparator
28215 Math\SpecialChar \menuseparator
28216 Change Formula Type
28218 already existing formulas can be converted to Align environments.
28221 \begin_layout Standard
28222 To add or delete columns, the math toolbar buttons
28223 \begin_inset Graphics
28224 filename ../images/tabular-feature_append-column.png
28230 \begin_inset Graphics
28231 filename ../images/tabular-feature_delete-column.png
28236 , respectively, or the menu
28238 Edit\SpecialChar \menuseparator
28244 \begin_layout Subsubsection
28245 Standard align Environment
28246 \begin_inset CommandInset label
28248 name "sub:Standard-align-Environment"
28256 \begin_layout Plain Layout
28257 Formula ! multiline ! align environment
28265 \begin_layout Standard
28266 This Align environment is created by presssing
28270 in a formula or by the menu
28272 Insert\SpecialChar \menuseparator
28273 Math\SpecialChar \menuseparator
28274 AMS align Environment
28279 \begin_layout Standard
28280 An example for two formulas set side by side, that are created with a four
28281 column align environment:
28282 \begin_inset Formula \begin{align*}
28283 A & =\sin(B) & C & =D\\
28284 C & \ne A & B & \ne D\end{align*}
28288 As it can be seen, the formulas in this environment are placed so as if
28297 \begin_layout Plain Layout
28305 \begin_inset CommandInset ref
28307 reference "sub:Variable-Space"
28318 before the first and after every even column.
28319 When the formula style
28325 \begin_layout Plain Layout
28327 \begin_inset CommandInset ref
28329 reference "sec:Formula-Styles"
28340 is used, the formula is set without the
28346 before the first column.
28349 \begin_layout Subsubsection
28350 Alignat Environment
28354 \begin_layout Plain Layout
28355 Formula ! multiline ! alignat environment
28363 \begin_layout Standard
28364 The alignat environment has no predefined column separation.
28365 It can be inserted manually with the spaces that are described
28366 \begin_inset CommandInset ref
28368 reference "sub:Space"
28375 \begin_layout Standard
28376 The above example in the alignat environment where 1
28377 \begin_inset space \thinspace{}
28380 cm space was inserted at the beginning of the second formula:
28381 \begin_inset Formula \begin{alignat*}{2}
28382 A & =\sin(B) & \hspace{1cm}C & =D\\
28383 C & \ne A & B & \ne D\end{alignat*}
28387 Because the column separation can be set separately for every column, this
28388 environment is especially suitable to set three and more formulas side
28392 \begin_layout Subsubsection
28393 Flalign Environment
28394 \begin_inset CommandInset label
28396 name "sub:Flalign-Environment"
28404 \begin_layout Plain Layout
28405 Formula ! multiline ! flalign environment
28413 \begin_layout Standard
28414 In this environment the first two columns are always set as much as possible
28415 to the left and the last two ones to the right.
28417 \begin_inset Formula \begin{flalign*}
28418 A & =1 & B & =2 & C & =3\\
28419 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28426 \begin_layout Standard
28427 By creating a flalign environment with an odd number of columns where an
28428 empty TeX-brace is inserted to the last column, several formulas in a document
28429 can be set to the left, although the formula style
28434 As example the indented formula
28435 \begin_inset CommandInset ref
28437 reference "eq:VolInt"
28442 \begin_inset Formula \begin{flalign}
28443 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28447 The first two columns contain the formula.
28448 To indent it as with the formula style
28453 \begin_inset space \thinspace{}
28456 pt space was inserted at the beginning of the first column.
28459 \begin_layout Subsection
28460 Eqnarray Environment
28461 \begin_inset CommandInset label
28463 name "sub:Eqnarray-Environment"
28471 \begin_layout Plain Layout
28472 Formula ! multiline ! eqnarray environment
28480 \begin_layout Standard
28481 When this environment has been created, three blue boxes appear.
28482 The content of the first box is right aligned, the content of the last
28484 The content of the middle box appears centered and a bit smaller, because
28485 it is designed to insert there only relation characters.
28486 \begin_inset Formula \begin{eqnarray*}
28487 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28489 A & = & A\end{eqnarray*}
28496 \begin_layout Subsection
28501 \begin_layout Plain Layout
28502 Formula ! multiline ! gather environment
28510 \begin_layout Standard
28511 This environment consists of only one centered column.
28512 Every line can be numbered.
28513 \begin_inset Formula \begin{gather}
28515 X=\textrm{-}1\end{gather}
28522 \begin_layout Subsection
28523 Multline Environment
28524 \begin_inset CommandInset label
28526 name "sub:Multline-Environment"
28534 \begin_layout Plain Layout
28535 Formula ! multiline ! multline environment
28543 \begin_layout Standard
28544 The multline environment consists, like the gather environment, of only
28546 But the first line is left aligned, the last one right aligned.
28547 All other lines are centered.
28548 Therefore this environment is suitable for long formulas.
28550 \begin_inset CommandInset ref
28552 reference "eq:lefteqn"
28556 in the multline environment:
28557 \begin_inset Formula \begin{multline}
28558 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}\\
28559 -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}\\
28560 =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}
28567 \begin_layout Standard
28568 In the output only the last (first) line of a multline environment appears
28569 numbered when the document numbering is right (left).
28573 \begin_layout Plain Layout
28574 numbering styles see
28575 \begin_inset CommandInset ref
28577 reference "sec:Formula-Styles"
28589 \begin_layout Standard
28598 \begin_layout Plain Layout
28616 \begin_layout Plain Layout
28626 a centered line can be right or left aligned, respectively.
28627 The commands are used as follows:
28630 \begin_layout Standard
28635 shoveright{line content}
28641 shoveleft{line content}
28644 \begin_layout Standard
28645 \begin_inset VSpace medskip
28656 \begin_layout Plain Layout
28666 specifies the distance of the first line from the left page margin.
28667 Predefined is the length 0
28668 \begin_inset space \thinspace{}
28674 \begin_layout Standard
28675 As example the above formula where the command
28678 \begin_layout Standard
28688 \begin_layout Standard
28689 was inserted in TeX-mode before:
28693 \begin_layout Plain Layout
28705 \begin_inset Formula \begin{multline}
28706 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}\\
28707 \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}}\\
28708 =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}
28716 \begin_layout Plain Layout
28727 The second line was left aligned using
28736 \begin_layout Subsection
28737 Multiline Formula Parts
28738 \begin_inset CommandInset label
28740 name "sub:Multiline-Formula-Parts"
28748 \begin_layout Plain Layout
28749 Formula ! multiline ! formula parts
28757 \begin_layout Standard
28758 To display only parts of a formula with multiple lines, one of the following
28759 environments are used:
28776 They can be inserted via the menu
28778 Insert\SpecialChar \menuseparator
28781 or by using the commands described in this section.
28784 \begin_layout Standard
28785 The first three have the same properties as the corresponding multiline
28786 formula environments, but it is possible to set further formula parts beside
28789 \begin_inset Formula \[
28790 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28791 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28792 \right\} \textrm{Uncertainty relations}\]
28799 \begin_layout Standard
28800 To get this formula, a displayed formula is created where the command
28808 \begin_layout Plain Layout
28819 A purple box appears around the blue formula box where now columns and
28820 lines can be added.
28821 Outside the multiline environment other formula parts can be set, like
28825 \begin_layout Standard
28826 The aligned environment is also suitable for long formulas whose lines are
28827 horizontally aligned.
28828 Using aligned in a displayed formula has the advantage that the formula
28829 number is vertically centered behind the lines.
28831 \begin_inset CommandInset ref
28833 reference "eq:kurzlang"
28837 in the aligned environment:
28838 \begin_inset Formula \begin{equation}
28839 \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}|}\\
28840 & -\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}
28848 \begin_layout Standard
28849 To use the environments
28871 \begin_layout Plain Layout
28889 \begin_layout Plain Layout
28907 \begin_layout Plain Layout
28915 are inserted, respectively.
28916 The split environment has the same properties as the aligned environment
28917 but it can only have two columns.
28920 \begin_layout Subsection
28921 Text in multiline Formulas
28922 \begin_inset CommandInset label
28924 name "sub:Text-in-multiline"
28932 \begin_layout Plain Layout
28942 \begin_layout Plain Layout
28943 Formula ! multiline ! text
28951 \begin_layout Standard
28952 In the Align environments, and the multline and gather environment, text
28953 can be inserted that will appear in a separate line and doesn't affect
28954 the column alignment.
28955 To do this, the command
28963 \begin_layout Plain Layout
28973 is used in the following scheme:
28976 \begin_layout Standard
28984 \begin_layout Standard
28985 The text should not be longer than a line because it cannot be hyphenated.
28986 As LyX doesn't yet support
28992 directly, the text is written as mathematical text.
28999 must hereby be at the beginning of a line and appears in the output above
29001 An example where the text was inserted at the beginning of the second line:
29002 \begin_inset Formula \begin{align}
29003 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29004 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29011 \begin_layout Section
29016 \begin_layout Plain Layout
29026 \begin_layout Plain Layout
29027 Formula ! numbering|see
29031 \begin_layout Plain Layout
29042 \begin_layout Plain Layout
29057 \begin_layout Subsection
29061 \begin_layout Standard
29062 Numbered formulas can be created with the menu
29064 Insert\SpecialChar \menuseparator
29065 Math\SpecialChar \menuseparator
29067 \begin_inset space ~
29075 \begin_inset space ~
29081 Existing formulas can be numbered with the menu
29083 Edit\SpecialChar \menuseparator
29084 Math\SpecialChar \menuseparator
29086 \begin_inset space ~
29094 \begin_inset space ~
29100 The formula number is displayed in LyX behind the formula as number sign
29102 The number sign is replaced in the output by the formula number.
29105 \begin_layout Standard
29106 When numbering is turned on in multiline formulas, all lines will be numbered.
29107 But the numbering can be controlled with the menu
29109 Edit\SpecialChar \menuseparator
29110 Math\SpecialChar \menuseparator
29112 \begin_inset space ~
29116 \begin_inset space ~
29120 \begin_inset space ~
29128 \begin_inset space ~
29136 \begin_layout Standard
29137 Except of inline formulas, all formulas can be numbered with two different
29139 \begin_inset CommandInset ref
29141 reference "sec:Formula-Styles"
29148 \begin_layout Subsection
29150 \begin_inset CommandInset label
29152 name "sub:Cross-References"
29160 \begin_layout Plain Layout
29161 Cross-references ! to formulas
29169 \begin_layout Standard
29170 All labeled formulas can be cross-referenced.
29171 A label is added by the menu
29173 Insert\SpecialChar \menuseparator
29176 or the toolbar button
29177 \begin_inset Graphics
29178 filename ../images/label-insert.png
29184 The cursor must hereby be inside a displayed formula.
29185 A dialog pops up displaying the prefix
29190 The label is inserted there behind the prefix.
29191 The predefined prefix means
29192 \begin_inset Quotes eld
29196 \begin_inset Quotes erd
29199 and makes it easier to find labels in large documents because it marks
29200 it as formula label to divide it from e.
29201 \begin_inset space \thinspace{}
29205 \begin_inset space ~
29209 To change a label, the menu
29211 Insert\SpecialChar \menuseparator
29217 \begin_layout Standard
29218 The name of the label is displayed in LyX within two parentheses behind
29220 A formula with a label is always numbered.
29223 \begin_layout Standard
29224 Cross-references are inserted via the menu
29226 Insert\SpecialChar \menuseparator
29229 or with the toolbar button
29230 \begin_inset Graphics
29231 filename ../images/dialog-show-new-inset_ref.png
29237 A formula cross-reference appears in the output as formula number.
29238 When in the cross-reference dialog window the format
29242 is chosen, the cross-reference appears in the output as formula number
29244 \begin_inset Newline newline
29247 By right-clicking on a cross-reference in LyX, one jumps to the formula
29248 that is referenced.
29251 \begin_layout Standard
29252 Here are as examples cross-references to formulas of the following subsections:
29253 \begin_inset Note Note
29256 \begin_layout Plain Layout
29257 Note the different cross-reference types.
29265 \begin_layout Standard
29267 \begin_inset CommandInset ref
29274 \begin_inset CommandInset ref
29282 \begin_inset CommandInset ref
29288 ) big Latin letters are used for the numbering in contrary to (
29289 \begin_inset CommandInset ref
29298 \begin_layout Standard
29299 \begin_inset VSpace medskip
29302 When the argument of
29310 \begin_layout Plain Layout
29318 \begin_inset CommandInset ref
29320 reference "sub:User-defined-Numbering"
29331 contains a box like in
29332 \begin_inset CommandInset ref
29334 reference "sub:Paragraph-Boxes"
29338 , the formula cannot be referenced.
29341 \begin_layout Subsection
29346 \begin_layout Plain Layout
29347 Formula numbering ! subnumbering
29355 \begin_layout Standard
29356 With the help of the commands
29360 begin{subequations}
29368 formulas can be subnumbered.
29369 Both commands are inserted in TeX-mode.
29372 \begin_layout Standard
29374 \begin_inset Formula \begin{equation}
29375 A=C-B\label{eq:a}\end{equation}
29383 \begin_layout Plain Layout
29387 addtocounter{equation}{-1}
29396 \begin_layout Plain Layout
29400 begin{subequations}
29406 \begin_inset VSpace -5mm
29410 \begin_inset Formula \begin{equation}
29411 B=C-A\label{eq:b}\end{equation}
29416 \begin_inset Formula \begin{equation}
29417 C=A+B\label{eq:c}\end{equation}
29424 \begin_layout Standard
29428 \begin_layout Plain Layout
29440 \begin_layout Standard
29441 To create the example, the following is done:
29444 \begin_layout Enumerate
29445 first formula is inserted
29448 \begin_layout Enumerate
29453 addtocounter{equation}{-1}
29455 begin{subequations}
29459 \begin_layout Plain Layout
29468 \begin_inset Newline newline
29473 is inserted after the first formula
29476 \begin_layout Enumerate
29477 second formula is inserted
29480 \begin_layout Enumerate
29481 third formula is inserted
29484 \begin_layout Enumerate
29491 is inserted after the third formula
29494 \begin_layout Standard
29495 Every formula between the commands
29507 is subnumbered as a, b,
29508 \begin_inset Newline linebreak
29511 c, \SpecialChar \ldots{}
29512 For multiline formulas every line will be subnumbered.
29513 All subnumbered formulas are treated as
29518 But as every numbered formula increases the counter
29522 by one, the command
29528 is needed to decrease it.
29529 Otherwise the formulas
29530 \begin_inset CommandInset ref
29537 \begin_inset CommandInset ref
29544 \begin_inset CommandInset ref
29550 would be numbered as
29551 \begin_inset CommandInset ref
29558 \begin_inset CommandInset ref
29565 \begin_inset CommandInset ref
29574 \begin_layout Standard
29575 By inserting the commands in TeX-mode, a space is created between the first
29578 \begin_inset space \thinspace{}
29581 mm vertical space is inserted after the command
29585 begin{subequations}
29588 When the formula style
29594 \begin_layout Plain Layout
29596 \begin_inset CommandInset ref
29598 reference "sec:Formula-Styles"
29610 \begin_inset space \thinspace{}
29613 mm space is inserted instead.
29616 \begin_layout Standard
29617 Here is an example for a multiline formula where the numbering was turned
29618 off for the second line:
29622 \begin_layout Plain Layout
29626 begin{subequations}
29632 \begin_inset Formula \begin{eqnarray}
29633 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29634 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29635 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29643 \begin_layout Plain Layout
29655 \begin_layout Subsection
29656 User-defined Numbering
29657 \begin_inset CommandInset label
29659 name "sub:User-defined-Numbering"
29667 \begin_layout Plain Layout
29668 Formula numbering ! user-defined
29676 \begin_layout Standard
29680 \begin_layout Plain Layout
29681 Formula numbering ! self-defined delimiters
29686 With the standard numbering parentheses are set around the formula number.
29687 To replace the parentheses for example by vertical bars, the following
29688 line is added to the LaTeX-preamble:
29691 \begin_layout Standard
29703 \begin_inset Note Note
29706 \begin_layout Plain Layout
29707 This macro is already declared in the LaTeX-preamble for testing.
29708 To activate it, remove the percent sign at the beginning.
29716 \begin_layout Standard
29717 To use other characters, the vertical bars besides the
29721 are replaced by one ore more characters.
29722 To get only the formula number the vertical bars are omitted.
29725 \begin_layout Standard
29726 \begin_inset VSpace bigskip
29729 When there should be an expression of your choice instead of the consecutive
29730 formula number in parentheses behind the formula, the command
29740 \begin_layout Plain Layout
29749 \begin_inset Formula \begin{equation}
29750 A+B=C\tag{something}\label{eq:tag}\end{equation}
29754 In this example the command
29762 \begin_layout Plain Layout
29773 was inserted to the formula.
29776 \begin_layout Standard
29785 \begin_layout Plain Layout
29796 is inserted instead, the star prevents the parentheses around the expression:
29797 \begin_inset Formula \[
29798 A+B=C\tag*{something}\]
29805 \begin_layout Standard
29806 \begin_inset VSpace bigskip
29809 To restart the formula numbering with new document parts or sections, the
29810 following command is used:
29813 \begin_layout Standard
29818 @addtoreset{equation}{part}
29824 \begin_layout Plain Layout
29829 \begin_layout Plain Layout
29840 \begin_layout Plain Layout
29853 \begin_layout Plain Layout
29864 \begin_layout Plain Layout
29877 \begin_inset Newline newline
29881 \begin_inset Newline newline
29888 @addtoreset{equation}{section}
29891 \begin_layout Standard
29892 To be able to use these commands in TeX-mode, the
29893 \begin_inset Quotes eld
29897 \begin_inset Quotes erd
29900 character has to be made
29901 \begin_inset Quotes eld
29905 \begin_inset Quotes erd
29908 for LaTeX using the command
29922 So the command sequence in TeX-mode is:
29925 \begin_layout Standard
29931 \begin_inset Newline newline
29936 @addtoreset{equation}{section}
29937 \begin_inset Newline newline
29945 \begin_layout Standard
29946 In the LaTeX-preamble
29958 can be omitted as they are automatically internally inserted by LyX.
29961 \begin_layout Standard
29976 \begin_layout Plain Layout
29981 is part of the LaTeX-package
29989 \begin_layout Plain Layout
29990 Packages ! carlisle
29995 that is part of every LaTeX standard installation.
30004 \begin_layout Plain Layout
30005 Packages ! remreset
30010 has to be loaded in the LaTeX-preamble with the line
30013 \begin_layout Standard
30018 usepackage{remreset}
30021 \begin_layout Standard
30032 \begin_layout Plain Layout
30037 \begin_layout Plain Layout
30048 \begin_layout Plain Layout
30061 \begin_layout Plain Layout
30072 \begin_layout Plain Layout
30084 can be used with the same scheme as
30093 \begin_layout Standard
30094 \begin_inset VSpace bigskip
30097 Sometimes formulas should be numbered in the following form:
30100 \begin_layout Standard
30103 (section number.formula number)
30106 \begin_layout Standard
30107 The formula number should start with every section with
30108 \begin_inset Quotes eld
30112 \begin_inset Quotes erd
30118 \begin_layout Standard
30119 For this case there is the command
30129 \begin_layout Plain Layout
30137 , which is used with the following scheme:
30140 \begin_layout Standard
30145 numberwithin{counter}{sectioning}
30148 \begin_layout Standard
30149 Counter denotes what kind of numbering is affected, sectioning denotes what
30150 number is before the dot.
30153 \begin_layout Standard
30154 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30157 \begin_layout Standard
30162 numberwithin{equation}{section}
30165 \begin_layout Standard
30166 This is the result:
30170 \begin_layout Plain Layout
30174 numberwithin{equation}{section}
30180 \begin_inset Formula \begin{equation}
30181 A+B=C\end{equation}
30188 \begin_layout Standard
30190 \begin_inset space \thinspace{}
30194 \begin_inset space ~
30197 tables so that the number of the part is the sectioning,
30198 \begin_inset Newline newline
30205 numberwithin{table}{part}
30210 \begin_layout Standard
30211 To go back to the standard numbering or to prevent this kind of numbering
30212 when it is defined by the document class, the following command is inserted
30213 as TeX-Code or to the LaTeX-preamble:
30216 \begin_layout Standard
30229 \begin_layout Plain Layout
30243 \begin_layout Plain Layout
30259 \begin_inset Newline newline
30267 \begin_inset Newline newline
30279 \begin_layout Standard
30286 uses internally the command
30292 , described above, that also needs to be reverted.
30296 \begin_layout Plain Layout
30303 \begin_layout Plain Layout
30307 @removefromreset{equation}{section}
30310 \begin_layout Plain Layout
30322 \begin_layout Subsection
30323 Numbering with Roman Numbers and Letters
30324 \begin_inset CommandInset label
30326 name "sub:Numbering-with-Roman"
30334 \begin_layout Plain Layout
30335 Formula numbering ! with letters
30344 \begin_layout Plain Layout
30345 Formula numbering ! with Roman numbers
30353 \begin_layout Standard
30354 Formulas can also be numbered with Roman numbers and Latin letters.
30355 To number for example with small Roman numbers, the command
30358 \begin_layout Standard
30370 \begin_layout Standard
30371 is inserted before the formula in TeX-mode.
30382 \begin_layout Plain Layout
30390 redefines the predefined command
30406 \begin_layout Plain Layout
30413 has the same scheme like the command
30419 that is described in
30420 \begin_inset CommandInset ref
30422 reference "sec:User-defined-commands"
30436 is the formula counter.
30443 is used as prefix for a counter, the value of the counter is output as
30445 When a formula is numbered, LaTeX sets internally the command
30451 behind the formula.
30460 \begin_layout Plain Layout
30470 outputs the counter as small Roman number.
30473 \begin_layout Standard
30474 All formulas behind the command
30484 are now numbered Roman.
30485 To switch to numbering with big Roman numbers, the command is inserted
30502 \begin_layout Plain Layout
30514 \begin_inset Quotes eld
30518 \begin_inset Quotes erd
30521 with small Latin letters there is the command
30531 \begin_layout Plain Layout
30539 , for big ones there is the command
30549 \begin_layout Plain Layout
30562 \begin_layout Standard
30563 \begin_inset Note Greyedout
30566 \begin_layout Plain Layout
30571 Only maximal 26 formulas can be numbered with Latin letters in one document.
30579 \begin_layout Standard
30583 \begin_layout Plain Layout
30599 \begin_layout Standard
30600 \begin_inset Formula \begin{equation}
30601 A=\textrm{small roman}\label{eq:rom}\end{equation}
30609 \begin_layout Plain Layout
30623 \begin_inset Formula \begin{equation}
30624 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30632 \begin_layout Plain Layout
30646 \begin_inset Formula \begin{equation}
30647 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30655 \begin_layout Plain Layout
30669 \begin_inset Formula \begin{equation}
30670 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30677 \begin_layout Standard
30678 To switch back to the default numbering, insert the command:
30681 \begin_layout Standard
30694 \begin_layout Plain Layout
30705 \begin_layout Standard
30709 \begin_layout Plain Layout
30723 \begin_inset Formula \begin{equation}
30724 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30731 \begin_layout Standard
30732 \begin_inset VSpace medskip
30735 As you see, formulas are numbered serially independent from the numbering
30737 When then numbering should start with
30738 \begin_inset Quotes eld
30742 \begin_inset Quotes erd
30745 when the style is changed, new equation counters have to be defined.
30746 A description about this can be found in the file
30747 \begin_inset CommandInset href
30749 target "Formula-numbering.lyx"
30756 \begin_layout Section
30757 User-defined commands
30758 \begin_inset CommandInset label
30760 name "sec:User-defined-commands"
30768 \begin_layout Plain Layout
30769 User-defined commands
30777 \begin_layout Standard
30778 Many LaTeX-commands are too long to be used frequently.
30779 But it is possible to define with the command
30789 \begin_layout Plain Layout
30797 new shorter commands.
30800 \begin_layout Standard
30801 The command scheme of
30810 \begin_layout Standard
30815 newcommand{new command name}[number of arguments][optional
30820 \begin_inset Newline newline
30827 \begin_layout Plain Layout
30842 \begin_layout Plain Layout
30849 {command definition}
30852 \begin_layout Standard
30853 \begin_inset Note Greyedout
30856 \begin_layout Plain Layout
30861 Assure that the name of the new command is not already used in your document
30862 or by LaTeX-packages that you use.
30863 When you for example define the command
30875 , you get an error message because
30881 is already defined as command for
30882 \begin_inset Quotes eld
30886 \begin_inset Formula $\le$
30890 \begin_inset Quotes erd
30901 \begin_layout Standard
30902 \begin_inset Note Greyedout
30905 \begin_layout Plain Layout
30910 The names of user-defined commands may only consist of Latin letters.
30918 \begin_layout Standard
30919 The number of arguments is an integer in the range 0
30920 \begin_inset space \thinspace{}
30924 \begin_inset space \thinspace{}
30927 9 and specifies how many arguments the new command should have.
30928 With the optional value a value for an optional argument can be predefined.
30929 When this is done, the
30937 rgument of the new command is automatically an optional one.
30940 \begin_layout Standard
30941 Here are some examples:
30944 \begin_layout Itemize
30945 To define the command
30957 , the LaTeX-preamble line is:
30961 \begin_layout Plain Layout
30973 \begin_inset Newline newline
30985 \begin_layout Itemize
30986 To define the command
30998 , the argument (that should be underlined) must be taken into account.
30999 For this the preamble line is:
31003 \begin_layout Plain Layout
31015 \begin_inset Newline newline
31030 \begin_layout Plain Layout
31042 \begin_inset Newline newline
31051 acts as argument placeholder, the
31055 behind it denotes that it is the placeholder for the first argument.
31058 \begin_layout Itemize
31066 \begin_inset space \thinspace{}
31070 \begin_inset space ~
31083 \begin_layout Plain Layout
31095 \begin_inset Newline newline
31104 framebox#1#2{$#3$}}
31110 \begin_layout Plain Layout
31122 \begin_inset Newline newline
31127 The two Dollar signs creates the extra formula needed for
31134 \begin_inset CommandInset ref
31136 reference "sub:Boxes-with-Frame"
31143 \begin_layout Itemize
31144 To create a new command for
31150 where the color for the box needn't to be specified, the argument for the
31151 color is defined optional:
31155 \begin_layout Plain Layout
31167 \begin_inset Newline newline
31176 fcolorbox{#2}{#1}{$#3$}}
31182 \begin_layout Plain Layout
31192 \begin_inset Newline newline
31195 When the color is not specified when using
31201 , the predefined color
31208 \begin_layout Standard
31209 A test of the new defined commands:
31212 \begin_layout Standard
31214 \begin_inset Tabular
31215 <lyxtabular version="3" rows="6" columns="2">
31217 <column alignment="center" valignment="top" width="0">
31218 <column alignment="center" valignment="top" width="0">
31220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31223 \begin_layout Plain Layout
31229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31232 \begin_layout Plain Layout
31234 \begin_inset Note Note
31237 \begin_layout Plain Layout
31244 is only used as spacer.
31256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31259 \begin_layout Plain Layout
31266 \begin_layout Plain Layout
31280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31283 \begin_layout Plain Layout
31284 \begin_inset Formula $A\gr B$
31294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31297 \begin_layout Plain Layout
31305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31308 \begin_layout Plain Layout
31309 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31322 \begin_layout Plain Layout
31326 \begin_inset Formula $\to$
31332 \begin_inset Formula $\to$
31343 \begin_layout Plain Layout
31357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31360 \begin_layout Plain Layout
31361 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31374 \begin_layout Plain Layout
31378 \begin_inset Formula $\to$
31389 \begin_layout Plain Layout
31403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31406 \begin_layout Plain Layout
31407 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31420 \begin_layout Plain Layout
31426 \begin_inset Formula $\to$
31437 \begin_layout Plain Layout
31451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31454 \begin_layout Plain Layout
31455 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31471 \begin_layout Section
31475 \begin_layout Standard
31476 LyX supports two types of commutative diagrams:
31484 that are explained in the following.
31487 \begin_layout Subsection
31492 \begin_layout Plain Layout
31501 \begin_layout Standard
31502 To create this type of diagrams, the LaTeX-package
31508 \begin_layout Plain Layout
31513 is part of every LaTeX standard installation.
31524 \begin_layout Plain Layout
31531 It is loaded in the LaTeX-preamble with the line
31534 \begin_layout Standard
31542 \begin_layout Standard
31543 Diagrams visualize relations and look like this:
31544 \begin_inset Formula \[
31545 \begin{CD}A@>>>B@>>>C\\
31547 F@<<<E@<<<D\end{CD}\]
31554 \begin_layout Standard
31555 To get them, the command
31563 \begin_layout Plain Layout
31573 is inserted to a formula.
31574 A blue box appears with two dashed lines where further commands can be
31580 a new line is created.
31581 Horizontal relations are inserted in odd, vertical in even formula lines.
31584 \begin_layout Standard
31585 To create the relations there are the following commands:
31588 \begin_layout Itemize
31593 creates a left arrow,
31604 \begin_layout Itemize
31609 creates an up arrow,
31617 a vertical equal sign
31620 \begin_layout Itemize
31626 is a placeholder for non-existent relations
31629 \begin_layout Standard
31630 All arrows can be labeled as follows:
31633 \begin_layout Itemize
31634 Is text inserted between the first and second < or >, resp., it is placed
31636 When it is inserted between the second and third one, it appears under
31640 \begin_layout Itemize
31641 When text for vertical arrows is inserted between the first and second A
31642 or V, resp., it is placed left beside the arrow.
31643 When it is inserted between the second and third one, it appears right
31645 If the text contains an A or V, these letters must be set into a TeX-brace.
31648 \begin_layout Standard
31649 As example a diagram with all possible relations:
31652 \begin_layout Standard
31653 \begin_inset Formula \[
31654 \begin{CD}A@>j>>B@>>k>C@=F\\
31656 D@<<j<E@>k>>F@=C\end{CD}\]
31663 \begin_layout Standard
31664 The command for this is:
31665 \begin_inset Newline newline
31676 \begin_layout Plain Layout
31685 A@>j>>B@>>k>C@=F Ctrl-Enter
31686 \begin_inset Newline newline
31693 \begin_layout Plain Layout
31708 \begin_layout Plain Layout
31721 \begin_layout Plain Layout
31733 \begin_inset Formula $\to$
31739 \begin_inset Newline newline
31746 \begin_layout Plain Layout
31761 \begin_layout Plain Layout
31774 \begin_layout Plain Layout
31784 \begin_layout Subsection
31789 \begin_layout Plain Layout
31790 Diagrams ! xymatrix
31798 \begin_layout Standard
31799 To be able to use xymatrices, the LaTeX-package
31804 A xymatrix is created by inserting the command
31811 Then you are able to add new matrix columns and rows like for normal matrices,
31813 \begin_inset CommandInset ref
31815 reference "sec:Matrices"
31822 \begin_layout Standard
31823 xymatrix offers many possibilities to create commutative diagrams and decoration
31824 s that are explained in detail in this manual:
31825 \begin_inset CommandInset href
31827 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31834 \begin_layout Standard
31835 \begin_inset Newpage newpage
31841 \begin_layout Section
31846 \begin_layout Plain Layout
31859 \begin_layout Plain Layout
31860 Other useful math tips can be found in
31861 \begin_inset CommandInset citation
31876 \begin_layout Plain Layout
31884 \begin_inset Note Note
31887 \begin_layout Plain Layout
31890 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31893 \begin_layout Plain Layout
31896 texorpdfstring is in section
31897 \begin_inset CommandInset ref
31899 reference "sub:Formulas-in-Section"
31912 \begin_layout Plain Layout
31922 \begin_layout Plain Layout
31927 \begin_layout Plain Layout
31934 Chemical characters
31938 \begin_layout Plain Layout
31953 \begin_layout Subsection
31954 Chemical Symbols and Equations
31955 \begin_inset CommandInset label
31957 name "sub:Chemical-Symbols-and"
31965 \begin_layout Plain Layout
31966 Chemical characters ! Symbols
31975 \begin_layout Plain Layout
31985 \begin_layout Plain Layout
31994 \begin_layout Standard
31995 An example text from chemistry:
31998 \begin_layout Quote
32000 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32003 -ion reacts with two
32004 \begin_inset Formula $\mathrm{Na^{+}}$
32007 -ions to sodium sulfate
32008 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32012 The chemical equation for this is:
32013 \begin_inset Formula \[
32014 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32021 \begin_layout Standard
32022 This chemical equation can directly be created as formula.
32023 To avoid that the symbols appear italic, everything is highlighted and
32024 changed by the shortcut
32027 \begin_inset space ~
32032 to the upright font style.
32036 \begin_layout Plain Layout
32042 \begin_inset CommandInset ref
32044 reference "sub:Font-Styles"
32056 \begin_layout Subsection
32061 \begin_layout Plain Layout
32070 \begin_layout Standard
32071 Negative numbers often look ugly in formulas because the minus sign before
32072 the number is set with the same length as the minus operator sign.
32073 When writing the negative number in normal text, the minus sign appears
32077 \begin_layout Standard
32078 Thus, the problem disappears when converting the minus sign to mathematical
32082 \begin_layout Standard
32083 An example to visualize the problem:
32086 \begin_layout Standard
32088 \begin_inset Tabular
32089 <lyxtabular version="3" rows="3" columns="2">
32091 <column alignment="right" valignment="top" width="0">
32092 <column alignment="left" valignment="top" width="0">
32094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32097 \begin_layout Plain Layout
32103 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32106 \begin_layout Plain Layout
32114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32117 \begin_layout Plain Layout
32123 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32126 \begin_layout Plain Layout
32127 \begin_inset Formula $x=-2$
32137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32140 \begin_layout Plain Layout
32146 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32149 \begin_layout Plain Layout
32150 \begin_inset Formula $x=\textrm{-}2$
32166 \begin_layout Subsection
32167 Comma as Decimal Separator
32171 \begin_layout Plain Layout
32180 \begin_layout Standard
32181 In LaTeX a comma inside a formula is used, according to the English convention,
32182 as number group separator.
32183 So there will be space added behind all commas in formulas.
32186 \begin_layout Standard
32187 To avoid this, the comma is highlighted and changed to mathematical text
32191 \begin_inset space ~
32199 \begin_layout Standard
32200 To use all formula commas in the document as decimal separator, the file
32209 \begin_layout Plain Layout
32214 is part of the LaTeX-package
32222 \begin_layout Plain Layout
32227 \begin_layout Plain Layout
32250 \begin_layout Plain Layout
32256 is loaded with the LaTeX-preamble line
32259 \begin_layout Standard
32267 \begin_layout Subsection
32269 \begin_inset CommandInset label
32271 name "sub:Physical-Vectors"
32279 \begin_layout Plain Layout
32288 \begin_layout Standard
32289 Predefined vectors are offered by the LaTeX-package
32297 \begin_layout Plain Layout
32302 should be part of every LaTeX standard installation.
32311 \begin_layout Plain Layout
32317 that is loaded with the LaTeX-preamble line
32320 \begin_layout Standard
32328 \begin_layout Standard
32332 \begin_layout Plain Layout
32342 \begin_inset Note Note
32345 \begin_layout Plain Layout
32346 The following table will only be displayed when the LaTeX-package
32355 The following commands are defined:
32358 \begin_layout Standard
32360 \begin_inset Tabular
32361 <lyxtabular version="3" rows="4" columns="2">
32363 <column alignment="center" valignment="top" width="0">
32364 <column alignment="center" valignment="top" width="0">
32366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32369 \begin_layout Plain Layout
32375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32378 \begin_layout Plain Layout
32386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32389 \begin_layout Plain Layout
32399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32402 \begin_layout Plain Layout
32403 \begin_inset Formula $\Bra{\psi}$
32413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32416 \begin_layout Plain Layout
32426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32429 \begin_layout Plain Layout
32430 \begin_inset Formula $\Ket{\psi}$
32440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32443 \begin_layout Plain Layout
32455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32458 \begin_layout Plain Layout
32459 \begin_inset Formula $\Braket{\psi|\phi}$
32475 \begin_layout Standard
32482 assures that all vertical bars are set in the size of the surrounding brackets:
32483 \begin_inset Formula \[
32484 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32492 \begin_layout Plain Layout
32502 \begin_inset Note Note
32505 \begin_layout Plain Layout
32506 The following will be displayed when the LaTeX-package
32518 \begin_layout Standard
32519 You need to install the LaTeX-package
32523 to see the rest of this subsection in the output.
32526 \begin_layout Standard
32530 \begin_layout Plain Layout
32542 \begin_layout Standard
32549 can also be achieved using the command
32555 , that is described in
32556 \begin_inset CommandInset ref
32558 reference "sub:Automatic-Bracket-Size"
32565 \begin_layout Subsection
32566 Self-defined Fractions
32567 \begin_inset CommandInset label
32569 name "sub:Self-defined-Fractions"
32577 \begin_layout Plain Layout
32578 Fractions ! self-defined
32586 \begin_layout Standard
32587 To define custom commands for fractions, the command
32597 \begin_layout Plain Layout
32605 is used in the following scheme:
32608 \begin_layout Standard
32621 bracket}{fraction bar thickness}{style}
32622 \begin_inset Newline newline
32629 \begin_layout Plain Layout
32644 \begin_layout Plain Layout
32651 {numerator}{denominator}
32654 \begin_layout Standard
32655 The style is a number in the range of 0
32656 \begin_inset space \thinspace{}
32660 \begin_inset space \thinspace{}
32666 \begin_layout Standard
32668 \begin_inset Tabular
32669 <lyxtabular version="3" rows="5" columns="2">
32671 <column alignment="center" valignment="top" width="0">
32672 <column alignment="center" valignment="top" width="0">
32674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32677 \begin_layout Plain Layout
32683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32686 \begin_layout Plain Layout
32694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32697 \begin_layout Plain Layout
32703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32706 \begin_layout Plain Layout
32707 display style formula
32714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32717 \begin_layout Plain Layout
32723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32726 \begin_layout Plain Layout
32734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32737 \begin_layout Plain Layout
32743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32746 \begin_layout Plain Layout
32754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32757 \begin_layout Plain Layout
32763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32766 \begin_layout Plain Layout
32780 \begin_layout Standard
32781 When no style is given, the size is adjusted to the surrounding environment
32782 like for the command
32791 \begin_layout Standard
32792 When no fraction bar thickness is given, the predefined value of 0.4
32793 \begin_inset space \thinspace{}
32799 \begin_layout Standard
32800 \begin_inset VSpace medskip
32803 For example, the commands
32816 \begin_inset CommandInset ref
32818 reference "sub:Fractions"
32822 are defined with the commands
32825 \begin_layout Standard
32834 genfrac{}{}{}{0}{#1}{#2}}
32837 \begin_layout Standard
32841 \begin_layout Standard
32850 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32853 \begin_layout Standard
32854 \begin_inset VSpace medskip
32857 To define a fraction where the fraction bar thickness can be given as optional
32858 argument, the following line is inserted to the LaTeX-preamble:
32861 \begin_layout Standard
32870 genfrac{}{}{#1}{}{#2}{#3}}
32873 \begin_layout Standard
32875 \begin_inset Formula \begin{align*}
32876 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32877 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32881 As one can see, the distance of the numerator and the denominator to the
32882 fraction bar is round about three times the bar thickness.
32885 \begin_layout Subsection
32887 \begin_inset CommandInset label
32889 name "sub:Canceled-Formulas"
32897 \begin_layout Plain Layout
32906 \begin_layout Standard
32907 To cancel formulas or formula parts, the LaTeX-package
32915 \begin_layout Plain Layout
32920 is part of every LaTeX standard installation.
32929 \begin_layout Plain Layout
32935 has to be loaded with the LaTeX-preamble line
32938 \begin_layout Standard
32943 usepackage[samesize]{cancel}
32946 \begin_layout Standard
32947 There are four ways to cancel formulas:
32950 \begin_layout Standard
32952 \begin_inset Tabular
32953 <lyxtabular version="3" rows="5" columns="2">
32955 <column alignment="center" valignment="top" width="0">
32956 <column alignment="center" valignment="top" width="0">
32958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32961 \begin_layout Plain Layout
32967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32970 \begin_layout Plain Layout
32972 \begin_inset Note Note
32975 \begin_layout Plain Layout
32988 are used here as spacer.
33000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33003 \begin_layout Plain Layout
33012 \begin_layout Plain Layout
33026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33029 \begin_layout Plain Layout
33030 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33043 \begin_layout Plain Layout
33052 \begin_layout Plain Layout
33066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33069 \begin_layout Plain Layout
33070 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33083 \begin_layout Plain Layout
33092 \begin_layout Plain Layout
33106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33109 \begin_layout Plain Layout
33110 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33123 \begin_layout Plain Layout
33127 \begin_inset Formula $\to$
33138 \begin_layout Plain Layout
33152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33155 \begin_layout Plain Layout
33156 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33172 \begin_layout Standard
33179 is especially suitable to visualize the reduction of fractions within formulas:
33180 \begin_inset Formula \[
33181 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33188 \begin_layout Subsection
33189 Formulas in Section Headings
33190 \begin_inset CommandInset label
33192 name "sub:Formulas-in-Section"
33200 \begin_layout Plain Layout
33201 Formula ! in section headings
33209 \begin_layout Standard
33210 When formulas are used in section headings, the following has to be taken
33214 \begin_layout Standard
33215 \begin_inset Note Greyedout
33218 \begin_layout Plain Layout
33227 \begin_layout Plain Layout
33228 Packages ! hyperref
33233 support is enabled in the document settings dialog under
33236 \begin_inset space ~
33241 , PDF-bookmarks are created for every section heading in the table of contents.
33242 If a section heading contains formulas, they are incorrectly displayed
33243 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33252 \begin_layout Standard
33253 Both problems can be solved by inserting at the end of the section heading
33254 a short title with the menu
33256 Insert\SpecialChar \menuseparator
33258 \begin_inset space ~
33264 Short titles are used as alternative for multiline section headings to
33265 keep the table of contents clearly arranged.
33266 Only the short title appears in the table of contents and therefore also
33267 in the PDF-bookmark.
33270 \begin_layout Standard
33271 When formulas should be used in the table of contents but
33275 is used, one can use the following command in TeX-mode:
33278 \begin_layout Standard
33283 texorpdfstring{part}{alternative}
33287 \begin_layout Plain Layout
33298 \begin_layout Standard
33299 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33300 This can be characters, formulas, footnotes, but also cross-references.
33301 The alternative is used instead of the part for the bookmark.
33304 \begin_layout Standard
33305 Here are two example headings:
33306 \begin_inset VSpace -3mm
33313 \begin_layout Plain Layout
33325 \begin_layout Subsubsection
33326 Heading without formula in table of contents
33327 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33331 \begin_inset OptArg
33334 \begin_layout Plain Layout
33335 Heading without formula in table of contents
33343 \begin_layout Subsubsection
33344 Heading with formula in table of contents
33348 \begin_layout Plain Layout
33358 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33365 \begin_layout Plain Layout
33375 \begin_layout Standard
33379 \begin_layout Plain Layout
33388 In the first heading a short title was used, in the second one
33397 \begin_layout Standard
33398 To get the same formatting as for the other headings, the complete heading
33407 \begin_layout Plain Layout
33409 \begin_inset CommandInset ref
33411 reference "sub:Bold-Formulas"
33423 \begin_layout Subsection
33424 Formulas in multi-column Text
33428 \begin_layout Plain Layout
33429 Formula ! in multi-column text
33437 \begin_layout Standard
33438 Formulas in multi-column text are often too wide to fit into a column and
33439 thus need to be set over the whole page width.
33440 This is done by using the LaTeX-package
33448 \begin_layout Plain Layout
33453 is part of every LaTeX standard installation.
33462 \begin_layout Plain Layout
33463 Packages ! multicol
33468 , that is loaded with the LaTeX-preamble line
33471 \begin_layout Standard
33476 usepackage{multicol}
33479 \begin_layout Standard
33480 \begin_inset Note Greyedout
33483 \begin_layout Plain Layout
33484 Note herby that the setting
33487 \begin_inset space ~
33494 Document\SpecialChar \menuseparator
33500 \begin_inset space ~
33520 \begin_layout Standard
33521 Before the multi-column text the command
33524 \begin_layout Standard
33529 begin{multicols}{column number}
33532 \begin_layout Standard
33533 is written in TeX-mode.
33534 The column number is a number in the range of 2
33535 \begin_inset space \thinspace{}
33539 \begin_inset space \thinspace{}
33543 Before the formula the multi-column text is ended by inserting the command
33546 \begin_layout Standard
33554 \begin_layout Standard
33558 \begin_layout Standard
33559 Due to the command some space is automatically added before the formula.
33561 \begin_inset space \thinspace{}
33564 mm vertical space is inserted before the formula.
33565 When the formula style
33571 \begin_layout Plain Layout
33573 \begin_inset CommandInset ref
33575 reference "sec:Formula-Styles"
33587 \begin_inset space \thinspace{}
33590 mm space is inserted instead.
33593 \begin_layout Standard
33594 As example a multi-column text with a displayed formula:
33597 \begin_layout Standard
33601 \begin_layout Plain Layout
33605 begin{multicols}{2}
33610 Das Spektrum wird fouriertransformiert.
33611 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33612 , Lösungsmittel) zu trennen.
33613 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33614 nun das Aussehen des Ausgangssignals.
33615 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33616 über alle Phasen integrieren muss.
33618 \begin_inset Formula $S$
33621 unser normiertes Ausgangssignal and
33622 \begin_inset Formula $P$
33625 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33629 \begin_layout Plain Layout
33639 \begin_inset VSpace -6mm
33643 \begin_inset Formula \begin{equation}
33644 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33652 \begin_layout Plain Layout
33656 begin{multicols}{2}
33662 \begin_inset Formula $S_{0}$
33665 das Signal ohne Gradient ist and the Normierungsbedingung
33666 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33670 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33672 \begin_inset Formula $\nicefrac{\pi}{2}$
33676 \begin_inset space \thinspace{}
33679 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33680 das Signal zusätzlich abschwächt.
33681 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33683 \begin_inset Formula $T_{2}$
33689 \begin_layout Standard
33693 \begin_layout Plain Layout
33705 \begin_layout Subsection
33706 Formulas with Description of Variables
33710 \begin_layout Plain Layout
33711 Formula ! with description of variables
33719 \begin_layout Standard
33720 To describe variables within a formula, like in formula
33721 \begin_inset CommandInset ref
33723 reference "eq:within"
33732 \begin_inset Formula $n$
33736 \begin_inset space ~
33739 matrix is used with left aligned columns for the
33740 \begin_inset Formula $n$
33747 \begin_layout Plain Layout
33749 \begin_inset CommandInset ref
33751 reference "sec:Matrices"
33760 To set the description in a smaller size, before the matrix e.
33761 \begin_inset space \thinspace{}
33765 \begin_inset space ~
33778 \begin_layout Plain Layout
33780 \begin_inset CommandInset ref
33782 reference "sub:Font-Sizes"
33794 \begin_layout Standard
33795 When the formula style
33801 \begin_layout Plain Layout
33803 \begin_inset CommandInset ref
33805 reference "sec:Formula-Styles"
33826 \begin_layout Plain Layout
33833 only works in formulas with the style
33838 \begin_inset CommandInset ref
33840 reference "sub:Variable-Space"
33849 is inserted before and after the matrix to have the same separation of
33850 the matrix from the equation and the side margin.
33853 \begin_layout Standard
33854 When the formula style
33858 is used, the method described in
33859 \begin_inset CommandInset ref
33861 reference "sub:Flalign-Environment"
33865 is used to indent formulas.
33867 \begin_inset CommandInset ref
33869 reference "eq:within"
33873 consists of five columns whereas in the first two columns contain the equation,
33874 the third the matrix, and the last one an empty TeX-brace.
33875 \begin_inset Formula \begin{flalign}
33876 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33877 \rho & \textrm{density}\\
33878 V & \textrm{volume}\\
33879 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33886 \begin_layout Subsection
33887 Upright small Greek Letters
33888 \begin_inset CommandInset label
33890 name "sub:Upright-small-Greek"
33898 \begin_layout Plain Layout
33899 Greek letters ! upright
33907 \begin_layout Standard
33908 Most of the math fonts only provide italic small Greek letters.
33909 But for symbols of elementary particles like pions and neutrinos, upright
33910 Greek letters are needed.
33919 \begin_layout Plain Layout
33924 is part of the LaTeX-package
33932 \begin_layout Plain Layout
33937 \begin_layout Plain Layout
33960 \begin_layout Plain Layout
33966 that is loaded with the LaTeX-preamble line
33969 \begin_layout Standard
33974 usepackage{upgreek}
33977 \begin_layout Standard
33983 \begin_layout Plain Layout
33993 \begin_inset Note Note
33996 \begin_layout Plain Layout
33997 The following table will only be displayed when the LaTeX-package
34006 They are created when the command for a small Greek letters is started
34012 For example the command
34019 \begin_inset Formula $\uptau$
34025 \begin_layout Standard
34026 With these commands reactions of elementary particles can be typeset:
34027 \begin_inset Formula \[
34028 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34035 \begin_layout Standard
34036 The upright letters are more bold and wider than the italic ones.
34037 They should therefore not be used for units like
34038 \begin_inset Quotes eld
34042 \begin_inset Quotes erd
34048 \begin_layout Standard
34052 \begin_layout Plain Layout
34062 \begin_inset Note Note
34065 \begin_layout Plain Layout
34066 The following will be displayed when the LaTeX-package
34078 \begin_layout Standard
34079 You need to install the LaTeX-package
34083 to see the rest of this subsection in the output.
34086 \begin_layout Standard
34090 \begin_layout Plain Layout
34102 \begin_layout Subsection
34103 Text Characters in Formulas
34104 \begin_inset CommandInset label
34106 name "sub:Text-Characters-in"
34114 \begin_layout Plain Layout
34123 \begin_layout Standard
34124 In some cases you might want to insert text characters directly into formulas.
34125 When for example the centered dot · is often used in formulas like
34126 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34129 , one would have to insert the command
34139 \begin_layout Plain Layout
34141 \begin_inset CommandInset ref
34143 reference "sub:Binary-Operators"
34152 all the time, because this character is defined in all encodings as text
34154 But the encoding can be changed by this LaTeX-preamble line:
34157 \begin_layout Standard
34162 Declare Inputtext{183}{
34172 f\SpecialChar \textcompwordmark{}
34176 \begin_layout Standard
34177 The character encoding (menu
34179 Document\SpecialChar \menuseparator
34180 Settings\SpecialChar \menuseparator
34183 ) specifies what character appears when a keyboard key is pressed.
34184 When the key for the character '·' is pressed, internally the command
34191 But this command is not available in a formula so that you would get LaTeX-erro
34193 With the changed encoding the right command is chosen automatically, depending
34194 on if the character was inserted into a formula or not.
34197 \begin_layout Standard
34198 The encoding of several characters is saved in definition files.
34199 Fore example the encoding
34203 is defined in the file
34207 that is in the installation folder of LaTeX.
34208 Encodings should only be changed via the LaTeX-preamble and not in the
34210 Otherwise own documents could not be edited by other LyX users working
34211 on other computers.
34214 \begin_layout Standard
34215 \begin_inset VSpace medskip
34218 Besides the centered dot, in this document the degree sign ° is defined
34219 with the following LaTeX-preamble line so that it can directly be inserted
34223 \begin_layout Standard
34228 DeclareInputtext{176}{
34238 f\SpecialChar \textcompwordmark{}
34242 \begin_layout Standard
34243 \begin_inset Newpage newpage
34249 \begin_layout Section
34251 Typographic Advises
34255 \begin_layout Plain Layout
34256 Typographic Advises
34264 \begin_layout Standard
34265 This section is a summary of the most important typographic rules, listed
34270 \begin_layout Plain Layout
34271 This collection was partly taken from the German semi-official dictionary
34273 \begin_inset Quotes eld
34277 \begin_inset Quotes erd
34281 \begin_inset CommandInset citation
34287 that lists some of the ISO rules.
34295 \begin_layout Itemize
34304 \begin_layout Plain Layout
34305 done with font styles, see
34306 \begin_inset CommandInset ref
34308 reference "sub:Font-Styles"
34318 \begin_inset space \thinspace{}
34322 \begin_inset Newline newline
34325 Between the value and the unit is the smallest space, see
34326 \begin_inset CommandInset ref
34328 reference "sub:Predefined-Space"
34333 \begin_inset Newline newline
34336 This convention is automatically fulfilled when the command
34343 When it is entered to a formula, two boxes appear.
34344 In the first one the value is inserted, in the second one the unit, and
34346 \begin_inset Formula $\unit[30]{km/h}$
34350 \begin_inset space \thinspace{}
34360 is not a real LaTeX command but the command
34366 , therefore you cannot use it in TeX code.
34369 \begin_layout Itemize
34370 Percent and perthousand signs are set like physical units:
34371 \begin_inset Newline newline
34375 \begin_inset space \thinspace{}
34381 \begin_layout Itemize
34382 The degree sign follows directly on the value: 15°, but not when it is used
34384 \begin_inset space \thinspace{}
34390 \begin_layout Itemize
34391 In numbers with more than four digits the smallest space is inserted before
34392 every third digit to group them:
34402 \begin_inset space \thinspace{}
34406 \begin_inset space \thinspace{}
34412 \begin_layout Itemize
34413 For dimensions like 120×90×40
34414 \begin_inset space \thinspace{}
34417 cm the multiplication sign
34418 \begin_inset Quotes eld
34422 \begin_inset Quotes erd
34426 It is available with the LaTeX-command
34432 , but can also directly be inserted with some keyboard definitions.
34435 \begin_layout Itemize
34436 Functions with names consisting of several letters are set upright to avoid
34438 \begin_inset CommandInset ref
34440 reference "sub:Predefined-Functions"
34447 \begin_layout Itemize
34448 Indices consisting of several letters, are set upright:
34449 \begin_inset Formula $E_{\mathrm{kin}}$
34453 \begin_inset Newline newline
34456 Components of matrices are set italic:
34457 \begin_inset Formula $\hat{H}_{kl}$
34463 \begin_layout Itemize
34464 The differentiation/integration operator 'd', the Euler's number 'e', and
34465 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34469 \begin_layout Standard
34470 \begin_inset Newpage newpage
34476 \begin_layout Section
34481 \begin_layout Plain Layout
34490 \begin_layout Standard
34491 Some characters and symbols can be created with several commands.
34492 Here is a list of the synonym commands:
34495 \begin_layout Standard
34496 \begin_inset VSpace bigskip
34500 \begin_inset space \hfill{}
34504 \begin_inset Tabular
34505 <lyxtabular version="3" rows="12" columns="2">
34507 <column alignment="center" valignment="top" width="0pt">
34508 <column alignment="center" valignment="top" width="0pt">
34510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34513 \begin_layout Plain Layout
34519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34522 \begin_layout Plain Layout
34524 \begin_inset Note Note
34527 \begin_layout Plain Layout
34534 is only used as spacer.
34546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34549 \begin_layout Plain Layout
34557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34560 \begin_layout Plain Layout
34564 \begin_layout Plain Layout
34577 \begin_layout Plain Layout
34591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34594 \begin_layout Plain Layout
34602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34605 \begin_layout Plain Layout
34615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34618 \begin_layout Plain Layout
34626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34629 \begin_layout Plain Layout
34639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34642 \begin_layout Plain Layout
34650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34653 \begin_layout Plain Layout
34661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34664 \begin_layout Plain Layout
34672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34675 \begin_layout Plain Layout
34683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34686 \begin_layout Plain Layout
34694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34697 \begin_layout Plain Layout
34707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34710 \begin_layout Plain Layout
34718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34721 \begin_layout Plain Layout
34731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34734 \begin_layout Plain Layout
34742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34745 \begin_layout Plain Layout
34755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34758 \begin_layout Plain Layout
34766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34769 \begin_layout Plain Layout
34779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34782 \begin_layout Plain Layout
34790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34793 \begin_layout Plain Layout
34801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34804 \begin_layout Plain Layout
34812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34815 \begin_layout Plain Layout
34827 \begin_inset space \hfill{}
34831 \begin_inset Tabular
34832 <lyxtabular version="3" rows="12" columns="2">
34834 <column alignment="center" valignment="top" width="0pt">
34835 <column alignment="center" valignment="top" width="0pt">
34837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34840 \begin_layout Plain Layout
34846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34849 \begin_layout Plain Layout
34857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34860 \begin_layout Plain Layout
34868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34871 \begin_layout Plain Layout
34883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34886 \begin_layout Plain Layout
34894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34897 \begin_layout Plain Layout
34907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34910 \begin_layout Plain Layout
34918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34921 \begin_layout Plain Layout
34931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34934 \begin_layout Plain Layout
34942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34945 \begin_layout Plain Layout
34953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34956 \begin_layout Plain Layout
34964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34967 \begin_layout Plain Layout
34975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34978 \begin_layout Plain Layout
34986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34989 \begin_layout Plain Layout
34999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35002 \begin_layout Plain Layout
35010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35013 \begin_layout Plain Layout
35023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35026 \begin_layout Plain Layout
35034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35037 \begin_layout Plain Layout
35047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35050 \begin_layout Plain Layout
35058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35061 \begin_layout Plain Layout
35071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35074 \begin_layout Plain Layout
35082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35085 \begin_layout Plain Layout
35095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35098 \begin_layout Plain Layout
35106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35109 \begin_layout Plain Layout
35123 \begin_inset space \hfill{}
35129 \begin_layout Standard
35130 \begin_inset Newpage newpage
35136 \begin_layout Bibliography
35137 \begin_inset CommandInset bibitem
35138 LatexCommand bibitem
35150 The LaTeX Companion
35153 Addison Wesley, 2004
35156 \begin_layout Bibliography
35157 \begin_inset CommandInset bibitem
35158 LatexCommand bibitem
35164 \begin_inset CommandInset href
35167 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35171 of LaTeX's math abilities
35174 \begin_layout Bibliography
35175 \begin_inset CommandInset bibitem
35176 LatexCommand bibitem
35181 LaTeX tips and tricks-
35182 \begin_inset CommandInset href
35185 target "http://tug.org/TeXnik/"
35192 \begin_layout Bibliography
35193 \begin_inset CommandInset bibitem
35194 LatexCommand bibitem
35200 \begin_inset CommandInset href
35203 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35211 \begin_layout Plain Layout
35223 \begin_layout Bibliography
35224 \begin_inset CommandInset bibitem
35225 LatexCommand bibitem
35231 \begin_inset CommandInset href
35234 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35238 of all symbols available with LaTeX-packages
35241 \begin_layout Bibliography
35242 \begin_inset CommandInset bibitem
35243 LatexCommand bibitem
35249 \begin_inset CommandInset href
35251 name "Documentation"
35252 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35256 of the LaTeX-package
35264 \begin_layout Plain Layout
35265 Packages ! hyperref
35273 \begin_layout Bibliography
35274 \begin_inset CommandInset bibitem
35275 LatexCommand bibitem
35281 \begin_inset CommandInset href
35284 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35295 \begin_inset CommandInset ref
35297 reference "sub:Operator-Limits"
35305 \begin_layout Plain Layout
35316 \begin_layout Bibliography
35317 \begin_inset CommandInset bibitem
35318 LatexCommand bibitem
35329 Auflage, Duden 2001
35332 \begin_layout Subsubsection*
35333 \begin_inset CommandInset index_print
35334 LatexCommand printindex