1 #LyX 1.6.5svn 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
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
45 \renewcommand{\equationautorefname}{\hspace{-\abc}}
46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
73 \usepackage[samesize]{cancel}
75 % enables calculation of values,
78 % for multiple table row and column cells
85 % for the Fourier transformation symbol
88 % center multirows (e.g. in sec. 13.3)
89 \renewcommand{\multirowsetup}{\centering}
91 % define a color, used in sec.9.3
92 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
94 % declare operators (see sec. 10.4 and sec. 15.2)
95 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
96 \DeclareMathOperator{\sgn}{sgn}
98 \newcommand{\spce}{\textvisiblespace}
100 % example definitions for sec. 20.1
101 \newcommand{\gr}{\Longrightarrow}
102 \newcommand{\us}[1]{\underline{#1}}
103 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
104 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
105 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
107 % example macro from sec. 19.4
108 %\def\tagform@#1{\maketag@@@{|#1|}}
110 % macro from sec. 10.2
111 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
112 \def\mathclap {\mathpalette \mathclapinternal}
113 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
115 % redefine the greyed out note
116 \renewenvironment{lyxgreyedout}
117 {\textcolor{blue}\bgroup}{\egroup}
119 % ------------------------------------
120 % used to check for needed LaTeX packages
123 % check for package eurosym
124 % used for the Euro symbol
126 \IfFileExists{eurosym.sty}
127 {\usepackage[gennarrow]{eurosym}
128 \setboolean{eurosym}{true}}
129 {\setboolean{eurosym}{false}}
131 % needed in sec. 22.4
132 % check for package braket
134 \IfFileExists{braket.sty}
136 \setboolean{braket}{true}}
137 {\setboolean{braket}{false}}
139 % needed in sec. 22.10
140 % check for package upgreek
142 \IfFileExists{upgreek.sty}
143 {\usepackage{upgreek}
144 \setboolean{upgreek}{true}}
145 {\setboolean{upgreek}{false}}
147 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
148 \use_default_options false
153 \font_typewriter default
154 \font_default_family default
164 \pdf_title "LyX's Math Manual"
165 \pdf_author "LyX Team, Uwe Stöhr"
166 \pdf_subject "LyX-documentation about math"
167 \pdf_keywords "LyX, Mathed"
169 \pdf_bookmarksnumbered true
170 \pdf_bookmarksopen true
171 \pdf_bookmarksopenlevel 1
172 \pdf_breaklinks false
176 \pdf_pdfusetitle false
177 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
184 \paperorientation portrait
187 \paragraph_separation skip
189 \quotes_language english
192 \paperpagestyle plain
196 \tracking_changes false
197 \output_changes false
205 LyX's detailed Math manual
213 \begin_layout Plain Layout
215 If you have comments or error corrections, please send them to the LyX Documenta
219 \begin_inset CommandInset href
221 name "lyx-docs@lists.lyx.org"
222 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
233 \begin_inset Note Note
236 \begin_layout Plain Layout
243 \begin_inset Newline newline
247 \begin_inset Newline newline
255 \begin_layout Standard
256 \begin_inset CommandInset toc
257 LatexCommand tableofcontents
264 \begin_layout Standard
265 \begin_inset Note Note
268 \begin_layout Plain Layout
269 To export this document to PDF, PS, or DVI the LaTeX-packages
282 If they are not installed you can export the document anyway but the sections
283 where the packages are required won't appear in the output.
286 \begin_layout Plain Layout
287 The latest PDF-version of this document can be found here:
288 \begin_inset Newline newline
293 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
301 \begin_layout Standard
302 \begin_inset Newpage newpage
308 \begin_layout Section
312 \begin_layout Standard
313 This document explains LyX's math features and is furthermore a collection
314 of LaTeX-commands used for mathematical characters and constructs.
315 The explanations are designed for the usage of commands.
316 It is therefore required that you have read the section
327 \begin_layout Standard
328 Most of the characters and many constructs explained in this manual are
329 also accessible via the menu
333 \SpecialChar \menuseparator
349 But everybody who has to write lots of formulas will notice that it is
350 much faster to use commands instead of the math toolbar.
351 Therefore this manual is focused on commands but also mentions the correspondin
352 g toolbar buttons when available.
355 \begin_layout Standard
356 If not specially mentioned the commands are only available within formulas.
357 To be able to use all commands explained in this document, the option
361 must be used in the document settings (menu
363 Document\SpecialChar \menuseparator
364 Settings\SpecialChar \menuseparator
375 \begin_layout Plain Layout
378 Use AMS math package automatically
384 \begin_layout Plain Layout
393 -math when math constructs are found that are supported by LyX.
401 \begin_layout Standard
402 This document doesn't list all
406 \begin_layout Plain Layout
419 \begin_layout Plain Layout
424 \begin_layout Plain Layout
433 -math commands is in the file
436 \begin_inset CommandInset href
439 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
445 , which is part of every LaTeX standard installation.
450 for lucidity reasons.
453 \begin_layout Section
457 \begin_layout Standard
458 To create an inline formula
462 \begin_layout Plain Layout
468 that is embedded into a text line, use one of the shortcuts
474 or the toolbar button
475 \begin_inset Graphics
476 filename ../images/math-mode.png
482 \begin_inset Newline newline
485 To create a display style formula
489 \begin_layout Plain Layout
490 Formula ! display style
495 that will appear bigger and in an own paragraph, use one of these shortcuts:
505 \begin_layout Standard
506 To change a display style formula to an inline formula, set the cursor into
507 the formula and use one of the shortcuts
515 Edit\SpecialChar \menuseparator
516 Math\SpecialChar \menuseparator
520 The same way is used to change an inline formula to a display style formula.
523 \begin_layout Standard
524 To display parts of an inline formula in the size of a display style formula,
533 \begin_layout Plain Layout
544 Then a new blue box appears in which the desired formula part is inserted.
547 \begin_layout Standard
548 Only inline formulas are allowed inside tables.
551 \begin_layout Standard
556 can be turned on in the menu
558 View\SpecialChar \menuseparator
562 When you click there on
563 \begin_inset Quotes eld
567 \begin_inset Quotes erd
570 the toolbar will be shown permanently at the bottom; this state is visualized
575 menu with a checkmark.
576 When you click in this state again on
577 \begin_inset Quotes eld
581 \begin_inset Quotes erd
592 is only shown when the cursor is within a formula; this state is visualized
593 by the renaming of the menu entry from
594 \begin_inset Quotes eld
598 \begin_inset Quotes erd
602 \begin_inset Quotes eld
610 \begin_inset Quotes erd
616 \begin_layout Standard
621 \begin_layout Plain Layout
627 is invoked by pressing the toolbar button
628 \begin_inset Graphics
629 filename ../images/ert-insert.png
636 Insert\SpecialChar \menuseparator
641 \begin_layout Plain Layout
657 \begin_inset Note Note
660 \begin_layout Plain Layout
661 In LyX there are three
662 \begin_inset Quotes eld
666 \begin_inset Quotes erd
669 that appear in the output with sub- and superscript letters: TeX, LaTeX,
673 \begin_layout Plain Layout
674 To avoid that these names are recognized as proper names, a TeX-brace pair
683 \begin_layout Standard
684 To change the LaTeX-preamble
688 \begin_layout Plain Layout
696 Document\SpecialChar \menuseparator
697 Settings\SpecialChar \menuseparator
702 \begin_layout Plain Layout
718 \begin_layout Standard
719 To edit matrices, case differentiations, and multiline formulas subsequently,
722 Edit\SpecialChar \menuseparator
727 Edit\SpecialChar \menuseparator
729 \begin_inset space \thinspace{}
733 \begin_inset space \thinspace{}
743 When lines and columns are swapped via the menu, the column or line where
744 the cursor is in is exchanged with the column to the right or the line
746 Is the cursor in the last column or row, the exchange is done with the
747 column to the left or the line above.
750 \begin_layout Standard
751 To write text in formulas
755 \begin_layout Plain Layout
756 For multiline formulas the command
763 \begin_inset CommandInset ref
765 reference "sub:Text-in-multiline"
782 \begin_layout Plain Layout
792 \begin_layout Plain Layout
799 This mode is invoked with the the shortcut
805 or by the insertion of the command
813 \begin_layout Plain Layout
824 The text appears black in LyX and can therefore be distinguished from the
825 other formula parts that appear blue.
826 In the output mathematical text is set upright, in contrary to other formula
830 \begin_layout Subsection*
834 \begin_layout Standard
835 Most of the LaTeX-commands for math constructs have the following scheme:
838 \begin_layout Standard
854 \begin_layout Standard
855 A command starts always with a backslash
856 \begin_inset Quotes gld
866 \begin_inset Quotes grd
870 To omit optional arguments, also omit the associated brackets.
871 The braces around the required arguments are named in this document as
876 \begin_layout Plain Layout
883 If you add in a formula a left brace to a command name, LyX creates automatical
885 In all other cases TeX-braces are created in formulas with the command
893 TeX-braces appear red in LyX, in contrary to normal braces that appear
895 In TeX-mode no command is needed to get TeX-braces.
896 TeX-braces don't appear in the output.
899 \begin_layout Standard
900 When commands without arguments, like commands for symbols are entered in
901 TeX-mode, a space character must
905 be behind the command to end it.
906 This space doesn't appear in the output.
907 When the space should appear in the output, the space must be followed
908 by a protected space in normal text.
911 \begin_layout Standard
912 A protected space is inserted with
915 arg "space-insert protected"
921 \begin_layout Subsection*
922 \begin_inset Newpage newpage
928 \begin_layout Itemize
933 \begin_layout Plain Layout
934 This visible space character can be created with the command
944 \begin_layout Plain Layout
952 , inserted in TeX-mode.
961 \begin_layout Plain Layout
974 denotes a space character to be input.
977 \begin_layout Itemize
979 \begin_inset Formula $\to$
982 denotes the usage of the corresponding arrow key on the keyboard.
985 \begin_layout Subsection*
989 \begin_layout Standard
991 \begin_inset Float table
997 \begin_layout Plain Layout
1001 \begin_layout Plain Layout
1002 \begin_inset CommandInset label
1004 name "tab:Available-units"
1016 \begin_layout Plain Layout
1018 \begin_inset Tabular
1019 <lyxtabular version="3" rows="13" columns="2">
1021 <column alignment="center" valignment="top" width="0">
1022 <column alignment="center" valignment="top" width="0">
1024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1027 \begin_layout Plain Layout
1033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1036 \begin_layout Plain Layout
1044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1047 \begin_layout Plain Layout
1053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1056 \begin_layout Plain Layout
1064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1067 \begin_layout Plain Layout
1073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1076 \begin_layout Plain Layout
1084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1087 \begin_layout Plain Layout
1093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1096 \begin_layout Plain Layout
1098 \begin_inset space \thinspace{}
1102 \begin_inset space \thinspace{}
1112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1115 \begin_layout Plain Layout
1121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1124 \begin_layout Plain Layout
1126 \begin_inset space \thinspace{}
1130 \begin_inset space \thinspace{}
1140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1143 \begin_layout Plain Layout
1149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1152 \begin_layout Plain Layout
1154 \begin_inset space \thinspace{}
1158 \begin_inset space \thinspace{}
1168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1171 \begin_layout Plain Layout
1177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1180 \begin_layout Plain Layout
1182 \begin_inset space \thinspace{}
1186 \begin_inset space \thinspace{}
1196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1199 \begin_layout Plain Layout
1205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1208 \begin_layout Plain Layout
1210 \begin_inset space \thinspace{}
1214 \begin_inset space \thinspace{}
1224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1227 \begin_layout Plain Layout
1233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1236 \begin_layout Plain Layout
1238 \begin_inset space \thinspace{}
1242 \begin_inset Formula $\approx$
1246 \begin_inset space \thinspace{}
1256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1259 \begin_layout Plain Layout
1265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1268 \begin_layout Plain Layout
1270 \begin_inset space \thinspace{}
1274 \begin_inset space \thinspace{}
1284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1287 \begin_layout Plain Layout
1293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1296 \begin_layout Plain Layout
1300 \begin_inset Quotes eld
1306 \begin_inset Quotes erd
1316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1319 \begin_layout Plain Layout
1325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1328 \begin_layout Plain Layout
1330 \begin_inset Quotes eld
1338 \begin_inset Quotes erd
1348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1351 \begin_layout Plain Layout
1357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1360 \begin_layout Plain Layout
1362 \begin_inset space \thinspace{}
1366 \begin_inset Formula $\nicefrac{1}{18}$
1370 \begin_inset space \thinspace{}
1391 \begin_layout Standard
1392 \begin_inset Newpage newpage
1398 \begin_layout Section
1402 \begin_layout Subsection
1407 \begin_layout Plain Layout
1417 \begin_layout Plain Layout
1427 \begin_layout Plain Layout
1432 \begin_layout Plain Layout
1443 \begin_layout Plain Layout
1459 \begin_layout Plain Layout
1464 \begin_layout Plain Layout
1475 \begin_layout Plain Layout
1490 \begin_layout Standard
1491 Indices are created with an underscore
1492 \begin_inset Quotes eld
1496 \begin_inset Quotes erd
1499 or via the math toolbar button
1500 \begin_inset Graphics
1501 filename ../images/math-subscript.png
1506 , exponents with a caret
1507 \begin_inset Quotes eld
1511 \begin_inset Quotes erd
1514 or via the math toolbar button
1515 \begin_inset Graphics
1516 filename ../images/math-superscript.png
1524 \begin_layout Standard
1526 \begin_inset Tabular
1527 <lyxtabular version="3" rows="4" columns="2">
1529 <column alignment="center" valignment="top" width="0pt">
1530 <column alignment="center" valignment="top" width="0pt">
1532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1535 \begin_layout Plain Layout
1541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1544 \begin_layout Plain Layout
1546 \begin_inset Note Note
1549 \begin_layout Plain Layout
1556 is only used as spacer.
1568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1571 \begin_layout Plain Layout
1577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1580 \begin_layout Plain Layout
1581 \begin_inset Formula $B_{V}$
1591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1594 \begin_layout Plain Layout
1600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1603 \begin_layout Plain Layout
1604 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1617 \begin_layout Plain Layout
1622 \begin_layout Plain Layout
1636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1639 \begin_layout Plain Layout
1640 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1656 \begin_layout Standard
1657 As the caret is in some languages an accent, vowels will be accentuated
1658 in this case and not set as exponents
1662 \begin_layout Plain Layout
1663 Depending on the used keyboard settings this can also happen for other character
1670 To get in this case exponents, press
1674 after the caret as in the last example.
1677 \begin_layout Subsection
1679 \begin_inset CommandInset label
1681 name "sub:Fractions"
1689 \begin_layout Plain Layout
1698 \begin_layout Standard
1699 Fractions are generated with the command
1709 \begin_layout Plain Layout
1717 or via the math toolbar button
1718 \begin_inset Graphics
1719 filename ../images/math/frac.png
1725 The font size is adjusted automatically, depending on whether the fraction
1726 is in an inline or display style formula.
1727 With the math toolbar button
1728 \begin_inset Graphics
1729 filename ../images/math/frac-square.png
1734 you can select different fraction types.
1737 \begin_layout Standard
1746 \begin_layout Plain Layout
1756 a fraction can be created that has in any case the size of a display style
1766 \begin_layout Plain Layout
1776 the fraction appears always with the size of an inline formula.
1780 \begin_layout Standard
1781 A line with the fraction
1782 \begin_inset Formula $\frac{1}{2}$
1785 that was created with the command
1794 \begin_layout Standard
1795 A line with the fraction
1796 \begin_inset Formula $\dfrac{1}{2}$
1799 that was created with the command
1808 \begin_layout Standard
1810 \begin_inset Tabular
1811 <lyxtabular version="3" rows="4" columns="2">
1813 <column alignment="center" valignment="top" width="0pt">
1814 <column alignment="center" valignment="top" width="0pt">
1816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1819 \begin_layout Plain Layout
1825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1828 \begin_layout Plain Layout
1830 \begin_inset Note Note
1833 \begin_layout Plain Layout
1840 is only used as spacer.
1852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1855 \begin_layout Plain Layout
1862 \begin_layout Plain Layout
1872 \begin_inset Formula $\downarrow$
1880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1883 \begin_layout Plain Layout
1884 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1897 \begin_layout Plain Layout
1904 \begin_layout Plain Layout
1914 \begin_inset Formula $\downarrow$
1922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1925 \begin_layout Plain Layout
1926 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1939 \begin_layout Plain Layout
1946 \begin_layout Plain Layout
1959 \begin_layout Plain Layout
1974 \begin_layout Plain Layout
1984 \begin_inset Formula $\downarrow$
1988 \begin_inset Formula $\downarrow\downarrow$
1996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1999 \begin_layout Plain Layout
2000 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2016 \begin_layout Standard
2017 \begin_inset VSpace bigskip
2021 \begin_inset Newpage newpage
2024 For nested fractions the command
2034 \begin_layout Plain Layout
2044 \begin_inset VSpace -3mm
2050 \begin_layout Standard
2051 \begin_inset Formula \begin{align*}
2052 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2053 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2060 \begin_layout Standard
2061 The command for the example above is:
2064 \begin_layout Standard
2073 \begin_layout Plain Layout
2083 \begin_inset Formula $\downarrow$
2092 \begin_layout Plain Layout
2107 \begin_layout Plain Layout
2117 \begin_inset Formula $\downarrow$
2121 \begin_inset Formula $\downarrow$
2127 \begin_layout Standard
2128 \begin_inset VSpace medskip
2134 \begin_layout Standard
2141 sets the fraction always in the size of a displayed formula, also when
2142 it is part of another fraction.
2145 \begin_layout Standard
2146 It is possible to specify the alignment of the numerator.
2153 is used to left align it, the command
2166 centers the numerator.
2167 These fractions demonstrate the different alignments:
2170 \begin_layout Standard
2171 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2175 \begin_inset Formula $\cfrac{A}{B+C}$
2179 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2185 \begin_layout Standard
2186 \begin_inset Note Greyedout
2189 \begin_layout Plain Layout
2206 are no real LaTeX commands but represent the command
2210 cfrac[alignment]{numerator}{denominator}
2213 Therefore you cannot use them in TeX code.
2221 \begin_layout Standard
2222 \begin_inset VSpace medskip
2225 It is often advantageous to combine
2238 \begin_inset Formula \[
2239 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2246 \begin_layout Standard
2247 For inline fractions with a sloped fraction stroke you can use the command
2258 \begin_layout Plain Layout
2267 \begin_inset Formula $\nicefrac{5}{31}$
2280 \begin_layout Plain Layout
2289 \begin_inset Formula $\unitfrac{5}{31}$
2292 There is furthermore the command
2298 that offers to write a fraction in combination with a number:
2299 \begin_inset Formula $\unitfrac[2]{1}{3}$
2305 \begin_layout Standard
2306 \begin_inset Note Greyedout
2309 \begin_layout Plain Layout
2320 is not a real LaTeX command but the command
2321 \begin_inset Newline newline
2328 unitfrac[number]{numerator}{denominator}
2331 Therefore you cannot use it in TeX code.
2339 \begin_layout Standard
2340 How to define own fractions where the fraction stroke can be changed, is
2342 \begin_inset CommandInset ref
2344 reference "sub:Self-defined-Fractions"
2351 \begin_layout Subsection
2356 \begin_layout Plain Layout
2365 \begin_layout Standard
2366 Square roots are created with
2376 \begin_layout Plain Layout
2384 or the math toolbar button
2385 \begin_inset Graphics
2386 filename ../images/math/sqrt.png
2391 , all other roots with the command
2401 \begin_layout Plain Layout
2409 or with the math toolbar button
2410 \begin_inset Graphics
2411 filename ../images/math/root.png
2419 \begin_layout Standard
2421 \begin_inset Tabular
2422 <lyxtabular version="3" rows="3" columns="2">
2424 <column alignment="center" valignment="top" width="0pt">
2425 <column alignment="center" valignment="top" width="0pt">
2427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2430 \begin_layout Plain Layout
2436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2439 \begin_layout Plain Layout
2441 \begin_inset Note Note
2444 \begin_layout Plain Layout
2451 is only used as spacer.
2463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2466 \begin_layout Plain Layout
2473 \begin_layout Plain Layout
2487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2490 \begin_layout Plain Layout
2491 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2501 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2504 \begin_layout Plain Layout
2511 \begin_layout Plain Layout
2521 \begin_inset Formula $\downarrow$
2529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2532 \begin_layout Plain Layout
2533 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2549 \begin_layout Standard
2550 A square root can also be created with
2556 when the root index field is left empty.
2559 \begin_layout Standard
2560 With certain indices the distance to the root is too small, like in this
2562 \begin_inset Formula $\sqrt[\beta]{B}$
2566 \begin_inset Newline newline
2570 \begin_inset Formula $\beta$
2574 To avoid this, the commands
2584 \begin_layout Plain Layout
2602 \begin_layout Plain Layout
2610 are used with the following scheme:
2613 \begin_layout Standard
2627 \begin_layout Standard
2628 Distance is the number of Big Points (unit bp;
2629 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2632 ), that the index should be moved to the left or top, resp..
2633 The commands are written to the index.
2634 This way the command
2635 \begin_inset Newline newline
2645 \begin_inset Formula $\to$
2651 \begin_inset Formula $\to$
2660 \begin_layout Plain Layout
2670 \begin_inset Formula $\to$
2674 \begin_inset Newline newline
2679 produces a correct typeset formula:
2680 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2686 \begin_layout Subsection
2687 Binomial Coefficients
2691 \begin_layout Plain Layout
2692 Binomial coefficients
2700 \begin_layout Standard
2701 Binomial coefficients are inserted with the command
2711 \begin_layout Plain Layout
2719 or with the submenu of the math toolbar button
2720 \begin_inset Graphics
2721 filename ../images/math/frac-square.png
2727 Analog to fractions (
2747 \begin_layout Plain Layout
2767 \begin_layout Plain Layout
2776 For other brackets around binomial coeficients there are the commands
2786 \begin_layout Plain Layout
2804 \begin_layout Plain Layout
2815 \begin_layout Standard
2817 \begin_inset Tabular
2818 <lyxtabular version="3" rows="6" columns="2">
2820 <column alignment="center" valignment="top" width="0pt">
2821 <column alignment="center" valignment="top" width="0pt">
2823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2826 \begin_layout Plain Layout
2832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2835 \begin_layout Plain Layout
2837 \begin_inset Note Note
2840 \begin_layout Plain Layout
2847 is only used as spacer.
2859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2862 \begin_layout Plain Layout
2869 \begin_layout Plain Layout
2879 \begin_inset Formula $\downarrow$
2887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2890 \begin_layout Plain Layout
2891 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2904 \begin_layout Plain Layout
2911 \begin_layout Plain Layout
2921 \begin_inset Formula $\downarrow$
2929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2932 \begin_layout Plain Layout
2933 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2946 \begin_layout Plain Layout
2953 \begin_layout Plain Layout
2963 \begin_inset Formula $\downarrow$
2971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2974 \begin_layout Plain Layout
2975 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2988 \begin_layout Plain Layout
2995 \begin_layout Plain Layout
3005 \begin_inset Formula $\downarrow$
3013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3016 \begin_layout Plain Layout
3017 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3030 \begin_layout Plain Layout
3037 \begin_layout Plain Layout
3047 \begin_inset Formula $\downarrow$
3055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3058 \begin_layout Plain Layout
3059 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3075 \begin_layout Subsection
3076 Case Differentiations
3080 \begin_layout Plain Layout
3081 Case differentiations
3089 \begin_layout Standard
3091 \begin_inset Tabular
3092 <lyxtabular version="3" rows="3" columns="2">
3094 <column alignment="center" valignment="top" width="0pt">
3095 <column alignment="center" valignment="top" width="0pt">
3097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3100 \begin_layout Plain Layout
3106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3109 \begin_layout Plain Layout
3117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3120 \begin_layout Plain Layout
3127 \begin_layout Plain Layout
3137 \begin_inset Formula $\to$
3144 \begin_layout Plain Layout
3157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3160 \begin_layout Plain Layout
3161 \begin_inset Formula $\begin{cases}
3172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3175 \begin_layout Plain Layout
3182 \begin_layout Plain Layout
3194 arg "newline-insert newline"
3202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3205 \begin_layout Plain Layout
3206 \begin_inset Formula $\begin{cases}
3207 A & \textrm{for }x>0\\
3208 B & \textrm{for }x=0\end{cases}$
3224 \begin_layout Standard
3231 or the usage of the math toolbar button
3232 \begin_inset Graphics
3233 filename ../images/math/cases.png
3238 you can create new lines with the shortcut
3241 arg "newline-insert newline"
3244 or the table toolbar button
3245 \begin_inset Graphics
3246 filename ../images/tabular-feature_append-row.png
3254 \begin_layout Standard
3261 is also available via the menu
3263 Insert\SpecialChar \menuseparator
3264 Math\SpecialChar \menuseparator
3270 \begin_layout Subsection
3275 \begin_layout Plain Layout
3284 \begin_layout Standard
3295 \begin_layout Plain Layout
3303 every character can be displayed canceled.
3304 The characters are quasi accentuated by a slash.
3307 \begin_layout Standard
3309 \begin_inset Tabular
3310 <lyxtabular version="3" rows="4" columns="2">
3312 <column alignment="center" valignment="top" width="0pt">
3313 <column alignment="center" valignment="top" width="0pt">
3315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3318 \begin_layout Plain Layout
3324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3327 \begin_layout Plain Layout
3335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3338 \begin_layout Plain Layout
3346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3349 \begin_layout Plain Layout
3350 \begin_inset Formula $\not=$
3360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3363 \begin_layout Plain Layout
3373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3376 \begin_layout Plain Layout
3377 \begin_inset Formula $\not\le$
3387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3390 \begin_layout Plain Layout
3400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3403 \begin_layout Plain Layout
3404 \begin_inset Formula $\not\parallel$
3420 \begin_layout Standard
3421 The last example shows, that not all negations look good.
3422 Therefore there are for some negations special commands (see
3423 \begin_inset CommandInset ref
3425 reference "sub:Mathematical-Symbols"
3430 \begin_inset CommandInset ref
3432 reference "sec:Relations"
3439 \begin_layout Subsection
3441 \begin_inset CommandInset label
3443 name "sub:Placeholders"
3451 \begin_layout Plain Layout
3461 \begin_layout Plain Layout
3462 Chemical characters ! Isotopes
3471 \begin_layout Plain Layout
3476 \begin_layout Plain Layout
3487 \begin_layout Plain Layout
3502 \begin_layout Standard
3504 \begin_inset space \thinspace{}
3508 \begin_inset space \space{}
3515 \begin_layout Plain Layout
3516 Typesetting isotopes and chemical symbols is described in
3517 \begin_inset CommandInset ref
3519 reference "sub:Chemical-Symbols-and"
3528 the following problem occurs:
3531 \begin_layout Standard
3533 \begin_inset Tabular
3534 <lyxtabular version="3" rows="2" columns="2">
3536 <column alignment="center" valignment="top" width="0pt">
3537 <column alignment="center" valignment="top" width="0pt">
3539 <cell alignment="center" valignment="top" usebox="none">
3542 \begin_layout Plain Layout
3543 Indices created with sub- and superscripts:
3548 <cell alignment="center" valignment="top" usebox="none">
3551 \begin_layout Plain Layout
3552 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3562 <cell alignment="center" valignment="top" usebox="none">
3565 \begin_layout Plain Layout
3571 <cell alignment="center" valignment="top" usebox="none">
3574 \begin_layout Plain Layout
3575 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3589 \begin_inset Note Note
3592 \begin_layout Plain Layout
3599 is only used as spacer.
3607 \begin_layout Standard
3608 The shorter index is by default placed below or above the first character
3609 of the longer index.
3610 To avoid this there is the command
3620 \begin_layout Plain Layout
3628 or the math toolbar button
3629 \begin_inset space \thinspace{}
3636 \begin_layout Plain Layout
3637 can be found in the submenu of the toolbar button
3638 \begin_inset Graphics
3639 filename ../images/math/space.png
3650 \begin_inset Graphics
3651 filename ../images/math/phantom.png
3656 that creates one or more phantom characters.
3663 a small blue box appears that is superposed with two red arrows.
3664 The arrows indicate that the complete width and height of the box content
3665 will be created as placeholder.
3666 Phantom characters are accordingly placeholders with the size of the characters.
3669 \begin_layout Standard
3671 \begin_inset Tabular
3672 <lyxtabular version="3" rows="4" columns="2">
3674 <column alignment="center" valignment="top" width="0">
3675 <column alignment="center" valignment="top" width="0">
3677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3680 \begin_layout Plain Layout
3686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3689 \begin_layout Plain Layout
3691 \begin_inset Note Note
3694 \begin_layout Plain Layout
3701 is only used as spacer.
3713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3716 \begin_layout Plain Layout
3721 \begin_layout Plain Layout
3736 \begin_layout Plain Layout
3746 \begin_inset Formula $\to$
3753 \begin_layout Plain Layout
3767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3770 \begin_layout Plain Layout
3771 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3784 \begin_layout Plain Layout
3789 \begin_layout Plain Layout
3804 \begin_layout Plain Layout
3814 \begin_inset Formula $\to$
3821 \begin_layout Plain Layout
3835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3838 \begin_layout Plain Layout
3839 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3852 \begin_layout Plain Layout
3859 \begin_layout Plain Layout
3874 \begin_layout Plain Layout
3884 \begin_inset Formula $\to$
3891 \begin_layout Plain Layout
3905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3908 \begin_layout Plain Layout
3909 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3925 \begin_layout Standard
3926 Furthermore there are the commands
3936 \begin_layout Plain Layout
3945 \begin_inset space ~
3949 \begin_inset Graphics
3950 filename ../images/math/vphantom.png
3965 \begin_layout Plain Layout
3974 \begin_inset space ~
3978 \begin_inset Graphics
3979 filename ../images/math/hphantom.png
3991 creates only space for the maximal height of the characters in the box
3992 but not for its width.
3999 creates only space for the width of the box content.
4000 Therefore the boxes of both commands have only one red arrow.
4003 \begin_layout Standard
4014 \begin_layout Plain Layout
4029 space for the height of the integral sign,
4033 \begin_layout Plain Layout
4040 creates an integral sign, see
4041 \begin_inset CommandInset ref
4043 reference "sub:Big-Operators"
4052 because this is the larger character.
4053 An example application is in
4054 \begin_inset CommandInset ref
4056 reference "sub:Multiline-Brackets"
4063 \begin_layout Subsection
4068 \begin_layout Plain Layout
4078 \begin_layout Plain Layout
4079 Formula ! underlined
4087 \begin_layout Standard
4089 \begin_inset Tabular
4090 <lyxtabular version="3" rows="4" columns="2">
4092 <column alignment="center" valignment="top" width="0pt">
4093 <column alignment="center" valignment="top" width="0pt">
4095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4098 \begin_layout Plain Layout
4104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4107 \begin_layout Plain Layout
4109 \begin_inset Note Note
4112 \begin_layout Plain Layout
4119 is only used as spacer.
4131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4134 \begin_layout Plain Layout
4141 \begin_layout Plain Layout
4154 \begin_layout Plain Layout
4167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4170 \begin_layout Plain Layout
4171 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4181 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4184 \begin_layout Plain Layout
4191 \begin_layout Plain Layout
4204 \begin_layout Plain Layout
4217 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4220 \begin_layout Plain Layout
4221 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4234 \begin_layout Plain Layout
4241 \begin_layout Plain Layout
4256 \begin_layout Plain Layout
4270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4273 \begin_layout Plain Layout
4274 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4290 \begin_layout Standard
4291 In the last example it doesn't matter if first
4306 \begin_layout Standard
4307 To double underline e.
4308 \begin_inset space \thinspace{}
4312 \begin_inset space \space{}
4324 \begin_layout Standard
4325 It is possible to place up to 6 lines above or below characters.
4328 \begin_layout Standard
4329 \begin_inset VSpace bigskip
4332 Custom lines can be created using the command
4342 \begin_layout Plain Layout
4350 which has the following scheme:
4353 \begin_layout Standard
4358 rule[vertical offset]{length}{thickness}
4361 \begin_layout Standard
4362 The optional vertical offset shifts the line upwards (or downwards, when
4363 the value is negative).
4365 \begin_inset CommandInset ref
4367 reference "tab:Available-units"
4371 can be used for the values.
4372 Here are two example lines created with the commands
4373 \begin_inset Newline newline
4380 rule[-2ex]{3cm}{2pt}
4391 \begin_layout Standard
4393 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4399 \begin_layout Standard
4406 can also be used for text when it is inserted in TeX-mode.
4409 \begin_layout Subsection
4411 \begin_inset CommandInset label
4421 \begin_layout Plain Layout
4430 \begin_layout Standard
4431 There are different types of ellipses available.
4435 \begin_layout Plain Layout
4436 In the math toolbar in the submenu of the button
4437 \begin_inset Graphics
4438 filename ../images/math/ldots.png
4448 For listings dots at the baseline are used (
4458 \begin_layout Plain Layout
4466 ), while for operations dots are needed that are on the same height as the
4477 \begin_layout Plain Layout
4486 When using the command
4496 \begin_layout Plain Layout
4504 , LaTeX decides on the basis of the next character what type is used.
4507 \begin_layout Standard
4509 \begin_inset Tabular
4510 <lyxtabular version="3" rows="8" columns="2">
4512 <column alignment="center" valignment="top" width="0pt">
4513 <column alignment="center" valignment="top" width="0pt">
4515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4518 \begin_layout Plain Layout
4524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4527 \begin_layout Plain Layout
4535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4538 \begin_layout Plain Layout
4543 \begin_layout Plain Layout
4558 \begin_layout Plain Layout
4572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4575 \begin_layout Plain Layout
4576 \begin_inset Formula $A_{1},\dots,A_{n}$
4586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4589 \begin_layout Plain Layout
4594 \begin_layout Plain Layout
4609 \begin_layout Plain Layout
4623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4626 \begin_layout Plain Layout
4627 \begin_inset Formula $A_{1}+\dots+A_{n}$
4637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4640 \begin_layout Plain Layout
4645 \begin_layout Plain Layout
4660 \begin_layout Plain Layout
4674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4677 \begin_layout Plain Layout
4678 \begin_inset Formula $A_{1},\ldots,A_{n}$
4688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4691 \begin_layout Plain Layout
4696 \begin_layout Plain Layout
4711 \begin_layout Plain Layout
4725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4728 \begin_layout Plain Layout
4729 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4742 \begin_layout Plain Layout
4750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4753 \begin_layout Plain Layout
4754 \begin_inset Formula $\vdots$
4764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4767 \begin_layout Plain Layout
4775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4778 \begin_layout Plain Layout
4779 \begin_inset Formula $\ddots$
4789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4792 \begin_layout Plain Layout
4794 \begin_inset space \thinspace{}
4797 matrix with the different dots
4802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4805 \begin_layout Plain Layout
4806 \begin_inset Formula $\begin{array}{ccc}
4807 A_{11} & \cdots & A_{1m}\\
4808 \vdots & \ddots & \vdots\\
4809 A_{n1} & \cdots & A_{nm}\end{array}$
4825 \begin_layout Standard
4826 The ellipses available in menu
4828 Insert\SpecialChar \menuseparator
4830 \begin_inset space ~
4844 \begin_layout Standard
4845 \begin_inset VSpace medskip
4848 Specially for matrices there are ellipses that span over several columns.
4849 They are created with the command
4859 \begin_layout Plain Layout
4867 , that has the following scheme:
4870 \begin_layout Standard
4875 hdotsfor[distance]{number of columns}
4878 \begin_layout Standard
4879 The number of columns specifies how many columns should be spanned.
4880 Distance is a factor for the distance between the dots.
4883 \begin_layout Standard
4884 In the following matrix the command
4890 was inserted in the first box of the second line, to get an ellipsis with
4891 a dot distance twice as long as with the command
4898 \begin_inset Formula \[
4899 \left(\begin{array}{cccc}
4902 q & w & e & r\end{array}\right)\]
4906 Note that the matrix fields that should be spanned must be empty, otherwise
4907 you get LaTeX-errors.
4910 \begin_layout Standard
4911 \begin_inset VSpace bigskip
4914 Furthermore you can fill with the command
4924 \begin_layout Plain Layout
4932 the rest of a line with dots.
4933 The effect of these commands is the same like with
4940 \begin_inset CommandInset ref
4942 reference "sub:Variable-Space"
4949 \begin_layout Standard
4950 For example the command
4958 \begin_layout Plain Layout
4972 \begin_layout Standard
4973 \begin_inset Formula $A\dotfill B$
4979 \begin_layout Standard
4986 there is for a line the command
4996 \begin_layout Plain Layout
5007 \begin_layout Standard
5008 \begin_inset Formula $A\hrulefill B$
5014 \begin_layout Standard
5015 To use the commands for text, they have to be inserted in TeX-mode.
5018 \begin_layout Section
5020 \begin_inset CommandInset label
5030 \begin_layout Plain Layout
5039 \begin_layout Standard
5040 Matrices can be inserted via the math toolbar button
5041 \begin_inset Graphics
5042 filename ../images/dialog-show_mathmatrix.png
5049 Insert\SpecialChar \menuseparator
5050 Math\SpecialChar \menuseparator
5054 You will be asked for the number of matrix columns and rows, and the alignment.
5055 The vertical alignment is hereby only of importance for matrices in inline
5059 \begin_layout Standard
5060 The first matrix is top
5061 \begin_inset Formula $\begin{array}[t]{cccc}
5064 C & F & I & L\end{array}$
5068 \begin_inset Formula $\begin{array}{cccc}
5071 C & F & I & L\end{array}$
5074 , and the third bottom
5075 \begin_inset Formula $\begin{array}[b]{cccc}
5078 C & F & I & L\end{array}$
5084 \begin_layout Standard
5085 The horizontal alignment specifies how the column entries should be aligned.
5086 It is set by entering a letter for every column.
5091 denotes left aligned,
5100 To create for example a 4
5105 \begin_inset space ~
5108 matrix where the first column is left aligned, the second and third are
5109 centered, and the last one is right aligned, one enters for the horizontal
5115 Normally are in a matrix all columns centered, therefore the default is
5116 for every column is a
5123 \begin_layout Standard
5124 Horizontal alignment:
5127 \begin_layout Standard
5133 \begin_inset Formula $\begin{array}{lll}
5136 C & F & 10000\end{array}$
5144 \begin_inset Formula $\begin{array}{ccc}
5147 C & F & 10000\end{array}$
5155 \begin_inset Formula $\begin{array}{rrr}
5158 C & F & 10000\end{array}$
5164 \begin_layout Standard
5165 To add or delete rows and columns subsequently, the math toolbar buttons
5167 \begin_inset Graphics
5168 filename ../images/tabular-feature_append-row.png
5174 \begin_inset Graphics
5175 filename ../images/tabular-feature_delete-row.png
5181 \begin_inset space \thinspace{}
5186 Edit\SpecialChar \menuseparator
5190 New rows can also be created with
5193 arg "newline-insert newline"
5199 \begin_layout Standard
5200 \begin_inset VSpace bigskip
5203 Parentheses around a matrix can can either be created with the commands
5214 \begin_layout Plain Layout
5232 \begin_layout Plain Layout
5243 \begin_inset space ~
5249 \begin_inset CommandInset ref
5251 reference "sub:Automatic-Bracket-Size"
5255 , or by using the following commands:
5256 \begin_inset VSpace medskip
5262 \begin_layout Standard
5263 \begin_inset space \hfill{}
5267 \begin_inset Tabular
5268 <lyxtabular version="3" rows="4" columns="2">
5270 <column alignment="center" valignment="top" width="0">
5271 <column alignment="center" valignment="top" width="0">
5273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5276 \begin_layout Plain Layout
5282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5285 \begin_layout Plain Layout
5287 \begin_inset Note Note
5290 \begin_layout Plain Layout
5297 is only used as spacer.
5309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5312 \begin_layout Plain Layout
5319 \begin_layout Plain Layout
5333 \begin_inset space \thinspace{}
5341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5344 \begin_layout Plain Layout
5345 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5346 0 & \textrm{-}\mathrm{i}\\
5347 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5360 \begin_layout Plain Layout
5367 \begin_layout Plain Layout
5381 \begin_inset space \thinspace{}
5389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5392 \begin_layout Plain Layout
5393 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5394 0 & \textrm{-}\mathrm{i}\\
5395 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5408 \begin_layout Plain Layout
5415 \begin_layout Plain Layout
5429 \begin_inset space \thinspace{}
5437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5440 \begin_layout Plain Layout
5441 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5442 0 & \textrm{-}\mathrm{i}\\
5443 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5457 \begin_inset space \hfill{}
5461 \begin_inset Tabular
5462 <lyxtabular version="3" rows="4" columns="2">
5464 <column alignment="center" valignment="top" width="0">
5465 <column alignment="center" valignment="top" width="0">
5467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5470 \begin_layout Plain Layout
5476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5479 \begin_layout Plain Layout
5487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5490 \begin_layout Plain Layout
5497 \begin_layout Plain Layout
5511 \begin_inset space \thinspace{}
5519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5522 \begin_layout Plain Layout
5523 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5524 0 & \textrm{-}\mathrm{i}\\
5525 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5538 \begin_layout Plain Layout
5545 \begin_layout Plain Layout
5559 \begin_inset space \thinspace{}
5567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5570 \begin_layout Plain Layout
5571 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5572 0 & \textrm{-}\mathrm{i}\\
5573 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5586 \begin_layout Plain Layout
5593 \begin_layout Plain Layout
5607 \begin_inset space \thinspace{}
5615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5618 \begin_layout Plain Layout
5619 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5620 0 & \textrm{-}\mathrm{i}\\
5621 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5635 \begin_inset space \hfill{}
5641 \begin_layout Standard
5642 \begin_inset VSpace medskip
5646 \begin_inset space \thinspace{}
5650 \begin_inset space \space{}
5659 is inserted, a blue box appears between two vertical lines where the matrix
5663 \begin_layout Standard
5664 \begin_inset VSpace bigskip
5667 As all multiline formulas are matrices, the length
5677 \begin_layout Plain Layout
5685 that is described in
5686 \begin_inset CommandInset ref
5688 reference "sub:Column-Separation"
5692 can also be used to change the column separation of matrices.
5695 \begin_layout Standard
5696 To change the row separation, the command
5706 \begin_layout Plain Layout
5715 It is used as follows:
5718 \begin_layout Standard
5725 arraystretch}{stretch factor}
5729 \begin_layout Plain Layout
5740 \begin_layout Standard
5747 assigns the stretch factor to the predefined command
5755 \begin_inset space \thinspace{}
5759 \begin_inset space \space{}
5762 the row separation, use the factor 2.
5763 This is then used for all following matrices.
5764 To go back to the original separation, assign the factor 1 to
5773 \begin_layout Standard
5774 To set matrices into a text line, the command
5784 \begin_layout Plain Layout
5793 When it is inserted a blue box with two dashed lines appears.
5794 In this box the matrix is inserted.
5797 \begin_layout Standard
5799 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5800 C & D\end{smallmatrix}\right)$
5806 \begin_layout Section
5807 Brackets and Delimiters
5811 \begin_layout Plain Layout
5821 \begin_layout Plain Layout
5830 \begin_layout Subsection
5831 Vertical Brackets and Delimiters
5835 \begin_layout Plain Layout
5844 \begin_layout Standard
5845 \begin_inset space \hfill{}
5849 \begin_inset Tabular
5850 <lyxtabular version="3" rows="9" columns="2">
5852 <column alignment="center" valignment="top" width="0pt">
5853 <column alignment="center" valignment="top" width="0pt">
5855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5858 \begin_layout Plain Layout
5864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5867 \begin_layout Plain Layout
5875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5878 \begin_layout Plain Layout
5884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5887 \begin_layout Plain Layout
5888 \begin_inset Formula $($
5898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5901 \begin_layout Plain Layout
5907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5910 \begin_layout Plain Layout
5911 \begin_inset Formula $\{$
5921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5924 \begin_layout Plain Layout
5930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5933 \begin_layout Plain Layout
5934 \begin_inset Formula $[$
5944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5947 \begin_layout Plain Layout
5955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5958 \begin_layout Plain Layout
5959 \begin_inset Formula $\langle$
5969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5972 \begin_layout Plain Layout
5980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5983 \begin_layout Plain Layout
5984 \begin_inset Formula $\lceil$
5994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5997 \begin_layout Plain Layout
6005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6008 \begin_layout Plain Layout
6009 \begin_inset Formula $\lfloor$
6019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6022 \begin_layout Plain Layout
6028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6031 \begin_layout Plain Layout
6032 \begin_inset Formula $/$
6042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6045 \begin_layout Plain Layout
6051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6054 \begin_layout Plain Layout
6055 \begin_inset Formula $|$
6069 \begin_inset space \hfill{}
6073 \begin_inset Tabular
6074 <lyxtabular version="3" rows="9" columns="2">
6076 <column alignment="center" valignment="top" width="0pt">
6077 <column alignment="center" valignment="top" width="0pt">
6079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6082 \begin_layout Plain Layout
6088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6091 \begin_layout Plain Layout
6099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6102 \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 $)$
6122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6125 \begin_layout Plain Layout
6131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6134 \begin_layout Plain Layout
6135 \begin_inset Formula $\}$
6145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6148 \begin_layout Plain Layout
6154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6157 \begin_layout Plain Layout
6158 \begin_inset Formula $]$
6168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6171 \begin_layout Plain Layout
6179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6182 \begin_layout Plain Layout
6183 \begin_inset Formula $\rangle$
6193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6196 \begin_layout Plain Layout
6204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6207 \begin_layout Plain Layout
6208 \begin_inset Formula $\rceil$
6218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6221 \begin_layout Plain Layout
6229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6232 \begin_layout Plain Layout
6233 \begin_inset Formula $\rfloor$
6243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6246 \begin_layout Plain Layout
6256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6259 \begin_layout Plain Layout
6260 \begin_inset Formula $\backslash$
6270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6273 \begin_layout Plain Layout
6281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6284 \begin_layout Plain Layout
6285 \begin_inset Formula $\|$
6299 \begin_inset space \hfill{}
6305 \begin_layout Standard
6308 \begin_inset Note Greyedout
6311 \begin_layout Plain Layout
6316 In TeX-mode the command
6326 \begin_layout Plain Layout
6334 must be used for the backslash, because the command
6342 produces there a line break.
6350 \begin_layout Standard
6351 For all characters listed above the size can be adjusted with the commands
6352 described in the following two subsections.
6353 When using these commands, the characters < and > can directly be used
6354 instead of the commands
6369 \begin_layout Subsubsection
6371 \begin_inset CommandInset label
6373 name "sub:Manual-Bracket-Size"
6381 \begin_layout Plain Layout
6382 Bracket size ! manual
6390 \begin_layout Standard
6391 The bracket size can be specified manually by the LaTeX-commands
6401 \begin_layout Plain Layout
6434 denotes the smallest and
6440 the largest bracket size.
6443 \begin_layout Standard
6444 These commands are used to emphasize levels of brackets:
6447 \begin_layout Standard
6449 \begin_inset Tabular
6450 <lyxtabular version="3" rows="2" columns="2">
6452 <column alignment="center" valignment="top" width="0pt">
6453 <column alignment="center" valignment="top" width="0pt">
6455 <cell alignment="center" valignment="top" usebox="none">
6458 \begin_layout Plain Layout
6459 all brackets in the same size:
6464 <cell alignment="center" valignment="top" usebox="none">
6467 \begin_layout Plain Layout
6468 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6478 <cell alignment="center" valignment="top" usebox="none">
6481 \begin_layout Plain Layout
6487 <cell alignment="center" valignment="top" usebox="none">
6490 \begin_layout Plain Layout
6491 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6505 \begin_inset Note Note
6508 \begin_layout Plain Layout
6515 is only used as spacer.
6523 \begin_layout Standard
6524 For the second formula the command
6534 \begin_layout Plain Layout
6548 \begin_layout Standard
6549 Here is an overview about all bracket sizes:
6552 \begin_layout Standard
6572 \begin_layout Plain Layout
6589 \begin_layout Plain Layout
6602 \begin_layout Plain Layout
6618 \begin_layout Standard
6620 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6626 \begin_layout Standard
6633 -commands there is the variant
6643 \begin_layout Plain Layout
6651 that adds a bit more space between the bracket and its content, and the
6668 \begin_layout Plain Layout
6678 , that don't add additional space.
6683 at the end of the command
6689 is for a left bracket; for a right bracket this will be replaced by an
6695 A left or right bracket can each be an opening or closing bracket.
6698 \begin_layout Standard
6699 In the following table is a comparison of the variants:
6702 \begin_layout Standard
6704 \begin_inset Tabular
6705 <lyxtabular version="3" rows="5" columns="2">
6707 <column alignment="center" valignment="middle" width="0">
6708 <column alignment="center" valignment="middle" width="0">
6710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6713 \begin_layout Plain Layout
6719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6722 \begin_layout Plain Layout
6724 \begin_inset Note Note
6727 \begin_layout Plain Layout
6734 is only used as spacer.
6746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6749 \begin_layout Plain Layout
6764 \begin_layout Plain Layout
6782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6785 \begin_layout Plain Layout
6786 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6799 \begin_layout Plain Layout
6814 \begin_layout Plain Layout
6832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6835 \begin_layout Plain Layout
6836 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6849 \begin_layout Plain Layout
6864 \begin_layout Plain Layout
6882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6885 \begin_layout Plain Layout
6886 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6899 \begin_layout Plain Layout
6911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6914 \begin_layout Plain Layout
6915 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6931 \begin_layout Subsubsection
6932 Automatic Bracket Size
6933 \begin_inset CommandInset label
6935 name "sub:Automatic-Bracket-Size"
6943 \begin_layout Plain Layout
6944 Bracket size ! automatic
6952 \begin_layout Standard
6953 Brackets with variable size can be inserted with the commands
6963 \begin_layout Plain Layout
6981 \begin_layout Plain Layout
6989 or via the math toolbar button
6990 \begin_inset Graphics
6991 filename ../images/dialog-show_mathdelimiter.png
7009 the wanted bracket must be inserted.
7010 The bracket size will then automatically be calculated for the output.
7013 \begin_layout Standard
7015 normal bracket: The command
7025 \begin_layout Plain Layout
7035 \begin_inset Formula $\downarrow$
7042 \begin_layout Plain Layout
7054 \begin_inset Formula \[
7062 \begin_layout Standard
7064 multiline bracket: The command
7076 \begin_layout Plain Layout
7086 \begin_inset Formula $\downarrow$
7093 \begin_layout Plain Layout
7107 \begin_inset Formula \[
7108 \ln\left(\frac{A}{C}\right)\]
7115 \begin_layout Standard
7131 \begin_inset space ~
7137 This has the advantage that you can see in LyX immediately the real bracket
7138 size and that the matching right bracket will be created too.
7139 \begin_inset Newline newline
7142 The command for the last example would then be:
7156 \begin_layout Plain Layout
7166 \begin_inset Formula $\downarrow$
7172 \begin_layout Standard
7173 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7174 For example the command
7184 \begin_layout Plain Layout
7194 \begin_inset Formula $\downarrow$
7201 \begin_layout Plain Layout
7217 \begin_inset Formula \[
7218 \left.\frac{A}{B}\right\} \]
7236 will be converted by LyX to brackets in the right size when the document
7237 is reloaded and an omitted bracket will appear as dashed line.
7240 \begin_layout Standard
7241 \begin_inset VSpace bigskip
7244 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7255 \begin_layout Plain Layout
7263 is additionally available for all brackets and limits.
7264 With this command the height of the following character is adapted to the
7265 one of the surrounding brackets, what is e.
7266 \begin_inset space \thinspace{}
7270 \begin_inset space \space{}
7273 needed for physical vectors:
7274 \begin_inset Formula \[
7275 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7279 For physical vectors there is a special LaTeX-package, described in
7280 \begin_inset CommandInset ref
7282 reference "sub:Physical-Vectors"
7289 \begin_layout Subsection
7294 \begin_layout Plain Layout
7295 Brackets ! horizontal
7303 \begin_layout Standard
7305 \begin_inset Tabular
7306 <lyxtabular version="3" rows="4" columns="2">
7308 <column alignment="center" valignment="top" width="0pt">
7309 <column alignment="center" valignment="top" width="0pt">
7311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7314 \begin_layout Plain Layout
7316 \begin_inset Note Note
7319 \begin_layout Plain Layout
7326 is only used as spacer.
7336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7339 \begin_layout Plain Layout
7347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7350 \begin_layout Plain Layout
7354 \begin_layout Plain Layout
7369 \begin_layout Plain Layout
7382 \begin_layout Plain Layout
7395 \begin_layout Plain Layout
7408 \begin_layout Plain Layout
7419 \begin_layout Plain Layout
7432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7435 \begin_layout Plain Layout
7436 \begin_inset Formula $\overbrace{A+B}^{3}$
7446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7449 \begin_layout Plain Layout
7453 \begin_layout Plain Layout
7468 \begin_layout Plain Layout
7481 \begin_layout Plain Layout
7494 \begin_layout Plain Layout
7505 \begin_layout Plain Layout
7518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7521 \begin_layout Plain Layout
7522 \begin_inset Formula $\underbrace{A+B}_{5}$
7532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7535 \begin_layout Plain Layout
7542 \begin_layout Plain Layout
7557 \begin_layout Plain Layout
7570 \begin_layout Plain Layout
7583 \begin_layout Plain Layout
7596 \begin_layout Plain Layout
7609 \begin_layout Plain Layout
7622 \begin_layout Plain Layout
7636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7639 \begin_layout Plain Layout
7640 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7656 \begin_layout Standard
7657 In the last example it doesn't matter if
7669 is inserted at first.
7672 \begin_layout Standard
7673 \begin_inset VSpace bigskip
7676 When brackets are needed that overlap each other, multiline formulas, as
7678 \begin_inset CommandInset ref
7680 reference "sec:Multiline-Formulas"
7685 \begin_inset Formula \begin{eqnarray*}
7686 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7687 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7691 In the first row the formula is inserted together with the first brace.
7692 It is hereby important that the space command
7696 \begin_layout Plain Layout
7697 Space commands are explained in
7698 \begin_inset CommandInset ref
7700 reference "sub:Predefined-Space"
7715 is inserted before the first
7716 \begin_inset Formula $d$
7719 , because the brace that ends behind the
7720 \begin_inset Formula $q$
7723 prevents that the following
7724 \begin_inset Quotes eld
7728 \begin_inset Quotes erd
7731 is surrounded by space.
7735 \begin_layout Plain Layout
7736 because a bracket is not handled as character, see
7737 \begin_inset CommandInset ref
7739 reference "sub:Binary-Operators"
7748 In the second row the second brace is inserted.
7749 As it should begin before the
7750 \begin_inset Formula $b$
7765 \begin_layout Plain Layout
7773 \begin_inset CommandInset ref
7775 reference "sub:Placeholders"
7784 This space is needed because the
7785 \begin_inset Quotes eld
7789 \begin_inset Quotes erd
7792 is also surrounded by space in the formula.
7793 The brace is placed under the command
7802 \begin_layout Standard
7803 It gets more complicated when brackets overlap each other, like in the following
7808 \begin_layout Plain Layout
7820 \begin_inset Formula \begin{eqnarray*}
7821 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7822 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7830 \begin_layout Plain Layout
7841 The first formula row is the same as the second row of the previous example,
7842 with the difference that the brace is above.
7843 The second row contains the formula together with the second brace.
7844 To avoid that there is space between the upper brace in the first row and
7845 the formula, the row spacing need to be reduced.
7846 This is not easily possible due to a bug in LyX
7850 \begin_layout Plain Layout
7851 \begin_inset CommandInset href
7853 name "LyX-bug #1505"
7854 target "http://www.lyx.org/trac/ticket/1505"
7864 As solution for the problem, the global formula row separation
7874 \begin_layout Plain Layout
7882 must be changed to -6
7883 \begin_inset space \thinspace{}
7886 pt before the formula with the command
7901 is set back after the formula to the standard value of 3
7902 \begin_inset space \thinspace{}
7905 pt using the same command.
7906 More about the row separation in formulas is explained in
7907 \begin_inset CommandInset ref
7909 reference "sub:Line-Separation"
7916 \begin_layout Section
7921 \begin_layout Plain Layout
7930 \begin_layout Standard
7931 Arrows can be inserted via the math toolbar button
7932 \begin_inset Graphics
7933 filename ../images/math/leftarrow.png
7938 or the commands listed in the following subsections.
7941 \begin_layout Standard
7942 \begin_inset Newpage newpage
7948 \begin_layout Subsection
7953 \begin_layout Plain Layout
7962 \begin_layout Standard
7963 \begin_inset space \hfill{}
7967 \begin_inset Tabular
7968 <lyxtabular version="3" rows="8" columns="2">
7970 <column alignment="center" valignment="top" width="0pt">
7971 <column alignment="center" valignment="top" width="0pt">
7973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7976 \begin_layout Plain Layout
7982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7985 \begin_layout Plain Layout
7993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7996 \begin_layout Plain Layout
8004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8007 \begin_layout Plain Layout
8008 \begin_inset Formula $\gets$
8018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8021 \begin_layout Plain Layout
8029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8032 \begin_layout Plain Layout
8033 \begin_inset Formula $\Leftarrow$
8043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8046 \begin_layout Plain Layout
8054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8057 \begin_layout Plain Layout
8058 \begin_inset Formula $\longleftarrow$
8068 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8071 \begin_layout Plain Layout
8079 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8082 \begin_layout Plain Layout
8083 \begin_inset Formula $\Longleftarrow$
8093 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8096 \begin_layout Plain Layout
8104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8107 \begin_layout Plain Layout
8108 \begin_inset Formula $\leftharpoonup$
8118 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8121 \begin_layout Plain Layout
8129 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8132 \begin_layout Plain Layout
8133 \begin_inset Formula $\leftharpoondown$
8143 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8146 \begin_layout Plain Layout
8154 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8157 \begin_layout Plain Layout
8158 \begin_inset Formula $\hookleftarrow$
8172 \begin_inset space \hfill{}
8176 \begin_inset Tabular
8177 <lyxtabular version="3" rows="8" columns="2">
8179 <column alignment="center" valignment="top" width="0pt">
8180 <column alignment="center" valignment="top" width="0pt">
8182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8185 \begin_layout Plain Layout
8191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8194 \begin_layout Plain Layout
8202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8205 \begin_layout Plain Layout
8213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8216 \begin_layout Plain Layout
8217 \begin_inset Formula $\to$
8227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8230 \begin_layout Plain Layout
8238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8241 \begin_layout Plain Layout
8242 \begin_inset Formula $\Rightarrow$
8252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8255 \begin_layout Plain Layout
8263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8266 \begin_layout Plain Layout
8267 \begin_inset Formula $\longrightarrow$
8277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8280 \begin_layout Plain Layout
8288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8291 \begin_layout Plain Layout
8292 \begin_inset Formula $\Longrightarrow$
8302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8305 \begin_layout Plain Layout
8313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8316 \begin_layout Plain Layout
8317 \begin_inset Formula $\rightharpoonup$
8327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8330 \begin_layout Plain Layout
8338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8341 \begin_layout Plain Layout
8342 \begin_inset Formula $\rightharpoondown$
8352 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8355 \begin_layout Plain Layout
8363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8366 \begin_layout Plain Layout
8367 \begin_inset Formula $\hookrightarrow$
8381 \begin_inset space \hfill{}
8387 \begin_layout Standard
8388 \begin_inset space \hfill{}
8392 \begin_inset Tabular
8393 <lyxtabular version="3" rows="6" columns="2">
8395 <column alignment="center" valignment="top" width="0pt">
8396 <column alignment="center" valignment="top" width="0pt">
8398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8401 \begin_layout Plain Layout
8407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8410 \begin_layout Plain Layout
8418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8421 \begin_layout Plain Layout
8429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8432 \begin_layout Plain Layout
8433 \begin_inset Formula $\leftrightarrow$
8443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8446 \begin_layout Plain Layout
8454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8457 \begin_layout Plain Layout
8458 \begin_inset Formula $\Leftrightarrow$
8468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8471 \begin_layout Plain Layout
8479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8482 \begin_layout Plain Layout
8483 \begin_inset Formula $\longleftrightarrow$
8493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8496 \begin_layout Plain Layout
8504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8507 \begin_layout Plain Layout
8508 \begin_inset Formula $\Longleftrightarrow$
8518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8521 \begin_layout Plain Layout
8529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8532 \begin_layout Plain Layout
8533 \begin_inset Formula $\rightleftharpoons$
8547 \begin_inset space \hspace{}
8552 \begin_inset space \hfill{}
8556 \begin_inset Tabular
8557 <lyxtabular version="3" rows="5" columns="2">
8559 <column alignment="center" valignment="top" width="0pt">
8560 <column alignment="center" valignment="top" width="0pt">
8562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8565 \begin_layout Plain Layout
8571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8574 \begin_layout Plain Layout
8582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8585 \begin_layout Plain Layout
8593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8596 \begin_layout Plain Layout
8597 \begin_inset Formula $\mapsto$
8607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8610 \begin_layout Plain Layout
8618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8621 \begin_layout Plain Layout
8622 \begin_inset Formula $\longmapsto$
8632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8635 \begin_layout Plain Layout
8643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8646 \begin_layout Plain Layout
8647 \begin_inset Formula $\leadsto$
8657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8660 \begin_layout Plain Layout
8668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8671 \begin_layout Plain Layout
8672 \begin_inset Formula $\dasharrow$
8686 \begin_inset space \hfill{}
8692 \begin_layout Standard
8693 \begin_inset VSpace medskip
8696 Arrows used as accent like e.
8697 \begin_inset space \thinspace{}
8701 \begin_inset space \space{}
8704 vector arrows are listed in
8705 \begin_inset CommandInset ref
8707 reference "sec:Accents"
8714 \begin_layout Standard
8715 \begin_inset VSpace bigskip
8718 Furthermore there are the labeled arrows
8722 \begin_layout Plain Layout
8738 \begin_layout Plain Layout
8756 \begin_layout Plain Layout
8763 \begin_layout Plain Layout
8778 When inserting one of these commands in a formula, an arrow with two blue
8779 boxes appear where the label can be inserted.
8780 The length of the arrow adapts to the label width.
8783 \begin_layout Standard
8785 \begin_inset Tabular
8786 <lyxtabular version="3" rows="3" columns="2">
8788 <column alignment="center" valignment="top" width="0pt">
8789 <column alignment="center" valignment="top" width="0pt">
8791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8794 \begin_layout Plain Layout
8800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8803 \begin_layout Plain Layout
8805 \begin_inset Note Note
8808 \begin_layout Plain Layout
8815 is only used as spacer.
8827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8830 \begin_layout Plain Layout
8837 \begin_layout Plain Layout
8847 \begin_inset Formula $\downarrow$
8851 \begin_inset Formula $\to$
8859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8862 \begin_layout Plain Layout
8863 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8876 \begin_layout Plain Layout
8883 \begin_layout Plain Layout
8893 \begin_inset Formula $\downarrow$
8897 \begin_inset Formula $\to$
8905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8908 \begin_layout Plain Layout
8909 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8925 \begin_layout Subsection
8926 Vertical and diagonal Arrows
8930 \begin_layout Plain Layout
8940 \begin_layout Plain Layout
8949 \begin_layout Standard
8950 \begin_inset space \hfill{}
8954 \begin_inset Tabular
8955 <lyxtabular version="3" rows="7" columns="2">
8957 <column alignment="center" valignment="top" width="0pt">
8958 <column alignment="center" valignment="top" width="0pt">
8960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8963 \begin_layout Plain Layout
8969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8972 \begin_layout Plain Layout
8980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8983 \begin_layout Plain Layout
8991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8994 \begin_layout Plain Layout
8995 \begin_inset Formula $\uparrow$
9005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9008 \begin_layout Plain Layout
9016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9019 \begin_layout Plain Layout
9020 \begin_inset Formula $\Uparrow$
9030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9033 \begin_layout Plain Layout
9041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9044 \begin_layout Plain Layout
9045 \begin_inset Formula $\updownarrow$
9055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9058 \begin_layout Plain Layout
9066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9069 \begin_layout Plain Layout
9070 \begin_inset Formula $\Updownarrow$
9080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9083 \begin_layout Plain Layout
9091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9094 \begin_layout Plain Layout
9095 \begin_inset Formula $\Downarrow$
9105 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9108 \begin_layout Plain Layout
9116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9119 \begin_layout Plain Layout
9120 \begin_inset Formula $\downarrow$
9134 \begin_inset space \hfill{}
9138 \begin_inset Tabular
9139 <lyxtabular version="3" rows="5" columns="2">
9141 <column alignment="center" valignment="top" width="0pt">
9142 <column alignment="center" valignment="top" width="0pt">
9144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9147 \begin_layout Plain Layout
9153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9156 \begin_layout Plain Layout
9164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9167 \begin_layout Plain Layout
9175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9178 \begin_layout Plain Layout
9179 \begin_inset Formula $\nearrow$
9189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9192 \begin_layout Plain Layout
9200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9203 \begin_layout Plain Layout
9204 \begin_inset Formula $\searrow$
9214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9217 \begin_layout Plain Layout
9225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9228 \begin_layout Plain Layout
9229 \begin_inset Formula $\swarrow$
9239 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9242 \begin_layout Plain Layout
9250 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9253 \begin_layout Plain Layout
9254 \begin_inset Formula $\nwarrow$
9268 \begin_inset space \hfill{}
9274 \begin_layout Standard
9275 \begin_inset VSpace medskip
9278 Vertical arrows can be used also as delimiter together with the commands
9280 \begin_inset CommandInset ref
9282 reference "sub:Manual-Bracket-Size"
9287 \begin_inset CommandInset ref
9289 reference "sub:Automatic-Bracket-Size"
9296 \begin_layout Standard
9297 \begin_inset Newpage newpage
9303 \begin_layout Section
9305 \begin_inset CommandInset label
9315 \begin_layout Plain Layout
9324 \begin_layout Standard
9325 Accents can be inserted via the math toolbar button
9326 \begin_inset Graphics
9327 filename ../images/math/hat.png
9332 or the commands listed in the following subsections.
9335 \begin_layout Subsection
9336 Accents for one Character
9340 \begin_layout Plain Layout
9353 \begin_layout Plain Layout
9355 \begin_inset CommandInset ref
9357 reference "sub:Accents-in-Text"
9370 \begin_layout Plain Layout
9378 \begin_inset Note Note
9381 \begin_layout Plain Layout
9384 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9387 \begin_layout Plain Layout
9390 texorpdfstring is in section
9391 \begin_inset CommandInset ref
9393 reference "sub:Formulas-in-Section"
9403 \begin_inset CommandInset label
9405 name "sub:Accents-for-one"
9413 \begin_layout Plain Layout
9414 Accents ! for one character
9422 \begin_layout Standard
9423 \begin_inset space \hfill{}
9427 \begin_inset Tabular
9428 <lyxtabular version="3" rows="8" columns="2">
9430 <column alignment="center" valignment="top" width="0pt">
9431 <column alignment="center" valignment="top" width="0pt">
9433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9436 \begin_layout Plain Layout
9442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9445 \begin_layout Plain Layout
9447 \begin_inset Note Note
9450 \begin_layout Plain Layout
9457 is only used as spacer.
9469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9472 \begin_layout Plain Layout
9479 \begin_layout Plain Layout
9493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9496 \begin_layout Plain Layout
9497 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9507 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9510 \begin_layout Plain Layout
9517 \begin_layout Plain Layout
9531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9534 \begin_layout Plain Layout
9535 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9545 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9548 \begin_layout Plain Layout
9555 \begin_layout Plain Layout
9569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9572 \begin_layout Plain Layout
9573 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9583 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9586 \begin_layout Plain Layout
9594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9597 \begin_layout Plain Layout
9598 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9608 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9611 \begin_layout Plain Layout
9618 \begin_layout Plain Layout
9631 \begin_layout Plain Layout
9642 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9645 \begin_layout Plain Layout
9646 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9656 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9659 \begin_layout Plain Layout
9666 \begin_layout Plain Layout
9680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9683 \begin_layout Plain Layout
9684 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9694 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9697 \begin_layout Plain Layout
9704 \begin_layout Plain Layout
9718 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9721 \begin_layout Plain Layout
9722 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9736 \begin_inset space \hfill{}
9740 \begin_inset Tabular
9741 <lyxtabular version="3" rows="7" columns="2">
9743 <column alignment="center" valignment="top" width="0pt">
9744 <column alignment="center" valignment="top" width="0pt">
9746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9749 \begin_layout Plain Layout
9755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9758 \begin_layout Plain Layout
9766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9769 \begin_layout Plain Layout
9776 \begin_layout Plain Layout
9790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9793 \begin_layout Plain Layout
9794 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
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 $\raisebox{5mm}{}\hat{A}$
9842 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9845 \begin_layout Plain Layout
9852 \begin_layout Plain Layout
9866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9869 \begin_layout Plain Layout
9870 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9880 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9883 \begin_layout Plain Layout
9890 \begin_layout Plain Layout
9904 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9907 \begin_layout Plain Layout
9908 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9918 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9921 \begin_layout Plain Layout
9928 \begin_layout Plain Layout
9942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9945 \begin_layout Plain Layout
9946 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9956 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9959 \begin_layout Plain Layout
9966 \begin_layout Plain Layout
9980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9983 \begin_layout Plain Layout
9984 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9998 \begin_inset space \hfill{}
10004 \begin_layout Standard
10005 \begin_inset VSpace bigskip
10011 \begin_layout Standard
10012 You can directly insert accents like é to formulas.
10013 LyX will transform them to the corresponding accent command.
10018 \begin_layout Plain Layout
10024 it is better to insert a quotation mark before the vowel.
10025 These two characters are then treated by LaTeX as
10029 character when the formula part with the umlaut is marked as German.
10037 \begin_inset Quotes eld
10041 \begin_inset Quotes erd
10044 umlauts are created as demonstrated in the following example:
10047 \begin_layout Standard
10048 \begin_inset VSpace -2mm
10054 \begin_layout Standard
10056 \begin_inset Tabular
10057 <lyxtabular version="3" rows="3" columns="2">
10059 <column alignment="center" valignment="top" width="0">
10060 <column alignment="center" valignment="top" width="0">
10062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10065 \begin_layout Plain Layout
10071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10074 \begin_layout Plain Layout
10076 \begin_inset Note Note
10079 \begin_layout Plain Layout
10087 \begin_inset space \thinspace{}
10090 pt space are only used as spacer.
10102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10105 \begin_layout Plain Layout
10108 \begin_inset Quotes grd
10116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10119 \begin_layout Plain Layout
10120 \begin_inset space \hspace{}
10127 \begin_inset Formula $"i$
10137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10140 \begin_layout Plain Layout
10147 \begin_layout Plain Layout
10161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10164 \begin_layout Plain Layout
10165 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10181 \begin_layout Standard
10182 Another advantage to
10188 is that umlauts can directly be converted to mathematical text because
10189 the accent commands above are
10195 in mathematical text
10198 To convert an accented character to mathematical text, only the character
10199 under the accent may be converted.
10200 This applies also for all other conversions, e.
10201 \begin_inset space \thinspace{}
10205 \begin_inset space \space{}
10211 \begin_layout Standard
10212 In mathematical text, umlauts and other accented characters can directly
10216 \begin_layout Subsection
10217 Accents for Operators
10221 \begin_layout Plain Layout
10222 Accents ! for operators
10230 \begin_layout Standard
10241 \begin_layout Plain Layout
10259 \begin_layout Plain Layout
10267 characters can be placed above or below an operator, respectively, to accent
10279 \begin_layout Plain Layout
10287 characters can be set before and behind an operator.
10288 The command scheme is:
10291 \begin_layout Standard
10307 \begin_layout Standard
10314 must always be before the operator that should be accented.
10315 You can accent with several characters and even with other operators and
10323 for example only characters behind an operator, write nothing between the
10324 first braces but don't omit the braces.
10327 \begin_layout Standard
10328 For example the command
10333 \begin_inset Formula $\to$
10343 \begin_inset Formula $\to$
10352 \begin_layout Plain Layout
10368 \begin_inset Formula \[
10369 \sideset{}{'}\sum_{k=1}^{n}\]
10376 \begin_layout Standard
10385 \begin_layout Plain Layout
10400 \begin_layout Plain Layout
10412 \begin_inset Formula $\uparrow$
10420 \begin_inset Formula \[
10421 \overset{a}{\maltese}\]
10425 As seen in the last example, with
10437 also symbols and characters can be accented; with
10443 this is not possible.
10446 \begin_layout Subsection
10447 Accents for several Characters
10451 \begin_layout Plain Layout
10452 Accents ! for several characters
10460 \begin_layout Standard
10461 \begin_inset space \hfill{}
10465 \begin_inset Tabular
10466 <lyxtabular version="3" rows="5" columns="2">
10468 <column alignment="center" valignment="top" width="0pt">
10469 <column alignment="center" valignment="top" width="0pt">
10471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10474 \begin_layout Plain Layout
10480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10483 \begin_layout Plain Layout
10485 \begin_inset Note Note
10488 \begin_layout Plain Layout
10495 is only used as spacer.
10507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10510 \begin_layout Plain Layout
10517 \begin_layout Plain Layout
10531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10534 \begin_layout Plain Layout
10535 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10545 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10548 \begin_layout Plain Layout
10555 \begin_layout Plain Layout
10569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10572 \begin_layout Plain Layout
10573 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10583 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10586 \begin_layout Plain Layout
10593 \begin_layout Plain Layout
10607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10610 \begin_layout Plain Layout
10611 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10624 \begin_layout Plain Layout
10627 underleftrightarrow
10631 \begin_layout Plain Layout
10645 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10648 \begin_layout Plain Layout
10649 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10663 \begin_inset space \hfill{}
10667 \begin_inset Tabular
10668 <lyxtabular version="3" rows="5" columns="2">
10670 <column alignment="center" valignment="top" width="0pt">
10671 <column alignment="center" valignment="top" width="0pt">
10673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10676 \begin_layout Plain Layout
10682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10685 \begin_layout Plain Layout
10693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10696 \begin_layout Plain Layout
10703 \begin_layout Plain Layout
10717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10720 \begin_layout Plain Layout
10721 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10734 \begin_layout Plain Layout
10741 \begin_layout Plain Layout
10755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10758 \begin_layout Plain Layout
10759 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10772 \begin_layout Plain Layout
10779 \begin_layout Plain Layout
10793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10796 \begin_layout Plain Layout
10797 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10810 \begin_layout Plain Layout
10817 \begin_layout Plain Layout
10831 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10834 \begin_layout Plain Layout
10835 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10849 \begin_inset space \hfill{}
10855 \begin_layout Standard
10856 \begin_inset VSpace medskip
10859 With these commands as many characters as you like can be accented.
10872 will only be set in the output with a length of three characters, as shown
10873 in the following example:
10874 \begin_inset Formula \[
10875 \widetilde{A+B=C-D}\]
10882 \begin_layout Standard
10893 \begin_layout Plain Layout
10911 \begin_layout Plain Layout
10919 described in the previous subsection it is also possible to accent several
10929 \begin_layout Plain Layout
10939 \begin_inset Formula $\downarrow$
10945 \begin_inset Formula \[
10946 \underset{***}{A=B}\]
10953 \begin_layout Section
10955 \begin_inset CommandInset label
10965 \begin_layout Plain Layout
10974 \begin_layout Subsection
10976 \begin_inset CommandInset label
10978 name "sub:Predefined-Space"
10986 \begin_layout Plain Layout
10987 Space ! horizontal ! predefined
10995 \begin_layout Standard
10996 Sometimes it is necessary to insert horizontal space to a formula.
10997 This is done by inserting a protected space (shortcut
11000 arg "space-insert protected"
11005 \begin_inset Quotes eld
11014 \begin_layout Plain Layout
11026 \begin_inset Quotes erd
11029 appears and by pressing
11033 several times one can select one of eight different space sizes.
11034 The spaces can also be inserted using the math toolbar button
11035 \begin_inset Graphics
11036 filename ../images/math/space.png
11041 or special commands.
11042 Independent from the inserted command, one can select the size again by
11050 \begin_layout Standard
11053 \begin_inset VSpace -5mm
11057 \begin_inset Tabular
11058 <lyxtabular version="3" rows="3" columns="7">
11060 <column alignment="center" valignment="middle" width="6.8cm">
11061 <column alignment="center" valignment="top" width="0">
11062 <column alignment="center" valignment="top" width="0">
11063 <column alignment="center" valignment="top" width="0">
11064 <column alignment="center" valignment="top" width="0">
11065 <column alignment="center" valignment="top" width="0">
11066 <column alignment="center" valignment="top" width="0">
11068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11071 \begin_layout Plain Layout
11077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11080 \begin_layout Plain Layout
11088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11091 \begin_layout Plain Layout
11099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11102 \begin_layout Plain Layout
11110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11113 \begin_layout Plain Layout
11121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11124 \begin_layout Plain Layout
11132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11135 \begin_layout Plain Layout
11145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11148 \begin_layout Plain Layout
11153 keystrokes after inserting the protected space
11158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11161 \begin_layout Plain Layout
11167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11170 \begin_layout Plain Layout
11176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11179 \begin_layout Plain Layout
11185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11188 \begin_layout Plain Layout
11194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11197 \begin_layout Plain Layout
11203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11206 \begin_layout Plain Layout
11214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11217 \begin_layout Plain Layout
11223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11226 \begin_layout Plain Layout
11227 \begin_inset Formula $A\, B$
11235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11238 \begin_layout Plain Layout
11239 \begin_inset Formula $A\: B$
11247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11250 \begin_layout Plain Layout
11251 \begin_inset Formula $A\; B$
11259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11262 \begin_layout Plain Layout
11263 \begin_inset Formula $A\quad B$
11271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11274 \begin_layout Plain Layout
11275 \begin_inset Formula $A\qquad B$
11283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11286 \begin_layout Plain Layout
11287 \begin_inset Formula $A\! B$
11303 \begin_layout Standard
11304 The last size seem to produce no space.
11305 It is displayed red in LyX contrary to the other sizes, because it is a
11307 There are two more negative spaces:
11310 \begin_layout Standard
11312 \begin_inset Tabular
11313 <lyxtabular version="3" rows="3" columns="3">
11315 <column alignment="center" valignment="middle" width="6.8cm">
11316 <column alignment="center" valignment="top" width="0pt">
11317 <column alignment="center" valignment="top" width="0pt">
11319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11322 \begin_layout Plain Layout
11328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11331 \begin_layout Plain Layout
11339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11342 \begin_layout Plain Layout
11352 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11355 \begin_layout Plain Layout
11360 keystrokes after inserting the protected space
11365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11368 \begin_layout Plain Layout
11374 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11377 \begin_layout Plain Layout
11385 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11388 \begin_layout Plain Layout
11394 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11397 \begin_layout Plain Layout
11398 \begin_inset Formula $A\negmedspace B$
11406 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11409 \begin_layout Plain Layout
11410 \begin_inset Formula $A\negthickspace B$
11426 \begin_layout Standard
11427 Negative spaces can lead to characters overlapping each other.
11428 Thus they can be used to enforce ligatures, what is e.
11429 \begin_inset space \thinspace{}
11433 \begin_inset space \space{}
11436 useful for summation operators:
11439 \begin_layout Standard
11441 \begin_inset Tabular
11442 <lyxtabular version="3" rows="3" columns="2">
11444 <column alignment="center" valignment="top" width="0">
11445 <column alignment="center" valignment="top" width="0">
11447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11450 \begin_layout Plain Layout
11456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11459 \begin_layout Plain Layout
11461 \begin_inset Note Note
11464 \begin_layout Plain Layout
11471 is only used as spacer.
11483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11486 \begin_layout Plain Layout
11495 \begin_layout Plain Layout
11509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11512 \begin_layout Plain Layout
11513 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11526 \begin_layout Plain Layout
11537 \begin_layout Plain Layout
11551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11554 \begin_layout Plain Layout
11555 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11571 \begin_layout Standard
11572 Relations like for example equal signs, are always surrounded by space.
11573 To suppress this, the equal sign is placed into a TeX-brace.
11574 The following example demonstrates this:
11577 \begin_layout Standard
11579 \begin_inset Tabular
11580 <lyxtabular version="3" rows="2" columns="2">
11582 <column alignment="center" valignment="top" width="0pt">
11583 <column alignment="center" valignment="top" width="0pt">
11585 <cell alignment="center" valignment="top" usebox="none">
11588 \begin_layout Plain Layout
11594 <cell alignment="center" valignment="top" usebox="none">
11597 \begin_layout Plain Layout
11598 \begin_inset Formula $A=B$
11608 <cell alignment="center" valignment="top" usebox="none">
11611 \begin_layout Plain Layout
11612 \begin_inset Note Note
11615 \begin_layout Plain Layout
11622 is only used as spacer.
11628 \begin_inset Formula $\raisebox{5mm}{}$
11631 equation without space
11636 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11639 \begin_layout Plain Layout
11640 \begin_inset Formula $A{=}B$
11656 \begin_layout Standard
11658 The command for the last formula is:
11663 \begin_inset Formula $\to$
11669 \begin_layout Standard
11670 \begin_inset VSpace bigskip
11673 Spaces are needed for physical units, because the space between the value
11674 and the unit is the smallest one and not a normal space.
11675 For units in text, the smallest space is inserted via the menu
11677 Insert\SpecialChar \menuseparator
11678 Formatting\SpecialChar \menuseparator
11680 \begin_inset space ~
11688 arg "space-insert thin"
11694 \begin_layout Standard
11695 An example to visualize the difference:
11698 \begin_layout Standard
11699 \begin_inset Tabular
11700 <lyxtabular version="3" rows="2" columns="2">
11702 <column alignment="left" valignment="top" width="0">
11703 <column alignment="left" valignment="top" width="0">
11705 <cell alignment="center" valignment="top" usebox="none">
11708 \begin_layout Plain Layout
11710 \begin_inset Formula $\cdot$
11718 <cell alignment="center" valignment="top" usebox="none">
11721 \begin_layout Plain Layout
11722 space between value and unit
11729 <cell alignment="center" valignment="top" usebox="none">
11732 \begin_layout Plain Layout
11734 \begin_inset space \thinspace{}
11738 \begin_inset Formula $\cdot$
11746 <cell alignment="center" valignment="top" usebox="none">
11749 \begin_layout Plain Layout
11750 smallest space between value and unit
11763 \begin_layout Subsection
11768 \begin_layout Plain Layout
11781 \begin_layout Plain Layout
11782 for vertical space in formulas see
11783 \begin_inset CommandInset ref
11785 reference "sub:Line-Separation"
11798 \begin_layout Plain Layout
11806 \begin_inset Note Note
11809 \begin_layout Plain Layout
11812 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11815 \begin_layout Plain Layout
11818 texorpdfstring is in section
11819 \begin_inset CommandInset ref
11821 reference "sub:Formulas-in-Section"
11831 \begin_inset CommandInset label
11833 name "sub:Variable-Space"
11841 \begin_layout Plain Layout
11842 Space ! horizontal ! variable
11850 \begin_layout Standard
11851 Space with a defined length can be inserted with the command
11861 \begin_layout Plain Layout
11871 \begin_inset Quotes eld
11880 \begin_layout Plain Layout
11892 \begin_inset Quotes erd
11896 The length can be specified by left-clicking on the
11897 \begin_inset Quotes eld
11906 \begin_layout Plain Layout
11918 \begin_inset Quotes erd
11922 The length may also be negative.
11923 To insert so many space that the formula uses all available space, the
11934 \begin_layout Plain Layout
11945 \begin_layout Standard
11946 \begin_inset VSpace -1mm
11952 \begin_layout Standard
11954 \begin_inset Tabular
11955 <lyxtabular version="3" rows="4" columns="2">
11957 <column alignment="center" valignment="top" width="0">
11958 <column alignment="center" valignment="top" width="0">
11960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11963 \begin_layout Plain Layout
11971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11974 \begin_layout Plain Layout
11982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11985 \begin_layout Plain Layout
11992 \begin_layout Plain Layout
12002 \begin_inset Formula $\to$
12008 \begin_inset space \thinspace{}
12016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12019 \begin_layout Plain Layout
12020 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12033 \begin_layout Plain Layout
12040 \begin_layout Plain Layout
12050 \begin_inset Formula $\to$
12056 \begin_inset space \thinspace{}
12064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12067 \begin_layout Plain Layout
12068 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12081 \begin_layout Plain Layout
12088 \begin_layout Plain Layout
12102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12105 \begin_layout Plain Layout
12106 \begin_inset Formula $A=A\hfill B=B$
12122 \begin_layout Standard
12123 In the last example the available space is given by the longest column entry
12125 In an inline formula the space depends on the length of the line in which
12133 Thus, when the line uses the full width, no space will be created.
12140 only has an effect on displayed formulas when the formula style
12145 (Formula styles are explained in
12146 \begin_inset CommandInset ref
12148 reference "sec:Formula-Styles"
12155 \begin_layout Standard
12162 , there are the commands
12174 that fill the space with a pattern, see
12175 \begin_inset CommandInset ref
12177 reference "sub:Ellipses"
12184 \begin_layout Standard
12185 For text, variable space can be inserted via the menu
12187 Insert\SpecialChar \menuseparator
12188 Formatting\SpecialChar \menuseparator
12190 \begin_inset space ~
12198 \begin_layout Standard
12199 This is a line with
12200 \begin_inset space \hspace{}
12205 \begin_inset space \thinspace{}
12211 \begin_layout Standard
12212 This is a line with
12213 \begin_inset space \hfill{}
12219 \begin_layout Subsection
12220 Space besides inline Formulas
12224 \begin_layout Plain Layout
12225 Space ! besides inline formulas
12233 \begin_layout Standard
12234 The space that surrounds inline formulas can be adjusted with the length
12243 \begin_layout Plain Layout
12254 The value of a length is set with the command
12262 \begin_layout Plain Layout
12272 that has the following scheme:
12275 \begin_layout Standard
12280 setlength{length name}{value}
12283 \begin_layout Standard
12291 \begin_inset space \thinspace{}
12297 \begin_layout Standard
12307 \begin_layout Standard
12308 is inserted in TeX-mode.
12310 \begin_inset space \thinspace{}
12313 mm space will now be set around all inline formulas:
12317 \begin_layout Plain Layout
12331 \begin_layout Standard
12332 This is a line with an inline formula
12333 \begin_inset Formula $A=B$
12337 \begin_inset space \thinspace{}
12340 mm surrounding space.
12344 \begin_layout Plain Layout
12358 \begin_layout Standard
12359 To return to the predefined value,
12365 is set to the value 0
12366 \begin_inset space \thinspace{}
12372 \begin_layout Section
12377 \begin_layout Plain Layout
12387 \begin_layout Plain Layout
12392 \begin_layout Plain Layout
12403 \begin_layout Plain Layout
12418 \begin_layout Standard
12419 Boxes for text are described in chapter
12426 \begin_inset space ~
12434 \begin_layout Subsection
12436 \begin_inset CommandInset label
12438 name "sub:Boxes-with-Frame"
12446 \begin_layout Plain Layout
12455 \begin_layout Standard
12456 It is possible to frame formulas or parts of it with the commands
12466 \begin_layout Plain Layout
12484 \begin_layout Plain Layout
12495 \begin_layout Standard
12496 When one of these commands is inserted to a formula, a blue box appears
12497 within a frame to enter formula parts.
12504 an additional formula has to be created by
12508 within this box, because the box content will otherwise be treated as mathemati
12516 is used, a new formula is automatically created inside the frame.
12519 \begin_layout Standard
12526 is not suitable to frame displayed formulas because the formula will always
12527 be set in the size of the text.
12534 is in contrary not suitable to frame inline formulas, because the formula
12535 will always be set in the size of a displayed formula.
12538 \begin_layout Standard
12545 there is the command
12555 \begin_layout Plain Layout
12563 where additionally the frame width and the alignment can be specified.
12570 is used in the following scheme:
12573 \begin_layout Standard
12578 framebox[frame width][position]{box content}
12581 \begin_layout Standard
12582 The position can either be
12599 right aligns the formula in the box.
12600 When no position is given, the formula will be centered.
12601 \begin_inset Newline newline
12604 Is no width given, also no position can be given.
12605 In this case the frame width is adjusted to the box content like for
12614 \begin_layout Standard
12621 is inserted, a box appears containing three blue boxes.
12622 The first two boxes are surrounded by brackets and denote the two optional
12624 The third box is for formula parts like for
12633 \begin_layout Standard
12635 \begin_inset Tabular
12636 <lyxtabular version="3" rows="5" columns="2">
12638 <column alignment="center" valignment="top" width="0">
12639 <column alignment="center" valignment="top" width="0">
12641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12644 \begin_layout Plain Layout
12650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12653 \begin_layout Plain Layout
12655 \begin_inset Note Note
12658 \begin_layout Plain Layout
12665 is only used as spacer.
12677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12680 \begin_layout Plain Layout
12687 \begin_layout Plain Layout
12706 \begin_layout Plain Layout
12720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12723 \begin_layout Plain Layout
12724 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12737 \begin_layout Plain Layout
12744 \begin_layout Plain Layout
12759 \begin_layout Plain Layout
12773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12776 \begin_layout Plain Layout
12777 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12790 \begin_layout Plain Layout
12797 \begin_layout Plain Layout
12811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12814 \begin_layout Plain Layout
12815 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12828 \begin_layout Plain Layout
12835 \begin_layout Plain Layout
12845 \begin_inset Formula $\to$
12849 \begin_inset Formula $\to$
12862 \begin_layout Plain Layout
12872 \begin_inset Formula $\downarrow$
12880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12883 \begin_layout Plain Layout
12884 \begin_inset Formula $\raisebox{6mm}{}$
12888 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12892 \begin_inset Formula $\raisebox{-4mm}{}$
12908 \begin_layout Standard
12909 The frame thickness can also be adjusted.
12910 To do this the following commands have to be inserted in TeX-mode before
12914 \begin_layout Standard
12924 \begin_inset Quotes eld
12928 \begin_inset Quotes erd
12942 \begin_inset Quotes eld
12946 \begin_inset Quotes erd
12952 \begin_layout Standard
12953 \begin_inset Quotes eld
12957 \begin_inset Quotes erd
12960 specifies the minimal distance between the frame and the first character
12962 An example for this is the following framed formula:
12966 \begin_layout Plain Layout
12978 \begin_inset Formula \[
12983 Before this formula the commands
12986 \begin_layout Standard
13008 \begin_layout Standard
13009 were inserted in TeX-mode.
13010 The given values are used for all following boxes.
13013 \begin_layout Standard
13014 To return to the standard frame size, the command
13017 \begin_layout Standard
13042 \begin_layout Plain Layout
13056 \begin_layout Standard
13057 is inserted in TeX-mode before the next formula.
13060 \begin_layout Subsection
13061 Boxes without Frame
13062 \begin_inset CommandInset label
13064 name "sub:Boxes-without-Frame"
13072 \begin_layout Plain Layout
13073 Boxes ! without frame
13081 \begin_layout Standard
13082 For boxes without a frame there are the following box commands:
13092 \begin_layout Plain Layout
13110 \begin_layout Plain Layout
13128 \begin_layout Plain Layout
13139 \begin_layout Standard
13146 a box can be super- or subscripted.
13147 But in contrary to normal super- and subscripting, the characters in the
13148 box keep their font size.
13155 is used in the following scheme:
13158 \begin_layout Standard
13163 raisebox{height}{box content}
13166 \begin_layout Standard
13167 When the box should contain a formula, an extra formula is needed like for
13178 \begin_inset Note Greyedout
13181 \begin_layout Plain Layout
13192 this extra formula is created by pressing
13196 twice instead of once because LyX doesn't yet support
13210 \begin_layout Standard
13212 \begin_inset Tabular
13213 <lyxtabular version="3" rows="4" columns="2">
13215 <column alignment="center" valignment="top" width="0">
13216 <column alignment="center" valignment="top" width="0">
13218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13221 \begin_layout Plain Layout
13227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13230 \begin_layout Plain Layout
13238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13241 \begin_layout Plain Layout
13245 \begin_inset Formula $\to$
13251 \begin_inset Formula $\to$
13259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13262 \begin_layout Plain Layout
13263 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13276 \begin_layout Plain Layout
13280 \begin_inset Formula $\to$
13286 \begin_inset Formula $\to$
13294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13297 \begin_layout Plain Layout
13298 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13311 \begin_layout Plain Layout
13315 \begin_inset Formula $\to$
13334 \begin_layout Plain Layout
13348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13351 \begin_layout Plain Layout
13352 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13368 \begin_layout Standard
13393 , with the difference that there is no frame.
13396 \begin_layout Subsection
13398 \begin_inset CommandInset label
13400 name "sub:Colored-Boxes"
13408 \begin_layout Plain Layout
13417 \begin_layout Standard
13418 To be able to use all commands explained in this section, the LaTeX-package
13427 \begin_layout Plain Layout
13432 is part of every LaTeX standard installation.
13441 \begin_layout Plain Layout
13447 has to be loaded in the LaTeX-preamble with the line
13451 \begin_layout Plain Layout
13452 When text is colored somewhere in the document with a predefined color,
13453 LyX loads the LaTeX-package
13458 Thus it is possible that the package is loaded twice, but this doesn't
13465 \begin_inset Note Note
13468 \begin_layout Plain Layout
13469 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13478 \begin_layout Standard
13486 \begin_layout Standard
13487 \begin_inset VSpace medskip
13490 To color boxes, the command
13500 \begin_layout Plain Layout
13508 is used in the following scheme:
13511 \begin_layout Standard
13516 colorbox{color}{box content}
13519 \begin_layout Standard
13520 The box content can also be a box and a
13526 can also be part of another box (see the 2nd and 3rd example).
13527 When the box should contain a formula, an extra formula has to be created,
13528 the same way as for
13538 \begin_layout Plain Layout
13539 This also applies for the command
13553 \begin_layout Standard
13554 One of the following predefined colors can be chosen:
13557 \begin_layout Standard
13591 \begin_layout Standard
13593 \begin_inset Tabular
13594 <lyxtabular version="3" rows="4" columns="2">
13596 <column alignment="center" valignment="top" width="0">
13597 <column alignment="center" valignment="top" width="0">
13599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13602 \begin_layout Plain Layout
13608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13611 \begin_layout Plain Layout
13613 \begin_inset Note Note
13616 \begin_layout Plain Layout
13623 is only used as spacer.
13635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13638 \begin_layout Plain Layout
13642 \begin_inset Formula $\to$
13652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13655 \begin_layout Plain Layout
13656 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13669 \begin_layout Plain Layout
13673 \begin_inset Formula $\to$
13684 \begin_layout Plain Layout
13698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13701 \begin_layout Plain Layout
13702 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13715 \begin_layout Plain Layout
13722 \begin_layout Plain Layout
13734 \begin_inset Formula $\to$
13753 \begin_layout Plain Layout
13767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13770 \begin_layout Plain Layout
13771 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13787 \begin_layout Standard
13794 only colors the box but not the characters in the box.
13795 To color all characters, the whole formula is highlighted and the wanted
13796 color is chosen in the
13799 \begin_inset space ~
13805 The dialog can be called with the toolbar button
13806 \begin_inset Graphics
13807 filename ../images/dialog-show_character.png
13814 Edit\SpecialChar \menuseparator
13816 \begin_inset space ~
13819 Style\SpecialChar \menuseparator
13823 The formula number has then the same color as the formula.
13824 When the formula number should get another color than the formula characters,
13825 the color must be changed within the formula.
13828 \begin_layout Standard
13832 \begin_layout Standard
13835 \begin_inset Formula \begin{equation}
13836 \int A=B\label{eq:red}\end{equation}
13843 \begin_inset Formula \begin{equation}
13844 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13851 \begin_layout Standard
13853 \begin_inset CommandInset ref
13859 is completely colored red.
13860 \begin_inset Newline newline
13864 \begin_inset CommandInset ref
13866 reference "eq:redgreen"
13870 was first completely colored green to set the color for the formula number.
13871 Subsequently the formula characters were colored red.
13874 \begin_layout Standard
13875 \begin_inset VSpace bigskip
13878 To color the frame different than the rest of the box, the command
13888 \begin_layout Plain Layout
13896 is used in the following scheme:
13899 \begin_layout Standard
13904 fcolorbox{frame color}{color}{box content}
13907 \begin_layout Standard
13914 is an extension of the command
13921 The frame width is set, like for
13944 \begin_layout Plain Layout
13956 \begin_inset Formula \[
13957 \fcolorbox{cyan}{magenta}{A=B}\]
13965 \begin_layout Plain Layout
13979 \begin_layout Standard
13980 This formula was created with the command
13981 \begin_inset Newline newline
13989 \begin_inset Formula $\to$
13995 \begin_inset Formula $\to$
14005 \begin_layout Standard
14006 \begin_inset VSpace bigskip
14009 To use other colors than the predefined ones, they have to be defined first.
14012 \begin_layout Standard
14013 One can for example define the color
14014 \begin_inset Quotes eld
14022 \begin_inset Quotes erd
14025 with the LaTeX-preamble line:
14028 \begin_layout Standard
14033 definecolor{darkgreen}{cmyk}{0.5,
14051 \begin_layout Plain Layout
14062 \begin_layout Standard
14067 is the color space that denotes the colors
14084 The four comma separated numbers are the portion factor for the corresponding
14085 colors of the color space.
14086 The factors can be in the range of 0
14087 \begin_inset space \thinspace{}
14091 \begin_inset space \thinspace{}
14099 also the color space
14103 can be used for definitions.
14120 , so that there are in this case three portion factors for the corresponding
14122 Furthermore there is the color space
14126 with one portion factor for the gray value.
14129 \begin_layout Standard
14130 As example a framed box with the new defined color
14134 where the characters have been colored
14139 \begin_inset Formula \begin{equation}
14140 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14147 \begin_layout Standard
14148 Self-defined colors can also be used for text with the help of the command
14159 \begin_layout Plain Layout
14168 \begin_layout Standard
14172 \begin_layout Plain Layout
14176 textcolor{darkgreen}{
14182 \begin_inset Quotes eld
14186 \begin_inset Quotes erd
14193 \begin_layout Plain Layout
14203 \begin_layout Standard
14214 \begin_layout Plain Layout
14222 is used in the scheme
14226 textcolor{color}{characters to color}
14231 \begin_layout Subsection
14233 \begin_inset CommandInset label
14235 name "sub:Paragraph-Boxes"
14243 \begin_layout Plain Layout
14244 Boxes ! as paragraph
14252 \begin_layout Standard
14253 A box that can contain several lines and paragraphs, a so called paragraph
14254 box (parbox), can be created with the menu
14256 Insert\SpecialChar \menuseparator
14259 or the toolbar button
14260 \begin_inset Graphics
14261 filename ../images/box-insert.png
14269 \begin_layout Standard
14270 The following example shows a framed parbox in a line:
14273 \begin_layout Standard
14274 \begin_inset VSpace medskip
14278 \begin_inset Box Boxed
14287 height_special "totalheight"
14290 \begin_layout Plain Layout
14291 This is a paragraph box.
14293 \begin_inset space \thinspace{}
14296 cm long and can also contain formulas:
14297 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14308 \begin_layout Standard
14309 \begin_inset VSpace medskip
14315 \begin_layout Standard
14316 Such a box is created by right-clicking on the gray box inset.
14317 A dialog pops up showing the box properties.
14331 \begin_inset space \thinspace{}
14336 Vertical Box Alignment
14341 \begin_layout Standard
14342 \begin_inset VSpace medskip
14345 In LaTeX a parbox is created with the command
14355 \begin_layout Plain Layout
14363 that has the following scheme:
14366 \begin_layout Standard
14371 parbox[position]{width}{box content}
14374 \begin_layout Standard
14388 for bottom means that the box is aligned within the surrounding text with
14394 for top this is done with the first line.
14395 When no position is given, the box will be vertically centered, see section
14403 \begin_inset space ~
14408 manual for examples.
14411 \begin_layout Standard
14412 \begin_inset VSpace bigskip
14415 To frame formulas completely, including the formula number, the formula
14416 must be set into a parbox.
14417 To do this, the command
14431 is inserted in TeX-mode before the formula.
14440 \begin_layout Plain Layout
14450 is hereby the line width set for the document.
14451 Because the frame is outside the parbox, 2
14452 \begin_inset space \thinspace{}
14455 times the frame separation and the frame thickness must be subtracted from
14457 As this is not automatically done by LyX due to a bug
14461 \begin_layout Plain Layout
14462 \begin_inset CommandInset href
14464 name "LyX-bug #4483"
14465 target "http://www.lyx.org/trac/ticket/4483"
14474 , TeX-mode has to be used.
14475 To be able to multiply and subtract in arguments, the LaTeX-package
14483 \begin_layout Plain Layout
14488 is part of every LaTeX standard installation.
14497 \begin_layout Plain Layout
14503 must be loaded in the LaTeX-preamble with the line
14506 \begin_layout Standard
14514 \begin_layout Standard
14515 Behind the formula both boxes are closed by entering
14520 Here is an example:
14524 \begin_layout Plain Layout
14538 \begin_layout Standard
14542 \begin_layout Plain Layout
14560 \begin_inset Formula \begin{equation}
14561 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14569 \begin_layout Plain Layout
14580 \begin_layout Plain Layout
14594 \begin_layout Standard
14595 \begin_inset VSpace medskip
14598 As a parbox is used as argument of
14604 , there is in this case no difference between
14619 \begin_layout Standard
14620 \begin_inset VSpace bigskip
14623 Paragraph boxes are very useful to comment formulas directly.
14630 is used in combination with the command
14644 \begin_inset CommandInset ref
14646 reference "sub:User-defined-Numbering"
14653 \begin_layout Standard
14654 An example of a formula commented with
14663 \begin_layout Standard
14667 \begin_layout Plain Layout
14680 This is a description.
14681 It is distinctly separated from the formula and multiline.
14685 \begin_layout Plain Layout
14697 \begin_layout Standard
14698 Such a formula must be inserted completely in TeX-mode because LyX does
14699 not yet support the command
14706 The formula is created with the following command sequence:
14709 \begin_layout Standard
14722 is inserted in TeX-mode.
14726 \begin_layout Plain Layout
14727 When the formula style
14739 can also be replaced by
14746 (formula styles see
14747 \begin_inset CommandInset ref
14749 reference "sec:Formula-Styles"
14758 Then the description follows as normal text, and finally
14764 is inserted in TeX-mode.
14777 hereby create a displayed formula.
14780 \begin_layout Standard
14787 can be seen in this example that was
14788 \begin_inset Quotes eld
14792 \begin_inset Quotes erd
14795 using the mathematical textmode:
14796 \begin_inset Formula \[
14797 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14804 \begin_layout Section
14809 \begin_layout Plain Layout
14818 \begin_layout Subsection
14820 \begin_inset CommandInset label
14822 name "sub:Big-Operators"
14830 \begin_layout Plain Layout
14840 \begin_layout Plain Layout
14850 \begin_layout Plain Layout
14859 \begin_layout Standard
14860 To be able to use all integral operators listed here, the option
14862 Use esint package automatically
14864 must be set in the document settings under
14867 \begin_inset space ~
14875 \begin_layout Standard
14876 \begin_inset space \hfill{}
14880 \begin_inset Tabular
14881 <lyxtabular version="3" rows="11" columns="2">
14883 <column alignment="center" valignment="top" width="0pt">
14884 <column alignment="center" valignment="top" width="0pt">
14886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14889 \begin_layout Plain Layout
14895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14898 \begin_layout Plain Layout
14906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14909 \begin_layout Plain Layout
14916 \begin_layout Plain Layout
14929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14932 \begin_layout Plain Layout
14933 \begin_inset Formula $\int$
14943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14946 \begin_layout Plain Layout
14954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14957 \begin_layout Plain Layout
14958 \begin_inset Formula $\oint$
14968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14971 \begin_layout Plain Layout
14979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14982 \begin_layout Plain Layout
14983 \begin_inset Formula $\ointctrclockwise$
14993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14996 \begin_layout Plain Layout
15004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15007 \begin_layout Plain Layout
15008 \begin_inset Formula $\ointclockwise$
15018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15021 \begin_layout Plain Layout
15029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15032 \begin_layout Plain Layout
15033 \begin_inset Formula $\sqint$
15043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15046 \begin_layout Plain Layout
15054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15057 \begin_layout Plain Layout
15059 \begin_inset Formula $\fint$
15069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15072 \begin_layout Plain Layout
15080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15083 \begin_layout Plain Layout
15085 \begin_inset Formula $\landupint$
15095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15098 \begin_layout Plain Layout
15106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15109 \begin_layout Plain Layout
15111 \begin_inset Formula $\landdownint$
15121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15124 \begin_layout Plain Layout
15132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15135 \begin_layout Plain Layout
15136 \begin_inset Formula $\bigcap$
15146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15149 \begin_layout Plain Layout
15157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15160 \begin_layout Plain Layout
15161 \begin_inset Formula $\bigcup$
15175 \begin_inset space \hfill{}
15179 \begin_inset Tabular
15180 <lyxtabular version="3" rows="11" columns="2">
15182 <column alignment="center" valignment="top" width="0pt">
15183 <column alignment="center" valignment="top" width="0pt">
15185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15188 \begin_layout Plain Layout
15194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15197 \begin_layout Plain Layout
15205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15208 \begin_layout Plain Layout
15215 \begin_layout Plain Layout
15228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15231 \begin_layout Plain Layout
15232 \begin_inset Formula $\sum$
15242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15245 \begin_layout Plain Layout
15252 \begin_layout Plain Layout
15265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15268 \begin_layout Plain Layout
15269 \begin_inset Formula $\prod$
15279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15282 \begin_layout Plain Layout
15290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15293 \begin_layout Plain Layout
15294 \begin_inset Formula $\coprod$
15304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15307 \begin_layout Plain Layout
15315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15318 \begin_layout Plain Layout
15319 \begin_inset Formula $\bigodot$
15329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15332 \begin_layout Plain Layout
15340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15343 \begin_layout Plain Layout
15344 \begin_inset Formula $\bigotimes$
15354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15357 \begin_layout Plain Layout
15365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15368 \begin_layout Plain Layout
15369 \begin_inset Formula $\bigoplus$
15379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15382 \begin_layout Plain Layout
15390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15393 \begin_layout Plain Layout
15394 \begin_inset Formula $\bigwedge$
15404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15407 \begin_layout Plain Layout
15415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15418 \begin_layout Plain Layout
15419 \begin_inset Formula $\bigvee$
15429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15432 \begin_layout Plain Layout
15440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15443 \begin_layout Plain Layout
15444 \begin_inset Formula $\bigsqcup$
15454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15457 \begin_layout Plain Layout
15465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15468 \begin_layout Plain Layout
15469 \begin_inset Formula $\biguplus$
15483 \begin_inset space \hfill{}
15489 \begin_layout Standard
15490 All big operators can also be inserted via the math toolbar button
15491 \begin_inset Graphics
15492 filename ../images/math/intop.png
15500 \begin_layout Standard
15501 The operators are called big because they are bigger than the sometimes
15502 equal looking binary operators.
15503 All big operators can have limits as described in the next subsection.
15506 \begin_layout Standard
15507 For all integral operators there is a second version available, ending on
15525 These operators are different from
15532 \begin_inset space \space{}
15535 in the style the operator limits are displayed, see
15536 \begin_inset CommandInset ref
15538 reference "sub:Operator-Limits"
15546 \begin_layout Subsubsection*
15547 Advice for Integrals
15550 \begin_layout Standard
15555 in an integral is an operator, that therefore has to be set upright.
15556 This is done by highlighting the
15560 and using the keyboard shortcut
15570 \begin_layout Plain Layout
15576 \begin_inset CommandInset ref
15578 reference "sub:Font-Styles"
15588 Finally the smallest space is inserted before the
15592 , as this is usual for operators.
15596 \begin_layout Standard
15598 \begin_inset Formula $\int A(x)dx$
15602 \begin_inset Newline newline
15609 \begin_layout Plain Layout
15619 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15625 \begin_layout Standard
15626 For multiple integrals there are the following commands:
15627 \begin_inset VSpace medskip
15633 \begin_layout Standard
15634 \begin_inset space \hfill{}
15638 \begin_inset Tabular
15639 <lyxtabular version="3" rows="4" columns="2">
15641 <column alignment="center" valignment="top" width="0">
15642 <column alignment="center" valignment="top" width="0">
15644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15647 \begin_layout Plain Layout
15653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15656 \begin_layout Plain Layout
15658 \begin_inset Note Note
15661 \begin_layout Plain Layout
15668 is only used as spacer.
15680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15683 \begin_layout Plain Layout
15691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15694 \begin_layout Plain Layout
15695 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15708 \begin_layout Plain Layout
15716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15719 \begin_layout Plain Layout
15720 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15733 \begin_layout Plain Layout
15741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15744 \begin_layout Plain Layout
15745 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15759 \begin_inset space \hfill{}
15763 \begin_inset Tabular
15764 <lyxtabular version="3" rows="4" columns="2">
15766 <column alignment="center" valignment="top" width="0">
15767 <column alignment="center" valignment="top" width="0">
15769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15772 \begin_layout Plain Layout
15778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15781 \begin_layout Plain Layout
15789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15792 \begin_layout Plain Layout
15800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15803 \begin_layout Plain Layout
15804 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15817 \begin_layout Plain Layout
15825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15828 \begin_layout Plain Layout
15829 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15842 \begin_layout Plain Layout
15850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15853 \begin_layout Plain Layout
15854 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15868 \begin_inset space \hfill{}
15874 \begin_layout Subsection
15876 \begin_inset CommandInset label
15878 name "sub:Operator-Limits"
15886 \begin_layout Plain Layout
15895 \begin_layout Standard
15896 Limits are created by super- and subscripts:
15899 \begin_layout Standard
15901 \begin_inset Tabular
15902 <lyxtabular version="3" rows="2" columns="2">
15904 <column alignment="center" valignment="top" width="0pt">
15905 <column alignment="center" valignment="top" width="0pt">
15907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15910 \begin_layout Plain Layout
15916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15919 \begin_layout Plain Layout
15921 \begin_inset Note Note
15924 \begin_layout Plain Layout
15931 is only used as spacer.
15943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15946 \begin_layout Plain Layout
15955 \begin_layout Plain Layout
15965 \begin_inset Formula $\to$
15969 \begin_inset Formula $\to$
15977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15980 \begin_layout Plain Layout
15981 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15997 \begin_layout Standard
15998 Limits of inline formulas are set right beside the operator.
15999 Limits in displayed formulas are set above or below the operator, except
16000 for integral limits.
16003 \begin_layout Standard
16004 To force that the limits are set beside the operator, the cursor is set
16005 directly behind the operator and the limits type is changed with the menu
16008 Edit\SpecialChar \menuseparator
16009 Math\SpecialChar \menuseparator
16028 \begin_layout Standard
16029 The default limits type is this:
16030 \begin_inset Formula \[
16031 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16035 This is how it looks when the limits type was changed to
16042 \begin_inset Formula \[
16043 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16047 For integrals, except those ending with
16063 etc., the limits are by default set beside the operator.
16064 But for multiple integrals the limits are often set below the operator.
16065 In the following example the limits type was therefore set to
16069 and so set below the integrals:
16070 \begin_inset Formula \begin{equation}
16071 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16078 \begin_layout Standard
16079 \begin_inset VSpace medskip
16082 To specify conditions for limits, the commands
16092 \begin_layout Plain Layout
16110 \begin_layout Plain Layout
16119 To create for example this expression
16120 \begin_inset Formula \begin{equation}
16121 \sum_{\begin{subarray}{c}
16123 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16130 \begin_layout Standard
16131 the following has to be done:
16132 \begin_inset Newline newline
16147 \begin_layout Plain Layout
16159 One is now in a blue box under the summation operator and insert there
16168 \begin_layout Plain Layout
16180 The blue box is now within a purple box and now several lines can be written
16182 A new line is created by inserting a line break (
16185 arg "newline-insert newline"
16190 \begin_inset Newline newline
16195 0<k<1000 Ctrl+Return
16196 \begin_inset Newline newline
16201 is typed in, a new box appears below for the new line.
16204 \begin_layout Standard
16205 The alignment of the lines can be changed to left aligned with the
16215 Edit\SpecialChar \menuseparator
16219 To get right alignment,
16227 \begin_layout Plain Layout
16238 is inserted at the beginning of the line.
16241 \begin_layout Standard
16254 with the difference that the lines are always centered.
16257 \begin_layout Standard
16258 \begin_inset VSpace bigskip
16262 \begin_inset CommandInset ref
16264 reference "eq:substack"
16268 there can be too much space beside an operator, because the characters
16269 following the operator are set beside the limits.
16272 \begin_layout Standard
16273 To avoid this, the following macro can be used in the LaTeX-preamble:
16276 \begin_layout Standard
16290 \begin_inset Newline newline
16302 \begin_inset Newline newline
16309 mathclapinternal #1#2{
16313 mathsurround =0pt #1{#2}$}}
16316 \begin_layout Standard
16317 This defines the command
16327 \begin_layout Plain Layout
16335 that sets the width of the limit to 0
16336 \begin_inset space \thinspace{}
16340 The command scheme is
16343 \begin_layout Standard
16351 \begin_layout Standard
16352 where the limit can consist of several conditions.
16355 \begin_layout Standard
16357 \begin_inset CommandInset ref
16359 reference "eq:substack"
16363 , one uses the command
16366 \begin_layout Standard
16379 \begin_layout Plain Layout
16388 0<k<1000 Ctrl+Return
16391 \begin_layout Standard
16392 to create the lower limit.
16393 The summand is now directly behind the summation operator:
16394 \begin_inset Formula \[
16395 \sum_{\mathclap{\substack{0<k<1000\\
16396 \\k\,\in\,\mathbb{N}}
16404 \begin_layout Standard
16405 \begin_inset VSpace bigskip
16408 How to use one limit for several operators is described in
16409 \begin_inset CommandInset ref
16411 reference "sub:Self-defined-Operators"
16418 \begin_layout Subsection
16420 \begin_inset CommandInset label
16422 name "sub:Binary-Operators"
16430 \begin_layout Plain Layout
16439 \begin_layout Standard
16440 Binary operators are surrounded by space when there is a character before
16442 \begin_inset VSpace medskip
16448 \begin_layout Standard
16449 \begin_inset space \hfill{}
16453 \begin_inset Tabular
16454 <lyxtabular version="3" rows="13" columns="2">
16456 <column alignment="center" valignment="top" width="0pt">
16457 <column alignment="center" valignment="top" width="0pt">
16459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16462 \begin_layout Plain Layout
16464 \begin_inset Note Note
16467 \begin_layout Plain Layout
16474 is only used as spacer.
16484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16487 \begin_layout Plain Layout
16495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16498 \begin_layout Plain Layout
16504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16507 \begin_layout Plain Layout
16508 \begin_inset Formula $+$
16518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16521 \begin_layout Plain Layout
16527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16530 \begin_layout Plain Layout
16531 \begin_inset Formula $-$
16541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16544 \begin_layout Plain Layout
16552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16555 \begin_layout Plain Layout
16556 \begin_inset Formula $\pm$
16566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16569 \begin_layout Plain Layout
16577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16580 \begin_layout Plain Layout
16581 \begin_inset Formula $\mp$
16591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16594 \begin_layout Plain Layout
16602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16605 \begin_layout Plain Layout
16606 \begin_inset Formula $\cdot$
16616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16619 \begin_layout Plain Layout
16627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16630 \begin_layout Plain Layout
16631 \begin_inset Formula $\times$
16641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16644 \begin_layout Plain Layout
16652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16655 \begin_layout Plain Layout
16656 \begin_inset Formula $\div$
16666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16669 \begin_layout Plain Layout
16673 \begin_layout Plain Layout
16686 \begin_layout Plain Layout
16698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16701 \begin_layout Plain Layout
16702 \begin_inset Formula $*$
16712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16715 \begin_layout Plain Layout
16723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16726 \begin_layout Plain Layout
16727 \begin_inset Formula $\star$
16737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16740 \begin_layout Plain Layout
16748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16751 \begin_layout Plain Layout
16752 \begin_inset Formula $\circ$
16762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16765 \begin_layout Plain Layout
16773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16776 \begin_layout Plain Layout
16777 \begin_inset Formula $\diamond$
16787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16790 \begin_layout Plain Layout
16798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16801 \begin_layout Plain Layout
16802 \begin_inset Formula $\bullet$
16816 \begin_inset space \hfill{}
16820 \begin_inset Tabular
16821 <lyxtabular version="3" rows="13" columns="2">
16823 <column alignment="center" valignment="top" width="0pt">
16824 <column alignment="center" valignment="top" width="0pt">
16826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16829 \begin_layout Plain Layout
16835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16838 \begin_layout Plain Layout
16846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16849 \begin_layout Plain Layout
16857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16860 \begin_layout Plain Layout
16861 \begin_inset Formula $\nabla$
16871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16874 \begin_layout Plain Layout
16882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16885 \begin_layout Plain Layout
16886 \begin_inset Formula $\bigtriangledown$
16896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16899 \begin_layout Plain Layout
16907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16910 \begin_layout Plain Layout
16911 \begin_inset Formula $\bigtriangleup$
16921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16924 \begin_layout Plain Layout
16932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16935 \begin_layout Plain Layout
16936 \begin_inset Formula $\Box$
16946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16949 \begin_layout Plain Layout
16957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16960 \begin_layout Plain Layout
16961 \begin_inset Formula $\cap$
16971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16974 \begin_layout Plain Layout
16982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16985 \begin_layout Plain Layout
16986 \begin_inset Formula $\cup$
16996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16999 \begin_layout Plain Layout
17007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17010 \begin_layout Plain Layout
17011 \begin_inset Formula $\dagger$
17021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17024 \begin_layout Plain Layout
17032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17035 \begin_layout Plain Layout
17036 \begin_inset Formula $\ddagger$
17046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17049 \begin_layout Plain Layout
17057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17060 \begin_layout Plain Layout
17061 \begin_inset Formula $\wr$
17071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17074 \begin_layout Plain Layout
17082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17085 \begin_layout Plain Layout
17086 \begin_inset Formula $\bigcirc$
17096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17099 \begin_layout Plain Layout
17107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17110 \begin_layout Plain Layout
17111 \begin_inset Formula $\wedge$
17121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17124 \begin_layout Plain Layout
17132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17135 \begin_layout Plain Layout
17136 \begin_inset Formula $\vee$
17150 \begin_inset space \hfill{}
17154 \begin_inset Tabular
17155 <lyxtabular version="3" rows="13" columns="2">
17157 <column alignment="center" valignment="top" width="0pt">
17158 <column alignment="center" valignment="top" width="0pt">
17160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17163 \begin_layout Plain Layout
17169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17172 \begin_layout Plain Layout
17180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17183 \begin_layout Plain Layout
17191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17194 \begin_layout Plain Layout
17195 \begin_inset Formula $\oplus$
17205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17208 \begin_layout Plain Layout
17216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17219 \begin_layout Plain Layout
17220 \begin_inset Formula $\ominus$
17230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17233 \begin_layout Plain Layout
17241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17244 \begin_layout Plain Layout
17245 \begin_inset Formula $\otimes$
17255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17258 \begin_layout Plain Layout
17266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17269 \begin_layout Plain Layout
17270 \begin_inset Formula $\oslash$
17280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17283 \begin_layout Plain Layout
17291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17294 \begin_layout Plain Layout
17295 \begin_inset Formula $\odot$
17305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17308 \begin_layout Plain Layout
17316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17319 \begin_layout Plain Layout
17320 \begin_inset Formula $\amalg$
17330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17333 \begin_layout Plain Layout
17341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17344 \begin_layout Plain Layout
17345 \begin_inset Formula $\uplus$
17355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17358 \begin_layout Plain Layout
17366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17369 \begin_layout Plain Layout
17370 \begin_inset Formula $\setminus$
17380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17383 \begin_layout Plain Layout
17391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17394 \begin_layout Plain Layout
17395 \begin_inset Formula $\sqcap$
17405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17408 \begin_layout Plain Layout
17416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17419 \begin_layout Plain Layout
17420 \begin_inset Formula $\sqcup$
17430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17433 \begin_layout Plain Layout
17441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17444 \begin_layout Plain Layout
17445 \begin_inset Formula $\triangleleft$
17455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17458 \begin_layout Plain Layout
17466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17469 \begin_layout Plain Layout
17470 \begin_inset Formula $\triangleright$
17484 \begin_inset space \hfill{}
17490 \begin_layout Standard
17491 All binary operators can also be inserted via the math toolbar button
17492 \begin_inset Graphics
17493 filename ../images/math/pm.png
17501 \begin_layout Standard
17502 To typeset the Laplace operator also
17519 \begin_inset Formula $\nabla^{2}$
17522 ) can be used instead of
17531 \begin_layout Standard
17538 Insert\SpecialChar \menuseparator
17550 \begin_layout Subsection
17551 Self-defined Operators
17552 \begin_inset CommandInset label
17554 name "sub:Self-defined-Operators"
17562 \begin_layout Plain Layout
17563 Operators ! self-defined
17571 \begin_layout Standard
17572 With the help of the command
17576 DeclareMathOperator
17582 \begin_layout Plain Layout
17587 DeclareMathOperator
17592 custom operators can be defined in the LaTeX-preamble.
17593 Its command scheme is:
17596 \begin_layout Standard
17601 DeclareMathOperator{new command}{display}
17604 \begin_layout Standard
17605 Display can be characters or symbols that define how the operator looks
17607 To define a big operator a * is set behind the command.
17608 All self-defined big operators can have limits as described in
17609 \begin_inset CommandInset ref
17611 reference "sub:Operator-Limits"
17618 \begin_layout Standard
17619 For example the LaTeX-preamble line
17622 \begin_layout Standard
17627 DeclareMathOperator*{
17634 \begin_layout Standard
17635 defines the command
17641 , that inserts a big operator consisting of the lozenge symbol from
17642 \begin_inset CommandInset ref
17644 reference "sub:Miscellaneous-Symbols"
17649 \begin_inset Formula \[
17650 \Lozenge_{n=1}^{\infty}\]
17654 The command for this formula is:
17665 \begin_inset Formula $\to$
17671 \begin_layout Standard
17672 \begin_inset VSpace bigskip
17675 When self-defined operators are not used several times in the document,
17676 they can also be defined with the commands
17686 \begin_layout Plain Layout
17704 \begin_layout Plain Layout
17712 , which have the following scheme:
17715 \begin_layout Standard
17729 \begin_layout Standard
17736 defines big operators,
17745 \begin_layout Standard
17753 \begin_inset space \thinspace{}
17757 \begin_inset space \space{}
17760 be used to use one limit for several operators:
17763 \begin_layout Standard
17764 \begin_inset Formula \[
17765 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17772 \begin_layout Standard
17773 The command for the formula above is:
17774 \begin_inset Newline newline
17793 \begin_layout Plain Layout
17805 \begin_inset Formula $\to$
17814 \begin_layout Plain Layout
17828 \begin_layout Section
17833 \begin_layout Plain Layout
17842 \begin_layout Subsection
17844 \begin_inset CommandInset label
17846 name "sub:Font-Styles"
17854 \begin_layout Plain Layout
17863 \begin_layout Standard
17864 Latin letters in formulas can be set in one of the following font styles:
17865 \begin_inset VSpace -2mm
17871 \begin_layout Standard
17873 \begin_inset Tabular
17874 <lyxtabular version="3" rows="6" columns="3">
17876 <column alignment="center" valignment="top" width="0">
17877 <column alignment="center" valignment="top" width="0">
17878 <column alignment="center" valignment="top" width="0">
17880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17883 \begin_layout Plain Layout
17889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17892 \begin_layout Plain Layout
17898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17901 \begin_layout Plain Layout
17909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17912 \begin_layout Plain Layout
17921 \begin_layout Plain Layout
17937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17940 \begin_layout Plain Layout
17941 \begin_inset Formula $\mathbb{ABC}$
17949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17952 \begin_layout Plain Layout
17965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17968 \begin_layout Plain Layout
17977 \begin_layout Plain Layout
17993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17996 \begin_layout Plain Layout
17997 \begin_inset Formula $\mathbf{AbC}$
18005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18008 \begin_layout Plain Layout
18021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18024 \begin_layout Plain Layout
18033 \begin_layout Plain Layout
18049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18052 \begin_layout Plain Layout
18053 \begin_inset Formula $\boldsymbol{AbC}$
18061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18064 \begin_layout Plain Layout
18067 arg "font-boldsymbol"
18077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18080 \begin_layout Plain Layout
18089 \begin_layout Plain Layout
18105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18108 \begin_layout Plain Layout
18109 \begin_inset Formula $\mathcal{ABC}$
18117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18120 \begin_layout Plain Layout
18133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18136 \begin_layout Plain Layout
18145 \begin_layout Plain Layout
18161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18164 \begin_layout Plain Layout
18165 \begin_inset Formula $\mathfrak{AbC}$
18173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18176 \begin_layout Plain Layout
18190 \begin_layout Standard
18192 \begin_inset Tabular
18193 <lyxtabular version="3" rows="5" columns="3">
18195 <column alignment="center" valignment="top" width="0">
18196 <column alignment="center" valignment="top" width="0">
18197 <column alignment="center" valignment="top" width="0">
18199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18202 \begin_layout Plain Layout
18208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18211 \begin_layout Plain Layout
18217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18220 \begin_layout Plain Layout
18228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18231 \begin_layout Plain Layout
18240 \begin_layout Plain Layout
18256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18259 \begin_layout Plain Layout
18260 \begin_inset Formula $\mathit{AbC}$
18268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18271 \begin_layout Plain Layout
18279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18282 \begin_layout Plain Layout
18291 \begin_layout Plain Layout
18307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18310 \begin_layout Plain Layout
18311 \begin_inset Formula $\mathrm{AbC}$
18319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18322 \begin_layout Plain Layout
18335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18338 \begin_layout Plain Layout
18347 \begin_layout Plain Layout
18363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18366 \begin_layout Plain Layout
18367 \begin_inset Formula $\mathsf{AbC}$
18375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18378 \begin_layout Plain Layout
18391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18394 \begin_layout Plain Layout
18403 \begin_layout Plain Layout
18419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18422 \begin_layout Plain Layout
18423 \begin_inset Formula $\mathtt{AbC}$
18431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18434 \begin_layout Plain Layout
18437 arg "font-typewriter"
18453 \begin_layout Standard
18454 \begin_inset Note Greyedout
18457 \begin_layout Plain Layout
18474 can only be used for big letters.
18482 \begin_layout Standard
18483 Predefined is the style
18492 \begin_layout Standard
18493 The style commands work also for letters in mathematical constructs:
18494 \begin_inset Formula \[
18495 \mathfrak{A=\frac{b}{C}}\]
18502 \begin_layout Standard
18503 Characters in mathematical text don't appear in a math font style but in
18504 the text font style
18511 That their style can't be set correctly via the text style dialog is a
18516 \begin_layout Plain Layout
18517 \begin_inset CommandInset href
18519 name "LyX-bug #4629"
18520 target "http://www.lyx.org/trac/ticket/4629"
18532 \begin_layout Standard
18533 Instead of the style commands the dialog
18535 Edit\SpecialChar \menuseparator
18536 Math\SpecialChar \menuseparator
18539 or the toolbar button
18540 \begin_inset Graphics
18541 filename ../images/math/font.png
18549 \begin_layout Subsection
18551 \begin_inset CommandInset label
18553 name "sub:Bold-Formulas"
18561 \begin_layout Plain Layout
18570 \begin_layout Standard
18571 To make a complete formula bold, the command
18577 from the previous subsection cannot be used, because it doesn't work for
18578 small Greek letters.
18579 Furthermore it prints Latin letters always upright, like in the following
18583 \begin_layout Standard
18584 \begin_inset Formula \[
18585 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18592 \begin_layout Standard
18593 To display the formula correctly, the command
18600 \begin_inset Formula \[
18601 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18605 It is also possible to set the formula in a
18607 boldmath environment
18610 This environment is created by inserting the command
18618 \begin_layout Plain Layout
18629 To end the environment, the command
18637 \begin_layout Plain Layout
18647 is inserted in TeX-mode.
18651 \begin_layout Plain Layout
18661 \begin_inset Formula \[
18662 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18670 \begin_layout Plain Layout
18682 \begin_layout Subsection
18687 \begin_layout Plain Layout
18696 \begin_layout Standard
18697 Formulas can be colored like normal text: Highlight a formula or a formula
18703 Here is a formula in magenta:
18704 \begin_inset Formula \[
18705 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18712 \begin_layout Standard
18713 You can also define your own colors as described in
18714 \begin_inset CommandInset ref
18716 reference "sub:Colored-Boxes"
18721 They can be used with the TeX code command
18731 \begin_layout Plain Layout
18742 \begin_layout Standard
18747 textcolor{color}{characters or formula}
18750 \begin_layout Standard
18751 The following example was colored completely dark green and partly red:
18754 \begin_layout Standard
18758 \begin_layout Plain Layout
18762 textcolor{darkgreen}{
18768 \begin_inset Formula \[
18769 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18777 \begin_layout Plain Layout
18787 \begin_layout Standard
18788 Due to a bug in LyX only complete formulas can be colored with self-defined
18793 \begin_layout Plain Layout
18794 \begin_inset CommandInset href
18796 name "LyX-bug #5269"
18797 target "http://www.lyx.org/trac/ticket/5269"
18809 \begin_layout Subsection
18811 \begin_inset CommandInset label
18813 name "sub:Font-Sizes"
18821 \begin_layout Plain Layout
18830 \begin_layout Standard
18831 For characters in formulas there are, analog to characters in text, the
18832 following size commands:
18835 \begin_layout Standard
18879 \begin_inset Newline newline
18901 \begin_layout Standard
18902 The size produced by the commands depends on the document font size, that
18903 corresponds with the command
18910 The other commands produce smaller or larger sizes than
18917 The font size can however not exceed a certain value.
18918 Is for example the document font size 12
18919 \begin_inset space \thinspace{}
18928 switches to the same size as
18938 \begin_layout Standard
18939 A size command is inserted in TeX-mode before the formula and sets the size
18940 for all following formula and text characters.
18941 To switch back to the initial size, the command
18947 is inserted behind the formula in TeX-mode.
18950 \begin_layout Standard
18951 Within a formula the size can only be changed for symbols or letters in
18953 To do this, the size command is inserted in mathematical text.
18954 All following characters until the end of the mathematical text or until
18955 another size command will have the selected size.
18957 \begin_inset VSpace -2mm
18963 \begin_layout Standard
18967 \begin_layout Plain Layout
18977 \begin_inset Formula \[
18978 A=\frac{B}{c}\cdot\maltese\]
18983 \begin_inset Formula \[
18984 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18992 \begin_layout Plain Layout
19004 \begin_layout Standard
19005 \begin_inset VSpace medskip
19008 Before both formulas the command
19015 The command for the second formula is:
19016 \begin_inset Newline newline
19027 \begin_layout Plain Layout
19042 \begin_layout Plain Layout
19057 \begin_layout Plain Layout
19072 \begin_layout Plain Layout
19082 \begin_inset Formula $\to$
19086 \begin_inset Formula $\to$
19090 \begin_inset Newline newline
19094 \begin_inset space \hspace*{}
19108 \begin_layout Plain Layout
19123 \begin_layout Plain Layout
19138 \begin_layout Plain Layout
19150 \begin_layout Standard
19151 If a symbol cannot be displayed in different sizes, it will always be displayed
19152 in the default size.
19155 \begin_layout Section
19160 \begin_layout Plain Layout
19169 \begin_layout Standard
19170 All Greek letters can also be inserted via the toolbar button
19171 \begin_inset Graphics
19172 filename ../images/math/alpha.png
19180 \begin_layout Subsection
19185 \begin_layout Plain Layout
19186 Greek letters ! small
19194 \begin_layout Standard
19195 \begin_inset space \hfill{}
19199 \begin_inset Tabular
19200 <lyxtabular version="3" rows="11" columns="2">
19202 <column alignment="center" valignment="top" width="0pt">
19203 <column alignment="center" valignment="top" width="0pt">
19205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19208 \begin_layout Plain Layout
19214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19217 \begin_layout Plain Layout
19225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19228 \begin_layout Plain Layout
19236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19239 \begin_layout Plain Layout
19240 \begin_inset Formula $\alpha$
19250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19253 \begin_layout Plain Layout
19261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19264 \begin_layout Plain Layout
19265 \begin_inset Formula $\beta$
19275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19278 \begin_layout Plain Layout
19286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19289 \begin_layout Plain Layout
19290 \begin_inset Formula $\gamma$
19300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19303 \begin_layout Plain Layout
19311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19314 \begin_layout Plain Layout
19315 \begin_inset Formula $\delta$
19325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19328 \begin_layout Plain Layout
19336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19339 \begin_layout Plain Layout
19340 \begin_inset Formula $\epsilon$
19350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19353 \begin_layout Plain Layout
19361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19364 \begin_layout Plain Layout
19365 \begin_inset Formula $\varepsilon$
19375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19378 \begin_layout Plain Layout
19386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19389 \begin_layout Plain Layout
19390 \begin_inset Formula $\zeta$
19400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19403 \begin_layout Plain Layout
19411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19414 \begin_layout Plain Layout
19415 \begin_inset Formula $\eta$
19425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19428 \begin_layout Plain Layout
19436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19439 \begin_layout Plain Layout
19440 \begin_inset Formula $\theta$
19450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19453 \begin_layout Plain Layout
19461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19464 \begin_layout Plain Layout
19465 \begin_inset Formula $\vartheta$
19479 \begin_inset space \hfill{}
19483 \begin_inset Tabular
19484 <lyxtabular version="3" rows="12" columns="2">
19486 <column alignment="center" valignment="top" width="0pt">
19487 <column alignment="center" valignment="top" width="0pt">
19489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19492 \begin_layout Plain Layout
19498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19501 \begin_layout Plain Layout
19509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19512 \begin_layout Plain Layout
19520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19523 \begin_layout Plain Layout
19524 \begin_inset Formula $\iota$
19534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19537 \begin_layout Plain Layout
19545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19548 \begin_layout Plain Layout
19549 \begin_inset Formula $\kappa$
19559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19562 \begin_layout Plain Layout
19570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19573 \begin_layout Plain Layout
19574 \begin_inset Formula $\varkappa$
19584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19587 \begin_layout Plain Layout
19595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19598 \begin_layout Plain Layout
19599 \begin_inset Formula $\lambda$
19609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19612 \begin_layout Plain Layout
19620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19623 \begin_layout Plain Layout
19624 \begin_inset Formula $\mu$
19634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19637 \begin_layout Plain Layout
19645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19648 \begin_layout Plain Layout
19649 \begin_inset Formula $\nu$
19659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19662 \begin_layout Plain Layout
19670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19673 \begin_layout Plain Layout
19674 \begin_inset Formula $\xi$
19684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19687 \begin_layout Plain Layout
19693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19696 \begin_layout Plain Layout
19697 \begin_inset Formula $o$
19707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19710 \begin_layout Plain Layout
19718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19721 \begin_layout Plain Layout
19722 \begin_inset Formula $\pi$
19732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19735 \begin_layout Plain Layout
19743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19746 \begin_layout Plain Layout
19747 \begin_inset Formula $\varpi$
19757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19760 \begin_layout Plain Layout
19768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19771 \begin_layout Plain Layout
19772 \begin_inset Formula $\rho$
19786 \begin_inset space \hfill{}
19790 \begin_inset Tabular
19791 <lyxtabular version="3" rows="11" columns="2">
19793 <column alignment="center" valignment="top" width="0pt">
19794 <column alignment="center" valignment="top" width="0pt">
19796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19799 \begin_layout Plain Layout
19805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19808 \begin_layout Plain Layout
19816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19819 \begin_layout Plain Layout
19827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19830 \begin_layout Plain Layout
19831 \begin_inset Formula $\varrho$
19841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19844 \begin_layout Plain Layout
19852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19855 \begin_layout Plain Layout
19856 \begin_inset Formula $\sigma$
19866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19869 \begin_layout Plain Layout
19877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19880 \begin_layout Plain Layout
19881 \begin_inset Formula $\varsigma$
19891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19894 \begin_layout Plain Layout
19902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19905 \begin_layout Plain Layout
19906 \begin_inset Formula $\tau$
19916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19919 \begin_layout Plain Layout
19927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19930 \begin_layout Plain Layout
19931 \begin_inset Formula $\upsilon$
19941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19944 \begin_layout Plain Layout
19952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19955 \begin_layout Plain Layout
19956 \begin_inset Formula $\phi$
19966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19969 \begin_layout Plain Layout
19977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19980 \begin_layout Plain Layout
19981 \begin_inset Formula $\varphi$
19991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19994 \begin_layout Plain Layout
20002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20005 \begin_layout Plain Layout
20006 \begin_inset Formula $\chi$
20016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20019 \begin_layout Plain Layout
20027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20030 \begin_layout Plain Layout
20031 \begin_inset Formula $\psi$
20041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20044 \begin_layout Plain Layout
20052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20055 \begin_layout Plain Layout
20056 \begin_inset Formula $\omega$
20070 \begin_inset space \hfill{}
20076 \begin_layout Standard
20077 \begin_inset VSpace medskip
20083 \begin_layout Standard
20084 How to create upright Greek letters is explained in
20085 \begin_inset CommandInset ref
20087 reference "sub:Upright-small-Greek"
20094 \begin_layout Subsection
20099 \begin_layout Plain Layout
20100 Greek letters ! big
20108 \begin_layout Standard
20109 \begin_inset space \hfill{}
20113 \begin_inset Tabular
20114 <lyxtabular version="3" rows="7" columns="2">
20116 <column alignment="center" valignment="top" width="0pt">
20117 <column alignment="center" valignment="top" width="0pt">
20119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20122 \begin_layout Plain Layout
20128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20131 \begin_layout Plain Layout
20139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20142 \begin_layout Plain Layout
20150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20153 \begin_layout Plain Layout
20154 \begin_inset Formula $\Gamma$
20164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20167 \begin_layout Plain Layout
20175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20178 \begin_layout Plain Layout
20179 \begin_inset Formula $\Delta$
20189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20192 \begin_layout Plain Layout
20200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20203 \begin_layout Plain Layout
20204 \begin_inset Formula $\Theta$
20214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20217 \begin_layout Plain Layout
20225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20228 \begin_layout Plain Layout
20229 \begin_inset Formula $\Lambda$
20239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20242 \begin_layout Plain Layout
20250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20253 \begin_layout Plain Layout
20254 \begin_inset Formula $\Xi$
20264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20267 \begin_layout Plain Layout
20275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20278 \begin_layout Plain Layout
20279 \begin_inset Formula $\Pi$
20293 \begin_inset space \hfill{}
20297 \begin_inset Tabular
20298 <lyxtabular version="3" rows="6" columns="2">
20300 <column alignment="center" valignment="top" width="0pt">
20301 <column alignment="center" valignment="top" width="0pt">
20303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20306 \begin_layout Plain Layout
20312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20315 \begin_layout Plain Layout
20323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20326 \begin_layout Plain Layout
20334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20337 \begin_layout Plain Layout
20338 \begin_inset Formula $\Sigma$
20348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20351 \begin_layout Plain Layout
20359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20362 \begin_layout Plain Layout
20363 \begin_inset Formula $\Upsilon$
20373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20376 \begin_layout Plain Layout
20384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20387 \begin_layout Plain Layout
20388 \begin_inset Formula $\Phi$
20398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20401 \begin_layout Plain Layout
20409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20412 \begin_layout Plain Layout
20413 \begin_inset Formula $\Psi$
20423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20426 \begin_layout Plain Layout
20434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20437 \begin_layout Plain Layout
20438 \begin_inset Formula $\Omega$
20452 \begin_inset space \hfill{}
20458 \begin_layout Standard
20459 \begin_inset VSpace medskip
20462 That the big Greek letters appear upright is caused by a design bug when
20464 To get correct italic big letters, begin every command with
20469 For example the command
20476 \begin_inset Formula $\varGamma$
20482 \begin_layout Subsection
20487 \begin_layout Plain Layout
20488 Greek letters ! bold
20496 \begin_layout Standard
20497 Greek letters cannot be set with different font styles like Latin letters.
20498 They can only be made bold with the command
20508 \begin_layout Plain Layout
20519 \begin_layout Standard
20521 \begin_inset Tabular
20522 <lyxtabular version="3" rows="3" columns="2">
20524 <column alignment="center" valignment="top" width="0">
20525 <column alignment="center" valignment="top" width="0">
20527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20530 \begin_layout Plain Layout
20536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20539 \begin_layout Plain Layout
20547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20550 \begin_layout Plain Layout
20562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20565 \begin_layout Plain Layout
20566 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20579 \begin_layout Plain Layout
20591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20594 \begin_layout Plain Layout
20595 \begin_inset Formula $\theta\boldsymbol{\theta}$
20611 \begin_layout Section
20616 \begin_layout Plain Layout
20629 \begin_layout Plain Layout
20630 A list with all symbols of most of the LaTeX-packages can be found in
20631 \begin_inset CommandInset citation
20646 \begin_layout Plain Layout
20654 \begin_inset Note Note
20657 \begin_layout Plain Layout
20660 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20663 \begin_layout Plain Layout
20666 texorpdfstring is in section
20667 \begin_inset CommandInset ref
20669 reference "sub:Formulas-in-Section"
20682 \begin_layout Plain Layout
20691 \begin_layout Standard
20692 Many of the symbols listed in this section can also be inserted via the
20694 \begin_inset Graphics
20695 filename ../images/math/nabla.png
20701 \begin_inset Graphics
20702 filename ../images/math/digamma.png
20710 \begin_layout Subsection
20711 Mathematical Symbols
20712 \begin_inset CommandInset label
20714 name "sub:Mathematical-Symbols"
20722 \begin_layout Plain Layout
20723 Symbols ! mathematical
20731 \begin_layout Standard
20732 \begin_inset space \hfill{}
20736 \begin_inset Tabular
20737 <lyxtabular version="3" rows="10" columns="2">
20739 <column alignment="center" valignment="top" width="0pt">
20740 <column alignment="center" valignment="top" width="0pt">
20742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20745 \begin_layout Plain Layout
20751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20754 \begin_layout Plain Layout
20762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20765 \begin_layout Plain Layout
20773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20776 \begin_layout Plain Layout
20777 \begin_inset Formula $\neg$
20787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20790 \begin_layout Plain Layout
20798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20801 \begin_layout Plain Layout
20802 \begin_inset Formula $\Im$
20812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20815 \begin_layout Plain Layout
20823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20826 \begin_layout Plain Layout
20827 \begin_inset Formula $\Re$
20837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20840 \begin_layout Plain Layout
20848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20851 \begin_layout Plain Layout
20852 \begin_inset Formula $\aleph$
20862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20865 \begin_layout Plain Layout
20873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20876 \begin_layout Plain Layout
20877 \begin_inset Formula $\partial$
20887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20890 \begin_layout Plain Layout
20898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20901 \begin_layout Plain Layout
20902 \begin_inset Formula $\infty$
20912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20915 \begin_layout Plain Layout
20923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20926 \begin_layout Plain Layout
20927 \begin_inset Formula $\wp$
20937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20940 \begin_layout Plain Layout
20948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20951 \begin_layout Plain Layout
20952 \begin_inset Formula $\imath$
20962 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20965 \begin_layout Plain Layout
20973 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20976 \begin_layout Plain Layout
20977 \begin_inset Formula $\jmath$
20991 \begin_inset space \hfill{}
20995 \begin_inset Tabular
20996 <lyxtabular version="3" rows="10" columns="2">
20998 <column alignment="center" valignment="top" width="0pt">
20999 <column alignment="center" valignment="top" width="0pt">
21001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21004 \begin_layout Plain Layout
21010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21013 \begin_layout Plain Layout
21015 \begin_inset Note Note
21018 \begin_layout Plain Layout
21025 is only used as spacer.
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 $\forall$
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 $\exists$
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 $\nexists$
21112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21115 \begin_layout Plain Layout
21123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21126 \begin_layout Plain Layout
21127 \begin_inset Formula $\emptyset$
21137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21140 \begin_layout Plain Layout
21148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21151 \begin_layout Plain Layout
21152 \begin_inset Formula $\varnothing$
21162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21165 \begin_layout Plain Layout
21173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21176 \begin_layout Plain Layout
21177 \begin_inset Formula $\dag$
21187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21190 \begin_layout Plain Layout
21198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21201 \begin_layout Plain Layout
21202 \begin_inset Formula $\ddag$
21212 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21215 \begin_layout Plain Layout
21223 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21226 \begin_layout Plain Layout
21230 \begin_layout Plain Layout
21240 \begin_inset Formula $\complement$
21247 \begin_layout Plain Layout
21261 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21264 \begin_layout Plain Layout
21272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21275 \begin_layout Plain Layout
21276 \begin_inset Formula $\Bbbk$
21290 \begin_inset space \hfill{}
21294 \begin_inset Tabular
21295 <lyxtabular version="3" rows="10" columns="2">
21297 <column alignment="center" valignment="top" width="0pt">
21298 <column alignment="center" valignment="top" width="0pt">
21300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21303 \begin_layout Plain Layout
21309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21312 \begin_layout Plain Layout
21320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21323 \begin_layout Plain Layout
21331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21334 \begin_layout Plain Layout
21335 \begin_inset Formula $\prime$
21345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21348 \begin_layout Plain Layout
21356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21359 \begin_layout Plain Layout
21360 \begin_inset Formula $\backprime$
21370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21373 \begin_layout Plain Layout
21381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21384 \begin_layout Plain Layout
21385 \begin_inset Formula $\mho$
21395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21398 \begin_layout Plain Layout
21406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21409 \begin_layout Plain Layout
21410 \begin_inset Formula $\triangle$
21420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21423 \begin_layout Plain Layout
21431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21434 \begin_layout Plain Layout
21435 \begin_inset Formula $\angle$
21445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21448 \begin_layout Plain Layout
21456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21459 \begin_layout Plain Layout
21460 \begin_inset Formula $\measuredangle$
21470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21473 \begin_layout Plain Layout
21481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21484 \begin_layout Plain Layout
21485 \begin_inset Formula $\sphericalangle$
21495 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21498 \begin_layout Plain Layout
21506 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21509 \begin_layout Plain Layout
21510 \begin_inset Formula $\top$
21520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21523 \begin_layout Plain Layout
21531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21534 \begin_layout Plain Layout
21535 \begin_inset Formula $\bot$
21549 \begin_inset space \hfill{}
21555 \begin_layout Subsection
21556 Miscellaneous Symbols
21557 \begin_inset CommandInset label
21559 name "sub:Miscellaneous-Symbols"
21567 \begin_layout Plain Layout
21568 Symbols ! miscellaneous
21576 \begin_layout Standard
21579 \begin_inset Tabular
21580 <lyxtabular version="3" rows="10" columns="2">
21582 <column alignment="center" valignment="top" width="0pt">
21583 <column alignment="center" valignment="top" width="0pt">
21585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21588 \begin_layout Plain Layout
21594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21597 \begin_layout Plain Layout
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 $\flat$
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 $\natural$
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 $\sharp$
21680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21683 \begin_layout Plain Layout
21691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21694 \begin_layout Plain Layout
21695 \begin_inset Formula $\surd$
21705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21708 \begin_layout Plain Layout
21716 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21719 \begin_layout Plain Layout
21720 \begin_inset Formula $\checkmark$
21730 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21733 \begin_layout Plain Layout
21741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21744 \begin_layout Plain Layout
21745 \begin_inset Formula $\yen$
21755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21758 \begin_layout Plain Layout
21766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21769 \begin_layout Plain Layout
21770 \begin_inset Formula $\pounds$
21780 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21783 \begin_layout Plain Layout
21789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21792 \begin_layout Plain Layout
21793 \begin_inset Formula $\$$
21803 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21806 \begin_layout Plain Layout
21812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21815 \begin_layout Plain Layout
21816 \begin_inset Formula $§$
21830 \begin_inset Tabular
21831 <lyxtabular version="3" rows="10" columns="2">
21833 <column alignment="center" valignment="top" width="0">
21834 <column alignment="center" valignment="top" width="0">
21836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21839 \begin_layout Plain Layout
21845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21848 \begin_layout Plain Layout
21856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21859 \begin_layout Plain Layout
21867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21870 \begin_layout Plain Layout
21871 \begin_inset Formula $\hbar$
21881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21884 \begin_layout Plain Layout
21892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21895 \begin_layout Plain Layout
21896 \begin_inset Formula $\hslash$
21906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21909 \begin_layout Plain Layout
21917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21920 \begin_layout Plain Layout
21921 \begin_inset Formula $\clubsuit$
21931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21934 \begin_layout Plain Layout
21942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21945 \begin_layout Plain Layout
21946 \begin_inset Formula $\spadesuit$
21956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21959 \begin_layout Plain Layout
21967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21970 \begin_layout Plain Layout
21971 \begin_inset Formula $\bigstar$
21981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21984 \begin_layout Plain Layout
21992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21995 \begin_layout Plain Layout
21996 \begin_inset Formula $\blacklozenge$
22006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22009 \begin_layout Plain Layout
22017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22020 \begin_layout Plain Layout
22021 \begin_inset Formula $\blacktriangle$
22031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22034 \begin_layout Plain Layout
22042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22045 \begin_layout Plain Layout
22046 \begin_inset Formula $\blacktriangledown$
22056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22059 \begin_layout Plain Layout
22067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22070 \begin_layout Plain Layout
22071 \begin_inset Formula $\bullet$
22085 \begin_inset Tabular
22086 <lyxtabular version="3" rows="10" columns="2">
22088 <column alignment="center" valignment="top" width="0pt">
22089 <column alignment="center" valignment="top" width="0pt">
22091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22094 \begin_layout Plain Layout
22100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22103 \begin_layout Plain Layout
22111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22114 \begin_layout Plain Layout
22122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22125 \begin_layout Plain Layout
22126 \begin_inset Formula $\diamondsuit$
22136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22139 \begin_layout Plain Layout
22147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22150 \begin_layout Plain Layout
22151 \begin_inset Formula $\Diamond$
22161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22164 \begin_layout Plain Layout
22172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22175 \begin_layout Plain Layout
22176 \begin_inset Formula $\heartsuit$
22186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22189 \begin_layout Plain Layout
22197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22200 \begin_layout Plain Layout
22201 \begin_inset Formula $\P$
22211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22214 \begin_layout Plain Layout
22222 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22225 \begin_layout Plain Layout
22226 \begin_inset Formula $\copyright$
22236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22239 \begin_layout Plain Layout
22247 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22250 \begin_layout Plain Layout
22251 \begin_inset Formula $\circledR$
22261 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22264 \begin_layout Plain Layout
22272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22275 \begin_layout Plain Layout
22276 \begin_inset Formula $\maltese$
22286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22289 \begin_layout Plain Layout
22297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22300 \begin_layout Plain Layout
22301 \begin_inset Formula $\diagup$
22311 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22314 \begin_layout Plain Layout
22322 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22325 \begin_layout Plain Layout
22326 \begin_inset Formula $\diagdown$
22342 \begin_layout Standard
22343 \begin_inset VSpace medskip
22346 More symbols are listed in
22347 \begin_inset CommandInset ref
22349 reference "sub:Miscellaneous-special-Characters"
22356 \begin_layout Standard
22357 Some symbols can be displayed in different sizes, see
22358 \begin_inset CommandInset ref
22360 reference "sub:Font-Sizes"
22367 \begin_layout Subsection
22372 \begin_layout Plain Layout
22373 Symbols ! Euro-symbol
22382 \begin_layout Plain Layout
22389 \begin_layout Plain Layout
22406 \begin_layout Standard
22407 To use the Euro symbol in formulas, the LaTeX-package
22415 \begin_layout Plain Layout
22421 must be installed and loaded with the LaTeX-preamble line
22424 \begin_layout Standard
22429 usepackage[gennarrow]{eurosym}
22432 \begin_layout Standard
22433 The Euro symbol can now be inserted with the command
22443 \begin_layout Plain Layout
22454 \begin_layout Standard
22455 The Euro symbol can directly be inserted with the € key in mathematical
22456 text, without having
22471 can also be inserted in TeX-mode.
22472 The official currency symbol can then be inserted with the command
22482 \begin_layout Plain Layout
22490 , that is only available in TeX-mode.
22493 \begin_layout Standard
22497 \begin_layout Plain Layout
22507 \begin_inset Note Note
22510 \begin_layout Plain Layout
22511 The following table will only be displayed when the LaTeX-package
22523 \begin_layout Standard
22524 An overview about the different Euro symbols:
22527 \begin_layout Standard
22529 \begin_inset Tabular
22530 <lyxtabular version="3" rows="4" columns="3">
22532 <column alignment="center" valignment="top" width="0pt">
22533 <column alignment="center" valignment="top" width="0pt">
22534 <column alignment="center" valignment="top" width="0pt">
22536 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22539 \begin_layout Plain Layout
22545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22548 \begin_layout Plain Layout
22554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22557 \begin_layout Plain Layout
22565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22568 \begin_layout Plain Layout
22574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22577 \begin_layout Plain Layout
22585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22588 \begin_layout Plain Layout
22589 \begin_inset Formula $\euro$
22599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22602 \begin_layout Plain Layout
22608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22611 \begin_layout Plain Layout
22617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22620 \begin_layout Plain Layout
22621 \begin_inset Formula $\mbox{€}$
22631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22634 \begin_layout Plain Layout
22640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22643 \begin_layout Plain Layout
22651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22654 \begin_layout Plain Layout
22658 \begin_layout Plain Layout
22680 \begin_layout Standard
22684 \begin_layout Plain Layout
22694 \begin_inset Note Note
22697 \begin_layout Plain Layout
22698 The following will be displayed when the LaTeX-package
22710 \begin_layout Standard
22711 You need to install the LaTeX-package
22715 to see the rest of this subsection in the output.
22718 \begin_layout Standard
22722 \begin_layout Plain Layout
22734 \begin_layout Standard
22735 \begin_inset Newpage newpage
22741 \begin_layout Section
22743 \begin_inset CommandInset label
22745 name "sec:Relations"
22753 \begin_layout Plain Layout
22763 \begin_layout Plain Layout
22768 \begin_layout Plain Layout
22779 \begin_layout Plain Layout
22794 \begin_layout Standard
22795 All relations can also be inserted via the toolbar button
22796 \begin_inset Graphics
22797 filename ../images/math/leq.png
22805 \begin_layout Standard
22806 \begin_inset space \hfill{}
22810 \begin_inset Tabular
22811 <lyxtabular version="3" rows="17" columns="2">
22813 <column alignment="center" valignment="top" width="0pt">
22814 <column alignment="center" valignment="top" width="0pt">
22816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22819 \begin_layout Plain Layout
22825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22828 \begin_layout Plain Layout
22836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22839 \begin_layout Plain Layout
22845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22848 \begin_layout Plain Layout
22849 \begin_inset Formula $<$
22859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22862 \begin_layout Plain Layout
22870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22873 \begin_layout Plain Layout
22874 \begin_inset Formula $\le$
22884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22887 \begin_layout Plain Layout
22895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22898 \begin_layout Plain Layout
22899 \begin_inset Formula $\ll$
22909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22912 \begin_layout Plain Layout
22920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22923 \begin_layout Plain Layout
22924 \begin_inset Formula $\prec$
22934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22937 \begin_layout Plain Layout
22945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22948 \begin_layout Plain Layout
22949 \begin_inset Formula $\preceq$
22959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22962 \begin_layout Plain Layout
22970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22973 \begin_layout Plain Layout
22974 \begin_inset Formula $\subset$
22984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22987 \begin_layout Plain Layout
22995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22998 \begin_layout Plain Layout
22999 \begin_inset Formula $\subseteq$
23009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23012 \begin_layout Plain Layout
23020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23023 \begin_layout Plain Layout
23024 \begin_inset Formula $\sqsubseteq$
23034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23037 \begin_layout Plain Layout
23045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23048 \begin_layout Plain Layout
23049 \begin_inset Formula $\in$
23059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23062 \begin_layout Plain Layout
23070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23073 \begin_layout Plain Layout
23074 \begin_inset Formula $\vdash$
23084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23087 \begin_layout Plain Layout
23095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23098 \begin_layout Plain Layout
23099 \begin_inset Formula $\smile$
23109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23112 \begin_layout Plain Layout
23120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23123 \begin_layout Plain Layout
23124 \begin_inset Formula $\lhd$
23134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23137 \begin_layout Plain Layout
23145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23148 \begin_layout Plain Layout
23149 \begin_inset Formula $\unlhd$
23159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23162 \begin_layout Plain Layout
23170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23173 \begin_layout Plain Layout
23174 \begin_inset Formula $\gtrless$
23184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23187 \begin_layout Plain Layout
23195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23198 \begin_layout Plain Layout
23199 \begin_inset Formula $\mid$
23209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23212 \begin_layout Plain Layout
23220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23223 \begin_layout Plain Layout
23224 \begin_inset Formula $\nmid$
23238 \begin_inset space \hfill{}
23242 \begin_inset Tabular
23243 <lyxtabular version="3" rows="17" columns="2">
23245 <column alignment="center" valignment="top" width="0pt">
23246 <column alignment="center" valignment="top" width="0pt">
23248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23251 \begin_layout Plain Layout
23257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23260 \begin_layout Plain Layout
23268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23271 \begin_layout Plain Layout
23277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23280 \begin_layout Plain Layout
23281 \begin_inset Formula $=$
23291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23294 \begin_layout Plain Layout
23302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23305 \begin_layout Plain Layout
23306 \begin_inset Formula $\not=$
23316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23319 \begin_layout Plain Layout
23327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23330 \begin_layout Plain Layout
23331 \begin_inset Formula $\equiv$
23341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23344 \begin_layout Plain Layout
23352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23355 \begin_layout Plain Layout
23356 \begin_inset Formula $\sim$
23366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23369 \begin_layout Plain Layout
23377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23380 \begin_layout Plain Layout
23381 \begin_inset Formula $\simeq$
23391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23394 \begin_layout Plain Layout
23402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23405 \begin_layout Plain Layout
23406 \begin_inset Formula $\approx$
23416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23419 \begin_layout Plain Layout
23427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23430 \begin_layout Plain Layout
23431 \begin_inset Formula $\cong$
23441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23444 \begin_layout Plain Layout
23452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23455 \begin_layout Plain Layout
23456 \begin_inset Formula $\bowtie$
23466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23469 \begin_layout Plain Layout
23477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23480 \begin_layout Plain Layout
23481 \begin_inset Formula $\notin$
23491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23494 \begin_layout Plain Layout
23502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23505 \begin_layout Plain Layout
23506 \begin_inset Formula $\perp$
23516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23519 \begin_layout Plain Layout
23527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23530 \begin_layout Plain Layout
23531 \begin_inset Formula $\propto$
23541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23544 \begin_layout Plain Layout
23552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23555 \begin_layout Plain Layout
23556 \begin_inset Formula $\asymp$
23566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23569 \begin_layout Plain Layout
23577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23580 \begin_layout Plain Layout
23581 \begin_inset Formula $\doteq$
23591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23594 \begin_layout Plain Layout
23602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23605 \begin_layout Plain Layout
23606 \begin_inset Formula $\circeq$
23616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23619 \begin_layout Plain Layout
23627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23630 \begin_layout Plain Layout
23631 \begin_inset Formula $\models$
23641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23644 \begin_layout Plain Layout
23652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23655 \begin_layout Plain Layout
23656 \begin_inset Formula $\widehat{=}$
23670 \begin_inset space \hfill{}
23674 \begin_inset Tabular
23675 <lyxtabular version="3" rows="17" columns="2">
23677 <column alignment="center" valignment="top" width="0pt">
23678 <column alignment="center" valignment="top" width="0pt">
23680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23683 \begin_layout Plain Layout
23689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23692 \begin_layout Plain Layout
23700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23703 \begin_layout Plain Layout
23709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23712 \begin_layout Plain Layout
23713 \begin_inset Formula $>$
23723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23726 \begin_layout Plain Layout
23734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23737 \begin_layout Plain Layout
23738 \begin_inset Formula $\ge$
23748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23751 \begin_layout Plain Layout
23759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23762 \begin_layout Plain Layout
23763 \begin_inset Formula $\gg$
23773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23776 \begin_layout Plain Layout
23784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23787 \begin_layout Plain Layout
23788 \begin_inset Formula $\succ$
23798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23801 \begin_layout Plain Layout
23809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23812 \begin_layout Plain Layout
23813 \begin_inset Formula $\succeq$
23823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23826 \begin_layout Plain Layout
23834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23837 \begin_layout Plain Layout
23838 \begin_inset Formula $\supset$
23848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23851 \begin_layout Plain Layout
23859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23862 \begin_layout Plain Layout
23863 \begin_inset Formula $\supseteq$
23873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23876 \begin_layout Plain Layout
23884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23887 \begin_layout Plain Layout
23888 \begin_inset Formula $\sqsupseteq$
23898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23901 \begin_layout Plain Layout
23909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23912 \begin_layout Plain Layout
23913 \begin_inset Formula $\ni$
23923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23926 \begin_layout Plain Layout
23934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23937 \begin_layout Plain Layout
23938 \begin_inset Formula $\dashv$
23948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23951 \begin_layout Plain Layout
23959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23962 \begin_layout Plain Layout
23963 \begin_inset Formula $\frown$
23973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23976 \begin_layout Plain Layout
23984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23987 \begin_layout Plain Layout
23988 \begin_inset Formula $\rhd$
23998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24001 \begin_layout Plain Layout
24009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24012 \begin_layout Plain Layout
24013 \begin_inset Formula $\unrhd$
24023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24026 \begin_layout Plain Layout
24034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24037 \begin_layout Plain Layout
24038 \begin_inset Formula $\lessgtr$
24048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24051 \begin_layout Plain Layout
24059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24062 \begin_layout Plain Layout
24063 \begin_inset Formula $\parallel$
24073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24076 \begin_layout Plain Layout
24084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24087 \begin_layout Plain Layout
24088 \begin_inset Formula $\nparallel$
24102 \begin_inset space \hfill{}
24108 \begin_layout Standard
24109 \begin_inset VSpace medskip
24124 are bigger than the equal looking operators
24139 \begin_layout Standard
24140 Relations are, in contrary to symbols, always surrounded by space.
24143 \begin_layout Standard
24144 Relations with labels can be created with the command
24154 \begin_layout Plain Layout
24165 \begin_layout Standard
24167 \begin_inset Tabular
24168 <lyxtabular version="3" rows="2" columns="2">
24170 <column alignment="center" valignment="top" width="0">
24171 <column alignment="center" valignment="top" width="0">
24173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24176 \begin_layout Plain Layout
24182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24185 \begin_layout Plain Layout
24187 \begin_inset Note Note
24190 \begin_layout Plain Layout
24197 is only used as spacer.
24209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24212 \begin_layout Plain Layout
24219 \begin_layout Plain Layout
24236 \begin_layout Plain Layout
24246 \begin_inset Formula $\downarrow$
24255 \begin_layout Plain Layout
24268 \begin_layout Plain Layout
24282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24285 \begin_layout Plain Layout
24286 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24302 \begin_layout Section
24306 \begin_layout Subsection
24307 Predefined Functions
24308 \begin_inset CommandInset label
24310 name "sub:Predefined-Functions"
24318 \begin_layout Plain Layout
24319 Functions ! predefined
24327 \begin_layout Standard
24328 In general, variables are set
24332 in mathematical expressions, but not function names, because
24333 \begin_inset Formula $sin$
24336 could be misunderstood as
24337 \begin_inset Formula $s\cdot i\cdot n$
24341 Therefore there are predefined functions, that are additionally a bit separated
24343 They are inserted as commands starting with a backslash before their name.
24346 \begin_layout Standard
24348 \begin_inset Tabular
24349 <lyxtabular version="3" rows="2" columns="4">
24351 <column alignment="center" valignment="top" width="0pt">
24352 <column alignment="center" valignment="top" width="0pt">
24353 <column alignment="center" valignment="top" width="0pt">
24354 <column alignment="center" valignment="top" width="0pt">
24356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24359 \begin_layout Plain Layout
24365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24368 \begin_layout Plain Layout
24374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24377 \begin_layout Plain Layout
24383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24386 \begin_layout Plain Layout
24394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24397 \begin_layout Plain Layout
24403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24406 \begin_layout Plain Layout
24407 \begin_inset Formula $Asin(x)+B$
24415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24418 \begin_layout Plain Layout
24426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24429 \begin_layout Plain Layout
24430 \begin_inset Formula $A\sin(x)+B$
24446 \begin_layout Standard
24447 The following functions are predefined:
24450 \begin_layout Standard
24451 \begin_inset VSpace -2mm
24457 \begin_layout Standard
24459 \begin_inset Tabular
24460 <lyxtabular version="3" rows="9" columns="4">
24462 <column alignment="center" valignment="top" width="0pt">
24463 <column alignment="center" valignment="top" width="0pt">
24464 <column alignment="center" valignment="top" width="0pt">
24465 <column alignment="center" valignment="top" width="0pt">
24467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24470 \begin_layout Plain Layout
24476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24479 \begin_layout Plain Layout
24485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24488 \begin_layout Plain Layout
24494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24497 \begin_layout Plain Layout
24505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24508 \begin_layout Plain Layout
24516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24519 \begin_layout Plain Layout
24527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24530 \begin_layout Plain Layout
24538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24541 \begin_layout Plain Layout
24551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24554 \begin_layout Plain Layout
24562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24565 \begin_layout Plain Layout
24573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24576 \begin_layout Plain Layout
24584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24587 \begin_layout Plain Layout
24597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24600 \begin_layout Plain Layout
24608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24611 \begin_layout Plain Layout
24619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24622 \begin_layout Plain Layout
24630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24633 \begin_layout Plain Layout
24643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24646 \begin_layout Plain Layout
24654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24657 \begin_layout Plain Layout
24665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24668 \begin_layout Plain Layout
24676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24679 \begin_layout Plain Layout
24689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24692 \begin_layout Plain Layout
24700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24703 \begin_layout Plain Layout
24711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24714 \begin_layout Plain Layout
24722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24725 \begin_layout Plain Layout
24735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24738 \begin_layout Plain Layout
24746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24749 \begin_layout Plain Layout
24757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24760 \begin_layout Plain Layout
24768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24771 \begin_layout Plain Layout
24781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24784 \begin_layout Plain Layout
24792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24795 \begin_layout Plain Layout
24803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24806 \begin_layout Plain Layout
24814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24817 \begin_layout Plain Layout
24827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24830 \begin_layout Plain Layout
24838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24841 \begin_layout Plain Layout
24849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24852 \begin_layout Plain Layout
24860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24863 \begin_layout Plain Layout
24879 \begin_layout Standard
24880 They can also be inserted with the math toolbar button
24881 \begin_inset Graphics
24882 filename ../images/math/functions.png
24890 \begin_layout Subsection
24891 Self-defined Functions
24895 \begin_layout Plain Layout
24896 Functions ! self-defined
24904 \begin_layout Standard
24905 To use a function that is not predefined, like for example the sign function
24906 sgn(x), there are two possibilities:
24909 \begin_layout Itemize
24910 Define the function by inserting the following line to the LaTeX-preamble
24914 \begin_layout Plain Layout
24919 DeclareMathOperator
24922 \begin_inset CommandInset ref
24924 reference "sub:Self-defined-Operators"
24934 \begin_inset Newline newline
24938 \begin_inset VSpace -3mm
24942 \begin_inset Newline newline
24949 DeclareMathOperator{
24957 \begin_layout Plain Layout
24962 DeclareMathOperator
24968 \begin_inset Newline newline
24972 \begin_inset VSpace -2mm
24976 \begin_inset Newline newline
24979 Now the new defined function can be called with the command
24988 \begin_layout Itemize
24989 Write the the formula as usual, mark the formula name, in our example the
24994 , and change it to mathematical text.
24995 At last a space is inserted between prefactor and function.
24998 \begin_layout Standard
24999 The result is the same with both methods as with a predefined function
25003 \begin_layout Plain Layout
25004 In LyX self-defined functions are displayed red, predefined ones black.
25012 \begin_layout Standard
25014 \begin_inset Tabular
25015 <lyxtabular version="3" rows="3" columns="2">
25017 <column alignment="center" valignment="top" width="0pt">
25018 <column alignment="center" valignment="top" width="0pt">
25020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25023 \begin_layout Plain Layout
25029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25032 \begin_layout Plain Layout
25040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25043 \begin_layout Plain Layout
25051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25054 \begin_layout Plain Layout
25055 \begin_inset Formula $A\sgn(x)+B$
25065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25068 \begin_layout Plain Layout
25072 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25083 \begin_layout Plain Layout
25084 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25100 \begin_layout Standard
25101 The first method is more suitable when the self-defined function should
25102 be used several times.
25105 \begin_layout Subsection
25110 \begin_layout Plain Layout
25119 \begin_layout Standard
25120 For limits there are defined besides
25130 \begin_layout Plain Layout
25150 furthermore the following functions:
25153 \begin_layout Standard
25155 \begin_inset Tabular
25156 <lyxtabular version="3" rows="5" columns="2">
25158 <column alignment="center" valignment="top" width="0">
25159 <column alignment="center" valignment="top" width="0">
25161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25164 \begin_layout Plain Layout
25170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25173 \begin_layout Plain Layout
25175 \begin_inset Note Note
25178 \begin_layout Plain Layout
25185 is only used as spacer.
25197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25200 \begin_layout Plain Layout
25208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25211 \begin_layout Plain Layout
25212 \begin_inset Formula $\varliminf$
25222 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25225 \begin_layout Plain Layout
25233 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25236 \begin_layout Plain Layout
25237 \begin_inset Formula $\varlimsup$
25247 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25250 \begin_layout Plain Layout
25258 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25261 \begin_layout Plain Layout
25262 \begin_inset Formula $\varprojlim$
25272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25275 \begin_layout Plain Layout
25283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25286 \begin_layout Plain Layout
25287 \begin_inset Formula $\varinjlim$
25291 \begin_inset Formula $\raisebox{-2.5mm}{}$
25307 \begin_layout Standard
25308 \begin_inset VSpace medskip
25311 The limit is created by inserting a subscript.
25312 It is set right beside the function in an inline formula:
25315 \begin_layout Standard
25317 \begin_inset Tabular
25318 <lyxtabular version="3" rows="2" columns="2">
25320 <column alignment="center" valignment="top" width="0pt">
25321 <column alignment="center" valignment="top" width="0pt">
25323 <cell alignment="center" valignment="top" usebox="none">
25326 \begin_layout Plain Layout
25332 <cell alignment="center" valignment="top" usebox="none">
25335 \begin_layout Plain Layout
25336 \begin_inset space \hspace{}
25341 \begin_inset Note Note
25344 \begin_layout Plain Layout
25351 are used here as spacer.
25363 <cell alignment="center" valignment="top" usebox="none">
25366 \begin_layout Plain Layout
25375 \begin_layout Plain Layout
25388 \begin_layout Plain Layout
25402 <cell alignment="center" valignment="top" usebox="none">
25405 \begin_layout Plain Layout
25406 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25422 \begin_layout Standard
25423 In a displayed formula the limit is set below the formula, as usual:
25424 \begin_inset Formula \[
25432 \begin_layout Subsection
25437 \begin_layout Plain Layout
25438 Functions ! modulo-
25446 \begin_layout Standard
25447 The modulo-function is special, because it exists in four variants.
25450 \begin_layout Standard
25451 The variants in a displayed formula:
25452 \begin_inset Formula \begin{align*}
25453 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25454 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25455 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25456 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25457 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25464 \begin_layout Standard
25465 In an inline formula less space is set before the function names for all
25469 \begin_layout Standard
25470 \begin_inset Newpage newpage
25476 \begin_layout Section
25481 \begin_layout Plain Layout
25490 \begin_layout Subsection
25491 Special Characters in Mathematical Text
25494 \begin_layout Standard
25495 The following commands can only be used in mathematical text or in TeX-mode:
25498 \begin_layout Standard
25499 \begin_inset space \hfill{}
25503 \begin_inset Tabular
25504 <lyxtabular version="3" rows="8" columns="2">
25506 <column alignment="block" valignment="top" width="0">
25507 <column alignment="block" valignment="top" width="0">
25509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25512 \begin_layout Plain Layout
25518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25521 \begin_layout Plain Layout
25529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25532 \begin_layout Plain Layout
25540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25543 \begin_layout Plain Layout
25544 \begin_inset Formula $\textrm{œ}$
25554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25557 \begin_layout Plain Layout
25565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25568 \begin_layout Plain Layout
25569 \begin_inset Formula $\textrm{Œ}$
25579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25582 \begin_layout Plain Layout
25590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25593 \begin_layout Plain Layout
25594 \begin_inset Formula $\textrm{æ}$
25604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25607 \begin_layout Plain Layout
25615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25618 \begin_layout Plain Layout
25619 \begin_inset Formula $\textrm{Æ}$
25629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25632 \begin_layout Plain Layout
25640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25643 \begin_layout Plain Layout
25644 \begin_inset Formula $\textrm{\aa}$
25654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25657 \begin_layout Plain Layout
25664 \begin_layout Plain Layout
25671 \begin_layout Plain Layout
25692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25695 \begin_layout Plain Layout
25696 \begin_inset Formula $\textrm{Å}$
25706 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25709 \begin_layout Plain Layout
25717 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25720 \begin_layout Plain Layout
25721 \begin_inset Formula $\textrm{ı}$
25735 \begin_inset space \hfill{}
25739 \begin_inset Tabular
25740 <lyxtabular version="3" rows="8" columns="2">
25742 <column alignment="block" valignment="top" width="0">
25743 <column alignment="center" valignment="top" width="0">
25745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25748 \begin_layout Plain Layout
25750 \begin_inset Note Note
25753 \begin_layout Plain Layout
25755 \begin_inset space \thinspace{}
25758 mm is used for separation, because otherwise the output will be ¡ and ¿
25769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25772 \begin_layout Plain Layout
25780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25783 \begin_layout Plain Layout
25791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25794 \begin_layout Plain Layout
25795 \begin_inset Formula $\textrm{ø}$
25805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25808 \begin_layout Plain Layout
25816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25819 \begin_layout Plain Layout
25820 \begin_inset Formula $\textrm{Ø}$
25830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25833 \begin_layout Plain Layout
25841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25844 \begin_layout Plain Layout
25845 \begin_inset Formula $\textrm{ł}$
25855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25858 \begin_layout Plain Layout
25866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25869 \begin_layout Plain Layout
25870 \begin_inset Formula $\textrm{Ł}$
25880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25883 \begin_layout Plain Layout
25885 \begin_inset space \hspace{}
25893 \begin_layout Plain Layout
25907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25910 \begin_layout Plain Layout
25911 \begin_inset Formula $\textrm{!`}$
25921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25924 \begin_layout Plain Layout
25926 \begin_inset space \hspace{}
25934 \begin_layout Plain Layout
25948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25951 \begin_layout Plain Layout
25952 \begin_inset Formula $\textrm{?`}$
25962 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25965 \begin_layout Plain Layout
25973 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25976 \begin_layout Plain Layout
25977 \begin_inset Formula $\textrm{ȷ}$
25991 \begin_inset space \hfill{}
25997 \begin_layout Standard
25999 \begin_inset Formula $\textrm{\textrm{Å}}$
26003 \begin_inset Formula $\textrm{\textrm{Ø}}$
26006 can also be inserted via the math toolbar button
26007 \begin_inset Graphics
26008 filename ../images/math/digamma.png
26016 \begin_layout Standard
26017 An exception are the commands
26020 \begin_inset space \hspace{}
26029 \begin_inset space \hspace{}
26035 , because they can be inserted in LyX directly to text.
26038 \begin_layout Subsection
26040 \begin_inset CommandInset label
26042 name "sub:Accents-in-Text"
26050 \begin_layout Plain Layout
26059 \begin_layout Standard
26060 With the following commands all letters can be accented.
26061 The commands must be inserted in TeX-mode.
26064 \begin_layout Standard
26065 \begin_inset space \hfill{}
26069 \begin_inset Tabular
26070 <lyxtabular version="3" rows="8" columns="2">
26072 <column alignment="block" valignment="top" width="0">
26073 <column alignment="block" valignment="top" width="0">
26075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26078 \begin_layout Plain Layout
26084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26087 \begin_layout Plain Layout
26095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26098 \begin_layout Plain Layout
26102 \begin_inset Quotes grd
26110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26113 \begin_layout Plain Layout
26117 \begin_layout Plain Layout
26133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26136 \begin_layout Plain Layout
26144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26147 \begin_layout Plain Layout
26151 \begin_layout Plain Layout
26167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26170 \begin_layout Plain Layout
26177 \begin_layout Plain Layout
26191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26194 \begin_layout Plain Layout
26198 \begin_layout Plain Layout
26214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26217 \begin_layout Plain Layout
26225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26228 \begin_layout Plain Layout
26232 \begin_layout Plain Layout
26248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26251 \begin_layout Plain Layout
26258 \begin_layout Plain Layout
26272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26275 \begin_layout Plain Layout
26279 \begin_layout Plain Layout
26295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26298 \begin_layout Plain Layout
26305 \begin_layout Plain Layout
26319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26322 \begin_layout Plain Layout
26326 \begin_layout Plain Layout
26342 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26345 \begin_layout Plain Layout
26352 \begin_layout Plain Layout
26366 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26369 \begin_layout Plain Layout
26373 \begin_layout Plain Layout
26393 \begin_inset space \hfill{}
26397 \begin_inset Tabular
26398 <lyxtabular version="3" rows="8" columns="2">
26400 <column alignment="block" valignment="top" width="0">
26401 <column alignment="center" valignment="top" width="0">
26403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26406 \begin_layout Plain Layout
26412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26415 \begin_layout Plain Layout
26423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26426 \begin_layout Plain Layout
26433 \begin_layout Plain Layout
26447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26450 \begin_layout Plain Layout
26454 \begin_layout Plain Layout
26470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26473 \begin_layout Plain Layout
26481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26484 \begin_layout Plain Layout
26488 \begin_layout Plain Layout
26504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26507 \begin_layout Plain Layout
26514 \begin_layout Plain Layout
26525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26528 \begin_layout Plain Layout
26532 \begin_layout Plain Layout
26548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26551 \begin_layout Plain Layout
26559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26562 \begin_layout Plain Layout
26566 \begin_layout Plain Layout
26582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26585 \begin_layout Plain Layout
26592 \begin_layout Plain Layout
26606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26609 \begin_layout Plain Layout
26613 \begin_layout Plain Layout
26629 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26632 \begin_layout Plain Layout
26639 \begin_layout Plain Layout
26653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26656 \begin_layout Plain Layout
26660 \begin_layout Plain Layout
26676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26679 \begin_layout Plain Layout
26686 \begin_layout Plain Layout
26700 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26703 \begin_layout Plain Layout
26707 \begin_layout Plain Layout
26727 \begin_inset space \hfill{}
26733 \begin_layout Standard
26734 \begin_inset VSpace medskip
26743 also two different characters can be accented.
26752 \begin_layout Plain Layout
26767 \begin_layout Plain Layout
26779 \begin_layout Standard
26792 can in combination with vowels directly be inserted with the keyboard without
26794 The same applies for the tilde
26798 \begin_layout Plain Layout
26799 This only applies for keyboards where the tilde is defined as accent.
26808 in combination with
26823 \begin_layout Standard
26866 , and accents inserted directly with the keyboard are also available in
26868 For the other accents there are special math commands to be used in formulas,
26870 \begin_inset CommandInset ref
26872 reference "sub:Accents-for-one"
26879 \begin_layout Standard
26880 \begin_inset VSpace bigskip
26883 Furthermore, with the command
26893 \begin_layout Plain Layout
26901 all numbers and letters can be set into a circle, quasi accented with a
26902 circle, similar to the the copyright symbol.
26905 \begin_layout Standard
26907 \begin_inset Tabular
26908 <lyxtabular version="3" rows="3" columns="2">
26910 <column alignment="center" valignment="top" width="0">
26911 <column alignment="center" valignment="top" width="0">
26913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26916 \begin_layout Plain Layout
26922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26925 \begin_layout Plain Layout
26927 \begin_inset Note Note
26930 \begin_layout Plain Layout
26937 is only used as spacer.
26949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26952 \begin_layout Plain Layout
26960 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26963 \begin_layout Plain Layout
26967 \begin_layout Plain Layout
26983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26986 \begin_layout Plain Layout
26997 raisebox{-1.5pt}{W}}
27002 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27005 \begin_layout Plain Layout
27006 \begin_inset Formula $\raisebox{4.5mm}{}$
27013 \begin_layout Plain Layout
27031 \begin_inset Formula $\raisebox{-2mm}{}$
27047 \begin_layout Standard
27048 One has to take care that the character fits in the circle.
27059 \begin_layout Plain Layout
27061 \begin_inset CommandInset ref
27063 reference "sub:Font-Sizes"
27072 specifies thereby the size of the circle.
27083 \begin_layout Plain Layout
27085 \begin_inset CommandInset ref
27087 reference "sub:Boxes-without-Frame"
27096 the character can be centered.
27099 \begin_layout Subsection
27104 \begin_layout Plain Layout
27113 \begin_layout Standard
27114 Minuscule numbers are created with the command
27124 \begin_layout Plain Layout
27133 The command can be used in formulas and in TeX-mode.
27134 The command scheme is:
27137 \begin_layout Standard
27142 oldstylenums{number}
27145 \begin_layout Standard
27150 oldstylenums{0123456789
27153 \begin_inset Formula $\oldstylenums{0123456789}$
27159 \begin_layout Subsection
27160 Miscellaneous special Characters
27161 \begin_inset CommandInset label
27163 name "sub:Miscellaneous-special-Characters"
27171 \begin_layout Plain Layout
27172 Special characters ! miscellaneous
27180 \begin_layout Standard
27181 The following characters can only be inserted to formulas by using commands:
27184 \begin_layout Standard
27186 \begin_inset Tabular
27187 <lyxtabular version="3" rows="4" columns="2">
27189 <column alignment="center" valignment="top" width="0">
27190 <column alignment="center" valignment="top" width="0">
27192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27195 \begin_layout Plain Layout
27201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27204 \begin_layout Plain Layout
27212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27215 \begin_layout Plain Layout
27222 \begin_layout Plain Layout
27236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27239 \begin_layout Plain Layout
27240 \begin_inset Formula $\mathcircumflex$
27250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27253 \begin_layout Plain Layout
27261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27264 \begin_layout Plain Layout
27265 \begin_inset Formula $\_$
27275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27278 \begin_layout Plain Layout
27283 \begin_layout Plain Layout
27298 \begin_layout Plain Layout
27311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27314 \begin_layout Plain Layout
27315 \begin_inset Formula $^{\circ}$
27331 \begin_layout Standard
27332 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27333 contains the following line
27337 \begin_layout Plain Layout
27338 More about this is described in
27339 \begin_inset CommandInset ref
27341 reference "sub:Text-Characters-in"
27353 \begin_layout Standard
27358 DeclareInputtext{176}{
27371 \begin_layout Standard
27372 \begin_inset Newpage newpage
27378 \begin_layout Section
27380 \begin_inset CommandInset label
27382 name "sec:Formula-Styles"
27390 \begin_layout Plain Layout
27399 \begin_layout Itemize
27400 There are two different alignment styles:
27404 \begin_layout Description
27405 Centered is the predefined standard
27408 \begin_layout Description
27409 Indented for this the option
27413 must be inserted in the menu
27415 Document\SpecialChar \menuseparator
27421 \begin_inset space ~
27427 \begin_layout Standard
27432 is used, the indentation can be adjusted with the length
27442 \begin_layout Plain Layout
27451 Should the distance be 15
27452 \begin_inset space \thinspace{}
27455 mm, the following command line is inserted in the LaTeX-preamble
27458 \begin_layout Standard
27468 \begin_layout Standard
27469 When no length is specified, the predefined value of 30
27470 \begin_inset space \thinspace{}
27477 \begin_layout Itemize
27478 And two different numbering styles:
27482 \begin_layout Description
27483 Right is the predefined standard
27486 \begin_layout Description
27487 Left for this the option
27491 must be inserted in the menu
27493 Document\SpecialChar \menuseparator
27499 \begin_inset space ~
27506 \begin_layout Standard
27515 can also be used together.
27516 In this case both options are inserted, separated by a comma.
27519 \begin_layout Standard
27520 The chosen styles are used for all displayed formulas of the document.
27521 When both, centered and indented formulas should be created in a document,
27527 The indented formulas are then set in a flalign environment, see
27528 \begin_inset CommandInset ref
27530 reference "sub:Flalign-Environment"
27537 \begin_layout Section
27539 \begin_inset CommandInset label
27541 name "sec:Multiline-Formulas"
27549 \begin_layout Plain Layout
27550 Formula ! multiline
27558 \begin_layout Subsection
27562 \begin_layout Standard
27563 In LyX multiline formulas are created by pressing
27568 arg "newline-insert newline"
27574 This creates either an
27576 eqnarray environment
27578 that is described in
27579 \begin_inset CommandInset ref
27581 reference "sub:Eqnarray-Environment"
27585 or, when the option
27587 Use AMS math package
27589 in the document settings is selected, an
27593 that is described in
27594 \begin_inset CommandInset ref
27596 reference "sub:Standard-align-Environment"
27603 \begin_layout Standard
27604 There are other multiline formula environments that can be created via the
27607 Insert\SpecialChar \menuseparator
27611 These environments are described in the following sections.
27614 \begin_layout Standard
27615 In all multiline formula environments a new line is created by pressing
27619 arg "newline-insert newline"
27623 To add or delete lines, the math toolbar buttons
27624 \begin_inset Graphics
27625 filename ../images/tabular-feature_append-row.png
27631 \begin_inset Graphics
27632 filename ../images/tabular-feature_delete-row.png
27637 , respectively, or the menu
27639 Edit\SpecialChar \menuseparator
27645 \begin_layout Subsubsection
27647 \begin_inset CommandInset label
27649 name "sub:Line-Separation"
27657 \begin_layout Plain Layout
27658 Formula ! multiline ! Line separation
27666 \begin_layout Standard
27667 There is sometimes not enough space in multiline formulas between the lines:
27668 \begin_inset Formula \begin{eqnarray*}
27669 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}\\
27670 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*}
27677 \begin_layout Standard
27678 In LaTeX additional line space is specified as optional argument of the
27680 This is not yet possible in LyX
27684 \begin_layout Plain Layout
27686 \begin_inset CommandInset href
27688 name "LyX-bug #1505"
27689 target "http://www.lyx.org/trac/ticket/1505"
27698 , therefore the whole formula must be inserted in TeX-mode.
27699 To add in our example space, the command
27707 is inserted at the end of the first line.
27712 \begin_layout Plain Layout
27719 \begin_layout Plain Layout
27721 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27724 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27731 \begin_layout Plain Layout
27735 left(B^{2}+x_{0}^{2}
27743 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27748 \begin_layout Plain Layout
27760 \begin_layout Standard
27761 \begin_inset VSpace bigskip
27764 To set the the line separation for all lines in a formula, the length
27774 \begin_layout Plain Layout
27784 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27795 \begin_inset space \thinspace{}
27800 \begin_inset space \thinspace{}
27803 mm additional line separation as in the previous example, the command
27806 \begin_layout Standard
27816 \begin_layout Standard
27817 is inserted in TeX-mode before the formula.
27818 This requires that the LaTeX-package
27826 \begin_layout Plain Layout
27831 is part of every LaTeX standard installation.
27840 \begin_layout Plain Layout
27846 was loaded in LaTeX-preamble with the line
27849 \begin_layout Standard
27857 \begin_layout Standard
27862 \begin_layout Plain Layout
27874 \begin_inset Formula \begin{eqnarray*}
27875 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}\\
27876 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*}
27883 \begin_layout Standard
27887 \begin_layout Plain Layout
27898 To get back to the predefined distance,
27904 is set to the value 3
27905 \begin_inset space \thinspace{}
27911 \begin_layout Subsubsection
27913 \begin_inset CommandInset label
27915 name "sub:Column-Separation"
27923 \begin_layout Plain Layout
27924 Formula ! multiline ! Column separation
27932 \begin_layout Standard
27933 Multiline formulas form a matrix.
27934 A formula in the eqnarray environment is for example a matrix with three
27936 By changing the column separation in this environment, the space beside
27937 the relation sign can be changed.
27940 \begin_layout Standard
27941 The column separation is specified with the length
27951 \begin_layout Plain Layout
27960 \begin_inset Newline newline
27963 column separation = 2
27964 \begin_inset space \thinspace{}
27974 \begin_inset Newline newline
27980 \begin_layout Standard
27990 \begin_layout Standard
27991 inserted in TeX-mode, sets for all following formulas a column separation
27993 \begin_inset space \thinspace{}
27997 To get back to the predefined distance,
28004 \begin_inset space \thinspace{}
28010 \begin_layout Standard
28012 \begin_inset space \thinspace{}
28015 cm column separation:
28019 \begin_layout Plain Layout
28031 \begin_inset Formula \begin{eqnarray*}
28033 C & \ne & A\end{eqnarray*}
28037 A formula with the predefined column separation for matrices of 10
28038 \begin_inset space \thinspace{}
28045 \begin_layout Plain Layout
28057 \begin_inset Formula \begin{eqnarray*}
28059 C & \ne & A\end{eqnarray*}
28066 \begin_layout Subsubsection
28071 \begin_layout Plain Layout
28080 \begin_layout Standard
28081 Long formulas can be typeset using these methods:
28084 \begin_layout Itemize
28085 When one side of the equation is much shorther than the line width, this
28086 one is chosen for the left side and the right side is typeset over two
28088 \begin_inset Formula \begin{eqnarray}
28089 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 \\
28090 & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:shortlong}\end{eqnarray}
28094 The minus sign at the beginning of the second line does normally not appear
28095 as operator because it is the first character of the line.
28096 Thus it would not be surrounded by space and could not be distinguished
28097 from the fraction bar.
28099 \begin_inset space \thinspace{}
28102 pt space was inserted behind the minus sign with the command
28112 \begin_layout Plain Layout
28120 \begin_inset CommandInset ref
28122 reference "sub:Variable-Space"
28135 \begin_layout Plain Layout
28146 \begin_layout Itemize
28147 When both sides of the equation are too long, the command
28157 \begin_layout Plain Layout
28166 It is inserted to the first column of the first line and effects that all
28167 further insertions overwrite the following columns:
28168 \begin_inset Formula \begin{eqnarray}
28169 \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 \\
28170 & & -\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 \\
28171 & & =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}
28175 After the insertion of
28181 , the cursor is in a purple box that is a bit shifted to the left from the
28183 In this the formula is inserted.
28184 \begin_inset Newline newline
28187 The content of the further lines is inserted to the second or another formula
28189 The greater the column number where it was inserted, the larger the indentation.
28190 \begin_inset VSpace medskip
28194 \begin_inset Newline newline
28198 \begin_inset Note Greyedout
28201 \begin_layout Plain Layout
28202 Note the following when using
28211 \begin_layout Itemize
28212 The formula doesn't use the full page width.
28214 \begin_inset space \thinspace{}
28218 \begin_inset space \space{}
28222 \begin_inset Formula $-B^{2}$
28225 is added to the first line in the above example, it would have been outside
28227 To better use the width, negative space can be inserted at the beginning
28231 \begin_layout Itemize
28232 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28237 \begin_layout Plain Layout
28238 \begin_inset CommandInset href
28240 name "LyX-bug #1429"
28241 target "http://www.lyx.org/trac/ticket/1429"
28250 One can only set the cursor at the beginning of the line and move it with
28259 \begin_layout Itemize
28260 Other methods to set long formulas are offered by the environments described
28262 \begin_inset CommandInset ref
28264 reference "sub:Multline-Environment"
28269 \begin_inset CommandInset ref
28271 reference "sub:Multiline-Formula-Parts"
28278 \begin_layout Subsubsection
28280 \begin_inset CommandInset label
28282 name "sub:Multiline-Brackets"
28290 \begin_layout Plain Layout
28291 Brackets ! for multiline expressions
28299 \begin_layout Standard
28300 For brackets spanning multiple lines the following problem occurs:
28301 \begin_inset Formula \begin{eqnarray*}
28302 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28303 & & \left.\cdots+B-D\right]\end{eqnarray*}
28310 \begin_layout Standard
28311 The closing bracket is smaller than the opening bracket because brackets
28312 with variable size may not span multiple lines.
28315 \begin_layout Standard
28316 To set the bracket size for the second line correctly, the first line is
28327 \begin_layout Plain Layout
28335 and the second line with
28343 \begin_layout Plain Layout
28357 \begin_inset CommandInset ref
28359 reference "sub:Automatic-Bracket-Size"
28374 \begin_layout Plain Layout
28400 \begin_layout Plain Layout
28419 \begin_layout Plain Layout
28438 \begin_layout Plain Layout
28450 \begin_inset Formula $\downarrow$
28459 \begin_layout Plain Layout
28467 is inserted, because the multiplication operator with its limits is the
28468 largest symbol in the first line and this should be the size for the bracket
28469 in the second line.
28472 \begin_layout Standard
28473 The result is this:
28474 \begin_inset Formula \begin{eqnarray*}
28475 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28476 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28483 \begin_layout Subsection
28487 \begin_layout Standard
28488 Align environments can be used for every kind of multiline formulas.
28489 They are specially useful to set several formulas side by side.
28492 \begin_layout Standard
28493 Align environments consist of columns.
28494 The odd columns are right aligned, the even ones left aligned.
28495 Every line in an Align environment can be numbered.
28498 \begin_layout Standard
28499 Align environments are created via the menu
28501 Insert\SpecialChar \menuseparator
28507 Edit\SpecialChar \menuseparator
28508 Math\SpecialChar \menuseparator
28509 Change Formula Type
28511 already existing formulas can be converted to Align environments.
28514 \begin_layout Standard
28515 To add or delete columns, the math toolbar buttons
28516 \begin_inset Graphics
28517 filename ../images/tabular-feature_append-column.png
28523 \begin_inset Graphics
28524 filename ../images/tabular-feature_delete-column.png
28529 , respectively, or the menu
28531 Edit\SpecialChar \menuseparator
28537 \begin_layout Subsubsection
28538 Standard align Environment
28539 \begin_inset CommandInset label
28541 name "sub:Standard-align-Environment"
28549 \begin_layout Plain Layout
28550 Formula ! multiline ! align environment
28558 \begin_layout Standard
28559 This Align environment is created by presssing
28562 arg "newline-insert newline"
28565 in a formula or by the menu
28567 Insert\SpecialChar \menuseparator
28568 Math\SpecialChar \menuseparator
28569 AMS align Environment
28574 \begin_layout Standard
28575 An example for two formulas set side by side, that are created with a four
28576 column align environment:
28577 \begin_inset Formula \begin{align*}
28578 A & =\sin(B) & C & =D\\
28579 C & \ne A & B & \ne D\end{align*}
28583 As it can be seen, the formulas in this environment are placed so as if
28592 \begin_layout Plain Layout
28600 \begin_inset CommandInset ref
28602 reference "sub:Variable-Space"
28613 before the first and after every even column.
28614 When the formula style
28620 \begin_layout Plain Layout
28622 \begin_inset CommandInset ref
28624 reference "sec:Formula-Styles"
28635 is used, the formula is set without the
28641 before the first column.
28644 \begin_layout Subsubsection
28645 Alignat Environment
28649 \begin_layout Plain Layout
28650 Formula ! multiline ! alignat environment
28658 \begin_layout Standard
28659 The alignat environment has no predefined column separation.
28660 It can be inserted manually with the spaces that are described
28661 \begin_inset CommandInset ref
28663 reference "sub:Space"
28670 \begin_layout Standard
28671 The above example in the alignat environment where 1
28672 \begin_inset space \thinspace{}
28675 cm space was inserted at the beginning of the second formula:
28676 \begin_inset Formula \begin{alignat*}{2}
28677 A & =\sin(B) & \hspace{1cm}C & =D\\
28678 C & \ne A & B & \ne D\end{alignat*}
28682 Because the column separation can be set separately for every column, this
28683 environment is especially suitable to set three and more formulas side
28687 \begin_layout Subsubsection
28688 Flalign Environment
28689 \begin_inset CommandInset label
28691 name "sub:Flalign-Environment"
28699 \begin_layout Plain Layout
28700 Formula ! multiline ! flalign environment
28708 \begin_layout Standard
28709 In this environment the first two columns are always set as much as possible
28710 to the left and the last two ones to the right.
28712 \begin_inset Formula \begin{flalign*}
28713 A & =1 & B & =2 & C & =3\\
28714 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28721 \begin_layout Standard
28722 By creating a flalign environment with an odd number of columns where an
28723 empty TeX-brace is inserted to the last column, several formulas in a document
28724 can be set to the left, although the formula style
28729 As example the indented formula
28730 \begin_inset CommandInset ref
28732 reference "eq:VolInt"
28737 \begin_inset Formula \begin{flalign}
28738 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28742 The first two columns contain the formula.
28743 To indent it as with the formula style
28748 \begin_inset space \thinspace{}
28751 pt space was inserted at the beginning of the first column.
28754 \begin_layout Subsection
28755 Eqnarray Environment
28756 \begin_inset CommandInset label
28758 name "sub:Eqnarray-Environment"
28766 \begin_layout Plain Layout
28767 Formula ! multiline ! eqnarray environment
28775 \begin_layout Standard
28776 When this environment has been created, three blue boxes appear.
28777 The content of the first box is right aligned, the content of the last
28779 The content of the middle box appears centered and a bit smaller, because
28780 it is designed to insert there only relation characters.
28781 \begin_inset Formula \begin{eqnarray*}
28782 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28784 A & = & A\end{eqnarray*}
28791 \begin_layout Subsection
28796 \begin_layout Plain Layout
28797 Formula ! multiline ! gather environment
28805 \begin_layout Standard
28806 This environment consists of only one centered column.
28807 Every line can be numbered.
28808 \begin_inset Formula \begin{gather}
28810 X=\textrm{-}1\end{gather}
28817 \begin_layout Subsection
28818 Multline Environment
28819 \begin_inset CommandInset label
28821 name "sub:Multline-Environment"
28829 \begin_layout Plain Layout
28830 Formula ! multiline ! multline environment
28838 \begin_layout Standard
28839 The multline environment consists, like the gather environment, of only
28841 But the first line is left aligned, the last one right aligned.
28842 All other lines are centered.
28843 Therefore this environment is suitable for long formulas.
28845 \begin_inset CommandInset ref
28847 reference "eq:lefteqn"
28851 in the multline environment:
28852 \begin_inset Formula \begin{multline}
28853 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}\\
28854 -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}\\
28855 =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}
28862 \begin_layout Standard
28863 In the output only the last (first) line of a multline environment appears
28864 numbered when the document numbering is right (left).
28868 \begin_layout Plain Layout
28869 numbering styles see
28870 \begin_inset CommandInset ref
28872 reference "sec:Formula-Styles"
28884 \begin_layout Standard
28893 \begin_layout Plain Layout
28911 \begin_layout Plain Layout
28921 a centered line can be right or left aligned, respectively.
28922 The commands are used as follows:
28925 \begin_layout Standard
28930 shoveright{line content}
28936 shoveleft{line content}
28939 \begin_layout Standard
28940 \begin_inset VSpace medskip
28951 \begin_layout Plain Layout
28961 specifies the distance of the first line from the left page margin.
28962 Predefined is the length 0
28963 \begin_inset space \thinspace{}
28969 \begin_layout Standard
28970 As example the above formula where the command
28973 \begin_layout Standard
28983 \begin_layout Standard
28984 was inserted in TeX-mode before:
28988 \begin_layout Plain Layout
29000 \begin_inset Formula \begin{multline}
29001 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}\\
29002 \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}}\\
29003 =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}
29011 \begin_layout Plain Layout
29022 The second line was left aligned using
29031 \begin_layout Subsection
29032 Multiline Formula Parts
29033 \begin_inset CommandInset label
29035 name "sub:Multiline-Formula-Parts"
29043 \begin_layout Plain Layout
29044 Formula ! multiline ! formula parts
29052 \begin_layout Standard
29053 To display only parts of a formula with multiple lines, one of the following
29054 environments are used:
29071 They can be inserted via the menu
29073 Insert\SpecialChar \menuseparator
29076 or by using the commands described in this section.
29079 \begin_layout Standard
29080 The first three have the same properties as the corresponding multiline
29081 formula environments, but it is possible to set further formula parts beside
29084 \begin_inset Formula \[
29085 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29086 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29087 \right\} \textrm{Uncertainty relations}\]
29094 \begin_layout Standard
29095 To get this formula, a displayed formula is created where the command
29103 \begin_layout Plain Layout
29114 A purple box appears around the blue formula box where now columns and
29115 lines can be added.
29116 Outside the multiline environment other formula parts can be set, like
29120 \begin_layout Standard
29121 The aligned environment is also suitable for long formulas whose lines are
29122 horizontally aligned.
29123 Using aligned in a displayed formula has the advantage that the formula
29124 number is vertically centered behind the lines.
29126 \begin_inset CommandInset ref
29128 reference "eq:shortlong"
29132 in the aligned environment:
29133 \begin_inset Formula \begin{equation}
29134 \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}|}\\
29135 & -\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}
29143 \begin_layout Standard
29144 To use the environments
29166 \begin_layout Plain Layout
29184 \begin_layout Plain Layout
29202 \begin_layout Plain Layout
29210 are inserted, respectively.
29211 The split environment has the same properties as the aligned environment
29212 but it can only have two columns.
29215 \begin_layout Subsection
29216 Text in multiline Formulas
29217 \begin_inset CommandInset label
29219 name "sub:Text-in-multiline"
29227 \begin_layout Plain Layout
29237 \begin_layout Plain Layout
29238 Formula ! multiline ! text
29246 \begin_layout Standard
29247 In the Align environments, and the multline and gather environment, text
29248 can be inserted that will appear in a separate line and doesn't affect
29249 the column alignment.
29250 To do this, the command
29258 \begin_layout Plain Layout
29268 is used in the following scheme:
29271 \begin_layout Standard
29279 \begin_layout Standard
29280 The text should not be longer than a line because it cannot be hyphenated.
29281 As LyX doesn't yet support
29287 directly, the text is written as mathematical text.
29294 must hereby be at the beginning of a line and appears in the output above
29296 An example where the text was inserted at the beginning of the second line:
29297 \begin_inset Formula \begin{align}
29298 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29299 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29306 \begin_layout Section
29311 \begin_layout Plain Layout
29321 \begin_layout Plain Layout
29322 Formula ! numbering|see
29326 \begin_layout Plain Layout
29337 \begin_layout Plain Layout
29352 \begin_layout Subsection
29356 \begin_layout Standard
29357 Numbered formulas can be created with the menu
29359 Insert\SpecialChar \menuseparator
29360 Math\SpecialChar \menuseparator
29362 \begin_inset space ~
29370 \begin_inset space ~
29376 Existing formulas can be numbered with the menu
29378 Edit\SpecialChar \menuseparator
29379 Math\SpecialChar \menuseparator
29381 \begin_inset space ~
29389 arg "math-number-toggle"
29393 The formula number is displayed in LyX behind the formula as number sign
29395 The number sign is replaced in the output by the formula number.
29398 \begin_layout Standard
29399 When numbering is turned on in multiline formulas, all lines will be numbered.
29400 But the numbering can be controlled with the menu
29402 Edit\SpecialChar \menuseparator
29403 Math\SpecialChar \menuseparator
29405 \begin_inset space ~
29409 \begin_inset space ~
29413 \begin_inset space ~
29421 arg "math-number-line-toggle"
29427 \begin_layout Standard
29428 Except for inline formulas, all formulas can be numbered with two different
29430 \begin_inset CommandInset ref
29432 reference "sec:Formula-Styles"
29439 \begin_layout Subsection
29444 \begin_layout Plain Layout
29445 Cross-references ! to formulas
29453 \begin_layout Standard
29454 All labeled formulas can be cross-referenced.
29455 A label is added by the menu
29457 Insert\SpecialChar \menuseparator
29460 or the toolbar button
29461 \begin_inset Graphics
29462 filename ../images/label-insert.png
29468 The cursor must hereby be inside a displayed formula.
29469 A dialog pops up displaying the prefix
29474 The label is inserted there behind the prefix.
29475 The predefined prefix means
29476 \begin_inset Quotes eld
29480 \begin_inset Quotes erd
29483 and makes it easier to find labels in large documents because it marks
29484 it as formula label to divide it from e.
29485 \begin_inset space \thinspace{}
29489 \begin_inset space \space{}
29493 To change a label, the menu
29495 Insert\SpecialChar \menuseparator
29501 \begin_layout Standard
29502 The name of the label is displayed in LyX within two parentheses behind
29504 A formula with a label is always numbered.
29507 \begin_layout Standard
29508 Cross-references are inserted via the menu
29510 Insert\SpecialChar \menuseparator
29513 or with the toolbar button
29514 \begin_inset Graphics
29515 filename ../images/dialog-show-new-inset_ref.png
29521 A formula cross-reference appears in the output as formula number.
29522 When in the cross-reference dialog window the format
29526 is chosen, the cross-reference appears in the output as formula number
29528 \begin_inset Newline newline
29531 By right-clicking on a cross-reference in LyX, one jumps to the formula
29532 that is referenced.
29535 \begin_layout Standard
29536 Here are as examples cross-references to formulas of the following subsections:
29537 \begin_inset Note Note
29540 \begin_layout Plain Layout
29541 Note the different cross-reference types.
29549 \begin_layout Standard
29551 \begin_inset CommandInset ref
29558 \begin_inset CommandInset ref
29566 \begin_inset CommandInset ref
29572 ) big Latin letters are used for the numbering in contrary to (
29573 \begin_inset CommandInset ref
29582 \begin_layout Standard
29583 \begin_inset VSpace medskip
29586 When the argument of
29594 \begin_layout Plain Layout
29602 \begin_inset CommandInset ref
29604 reference "sub:User-defined-Numbering"
29615 contains a box like in
29616 \begin_inset CommandInset ref
29618 reference "sub:Paragraph-Boxes"
29622 , the formula cannot be referenced.
29625 \begin_layout Subsection
29630 \begin_layout Plain Layout
29631 Formula numbering ! subnumbering
29639 \begin_layout Standard
29640 With the help of the commands
29644 begin{subequations}
29652 formulas can be subnumbered.
29653 Both commands are inserted in TeX-mode.
29656 \begin_layout Standard
29658 \begin_inset Formula \begin{equation}
29659 A=C-B\label{eq:a}\end{equation}
29667 \begin_layout Plain Layout
29671 addtocounter{equation}{-1}
29680 \begin_layout Plain Layout
29684 begin{subequations}
29690 \begin_inset VSpace -5mm
29694 \begin_inset Formula \begin{equation}
29695 B=C-A\label{eq:b}\end{equation}
29700 \begin_inset Formula \begin{equation}
29701 C=A+B\label{eq:c}\end{equation}
29708 \begin_layout Standard
29712 \begin_layout Plain Layout
29724 \begin_layout Standard
29725 To create the example, the following is done:
29728 \begin_layout Enumerate
29729 first formula is inserted
29732 \begin_layout Enumerate
29737 addtocounter{equation}{-1}
29739 begin{subequations}
29743 \begin_layout Plain Layout
29752 \begin_inset Newline newline
29757 is inserted after the first formula
29760 \begin_layout Enumerate
29761 second formula is inserted
29764 \begin_layout Enumerate
29765 third formula is inserted
29768 \begin_layout Enumerate
29775 is inserted after the third formula
29778 \begin_layout Standard
29779 Every formula between the commands
29791 is subnumbered as a, b,
29792 \begin_inset Newline linebreak
29795 c, \SpecialChar \ldots{}
29796 For multiline formulas every line will be subnumbered.
29797 All subnumbered formulas are treated as
29802 But as every numbered formula increases the counter
29806 by one, the command
29812 is needed to decrease it.
29813 Otherwise the formulas
29814 \begin_inset CommandInset ref
29821 \begin_inset CommandInset ref
29828 \begin_inset CommandInset ref
29834 would be numbered as
29835 \begin_inset CommandInset ref
29842 \begin_inset CommandInset ref
29849 \begin_inset CommandInset ref
29858 \begin_layout Standard
29859 By inserting the commands in TeX-mode, a space is created between the first
29862 \begin_inset space \thinspace{}
29865 mm vertical space is inserted after the command
29869 begin{subequations}
29872 When the formula style
29878 \begin_layout Plain Layout
29880 \begin_inset CommandInset ref
29882 reference "sec:Formula-Styles"
29894 \begin_inset space \thinspace{}
29897 mm space is inserted instead.
29900 \begin_layout Standard
29901 Here is an example for a multiline formula where the numbering was turned
29902 off for the second line:
29906 \begin_layout Plain Layout
29910 begin{subequations}
29916 \begin_inset Formula \begin{eqnarray}
29917 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29918 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29919 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29927 \begin_layout Plain Layout
29939 \begin_layout Subsection
29940 User-defined Numbering
29941 \begin_inset CommandInset label
29943 name "sub:User-defined-Numbering"
29951 \begin_layout Plain Layout
29952 Formula numbering ! user-defined
29960 \begin_layout Standard
29964 \begin_layout Plain Layout
29965 Formula numbering ! self-defined delimiters
29970 With the standard numbering parentheses are set around the formula number.
29971 To replace the parentheses for example by vertical bars, the following
29972 line is added to the LaTeX-preamble:
29975 \begin_layout Standard
29987 \begin_inset Note Note
29990 \begin_layout Plain Layout
29991 This macro is already declared in the LaTeX-preamble for testing.
29992 To activate it, remove the percent sign at the beginning.
30000 \begin_layout Standard
30001 To use other characters, the vertical bars besides the
30005 are replaced by one ore more characters.
30006 To get only the formula number the vertical bars are omitted.
30009 \begin_layout Standard
30010 \begin_inset VSpace bigskip
30013 When there should be an expression of your choice instead of the consecutive
30014 formula number in parentheses behind the formula, the command
30024 \begin_layout Plain Layout
30033 \begin_inset Formula \begin{equation}
30034 A+B=C\tag{something}\label{eq:tag}\end{equation}
30038 In this example the command
30046 \begin_layout Plain Layout
30057 was inserted to the formula.
30060 \begin_layout Standard
30069 \begin_layout Plain Layout
30080 is inserted instead, the star prevents the parentheses around the expression:
30081 \begin_inset Formula \[
30082 A+B=C\tag*{something}\]
30089 \begin_layout Standard
30090 \begin_inset VSpace bigskip
30093 To restart the formula numbering with new document parts or sections, the
30094 following command is used:
30097 \begin_layout Standard
30102 @addtoreset{equation}{part}
30108 \begin_layout Plain Layout
30113 \begin_layout Plain Layout
30124 \begin_layout Plain Layout
30137 \begin_layout Plain Layout
30148 \begin_layout Plain Layout
30161 \begin_inset Newline newline
30165 \begin_inset Newline newline
30172 @addtoreset{equation}{section}
30175 \begin_layout Standard
30176 To be able to use these commands in TeX-mode, the
30177 \begin_inset Quotes eld
30181 \begin_inset Quotes erd
30184 character has to be made
30185 \begin_inset Quotes eld
30189 \begin_inset Quotes erd
30192 for LaTeX using the command
30206 So the command sequence in TeX-mode is:
30209 \begin_layout Standard
30215 \begin_inset Newline newline
30220 @addtoreset{equation}{section}
30221 \begin_inset Newline newline
30229 \begin_layout Standard
30230 In the LaTeX-preamble
30242 can be omitted as they are automatically internally inserted by LyX.
30245 \begin_layout Standard
30260 \begin_layout Plain Layout
30265 is part of the LaTeX-package
30273 \begin_layout Plain Layout
30274 Packages ! carlisle
30279 that is part of every LaTeX standard installation.
30288 \begin_layout Plain Layout
30289 Packages ! remreset
30294 has to be loaded in the LaTeX-preamble with the line
30297 \begin_layout Standard
30302 usepackage{remreset}
30305 \begin_layout Standard
30316 \begin_layout Plain Layout
30321 \begin_layout Plain Layout
30332 \begin_layout Plain Layout
30345 \begin_layout Plain Layout
30356 \begin_layout Plain Layout
30368 can be used with the same scheme as
30377 \begin_layout Standard
30378 \begin_inset VSpace bigskip
30381 Sometimes formulas should be numbered in the following form:
30384 \begin_layout Standard
30387 (section number.formula number)
30390 \begin_layout Standard
30391 The formula number should start with every section with
30392 \begin_inset Quotes eld
30396 \begin_inset Quotes erd
30402 \begin_layout Standard
30403 For this case there is the command
30413 \begin_layout Plain Layout
30421 , which is used with the following scheme:
30424 \begin_layout Standard
30429 numberwithin{counter}{sectioning}
30432 \begin_layout Standard
30433 Counter denotes what kind of numbering is affected, sectioning denotes what
30434 number is before the dot.
30437 \begin_layout Standard
30438 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30441 \begin_layout Standard
30446 numberwithin{equation}{section}
30449 \begin_layout Standard
30450 This is the result:
30454 \begin_layout Plain Layout
30458 numberwithin{equation}{section}
30464 \begin_inset Formula \begin{equation}
30465 A+B=C\end{equation}
30472 \begin_layout Standard
30474 \begin_inset space \thinspace{}
30478 \begin_inset space \space{}
30481 tables so that the number of the part is the sectioning,
30482 \begin_inset Newline newline
30489 numberwithin{table}{part}
30494 \begin_layout Standard
30495 To go back to the standard numbering or to prevent this kind of numbering
30496 when it is defined by the document class, the following command is inserted
30497 as TeX-Code or to the LaTeX-preamble:
30500 \begin_layout Standard
30513 \begin_layout Plain Layout
30527 \begin_layout Plain Layout
30543 \begin_inset Newline newline
30551 \begin_inset Newline newline
30563 \begin_layout Standard
30570 uses internally the command
30576 , described above, that also needs to be reverted.
30580 \begin_layout Plain Layout
30587 \begin_layout Plain Layout
30591 @removefromreset{equation}{section}
30594 \begin_layout Plain Layout
30606 \begin_layout Subsection
30607 Numbering with Roman Numbers and Letters
30611 \begin_layout Plain Layout
30612 Formula numbering ! with letters
30621 \begin_layout Plain Layout
30622 Formula numbering ! with Roman numbers
30630 \begin_layout Standard
30631 Formulas can also be numbered with Roman numbers and Latin letters.
30632 To number for example with small Roman numbers, the command
30635 \begin_layout Standard
30647 \begin_layout Standard
30648 is inserted before the formula in TeX-mode.
30659 \begin_layout Plain Layout
30667 redefines the predefined command
30683 \begin_layout Plain Layout
30690 has the same scheme like the command
30696 that is described in
30697 \begin_inset CommandInset ref
30699 reference "sub:The-Command-newcommand"
30712 is the formula counter.
30719 is used as prefix for a counter, the value of the counter is output as
30721 When a formula is numbered, LaTeX sets internally the command
30727 behind the formula.
30736 \begin_layout Plain Layout
30746 outputs the counter as small Roman number.
30749 \begin_layout Standard
30750 All formulas behind the command
30760 are now numbered Roman.
30761 To switch to numbering with big Roman numbers, the command is inserted
30778 \begin_layout Plain Layout
30790 \begin_inset Quotes eld
30794 \begin_inset Quotes erd
30797 with small Latin letters there is the command
30807 \begin_layout Plain Layout
30815 , for big ones there is the command
30825 \begin_layout Plain Layout
30838 \begin_layout Standard
30839 \begin_inset Note Greyedout
30842 \begin_layout Plain Layout
30847 Only maximal 26 formulas can be numbered with Latin letters in one document.
30855 \begin_layout Standard
30856 \begin_inset Newpage pagebreak
30862 \begin_layout Standard
30866 \begin_layout Plain Layout
30882 \begin_layout Standard
30883 \begin_inset Formula \begin{equation}
30884 A=\textrm{small roman}\end{equation}
30892 \begin_layout Plain Layout
30906 \begin_inset Formula \begin{equation}
30907 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30915 \begin_layout Plain Layout
30929 \begin_inset Formula \begin{equation}
30930 C=\textrm{small Latin}\end{equation}
30938 \begin_layout Plain Layout
30952 \begin_inset Formula \begin{equation}
30953 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30960 \begin_layout Standard
30961 To switch back to the default numbering, insert the command:
30964 \begin_layout Standard
30977 \begin_layout Plain Layout
30988 \begin_layout Standard
30992 \begin_layout Plain Layout
31006 \begin_inset Formula \begin{equation}
31007 E=\textrm{Arabic}\end{equation}
31014 \begin_layout Standard
31015 \begin_inset VSpace medskip
31018 As you see, formulas are numbered serially independent from the numbering
31020 When then numbering should start with
31021 \begin_inset Quotes eld
31025 \begin_inset Quotes erd
31028 when the style is changed, new equation counters have to be defined.
31029 A description about this can be found in the file
31030 \begin_inset CommandInset href
31032 name "Formula-numbering.lyx"
31033 target "run:Formula-numbering.lyx"
31040 \begin_layout Section
31041 Chemical Symbols and Equations
31042 \begin_inset CommandInset label
31044 name "sub:Chemical-Symbols-and"
31052 \begin_layout Plain Layout
31053 Chemical characters ! Symbols
31062 \begin_layout Plain Layout
31072 \begin_layout Plain Layout
31081 \begin_layout Standard
31082 An example text from chemistry:
31085 \begin_layout Quote
31087 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31090 -ion reacts with two
31091 \begin_inset Formula $\mathrm{Na^{+}}$
31094 -ions to sodium sulfate
31095 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31099 The chemical equation for this is:
31100 \begin_inset Formula \begin{equation}
31101 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31108 \begin_layout Standard
31109 This chemical equation can directly be created as formula.
31110 To avoid that the symbols appear italic, everything is highlighted and
31111 changed by the shortcut
31117 to the upright font style.
31121 \begin_layout Plain Layout
31127 \begin_inset CommandInset ref
31129 reference "sub:Font-Styles"
31141 \begin_layout Standard
31142 A more convenient way to typeset chemical formulas is to use the command
31153 \begin_layout Plain Layout
31161 that is available when the LaTeX-package
31169 \begin_layout Plain Layout
31182 to a formula a new blue box appears where chemical formulas can be inserted
31183 in an intuitive way.
31186 \begin_layout Standard
31188 \begin_inset Tabular
31189 <lyxtabular version="3" rows="9" columns="2">
31191 <column alignment="center" valignment="top" width="0">
31192 <column alignment="center" valignment="top" width="0">
31194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31197 \begin_layout Plain Layout
31203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31206 \begin_layout Plain Layout
31208 \begin_inset Note Note
31211 \begin_layout Plain Layout
31218 is only used as spacer.
31230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31233 \begin_layout Plain Layout
31240 \begin_layout Plain Layout
31254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31257 \begin_layout Plain Layout
31258 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31271 \begin_layout Plain Layout
31278 \begin_layout Plain Layout
31292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31295 \begin_layout Plain Layout
31296 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31309 \begin_layout Plain Layout
31316 \begin_layout Plain Layout
31330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31333 \begin_layout Plain Layout
31334 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31347 \begin_layout Plain Layout
31354 \begin_layout Plain Layout
31368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31371 \begin_layout Plain Layout
31372 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31385 \begin_layout Plain Layout
31392 \begin_layout Plain Layout
31407 \begin_layout Plain Layout
31422 \begin_layout Plain Layout
31436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31439 \begin_layout Plain Layout
31440 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31453 \begin_layout Plain Layout
31460 \begin_layout Plain Layout
31470 \begin_inset Formula $\downarrow$
31474 \begin_inset Formula $\to$
31482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31485 \begin_layout Plain Layout
31486 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31499 \begin_layout Plain Layout
31506 \begin_layout Plain Layout
31519 \begin_layout Plain Layout
31532 \begin_layout Plain Layout
31545 \begin_layout Plain Layout
31558 \begin_layout Plain Layout
31572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31575 \begin_layout Plain Layout
31576 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31589 \begin_layout Plain Layout
31596 \begin_layout Plain Layout
31609 \begin_layout Plain Layout
31622 \begin_layout Plain Layout
31635 \begin_layout Plain Layout
31652 \begin_layout Plain Layout
31666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31669 \begin_layout Plain Layout
31670 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
31686 \begin_layout Standard
31687 \begin_inset Note Greyedout
31690 \begin_layout Plain Layout
31695 Inserting a formula to a
31701 box will lead to LaTeX errors.
31702 In this case TeX code has to be used like for
31716 \begin_layout Plain Layout
31737 \begin_layout Standard
31744 the command for equation
31745 \begin_inset space ~
31749 \begin_inset CommandInset ref
31751 reference "eq:chem-reaction"
31756 \begin_inset Newline newline
31767 \begin_layout Plain Layout
31780 \begin_layout Plain Layout
31793 \begin_layout Plain Layout
31806 \begin_layout Plain Layout
31819 \begin_layout Plain Layout
31832 \begin_layout Plain Layout
31844 \begin_layout Standard
31845 To create multiline chemical equations first a multiline formula is created
31847 \begin_inset CommandInset ref
31849 reference "sec:Multiline-Formulas"
31854 Afterwards the command
31860 is used in every small blue box of the formula.
31862 \begin_inset CommandInset ref
31864 reference "eq:TEOS-reaction-1"
31869 \begin_inset CommandInset ref
31871 reference "eq:TEOS-reaction-2"
31875 are an example of a multi-stage chemical reaction where every equation
31876 has its own number.
31877 \begin_inset Formula \begin{eqnarray}
31878 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31879 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}\end{eqnarray}
31886 \begin_layout Standard
31897 package provides the command
31907 \begin_layout Plain Layout
31915 that has to be used for special cases.
31916 For more information about
31922 and more examples have a look at the documentation of
31927 \begin_inset CommandInset citation
31936 \begin_layout Section
31940 \begin_layout Standard
31941 LyX supports two types of commutative diagrams:
31949 that are explained in the following.
31952 \begin_layout Subsection
31957 \begin_layout Plain Layout
31966 \begin_layout Standard
31967 Diagrams of this type visualize relations by vertical and horizontal lines
31969 \begin_inset Formula \[
31970 \begin{CD}A@>>>B@>>>C\\
31972 F@<<<E@<<<D\end{CD}\]
31979 \begin_layout Standard
31980 To get them, the command
31988 \begin_layout Plain Layout
31998 is inserted to a formula.
31999 A blue box appears with two dashed lines where further commands can be
32004 arg "newline-insert newline"
32007 a new line is created.
32008 Horizontal relations are inserted in odd, vertical in even formula lines.
32011 \begin_layout Standard
32012 To create the relations there are the following commands:
32015 \begin_layout Itemize
32020 creates a left arrow,
32031 \begin_layout Itemize
32036 creates an up arrow,
32044 a vertical equal sign
32047 \begin_layout Itemize
32053 is a placeholder for non-existent relations
32056 \begin_layout Standard
32057 All arrows can be labeled as follows:
32060 \begin_layout Itemize
32061 Is text inserted between the first and second < or >, resp., it is placed
32063 When it is inserted between the second and third one, it appears under
32067 \begin_layout Itemize
32068 When text for vertical arrows is inserted between the first and second A
32069 or V, resp., it is placed left beside the arrow.
32070 When it is inserted between the second and third one, it appears right
32072 If the text contains an A or V, these letters must be set into a TeX-brace.
32075 \begin_layout Standard
32076 As example a diagram with all possible relations:
32079 \begin_layout Standard
32080 \begin_inset Formula \[
32081 \begin{CD}A@>j>>B@>>k>C@=F\\
32083 D@<<j<E@>k>>F@=C\end{CD}\]
32090 \begin_layout Standard
32091 The command for this is:
32092 \begin_inset Newline newline
32103 \begin_layout Plain Layout
32112 A@>j>>B@>>k>C@=F Ctrl+Return
32113 \begin_inset Newline newline
32120 \begin_layout Plain Layout
32135 \begin_layout Plain Layout
32148 \begin_layout Plain Layout
32160 \begin_inset Formula $\to$
32166 \begin_inset Newline newline
32173 \begin_layout Plain Layout
32188 \begin_layout Plain Layout
32201 \begin_layout Plain Layout
32211 \begin_layout Subsection
32216 \begin_layout Plain Layout
32217 Diagrams ! xymatrix
32225 \begin_layout Standard
32226 To be able to use xymatrices, the LaTeX-package
32231 A xymatrix is created by inserting the command
32238 Then you are able to add new matrix columns and rows like for normal matrices,
32240 \begin_inset CommandInset ref
32242 reference "sec:Matrices"
32249 \begin_layout Standard
32250 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32252 All possibilities to create commutative diagrams and decorations are explained
32257 that you find in the menu
32259 Help\SpecialChar \menuseparator
32261 \begin_inset space ~
32264 Manuals\SpecialChar \menuseparator
32266 \begin_inset space ~
32274 \begin_layout Standard
32275 \begin_inset Newpage newpage
32281 \begin_layout Section
32282 User-defined Commands
32286 \begin_layout Plain Layout
32287 User-defined commands
32295 \begin_layout Standard
32296 \begin_inset Note Greyedout
32299 \begin_layout Plain Layout
32304 The names of user-defined commands and macros may only consist of Latin
32313 \begin_layout Subsection
32317 \begin_inset CommandInset label
32319 name "sub:The-Command-newcommand"
32327 \begin_layout Plain Layout
32328 User-defined commands !
32339 \begin_layout Plain Layout
32350 \begin_layout Standard
32351 Many LaTeX-commands are too long to be used frequently.
32352 But it is possible to define with the command
32358 new shorter commands.
32361 \begin_layout Standard
32362 The command scheme of
32371 \begin_layout Standard
32376 newcommand{new command name}[number of arguments][optional
32381 \begin_inset Newline newline
32388 \begin_layout Plain Layout
32403 \begin_layout Plain Layout
32410 {command definition}
32413 \begin_layout Standard
32414 \begin_inset Note Greyedout
32417 \begin_layout Plain Layout
32422 Assure that the name of the new command is not already used in your document
32423 or by LaTeX-packages that you use.
32424 When you for example define the command
32436 , you get an error message because
32442 is already defined as command for
32443 \begin_inset Quotes eld
32447 \begin_inset Formula $\le$
32451 \begin_inset Quotes erd
32462 \begin_layout Standard
32463 The number of arguments is an integer in the range 0
32464 \begin_inset space \thinspace{}
32468 \begin_inset space \thinspace{}
32471 9 and specifies how many arguments the new command should have.
32472 With the optional value a value for an optional argument can be predefined.
32473 When this is done, the
32481 rgument of the new command is automatically an optional one.
32484 \begin_layout Standard
32485 Here are some examples:
32488 \begin_layout Itemize
32489 To define the command
32501 , the LaTeX-preamble line is:
32502 \begin_inset VSpace medskip
32506 \begin_inset Newline newline
32520 \begin_layout Itemize
32521 To define the command
32533 , the argument (that should be underlined) must be taken into account.
32534 For this the preamble line is:
32535 \begin_inset VSpace medskip
32539 \begin_inset Newline newline
32553 \begin_inset VSpace medskip
32557 \begin_inset Newline newline
32564 acts as argument placeholder, the
32568 behind it denotes that it is the placeholder for the first argument.
32571 \begin_layout Itemize
32579 \begin_inset space \thinspace{}
32583 \begin_inset space \space{}
32593 \begin_inset VSpace medskip
32597 \begin_inset Newline newline
32608 framebox#1#2{$#3$}}
32611 \begin_inset VSpace medskip
32615 \begin_inset Newline newline
32618 The two Dollar signs creates the extra formula needed for
32625 \begin_inset CommandInset ref
32627 reference "sub:Boxes-with-Frame"
32634 \begin_layout Itemize
32635 To create a new command for
32641 where the color for the box needn't to be specified, the argument for the
32642 color is defined optional:
32643 \begin_inset VSpace medskip
32647 \begin_inset Newline newline
32658 fcolorbox{#2}{#1}{$#3$}}
32661 \begin_inset VSpace medskip
32665 \begin_inset Newline newline
32668 When the color is not specified when using
32674 , the predefined color
32681 \begin_layout Standard
32682 A test of the new defined commands:
32685 \begin_layout Standard
32687 \begin_inset Tabular
32688 <lyxtabular version="3" rows="6" columns="2">
32690 <column alignment="center" valignment="top" width="0">
32691 <column alignment="center" valignment="top" width="0">
32693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32696 \begin_layout Plain Layout
32702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32705 \begin_layout Plain Layout
32707 \begin_inset Note Note
32710 \begin_layout Plain Layout
32717 is only used as spacer.
32729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32732 \begin_layout Plain Layout
32739 \begin_layout Plain Layout
32753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32756 \begin_layout Plain Layout
32757 \begin_inset Formula $A\gr B$
32767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32770 \begin_layout Plain Layout
32778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32781 \begin_layout Plain Layout
32782 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32795 \begin_layout Plain Layout
32799 \begin_inset Formula $\to$
32805 \begin_inset Formula $\to$
32816 \begin_layout Plain Layout
32830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32833 \begin_layout Plain Layout
32834 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
32844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32847 \begin_layout Plain Layout
32851 \begin_inset Formula $\to$
32862 \begin_layout Plain Layout
32876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32879 \begin_layout Plain Layout
32880 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32893 \begin_layout Plain Layout
32899 \begin_inset Formula $\to$
32910 \begin_layout Plain Layout
32924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32927 \begin_layout Plain Layout
32928 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
32944 \begin_layout Subsection
32949 \begin_layout Plain Layout
32950 User-defined commands! Math macros
32959 \begin_layout Plain Layout
32968 \begin_layout Standard
32969 User-defined commands are especially convenient for complex expressions.
32970 When you are for example dealing in a document with quadratic equations,
32971 the same solution type occurs several times.
32972 The general form of a quadratic equation is
32973 \begin_inset Formula \[
32974 0=\lambda^{2}+p\lambda+q\]
32978 The general form of the solution is
32979 \begin_inset Formula \[
32980 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
32987 \begin_layout Standard
32988 To define a command for the solution formula where only the three parameters
32990 \begin_inset Formula $\lambda$
32994 \begin_inset Formula $p$
32998 \begin_inset Formula $q$
33001 need to be specified and the index of
33002 \begin_inset Formula $\lambda$
33005 can be given optionally, the LaTeX-preamble line is
33006 \begin_inset Newline newline
33022 \begin_inset Newline newline
33029 \begin_layout Plain Layout
33044 \begin_layout Plain Layout
33055 frac{#3^{2}}{4}-#4}}
33058 \begin_layout Standard
33059 To create with this the solution formula, the command
33060 \begin_inset Newline newline
33070 \begin_inset Formula $\to$
33076 \begin_inset Formula $\to$
33083 is inserted to a formula
33088 \begin_layout Standard
33089 The definition of the new command is unintuitive because one has to know
33090 the schemes of all used LaTeX commands, e.
33091 \begin_inset space \thinspace{}
33095 \begin_inset space \space{}
33098 that a fraction is inserted in LaTeX as
33102 frac{numerator}{denominator}
33105 Furthermore one can easily forget a brace in the definition and cannot
33106 see in LyX what the new command is doing.
33107 To avoid these problems LyX offers the possibility to use math macros instead
33117 \begin_layout Standard
33118 A math macro is created by using the menu
33120 Insert\SpecialChar \menuseparator
33121 Math\SpecialChar \menuseparator
33124 or the toolbar button
33125 \begin_inset Graphics
33126 filename ../images/math-macro_newmacroname_newcommand.png
33132 The math macro toolbar appears together with the following box where the
33134 \begin_inset Newline newline
33138 \begin_inset space \hspace*{\fill}
33142 \begin_inset Graphics
33143 filename clipart/macrobox.png
33148 \begin_inset space \hspace*{\fill}
33152 \begin_inset Newline newline
33156 \begin_inset FormulaMacro
33157 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33162 newmacroname is the default name of the macro that should be changed to
33163 something sensible.
33164 The wanted formula is inserted in the first blue box.
33165 An argument placeholder is inserted with the command
33172 \begin_inset space \thinspace{}
33176 \begin_inset space \space{}
33185 or by using the macro toolbar button
33186 \begin_inset Graphics
33187 filename ../images/math-macro-add-param.png
33193 Argument placeholders are displayed red.
33194 Maximum 9 arguments are possible.
33195 Optional arguments are created with the toolbar button
33196 \begin_inset Graphics
33197 filename ../images/math-macro-add-optional-param.png
33203 The first non-optional argument can be transformed to an optional one with
33205 \begin_inset Graphics
33206 filename ../images/math-macro-make-optional.png
33212 In the second blue box the appearance of the macro in LyX can be defined.
33213 Normally you want to see it as it is defined, so the box is kept empty.
33214 But when you have created a macro that needs lot of space on the screen,
33215 you can insert in the box for example
33216 \begin_inset Newline newline
33246 \begin_inset Newline newline
33251 For the macro only the arguments with the macro name in front of them will
33252 then be displayed in LyX, leading to a better overview.
33253 The formula appears in the output as defined in the first box.
33254 \begin_inset Newline newline
33257 The appearance of macros in formulas can furthermore be changed for single
33258 macros by setting the cursor in the macro and using the menu
33260 View\SpecialChar \menuseparator
33262 \begin_inset space ~
33266 \begin_inset space ~
33274 \begin_layout Standard
33275 To use a macro, the macro name is inserted as command to a formula, in our
33283 Our macro looks in LyX like this:
33284 \begin_inset Newline newline
33288 \begin_inset space \hspace*{\fill}
33292 \begin_inset Graphics
33293 filename clipart/macrouse.png
33298 \begin_inset space \hspace*{\fill}
33302 \begin_inset Newline newline
33305 Here is our macro example with the arguments
33306 \begin_inset Formula $x$
33310 \begin_inset Formula $\ln(x)$
33314 \begin_inset Formula $B$
33320 \begin_layout Standard
33321 \begin_inset Formula \[
33329 \begin_layout Standard
33330 LyX offers in the menu
33332 Tools\SpecialChar \menuseparator
33333 Preferences\SpecialChar \menuseparator
33334 Editing\SpecialChar \menuseparator
33337 different styles to edit macros.
33338 To find the style that suits you the most, choose a style and set the cursor
33339 in a macro formula to see the difference.
33342 \begin_layout Standard
33343 A math macro is transformed internally to a
33349 command when exporting the document.
33356 command is not placed in the LaTeX-preamble, therefore macros can only
33357 be used in formulas that are in the document below the macro definition
33361 \begin_layout Standard
33362 Math macros can also be directly be created from a
33369 When writing for example the command
33372 \begin_inset Newline newline
33381 xleftarrow[#2]{#1}}
33382 \begin_inset Newline newline
33387 in LyX as normal text, highlighting it completely and using then the shortcut
33392 , the command will be transformed to a math macro.
33393 Using this method you need to be careful that the
33399 command is typed correctly, otherwise you get a faulty macro leading to
33403 \begin_layout Standard
33404 Math macros currently yet have the problem that further formulas in macro
33405 definitions are handled wrongly.
33406 Therefore the example
33413 \begin_inset CommandInset ref
33415 reference "sub:The-Command-newcommand"
33419 cannot be created as macro.
33422 \begin_layout Standard
33423 When the cursor is in a macro definition box, you will see the macro toolbar
33427 \begin_layout Standard
33428 \begin_inset VSpace defskip
33434 \begin_layout Standard
33435 \begin_inset Graphics
33436 filename clipart/MacroToolbar.png
33444 \begin_layout Plain Layout
33453 \begin_layout Standard
33454 \begin_inset VSpace defskip
33460 \begin_layout Standard
33461 The macro toolbar contains from left to right the following buttons:
33464 \begin_layout Standard
33465 \begin_inset VSpace defskip
33471 \begin_layout Standard
33472 \begin_inset Tabular
33473 <lyxtabular version="3" rows="9" columns="2">
33474 <features islongtable="true">
33475 <column alignment="left" valignment="top" width="0">
33476 <column alignment="left" valignment="top" width="85col%">
33477 <row interlinespace="2.5mm">
33478 <cell alignment="center" valignment="top" usebox="none">
33481 \begin_layout Plain Layout
33482 \begin_inset Graphics
33483 filename ../images/math-macro-remove-param.png
33484 BoundingBox 0bp 5bp 20bp 25bp
33485 rotateOrigin center
33494 <cell alignment="center" valignment="top" usebox="none">
33497 \begin_layout Plain Layout
33500 Edit\SpecialChar \menuseparator
33501 Math\SpecialChar \menuseparator
33503 \begin_inset space ~
33506 Definition\SpecialChar \menuseparator
33507 Remove Last Argument
33513 <row interlinespace="2.5mm">
33514 <cell alignment="center" valignment="top" usebox="none">
33517 \begin_layout Plain Layout
33518 \begin_inset Graphics
33519 filename ../images/math-macro-add-param.png
33520 BoundingBox 0bp 5bp 20bp 25bp
33521 rotateOrigin center
33530 <cell alignment="center" valignment="top" usebox="none">
33533 \begin_layout Plain Layout
33536 Edit\SpecialChar \menuseparator
33537 Math\SpecialChar \menuseparator
33539 \begin_inset space ~
33542 Definition\SpecialChar \menuseparator
33549 <row interlinespace="2.5mm">
33550 <cell alignment="center" valignment="top" usebox="none">
33553 \begin_layout Plain Layout
33554 \begin_inset Graphics
33555 filename ../images/math-macro-make-optional.png
33556 BoundingBox 0bp 5bp 20bp 25bp
33557 rotateOrigin center
33566 <cell alignment="center" valignment="top" usebox="none">
33569 \begin_layout Plain Layout
33572 Edit\SpecialChar \menuseparator
33573 Math\SpecialChar \menuseparator
33575 \begin_inset space ~
33578 Definition\SpecialChar \menuseparator
33579 Make First Non-Optional into
33580 \begin_inset Newline newline
33587 \begin_layout Plain Layout
33596 Edit\SpecialChar \menuseparator
33597 Math\SpecialChar \menuseparator
33599 \begin_inset space ~
33602 Definition\SpecialChar \menuseparator
33607 \begin_layout Plain Layout
33620 <row interlinespace="2.5mm">
33621 <cell alignment="center" valignment="top" usebox="none">
33624 \begin_layout Plain Layout
33625 \begin_inset Graphics
33626 filename ../images/math-macro-make-nonoptional.png
33627 BoundingBox 0bp 5bp 20bp 25bp
33628 rotateOrigin center
33637 <cell alignment="center" valignment="top" usebox="none">
33640 \begin_layout Plain Layout
33643 Edit\SpecialChar \menuseparator
33644 Math\SpecialChar \menuseparator
33646 \begin_inset space ~
33649 Definition\SpecialChar \menuseparator
33650 Make Last Optional into
33651 \begin_inset Newline newline
33658 \begin_layout Plain Layout
33667 Edit\SpecialChar \menuseparator
33668 Math\SpecialChar \menuseparator
33670 \begin_inset space ~
33673 Definition\SpecialChar \menuseparator
33678 \begin_layout Plain Layout
33685 Non-Optional Argument
33691 <row interlinespace="2.5mm">
33692 <cell alignment="center" valignment="top" usebox="none">
33695 \begin_layout Plain Layout
33696 \begin_inset Graphics
33697 filename ../images/math-macro-remove-optional-param.png
33698 BoundingBox 0bp 5bp 20bp 25bp
33699 rotateOrigin center
33708 <cell alignment="center" valignment="top" usebox="none">
33711 \begin_layout Plain Layout
33714 Edit\SpecialChar \menuseparator
33715 Math\SpecialChar \menuseparator
33717 \begin_inset space ~
33720 Definition\SpecialChar \menuseparator
33721 Remove Optional Argument
33727 <row interlinespace="2.5mm">
33728 <cell alignment="center" valignment="top" usebox="none">
33731 \begin_layout Plain Layout
33732 \begin_inset Graphics
33733 filename ../images/math-macro-add-optional-param.png
33734 BoundingBox 0bp 5bp 20bp 25bp
33735 rotateOrigin center
33744 <cell alignment="center" valignment="top" usebox="none">
33747 \begin_layout Plain Layout
33750 Edit\SpecialChar \menuseparator
33751 Math\SpecialChar \menuseparator
33753 \begin_inset space ~
33756 Definition\SpecialChar \menuseparator
33757 Insert Optional Argument
33763 <row interlinespace="2.5mm">
33764 <cell alignment="center" valignment="top" usebox="none">
33767 \begin_layout Plain Layout
33768 \begin_inset Graphics
33769 filename ../images/math-macro-remove-greedy-param.png
33770 BoundingBox 0bp 5bp 20bp 25bp
33771 rotateOrigin center
33780 <cell alignment="center" valignment="top" usebox="none">
33783 \begin_layout Plain Layout
33786 Edit\SpecialChar \menuseparator
33787 Math\SpecialChar \menuseparator
33789 \begin_inset space ~
33792 Definition\SpecialChar \menuseparator
33793 Remove Last Argument
33794 \begin_inset Newline newline
33801 \begin_layout Plain Layout
33810 Edit\SpecialChar \menuseparator
33811 Math\SpecialChar \menuseparator
33813 \begin_inset space ~
33816 Definition\SpecialChar \menuseparator
33821 \begin_layout Plain Layout
33828 Spitting Out To The Right
33834 <row interlinespace="2.5mm">
33835 <cell alignment="center" valignment="top" usebox="none">
33838 \begin_layout Plain Layout
33839 \begin_inset Graphics
33840 filename ../images/math-macro-append-greedy-param.png
33841 BoundingBox 0bp 5bp 20bp 25bp
33842 rotateOrigin center
33851 <cell alignment="center" valignment="top" usebox="none">
33854 \begin_layout Plain Layout
33857 Edit\SpecialChar \menuseparator
33858 Math\SpecialChar \menuseparator
33860 \begin_inset space ~
33863 Definition\SpecialChar \menuseparator
33865 \begin_inset Newline newline
33872 \begin_layout Plain Layout
33881 Edit\SpecialChar \menuseparator
33882 Math\SpecialChar \menuseparator
33884 \begin_inset space ~
33887 Definition\SpecialChar \menuseparator
33892 \begin_layout Plain Layout
33899 Eating From The Right
33905 <row interlinespace="2.5mm">
33906 <cell alignment="center" valignment="top" usebox="none">
33909 \begin_layout Plain Layout
33910 \begin_inset Graphics
33911 filename ../images/math-macro-add-greedy-optional-param.png
33912 BoundingBox 0bp 5bp 20bp 25bp
33913 rotateOrigin center
33922 <cell alignment="center" valignment="top" usebox="none">
33925 \begin_layout Plain Layout
33928 Edit\SpecialChar \menuseparator
33929 Math\SpecialChar \menuseparator
33931 \begin_inset space ~
33934 Definition\SpecialChar \menuseparator
33935 Append Optional Argument
33936 \begin_inset Newline newline
33943 \begin_layout Plain Layout
33952 Edit\SpecialChar \menuseparator
33953 Math\SpecialChar \menuseparator
33955 \begin_inset space ~
33958 Definition\SpecialChar \menuseparator
33963 \begin_layout Plain Layout
33970 Eating From The Right
33983 \begin_layout Standard
33984 \begin_inset Newpage newpage
33990 \begin_layout Section
33995 \begin_layout Plain Layout
34008 \begin_layout Plain Layout
34009 Other useful math tips can be found in
34010 \begin_inset CommandInset citation
34025 \begin_layout Plain Layout
34033 \begin_inset Note Note
34036 \begin_layout Plain Layout
34039 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
34042 \begin_layout Plain Layout
34045 texorpdfstring is in section
34046 \begin_inset CommandInset ref
34048 reference "sub:Formulas-in-Section"
34061 \begin_layout Plain Layout
34071 \begin_layout Plain Layout
34076 \begin_layout Plain Layout
34083 Chemical characters
34087 \begin_layout Plain Layout
34102 \begin_layout Subsection
34107 \begin_layout Plain Layout
34116 \begin_layout Standard
34117 Negative numbers often look ugly in formulas because the minus sign before
34118 the number is set with the same length as the minus operator sign.
34119 When writing the negative number in normal text, the minus sign appears
34123 \begin_layout Standard
34124 Thus, the problem disappears when converting the minus sign to mathematical
34128 \begin_layout Standard
34129 An example to visualize the problem:
34132 \begin_layout Standard
34134 \begin_inset Tabular
34135 <lyxtabular version="3" rows="3" columns="2">
34137 <column alignment="right" valignment="top" width="0">
34138 <column alignment="left" valignment="top" width="0">
34140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34143 \begin_layout Plain Layout
34149 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34152 \begin_layout Plain Layout
34160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34163 \begin_layout Plain Layout
34169 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34172 \begin_layout Plain Layout
34173 \begin_inset Formula $x=-2$
34183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34186 \begin_layout Plain Layout
34192 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34195 \begin_layout Plain Layout
34196 \begin_inset Formula $x=\textrm{-}2$
34212 \begin_layout Subsection
34213 Comma as decimal Separator
34217 \begin_layout Plain Layout
34226 \begin_layout Standard
34227 In LaTeX a comma inside a formula is used, according to the English convention,
34228 as number group separator.
34229 So there will be space added behind all commas in formulas.
34232 \begin_layout Standard
34233 To avoid this, the comma is highlighted and changed to mathematical text
34243 \begin_layout Standard
34244 To use all formula commas in the document as decimal separator, the file
34253 \begin_layout Plain Layout
34258 is part of the LaTeX-package
34266 \begin_layout Plain Layout
34271 \begin_layout Plain Layout
34294 \begin_layout Plain Layout
34300 is loaded with the LaTeX-preamble line
34303 \begin_layout Standard
34311 \begin_layout Subsection
34313 \begin_inset CommandInset label
34315 name "sub:Physical-Vectors"
34323 \begin_layout Plain Layout
34332 \begin_layout Standard
34333 Predefined vectors are offered by the LaTeX-package
34341 \begin_layout Plain Layout
34346 should be part of every LaTeX standard installation.
34355 \begin_layout Plain Layout
34361 that is loaded with the LaTeX-preamble line
34364 \begin_layout Standard
34372 \begin_layout Standard
34376 \begin_layout Plain Layout
34386 \begin_inset Note Note
34389 \begin_layout Plain Layout
34390 The following table will only be displayed when the LaTeX-package
34399 The following commands are defined:
34402 \begin_layout Standard
34404 \begin_inset Tabular
34405 <lyxtabular version="3" rows="4" columns="2">
34407 <column alignment="center" valignment="top" width="0">
34408 <column alignment="center" valignment="top" width="0">
34410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34413 \begin_layout Plain Layout
34419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34422 \begin_layout Plain Layout
34430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34433 \begin_layout Plain Layout
34443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34446 \begin_layout Plain Layout
34447 \begin_inset Formula $\Bra{\psi}$
34457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34460 \begin_layout Plain Layout
34470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34473 \begin_layout Plain Layout
34474 \begin_inset Formula $\Ket{\psi}$
34484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34487 \begin_layout Plain Layout
34499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34502 \begin_layout Plain Layout
34503 \begin_inset Formula $\Braket{\psi|\phi}$
34519 \begin_layout Standard
34526 assures that all vertical bars are set in the size of the surrounding brackets:
34527 \begin_inset Formula \[
34528 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34536 \begin_layout Plain Layout
34546 \begin_inset Note Note
34549 \begin_layout Plain Layout
34550 The following will be displayed when the LaTeX-package
34562 \begin_layout Standard
34563 You need to install the LaTeX-package
34567 to see the rest of this subsection in the output.
34570 \begin_layout Standard
34574 \begin_layout Plain Layout
34586 \begin_layout Standard
34593 can also be achieved using the command
34599 , that is described in
34600 \begin_inset CommandInset ref
34602 reference "sub:Automatic-Bracket-Size"
34609 \begin_layout Subsection
34610 Self-defined Fractions
34611 \begin_inset CommandInset label
34613 name "sub:Self-defined-Fractions"
34621 \begin_layout Plain Layout
34622 Fractions ! self-defined
34630 \begin_layout Standard
34631 To define custom commands for fractions, the command
34641 \begin_layout Plain Layout
34649 is used in the following scheme:
34652 \begin_layout Standard
34665 bracket}{fraction bar thickness}{style}
34666 \begin_inset Newline newline
34673 \begin_layout Plain Layout
34688 \begin_layout Plain Layout
34695 {numerator}{denominator}
34698 \begin_layout Standard
34699 The style is a number in the range of 0
34700 \begin_inset space \thinspace{}
34704 \begin_inset space \thinspace{}
34710 \begin_layout Standard
34712 \begin_inset Tabular
34713 <lyxtabular version="3" rows="5" columns="2">
34715 <column alignment="center" valignment="top" width="0">
34716 <column alignment="center" valignment="top" width="0">
34718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34721 \begin_layout Plain Layout
34727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34730 \begin_layout Plain Layout
34738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34741 \begin_layout Plain Layout
34747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34750 \begin_layout Plain Layout
34751 display style formula
34758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34761 \begin_layout Plain Layout
34767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34770 \begin_layout Plain Layout
34778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34781 \begin_layout Plain Layout
34787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34790 \begin_layout Plain Layout
34798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34801 \begin_layout Plain Layout
34807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34810 \begin_layout Plain Layout
34824 \begin_layout Standard
34825 When no style is given, the size is adjusted to the surrounding environment
34826 like for the command
34835 \begin_layout Standard
34836 When no fraction bar thickness is given, the predefined value of 0.4
34837 \begin_inset space \thinspace{}
34843 \begin_layout Standard
34844 \begin_inset VSpace medskip
34847 For example, the commands
34860 \begin_inset CommandInset ref
34862 reference "sub:Fractions"
34866 are defined with the commands
34869 \begin_layout Standard
34878 genfrac{}{}{}{0}{#1}{#2}}
34881 \begin_layout Standard
34885 \begin_layout Standard
34894 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34897 \begin_layout Standard
34898 \begin_inset VSpace medskip
34901 To define a fraction where the fraction bar thickness can be given as optional
34902 argument, the following line is inserted to the LaTeX-preamble:
34905 \begin_layout Standard
34914 genfrac{}{}{#1}{}{#2}{#3}}
34917 \begin_layout Standard
34919 \begin_inset Formula \begin{align*}
34920 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34921 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34925 As one can see, the distance of the numerator and the denominator to the
34926 fraction bar is round about three times the bar thickness.
34929 \begin_layout Subsection
34934 \begin_layout Plain Layout
34943 \begin_layout Standard
34944 To cancel formulas or formula parts, the LaTeX-package
34952 \begin_layout Plain Layout
34957 is part of every LaTeX standard installation.
34966 \begin_layout Plain Layout
34972 has to be loaded with the LaTeX-preamble line
34975 \begin_layout Standard
34980 usepackage[samesize]{cancel}
34983 \begin_layout Standard
34984 There are four ways to cancel formulas:
34987 \begin_layout Standard
34989 \begin_inset Tabular
34990 <lyxtabular version="3" rows="5" columns="2">
34992 <column alignment="center" valignment="top" width="0">
34993 <column alignment="center" valignment="top" width="0">
34995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34998 \begin_layout Plain Layout
35004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35007 \begin_layout Plain Layout
35009 \begin_inset Note Note
35012 \begin_layout Plain Layout
35019 are used here as spacer.
35031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35034 \begin_layout Plain Layout
35043 \begin_layout Plain Layout
35057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35060 \begin_layout Plain Layout
35061 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35074 \begin_layout Plain Layout
35083 \begin_layout Plain Layout
35097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35100 \begin_layout Plain Layout
35101 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35114 \begin_layout Plain Layout
35123 \begin_layout Plain Layout
35137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35140 \begin_layout Plain Layout
35141 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35154 \begin_layout Plain Layout
35158 \begin_inset Formula $\to$
35169 \begin_layout Plain Layout
35183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35186 \begin_layout Plain Layout
35187 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35203 \begin_layout Standard
35210 is especially suitable to visualize the reduction of fractions within formulas:
35211 \begin_inset Formula \[
35212 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35219 \begin_layout Subsection
35220 Formulas in Section Headings
35221 \begin_inset CommandInset label
35223 name "sub:Formulas-in-Section"
35231 \begin_layout Plain Layout
35232 Formula ! in section headings
35240 \begin_layout Standard
35241 When formulas are used in section headings, the following has to be taken
35245 \begin_layout Standard
35246 \begin_inset Note Greyedout
35249 \begin_layout Plain Layout
35258 \begin_layout Plain Layout
35259 Packages ! hyperref
35264 support is enabled in the document settings dialog under
35267 \begin_inset space ~
35272 , PDF-bookmarks are created for every section heading in the table of contents.
35273 If a section heading contains formulas, they are incorrectly displayed
35274 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35283 \begin_layout Standard
35284 Both problems can be solved by inserting at the end of the section heading
35285 a short title with the menu
35287 Insert\SpecialChar \menuseparator
35289 \begin_inset space ~
35295 Short titles are used as alternative for multiline section headings to
35296 keep the table of contents clearly arranged.
35297 Only the short title appears in the table of contents and therefore also
35298 in the PDF-bookmark.
35301 \begin_layout Standard
35302 When formulas should be used in the table of contents but
35306 is used, one can use the following command in TeX-mode:
35309 \begin_layout Standard
35314 texorpdfstring{part}{alternative}
35318 \begin_layout Plain Layout
35329 \begin_layout Standard
35330 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35331 This can be characters, formulas, footnotes, but also cross-references.
35332 The alternative is used instead of the part for the bookmark.
35335 \begin_layout Standard
35336 Here are two example headings:
35337 \begin_inset VSpace -3mm
35344 \begin_layout Plain Layout
35356 \begin_layout Subsubsection
35357 Heading without formula in table of contents
35358 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35362 \begin_inset OptArg
35365 \begin_layout Plain Layout
35366 Heading without formula in table of contents
35374 \begin_layout Subsubsection
35375 Heading with formula in table of contents
35379 \begin_layout Plain Layout
35389 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35396 \begin_layout Plain Layout
35406 \begin_layout Standard
35410 \begin_layout Plain Layout
35419 In the first heading a short title was used, in the second one
35428 \begin_layout Standard
35429 To get the same formatting as for the other headings, the complete heading
35438 \begin_layout Plain Layout
35440 \begin_inset CommandInset ref
35442 reference "sub:Bold-Formulas"
35454 \begin_layout Subsection
35455 Formulas in multi-column Text
35459 \begin_layout Plain Layout
35460 Formula ! in multi-column text
35468 \begin_layout Standard
35469 Formulas in multi-column text are often too wide to fit into a column and
35470 thus need to be set over the whole page width.
35471 This is done by using the LaTeX-package
35479 \begin_layout Plain Layout
35484 is part of every LaTeX standard installation.
35493 \begin_layout Plain Layout
35494 Packages ! multicol
35499 , that is loaded with the LaTeX-preamble line
35502 \begin_layout Standard
35507 usepackage{multicol}
35510 \begin_layout Standard
35511 \begin_inset Note Greyedout
35514 \begin_layout Plain Layout
35515 Note herby that the setting
35518 \begin_inset space ~
35525 Document\SpecialChar \menuseparator
35531 \begin_inset space ~
35551 \begin_layout Standard
35552 Before the multi-column text the command
35555 \begin_layout Standard
35560 begin{multicols}{column number}
35563 \begin_layout Standard
35564 is written in TeX-mode.
35565 The column number is a number in the range of 2
35566 \begin_inset space \thinspace{}
35570 \begin_inset space \thinspace{}
35574 Before the formula the multi-column text is ended by inserting the command
35577 \begin_layout Standard
35585 \begin_layout Standard
35589 \begin_layout Standard
35590 Due to the command some space is automatically added before the formula.
35592 \begin_inset space \thinspace{}
35595 mm vertical space is inserted before the formula.
35596 When the formula style
35602 \begin_layout Plain Layout
35604 \begin_inset CommandInset ref
35606 reference "sec:Formula-Styles"
35618 \begin_inset space \thinspace{}
35621 mm space is inserted instead.
35624 \begin_layout Standard
35625 As example a multi-column text with a displayed formula:
35628 \begin_layout Standard
35634 \begin_layout Plain Layout
35638 begin{multicols}{2}
35643 Das Spektrum wird fouriertransformiert.
35644 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35645 , Lösungsmittel) zu trennen.
35646 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35647 nun das Aussehen des Ausgangssignals.
35648 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35649 über alle Phasen integrieren muss.
35651 \begin_inset Formula $S$
35654 unser normiertes Ausgangssignal und
35655 \begin_inset Formula $P$
35658 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35662 \begin_layout Plain Layout
35672 \begin_inset VSpace -6mm
35676 \begin_inset Formula \begin{equation}
35677 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35685 \begin_layout Plain Layout
35689 begin{multicols}{2}
35695 \begin_inset Formula $S_{0}$
35698 das Signal ohne Gradient ist und die Normierungsbedingung
35699 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35703 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35705 \begin_inset Formula $\nicefrac{\pi}{2}$
35709 \begin_inset space \thinspace{}
35712 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35713 das Signal zusätzlich abschwächt.
35714 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35716 \begin_inset Formula $T_{2}$
35722 \begin_layout Standard
35728 \begin_layout Plain Layout
35740 \begin_layout Subsection
35741 Formulas with Description of Variables
35745 \begin_layout Plain Layout
35746 Formula ! with description of variables
35754 \begin_layout Standard
35755 To describe variables within a formula, like in formula
35756 \begin_inset CommandInset ref
35758 reference "eq:within"
35767 \begin_inset Formula $n$
35771 \begin_inset space ~
35774 matrix is used with left aligned columns for the
35775 \begin_inset Formula $n$
35782 \begin_layout Plain Layout
35784 \begin_inset CommandInset ref
35786 reference "sec:Matrices"
35795 To set the description in a smaller size, before the matrix e.
35796 \begin_inset space \thinspace{}
35800 \begin_inset space \space{}
35813 \begin_layout Plain Layout
35815 \begin_inset CommandInset ref
35817 reference "sub:Font-Sizes"
35829 \begin_layout Standard
35830 When the formula style
35836 \begin_layout Plain Layout
35838 \begin_inset CommandInset ref
35840 reference "sec:Formula-Styles"
35861 \begin_layout Plain Layout
35868 only works in formulas with the style
35873 \begin_inset CommandInset ref
35875 reference "sub:Variable-Space"
35884 is inserted before and after the matrix to have the same separation of
35885 the matrix from the equation and the side margin.
35888 \begin_layout Standard
35889 When the formula style
35893 is used, the method described in
35894 \begin_inset CommandInset ref
35896 reference "sub:Flalign-Environment"
35900 is used to indent formulas.
35902 \begin_inset CommandInset ref
35904 reference "eq:within"
35908 consists of five columns whereas in the first two columns contain the equation,
35909 the third the matrix, and the last one an empty TeX-brace.
35910 \begin_inset Formula \begin{flalign}
35911 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35912 \rho & \textrm{density}\\
35913 V & \textrm{volume}\\
35914 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35921 \begin_layout Subsection
35922 Upright small Greek Letters
35923 \begin_inset CommandInset label
35925 name "sub:Upright-small-Greek"
35933 \begin_layout Plain Layout
35934 Greek letters ! upright
35942 \begin_layout Standard
35943 Most of the math fonts only provide italic small Greek letters.
35944 But for symbols of elementary particles like pions and neutrinos, upright
35945 Greek letters are needed.
35954 \begin_layout Plain Layout
35959 is part of the LaTeX-package
35967 \begin_layout Plain Layout
35972 \begin_layout Plain Layout
35995 \begin_layout Plain Layout
36001 that is loaded with the LaTeX-preamble line
36004 \begin_layout Standard
36009 usepackage{upgreek}
36012 \begin_layout Standard
36018 \begin_layout Plain Layout
36028 \begin_inset Note Note
36031 \begin_layout Plain Layout
36032 The following table will only be displayed when the LaTeX-package
36041 They are created when the command for a small Greek letters is started
36047 For example the command
36054 \begin_inset Formula $\uptau$
36060 \begin_layout Standard
36061 With these commands reactions of elementary particles can be typeset:
36062 \begin_inset Formula \[
36063 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36070 \begin_layout Standard
36071 The upright letters are more bold and wider than the italic ones.
36072 They should therefore not be used for units like
36073 \begin_inset Quotes eld
36077 \begin_inset Quotes erd
36083 \begin_layout Standard
36087 \begin_layout Plain Layout
36097 \begin_inset Note Note
36100 \begin_layout Plain Layout
36101 The following will be displayed when the LaTeX-package
36113 \begin_layout Standard
36114 You need to install the LaTeX-package
36118 to see the rest of this subsection in the output.
36121 \begin_layout Standard
36125 \begin_layout Plain Layout
36137 \begin_layout Subsection
36138 Text Characters in Formulas
36139 \begin_inset CommandInset label
36141 name "sub:Text-Characters-in"
36149 \begin_layout Plain Layout
36158 \begin_layout Standard
36159 In some cases you might want to insert text characters directly into formulas.
36160 When for example the centered dot · is often used in formulas like
36161 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36164 , one would have to insert the command
36174 \begin_layout Plain Layout
36176 \begin_inset CommandInset ref
36178 reference "sub:Binary-Operators"
36187 all the time, because this character is defined in all encodings as text
36189 But the encoding can be changed by this LaTeX-preamble line:
36192 \begin_layout Standard
36197 Declare Inputtext{183}{
36207 f\SpecialChar \textcompwordmark{}
36211 \begin_layout Standard
36212 The character encoding (menu
36214 Document\SpecialChar \menuseparator
36215 Settings\SpecialChar \menuseparator
36218 ) specifies what character appears when a keyboard key is pressed.
36219 When the key for the character '·' is pressed, internally the command
36226 But this command is not available in a formula so that you would get LaTeX-erro
36228 With the changed encoding the right command is chosen automatically, depending
36229 on if the character was inserted into a formula or not.
36232 \begin_layout Standard
36233 The encoding of several characters is saved in definition files.
36234 Fore example the encoding
36238 is defined in the file
36242 that is in the installation folder of LaTeX.
36243 Encodings should only be changed via the LaTeX-preamble and not in the
36245 Otherwise own documents could not be edited by other LyX users working
36246 on other computers.
36249 \begin_layout Standard
36250 \begin_inset VSpace medskip
36253 Besides the centered dot, in this document the degree sign ° is defined
36254 with the following LaTeX-preamble line so that it can directly be inserted
36258 \begin_layout Standard
36263 DeclareInputtext{176}{
36273 f\SpecialChar \textcompwordmark{}
36277 \begin_layout Standard
36278 \begin_inset Newpage newpage
36284 \begin_layout Section
36290 \begin_layout Plain Layout
36299 \begin_layout Standard
36300 This section is a summary of the most important typographic rules, listed
36305 \begin_layout Plain Layout
36306 This collection was partly taken from the German semi-official dictionary
36308 \begin_inset Quotes eld
36312 \begin_inset Quotes erd
36316 \begin_inset CommandInset citation
36322 that lists some of the ISO rules.
36330 \begin_layout Itemize
36339 \begin_layout Plain Layout
36340 done with font styles, see
36341 \begin_inset CommandInset ref
36343 reference "sub:Font-Styles"
36353 \begin_inset space \thinspace{}
36357 \begin_inset Newline newline
36360 Between the value and the unit is the smallest space, see
36361 \begin_inset CommandInset ref
36363 reference "sub:Predefined-Space"
36368 \begin_inset Newline newline
36371 This convention is automatically fulfilled when the command
36378 When it is entered to a formula, two boxes appear.
36379 In the first one the value is inserted, in the second one the unit, and
36381 \begin_inset Formula $\unit[30]{km/h}$
36385 \begin_inset space \thinspace{}
36395 is not a real LaTeX command but the command
36401 , therefore you cannot use it in TeX code.
36404 \begin_layout Itemize
36405 Percent and perthousand signs are set like physical units:
36406 \begin_inset Newline newline
36410 \begin_inset space \thinspace{}
36416 \begin_layout Itemize
36417 The degree sign follows directly on the value: 15°, but not when it is used
36419 \begin_inset space \thinspace{}
36425 \begin_layout Itemize
36426 In numbers with more than four digits the smallest space is inserted before
36427 every third digit to group them:
36437 \begin_inset space \thinspace{}
36441 \begin_inset space \thinspace{}
36447 \begin_layout Itemize
36448 For dimensions like 120×90×40
36449 \begin_inset space \thinspace{}
36452 cm the multiplication sign
36453 \begin_inset Quotes eld
36457 \begin_inset Quotes erd
36461 It is available either via the command
36469 Insert\SpecialChar \menuseparator
36470 Special Character\SpecialChar \menuseparator
36476 \begin_layout Itemize
36477 Functions with names consisting of several letters are set upright to avoid
36479 \begin_inset CommandInset ref
36481 reference "sub:Predefined-Functions"
36488 \begin_layout Itemize
36489 Indices consisting of several letters, are set upright:
36490 \begin_inset Formula $E_{\mathrm{kin}}$
36494 \begin_inset Newline newline
36497 Components of matrices are set italic:
36498 \begin_inset Formula $\hat{H}_{kl}$
36504 \begin_layout Itemize
36505 The differentiation/integration operator 'd', the Euler's number 'e', and
36506 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36510 \begin_layout Itemize
36511 The character that denotes a
36515 transformation is inserted either by the command
36523 \begin_layout Plain Layout
36540 \begin_layout Plain Layout
36550 Insert\SpecialChar \menuseparator
36551 Special Character\SpecialChar \menuseparator
36552 Symbols\SpecialChar \menuseparator
36554 \begin_inset space ~
36560 \begin_inset Formula $\mathscr{F}$
36564 \begin_inset Newline newline
36567 To be able to use the command
36573 , the LaTeX package
36581 \begin_layout Plain Layout
36582 Packages ! mathrsfs
36587 needs to be loaded with the LaTeX-preamble line
36591 usepackage{mathrsfs}
36596 \begin_layout Standard
36597 \begin_inset Newpage newpage
36603 \begin_layout Section
36608 \begin_layout Plain Layout
36617 \begin_layout Standard
36618 Some characters and symbols can be created with several commands.
36619 Here is a list of the synonym commands:
36622 \begin_layout Standard
36623 \begin_inset VSpace bigskip
36627 \begin_inset space \hfill{}
36631 \begin_inset Tabular
36632 <lyxtabular version="3" rows="12" columns="2">
36634 <column alignment="center" valignment="top" width="0pt">
36635 <column alignment="center" valignment="top" width="0pt">
36637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36640 \begin_layout Plain Layout
36646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36649 \begin_layout Plain Layout
36651 \begin_inset Note Note
36654 \begin_layout Plain Layout
36661 is only used as spacer.
36673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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