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,
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43 \settowidth{\abc}{\space}
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46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
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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 % check for package braket
132 % used for physical vectors
134 \IfFileExists{braket.sty}
136 \setboolean{braket}{true}}
137 {\setboolean{braket}{false}}
139 % check for package upgreek
141 \IfFileExists{upgreek.sty}
142 {\usepackage{upgreek}
143 \setboolean{upgreek}{true}}
144 {\setboolean{upgreek}{false}}
146 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
147 \use_default_options false
152 \font_typewriter default
153 \font_default_family default
163 \pdf_title "LyX's Math Manual"
164 \pdf_author "LyX Team, Uwe Stöhr"
165 \pdf_subject "LyX-documentation about math"
166 \pdf_keywords "LyX, Mathed"
168 \pdf_bookmarksnumbered true
169 \pdf_bookmarksopen true
170 \pdf_bookmarksopenlevel 1
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183 \paperorientation portrait
186 \paragraph_separation skip
188 \quotes_language english
191 \paperpagestyle plain
195 \tracking_changes false
196 \output_changes false
204 LyX's detailed Math manual
212 \begin_layout Plain Layout
214 If you have comments or error corrections, please send them to the LyX Documenta
218 \begin_inset CommandInset href
220 name "lyx-docs@lists.lyx.org"
221 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
232 \begin_inset Note Note
235 \begin_layout Plain Layout
242 \begin_inset Newline newline
246 \begin_inset Newline newline
254 \begin_layout Standard
255 \begin_inset CommandInset toc
256 LatexCommand tableofcontents
263 \begin_layout Standard
264 \begin_inset Note Note
267 \begin_layout Plain Layout
268 To export this document to PDF, PS, or DVI the LaTeX-packages
281 If they are not installed you can export the document anyway but the sections
282 where the packages are required won't appear in the output.
285 \begin_layout Plain Layout
286 The latest PDF-version of this document can be found here:
287 \begin_inset Newline newline
292 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
300 \begin_layout Standard
301 \begin_inset Newpage newpage
307 \begin_layout Section
311 \begin_layout Standard
312 This document explains LyX's math features and is furthermore a collection
313 of LaTeX-commands used for mathematical characters and constructs.
314 The explanations are designed for the usage of commands.
315 It is therefore required that you have read the section
326 \begin_layout Standard
327 Most of the characters and many constructs explained in this manual are
328 also accessible via the menu
332 \SpecialChar \menuseparator
348 But everybody who has to write lots of formulas will notice that it is
349 much faster to use commands instead of the math toolbar.
350 Therefore this manual is focused on commands but also mentions the correspondin
351 g toolbar buttons when available.
354 \begin_layout Standard
355 If not specially mentioned the commands are only available within formulas.
356 To be able to use all commands explained in this document, the option
360 must be used in the document settings (menu
362 Document\SpecialChar \menuseparator
363 Settings\SpecialChar \menuseparator
374 \begin_layout Plain Layout
377 Use AMS math package automatically
383 \begin_layout Plain Layout
392 -math when math constructs are found that are supported by LyX.
400 \begin_layout Standard
401 This document doesn't list all
405 \begin_layout Plain Layout
418 \begin_layout Plain Layout
423 \begin_layout Plain Layout
432 -math commands is in the file
435 \begin_inset CommandInset href
438 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
444 , which is part of every LaTeX standard installation.
449 for lucidity reasons.
452 \begin_layout Section
456 \begin_layout Standard
457 To create an inline formula
461 \begin_layout Plain Layout
467 that is embedded into a text line, use one of the shortcuts
473 or the toolbar button
474 \begin_inset Graphics
475 filename ../images/math-mode.png
481 \begin_inset Newline newline
484 To create a display style formula
488 \begin_layout Plain Layout
489 Formula ! display style
494 that will appear bigger and in an own paragraph, use one of these shortcuts:
504 \begin_layout Standard
505 To change a display style formula to an inline formula, set the cursor into
506 the formula and use one of the shortcuts
514 Edit\SpecialChar \menuseparator
515 Math\SpecialChar \menuseparator
519 The same way is used to change an inline formula to a display style formula.
522 \begin_layout Standard
523 To display parts of an inline formula in the size of a display style formula,
532 \begin_layout Plain Layout
543 Then a new blue box appears in which the desired formula part is inserted.
546 \begin_layout Standard
547 Only inline formulas are allowed inside tables.
550 \begin_layout Standard
555 can be turned on in the menu
557 View\SpecialChar \menuseparator
561 When you click there on
562 \begin_inset Quotes eld
566 \begin_inset Quotes erd
569 the toolbar will be shown permanently at the bottom; this state is visualized
574 menu with a checkmark.
575 When you click in this state again on
576 \begin_inset Quotes eld
580 \begin_inset Quotes erd
591 is only shown when the cursor is within a formula; this state is visualized
592 by the renaming of the menu entry from
593 \begin_inset Quotes eld
597 \begin_inset Quotes erd
601 \begin_inset Quotes eld
609 \begin_inset Quotes erd
615 \begin_layout Standard
620 \begin_layout Plain Layout
626 is invoked by pressing the toolbar button
627 \begin_inset Graphics
628 filename ../images/ert-insert.png
635 Insert\SpecialChar \menuseparator
640 \begin_layout Plain Layout
656 \begin_inset Note Note
659 \begin_layout Plain Layout
660 In LyX there are three
661 \begin_inset Quotes eld
665 \begin_inset Quotes erd
668 that appear in the output with sub- and superscript letters: TeX, LaTeX,
672 \begin_layout Plain Layout
673 To avoid that these names are recognized as proper names, a TeX-brace pair
682 \begin_layout Standard
683 To change the LaTeX-preamble
687 \begin_layout Plain Layout
695 Document\SpecialChar \menuseparator
696 Settings\SpecialChar \menuseparator
701 \begin_layout Plain Layout
717 \begin_layout Standard
718 To edit matrices, case differentiations, and multiline formulas subsequently,
721 Edit\SpecialChar \menuseparator
726 Edit\SpecialChar \menuseparator
728 \begin_inset space \thinspace{}
732 \begin_inset space \thinspace{}
742 When lines and columns are swapped via the menu, the column or line where
743 the cursor is in is exchanged with the column to the right or the line
745 Is the cursor in the last column or row, the exchange is done with the
746 column to the left or the line above.
749 \begin_layout Standard
750 To write text in formulas
754 \begin_layout Plain Layout
755 For multiline formulas the command
762 \begin_inset CommandInset ref
764 reference "sub:Text-in-multiline"
781 \begin_layout Plain Layout
791 \begin_layout Plain Layout
798 This mode is invoked with the the shortcut
804 or by the insertion of the command
812 \begin_layout Plain Layout
823 The text appears black in LyX and can therefore be distinguished from the
824 other formula parts that appear blue.
825 In the output mathematical text is set upright, in contrary to other formula
829 \begin_layout Subsection*
833 \begin_layout Standard
834 Most of the LaTeX-commands for math constructs have the following scheme:
837 \begin_layout Standard
853 \begin_layout Standard
854 A command starts always with a backslash
855 \begin_inset Quotes gld
865 \begin_inset Quotes grd
869 To omit optional arguments, also omit the associated brackets.
870 The braces around the required arguments are named in this document as
875 \begin_layout Plain Layout
882 If you add in a formula a left brace to a command name, LyX creates automatical
884 In all other cases TeX-braces are created in formulas with the command
892 TeX-braces appear red in LyX, in contrary to normal braces that appear
894 In TeX-mode no command is needed to get TeX-braces.
895 TeX-braces don't appear in the output.
898 \begin_layout Standard
899 When commands without arguments, like commands for symbols are entered in
900 TeX-mode, a space character must
904 be behind the command to end it.
905 This space doesn't appear in the output.
906 When the space should appear in the output, the space must be followed
907 by a protected space in normal text.
910 \begin_layout Standard
911 A protected space is inserted with
914 arg "space-insert protected"
920 \begin_layout Subsection*
921 \begin_inset Newpage newpage
927 \begin_layout Itemize
932 \begin_layout Plain Layout
933 This visible space character can be created with the command
943 \begin_layout Plain Layout
951 , inserted in TeX-mode.
960 \begin_layout Plain Layout
973 denotes a space character to be input.
976 \begin_layout Itemize
978 \begin_inset Formula $\to$
981 denotes the usage of the corresponding arrow key on the keyboard.
984 \begin_layout Subsection*
988 \begin_layout Standard
990 \begin_inset Float table
996 \begin_layout Plain Layout
1000 \begin_layout Plain Layout
1001 \begin_inset CommandInset label
1003 name "tab:Available-units"
1015 \begin_layout Plain Layout
1017 \begin_inset Tabular
1018 <lyxtabular version="3" rows="13" columns="2">
1020 <column alignment="center" valignment="top" width="0">
1021 <column alignment="center" valignment="top" width="0">
1023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1026 \begin_layout Plain Layout
1032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1035 \begin_layout Plain Layout
1043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1046 \begin_layout Plain Layout
1052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1055 \begin_layout Plain Layout
1063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1066 \begin_layout Plain Layout
1072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1075 \begin_layout Plain Layout
1083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1086 \begin_layout Plain Layout
1092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1095 \begin_layout Plain Layout
1097 \begin_inset space \thinspace{}
1101 \begin_inset space \thinspace{}
1111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1114 \begin_layout Plain Layout
1120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1123 \begin_layout Plain Layout
1125 \begin_inset space \thinspace{}
1129 \begin_inset space \thinspace{}
1139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1142 \begin_layout Plain Layout
1148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1151 \begin_layout Plain Layout
1153 \begin_inset space \thinspace{}
1157 \begin_inset space \thinspace{}
1167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1170 \begin_layout Plain Layout
1176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1179 \begin_layout Plain Layout
1181 \begin_inset space \thinspace{}
1185 \begin_inset space \thinspace{}
1195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1198 \begin_layout Plain Layout
1204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1207 \begin_layout Plain Layout
1209 \begin_inset space \thinspace{}
1213 \begin_inset space \thinspace{}
1223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1226 \begin_layout Plain Layout
1232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1235 \begin_layout Plain Layout
1237 \begin_inset space \thinspace{}
1241 \begin_inset Formula $\approx$
1245 \begin_inset space \thinspace{}
1255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1258 \begin_layout Plain Layout
1264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1267 \begin_layout Plain Layout
1269 \begin_inset space \thinspace{}
1273 \begin_inset space \thinspace{}
1283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1286 \begin_layout Plain Layout
1292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1295 \begin_layout Plain Layout
1299 \begin_inset Quotes eld
1305 \begin_inset Quotes erd
1315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1318 \begin_layout Plain Layout
1324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1327 \begin_layout Plain Layout
1329 \begin_inset Quotes eld
1337 \begin_inset Quotes erd
1347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1350 \begin_layout Plain Layout
1356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1359 \begin_layout Plain Layout
1361 \begin_inset space \thinspace{}
1365 \begin_inset Formula $\nicefrac{1}{18}$
1369 \begin_inset space \thinspace{}
1390 \begin_layout Standard
1391 \begin_inset Newpage newpage
1397 \begin_layout Section
1401 \begin_layout Subsection
1406 \begin_layout Plain Layout
1416 \begin_layout Plain Layout
1426 \begin_layout Plain Layout
1431 \begin_layout Plain Layout
1442 \begin_layout Plain Layout
1458 \begin_layout Plain Layout
1463 \begin_layout Plain Layout
1474 \begin_layout Plain Layout
1489 \begin_layout Standard
1490 Indices are created with an underscore
1491 \begin_inset Quotes eld
1495 \begin_inset Quotes erd
1498 or via the math toolbar button
1499 \begin_inset Graphics
1500 filename ../images/math-subscript.png
1505 , exponents with a caret
1506 \begin_inset Quotes eld
1510 \begin_inset Quotes erd
1513 or via the math toolbar button
1514 \begin_inset Graphics
1515 filename ../images/math-superscript.png
1523 \begin_layout Standard
1525 \begin_inset Tabular
1526 <lyxtabular version="3" rows="4" columns="2">
1528 <column alignment="center" valignment="top" width="0pt">
1529 <column alignment="center" valignment="top" width="0pt">
1531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1534 \begin_layout Plain Layout
1540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1543 \begin_layout Plain Layout
1545 \begin_inset Note Note
1548 \begin_layout Plain Layout
1555 is only used as spacer.
1567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1570 \begin_layout Plain Layout
1576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1579 \begin_layout Plain Layout
1580 \begin_inset Formula $B_{V}$
1590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1593 \begin_layout Plain Layout
1599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1602 \begin_layout Plain Layout
1603 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1616 \begin_layout Plain Layout
1621 \begin_layout Plain Layout
1635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1638 \begin_layout Plain Layout
1639 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1655 \begin_layout Standard
1656 As the caret is in some languages an accent, vowels will be accentuated
1657 in this case and not set as exponents
1661 \begin_layout Plain Layout
1662 Depending on the used keyboard settings this can also happen for other character
1669 To get in this case exponents, press
1673 after the caret as in the last example.
1676 \begin_layout Subsection
1678 \begin_inset CommandInset label
1680 name "sub:Fractions"
1688 \begin_layout Plain Layout
1697 \begin_layout Standard
1698 Fractions are generated with the command
1708 \begin_layout Plain Layout
1716 or via the math toolbar button
1717 \begin_inset Graphics
1718 filename ../images/math/frac.png
1724 The font size is adjusted automatically, depending on whether the fraction
1725 is in an inline or display style formula.
1726 With the math toolbar button
1727 \begin_inset Graphics
1728 filename ../images/math/frac-square.png
1733 you can select different fraction types.
1736 \begin_layout Standard
1745 \begin_layout Plain Layout
1755 a fraction can be created that has in any case the size of a display style
1765 \begin_layout Plain Layout
1775 the fraction appears always with the size of an inline formula.
1779 \begin_layout Standard
1780 A line with the fraction
1781 \begin_inset Formula $\frac{1}{2}$
1784 that was created with the command
1793 \begin_layout Standard
1794 A line with the fraction
1795 \begin_inset Formula $\dfrac{1}{2}$
1798 that was created with the command
1807 \begin_layout Standard
1809 \begin_inset Tabular
1810 <lyxtabular version="3" rows="4" columns="2">
1812 <column alignment="center" valignment="top" width="0pt">
1813 <column alignment="center" valignment="top" width="0pt">
1815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1818 \begin_layout Plain Layout
1824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1827 \begin_layout Plain Layout
1829 \begin_inset Note Note
1832 \begin_layout Plain Layout
1839 is only used as spacer.
1851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1854 \begin_layout Plain Layout
1861 \begin_layout Plain Layout
1871 \begin_inset Formula $\downarrow$
1879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1882 \begin_layout Plain Layout
1883 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1896 \begin_layout Plain Layout
1903 \begin_layout Plain Layout
1913 \begin_inset Formula $\downarrow$
1921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1924 \begin_layout Plain Layout
1925 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1938 \begin_layout Plain Layout
1945 \begin_layout Plain Layout
1958 \begin_layout Plain Layout
1973 \begin_layout Plain Layout
1983 \begin_inset Formula $\downarrow$
1987 \begin_inset Formula $\downarrow\downarrow$
1995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1998 \begin_layout Plain Layout
1999 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2015 \begin_layout Standard
2016 \begin_inset VSpace bigskip
2020 \begin_inset Newpage newpage
2023 For nested fractions the command
2033 \begin_layout Plain Layout
2043 \begin_inset VSpace -3mm
2049 \begin_layout Standard
2050 \begin_inset Formula \begin{align*}
2051 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2052 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2059 \begin_layout Standard
2060 The command for the example above is:
2063 \begin_layout Standard
2072 \begin_layout Plain Layout
2082 \begin_inset Formula $\downarrow$
2091 \begin_layout Plain Layout
2106 \begin_layout Plain Layout
2116 \begin_inset Formula $\downarrow$
2120 \begin_inset Formula $\downarrow$
2126 \begin_layout Standard
2127 \begin_inset VSpace medskip
2133 \begin_layout Standard
2140 sets the fraction always in the size of a displayed formula, also when
2141 it is part of another fraction.
2144 \begin_layout Standard
2145 It is possible to specify the alignment of the numerator.
2152 is used to left align it, the command
2165 centers the numerator.
2166 These fractions demonstrate the different alignments:
2169 \begin_layout Standard
2170 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2174 \begin_inset Formula $\cfrac{A}{B+C}$
2178 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2184 \begin_layout Standard
2185 \begin_inset Note Greyedout
2188 \begin_layout Plain Layout
2205 are no real LaTeX commands but represent the command
2209 cfrac[alignment]{numerator}{denominator}
2212 Therefore you cannot use them in TeX code.
2220 \begin_layout Standard
2221 \begin_inset VSpace medskip
2224 It is often advantageous to combine
2237 \begin_inset Formula \[
2238 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2245 \begin_layout Standard
2246 For inline fractions with a sloped fraction stroke you can use the command
2257 \begin_layout Plain Layout
2266 \begin_inset Formula $\nicefrac{5}{31}$
2279 \begin_layout Plain Layout
2288 \begin_inset Formula $\unitfrac{5}{31}$
2291 There is furthermore the command
2297 that offers to write a fraction in combination with a number:
2298 \begin_inset Formula $\unitfrac[2]{1}{3}$
2304 \begin_layout Standard
2305 \begin_inset Note Greyedout
2308 \begin_layout Plain Layout
2319 is not a real LaTeX command but the command
2320 \begin_inset Newline newline
2327 unitfrac[number]{numerator}{denominator}
2330 Therefore you cannot use it in TeX code.
2338 \begin_layout Standard
2339 How to define own fractions where the fraction stroke can be changed, is
2341 \begin_inset CommandInset ref
2343 reference "sub:Self-defined-Fractions"
2350 \begin_layout Subsection
2355 \begin_layout Plain Layout
2364 \begin_layout Standard
2365 Square roots are created with
2375 \begin_layout Plain Layout
2383 or the math toolbar button
2384 \begin_inset Graphics
2385 filename ../images/math/sqrt.png
2390 , all other roots with the command
2400 \begin_layout Plain Layout
2408 or with the math toolbar button
2409 \begin_inset Graphics
2410 filename ../images/math/root.png
2418 \begin_layout Standard
2420 \begin_inset Tabular
2421 <lyxtabular version="3" rows="3" columns="2">
2423 <column alignment="center" valignment="top" width="0pt">
2424 <column alignment="center" valignment="top" width="0pt">
2426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2429 \begin_layout Plain Layout
2435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2438 \begin_layout Plain Layout
2440 \begin_inset Note Note
2443 \begin_layout Plain Layout
2450 is only used as spacer.
2462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2465 \begin_layout Plain Layout
2472 \begin_layout Plain Layout
2486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2489 \begin_layout Plain Layout
2490 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2500 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2503 \begin_layout Plain Layout
2510 \begin_layout Plain Layout
2520 \begin_inset Formula $\downarrow$
2528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2531 \begin_layout Plain Layout
2532 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2548 \begin_layout Standard
2549 A square root can also be created with
2555 when the root index field is left empty.
2558 \begin_layout Standard
2559 With certain indices the distance to the root is too small, like in this
2561 \begin_inset Formula $\sqrt[\beta]{B}$
2565 \begin_inset Newline newline
2569 \begin_inset Formula $\beta$
2573 To avoid this, the commands
2583 \begin_layout Plain Layout
2601 \begin_layout Plain Layout
2609 are used with the following scheme:
2612 \begin_layout Standard
2626 \begin_layout Standard
2627 Distance is the number of Big Points (unit bp;
2628 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2631 ), that the index should be moved to the left or top, resp..
2632 The commands are written to the index.
2633 This way the command
2634 \begin_inset Newline newline
2644 \begin_inset Formula $\to$
2650 \begin_inset Formula $\to$
2659 \begin_layout Plain Layout
2669 \begin_inset Formula $\to$
2673 \begin_inset Newline newline
2678 produces a correct typeset formula:
2679 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2685 \begin_layout Subsection
2686 Binomial Coefficients
2690 \begin_layout Plain Layout
2691 Binomial coefficients
2699 \begin_layout Standard
2700 Binomial coefficients are inserted with the command
2710 \begin_layout Plain Layout
2718 or with the submenu of the math toolbar button
2719 \begin_inset Graphics
2720 filename ../images/math/frac-square.png
2726 Analog to fractions (
2746 \begin_layout Plain Layout
2766 \begin_layout Plain Layout
2775 For other brackets around binomial coeficients there are the commands
2785 \begin_layout Plain Layout
2803 \begin_layout Plain Layout
2814 \begin_layout Standard
2816 \begin_inset Tabular
2817 <lyxtabular version="3" rows="6" columns="2">
2819 <column alignment="center" valignment="top" width="0pt">
2820 <column alignment="center" valignment="top" width="0pt">
2822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2825 \begin_layout Plain Layout
2831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2834 \begin_layout Plain Layout
2836 \begin_inset Note Note
2839 \begin_layout Plain Layout
2846 is only used as spacer.
2858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2861 \begin_layout Plain Layout
2868 \begin_layout Plain Layout
2878 \begin_inset Formula $\downarrow$
2886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2889 \begin_layout Plain Layout
2890 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2903 \begin_layout Plain Layout
2910 \begin_layout Plain Layout
2920 \begin_inset Formula $\downarrow$
2928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2931 \begin_layout Plain Layout
2932 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2945 \begin_layout Plain Layout
2952 \begin_layout Plain Layout
2962 \begin_inset Formula $\downarrow$
2970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2973 \begin_layout Plain Layout
2974 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2987 \begin_layout Plain Layout
2994 \begin_layout Plain Layout
3004 \begin_inset Formula $\downarrow$
3012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3015 \begin_layout Plain Layout
3016 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3029 \begin_layout Plain Layout
3036 \begin_layout Plain Layout
3046 \begin_inset Formula $\downarrow$
3054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3057 \begin_layout Plain Layout
3058 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3074 \begin_layout Subsection
3075 Case Differentiations
3079 \begin_layout Plain Layout
3080 Case differentiations
3088 \begin_layout Standard
3090 \begin_inset Tabular
3091 <lyxtabular version="3" rows="3" columns="2">
3093 <column alignment="center" valignment="top" width="0pt">
3094 <column alignment="center" valignment="top" width="0pt">
3096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3099 \begin_layout Plain Layout
3105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3108 \begin_layout Plain Layout
3116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3119 \begin_layout Plain Layout
3126 \begin_layout Plain Layout
3136 \begin_inset Formula $\to$
3143 \begin_layout Plain Layout
3156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3159 \begin_layout Plain Layout
3160 \begin_inset Formula $\begin{cases}
3171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3174 \begin_layout Plain Layout
3181 \begin_layout Plain Layout
3193 arg "newline-insert newline"
3201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3204 \begin_layout Plain Layout
3205 \begin_inset Formula $\begin{cases}
3206 A & \textrm{for }x>0\\
3207 B & \textrm{for }x=0\end{cases}$
3223 \begin_layout Standard
3230 or the usage of the math toolbar button
3231 \begin_inset Graphics
3232 filename ../images/math/cases.png
3237 you can create new lines with the shortcut
3240 arg "newline-insert newline"
3243 or the table toolbar button
3244 \begin_inset Graphics
3245 filename ../images/tabular-feature_append-row.png
3253 \begin_layout Standard
3260 is also available via the menu
3262 Insert\SpecialChar \menuseparator
3263 Math\SpecialChar \menuseparator
3269 \begin_layout Subsection
3274 \begin_layout Plain Layout
3283 \begin_layout Standard
3294 \begin_layout Plain Layout
3302 every character can be displayed canceled.
3303 The characters are quasi accentuated by a slash.
3306 \begin_layout Standard
3308 \begin_inset Tabular
3309 <lyxtabular version="3" rows="4" columns="2">
3311 <column alignment="center" valignment="top" width="0pt">
3312 <column alignment="center" valignment="top" width="0pt">
3314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3317 \begin_layout Plain Layout
3323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3326 \begin_layout Plain Layout
3334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3337 \begin_layout Plain Layout
3345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3348 \begin_layout Plain Layout
3349 \begin_inset Formula $\not=$
3359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3362 \begin_layout Plain Layout
3372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3375 \begin_layout Plain Layout
3376 \begin_inset Formula $\not\le$
3386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3389 \begin_layout Plain Layout
3399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3402 \begin_layout Plain Layout
3403 \begin_inset Formula $\not\parallel$
3419 \begin_layout Standard
3420 The last example shows, that not all negations look good.
3421 Therefore there are for some negations special commands (see
3422 \begin_inset CommandInset ref
3424 reference "sub:Mathematical-Symbols"
3429 \begin_inset CommandInset ref
3431 reference "sec:Relations"
3438 \begin_layout Subsection
3440 \begin_inset CommandInset label
3442 name "sub:Placeholders"
3450 \begin_layout Plain Layout
3460 \begin_layout Plain Layout
3461 Chemical characters ! Isotopes
3470 \begin_layout Plain Layout
3475 \begin_layout Plain Layout
3486 \begin_layout Plain Layout
3501 \begin_layout Standard
3503 \begin_inset space \thinspace{}
3507 \begin_inset space \space{}
3514 \begin_layout Plain Layout
3515 Typesetting isotopes and chemical symbols is described in
3516 \begin_inset CommandInset ref
3518 reference "sub:Chemical-Symbols-and"
3527 the following problem occurs:
3530 \begin_layout Standard
3532 \begin_inset Tabular
3533 <lyxtabular version="3" rows="2" columns="2">
3535 <column alignment="center" valignment="top" width="0pt">
3536 <column alignment="center" valignment="top" width="0pt">
3538 <cell alignment="center" valignment="top" usebox="none">
3541 \begin_layout Plain Layout
3542 Indices created with sub- and superscripts:
3547 <cell alignment="center" valignment="top" usebox="none">
3550 \begin_layout Plain Layout
3551 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3561 <cell alignment="center" valignment="top" usebox="none">
3564 \begin_layout Plain Layout
3570 <cell alignment="center" valignment="top" usebox="none">
3573 \begin_layout Plain Layout
3574 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3588 \begin_inset Note Note
3591 \begin_layout Plain Layout
3598 is only used as spacer.
3606 \begin_layout Standard
3607 The shorter index is by default placed below or above the first character
3608 of the longer index.
3609 To avoid this there is the command
3619 \begin_layout Plain Layout
3627 or the math toolbar button
3628 \begin_inset space \thinspace{}
3635 \begin_layout Plain Layout
3636 can be found in the submenu of the toolbar button
3637 \begin_inset Graphics
3638 filename ../images/math/space.png
3649 \begin_inset Graphics
3650 filename ../images/math/phantom.png
3655 that creates one or more phantom characters.
3662 a small blue box appears that is superposed with two red arrows.
3663 The arrows indicate that the complete width and height of the box content
3664 will be created as placeholder.
3665 Phantom characters are accordingly placeholders with the size of the characters.
3668 \begin_layout Standard
3670 \begin_inset Tabular
3671 <lyxtabular version="3" rows="4" columns="2">
3673 <column alignment="center" valignment="top" width="0">
3674 <column alignment="center" valignment="top" width="0">
3676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3679 \begin_layout Plain Layout
3685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3688 \begin_layout Plain Layout
3690 \begin_inset Note Note
3693 \begin_layout Plain Layout
3700 is only used as spacer.
3712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3715 \begin_layout Plain Layout
3720 \begin_layout Plain Layout
3735 \begin_layout Plain Layout
3745 \begin_inset Formula $\to$
3752 \begin_layout Plain Layout
3766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3769 \begin_layout Plain Layout
3770 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3783 \begin_layout Plain Layout
3788 \begin_layout Plain Layout
3803 \begin_layout Plain Layout
3813 \begin_inset Formula $\to$
3820 \begin_layout Plain Layout
3834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3837 \begin_layout Plain Layout
3838 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3851 \begin_layout Plain Layout
3858 \begin_layout Plain Layout
3873 \begin_layout Plain Layout
3883 \begin_inset Formula $\to$
3890 \begin_layout Plain Layout
3904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3907 \begin_layout Plain Layout
3908 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3924 \begin_layout Standard
3925 Furthermore there are the commands
3935 \begin_layout Plain Layout
3944 \begin_inset space ~
3948 \begin_inset Graphics
3949 filename ../images/math/vphantom.png
3964 \begin_layout Plain Layout
3973 \begin_inset space ~
3977 \begin_inset Graphics
3978 filename ../images/math/hphantom.png
3990 creates only space for the maximal height of the characters in the box
3991 but not for its width.
3998 creates only space for the width of the box content.
3999 Therefore the boxes of both commands have only one red arrow.
4002 \begin_layout Standard
4013 \begin_layout Plain Layout
4028 space for the height of the integral sign,
4032 \begin_layout Plain Layout
4039 creates an integral sign, see
4040 \begin_inset CommandInset ref
4042 reference "sub:Big-Operators"
4051 because this is the larger character.
4052 An example application is in
4053 \begin_inset CommandInset ref
4055 reference "sub:Multiline-Brackets"
4062 \begin_layout Subsection
4067 \begin_layout Plain Layout
4077 \begin_layout Plain Layout
4078 Formula ! underlined
4086 \begin_layout Standard
4088 \begin_inset Tabular
4089 <lyxtabular version="3" rows="4" columns="2">
4091 <column alignment="center" valignment="top" width="0pt">
4092 <column alignment="center" valignment="top" width="0pt">
4094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4097 \begin_layout Plain Layout
4103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4106 \begin_layout Plain Layout
4108 \begin_inset Note Note
4111 \begin_layout Plain Layout
4118 is only used as spacer.
4130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4133 \begin_layout Plain Layout
4140 \begin_layout Plain Layout
4153 \begin_layout Plain Layout
4166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4169 \begin_layout Plain Layout
4170 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4183 \begin_layout Plain Layout
4190 \begin_layout Plain Layout
4203 \begin_layout Plain Layout
4216 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4219 \begin_layout Plain Layout
4220 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4233 \begin_layout Plain Layout
4240 \begin_layout Plain Layout
4255 \begin_layout Plain Layout
4269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4272 \begin_layout Plain Layout
4273 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4289 \begin_layout Standard
4290 In the last example it doesn't matter if first
4305 \begin_layout Standard
4306 To double underline e.
4307 \begin_inset space \thinspace{}
4311 \begin_inset space \space{}
4323 \begin_layout Standard
4324 It is possible to place up to 6 lines above or below characters.
4327 \begin_layout Standard
4328 \begin_inset VSpace bigskip
4331 Custom lines can be created using the command
4341 \begin_layout Plain Layout
4349 which has the following scheme:
4352 \begin_layout Standard
4357 rule[vertical offset]{length}{thickness}
4360 \begin_layout Standard
4361 The optional vertical offset shifts the line upwards (or downwards, when
4362 the value is negative).
4364 \begin_inset CommandInset ref
4366 reference "tab:Available-units"
4370 can be used for the values.
4371 Here are two example lines created with the commands
4372 \begin_inset Newline newline
4379 rule[-2ex]{3cm}{2pt}
4390 \begin_layout Standard
4392 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4398 \begin_layout Standard
4405 can also be used for text when it is inserted in TeX-mode.
4408 \begin_layout Subsection
4410 \begin_inset CommandInset label
4420 \begin_layout Plain Layout
4429 \begin_layout Standard
4430 There are different types of ellipses available.
4434 \begin_layout Plain Layout
4435 In the math toolbar in the submenu of the button
4436 \begin_inset Graphics
4437 filename ../images/math/ldots.png
4447 For listings dots at the baseline are used (
4457 \begin_layout Plain Layout
4465 ), while for operations dots are needed that are on the same height as the
4476 \begin_layout Plain Layout
4485 When using the command
4495 \begin_layout Plain Layout
4503 , LaTeX decides on the basis of the next character what type is used.
4506 \begin_layout Standard
4508 \begin_inset Tabular
4509 <lyxtabular version="3" rows="8" columns="2">
4511 <column alignment="center" valignment="top" width="0pt">
4512 <column alignment="center" valignment="top" width="0pt">
4514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4517 \begin_layout Plain Layout
4523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4526 \begin_layout Plain Layout
4534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4537 \begin_layout Plain Layout
4542 \begin_layout Plain Layout
4557 \begin_layout Plain Layout
4571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4574 \begin_layout Plain Layout
4575 \begin_inset Formula $A_{1},\dots,A_{n}$
4585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4588 \begin_layout Plain Layout
4593 \begin_layout Plain Layout
4608 \begin_layout Plain Layout
4622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4625 \begin_layout Plain Layout
4626 \begin_inset Formula $A_{1}+\dots+A_{n}$
4636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4639 \begin_layout Plain Layout
4644 \begin_layout Plain Layout
4659 \begin_layout Plain Layout
4673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4676 \begin_layout Plain Layout
4677 \begin_inset Formula $A_{1},\ldots,A_{n}$
4687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4690 \begin_layout Plain Layout
4695 \begin_layout Plain Layout
4710 \begin_layout Plain Layout
4724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4727 \begin_layout Plain Layout
4728 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4741 \begin_layout Plain Layout
4749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4752 \begin_layout Plain Layout
4753 \begin_inset Formula $\vdots$
4763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4766 \begin_layout Plain Layout
4774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4777 \begin_layout Plain Layout
4778 \begin_inset Formula $\ddots$
4788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4791 \begin_layout Plain Layout
4793 \begin_inset space \thinspace{}
4796 matrix with the different dots
4801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4804 \begin_layout Plain Layout
4805 \begin_inset Formula $\begin{array}{ccc}
4806 A_{11} & \cdots & A_{1m}\\
4807 \vdots & \ddots & \vdots\\
4808 A_{n1} & \cdots & A_{nm}\end{array}$
4824 \begin_layout Standard
4825 The ellipses available in menu
4827 Insert\SpecialChar \menuseparator
4829 \begin_inset space ~
4843 \begin_layout Standard
4844 \begin_inset VSpace medskip
4847 Specially for matrices there are ellipses that span over several columns.
4848 They are created with the command
4858 \begin_layout Plain Layout
4866 , that has the following scheme:
4869 \begin_layout Standard
4874 hdotsfor[distance]{number of columns}
4877 \begin_layout Standard
4878 The number of columns specifies how many columns should be spanned.
4879 Distance is a factor for the distance between the dots.
4882 \begin_layout Standard
4883 In the following matrix the command
4889 was inserted in the first box of the second line, to get an ellipsis with
4890 a dot distance twice as long as with the command
4897 \begin_inset Formula \[
4898 \left(\begin{array}{cccc}
4901 q & w & e & r\end{array}\right)\]
4905 Note that the matrix fields that should be spanned must be empty, otherwise
4906 you get LaTeX-errors.
4909 \begin_layout Standard
4910 \begin_inset VSpace bigskip
4913 Furthermore you can fill with the command
4923 \begin_layout Plain Layout
4931 the rest of a line with dots.
4932 The effect of these commands is the same like with
4939 \begin_inset CommandInset ref
4941 reference "sub:Variable-Space"
4948 \begin_layout Standard
4949 For example the command
4957 \begin_layout Plain Layout
4971 \begin_layout Standard
4972 \begin_inset Formula $A\dotfill B$
4978 \begin_layout Standard
4985 there is for a line the command
4995 \begin_layout Plain Layout
5006 \begin_layout Standard
5007 \begin_inset Formula $A\hrulefill B$
5013 \begin_layout Standard
5014 To use the commands for text, they have to be inserted in TeX-mode.
5017 \begin_layout Section
5019 \begin_inset CommandInset label
5029 \begin_layout Plain Layout
5038 \begin_layout Standard
5039 Matrices can be inserted via the math toolbar button
5040 \begin_inset Graphics
5041 filename ../images/dialog-show_mathmatrix.png
5048 Insert\SpecialChar \menuseparator
5049 Math\SpecialChar \menuseparator
5053 You will be asked for the number of matrix columns and rows, and the alignment.
5054 The vertical alignment is hereby only of importance for matrices in inline
5058 \begin_layout Standard
5059 The first matrix is top
5060 \begin_inset Formula $\begin{array}[t]{cccc}
5063 C & F & I & L\end{array}$
5067 \begin_inset Formula $\begin{array}{cccc}
5070 C & F & I & L\end{array}$
5073 , and the third bottom
5074 \begin_inset Formula $\begin{array}[b]{cccc}
5077 C & F & I & L\end{array}$
5083 \begin_layout Standard
5084 The horizontal alignment specifies how the column entries should be aligned.
5085 It is set by entering a letter for every column.
5090 denotes left aligned,
5099 To create for example a 4
5104 \begin_inset space ~
5107 matrix where the first column is left aligned, the second and third are
5108 centered, and the last one is right aligned, one enters for the horizontal
5114 Normally are in a matrix all columns centered, therefore the default is
5115 for every column is a
5122 \begin_layout Standard
5123 Horizontal alignment:
5126 \begin_layout Standard
5132 \begin_inset Formula $\begin{array}{lll}
5135 C & F & 10000\end{array}$
5143 \begin_inset Formula $\begin{array}{ccc}
5146 C & F & 10000\end{array}$
5154 \begin_inset Formula $\begin{array}{rrr}
5157 C & F & 10000\end{array}$
5163 \begin_layout Standard
5164 To add or delete rows and columns subsequently, the math toolbar buttons
5166 \begin_inset Graphics
5167 filename ../images/tabular-feature_append-row.png
5173 \begin_inset Graphics
5174 filename ../images/tabular-feature_delete-row.png
5180 \begin_inset space \thinspace{}
5185 Edit\SpecialChar \menuseparator
5189 New rows can also be created with
5192 arg "newline-insert newline"
5198 \begin_layout Standard
5199 \begin_inset VSpace bigskip
5202 Parentheses around a matrix can can either be created with the commands
5213 \begin_layout Plain Layout
5231 \begin_layout Plain Layout
5242 \begin_inset space ~
5248 \begin_inset CommandInset ref
5250 reference "sub:Automatic-Bracket-Size"
5254 , or by using the following commands:
5255 \begin_inset VSpace medskip
5261 \begin_layout Standard
5262 \begin_inset space \hfill{}
5266 \begin_inset Tabular
5267 <lyxtabular version="3" rows="4" columns="2">
5269 <column alignment="center" valignment="top" width="0">
5270 <column alignment="center" valignment="top" width="0">
5272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5275 \begin_layout Plain Layout
5281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5284 \begin_layout Plain Layout
5286 \begin_inset Note Note
5289 \begin_layout Plain Layout
5296 is only used as spacer.
5308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5311 \begin_layout Plain Layout
5318 \begin_layout Plain Layout
5332 \begin_inset space \thinspace{}
5340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5343 \begin_layout Plain Layout
5344 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5345 0 & \textrm{-}\mathrm{i}\\
5346 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5359 \begin_layout Plain Layout
5366 \begin_layout Plain Layout
5380 \begin_inset space \thinspace{}
5388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5391 \begin_layout Plain Layout
5392 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5393 0 & \textrm{-}\mathrm{i}\\
5394 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5407 \begin_layout Plain Layout
5414 \begin_layout Plain Layout
5428 \begin_inset space \thinspace{}
5436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5439 \begin_layout Plain Layout
5440 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5441 0 & \textrm{-}\mathrm{i}\\
5442 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5456 \begin_inset space \hfill{}
5460 \begin_inset Tabular
5461 <lyxtabular version="3" rows="4" columns="2">
5463 <column alignment="center" valignment="top" width="0">
5464 <column alignment="center" valignment="top" width="0">
5466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5469 \begin_layout Plain Layout
5475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5478 \begin_layout Plain Layout
5486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5489 \begin_layout Plain Layout
5496 \begin_layout Plain Layout
5510 \begin_inset space \thinspace{}
5518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5521 \begin_layout Plain Layout
5522 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5523 0 & \textrm{-}\mathrm{i}\\
5524 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5537 \begin_layout Plain Layout
5544 \begin_layout Plain Layout
5558 \begin_inset space \thinspace{}
5566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5569 \begin_layout Plain Layout
5570 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5571 0 & \textrm{-}\mathrm{i}\\
5572 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5585 \begin_layout Plain Layout
5592 \begin_layout Plain Layout
5606 \begin_inset space \thinspace{}
5614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5617 \begin_layout Plain Layout
5618 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5619 0 & \textrm{-}\mathrm{i}\\
5620 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5634 \begin_inset space \hfill{}
5640 \begin_layout Standard
5641 \begin_inset VSpace medskip
5645 \begin_inset space \thinspace{}
5649 \begin_inset space \space{}
5658 is inserted, a blue box appears between two vertical lines where the matrix
5662 \begin_layout Standard
5663 \begin_inset VSpace bigskip
5666 As all multiline formulas are matrices, the length
5676 \begin_layout Plain Layout
5684 that is described in
5685 \begin_inset CommandInset ref
5687 reference "sub:Column-Separation"
5691 can also be used to change the column separation of matrices.
5694 \begin_layout Standard
5695 To change the row separation, the command
5705 \begin_layout Plain Layout
5714 It is used as follows:
5717 \begin_layout Standard
5724 arraystretch}{stretch factor}
5728 \begin_layout Plain Layout
5739 \begin_layout Standard
5746 assigns the stretch factor to the predefined command
5754 \begin_inset space \thinspace{}
5758 \begin_inset space \space{}
5761 the row separation, use the factor 2.
5762 This is then used for all following matrices.
5763 To go back to the original separation, assign the factor 1 to
5772 \begin_layout Standard
5773 To set matrices into a text line, the command
5783 \begin_layout Plain Layout
5792 When it is inserted a blue box with two dashed lines appears.
5793 In this box the matrix is inserted.
5796 \begin_layout Standard
5798 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5799 C & D\end{smallmatrix}\right)$
5805 \begin_layout Section
5806 Brackets and Delimiters
5810 \begin_layout Plain Layout
5820 \begin_layout Plain Layout
5829 \begin_layout Subsection
5830 Vertical Brackets and Delimiters
5834 \begin_layout Plain Layout
5843 \begin_layout Standard
5844 \begin_inset space \hfill{}
5848 \begin_inset Tabular
5849 <lyxtabular version="3" rows="9" columns="2">
5851 <column alignment="center" valignment="top" width="0pt">
5852 <column alignment="center" valignment="top" width="0pt">
5854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5857 \begin_layout Plain Layout
5863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5866 \begin_layout Plain Layout
5874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5877 \begin_layout Plain Layout
5883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5886 \begin_layout Plain Layout
5887 \begin_inset Formula $($
5897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5900 \begin_layout Plain Layout
5906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5909 \begin_layout Plain Layout
5910 \begin_inset Formula $\{$
5920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5923 \begin_layout Plain Layout
5929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5932 \begin_layout Plain Layout
5933 \begin_inset Formula $[$
5943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5946 \begin_layout Plain Layout
5954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5957 \begin_layout Plain Layout
5958 \begin_inset Formula $\langle$
5968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5971 \begin_layout Plain Layout
5979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5982 \begin_layout Plain Layout
5983 \begin_inset Formula $\lceil$
5993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5996 \begin_layout Plain Layout
6004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6007 \begin_layout Plain Layout
6008 \begin_inset Formula $\lfloor$
6018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6021 \begin_layout Plain Layout
6027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6030 \begin_layout Plain Layout
6031 \begin_inset Formula $/$
6041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6044 \begin_layout Plain Layout
6050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6053 \begin_layout Plain Layout
6054 \begin_inset Formula $|$
6068 \begin_inset space \hfill{}
6072 \begin_inset Tabular
6073 <lyxtabular version="3" rows="9" columns="2">
6075 <column alignment="center" valignment="top" width="0pt">
6076 <column alignment="center" valignment="top" width="0pt">
6078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6081 \begin_layout Plain Layout
6087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6090 \begin_layout Plain Layout
6098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6101 \begin_layout Plain Layout
6107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6110 \begin_layout Plain Layout
6111 \begin_inset Formula $)$
6121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6124 \begin_layout Plain Layout
6130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6133 \begin_layout Plain Layout
6134 \begin_inset Formula $\}$
6144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6147 \begin_layout Plain Layout
6153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6156 \begin_layout Plain Layout
6157 \begin_inset Formula $]$
6167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6170 \begin_layout Plain Layout
6178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6181 \begin_layout Plain Layout
6182 \begin_inset Formula $\rangle$
6192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6195 \begin_layout Plain Layout
6203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6206 \begin_layout Plain Layout
6207 \begin_inset Formula $\rceil$
6217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6220 \begin_layout Plain Layout
6228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6231 \begin_layout Plain Layout
6232 \begin_inset Formula $\rfloor$
6242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6245 \begin_layout Plain Layout
6255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6258 \begin_layout Plain Layout
6259 \begin_inset Formula $\backslash$
6269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6272 \begin_layout Plain Layout
6280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6283 \begin_layout Plain Layout
6284 \begin_inset Formula $\|$
6298 \begin_inset space \hfill{}
6304 \begin_layout Standard
6307 \begin_inset Note Greyedout
6310 \begin_layout Plain Layout
6315 In TeX-mode the command
6325 \begin_layout Plain Layout
6333 must be used for the backslash, because the command
6341 produces there a line break.
6349 \begin_layout Standard
6350 For all characters listed above the size can be adjusted with the commands
6351 described in the following two subsections.
6352 When using these commands, the characters < and > can directly be used
6353 instead of the commands
6368 \begin_layout Subsubsection
6370 \begin_inset CommandInset label
6372 name "sub:Manual-Bracket-Size"
6380 \begin_layout Plain Layout
6381 Bracket size ! manual
6389 \begin_layout Standard
6390 The bracket size can be specified manually by the LaTeX-commands
6400 \begin_layout Plain Layout
6433 denotes the smallest and
6439 the largest bracket size.
6442 \begin_layout Standard
6443 These commands are used to emphasize levels of brackets:
6446 \begin_layout Standard
6448 \begin_inset Tabular
6449 <lyxtabular version="3" rows="2" columns="2">
6451 <column alignment="center" valignment="top" width="0pt">
6452 <column alignment="center" valignment="top" width="0pt">
6454 <cell alignment="center" valignment="top" usebox="none">
6457 \begin_layout Plain Layout
6458 all brackets in the same size:
6463 <cell alignment="center" valignment="top" usebox="none">
6466 \begin_layout Plain Layout
6467 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6477 <cell alignment="center" valignment="top" usebox="none">
6480 \begin_layout Plain Layout
6486 <cell alignment="center" valignment="top" usebox="none">
6489 \begin_layout Plain Layout
6490 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6504 \begin_inset Note Note
6507 \begin_layout Plain Layout
6514 is only used as spacer.
6522 \begin_layout Standard
6523 For the second formula the command
6533 \begin_layout Plain Layout
6547 \begin_layout Standard
6548 Here is an overview about all bracket sizes:
6551 \begin_layout Standard
6571 \begin_layout Plain Layout
6588 \begin_layout Plain Layout
6601 \begin_layout Plain Layout
6617 \begin_layout Standard
6619 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6625 \begin_layout Standard
6632 -commands there is the variant
6642 \begin_layout Plain Layout
6650 that adds a bit more space between the bracket and its content, and the
6667 \begin_layout Plain Layout
6677 , that don't add additional space.
6682 at the end of the command
6688 is for a left bracket; for a right bracket this will be replaced by an
6694 A left or right bracket can each be an opening or closing bracket.
6697 \begin_layout Standard
6698 In the following table is a comparison of the variants:
6701 \begin_layout Standard
6703 \begin_inset Tabular
6704 <lyxtabular version="3" rows="5" columns="2">
6706 <column alignment="center" valignment="middle" width="0">
6707 <column alignment="center" valignment="middle" width="0">
6709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6712 \begin_layout Plain Layout
6718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6721 \begin_layout Plain Layout
6723 \begin_inset Note Note
6726 \begin_layout Plain Layout
6733 is only used as spacer.
6745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6748 \begin_layout Plain Layout
6763 \begin_layout Plain Layout
6781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6784 \begin_layout Plain Layout
6785 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6798 \begin_layout Plain Layout
6813 \begin_layout Plain Layout
6831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6834 \begin_layout Plain Layout
6835 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6848 \begin_layout Plain Layout
6863 \begin_layout Plain Layout
6881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6884 \begin_layout Plain Layout
6885 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6898 \begin_layout Plain Layout
6910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6913 \begin_layout Plain Layout
6914 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6930 \begin_layout Subsubsection
6931 Automatic Bracket Size
6932 \begin_inset CommandInset label
6934 name "sub:Automatic-Bracket-Size"
6942 \begin_layout Plain Layout
6943 Bracket size ! automatic
6951 \begin_layout Standard
6952 Brackets with variable size can be inserted with the commands
6962 \begin_layout Plain Layout
6980 \begin_layout Plain Layout
6988 or via the math toolbar button
6989 \begin_inset Graphics
6990 filename ../images/dialog-show_mathdelimiter.png
7008 the wanted bracket must be inserted.
7009 The bracket size will then automatically be calculated for the output.
7012 \begin_layout Standard
7014 normal bracket: The command
7024 \begin_layout Plain Layout
7034 \begin_inset Formula $\downarrow$
7041 \begin_layout Plain Layout
7053 \begin_inset Formula \[
7061 \begin_layout Standard
7063 multiline bracket: The command
7075 \begin_layout Plain Layout
7085 \begin_inset Formula $\downarrow$
7092 \begin_layout Plain Layout
7106 \begin_inset Formula \[
7107 \ln\left(\frac{A}{C}\right)\]
7114 \begin_layout Standard
7130 \begin_inset space ~
7136 This has the advantage that you can see in LyX immediately the real bracket
7137 size and that the matching right bracket will be created too.
7138 \begin_inset Newline newline
7141 The command for the last example would then be:
7155 \begin_layout Plain Layout
7165 \begin_inset Formula $\downarrow$
7171 \begin_layout Standard
7172 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7173 For example the command
7183 \begin_layout Plain Layout
7193 \begin_inset Formula $\downarrow$
7200 \begin_layout Plain Layout
7216 \begin_inset Formula \[
7217 \left.\frac{A}{B}\right\} \]
7235 will be converted by LyX to brackets in the right size when the document
7236 is reloaded and an omitted bracket will appear as dashed line.
7239 \begin_layout Standard
7240 \begin_inset VSpace bigskip
7243 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7254 \begin_layout Plain Layout
7262 is additionally available for all brackets and limits.
7263 With this command the height of the following character is adapted to the
7264 one of the surrounding brackets, what is e.
7265 \begin_inset space \thinspace{}
7269 \begin_inset space \space{}
7272 needed for physical vectors:
7273 \begin_inset Formula \[
7274 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7278 For physical vectors there is a special LaTeX-package, described in
7279 \begin_inset CommandInset ref
7281 reference "sub:Physical-Vectors"
7288 \begin_layout Subsection
7293 \begin_layout Plain Layout
7294 Brackets ! horizontal
7302 \begin_layout Standard
7304 \begin_inset Tabular
7305 <lyxtabular version="3" rows="4" columns="2">
7307 <column alignment="center" valignment="top" width="0pt">
7308 <column alignment="center" valignment="top" width="0pt">
7310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7313 \begin_layout Plain Layout
7315 \begin_inset Note Note
7318 \begin_layout Plain Layout
7325 is only used as spacer.
7335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7338 \begin_layout Plain Layout
7346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7349 \begin_layout Plain Layout
7353 \begin_layout Plain Layout
7368 \begin_layout Plain Layout
7381 \begin_layout Plain Layout
7394 \begin_layout Plain Layout
7407 \begin_layout Plain Layout
7418 \begin_layout Plain Layout
7431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7434 \begin_layout Plain Layout
7435 \begin_inset Formula $\overbrace{A+B}^{3}$
7445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7448 \begin_layout Plain Layout
7452 \begin_layout Plain Layout
7467 \begin_layout Plain Layout
7480 \begin_layout Plain Layout
7493 \begin_layout Plain Layout
7504 \begin_layout Plain Layout
7517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7520 \begin_layout Plain Layout
7521 \begin_inset Formula $\underbrace{A+B}_{5}$
7531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7534 \begin_layout Plain Layout
7541 \begin_layout Plain Layout
7556 \begin_layout Plain Layout
7569 \begin_layout Plain Layout
7582 \begin_layout Plain Layout
7595 \begin_layout Plain Layout
7608 \begin_layout Plain Layout
7621 \begin_layout Plain Layout
7635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7638 \begin_layout Plain Layout
7639 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7655 \begin_layout Standard
7656 In the last example it doesn't matter if
7668 is inserted at first.
7671 \begin_layout Standard
7672 \begin_inset VSpace bigskip
7675 When brackets are needed that overlap each other, multiline formulas, as
7677 \begin_inset CommandInset ref
7679 reference "sec:Multiline-Formulas"
7684 \begin_inset Formula \begin{eqnarray*}
7685 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7686 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7690 In the first row the formula is inserted together with the first brace.
7691 It is hereby important that the space command
7695 \begin_layout Plain Layout
7696 Space commands are explained in
7697 \begin_inset CommandInset ref
7699 reference "sub:Predefined-Space"
7714 is inserted before the first
7715 \begin_inset Formula $d$
7718 , because the brace that ends behind the
7719 \begin_inset Formula $q$
7722 prevents that the following
7723 \begin_inset Quotes eld
7727 \begin_inset Quotes erd
7730 is surrounded by space.
7734 \begin_layout Plain Layout
7735 because a bracket is not handled as character, see
7736 \begin_inset CommandInset ref
7738 reference "sub:Binary-Operators"
7747 In the second row the second brace is inserted.
7748 As it should begin before the
7749 \begin_inset Formula $b$
7764 \begin_layout Plain Layout
7772 \begin_inset CommandInset ref
7774 reference "sub:Placeholders"
7783 This space is needed because the
7784 \begin_inset Quotes eld
7788 \begin_inset Quotes erd
7791 is also surrounded by space in the formula.
7792 The brace is placed under the command
7801 \begin_layout Standard
7802 It gets more complicated when brackets overlap each other, like in the following
7807 \begin_layout Plain Layout
7819 \begin_inset Formula \begin{eqnarray*}
7820 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7821 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7829 \begin_layout Plain Layout
7840 The first formula row is the same as the second row of the previous example,
7841 with the difference that the brace is above.
7842 The second row contains the formula together with the second brace.
7843 To avoid that there is space between the upper brace in the first row and
7844 the formula, the row spacing need to be reduced.
7845 This is not easily possible due to a bug in LyX
7849 \begin_layout Plain Layout
7850 \begin_inset CommandInset href
7852 name "LyX-bug #1505"
7853 target "http://www.lyx.org/trac/ticket/1505"
7863 As solution for the problem, the global formula row separation
7873 \begin_layout Plain Layout
7881 must be changed to -6
7882 \begin_inset space \thinspace{}
7885 pt before the formula with the command
7900 is set back after the formula to the standard value of 3
7901 \begin_inset space \thinspace{}
7904 pt using the same command.
7905 More about the row separation in formulas is explained in
7906 \begin_inset CommandInset ref
7908 reference "sub:Line-Separation"
7915 \begin_layout Section
7920 \begin_layout Plain Layout
7929 \begin_layout Standard
7930 Arrows can be inserted via the math toolbar button
7931 \begin_inset Graphics
7932 filename ../images/math/leftarrow.png
7937 or the commands listed in the following subsections.
7940 \begin_layout Standard
7941 \begin_inset Newpage newpage
7947 \begin_layout Subsection
7952 \begin_layout Plain Layout
7961 \begin_layout Standard
7962 \begin_inset space \hfill{}
7966 \begin_inset Tabular
7967 <lyxtabular version="3" rows="8" columns="2">
7969 <column alignment="center" valignment="top" width="0pt">
7970 <column alignment="center" valignment="top" width="0pt">
7972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7975 \begin_layout Plain Layout
7981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7984 \begin_layout Plain Layout
7992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7995 \begin_layout Plain Layout
8003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8006 \begin_layout Plain Layout
8007 \begin_inset Formula $\gets$
8017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8020 \begin_layout Plain Layout
8028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8031 \begin_layout Plain Layout
8032 \begin_inset Formula $\Leftarrow$
8042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8045 \begin_layout Plain Layout
8053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8056 \begin_layout Plain Layout
8057 \begin_inset Formula $\longleftarrow$
8067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8070 \begin_layout Plain Layout
8078 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8081 \begin_layout Plain Layout
8082 \begin_inset Formula $\Longleftarrow$
8092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8095 \begin_layout Plain Layout
8103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8106 \begin_layout Plain Layout
8107 \begin_inset Formula $\leftharpoonup$
8117 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8120 \begin_layout Plain Layout
8128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8131 \begin_layout Plain Layout
8132 \begin_inset Formula $\leftharpoondown$
8142 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8145 \begin_layout Plain Layout
8153 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8156 \begin_layout Plain Layout
8157 \begin_inset Formula $\hookleftarrow$
8171 \begin_inset space \hfill{}
8175 \begin_inset Tabular
8176 <lyxtabular version="3" rows="8" columns="2">
8178 <column alignment="center" valignment="top" width="0pt">
8179 <column alignment="center" valignment="top" width="0pt">
8181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8184 \begin_layout Plain Layout
8190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8193 \begin_layout Plain Layout
8201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8204 \begin_layout Plain Layout
8212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8215 \begin_layout Plain Layout
8216 \begin_inset Formula $\to$
8226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8229 \begin_layout Plain Layout
8237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8240 \begin_layout Plain Layout
8241 \begin_inset Formula $\Rightarrow$
8251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8254 \begin_layout Plain Layout
8262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8265 \begin_layout Plain Layout
8266 \begin_inset Formula $\longrightarrow$
8276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8279 \begin_layout Plain Layout
8287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8290 \begin_layout Plain Layout
8291 \begin_inset Formula $\Longrightarrow$
8301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8304 \begin_layout Plain Layout
8312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8315 \begin_layout Plain Layout
8316 \begin_inset Formula $\rightharpoonup$
8326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8329 \begin_layout Plain Layout
8337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8340 \begin_layout Plain Layout
8341 \begin_inset Formula $\rightharpoondown$
8351 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8354 \begin_layout Plain Layout
8362 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8365 \begin_layout Plain Layout
8366 \begin_inset Formula $\hookrightarrow$
8380 \begin_inset space \hfill{}
8386 \begin_layout Standard
8387 \begin_inset space \hfill{}
8391 \begin_inset Tabular
8392 <lyxtabular version="3" rows="6" columns="2">
8394 <column alignment="center" valignment="top" width="0pt">
8395 <column alignment="center" valignment="top" width="0pt">
8397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8400 \begin_layout Plain Layout
8406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8409 \begin_layout Plain Layout
8417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8420 \begin_layout Plain Layout
8428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8431 \begin_layout Plain Layout
8432 \begin_inset Formula $\leftrightarrow$
8442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8445 \begin_layout Plain Layout
8453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8456 \begin_layout Plain Layout
8457 \begin_inset Formula $\Leftrightarrow$
8467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8470 \begin_layout Plain Layout
8478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8481 \begin_layout Plain Layout
8482 \begin_inset Formula $\longleftrightarrow$
8492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8495 \begin_layout Plain Layout
8503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8506 \begin_layout Plain Layout
8507 \begin_inset Formula $\Longleftrightarrow$
8517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8520 \begin_layout Plain Layout
8528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8531 \begin_layout Plain Layout
8532 \begin_inset Formula $\rightleftharpoons$
8546 \begin_inset space \hspace{}
8551 \begin_inset space \hfill{}
8555 \begin_inset Tabular
8556 <lyxtabular version="3" rows="5" columns="2">
8558 <column alignment="center" valignment="top" width="0pt">
8559 <column alignment="center" valignment="top" width="0pt">
8561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8564 \begin_layout Plain Layout
8570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8573 \begin_layout Plain Layout
8581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8584 \begin_layout Plain Layout
8592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8595 \begin_layout Plain Layout
8596 \begin_inset Formula $\mapsto$
8606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8609 \begin_layout Plain Layout
8617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8620 \begin_layout Plain Layout
8621 \begin_inset Formula $\longmapsto$
8631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8634 \begin_layout Plain Layout
8642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8645 \begin_layout Plain Layout
8646 \begin_inset Formula $\leadsto$
8656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8659 \begin_layout Plain Layout
8667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8670 \begin_layout Plain Layout
8671 \begin_inset Formula $\dasharrow$
8685 \begin_inset space \hfill{}
8691 \begin_layout Standard
8692 \begin_inset VSpace medskip
8695 Arrows used as accent like e.
8696 \begin_inset space \thinspace{}
8700 \begin_inset space \space{}
8703 vector arrows are listed in
8704 \begin_inset CommandInset ref
8706 reference "sec:Accents"
8713 \begin_layout Standard
8714 \begin_inset VSpace bigskip
8717 Furthermore there are the labeled arrows
8721 \begin_layout Plain Layout
8737 \begin_layout Plain Layout
8755 \begin_layout Plain Layout
8762 \begin_layout Plain Layout
8777 When inserting one of these commands in a formula, an arrow with two blue
8778 boxes appear where the label can be inserted.
8779 The length of the arrow adapts to the label width.
8782 \begin_layout Standard
8784 \begin_inset Tabular
8785 <lyxtabular version="3" rows="3" columns="2">
8787 <column alignment="center" valignment="top" width="0pt">
8788 <column alignment="center" valignment="top" width="0pt">
8790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8793 \begin_layout Plain Layout
8799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8802 \begin_layout Plain Layout
8804 \begin_inset Note Note
8807 \begin_layout Plain Layout
8814 is only used as spacer.
8826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8829 \begin_layout Plain Layout
8836 \begin_layout Plain Layout
8846 \begin_inset Formula $\downarrow$
8850 \begin_inset Formula $\to$
8858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8861 \begin_layout Plain Layout
8862 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8875 \begin_layout Plain Layout
8882 \begin_layout Plain Layout
8892 \begin_inset Formula $\downarrow$
8896 \begin_inset Formula $\to$
8904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8907 \begin_layout Plain Layout
8908 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8924 \begin_layout Subsection
8925 Vertical and diagonal Arrows
8929 \begin_layout Plain Layout
8939 \begin_layout Plain Layout
8948 \begin_layout Standard
8949 \begin_inset space \hfill{}
8953 \begin_inset Tabular
8954 <lyxtabular version="3" rows="7" columns="2">
8956 <column alignment="center" valignment="top" width="0pt">
8957 <column alignment="center" valignment="top" width="0pt">
8959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8962 \begin_layout Plain Layout
8968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8971 \begin_layout Plain Layout
8979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8982 \begin_layout Plain Layout
8990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8993 \begin_layout Plain Layout
8994 \begin_inset Formula $\uparrow$
9004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9007 \begin_layout Plain Layout
9015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9018 \begin_layout Plain Layout
9019 \begin_inset Formula $\Uparrow$
9029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9032 \begin_layout Plain Layout
9040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9043 \begin_layout Plain Layout
9044 \begin_inset Formula $\updownarrow$
9054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9057 \begin_layout Plain Layout
9065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9068 \begin_layout Plain Layout
9069 \begin_inset Formula $\Updownarrow$
9079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9082 \begin_layout Plain Layout
9090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9093 \begin_layout Plain Layout
9094 \begin_inset Formula $\Downarrow$
9104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9107 \begin_layout Plain Layout
9115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9118 \begin_layout Plain Layout
9119 \begin_inset Formula $\downarrow$
9133 \begin_inset space \hfill{}
9137 \begin_inset Tabular
9138 <lyxtabular version="3" rows="5" columns="2">
9140 <column alignment="center" valignment="top" width="0pt">
9141 <column alignment="center" valignment="top" width="0pt">
9143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9146 \begin_layout Plain Layout
9152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9155 \begin_layout Plain Layout
9163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9166 \begin_layout Plain Layout
9174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9177 \begin_layout Plain Layout
9178 \begin_inset Formula $\nearrow$
9188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9191 \begin_layout Plain Layout
9199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9202 \begin_layout Plain Layout
9203 \begin_inset Formula $\searrow$
9213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9216 \begin_layout Plain Layout
9224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9227 \begin_layout Plain Layout
9228 \begin_inset Formula $\swarrow$
9238 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9241 \begin_layout Plain Layout
9249 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9252 \begin_layout Plain Layout
9253 \begin_inset Formula $\nwarrow$
9267 \begin_inset space \hfill{}
9273 \begin_layout Standard
9274 \begin_inset VSpace medskip
9277 Vertical arrows can be used also as delimiter together with the commands
9279 \begin_inset CommandInset ref
9281 reference "sub:Manual-Bracket-Size"
9286 \begin_inset CommandInset ref
9288 reference "sub:Automatic-Bracket-Size"
9295 \begin_layout Standard
9296 \begin_inset Newpage newpage
9302 \begin_layout Section
9304 \begin_inset CommandInset label
9314 \begin_layout Plain Layout
9323 \begin_layout Standard
9324 Accents can be inserted via the math toolbar button
9325 \begin_inset Graphics
9326 filename ../images/math/hat.png
9331 or the commands listed in the following subsections.
9334 \begin_layout Subsection
9335 Accents for one Character
9339 \begin_layout Plain Layout
9352 \begin_layout Plain Layout
9354 \begin_inset CommandInset ref
9356 reference "sub:Accents-in-Text"
9369 \begin_layout Plain Layout
9377 \begin_inset Note Note
9380 \begin_layout Plain Layout
9383 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9386 \begin_layout Plain Layout
9389 texorpdfstring is in section
9390 \begin_inset CommandInset ref
9392 reference "sub:Formulas-in-Section"
9402 \begin_inset CommandInset label
9404 name "sub:Accents-for-one"
9412 \begin_layout Plain Layout
9413 Accents ! for one character
9421 \begin_layout Standard
9422 \begin_inset space \hfill{}
9426 \begin_inset Tabular
9427 <lyxtabular version="3" rows="8" columns="2">
9429 <column alignment="center" valignment="top" width="0pt">
9430 <column alignment="center" valignment="top" width="0pt">
9432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9435 \begin_layout Plain Layout
9441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9444 \begin_layout Plain Layout
9446 \begin_inset Note Note
9449 \begin_layout Plain Layout
9456 is only used as spacer.
9468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9471 \begin_layout Plain Layout
9478 \begin_layout Plain Layout
9492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9495 \begin_layout Plain Layout
9496 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9506 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9509 \begin_layout Plain Layout
9516 \begin_layout Plain Layout
9530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9533 \begin_layout Plain Layout
9534 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9547 \begin_layout Plain Layout
9554 \begin_layout Plain Layout
9568 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9571 \begin_layout Plain Layout
9572 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9582 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9585 \begin_layout Plain Layout
9593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9596 \begin_layout Plain Layout
9597 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9610 \begin_layout Plain Layout
9617 \begin_layout Plain Layout
9630 \begin_layout Plain Layout
9641 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9644 \begin_layout Plain Layout
9645 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9655 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9658 \begin_layout Plain Layout
9665 \begin_layout Plain Layout
9679 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9682 \begin_layout Plain Layout
9683 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9696 \begin_layout Plain Layout
9703 \begin_layout Plain Layout
9717 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9720 \begin_layout Plain Layout
9721 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9735 \begin_inset space \hfill{}
9739 \begin_inset Tabular
9740 <lyxtabular version="3" rows="7" columns="2">
9742 <column alignment="center" valignment="top" width="0pt">
9743 <column alignment="center" valignment="top" width="0pt">
9745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9748 \begin_layout Plain Layout
9754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9757 \begin_layout Plain Layout
9765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9768 \begin_layout Plain Layout
9775 \begin_layout Plain Layout
9789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9792 \begin_layout Plain Layout
9793 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9803 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9806 \begin_layout Plain Layout
9813 \begin_layout Plain Layout
9827 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9830 \begin_layout Plain Layout
9831 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9841 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9844 \begin_layout Plain Layout
9851 \begin_layout Plain Layout
9865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9868 \begin_layout Plain Layout
9869 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9879 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9882 \begin_layout Plain Layout
9889 \begin_layout Plain Layout
9903 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9906 \begin_layout Plain Layout
9907 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9917 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9920 \begin_layout Plain Layout
9927 \begin_layout Plain Layout
9941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9944 \begin_layout Plain Layout
9945 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9958 \begin_layout Plain Layout
9965 \begin_layout Plain Layout
9979 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9982 \begin_layout Plain Layout
9983 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9997 \begin_inset space \hfill{}
10003 \begin_layout Standard
10004 \begin_inset VSpace bigskip
10010 \begin_layout Standard
10011 You can directly insert accents like é to formulas.
10012 LyX will transform them to the corresponding accent command.
10017 \begin_layout Plain Layout
10023 it is better to insert a quotation mark before the vowel.
10024 These two characters are then treated by LaTeX as
10028 character when the formula part with the umlaut is marked as German.
10036 \begin_inset Quotes eld
10040 \begin_inset Quotes erd
10043 umlauts are created as demonstrated in the following example:
10046 \begin_layout Standard
10047 \begin_inset VSpace -2mm
10053 \begin_layout Standard
10055 \begin_inset Tabular
10056 <lyxtabular version="3" rows="3" columns="2">
10058 <column alignment="center" valignment="top" width="0">
10059 <column alignment="center" valignment="top" width="0">
10061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10064 \begin_layout Plain Layout
10070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10073 \begin_layout Plain Layout
10075 \begin_inset Note Note
10078 \begin_layout Plain Layout
10086 \begin_inset space \thinspace{}
10089 pt space are only used as spacer.
10101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10104 \begin_layout Plain Layout
10107 \begin_inset Quotes grd
10115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10118 \begin_layout Plain Layout
10119 \begin_inset space \hspace{}
10126 \begin_inset Formula $"i$
10136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10139 \begin_layout Plain Layout
10146 \begin_layout Plain Layout
10160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10163 \begin_layout Plain Layout
10164 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10180 \begin_layout Standard
10181 Another advantage to
10187 is that umlauts can directly be converted to mathematical text because
10188 the accent commands above are
10194 in mathematical text
10197 To convert an accented character to mathematical text, only the character
10198 under the accent may be converted.
10199 This applies also for all other conversions, e.
10200 \begin_inset space \thinspace{}
10204 \begin_inset space \space{}
10210 \begin_layout Standard
10211 In mathematical text, umlauts and other accented characters can directly
10215 \begin_layout Subsection
10216 Accents for Operators
10220 \begin_layout Plain Layout
10221 Accents ! for operators
10229 \begin_layout Standard
10240 \begin_layout Plain Layout
10258 \begin_layout Plain Layout
10266 characters can be placed above or below an operator, respectively, to accent
10278 \begin_layout Plain Layout
10286 characters can be set before and behind an operator.
10287 The command scheme is:
10290 \begin_layout Standard
10306 \begin_layout Standard
10313 must always be before the operator that should be accented.
10314 You can accent with several characters and even with other operators and
10322 for example only characters behind an operator, write nothing between the
10323 first braces but don't omit the braces.
10326 \begin_layout Standard
10327 For example the command
10332 \begin_inset Formula $\to$
10342 \begin_inset Formula $\to$
10351 \begin_layout Plain Layout
10367 \begin_inset Formula \[
10368 \sideset{}{'}\sum_{k=1}^{n}\]
10375 \begin_layout Standard
10384 \begin_layout Plain Layout
10399 \begin_layout Plain Layout
10411 \begin_inset Formula $\uparrow$
10419 \begin_inset Formula \[
10420 \overset{a}{\maltese}\]
10424 As seen in the last example, with
10436 also symbols and characters can be accented; with
10442 this is not possible.
10445 \begin_layout Subsection
10446 Accents for several Characters
10450 \begin_layout Plain Layout
10451 Accents ! for several characters
10459 \begin_layout Standard
10460 \begin_inset space \hfill{}
10464 \begin_inset Tabular
10465 <lyxtabular version="3" rows="5" columns="2">
10467 <column alignment="center" valignment="top" width="0pt">
10468 <column alignment="center" valignment="top" width="0pt">
10470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10473 \begin_layout Plain Layout
10479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10482 \begin_layout Plain Layout
10484 \begin_inset Note Note
10487 \begin_layout Plain Layout
10494 is only used as spacer.
10506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10509 \begin_layout Plain Layout
10516 \begin_layout Plain Layout
10530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10533 \begin_layout Plain Layout
10534 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10547 \begin_layout Plain Layout
10554 \begin_layout Plain Layout
10568 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10571 \begin_layout Plain Layout
10572 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10582 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10585 \begin_layout Plain Layout
10592 \begin_layout Plain Layout
10606 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10609 \begin_layout Plain Layout
10610 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10623 \begin_layout Plain Layout
10626 underleftrightarrow
10630 \begin_layout Plain Layout
10644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10647 \begin_layout Plain Layout
10648 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10662 \begin_inset space \hfill{}
10666 \begin_inset Tabular
10667 <lyxtabular version="3" rows="5" columns="2">
10669 <column alignment="center" valignment="top" width="0pt">
10670 <column alignment="center" valignment="top" width="0pt">
10672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10675 \begin_layout Plain Layout
10681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10684 \begin_layout Plain Layout
10692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10695 \begin_layout Plain Layout
10702 \begin_layout Plain Layout
10716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10719 \begin_layout Plain Layout
10720 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10730 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10733 \begin_layout Plain Layout
10740 \begin_layout Plain Layout
10754 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10757 \begin_layout Plain Layout
10758 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10768 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10771 \begin_layout Plain Layout
10778 \begin_layout Plain Layout
10792 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10795 \begin_layout Plain Layout
10796 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10806 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10809 \begin_layout Plain Layout
10816 \begin_layout Plain Layout
10830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10833 \begin_layout Plain Layout
10834 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10848 \begin_inset space \hfill{}
10854 \begin_layout Standard
10855 \begin_inset VSpace medskip
10858 With these commands as many characters as you like can be accented.
10871 will only be set in the output with a length of three characters, as shown
10872 in the following example:
10873 \begin_inset Formula \[
10874 \widetilde{A+B=C-D}\]
10881 \begin_layout Standard
10892 \begin_layout Plain Layout
10910 \begin_layout Plain Layout
10918 described in the previous subsection it is also possible to accent several
10928 \begin_layout Plain Layout
10938 \begin_inset Formula $\downarrow$
10944 \begin_inset Formula \[
10945 \underset{***}{A=B}\]
10952 \begin_layout Section
10954 \begin_inset CommandInset label
10964 \begin_layout Plain Layout
10973 \begin_layout Subsection
10975 \begin_inset CommandInset label
10977 name "sub:Predefined-Space"
10985 \begin_layout Plain Layout
10986 Space ! horizontal ! predefined
10994 \begin_layout Standard
10995 Sometimes it is necessary to insert horizontal space to a formula.
10996 This is done by inserting a protected space (shortcut
10999 arg "space-insert protected"
11004 \begin_inset Quotes eld
11013 \begin_layout Plain Layout
11025 \begin_inset Quotes erd
11028 appears and by pressing
11032 several times one can select one of eight different space sizes.
11033 The spaces can also be inserted using the math toolbar button
11034 \begin_inset Graphics
11035 filename ../images/math/space.png
11040 or special commands.
11041 Independent from the inserted command, one can select the size again by
11049 \begin_layout Standard
11052 \begin_inset VSpace -5mm
11056 \begin_inset Tabular
11057 <lyxtabular version="3" rows="3" columns="7">
11059 <column alignment="center" valignment="middle" width="6.8cm">
11060 <column alignment="center" valignment="top" width="0">
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">
11067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11070 \begin_layout Plain Layout
11076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11079 \begin_layout Plain Layout
11087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11090 \begin_layout Plain Layout
11098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11101 \begin_layout Plain Layout
11109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11112 \begin_layout Plain Layout
11120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11123 \begin_layout Plain Layout
11131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11134 \begin_layout Plain Layout
11144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11147 \begin_layout Plain Layout
11152 keystrokes after inserting the protected space
11157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11160 \begin_layout Plain Layout
11166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11169 \begin_layout Plain Layout
11175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11178 \begin_layout Plain Layout
11184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11187 \begin_layout Plain Layout
11193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11196 \begin_layout Plain Layout
11202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11205 \begin_layout Plain Layout
11213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11216 \begin_layout Plain Layout
11222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11225 \begin_layout Plain Layout
11226 \begin_inset Formula $A\, B$
11234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11237 \begin_layout Plain Layout
11238 \begin_inset Formula $A\: B$
11246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11249 \begin_layout Plain Layout
11250 \begin_inset Formula $A\; B$
11258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11261 \begin_layout Plain Layout
11262 \begin_inset Formula $A\quad B$
11270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11273 \begin_layout Plain Layout
11274 \begin_inset Formula $A\qquad B$
11282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11285 \begin_layout Plain Layout
11286 \begin_inset Formula $A\! B$
11302 \begin_layout Standard
11303 The last size seem to produce no space.
11304 It is displayed red in LyX contrary to the other sizes, because it is a
11306 There are two more negative spaces:
11309 \begin_layout Standard
11311 \begin_inset Tabular
11312 <lyxtabular version="3" rows="3" columns="3">
11314 <column alignment="center" valignment="middle" width="6.8cm">
11315 <column alignment="center" valignment="top" width="0pt">
11316 <column alignment="center" valignment="top" width="0pt">
11318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11321 \begin_layout Plain Layout
11327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11330 \begin_layout Plain Layout
11338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11341 \begin_layout Plain Layout
11351 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11354 \begin_layout Plain Layout
11359 keystrokes after inserting the protected space
11364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11367 \begin_layout Plain Layout
11373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11376 \begin_layout Plain Layout
11384 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11387 \begin_layout Plain Layout
11393 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11396 \begin_layout Plain Layout
11397 \begin_inset Formula $A\negmedspace B$
11405 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11408 \begin_layout Plain Layout
11409 \begin_inset Formula $A\negthickspace B$
11425 \begin_layout Standard
11426 Negative spaces can lead to characters overlapping each other.
11427 Thus they can be used to enforce ligatures, what is e.
11428 \begin_inset space \thinspace{}
11432 \begin_inset space \space{}
11435 useful for summation operators:
11438 \begin_layout Standard
11440 \begin_inset Tabular
11441 <lyxtabular version="3" rows="3" columns="2">
11443 <column alignment="center" valignment="top" width="0">
11444 <column alignment="center" valignment="top" width="0">
11446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11449 \begin_layout Plain Layout
11455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11458 \begin_layout Plain Layout
11460 \begin_inset Note Note
11463 \begin_layout Plain Layout
11470 is only used as spacer.
11482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11485 \begin_layout Plain Layout
11494 \begin_layout Plain Layout
11508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11511 \begin_layout Plain Layout
11512 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11525 \begin_layout Plain Layout
11536 \begin_layout Plain Layout
11550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11553 \begin_layout Plain Layout
11554 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11570 \begin_layout Standard
11571 Relations like for example equal signs, are always surrounded by space.
11572 To suppress this, the equal sign is placed into a TeX-brace.
11573 The following example demonstrates this:
11576 \begin_layout Standard
11578 \begin_inset Tabular
11579 <lyxtabular version="3" rows="2" columns="2">
11581 <column alignment="center" valignment="top" width="0pt">
11582 <column alignment="center" valignment="top" width="0pt">
11584 <cell alignment="center" valignment="top" usebox="none">
11587 \begin_layout Plain Layout
11593 <cell alignment="center" valignment="top" usebox="none">
11596 \begin_layout Plain Layout
11597 \begin_inset Formula $A=B$
11607 <cell alignment="center" valignment="top" usebox="none">
11610 \begin_layout Plain Layout
11611 \begin_inset Note Note
11614 \begin_layout Plain Layout
11621 is only used as spacer.
11627 \begin_inset Formula $\raisebox{5mm}{}$
11630 equation without space
11635 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11638 \begin_layout Plain Layout
11639 \begin_inset Formula $A{=}B$
11655 \begin_layout Standard
11657 The command for the last formula is:
11662 \begin_inset Formula $\to$
11668 \begin_layout Standard
11669 \begin_inset VSpace bigskip
11672 Spaces are needed for physical units, because the space between the value
11673 and the unit is the smallest one and not a normal space.
11674 For units in text, the smallest space is inserted via the menu
11676 Insert\SpecialChar \menuseparator
11677 Formatting\SpecialChar \menuseparator
11679 \begin_inset space ~
11687 arg "space-insert thin"
11693 \begin_layout Standard
11694 An example to visualize the difference:
11697 \begin_layout Standard
11698 \begin_inset Tabular
11699 <lyxtabular version="3" rows="2" columns="2">
11701 <column alignment="left" valignment="top" width="0">
11702 <column alignment="left" valignment="top" width="0">
11704 <cell alignment="center" valignment="top" usebox="none">
11707 \begin_layout Plain Layout
11709 \begin_inset Formula $\cdot$
11717 <cell alignment="center" valignment="top" usebox="none">
11720 \begin_layout Plain Layout
11721 space between value and unit
11728 <cell alignment="center" valignment="top" usebox="none">
11731 \begin_layout Plain Layout
11733 \begin_inset space \thinspace{}
11737 \begin_inset Formula $\cdot$
11745 <cell alignment="center" valignment="top" usebox="none">
11748 \begin_layout Plain Layout
11749 smallest space between value and unit
11762 \begin_layout Subsection
11767 \begin_layout Plain Layout
11780 \begin_layout Plain Layout
11781 for vertical space in formulas see
11782 \begin_inset CommandInset ref
11784 reference "sub:Line-Separation"
11797 \begin_layout Plain Layout
11805 \begin_inset Note Note
11808 \begin_layout Plain Layout
11811 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11814 \begin_layout Plain Layout
11817 texorpdfstring is in section
11818 \begin_inset CommandInset ref
11820 reference "sub:Formulas-in-Section"
11830 \begin_inset CommandInset label
11832 name "sub:Variable-Space"
11840 \begin_layout Plain Layout
11841 Space ! horizontal ! variable
11849 \begin_layout Standard
11850 Space with a defined length can be inserted with the command
11860 \begin_layout Plain Layout
11870 \begin_inset Quotes eld
11879 \begin_layout Plain Layout
11891 \begin_inset Quotes erd
11895 The length can be specified by left-clicking on the
11896 \begin_inset Quotes eld
11905 \begin_layout Plain Layout
11917 \begin_inset Quotes erd
11921 The length may also be negative.
11922 To insert so many space that the formula uses all available space, the
11933 \begin_layout Plain Layout
11944 \begin_layout Standard
11945 \begin_inset VSpace -1mm
11951 \begin_layout Standard
11953 \begin_inset Tabular
11954 <lyxtabular version="3" rows="4" columns="2">
11956 <column alignment="center" valignment="top" width="0">
11957 <column alignment="center" valignment="top" width="0">
11959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11962 \begin_layout Plain Layout
11970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11973 \begin_layout Plain Layout
11981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11984 \begin_layout Plain Layout
11991 \begin_layout Plain Layout
12001 \begin_inset Formula $\to$
12007 \begin_inset space \thinspace{}
12015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12018 \begin_layout Plain Layout
12019 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12032 \begin_layout Plain Layout
12039 \begin_layout Plain Layout
12049 \begin_inset Formula $\to$
12055 \begin_inset space \thinspace{}
12063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12066 \begin_layout Plain Layout
12067 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12080 \begin_layout Plain Layout
12087 \begin_layout Plain Layout
12101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12104 \begin_layout Plain Layout
12105 \begin_inset Formula $A=A\hfill B=B$
12121 \begin_layout Standard
12122 In the last example the available space is given by the longest column entry
12124 In an inline formula the space depends on the length of the line in which
12132 Thus, when the line uses the full width, no space will be created.
12139 only has an effect on displayed formulas when the formula style
12144 (Formula styles are explained in
12145 \begin_inset CommandInset ref
12147 reference "sec:Formula-Styles"
12154 \begin_layout Standard
12161 , there are the commands
12173 that fill the space with a pattern, see
12174 \begin_inset CommandInset ref
12176 reference "sub:Ellipses"
12183 \begin_layout Standard
12184 For text, variable space can be inserted via the menu
12186 Insert\SpecialChar \menuseparator
12187 Formatting\SpecialChar \menuseparator
12189 \begin_inset space ~
12197 \begin_layout Standard
12198 This is a line with
12199 \begin_inset space \hspace{}
12204 \begin_inset space \thinspace{}
12210 \begin_layout Standard
12211 This is a line with
12212 \begin_inset space \hfill{}
12218 \begin_layout Subsection
12219 Space besides inline Formulas
12223 \begin_layout Plain Layout
12224 Space ! besides inline formulas
12232 \begin_layout Standard
12233 The space that surrounds inline formulas can be adjusted with the length
12242 \begin_layout Plain Layout
12253 The value of a length is set with the command
12261 \begin_layout Plain Layout
12271 that has the following scheme:
12274 \begin_layout Standard
12279 setlength{length name}{value}
12282 \begin_layout Standard
12290 \begin_inset space \thinspace{}
12296 \begin_layout Standard
12306 \begin_layout Standard
12307 is inserted in TeX-mode.
12309 \begin_inset space \thinspace{}
12312 mm space will now be set around all inline formulas:
12316 \begin_layout Plain Layout
12330 \begin_layout Standard
12331 This is a line with an inline formula
12332 \begin_inset Formula $A=B$
12336 \begin_inset space \thinspace{}
12339 mm surrounding space.
12343 \begin_layout Plain Layout
12357 \begin_layout Standard
12358 To return to the predefined value,
12364 is set to the value 0
12365 \begin_inset space \thinspace{}
12371 \begin_layout Section
12376 \begin_layout Plain Layout
12386 \begin_layout Plain Layout
12391 \begin_layout Plain Layout
12402 \begin_layout Plain Layout
12417 \begin_layout Standard
12418 Boxes for text are described in chapter
12425 \begin_inset space ~
12433 \begin_layout Subsection
12435 \begin_inset CommandInset label
12437 name "sub:Boxes-with-Frame"
12445 \begin_layout Plain Layout
12454 \begin_layout Standard
12455 It is possible to frame formulas or parts of it with the commands
12465 \begin_layout Plain Layout
12483 \begin_layout Plain Layout
12494 \begin_layout Standard
12495 When one of these commands is inserted to a formula, a blue box appears
12496 within a frame to enter formula parts.
12503 an additional formula has to be created by
12507 within this box, because the box content will otherwise be treated as mathemati
12515 is used, a new formula is automatically created inside the frame.
12518 \begin_layout Standard
12525 is not suitable to frame displayed formulas because the formula will always
12526 be set in the size of the text.
12533 is in contrary not suitable to frame inline formulas, because the formula
12534 will always be set in the size of a displayed formula.
12537 \begin_layout Standard
12544 there is the command
12554 \begin_layout Plain Layout
12562 where additionally the frame width and the alignment can be specified.
12569 is used in the following scheme:
12572 \begin_layout Standard
12577 framebox[frame width][position]{box content}
12580 \begin_layout Standard
12581 The position can either be
12598 right aligns the formula in the box.
12599 When no position is given, the formula will be centered.
12600 \begin_inset Newline newline
12603 Is no width given, also no position can be given.
12604 In this case the frame width is adjusted to the box content like for
12613 \begin_layout Standard
12620 is inserted, a box appears containing three blue boxes.
12621 The first two boxes are surrounded by brackets and denote the two optional
12623 The third box is for formula parts like for
12632 \begin_layout Standard
12634 \begin_inset Tabular
12635 <lyxtabular version="3" rows="5" columns="2">
12637 <column alignment="center" valignment="top" width="0">
12638 <column alignment="center" valignment="top" width="0">
12640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12643 \begin_layout Plain Layout
12649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12652 \begin_layout Plain Layout
12654 \begin_inset Note Note
12657 \begin_layout Plain Layout
12664 is only used as spacer.
12676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12679 \begin_layout Plain Layout
12686 \begin_layout Plain Layout
12705 \begin_layout Plain Layout
12719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12722 \begin_layout Plain Layout
12723 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12736 \begin_layout Plain Layout
12743 \begin_layout Plain Layout
12758 \begin_layout Plain Layout
12772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12775 \begin_layout Plain Layout
12776 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12789 \begin_layout Plain Layout
12796 \begin_layout Plain Layout
12810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12813 \begin_layout Plain Layout
12814 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12827 \begin_layout Plain Layout
12834 \begin_layout Plain Layout
12844 \begin_inset Formula $\to$
12848 \begin_inset Formula $\to$
12861 \begin_layout Plain Layout
12871 \begin_inset Formula $\downarrow$
12879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12882 \begin_layout Plain Layout
12883 \begin_inset Formula $\raisebox{6mm}{}$
12887 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12891 \begin_inset Formula $\raisebox{-4mm}{}$
12907 \begin_layout Standard
12908 The frame thickness can also be adjusted.
12909 To do this the following commands have to be inserted in TeX-mode before
12913 \begin_layout Standard
12923 \begin_inset Quotes eld
12927 \begin_inset Quotes erd
12941 \begin_inset Quotes eld
12945 \begin_inset Quotes erd
12951 \begin_layout Standard
12952 \begin_inset Quotes eld
12956 \begin_inset Quotes erd
12959 specifies the minimal distance between the frame and the first character
12961 An example for this is the following framed formula:
12965 \begin_layout Plain Layout
12977 \begin_inset Formula \[
12982 Before this formula the commands
12985 \begin_layout Standard
13007 \begin_layout Standard
13008 were inserted in TeX-mode.
13009 The given values are used for all following boxes.
13012 \begin_layout Standard
13013 To return to the standard frame size, the command
13016 \begin_layout Standard
13041 \begin_layout Plain Layout
13055 \begin_layout Standard
13056 is inserted in TeX-mode before the next formula.
13059 \begin_layout Subsection
13060 Boxes without Frame
13061 \begin_inset CommandInset label
13063 name "sub:Boxes-without-Frame"
13071 \begin_layout Plain Layout
13072 Boxes ! without frame
13080 \begin_layout Standard
13081 For boxes without a frame there are the following box commands:
13091 \begin_layout Plain Layout
13109 \begin_layout Plain Layout
13127 \begin_layout Plain Layout
13138 \begin_layout Standard
13145 a box can be super- or subscripted.
13146 But in contrary to normal super- and subscripting, the characters in the
13147 box keep their font size.
13154 is used in the following scheme:
13157 \begin_layout Standard
13162 raisebox{height}{box content}
13165 \begin_layout Standard
13166 When the box should contain a formula, an extra formula is needed like for
13177 \begin_inset Note Greyedout
13180 \begin_layout Plain Layout
13191 this extra formula is created by pressing
13195 twice instead of once because LyX doesn't yet support
13209 \begin_layout Standard
13211 \begin_inset Tabular
13212 <lyxtabular version="3" rows="4" columns="2">
13214 <column alignment="center" valignment="top" width="0">
13215 <column alignment="center" valignment="top" width="0">
13217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13220 \begin_layout Plain Layout
13226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13229 \begin_layout Plain Layout
13237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13240 \begin_layout Plain Layout
13244 \begin_inset Formula $\to$
13250 \begin_inset Formula $\to$
13258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13261 \begin_layout Plain Layout
13262 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13275 \begin_layout Plain Layout
13279 \begin_inset Formula $\to$
13285 \begin_inset Formula $\to$
13293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13296 \begin_layout Plain Layout
13297 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13310 \begin_layout Plain Layout
13314 \begin_inset Formula $\to$
13333 \begin_layout Plain Layout
13347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13350 \begin_layout Plain Layout
13351 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13367 \begin_layout Standard
13392 , with the difference that there is no frame.
13395 \begin_layout Subsection
13397 \begin_inset CommandInset label
13399 name "sub:Colored-Boxes"
13407 \begin_layout Plain Layout
13416 \begin_layout Standard
13417 To be able to use all commands explained in this section, the LaTeX-package
13426 \begin_layout Plain Layout
13431 is part of every LaTeX standard installation.
13440 \begin_layout Plain Layout
13446 has to be loaded in the LaTeX-preamble with the line
13450 \begin_layout Plain Layout
13451 When text is colored somewhere in the document with a predefined color,
13452 LyX loads the LaTeX-package
13457 Thus it is possible that the package is loaded twice, but this doesn't
13464 \begin_inset Note Note
13467 \begin_layout Plain Layout
13468 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13477 \begin_layout Standard
13485 \begin_layout Standard
13486 \begin_inset VSpace medskip
13489 To color boxes, the command
13499 \begin_layout Plain Layout
13507 is used in the following scheme:
13510 \begin_layout Standard
13515 colorbox{color}{box content}
13518 \begin_layout Standard
13519 The box content can also be a box and a
13525 can also be part of another box (see the 2nd and 3rd example).
13526 When the box should contain a formula, an extra formula has to be created,
13527 the same way as for
13537 \begin_layout Plain Layout
13538 This also applies for the command
13552 \begin_layout Standard
13553 One of the following predefined colors can be chosen:
13556 \begin_layout Standard
13590 \begin_layout Standard
13592 \begin_inset Tabular
13593 <lyxtabular version="3" rows="4" columns="2">
13595 <column alignment="center" valignment="top" width="0">
13596 <column alignment="center" valignment="top" width="0">
13598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13601 \begin_layout Plain Layout
13607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13610 \begin_layout Plain Layout
13612 \begin_inset Note Note
13615 \begin_layout Plain Layout
13622 is only used as spacer.
13634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13637 \begin_layout Plain Layout
13641 \begin_inset Formula $\to$
13651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13654 \begin_layout Plain Layout
13655 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13668 \begin_layout Plain Layout
13672 \begin_inset Formula $\to$
13683 \begin_layout Plain Layout
13697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13700 \begin_layout Plain Layout
13701 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13714 \begin_layout Plain Layout
13721 \begin_layout Plain Layout
13733 \begin_inset Formula $\to$
13752 \begin_layout Plain Layout
13766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13769 \begin_layout Plain Layout
13770 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13786 \begin_layout Standard
13793 only colors the box but not the characters in the box.
13794 To color all characters, the whole formula is highlighted and the wanted
13795 color is chosen in the
13798 \begin_inset space ~
13804 The dialog can be called with the toolbar button
13805 \begin_inset Graphics
13806 filename ../images/dialog-show_character.png
13813 Edit\SpecialChar \menuseparator
13815 \begin_inset space ~
13818 Style\SpecialChar \menuseparator
13822 The formula number has then the same color as the formula.
13823 When the formula number should get another color than the formula characters,
13824 the color must be changed within the formula.
13827 \begin_layout Standard
13831 \begin_layout Standard
13834 \begin_inset Formula \begin{equation}
13835 \int A=B\label{eq:red}\end{equation}
13842 \begin_inset Formula \begin{equation}
13843 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13850 \begin_layout Standard
13852 \begin_inset CommandInset ref
13858 is completely colored red.
13859 \begin_inset Newline newline
13863 \begin_inset CommandInset ref
13865 reference "eq:redgreen"
13869 was first completely colored green to set the color for the formula number.
13870 Subsequently the formula characters were colored red.
13873 \begin_layout Standard
13874 \begin_inset VSpace bigskip
13877 To color the frame different than the rest of the box, the command
13887 \begin_layout Plain Layout
13895 is used in the following scheme:
13898 \begin_layout Standard
13903 fcolorbox{frame color}{color}{box content}
13906 \begin_layout Standard
13913 is an extension of the command
13920 The frame width is set, like for
13943 \begin_layout Plain Layout
13955 \begin_inset Formula \[
13956 \fcolorbox{cyan}{magenta}{A=B}\]
13964 \begin_layout Plain Layout
13978 \begin_layout Standard
13979 This formula was created with the command
13980 \begin_inset Newline newline
13988 \begin_inset Formula $\to$
13994 \begin_inset Formula $\to$
14004 \begin_layout Standard
14005 \begin_inset VSpace bigskip
14008 To use other colors than the predefined ones, they have to be defined first.
14011 \begin_layout Standard
14012 One can for example define the color
14013 \begin_inset Quotes eld
14021 \begin_inset Quotes erd
14024 with the LaTeX-preamble line:
14027 \begin_layout Standard
14032 definecolor{darkgreen}{cmyk}{0.5,
14050 \begin_layout Plain Layout
14061 \begin_layout Standard
14066 is the color space that denotes the colors
14083 The four comma separated numbers are the portion factor for the corresponding
14084 colors of the color space.
14085 The factors can be in the range of 0
14086 \begin_inset space \thinspace{}
14090 \begin_inset space \thinspace{}
14098 also the color space
14102 can be used for definitions.
14119 , so that there are in this case three portion factors for the corresponding
14121 Furthermore there is the color space
14125 with one portion factor for the gray value.
14128 \begin_layout Standard
14129 As example a framed box with the new defined color
14133 where the characters have been colored
14138 \begin_inset Formula \begin{equation}
14139 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14146 \begin_layout Standard
14147 Self-defined colors can also be used for text with the help of the command
14158 \begin_layout Plain Layout
14167 \begin_layout Standard
14171 \begin_layout Plain Layout
14175 textcolor{darkgreen}{
14181 \begin_inset Quotes eld
14185 \begin_inset Quotes erd
14192 \begin_layout Plain Layout
14202 \begin_layout Standard
14213 \begin_layout Plain Layout
14221 is used in the scheme
14225 textcolor{color}{characters to color}
14230 \begin_layout Subsection
14232 \begin_inset CommandInset label
14234 name "sub:Paragraph-Boxes"
14242 \begin_layout Plain Layout
14243 Boxes ! as paragraph
14251 \begin_layout Standard
14252 A box that can contain several lines and paragraphs, a so called paragraph
14253 box (parbox), can be created with the menu
14255 Insert\SpecialChar \menuseparator
14258 or the toolbar button
14259 \begin_inset Graphics
14260 filename ../images/box-insert.png
14268 \begin_layout Standard
14269 The following example shows a framed parbox in a line:
14272 \begin_layout Standard
14273 \begin_inset VSpace medskip
14277 \begin_inset Box Boxed
14286 height_special "totalheight"
14289 \begin_layout Plain Layout
14290 This is a paragraph box.
14292 \begin_inset space \thinspace{}
14295 cm long and can also contain formulas:
14296 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14307 \begin_layout Standard
14308 \begin_inset VSpace medskip
14314 \begin_layout Standard
14315 Such a box is created by right-clicking on the gray box inset.
14316 A dialog pops up showing the box properties.
14330 \begin_inset space \thinspace{}
14335 Vertical Box Alignment
14340 \begin_layout Standard
14341 \begin_inset VSpace medskip
14344 In LaTeX a parbox is created with the command
14354 \begin_layout Plain Layout
14362 that has the following scheme:
14365 \begin_layout Standard
14370 parbox[position]{width}{box content}
14373 \begin_layout Standard
14387 for bottom means that the box is aligned within the surrounding text with
14393 for top this is done with the first line.
14394 When no position is given, the box will be vertically centered, see section
14402 \begin_inset space ~
14407 manual for examples.
14410 \begin_layout Standard
14411 \begin_inset VSpace bigskip
14414 To frame formulas completely, including the formula number, the formula
14415 must be set into a parbox.
14416 To do this, the command
14430 is inserted in TeX-mode before the formula.
14439 \begin_layout Plain Layout
14449 is hereby the line width set for the document.
14450 Because the frame is outside the parbox, 2
14451 \begin_inset space \thinspace{}
14454 times the frame separation and the frame thickness must be subtracted from
14456 As this is not automatically done by LyX due to a bug
14460 \begin_layout Plain Layout
14461 \begin_inset CommandInset href
14463 name "LyX-bug #4483"
14464 target "http://www.lyx.org/trac/ticket/4483"
14473 , TeX-mode has to be used.
14474 To be able to multiply and subtract in arguments, the LaTeX-package
14482 \begin_layout Plain Layout
14487 is part of every LaTeX standard installation.
14496 \begin_layout Plain Layout
14502 must be loaded in the LaTeX-preamble with the line
14505 \begin_layout Standard
14513 \begin_layout Standard
14514 Behind the formula both boxes are closed by entering
14519 Here is an example:
14523 \begin_layout Plain Layout
14537 \begin_layout Standard
14541 \begin_layout Plain Layout
14559 \begin_inset Formula \begin{equation}
14560 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14568 \begin_layout Plain Layout
14579 \begin_layout Plain Layout
14593 \begin_layout Standard
14594 \begin_inset VSpace medskip
14597 As a parbox is used as argument of
14603 , there is in this case no difference between
14618 \begin_layout Standard
14619 \begin_inset VSpace bigskip
14622 Paragraph boxes are very useful to comment formulas directly.
14629 is used in combination with the command
14643 \begin_inset CommandInset ref
14645 reference "sub:User-defined-Numbering"
14652 \begin_layout Standard
14653 An example of a formula commented with
14662 \begin_layout Standard
14666 \begin_layout Plain Layout
14679 This is a description.
14680 It is distinctly separated from the formula and multiline.
14684 \begin_layout Plain Layout
14696 \begin_layout Standard
14697 Such a formula must be inserted completely in TeX-mode because LyX does
14698 not yet support the command
14705 The formula is created with the following command sequence:
14708 \begin_layout Standard
14721 is inserted in TeX-mode.
14725 \begin_layout Plain Layout
14726 When the formula style
14738 can also be replaced by
14745 (formula styles see
14746 \begin_inset CommandInset ref
14748 reference "sec:Formula-Styles"
14757 Then the description follows as normal text, and finally
14763 is inserted in TeX-mode.
14776 hereby create a displayed formula.
14779 \begin_layout Standard
14786 can be seen in this example that was
14787 \begin_inset Quotes eld
14791 \begin_inset Quotes erd
14794 using the mathematical textmode:
14795 \begin_inset Formula \[
14796 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14803 \begin_layout Section
14808 \begin_layout Plain Layout
14817 \begin_layout Subsection
14819 \begin_inset CommandInset label
14821 name "sub:Big-Operators"
14829 \begin_layout Plain Layout
14839 \begin_layout Plain Layout
14849 \begin_layout Plain Layout
14858 \begin_layout Standard
14859 To be able to use all integral operators listed here, the option
14861 Use esint package automatically
14863 must be set in the document settings under
14866 \begin_inset space ~
14874 \begin_layout Standard
14875 \begin_inset space \hfill{}
14879 \begin_inset Tabular
14880 <lyxtabular version="3" rows="11" columns="2">
14882 <column alignment="center" valignment="top" width="0pt">
14883 <column alignment="center" valignment="top" width="0pt">
14885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14888 \begin_layout Plain Layout
14894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14897 \begin_layout Plain Layout
14905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14908 \begin_layout Plain Layout
14915 \begin_layout Plain Layout
14928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14931 \begin_layout Plain Layout
14932 \begin_inset Formula $\int$
14942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14945 \begin_layout Plain Layout
14953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14956 \begin_layout Plain Layout
14957 \begin_inset Formula $\oint$
14967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14970 \begin_layout Plain Layout
14978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14981 \begin_layout Plain Layout
14982 \begin_inset Formula $\ointctrclockwise$
14992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14995 \begin_layout Plain Layout
15003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15006 \begin_layout Plain Layout
15007 \begin_inset Formula $\ointclockwise$
15017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15020 \begin_layout Plain Layout
15028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15031 \begin_layout Plain Layout
15032 \begin_inset Formula $\sqint$
15042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15045 \begin_layout Plain Layout
15053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15056 \begin_layout Plain Layout
15058 \begin_inset Formula $\fint$
15068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15071 \begin_layout Plain Layout
15079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15082 \begin_layout Plain Layout
15084 \begin_inset Formula $\landupint$
15094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15097 \begin_layout Plain Layout
15105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15108 \begin_layout Plain Layout
15110 \begin_inset Formula $\landdownint$
15120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15123 \begin_layout Plain Layout
15131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15134 \begin_layout Plain Layout
15135 \begin_inset Formula $\bigcap$
15145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15148 \begin_layout Plain Layout
15156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15159 \begin_layout Plain Layout
15160 \begin_inset Formula $\bigcup$
15174 \begin_inset space \hfill{}
15178 \begin_inset Tabular
15179 <lyxtabular version="3" rows="11" columns="2">
15181 <column alignment="center" valignment="top" width="0pt">
15182 <column alignment="center" valignment="top" width="0pt">
15184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15187 \begin_layout Plain Layout
15193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15196 \begin_layout Plain Layout
15204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15207 \begin_layout Plain Layout
15214 \begin_layout Plain Layout
15227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15230 \begin_layout Plain Layout
15231 \begin_inset Formula $\sum$
15241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15244 \begin_layout Plain Layout
15251 \begin_layout Plain Layout
15264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15267 \begin_layout Plain Layout
15268 \begin_inset Formula $\prod$
15278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15281 \begin_layout Plain Layout
15289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15292 \begin_layout Plain Layout
15293 \begin_inset Formula $\coprod$
15303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15306 \begin_layout Plain Layout
15314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15317 \begin_layout Plain Layout
15318 \begin_inset Formula $\bigodot$
15328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15331 \begin_layout Plain Layout
15339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15342 \begin_layout Plain Layout
15343 \begin_inset Formula $\bigotimes$
15353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15356 \begin_layout Plain Layout
15364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15367 \begin_layout Plain Layout
15368 \begin_inset Formula $\bigoplus$
15378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15381 \begin_layout Plain Layout
15389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15392 \begin_layout Plain Layout
15393 \begin_inset Formula $\bigwedge$
15403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15406 \begin_layout Plain Layout
15414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15417 \begin_layout Plain Layout
15418 \begin_inset Formula $\bigvee$
15428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15431 \begin_layout Plain Layout
15439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15442 \begin_layout Plain Layout
15443 \begin_inset Formula $\bigsqcup$
15453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15456 \begin_layout Plain Layout
15464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15467 \begin_layout Plain Layout
15468 \begin_inset Formula $\biguplus$
15482 \begin_inset space \hfill{}
15488 \begin_layout Standard
15489 All big operators can also be inserted via the math toolbar button
15490 \begin_inset Graphics
15491 filename ../images/math/intop.png
15499 \begin_layout Standard
15500 The operators are called big because they are bigger than the sometimes
15501 equal looking binary operators.
15502 All big operators can have limits as described in the next subsection.
15505 \begin_layout Standard
15506 For all integral operators there is a second version available, ending on
15524 These operators are different from
15531 \begin_inset space \space{}
15534 in the style the operator limits are displayed, see
15535 \begin_inset CommandInset ref
15537 reference "sub:Operator-Limits"
15545 \begin_layout Subsubsection*
15546 Advice for Integrals
15549 \begin_layout Standard
15554 in an integral is an operator, that therefore has to be set upright.
15555 This is done by highlighting the
15559 and using the keyboard shortcut
15569 \begin_layout Plain Layout
15575 \begin_inset CommandInset ref
15577 reference "sub:Font-Styles"
15587 Finally the smallest space is inserted before the
15591 , as this is usual for operators.
15595 \begin_layout Standard
15597 \begin_inset Formula $\int A(x)dx$
15601 \begin_inset Newline newline
15608 \begin_layout Plain Layout
15618 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15624 \begin_layout Standard
15625 For multiple integrals there are the following commands:
15626 \begin_inset VSpace medskip
15632 \begin_layout Standard
15633 \begin_inset space \hfill{}
15637 \begin_inset Tabular
15638 <lyxtabular version="3" rows="4" columns="2">
15640 <column alignment="center" valignment="top" width="0">
15641 <column alignment="center" valignment="top" width="0">
15643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15646 \begin_layout Plain Layout
15652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15655 \begin_layout Plain Layout
15657 \begin_inset Note Note
15660 \begin_layout Plain Layout
15667 is only used as spacer.
15679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15682 \begin_layout Plain Layout
15690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15693 \begin_layout Plain Layout
15694 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15707 \begin_layout Plain Layout
15715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15718 \begin_layout Plain Layout
15719 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15732 \begin_layout Plain Layout
15740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15743 \begin_layout Plain Layout
15744 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15758 \begin_inset space \hfill{}
15762 \begin_inset Tabular
15763 <lyxtabular version="3" rows="4" columns="2">
15765 <column alignment="center" valignment="top" width="0">
15766 <column alignment="center" valignment="top" width="0">
15768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15771 \begin_layout Plain Layout
15777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15780 \begin_layout Plain Layout
15788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15791 \begin_layout Plain Layout
15799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15802 \begin_layout Plain Layout
15803 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15816 \begin_layout Plain Layout
15824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15827 \begin_layout Plain Layout
15828 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15841 \begin_layout Plain Layout
15849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15852 \begin_layout Plain Layout
15853 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15867 \begin_inset space \hfill{}
15873 \begin_layout Subsection
15875 \begin_inset CommandInset label
15877 name "sub:Operator-Limits"
15885 \begin_layout Plain Layout
15894 \begin_layout Standard
15895 Limits are created by super- and subscripts:
15898 \begin_layout Standard
15900 \begin_inset Tabular
15901 <lyxtabular version="3" rows="2" columns="2">
15903 <column alignment="center" valignment="top" width="0pt">
15904 <column alignment="center" valignment="top" width="0pt">
15906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15909 \begin_layout Plain Layout
15915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15918 \begin_layout Plain Layout
15920 \begin_inset Note Note
15923 \begin_layout Plain Layout
15930 is only used as spacer.
15942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15945 \begin_layout Plain Layout
15954 \begin_layout Plain Layout
15964 \begin_inset Formula $\to$
15968 \begin_inset Formula $\to$
15976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15979 \begin_layout Plain Layout
15980 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15996 \begin_layout Standard
15997 Limits of inline formulas are set right beside the operator.
15998 Limits in displayed formulas are set above or below the operator, except
15999 for integral limits.
16002 \begin_layout Standard
16003 To force that the limits are set beside the operator, the cursor is set
16004 directly behind the operator and the limits type is changed with the menu
16007 Edit\SpecialChar \menuseparator
16008 Math\SpecialChar \menuseparator
16027 \begin_layout Standard
16028 The default limits type is this:
16029 \begin_inset Formula \[
16030 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16034 This is how it looks when the limits type was changed to
16041 \begin_inset Formula \[
16042 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16046 For integrals, except those ending with
16062 etc., the limits are by default set beside the operator.
16063 But for multiple integrals the limits are often set below the operator.
16064 In the following example the limits type was therefore set to
16068 and so set below the integrals:
16069 \begin_inset Formula \begin{equation}
16070 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16077 \begin_layout Standard
16078 \begin_inset VSpace medskip
16081 To specify conditions for limits, the commands
16091 \begin_layout Plain Layout
16109 \begin_layout Plain Layout
16118 To create for example this expression
16119 \begin_inset Formula \begin{equation}
16120 \sum_{\begin{subarray}{c}
16122 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16129 \begin_layout Standard
16130 the following has to be done:
16131 \begin_inset Newline newline
16146 \begin_layout Plain Layout
16158 One is now in a blue box under the summation operator and insert there
16167 \begin_layout Plain Layout
16179 The blue box is now within a purple box and now several lines can be written
16181 A new line is created by inserting a line break (
16184 arg "newline-insert newline"
16189 \begin_inset Newline newline
16194 0<k<1000 Ctrl+Return
16195 \begin_inset Newline newline
16200 is typed in, a new box appears below for the new line.
16203 \begin_layout Standard
16204 The alignment of the lines can be changed to left aligned with the
16214 Edit\SpecialChar \menuseparator
16218 To get right alignment,
16226 \begin_layout Plain Layout
16237 is inserted at the beginning of the line.
16240 \begin_layout Standard
16253 with the difference that the lines are always centered.
16256 \begin_layout Standard
16257 \begin_inset VSpace bigskip
16261 \begin_inset CommandInset ref
16263 reference "eq:substack"
16267 there can be too much space beside an operator, because the characters
16268 following the operator are set beside the limits.
16271 \begin_layout Standard
16272 To avoid this, the following macro can be used in the LaTeX-preamble:
16275 \begin_layout Standard
16289 \begin_inset Newline newline
16301 \begin_inset Newline newline
16308 mathclapinternal #1#2{
16312 mathsurround =0pt #1{#2}$}}
16315 \begin_layout Standard
16316 This defines the command
16326 \begin_layout Plain Layout
16334 that sets the width of the limit to 0
16335 \begin_inset space \thinspace{}
16339 The command scheme is
16342 \begin_layout Standard
16350 \begin_layout Standard
16351 where the limit can consist of several conditions.
16354 \begin_layout Standard
16356 \begin_inset CommandInset ref
16358 reference "eq:substack"
16362 , one uses the command
16365 \begin_layout Standard
16378 \begin_layout Plain Layout
16387 0<k<1000 Ctrl+Return
16390 \begin_layout Standard
16391 to create the lower limit.
16392 The summand is now directly behind the summation operator:
16393 \begin_inset Formula \[
16394 \sum_{\mathclap{\substack{0<k<1000\\
16395 \\k\,\in\,\mathbb{N}}
16403 \begin_layout Standard
16404 \begin_inset VSpace bigskip
16407 How to use one limit for several operators is described in
16408 \begin_inset CommandInset ref
16410 reference "sub:Self-defined-Operators"
16417 \begin_layout Subsection
16419 \begin_inset CommandInset label
16421 name "sub:Binary-Operators"
16429 \begin_layout Plain Layout
16438 \begin_layout Standard
16439 Binary operators are surrounded by space when there is a character before
16441 \begin_inset VSpace medskip
16447 \begin_layout Standard
16448 \begin_inset space \hfill{}
16452 \begin_inset Tabular
16453 <lyxtabular version="3" rows="13" columns="2">
16455 <column alignment="center" valignment="top" width="0pt">
16456 <column alignment="center" valignment="top" width="0pt">
16458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16461 \begin_layout Plain Layout
16463 \begin_inset Note Note
16466 \begin_layout Plain Layout
16473 is only used as spacer.
16483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16486 \begin_layout Plain Layout
16494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16497 \begin_layout Plain Layout
16503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16506 \begin_layout Plain Layout
16507 \begin_inset Formula $+$
16517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16520 \begin_layout Plain Layout
16526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16529 \begin_layout Plain Layout
16530 \begin_inset Formula $-$
16540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16543 \begin_layout Plain Layout
16551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16554 \begin_layout Plain Layout
16555 \begin_inset Formula $\pm$
16565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16568 \begin_layout Plain Layout
16576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16579 \begin_layout Plain Layout
16580 \begin_inset Formula $\mp$
16590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16593 \begin_layout Plain Layout
16601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16604 \begin_layout Plain Layout
16605 \begin_inset Formula $\cdot$
16615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16618 \begin_layout Plain Layout
16626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16629 \begin_layout Plain Layout
16630 \begin_inset Formula $\times$
16640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16643 \begin_layout Plain Layout
16651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16654 \begin_layout Plain Layout
16655 \begin_inset Formula $\div$
16665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16668 \begin_layout Plain Layout
16672 \begin_layout Plain Layout
16685 \begin_layout Plain Layout
16697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16700 \begin_layout Plain Layout
16701 \begin_inset Formula $*$
16711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16714 \begin_layout Plain Layout
16722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16725 \begin_layout Plain Layout
16726 \begin_inset Formula $\star$
16736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16739 \begin_layout Plain Layout
16747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16750 \begin_layout Plain Layout
16751 \begin_inset Formula $\circ$
16761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16764 \begin_layout Plain Layout
16772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16775 \begin_layout Plain Layout
16776 \begin_inset Formula $\diamond$
16786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16789 \begin_layout Plain Layout
16797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16800 \begin_layout Plain Layout
16801 \begin_inset Formula $\bullet$
16815 \begin_inset space \hfill{}
16819 \begin_inset Tabular
16820 <lyxtabular version="3" rows="13" columns="2">
16822 <column alignment="center" valignment="top" width="0pt">
16823 <column alignment="center" valignment="top" width="0pt">
16825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16828 \begin_layout Plain Layout
16834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16837 \begin_layout Plain Layout
16845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16848 \begin_layout Plain Layout
16856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16859 \begin_layout Plain Layout
16860 \begin_inset Formula $\nabla$
16870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16873 \begin_layout Plain Layout
16881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16884 \begin_layout Plain Layout
16885 \begin_inset Formula $\bigtriangledown$
16895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16898 \begin_layout Plain Layout
16906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16909 \begin_layout Plain Layout
16910 \begin_inset Formula $\bigtriangleup$
16920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16923 \begin_layout Plain Layout
16931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16934 \begin_layout Plain Layout
16935 \begin_inset Formula $\Box$
16945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16948 \begin_layout Plain Layout
16956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16959 \begin_layout Plain Layout
16960 \begin_inset Formula $\cap$
16970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16973 \begin_layout Plain Layout
16981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16984 \begin_layout Plain Layout
16985 \begin_inset Formula $\cup$
16995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16998 \begin_layout Plain Layout
17006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17009 \begin_layout Plain Layout
17010 \begin_inset Formula $\dagger$
17020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17023 \begin_layout Plain Layout
17031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17034 \begin_layout Plain Layout
17035 \begin_inset Formula $\ddagger$
17045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17048 \begin_layout Plain Layout
17056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17059 \begin_layout Plain Layout
17060 \begin_inset Formula $\wr$
17070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17073 \begin_layout Plain Layout
17081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17084 \begin_layout Plain Layout
17085 \begin_inset Formula $\bigcirc$
17095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17098 \begin_layout Plain Layout
17106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17109 \begin_layout Plain Layout
17110 \begin_inset Formula $\wedge$
17120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17123 \begin_layout Plain Layout
17131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17134 \begin_layout Plain Layout
17135 \begin_inset Formula $\vee$
17149 \begin_inset space \hfill{}
17153 \begin_inset Tabular
17154 <lyxtabular version="3" rows="13" columns="2">
17156 <column alignment="center" valignment="top" width="0pt">
17157 <column alignment="center" valignment="top" width="0pt">
17159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17162 \begin_layout Plain Layout
17168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17171 \begin_layout Plain Layout
17179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17182 \begin_layout Plain Layout
17190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17193 \begin_layout Plain Layout
17194 \begin_inset Formula $\oplus$
17204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17207 \begin_layout Plain Layout
17215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17218 \begin_layout Plain Layout
17219 \begin_inset Formula $\ominus$
17229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17232 \begin_layout Plain Layout
17240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17243 \begin_layout Plain Layout
17244 \begin_inset Formula $\otimes$
17254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17257 \begin_layout Plain Layout
17265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17268 \begin_layout Plain Layout
17269 \begin_inset Formula $\oslash$
17279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17282 \begin_layout Plain Layout
17290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17293 \begin_layout Plain Layout
17294 \begin_inset Formula $\odot$
17304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17307 \begin_layout Plain Layout
17315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17318 \begin_layout Plain Layout
17319 \begin_inset Formula $\amalg$
17329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17332 \begin_layout Plain Layout
17340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17343 \begin_layout Plain Layout
17344 \begin_inset Formula $\uplus$
17354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17357 \begin_layout Plain Layout
17365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17368 \begin_layout Plain Layout
17369 \begin_inset Formula $\setminus$
17379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17382 \begin_layout Plain Layout
17390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17393 \begin_layout Plain Layout
17394 \begin_inset Formula $\sqcap$
17404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17407 \begin_layout Plain Layout
17415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17418 \begin_layout Plain Layout
17419 \begin_inset Formula $\sqcup$
17429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17432 \begin_layout Plain Layout
17440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17443 \begin_layout Plain Layout
17444 \begin_inset Formula $\triangleleft$
17454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17457 \begin_layout Plain Layout
17465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17468 \begin_layout Plain Layout
17469 \begin_inset Formula $\triangleright$
17483 \begin_inset space \hfill{}
17489 \begin_layout Standard
17490 All binary operators can also be inserted via the math toolbar button
17491 \begin_inset Graphics
17492 filename ../images/math/pm.png
17500 \begin_layout Standard
17501 To typeset the Laplace operator also
17518 \begin_inset Formula $\nabla^{2}$
17521 ) can be used instead of
17530 \begin_layout Standard
17537 Insert\SpecialChar \menuseparator
17549 \begin_layout Subsection
17550 Self-defined Operators
17551 \begin_inset CommandInset label
17553 name "sub:Self-defined-Operators"
17561 \begin_layout Plain Layout
17562 Operators ! self-defined
17570 \begin_layout Standard
17571 With the help of the command
17575 DeclareMathOperator
17581 \begin_layout Plain Layout
17586 DeclareMathOperator
17591 custom operators can be defined in the LaTeX-preamble.
17592 Its command scheme is:
17595 \begin_layout Standard
17600 DeclareMathOperator{new command}{display}
17603 \begin_layout Standard
17604 Display can be characters or symbols that define how the operator looks
17606 To define a big operator a * is set behind the command.
17607 All self-defined big operators can have limits as described in
17608 \begin_inset CommandInset ref
17610 reference "sub:Operator-Limits"
17617 \begin_layout Standard
17618 For example the LaTeX-preamble line
17621 \begin_layout Standard
17626 DeclareMathOperator*{
17633 \begin_layout Standard
17634 defines the command
17640 , that inserts a big operator consisting of the lozenge symbol from
17641 \begin_inset CommandInset ref
17643 reference "sub:Miscellaneous-Symbols"
17648 \begin_inset Formula \[
17649 \Lozenge_{n=1}^{\infty}\]
17653 The command for this formula is:
17664 \begin_inset Formula $\to$
17670 \begin_layout Standard
17671 \begin_inset VSpace bigskip
17674 When self-defined operators are not used several times in the document,
17675 they can also be defined with the commands
17685 \begin_layout Plain Layout
17703 \begin_layout Plain Layout
17711 , which have the following scheme:
17714 \begin_layout Standard
17728 \begin_layout Standard
17735 defines big operators,
17744 \begin_layout Standard
17752 \begin_inset space \thinspace{}
17756 \begin_inset space \space{}
17759 be used to use one limit for several operators:
17762 \begin_layout Standard
17763 \begin_inset Formula \[
17764 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17771 \begin_layout Standard
17772 The command for the formula above is:
17773 \begin_inset Newline newline
17792 \begin_layout Plain Layout
17804 \begin_inset Formula $\to$
17813 \begin_layout Plain Layout
17827 \begin_layout Section
17832 \begin_layout Plain Layout
17841 \begin_layout Subsection
17843 \begin_inset CommandInset label
17845 name "sub:Font-Styles"
17853 \begin_layout Plain Layout
17862 \begin_layout Standard
17863 Latin letters in formulas can be set in one of the following font styles:
17864 \begin_inset VSpace -2mm
17870 \begin_layout Standard
17872 \begin_inset Tabular
17873 <lyxtabular version="3" rows="6" columns="3">
17875 <column alignment="center" valignment="top" width="0">
17876 <column alignment="center" valignment="top" width="0">
17877 <column alignment="center" valignment="top" width="0">
17879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17882 \begin_layout Plain Layout
17888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17891 \begin_layout Plain Layout
17897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17900 \begin_layout Plain Layout
17908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17911 \begin_layout Plain Layout
17920 \begin_layout Plain Layout
17936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17939 \begin_layout Plain Layout
17940 \begin_inset Formula $\mathbb{ABC}$
17948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17951 \begin_layout Plain Layout
17964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17967 \begin_layout Plain Layout
17976 \begin_layout Plain Layout
17992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17995 \begin_layout Plain Layout
17996 \begin_inset Formula $\mathbf{AbC}$
18004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18007 \begin_layout Plain Layout
18020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18023 \begin_layout Plain Layout
18032 \begin_layout Plain Layout
18048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18051 \begin_layout Plain Layout
18052 \begin_inset Formula $\boldsymbol{AbC}$
18060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18063 \begin_layout Plain Layout
18066 arg "font-boldsymbol"
18076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18079 \begin_layout Plain Layout
18088 \begin_layout Plain Layout
18104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18107 \begin_layout Plain Layout
18108 \begin_inset Formula $\mathcal{ABC}$
18116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18119 \begin_layout Plain Layout
18132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18135 \begin_layout Plain Layout
18144 \begin_layout Plain Layout
18160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18163 \begin_layout Plain Layout
18164 \begin_inset Formula $\mathfrak{AbC}$
18172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18175 \begin_layout Plain Layout
18189 \begin_layout Standard
18191 \begin_inset Tabular
18192 <lyxtabular version="3" rows="5" columns="3">
18194 <column alignment="center" valignment="top" width="0">
18195 <column alignment="center" valignment="top" width="0">
18196 <column alignment="center" valignment="top" width="0">
18198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18201 \begin_layout Plain Layout
18207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18210 \begin_layout Plain Layout
18216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18219 \begin_layout Plain Layout
18227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18230 \begin_layout Plain Layout
18239 \begin_layout Plain Layout
18255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18258 \begin_layout Plain Layout
18259 \begin_inset Formula $\mathit{AbC}$
18267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18270 \begin_layout Plain Layout
18278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18281 \begin_layout Plain Layout
18290 \begin_layout Plain Layout
18306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18309 \begin_layout Plain Layout
18310 \begin_inset Formula $\mathrm{AbC}$
18318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18321 \begin_layout Plain Layout
18334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18337 \begin_layout Plain Layout
18346 \begin_layout Plain Layout
18362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18365 \begin_layout Plain Layout
18366 \begin_inset Formula $\mathsf{AbC}$
18374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18377 \begin_layout Plain Layout
18390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18393 \begin_layout Plain Layout
18402 \begin_layout Plain Layout
18418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18421 \begin_layout Plain Layout
18422 \begin_inset Formula $\mathtt{AbC}$
18430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18433 \begin_layout Plain Layout
18436 arg "font-typewriter"
18452 \begin_layout Standard
18453 \begin_inset Note Greyedout
18456 \begin_layout Plain Layout
18473 can only be used for big letters.
18481 \begin_layout Standard
18482 Predefined is the style
18491 \begin_layout Standard
18492 The style commands work also for letters in mathematical constructs:
18493 \begin_inset Formula \[
18494 \mathfrak{A=\frac{b}{C}}\]
18501 \begin_layout Standard
18502 Characters in mathematical text don't appear in a math font style but in
18503 the text font style
18510 That their style can't be set correctly via the text style dialog is a
18515 \begin_layout Plain Layout
18516 \begin_inset CommandInset href
18518 name "LyX-bug #4629"
18519 target "http://www.lyx.org/trac/ticket/4629"
18531 \begin_layout Standard
18532 Instead of the style commands the dialog
18534 Edit\SpecialChar \menuseparator
18535 Math\SpecialChar \menuseparator
18538 or the toolbar button
18539 \begin_inset Graphics
18540 filename ../images/math/font.png
18548 \begin_layout Subsection
18550 \begin_inset CommandInset label
18552 name "sub:Bold-Formulas"
18560 \begin_layout Plain Layout
18569 \begin_layout Standard
18570 To make a complete formula bold, the command
18576 from the previous subsection cannot be used, because it doesn't work for
18577 small Greek letters.
18578 Furthermore it prints Latin letters always upright, like in the following
18582 \begin_layout Standard
18583 \begin_inset Formula \[
18584 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18591 \begin_layout Standard
18592 To display the formula correctly, the command
18599 \begin_inset Formula \[
18600 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18604 It is also possible to set the formula in a
18606 boldmath environment
18609 This environment is created by inserting the command
18617 \begin_layout Plain Layout
18628 To end the environment, the command
18636 \begin_layout Plain Layout
18646 is inserted in TeX-mode.
18650 \begin_layout Plain Layout
18660 \begin_inset Formula \[
18661 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18669 \begin_layout Plain Layout
18681 \begin_layout Subsection
18686 \begin_layout Plain Layout
18695 \begin_layout Standard
18696 Formulas can be colored like normal text: Highlight a formula or a formula
18702 Here is a formula in magenta:
18703 \begin_inset Formula \[
18704 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18711 \begin_layout Standard
18712 You can also define your own colors as described in
18713 \begin_inset CommandInset ref
18715 reference "sub:Colored-Boxes"
18720 They can be used with the TeX code command
18730 \begin_layout Plain Layout
18741 \begin_layout Standard
18746 textcolor{color}{characters or formula}
18749 \begin_layout Standard
18750 The following example was colored completely dark green and partly red:
18753 \begin_layout Standard
18757 \begin_layout Plain Layout
18761 textcolor{darkgreen}{
18767 \begin_inset Formula \[
18768 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18776 \begin_layout Plain Layout
18786 \begin_layout Standard
18787 Due to a bug in LyX only complete formulas can be colored with self-defined
18792 \begin_layout Plain Layout
18793 \begin_inset CommandInset href
18795 name "LyX-bug #5269"
18796 target "http://www.lyx.org/trac/ticket/5269"
18808 \begin_layout Subsection
18810 \begin_inset CommandInset label
18812 name "sub:Font-Sizes"
18820 \begin_layout Plain Layout
18829 \begin_layout Standard
18830 For characters in formulas there are, analog to characters in text, the
18831 following size commands:
18834 \begin_layout Standard
18878 \begin_inset Newline newline
18900 \begin_layout Standard
18901 The size produced by the commands depends on the document font size, that
18902 corresponds with the command
18909 The other commands produce smaller or larger sizes than
18916 The font size can however not exceed a certain value.
18917 Is for example the document font size 12
18918 \begin_inset space \thinspace{}
18927 switches to the same size as
18937 \begin_layout Standard
18938 A size command is inserted in TeX-mode before the formula and sets the size
18939 for all following formula and text characters.
18940 To switch back to the initial size, the command
18946 is inserted behind the formula in TeX-mode.
18949 \begin_layout Standard
18950 Within a formula the size can only be changed for symbols or letters in
18952 To do this, the size command is inserted in mathematical text.
18953 All following characters until the end of the mathematical text or until
18954 another size command will have the selected size.
18956 \begin_inset VSpace -2mm
18962 \begin_layout Standard
18966 \begin_layout Plain Layout
18976 \begin_inset Formula \[
18977 A=\frac{B}{c}\cdot\maltese\]
18982 \begin_inset Formula \[
18983 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18991 \begin_layout Plain Layout
19003 \begin_layout Standard
19004 \begin_inset VSpace medskip
19007 Before both formulas the command
19014 The command for the second formula is:
19015 \begin_inset Newline newline
19026 \begin_layout Plain Layout
19041 \begin_layout Plain Layout
19056 \begin_layout Plain Layout
19071 \begin_layout Plain Layout
19081 \begin_inset Formula $\to$
19085 \begin_inset Formula $\to$
19089 \begin_inset Newline newline
19093 \begin_inset space \hspace*{}
19107 \begin_layout Plain Layout
19122 \begin_layout Plain Layout
19137 \begin_layout Plain Layout
19149 \begin_layout Standard
19150 If a symbol cannot be displayed in different sizes, it will always be displayed
19151 in the default size.
19154 \begin_layout Section
19159 \begin_layout Plain Layout
19168 \begin_layout Standard
19169 All Greek letters can also be inserted via the toolbar button
19170 \begin_inset Graphics
19171 filename ../images/math/alpha.png
19179 \begin_layout Subsection
19184 \begin_layout Plain Layout
19185 Greek letters ! small
19193 \begin_layout Standard
19194 \begin_inset space \hfill{}
19198 \begin_inset Tabular
19199 <lyxtabular version="3" rows="11" columns="2">
19201 <column alignment="center" valignment="top" width="0pt">
19202 <column alignment="center" valignment="top" width="0pt">
19204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19207 \begin_layout Plain Layout
19213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19216 \begin_layout Plain Layout
19224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19227 \begin_layout Plain Layout
19235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19238 \begin_layout Plain Layout
19239 \begin_inset Formula $\alpha$
19249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19252 \begin_layout Plain Layout
19260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19263 \begin_layout Plain Layout
19264 \begin_inset Formula $\beta$
19274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19277 \begin_layout Plain Layout
19285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19288 \begin_layout Plain Layout
19289 \begin_inset Formula $\gamma$
19299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19302 \begin_layout Plain Layout
19310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19313 \begin_layout Plain Layout
19314 \begin_inset Formula $\delta$
19324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19327 \begin_layout Plain Layout
19335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19338 \begin_layout Plain Layout
19339 \begin_inset Formula $\epsilon$
19349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19352 \begin_layout Plain Layout
19360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19363 \begin_layout Plain Layout
19364 \begin_inset Formula $\varepsilon$
19374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19377 \begin_layout Plain Layout
19385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19388 \begin_layout Plain Layout
19389 \begin_inset Formula $\zeta$
19399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19402 \begin_layout Plain Layout
19410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19413 \begin_layout Plain Layout
19414 \begin_inset Formula $\eta$
19424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19427 \begin_layout Plain Layout
19435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19438 \begin_layout Plain Layout
19439 \begin_inset Formula $\theta$
19449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19452 \begin_layout Plain Layout
19460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19463 \begin_layout Plain Layout
19464 \begin_inset Formula $\vartheta$
19478 \begin_inset space \hfill{}
19482 \begin_inset Tabular
19483 <lyxtabular version="3" rows="12" columns="2">
19485 <column alignment="center" valignment="top" width="0pt">
19486 <column alignment="center" valignment="top" width="0pt">
19488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19491 \begin_layout Plain Layout
19497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19500 \begin_layout Plain Layout
19508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19511 \begin_layout Plain Layout
19519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19522 \begin_layout Plain Layout
19523 \begin_inset Formula $\iota$
19533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19536 \begin_layout Plain Layout
19544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19547 \begin_layout Plain Layout
19548 \begin_inset Formula $\kappa$
19558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19561 \begin_layout Plain Layout
19569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19572 \begin_layout Plain Layout
19573 \begin_inset Formula $\varkappa$
19583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19586 \begin_layout Plain Layout
19594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19597 \begin_layout Plain Layout
19598 \begin_inset Formula $\lambda$
19608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19611 \begin_layout Plain Layout
19619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19622 \begin_layout Plain Layout
19623 \begin_inset Formula $\mu$
19633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19636 \begin_layout Plain Layout
19644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19647 \begin_layout Plain Layout
19648 \begin_inset Formula $\nu$
19658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19661 \begin_layout Plain Layout
19669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19672 \begin_layout Plain Layout
19673 \begin_inset Formula $\xi$
19683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19686 \begin_layout Plain Layout
19692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19695 \begin_layout Plain Layout
19696 \begin_inset Formula $o$
19706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19709 \begin_layout Plain Layout
19717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19720 \begin_layout Plain Layout
19721 \begin_inset Formula $\pi$
19731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19734 \begin_layout Plain Layout
19742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19745 \begin_layout Plain Layout
19746 \begin_inset Formula $\varpi$
19756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19759 \begin_layout Plain Layout
19767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19770 \begin_layout Plain Layout
19771 \begin_inset Formula $\rho$
19785 \begin_inset space \hfill{}
19789 \begin_inset Tabular
19790 <lyxtabular version="3" rows="11" columns="2">
19792 <column alignment="center" valignment="top" width="0pt">
19793 <column alignment="center" valignment="top" width="0pt">
19795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19798 \begin_layout Plain Layout
19804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19807 \begin_layout Plain Layout
19815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19818 \begin_layout Plain Layout
19826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19829 \begin_layout Plain Layout
19830 \begin_inset Formula $\varrho$
19840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19843 \begin_layout Plain Layout
19851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19854 \begin_layout Plain Layout
19855 \begin_inset Formula $\sigma$
19865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19868 \begin_layout Plain Layout
19876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19879 \begin_layout Plain Layout
19880 \begin_inset Formula $\varsigma$
19890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19893 \begin_layout Plain Layout
19901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19904 \begin_layout Plain Layout
19905 \begin_inset Formula $\tau$
19915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19918 \begin_layout Plain Layout
19926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19929 \begin_layout Plain Layout
19930 \begin_inset Formula $\upsilon$
19940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19943 \begin_layout Plain Layout
19951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19954 \begin_layout Plain Layout
19955 \begin_inset Formula $\phi$
19965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19968 \begin_layout Plain Layout
19976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19979 \begin_layout Plain Layout
19980 \begin_inset Formula $\varphi$
19990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19993 \begin_layout Plain Layout
20001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20004 \begin_layout Plain Layout
20005 \begin_inset Formula $\chi$
20015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20018 \begin_layout Plain Layout
20026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20029 \begin_layout Plain Layout
20030 \begin_inset Formula $\psi$
20040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20043 \begin_layout Plain Layout
20051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20054 \begin_layout Plain Layout
20055 \begin_inset Formula $\omega$
20069 \begin_inset space \hfill{}
20075 \begin_layout Standard
20076 \begin_inset VSpace medskip
20082 \begin_layout Standard
20083 How to create upright Greek letters is explained in
20084 \begin_inset CommandInset ref
20086 reference "sub:Upright-small-Greek"
20093 \begin_layout Subsection
20098 \begin_layout Plain Layout
20099 Greek letters ! big
20107 \begin_layout Standard
20108 \begin_inset space \hfill{}
20112 \begin_inset Tabular
20113 <lyxtabular version="3" rows="7" columns="2">
20115 <column alignment="center" valignment="top" width="0pt">
20116 <column alignment="center" valignment="top" width="0pt">
20118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20121 \begin_layout Plain Layout
20127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20130 \begin_layout Plain Layout
20138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20141 \begin_layout Plain Layout
20149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20152 \begin_layout Plain Layout
20153 \begin_inset Formula $\Gamma$
20163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20166 \begin_layout Plain Layout
20174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20177 \begin_layout Plain Layout
20178 \begin_inset Formula $\Delta$
20188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20191 \begin_layout Plain Layout
20199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20202 \begin_layout Plain Layout
20203 \begin_inset Formula $\Theta$
20213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20216 \begin_layout Plain Layout
20224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20227 \begin_layout Plain Layout
20228 \begin_inset Formula $\Lambda$
20238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20241 \begin_layout Plain Layout
20249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20252 \begin_layout Plain Layout
20253 \begin_inset Formula $\Xi$
20263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20266 \begin_layout Plain Layout
20274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20277 \begin_layout Plain Layout
20278 \begin_inset Formula $\Pi$
20292 \begin_inset space \hfill{}
20296 \begin_inset Tabular
20297 <lyxtabular version="3" rows="6" columns="2">
20299 <column alignment="center" valignment="top" width="0pt">
20300 <column alignment="center" valignment="top" width="0pt">
20302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20305 \begin_layout Plain Layout
20311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20314 \begin_layout Plain Layout
20322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20325 \begin_layout Plain Layout
20333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20336 \begin_layout Plain Layout
20337 \begin_inset Formula $\Sigma$
20347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20350 \begin_layout Plain Layout
20358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20361 \begin_layout Plain Layout
20362 \begin_inset Formula $\Upsilon$
20372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20375 \begin_layout Plain Layout
20383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20386 \begin_layout Plain Layout
20387 \begin_inset Formula $\Phi$
20397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20400 \begin_layout Plain Layout
20408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20411 \begin_layout Plain Layout
20412 \begin_inset Formula $\Psi$
20422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20425 \begin_layout Plain Layout
20433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20436 \begin_layout Plain Layout
20437 \begin_inset Formula $\Omega$
20451 \begin_inset space \hfill{}
20457 \begin_layout Standard
20458 \begin_inset VSpace medskip
20461 That the big Greek letters appear upright is caused by a design bug when
20463 To get correct italic big letters, begin every command with
20468 For example the command
20475 \begin_inset Formula $\varGamma$
20481 \begin_layout Subsection
20486 \begin_layout Plain Layout
20487 Greek letters ! bold
20495 \begin_layout Standard
20496 Greek letters cannot be set with different font styles like Latin letters.
20497 They can only be made bold with the command
20507 \begin_layout Plain Layout
20518 \begin_layout Standard
20520 \begin_inset Tabular
20521 <lyxtabular version="3" rows="3" columns="2">
20523 <column alignment="center" valignment="top" width="0">
20524 <column alignment="center" valignment="top" width="0">
20526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20529 \begin_layout Plain Layout
20535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20538 \begin_layout Plain Layout
20546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20549 \begin_layout Plain Layout
20561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20564 \begin_layout Plain Layout
20565 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20578 \begin_layout Plain Layout
20590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20593 \begin_layout Plain Layout
20594 \begin_inset Formula $\theta\boldsymbol{\theta}$
20610 \begin_layout Section
20615 \begin_layout Plain Layout
20628 \begin_layout Plain Layout
20629 A list with all symbols of most of the LaTeX-packages can be found in
20630 \begin_inset CommandInset citation
20645 \begin_layout Plain Layout
20653 \begin_inset Note Note
20656 \begin_layout Plain Layout
20659 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20662 \begin_layout Plain Layout
20665 texorpdfstring is in section
20666 \begin_inset CommandInset ref
20668 reference "sub:Formulas-in-Section"
20681 \begin_layout Plain Layout
20690 \begin_layout Standard
20691 Many of the symbols listed in this section can also be inserted via the
20693 \begin_inset Graphics
20694 filename ../images/math/nabla.png
20700 \begin_inset Graphics
20701 filename ../images/math/digamma.png
20709 \begin_layout Subsection
20710 Mathematical Symbols
20711 \begin_inset CommandInset label
20713 name "sub:Mathematical-Symbols"
20721 \begin_layout Plain Layout
20722 Symbols ! mathematical
20730 \begin_layout Standard
20731 \begin_inset space \hfill{}
20735 \begin_inset Tabular
20736 <lyxtabular version="3" rows="10" columns="2">
20738 <column alignment="center" valignment="top" width="0pt">
20739 <column alignment="center" valignment="top" width="0pt">
20741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20744 \begin_layout Plain Layout
20750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20753 \begin_layout Plain Layout
20761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20764 \begin_layout Plain Layout
20772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20775 \begin_layout Plain Layout
20776 \begin_inset Formula $\neg$
20786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20789 \begin_layout Plain Layout
20797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20800 \begin_layout Plain Layout
20801 \begin_inset Formula $\Im$
20811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20814 \begin_layout Plain Layout
20822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20825 \begin_layout Plain Layout
20826 \begin_inset Formula $\Re$
20836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20839 \begin_layout Plain Layout
20847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20850 \begin_layout Plain Layout
20851 \begin_inset Formula $\aleph$
20861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20864 \begin_layout Plain Layout
20872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20875 \begin_layout Plain Layout
20876 \begin_inset Formula $\partial$
20886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20889 \begin_layout Plain Layout
20897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20900 \begin_layout Plain Layout
20901 \begin_inset Formula $\infty$
20911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20914 \begin_layout Plain Layout
20922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20925 \begin_layout Plain Layout
20926 \begin_inset Formula $\wp$
20936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20939 \begin_layout Plain Layout
20947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20950 \begin_layout Plain Layout
20951 \begin_inset Formula $\imath$
20961 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20964 \begin_layout Plain Layout
20972 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20975 \begin_layout Plain Layout
20976 \begin_inset Formula $\jmath$
20990 \begin_inset space \hfill{}
20994 \begin_inset Tabular
20995 <lyxtabular version="3" rows="10" columns="2">
20997 <column alignment="center" valignment="top" width="0pt">
20998 <column alignment="center" valignment="top" width="0pt">
21000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21003 \begin_layout Plain Layout
21009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21012 \begin_layout Plain Layout
21014 \begin_inset Note Note
21017 \begin_layout Plain Layout
21024 is only used as spacer.
21036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21039 \begin_layout Plain Layout
21047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21050 \begin_layout Plain Layout
21051 \begin_inset Formula $\forall$
21061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21064 \begin_layout Plain Layout
21072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21075 \begin_layout Plain Layout
21076 \begin_inset Formula $\exists$
21086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21089 \begin_layout Plain Layout
21097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21100 \begin_layout Plain Layout
21101 \begin_inset Formula $\nexists$
21111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21114 \begin_layout Plain Layout
21122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21125 \begin_layout Plain Layout
21126 \begin_inset Formula $\emptyset$
21136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21139 \begin_layout Plain Layout
21147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21150 \begin_layout Plain Layout
21151 \begin_inset Formula $\varnothing$
21161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21164 \begin_layout Plain Layout
21172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21175 \begin_layout Plain Layout
21176 \begin_inset Formula $\dag$
21186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21189 \begin_layout Plain Layout
21197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21200 \begin_layout Plain Layout
21201 \begin_inset Formula $\ddag$
21211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21214 \begin_layout Plain Layout
21222 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21225 \begin_layout Plain Layout
21229 \begin_layout Plain Layout
21239 \begin_inset Formula $\complement$
21246 \begin_layout Plain Layout
21260 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21263 \begin_layout Plain Layout
21271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21274 \begin_layout Plain Layout
21275 \begin_inset Formula $\Bbbk$
21289 \begin_inset space \hfill{}
21293 \begin_inset Tabular
21294 <lyxtabular version="3" rows="10" columns="2">
21296 <column alignment="center" valignment="top" width="0pt">
21297 <column alignment="center" valignment="top" width="0pt">
21299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21302 \begin_layout Plain Layout
21308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21311 \begin_layout Plain Layout
21319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21322 \begin_layout Plain Layout
21330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21333 \begin_layout Plain Layout
21334 \begin_inset Formula $\prime$
21344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21347 \begin_layout Plain Layout
21355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21358 \begin_layout Plain Layout
21359 \begin_inset Formula $\backprime$
21369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21372 \begin_layout Plain Layout
21380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21383 \begin_layout Plain Layout
21384 \begin_inset Formula $\mho$
21394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21397 \begin_layout Plain Layout
21405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21408 \begin_layout Plain Layout
21409 \begin_inset Formula $\triangle$
21419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21422 \begin_layout Plain Layout
21430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21433 \begin_layout Plain Layout
21434 \begin_inset Formula $\angle$
21444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21447 \begin_layout Plain Layout
21455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21458 \begin_layout Plain Layout
21459 \begin_inset Formula $\measuredangle$
21469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21472 \begin_layout Plain Layout
21480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21483 \begin_layout Plain Layout
21484 \begin_inset Formula $\sphericalangle$
21494 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21497 \begin_layout Plain Layout
21505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21508 \begin_layout Plain Layout
21509 \begin_inset Formula $\top$
21519 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21522 \begin_layout Plain Layout
21530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21533 \begin_layout Plain Layout
21534 \begin_inset Formula $\bot$
21548 \begin_inset space \hfill{}
21554 \begin_layout Subsection
21555 Miscellaneous Symbols
21556 \begin_inset CommandInset label
21558 name "sub:Miscellaneous-Symbols"
21566 \begin_layout Plain Layout
21567 Symbols ! miscellaneous
21575 \begin_layout Standard
21578 \begin_inset Tabular
21579 <lyxtabular version="3" rows="10" columns="2">
21581 <column alignment="center" valignment="top" width="0pt">
21582 <column alignment="center" valignment="top" width="0pt">
21584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21587 \begin_layout Plain Layout
21593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21596 \begin_layout Plain Layout
21604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21607 \begin_layout Plain Layout
21615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21618 \begin_layout Plain Layout
21619 \begin_inset Formula $\flat$
21629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21632 \begin_layout Plain Layout
21640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21643 \begin_layout Plain Layout
21644 \begin_inset Formula $\natural$
21654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21657 \begin_layout Plain Layout
21665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21668 \begin_layout Plain Layout
21669 \begin_inset Formula $\sharp$
21679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21682 \begin_layout Plain Layout
21690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21693 \begin_layout Plain Layout
21694 \begin_inset Formula $\surd$
21704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21707 \begin_layout Plain Layout
21715 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21718 \begin_layout Plain Layout
21719 \begin_inset Formula $\checkmark$
21729 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21732 \begin_layout Plain Layout
21740 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21743 \begin_layout Plain Layout
21744 \begin_inset Formula $\yen$
21754 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21757 \begin_layout Plain Layout
21765 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21768 \begin_layout Plain Layout
21769 \begin_inset Formula $\pounds$
21779 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21782 \begin_layout Plain Layout
21788 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21791 \begin_layout Plain Layout
21792 \begin_inset Formula $\$$
21802 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21805 \begin_layout Plain Layout
21811 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21814 \begin_layout Plain Layout
21815 \begin_inset Formula $§$
21829 \begin_inset Tabular
21830 <lyxtabular version="3" rows="10" columns="2">
21832 <column alignment="center" valignment="top" width="0">
21833 <column alignment="center" valignment="top" width="0">
21835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21838 \begin_layout Plain Layout
21844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21847 \begin_layout Plain Layout
21855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21858 \begin_layout Plain Layout
21866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21869 \begin_layout Plain Layout
21870 \begin_inset Formula $\hbar$
21880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21883 \begin_layout Plain Layout
21891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21894 \begin_layout Plain Layout
21895 \begin_inset Formula $\hslash$
21905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21908 \begin_layout Plain Layout
21916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21919 \begin_layout Plain Layout
21920 \begin_inset Formula $\clubsuit$
21930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21933 \begin_layout Plain Layout
21941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21944 \begin_layout Plain Layout
21945 \begin_inset Formula $\spadesuit$
21955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21958 \begin_layout Plain Layout
21966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21969 \begin_layout Plain Layout
21970 \begin_inset Formula $\bigstar$
21980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21983 \begin_layout Plain Layout
21991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21994 \begin_layout Plain Layout
21995 \begin_inset Formula $\blacklozenge$
22005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22008 \begin_layout Plain Layout
22016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22019 \begin_layout Plain Layout
22020 \begin_inset Formula $\blacktriangle$
22030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22033 \begin_layout Plain Layout
22041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22044 \begin_layout Plain Layout
22045 \begin_inset Formula $\blacktriangledown$
22055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22058 \begin_layout Plain Layout
22066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22069 \begin_layout Plain Layout
22070 \begin_inset Formula $\bullet$
22084 \begin_inset Tabular
22085 <lyxtabular version="3" rows="10" columns="2">
22087 <column alignment="center" valignment="top" width="0pt">
22088 <column alignment="center" valignment="top" width="0pt">
22090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22093 \begin_layout Plain Layout
22099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22102 \begin_layout Plain Layout
22110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22113 \begin_layout Plain Layout
22121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22124 \begin_layout Plain Layout
22125 \begin_inset Formula $\diamondsuit$
22135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22138 \begin_layout Plain Layout
22146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22149 \begin_layout Plain Layout
22150 \begin_inset Formula $\Diamond$
22160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22163 \begin_layout Plain Layout
22171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22174 \begin_layout Plain Layout
22175 \begin_inset Formula $\heartsuit$
22185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22188 \begin_layout Plain Layout
22196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22199 \begin_layout Plain Layout
22200 \begin_inset Formula $\P$
22210 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22213 \begin_layout Plain Layout
22221 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22224 \begin_layout Plain Layout
22225 \begin_inset Formula $\copyright$
22235 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22238 \begin_layout Plain Layout
22246 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22249 \begin_layout Plain Layout
22250 \begin_inset Formula $\circledR$
22260 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22263 \begin_layout Plain Layout
22271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22274 \begin_layout Plain Layout
22275 \begin_inset Formula $\maltese$
22285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22288 \begin_layout Plain Layout
22296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22299 \begin_layout Plain Layout
22300 \begin_inset Formula $\diagup$
22310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22313 \begin_layout Plain Layout
22321 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22324 \begin_layout Plain Layout
22325 \begin_inset Formula $\diagdown$
22341 \begin_layout Standard
22342 \begin_inset VSpace medskip
22345 More symbols are listed in
22346 \begin_inset CommandInset ref
22348 reference "sub:Miscellaneous-special-Characters"
22355 \begin_layout Standard
22356 Some symbols can be displayed in different sizes, see
22357 \begin_inset CommandInset ref
22359 reference "sub:Font-Sizes"
22366 \begin_layout Subsection
22371 \begin_layout Plain Layout
22372 Symbols ! Euro-symbol
22381 \begin_layout Plain Layout
22388 \begin_layout Plain Layout
22405 \begin_layout Standard
22406 To use the Euro symbol in formulas, the LaTeX-package
22414 \begin_layout Plain Layout
22420 must be installed and loaded with the LaTeX-preamble line
22423 \begin_layout Standard
22428 usepackage[gennarrow]{eurosym}
22431 \begin_layout Standard
22432 The Euro symbol can now be inserted with the command
22442 \begin_layout Plain Layout
22453 \begin_layout Standard
22454 The Euro symbol can directly be inserted with the € key in mathematical
22455 text, without having
22470 can also be inserted in TeX-mode.
22471 The official currency symbol can then be inserted with the command
22481 \begin_layout Plain Layout
22489 , that is only available in TeX-mode.
22492 \begin_layout Standard
22496 \begin_layout Plain Layout
22506 \begin_inset Note Note
22509 \begin_layout Plain Layout
22510 The following table will only be displayed when the LaTeX-package
22522 \begin_layout Standard
22523 An overview about the different Euro symbols:
22526 \begin_layout Standard
22528 \begin_inset Tabular
22529 <lyxtabular version="3" rows="4" columns="3">
22531 <column alignment="center" valignment="top" width="0pt">
22532 <column alignment="center" valignment="top" width="0pt">
22533 <column alignment="center" valignment="top" width="0pt">
22535 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22538 \begin_layout Plain Layout
22544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22547 \begin_layout Plain Layout
22553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22556 \begin_layout Plain Layout
22564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22567 \begin_layout Plain Layout
22573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22576 \begin_layout Plain Layout
22584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22587 \begin_layout Plain Layout
22588 \begin_inset Formula $\euro$
22598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22601 \begin_layout Plain Layout
22607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22610 \begin_layout Plain Layout
22616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22619 \begin_layout Plain Layout
22620 \begin_inset Formula $\mbox{€}$
22630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22633 \begin_layout Plain Layout
22639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22642 \begin_layout Plain Layout
22650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22653 \begin_layout Plain Layout
22657 \begin_layout Plain Layout
22679 \begin_layout Standard
22683 \begin_layout Plain Layout
22693 \begin_inset Note Note
22696 \begin_layout Plain Layout
22697 The following will be displayed when the LaTeX-package
22709 \begin_layout Standard
22710 You need to install the LaTeX-package
22714 to see the rest of this subsection in the output.
22717 \begin_layout Standard
22721 \begin_layout Plain Layout
22733 \begin_layout Standard
22734 \begin_inset Newpage newpage
22740 \begin_layout Section
22742 \begin_inset CommandInset label
22744 name "sec:Relations"
22752 \begin_layout Plain Layout
22762 \begin_layout Plain Layout
22767 \begin_layout Plain Layout
22778 \begin_layout Plain Layout
22793 \begin_layout Standard
22794 All relations can also be inserted via the toolbar button
22795 \begin_inset Graphics
22796 filename ../images/math/leq.png
22804 \begin_layout Standard
22805 \begin_inset space \hfill{}
22809 \begin_inset Tabular
22810 <lyxtabular version="3" rows="17" columns="2">
22812 <column alignment="center" valignment="top" width="0pt">
22813 <column alignment="center" valignment="top" width="0pt">
22815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22818 \begin_layout Plain Layout
22824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22827 \begin_layout Plain Layout
22835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22838 \begin_layout Plain Layout
22844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22847 \begin_layout Plain Layout
22848 \begin_inset Formula $<$
22858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22861 \begin_layout Plain Layout
22869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22872 \begin_layout Plain Layout
22873 \begin_inset Formula $\le$
22883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22886 \begin_layout Plain Layout
22894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22897 \begin_layout Plain Layout
22898 \begin_inset Formula $\ll$
22908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22911 \begin_layout Plain Layout
22919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22922 \begin_layout Plain Layout
22923 \begin_inset Formula $\prec$
22933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22936 \begin_layout Plain Layout
22944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22947 \begin_layout Plain Layout
22948 \begin_inset Formula $\preceq$
22958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22961 \begin_layout Plain Layout
22969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22972 \begin_layout Plain Layout
22973 \begin_inset Formula $\subset$
22983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22986 \begin_layout Plain Layout
22994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22997 \begin_layout Plain Layout
22998 \begin_inset Formula $\subseteq$
23008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23011 \begin_layout Plain Layout
23019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23022 \begin_layout Plain Layout
23023 \begin_inset Formula $\sqsubseteq$
23033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23036 \begin_layout Plain Layout
23044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23047 \begin_layout Plain Layout
23048 \begin_inset Formula $\in$
23058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23061 \begin_layout Plain Layout
23069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23072 \begin_layout Plain Layout
23073 \begin_inset Formula $\vdash$
23083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23086 \begin_layout Plain Layout
23094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23097 \begin_layout Plain Layout
23098 \begin_inset Formula $\smile$
23108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23111 \begin_layout Plain Layout
23119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23122 \begin_layout Plain Layout
23123 \begin_inset Formula $\lhd$
23133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23136 \begin_layout Plain Layout
23144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23147 \begin_layout Plain Layout
23148 \begin_inset Formula $\unlhd$
23158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23161 \begin_layout Plain Layout
23169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23172 \begin_layout Plain Layout
23173 \begin_inset Formula $\gtrless$
23183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23186 \begin_layout Plain Layout
23194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23197 \begin_layout Plain Layout
23198 \begin_inset Formula $\mid$
23208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23211 \begin_layout Plain Layout
23219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23222 \begin_layout Plain Layout
23223 \begin_inset Formula $\nmid$
23237 \begin_inset space \hfill{}
23241 \begin_inset Tabular
23242 <lyxtabular version="3" rows="17" columns="2">
23244 <column alignment="center" valignment="top" width="0pt">
23245 <column alignment="center" valignment="top" width="0pt">
23247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23250 \begin_layout Plain Layout
23256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23259 \begin_layout Plain Layout
23267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23270 \begin_layout Plain Layout
23276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23279 \begin_layout Plain Layout
23280 \begin_inset Formula $=$
23290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23293 \begin_layout Plain Layout
23301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23304 \begin_layout Plain Layout
23305 \begin_inset Formula $\not=$
23315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23318 \begin_layout Plain Layout
23326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23329 \begin_layout Plain Layout
23330 \begin_inset Formula $\equiv$
23340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23343 \begin_layout Plain Layout
23351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23354 \begin_layout Plain Layout
23355 \begin_inset Formula $\sim$
23365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23368 \begin_layout Plain Layout
23376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23379 \begin_layout Plain Layout
23380 \begin_inset Formula $\simeq$
23390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23393 \begin_layout Plain Layout
23401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23404 \begin_layout Plain Layout
23405 \begin_inset Formula $\approx$
23415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23418 \begin_layout Plain Layout
23426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23429 \begin_layout Plain Layout
23430 \begin_inset Formula $\cong$
23440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23443 \begin_layout Plain Layout
23451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23454 \begin_layout Plain Layout
23455 \begin_inset Formula $\bowtie$
23465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23468 \begin_layout Plain Layout
23476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23479 \begin_layout Plain Layout
23480 \begin_inset Formula $\notin$
23490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23493 \begin_layout Plain Layout
23501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23504 \begin_layout Plain Layout
23505 \begin_inset Formula $\perp$
23515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23518 \begin_layout Plain Layout
23526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23529 \begin_layout Plain Layout
23530 \begin_inset Formula $\propto$
23540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23543 \begin_layout Plain Layout
23551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23554 \begin_layout Plain Layout
23555 \begin_inset Formula $\asymp$
23565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23568 \begin_layout Plain Layout
23576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23579 \begin_layout Plain Layout
23580 \begin_inset Formula $\doteq$
23590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23593 \begin_layout Plain Layout
23601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23604 \begin_layout Plain Layout
23605 \begin_inset Formula $\circeq$
23615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23618 \begin_layout Plain Layout
23626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23629 \begin_layout Plain Layout
23630 \begin_inset Formula $\models$
23640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23643 \begin_layout Plain Layout
23651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23654 \begin_layout Plain Layout
23655 \begin_inset Formula $\widehat{=}$
23669 \begin_inset space \hfill{}
23673 \begin_inset Tabular
23674 <lyxtabular version="3" rows="17" columns="2">
23676 <column alignment="center" valignment="top" width="0pt">
23677 <column alignment="center" valignment="top" width="0pt">
23679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23682 \begin_layout Plain Layout
23688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23691 \begin_layout Plain Layout
23699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23702 \begin_layout Plain Layout
23708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23711 \begin_layout Plain Layout
23712 \begin_inset Formula $>$
23722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23725 \begin_layout Plain Layout
23733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23736 \begin_layout Plain Layout
23737 \begin_inset Formula $\ge$
23747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23750 \begin_layout Plain Layout
23758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23761 \begin_layout Plain Layout
23762 \begin_inset Formula $\gg$
23772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23775 \begin_layout Plain Layout
23783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23786 \begin_layout Plain Layout
23787 \begin_inset Formula $\succ$
23797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23800 \begin_layout Plain Layout
23808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23811 \begin_layout Plain Layout
23812 \begin_inset Formula $\succeq$
23822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23825 \begin_layout Plain Layout
23833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23836 \begin_layout Plain Layout
23837 \begin_inset Formula $\supset$
23847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23850 \begin_layout Plain Layout
23858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23861 \begin_layout Plain Layout
23862 \begin_inset Formula $\supseteq$
23872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23875 \begin_layout Plain Layout
23883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23886 \begin_layout Plain Layout
23887 \begin_inset Formula $\sqsupseteq$
23897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23900 \begin_layout Plain Layout
23908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23911 \begin_layout Plain Layout
23912 \begin_inset Formula $\ni$
23922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23925 \begin_layout Plain Layout
23933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23936 \begin_layout Plain Layout
23937 \begin_inset Formula $\dashv$
23947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23950 \begin_layout Plain Layout
23958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23961 \begin_layout Plain Layout
23962 \begin_inset Formula $\frown$
23972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23975 \begin_layout Plain Layout
23983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23986 \begin_layout Plain Layout
23987 \begin_inset Formula $\rhd$
23997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24000 \begin_layout Plain Layout
24008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24011 \begin_layout Plain Layout
24012 \begin_inset Formula $\unrhd$
24022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24025 \begin_layout Plain Layout
24033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24036 \begin_layout Plain Layout
24037 \begin_inset Formula $\lessgtr$
24047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24050 \begin_layout Plain Layout
24058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24061 \begin_layout Plain Layout
24062 \begin_inset Formula $\parallel$
24072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24075 \begin_layout Plain Layout
24083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24086 \begin_layout Plain Layout
24087 \begin_inset Formula $\nparallel$
24101 \begin_inset space \hfill{}
24107 \begin_layout Standard
24108 \begin_inset VSpace medskip
24123 are bigger than the equal looking operators
24138 \begin_layout Standard
24139 Relations are, in contrary to symbols, always surrounded by space.
24142 \begin_layout Standard
24143 Relations with labels can be created with the command
24153 \begin_layout Plain Layout
24164 \begin_layout Standard
24166 \begin_inset Tabular
24167 <lyxtabular version="3" rows="2" columns="2">
24169 <column alignment="center" valignment="top" width="0">
24170 <column alignment="center" valignment="top" width="0">
24172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24175 \begin_layout Plain Layout
24181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24184 \begin_layout Plain Layout
24186 \begin_inset Note Note
24189 \begin_layout Plain Layout
24196 is only used as spacer.
24208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24211 \begin_layout Plain Layout
24218 \begin_layout Plain Layout
24235 \begin_layout Plain Layout
24245 \begin_inset Formula $\downarrow$
24254 \begin_layout Plain Layout
24267 \begin_layout Plain Layout
24281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24284 \begin_layout Plain Layout
24285 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24301 \begin_layout Section
24305 \begin_layout Subsection
24306 Predefined Functions
24307 \begin_inset CommandInset label
24309 name "sub:Predefined-Functions"
24317 \begin_layout Plain Layout
24318 Functions ! predefined
24326 \begin_layout Standard
24327 In general, variables are set
24331 in mathematical expressions, but not function names, because
24332 \begin_inset Formula $sin$
24335 could be misunderstood as
24336 \begin_inset Formula $s\cdot i\cdot n$
24340 Therefore there are predefined functions, that are additionally a bit separated
24342 They are inserted as commands starting with a backslash before their name.
24345 \begin_layout Standard
24347 \begin_inset Tabular
24348 <lyxtabular version="3" rows="2" columns="4">
24350 <column alignment="center" valignment="top" width="0pt">
24351 <column alignment="center" valignment="top" width="0pt">
24352 <column alignment="center" valignment="top" width="0pt">
24353 <column alignment="center" valignment="top" width="0pt">
24355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24358 \begin_layout Plain Layout
24364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24367 \begin_layout Plain Layout
24373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24376 \begin_layout Plain Layout
24382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24385 \begin_layout Plain Layout
24393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24396 \begin_layout Plain Layout
24402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24405 \begin_layout Plain Layout
24406 \begin_inset Formula $Asin(x)+B$
24414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24417 \begin_layout Plain Layout
24425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24428 \begin_layout Plain Layout
24429 \begin_inset Formula $A\sin(x)+B$
24445 \begin_layout Standard
24446 The following functions are predefined:
24449 \begin_layout Standard
24450 \begin_inset VSpace -2mm
24456 \begin_layout Standard
24458 \begin_inset Tabular
24459 <lyxtabular version="3" rows="9" columns="4">
24461 <column alignment="center" valignment="top" width="0pt">
24462 <column alignment="center" valignment="top" width="0pt">
24463 <column alignment="center" valignment="top" width="0pt">
24464 <column alignment="center" valignment="top" width="0pt">
24466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24469 \begin_layout Plain Layout
24475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24478 \begin_layout Plain Layout
24484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24487 \begin_layout Plain Layout
24493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24496 \begin_layout Plain Layout
24504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24507 \begin_layout Plain Layout
24515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24518 \begin_layout Plain Layout
24526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24529 \begin_layout Plain Layout
24537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24540 \begin_layout Plain Layout
24550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24553 \begin_layout Plain Layout
24561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24564 \begin_layout Plain Layout
24572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24575 \begin_layout Plain Layout
24583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24586 \begin_layout Plain Layout
24596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24599 \begin_layout Plain Layout
24607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24610 \begin_layout Plain Layout
24618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24621 \begin_layout Plain Layout
24629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24632 \begin_layout Plain Layout
24642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24645 \begin_layout Plain Layout
24653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24656 \begin_layout Plain Layout
24664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24667 \begin_layout Plain Layout
24675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24678 \begin_layout Plain Layout
24688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24691 \begin_layout Plain Layout
24699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24702 \begin_layout Plain Layout
24710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24713 \begin_layout Plain Layout
24721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24724 \begin_layout Plain Layout
24734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24737 \begin_layout Plain Layout
24745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24748 \begin_layout Plain Layout
24756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24759 \begin_layout Plain Layout
24767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24770 \begin_layout Plain Layout
24780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24783 \begin_layout Plain Layout
24791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24794 \begin_layout Plain Layout
24802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24805 \begin_layout Plain Layout
24813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24816 \begin_layout Plain Layout
24826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24829 \begin_layout Plain Layout
24837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24840 \begin_layout Plain Layout
24848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24851 \begin_layout Plain Layout
24859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24862 \begin_layout Plain Layout
24878 \begin_layout Standard
24879 They can also be inserted with the math toolbar button
24880 \begin_inset Graphics
24881 filename ../images/math/functions.png
24889 \begin_layout Subsection
24890 Self-defined Functions
24894 \begin_layout Plain Layout
24895 Functions ! self-defined
24903 \begin_layout Standard
24904 To use a function that is not predefined, like for example the sign function
24905 sgn(x), there are two possibilities:
24908 \begin_layout Itemize
24909 Define the function by inserting the following line to the LaTeX-preamble
24913 \begin_layout Plain Layout
24918 DeclareMathOperator
24921 \begin_inset CommandInset ref
24923 reference "sub:Self-defined-Operators"
24933 \begin_inset Newline newline
24937 \begin_inset VSpace -3mm
24941 \begin_inset Newline newline
24948 DeclareMathOperator{
24956 \begin_layout Plain Layout
24961 DeclareMathOperator
24967 \begin_inset Newline newline
24971 \begin_inset VSpace -2mm
24975 \begin_inset Newline newline
24978 Now the new defined function can be called with the command
24987 \begin_layout Itemize
24988 Write the the formula as usual, mark the formula name, in our example the
24993 , and change it to mathematical text.
24994 At last a space is inserted between prefactor and function.
24997 \begin_layout Standard
24998 The result is the same with both methods as with a predefined function
25002 \begin_layout Plain Layout
25003 In LyX self-defined functions are displayed red, predefined ones black.
25011 \begin_layout Standard
25013 \begin_inset Tabular
25014 <lyxtabular version="3" rows="3" columns="2">
25016 <column alignment="center" valignment="top" width="0pt">
25017 <column alignment="center" valignment="top" width="0pt">
25019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25022 \begin_layout Plain Layout
25028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25031 \begin_layout Plain Layout
25039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25042 \begin_layout Plain Layout
25050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25053 \begin_layout Plain Layout
25054 \begin_inset Formula $A\sgn(x)+B$
25064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25067 \begin_layout Plain Layout
25071 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25082 \begin_layout Plain Layout
25083 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25099 \begin_layout Standard
25100 The first method is more suitable when the self-defined function should
25101 be used several times.
25104 \begin_layout Subsection
25109 \begin_layout Plain Layout
25118 \begin_layout Standard
25119 For limits there are defined besides
25129 \begin_layout Plain Layout
25149 furthermore the following functions:
25152 \begin_layout Standard
25154 \begin_inset Tabular
25155 <lyxtabular version="3" rows="5" columns="2">
25157 <column alignment="center" valignment="top" width="0">
25158 <column alignment="center" valignment="top" width="0">
25160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25163 \begin_layout Plain Layout
25169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25172 \begin_layout Plain Layout
25174 \begin_inset Note Note
25177 \begin_layout Plain Layout
25184 is only used as spacer.
25196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25199 \begin_layout Plain Layout
25207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25210 \begin_layout Plain Layout
25211 \begin_inset Formula $\varliminf$
25221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25224 \begin_layout Plain Layout
25232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25235 \begin_layout Plain Layout
25236 \begin_inset Formula $\varlimsup$
25246 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25249 \begin_layout Plain Layout
25257 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25260 \begin_layout Plain Layout
25261 \begin_inset Formula $\varprojlim$
25271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25274 \begin_layout Plain Layout
25282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25285 \begin_layout Plain Layout
25286 \begin_inset Formula $\varinjlim$
25290 \begin_inset Formula $\raisebox{-2.5mm}{}$
25306 \begin_layout Standard
25307 \begin_inset VSpace medskip
25310 The limit is created by inserting a subscript.
25311 It is set right beside the function in an inline formula:
25314 \begin_layout Standard
25316 \begin_inset Tabular
25317 <lyxtabular version="3" rows="2" columns="2">
25319 <column alignment="center" valignment="top" width="0pt">
25320 <column alignment="center" valignment="top" width="0pt">
25322 <cell alignment="center" valignment="top" usebox="none">
25325 \begin_layout Plain Layout
25331 <cell alignment="center" valignment="top" usebox="none">
25334 \begin_layout Plain Layout
25335 \begin_inset space \hspace{}
25340 \begin_inset Note Note
25343 \begin_layout Plain Layout
25350 are used here as spacer.
25362 <cell alignment="center" valignment="top" usebox="none">
25365 \begin_layout Plain Layout
25374 \begin_layout Plain Layout
25387 \begin_layout Plain Layout
25401 <cell alignment="center" valignment="top" usebox="none">
25404 \begin_layout Plain Layout
25405 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25421 \begin_layout Standard
25422 In a displayed formula the limit is set below the formula, as usual:
25423 \begin_inset Formula \[
25431 \begin_layout Subsection
25436 \begin_layout Plain Layout
25437 Functions ! modulo-
25445 \begin_layout Standard
25446 The modulo-function is special, because it exists in four variants.
25449 \begin_layout Standard
25450 The variants in a displayed formula:
25451 \begin_inset Formula \begin{align*}
25452 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25453 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25454 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25455 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25456 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25463 \begin_layout Standard
25464 In an inline formula less space is set before the function names for all
25468 \begin_layout Standard
25469 \begin_inset Newpage newpage
25475 \begin_layout Section
25480 \begin_layout Plain Layout
25489 \begin_layout Subsection
25490 Special Characters in Mathematical Text
25493 \begin_layout Standard
25494 The following commands can only be used in mathematical text or in TeX-mode:
25497 \begin_layout Standard
25498 \begin_inset space \hfill{}
25502 \begin_inset Tabular
25503 <lyxtabular version="3" rows="8" columns="2">
25505 <column alignment="block" valignment="top" width="0">
25506 <column alignment="block" valignment="top" width="0">
25508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25511 \begin_layout Plain Layout
25517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25520 \begin_layout Plain Layout
25528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25531 \begin_layout Plain Layout
25539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25542 \begin_layout Plain Layout
25543 \begin_inset Formula $\textrm{œ}$
25553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25556 \begin_layout Plain Layout
25564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25567 \begin_layout Plain Layout
25568 \begin_inset Formula $\textrm{Œ}$
25578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25581 \begin_layout Plain Layout
25589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25592 \begin_layout Plain Layout
25593 \begin_inset Formula $\textrm{æ}$
25603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25606 \begin_layout Plain Layout
25614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25617 \begin_layout Plain Layout
25618 \begin_inset Formula $\textrm{Æ}$
25628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25631 \begin_layout Plain Layout
25639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25642 \begin_layout Plain Layout
25643 \begin_inset Formula $\textrm{\aa}$
25653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25656 \begin_layout Plain Layout
25663 \begin_layout Plain Layout
25670 \begin_layout Plain Layout
25691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25694 \begin_layout Plain Layout
25695 \begin_inset Formula $\textrm{Å}$
25705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25708 \begin_layout Plain Layout
25716 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25719 \begin_layout Plain Layout
25720 \begin_inset Formula $\textrm{ı}$
25734 \begin_inset space \hfill{}
25738 \begin_inset Tabular
25739 <lyxtabular version="3" rows="8" columns="2">
25741 <column alignment="block" valignment="top" width="0">
25742 <column alignment="center" valignment="top" width="0">
25744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25747 \begin_layout Plain Layout
25749 \begin_inset Note Note
25752 \begin_layout Plain Layout
25754 \begin_inset space \thinspace{}
25757 mm is used for separation, because otherwise the output will be ¡ and ¿
25768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25771 \begin_layout Plain Layout
25779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25782 \begin_layout Plain Layout
25790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25793 \begin_layout Plain Layout
25794 \begin_inset Formula $\textrm{ø}$
25804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25807 \begin_layout Plain Layout
25815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25818 \begin_layout Plain Layout
25819 \begin_inset Formula $\textrm{Ø}$
25829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25832 \begin_layout Plain Layout
25840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25843 \begin_layout Plain Layout
25844 \begin_inset Formula $\textrm{ł}$
25854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25857 \begin_layout Plain Layout
25865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25868 \begin_layout Plain Layout
25869 \begin_inset Formula $\textrm{Ł}$
25879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25882 \begin_layout Plain Layout
25884 \begin_inset space \hspace{}
25892 \begin_layout Plain Layout
25906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25909 \begin_layout Plain Layout
25910 \begin_inset Formula $\textrm{!`}$
25920 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25923 \begin_layout Plain Layout
25925 \begin_inset space \hspace{}
25933 \begin_layout Plain Layout
25947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25950 \begin_layout Plain Layout
25951 \begin_inset Formula $\textrm{?`}$
25961 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25964 \begin_layout Plain Layout
25972 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25975 \begin_layout Plain Layout
25976 \begin_inset Formula $\textrm{ȷ}$
25990 \begin_inset space \hfill{}
25996 \begin_layout Standard
25998 \begin_inset Formula $\textrm{\textrm{Å}}$
26002 \begin_inset Formula $\textrm{\textrm{Ø}}$
26005 can also be inserted via the math toolbar button
26006 \begin_inset Graphics
26007 filename ../images/math/digamma.png
26015 \begin_layout Standard
26016 An exception are the commands
26019 \begin_inset space \hspace{}
26028 \begin_inset space \hspace{}
26034 , because they can be inserted in LyX directly to text.
26037 \begin_layout Subsection
26039 \begin_inset CommandInset label
26041 name "sub:Accents-in-Text"
26049 \begin_layout Plain Layout
26058 \begin_layout Standard
26059 With the following commands all letters can be accented.
26060 The commands must be inserted in TeX-mode.
26063 \begin_layout Standard
26064 \begin_inset space \hfill{}
26068 \begin_inset Tabular
26069 <lyxtabular version="3" rows="8" columns="2">
26071 <column alignment="block" valignment="top" width="0">
26072 <column alignment="block" valignment="top" width="0">
26074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26077 \begin_layout Plain Layout
26083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26086 \begin_layout Plain Layout
26094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26097 \begin_layout Plain Layout
26101 \begin_inset Quotes grd
26109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26112 \begin_layout Plain Layout
26116 \begin_layout Plain Layout
26132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26135 \begin_layout Plain Layout
26143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26146 \begin_layout Plain Layout
26150 \begin_layout Plain Layout
26166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26169 \begin_layout Plain Layout
26176 \begin_layout Plain Layout
26190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26193 \begin_layout Plain Layout
26197 \begin_layout Plain Layout
26213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26216 \begin_layout Plain Layout
26224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26227 \begin_layout Plain Layout
26231 \begin_layout Plain Layout
26247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26250 \begin_layout Plain Layout
26257 \begin_layout Plain Layout
26271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26274 \begin_layout Plain Layout
26278 \begin_layout Plain Layout
26294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26297 \begin_layout Plain Layout
26304 \begin_layout Plain Layout
26318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26321 \begin_layout Plain Layout
26325 \begin_layout Plain Layout
26341 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26344 \begin_layout Plain Layout
26351 \begin_layout Plain Layout
26365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26368 \begin_layout Plain Layout
26372 \begin_layout Plain Layout
26392 \begin_inset space \hfill{}
26396 \begin_inset Tabular
26397 <lyxtabular version="3" rows="8" columns="2">
26399 <column alignment="block" valignment="top" width="0">
26400 <column alignment="center" valignment="top" width="0">
26402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26405 \begin_layout Plain Layout
26411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26414 \begin_layout Plain Layout
26422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26425 \begin_layout Plain Layout
26432 \begin_layout Plain Layout
26446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26449 \begin_layout Plain Layout
26453 \begin_layout Plain Layout
26469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26472 \begin_layout Plain Layout
26480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26483 \begin_layout Plain Layout
26487 \begin_layout Plain Layout
26503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26506 \begin_layout Plain Layout
26513 \begin_layout Plain Layout
26524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26527 \begin_layout Plain Layout
26531 \begin_layout Plain Layout
26547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26550 \begin_layout Plain Layout
26558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26561 \begin_layout Plain Layout
26565 \begin_layout Plain Layout
26581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26584 \begin_layout Plain Layout
26591 \begin_layout Plain Layout
26605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26608 \begin_layout Plain Layout
26612 \begin_layout Plain Layout
26628 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26631 \begin_layout Plain Layout
26638 \begin_layout Plain Layout
26652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26655 \begin_layout Plain Layout
26659 \begin_layout Plain Layout
26675 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26678 \begin_layout Plain Layout
26685 \begin_layout Plain Layout
26699 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26702 \begin_layout Plain Layout
26706 \begin_layout Plain Layout
26726 \begin_inset space \hfill{}
26732 \begin_layout Standard
26733 \begin_inset VSpace medskip
26742 also two different characters can be accented.
26751 \begin_layout Plain Layout
26766 \begin_layout Plain Layout
26778 \begin_layout Standard
26791 can in combination with vowels directly be inserted with the keyboard without
26793 The same applies for the tilde
26797 \begin_layout Plain Layout
26798 This only applies for keyboards where the tilde is defined as accent.
26807 in combination with
26822 \begin_layout Standard
26865 , and accents inserted directly with the keyboard are also available in
26867 For the other accents there are special math commands to be used in formulas,
26869 \begin_inset CommandInset ref
26871 reference "sub:Accents-for-one"
26878 \begin_layout Standard
26879 \begin_inset VSpace bigskip
26882 Furthermore, with the command
26892 \begin_layout Plain Layout
26900 all numbers and letters can be set into a circle, quasi accented with a
26901 circle, similar to the the copyright symbol.
26904 \begin_layout Standard
26906 \begin_inset Tabular
26907 <lyxtabular version="3" rows="3" columns="2">
26909 <column alignment="center" valignment="top" width="0">
26910 <column alignment="center" valignment="top" width="0">
26912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26915 \begin_layout Plain Layout
26921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26924 \begin_layout Plain Layout
26926 \begin_inset Note Note
26929 \begin_layout Plain Layout
26936 is only used as spacer.
26948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26951 \begin_layout Plain Layout
26959 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26962 \begin_layout Plain Layout
26966 \begin_layout Plain Layout
26982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26985 \begin_layout Plain Layout
26996 raisebox{-1.5pt}{W}}
27001 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27004 \begin_layout Plain Layout
27005 \begin_inset Formula $\raisebox{4.5mm}{}$
27012 \begin_layout Plain Layout
27030 \begin_inset Formula $\raisebox{-2mm}{}$
27046 \begin_layout Standard
27047 One has to take care that the character fits in the circle.
27058 \begin_layout Plain Layout
27060 \begin_inset CommandInset ref
27062 reference "sub:Font-Sizes"
27071 specifies thereby the size of the circle.
27082 \begin_layout Plain Layout
27084 \begin_inset CommandInset ref
27086 reference "sub:Boxes-without-Frame"
27095 the character can be centered.
27098 \begin_layout Subsection
27103 \begin_layout Plain Layout
27112 \begin_layout Standard
27113 Minuscule numbers are created with the command
27123 \begin_layout Plain Layout
27132 The command can be used in formulas and in TeX-mode.
27133 The command scheme is:
27136 \begin_layout Standard
27141 oldstylenums{number}
27144 \begin_layout Standard
27149 oldstylenums{0123456789
27152 \begin_inset Formula $\oldstylenums{0123456789}$
27158 \begin_layout Subsection
27159 Miscellaneous special Characters
27160 \begin_inset CommandInset label
27162 name "sub:Miscellaneous-special-Characters"
27170 \begin_layout Plain Layout
27171 Special characters ! miscellaneous
27179 \begin_layout Standard
27180 The following characters can only be inserted to formulas by using commands:
27183 \begin_layout Standard
27185 \begin_inset Tabular
27186 <lyxtabular version="3" rows="4" columns="2">
27188 <column alignment="center" valignment="top" width="0">
27189 <column alignment="center" valignment="top" width="0">
27191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27194 \begin_layout Plain Layout
27200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27203 \begin_layout Plain Layout
27211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27214 \begin_layout Plain Layout
27221 \begin_layout Plain Layout
27235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27238 \begin_layout Plain Layout
27239 \begin_inset Formula $\mathcircumflex$
27249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27252 \begin_layout Plain Layout
27260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27263 \begin_layout Plain Layout
27264 \begin_inset Formula $\_$
27274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27277 \begin_layout Plain Layout
27282 \begin_layout Plain Layout
27297 \begin_layout Plain Layout
27310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27313 \begin_layout Plain Layout
27314 \begin_inset Formula $^{\circ}$
27330 \begin_layout Standard
27331 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27332 contains the following line
27336 \begin_layout Plain Layout
27337 More about this is described in
27338 \begin_inset CommandInset ref
27340 reference "sub:Text-Characters-in"
27352 \begin_layout Standard
27357 DeclareInputtext{176}{
27370 \begin_layout Standard
27371 \begin_inset Newpage newpage
27377 \begin_layout Section
27379 \begin_inset CommandInset label
27381 name "sec:Formula-Styles"
27389 \begin_layout Plain Layout
27398 \begin_layout Itemize
27399 There are two different alignment styles:
27403 \begin_layout Description
27404 Centered is the predefined standard
27407 \begin_layout Description
27408 Indented for this the option
27412 must be inserted in the menu
27414 Document\SpecialChar \menuseparator
27420 \begin_inset space ~
27426 \begin_layout Standard
27431 is used, the indentation can be adjusted with the length
27441 \begin_layout Plain Layout
27450 Should the distance be 15
27451 \begin_inset space \thinspace{}
27454 mm, the following command line is inserted in the LaTeX-preamble
27457 \begin_layout Standard
27467 \begin_layout Standard
27468 When no length is specified, the predefined value of 30
27469 \begin_inset space \thinspace{}
27476 \begin_layout Itemize
27477 And two different numbering styles:
27481 \begin_layout Description
27482 Right is the predefined standard
27485 \begin_layout Description
27486 Left for this the option
27490 must be inserted in the menu
27492 Document\SpecialChar \menuseparator
27498 \begin_inset space ~
27505 \begin_layout Standard
27514 can also be used together.
27515 In this case both options are inserted, separated by a comma.
27518 \begin_layout Standard
27519 The chosen styles are used for all displayed formulas of the document.
27520 When both, centered and indented formulas should be created in a document,
27526 The indented formulas are then set in a flalign environment, see
27527 \begin_inset CommandInset ref
27529 reference "sub:Flalign-Environment"
27536 \begin_layout Section
27538 \begin_inset CommandInset label
27540 name "sec:Multiline-Formulas"
27548 \begin_layout Plain Layout
27549 Formula ! multiline
27557 \begin_layout Subsection
27561 \begin_layout Standard
27562 In LyX multiline formulas are created by pressing
27567 arg "newline-insert newline"
27573 This creates either an
27575 eqnarray environment
27577 that is described in
27578 \begin_inset CommandInset ref
27580 reference "sub:Eqnarray-Environment"
27584 or, when the option
27586 Use AMS math package
27588 in the document settings is selected, an
27592 that is described in
27593 \begin_inset CommandInset ref
27595 reference "sub:Standard-align-Environment"
27602 \begin_layout Standard
27603 There are other multiline formula environments that can be created via the
27606 Insert\SpecialChar \menuseparator
27610 These environments are described in the following sections.
27613 \begin_layout Standard
27614 In all multiline formula environments a new line is created by pressing
27618 arg "newline-insert newline"
27622 To add or delete lines, the math toolbar buttons
27623 \begin_inset Graphics
27624 filename ../images/tabular-feature_append-row.png
27630 \begin_inset Graphics
27631 filename ../images/tabular-feature_delete-row.png
27636 , respectively, or the menu
27638 Edit\SpecialChar \menuseparator
27644 \begin_layout Subsubsection
27646 \begin_inset CommandInset label
27648 name "sub:Line-Separation"
27656 \begin_layout Plain Layout
27657 Formula ! multiline ! Line separation
27665 \begin_layout Standard
27666 There is sometimes not enough space in multiline formulas between the lines:
27667 \begin_inset Formula \begin{eqnarray*}
27668 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}\\
27669 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*}
27676 \begin_layout Standard
27677 In LaTeX additional line space is specified as optional argument of the
27679 This is not yet possible in LyX
27683 \begin_layout Plain Layout
27685 \begin_inset CommandInset href
27687 name "LyX-bug #1505"
27688 target "http://www.lyx.org/trac/ticket/1505"
27697 , therefore the whole formula must be inserted in TeX-mode.
27698 To add in our example space, the command
27706 is inserted at the end of the first line.
27711 \begin_layout Plain Layout
27718 \begin_layout Plain Layout
27720 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27723 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27730 \begin_layout Plain Layout
27734 left(B^{2}+x_{0}^{2}
27742 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27747 \begin_layout Plain Layout
27759 \begin_layout Standard
27760 \begin_inset VSpace bigskip
27763 To set the the line separation for all lines in a formula, the length
27773 \begin_layout Plain Layout
27783 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27794 \begin_inset space \thinspace{}
27799 \begin_inset space \thinspace{}
27802 mm additional line separation as in the previous example, the command
27805 \begin_layout Standard
27815 \begin_layout Standard
27816 is inserted in TeX-mode before the formula.
27817 This requires that the LaTeX-package
27825 \begin_layout Plain Layout
27830 is part of every LaTeX standard installation.
27839 \begin_layout Plain Layout
27845 was loaded in LaTeX-preamble with the line
27848 \begin_layout Standard
27856 \begin_layout Standard
27861 \begin_layout Plain Layout
27873 \begin_inset Formula \begin{eqnarray*}
27874 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}\\
27875 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*}
27882 \begin_layout Standard
27886 \begin_layout Plain Layout
27897 To get back to the predefined distance,
27903 is set to the value 3
27904 \begin_inset space \thinspace{}
27910 \begin_layout Subsubsection
27912 \begin_inset CommandInset label
27914 name "sub:Column-Separation"
27922 \begin_layout Plain Layout
27923 Formula ! multiline ! Column separation
27931 \begin_layout Standard
27932 Multiline formulas form a matrix.
27933 A formula in the eqnarray environment is for example a matrix with three
27935 By changing the column separation in this environment, the space beside
27936 the relation sign can be changed.
27939 \begin_layout Standard
27940 The column separation is specified with the length
27950 \begin_layout Plain Layout
27959 \begin_inset Newline newline
27962 column separation = 2
27963 \begin_inset space \thinspace{}
27973 \begin_inset Newline newline
27979 \begin_layout Standard
27989 \begin_layout Standard
27990 inserted in TeX-mode, sets for all following formulas a column separation
27992 \begin_inset space \thinspace{}
27996 To get back to the predefined distance,
28003 \begin_inset space \thinspace{}
28009 \begin_layout Standard
28011 \begin_inset space \thinspace{}
28014 cm column separation:
28018 \begin_layout Plain Layout
28030 \begin_inset Formula \begin{eqnarray*}
28032 C & \ne & A\end{eqnarray*}
28036 A formula with the predefined column separation for matrices of 10
28037 \begin_inset space \thinspace{}
28044 \begin_layout Plain Layout
28056 \begin_inset Formula \begin{eqnarray*}
28058 C & \ne & A\end{eqnarray*}
28065 \begin_layout Subsubsection
28070 \begin_layout Plain Layout
28079 \begin_layout Standard
28080 Long formulas can be typeset using these methods:
28083 \begin_layout Itemize
28084 When one side of the equation is much shorther than the line width, this
28085 one is chosen for the left side and the right side is typeset over two
28087 \begin_inset Formula \begin{eqnarray}
28088 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 \\
28089 & & -\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}
28093 The minus sign at the beginning of the second line does normally not appear
28094 as operator because it is the first character of the line.
28095 Thus it would not be surrounded by space and could not be distinguished
28096 from the fraction bar.
28098 \begin_inset space \thinspace{}
28101 pt space was inserted behind the minus sign with the command
28111 \begin_layout Plain Layout
28119 \begin_inset CommandInset ref
28121 reference "sub:Variable-Space"
28134 \begin_layout Plain Layout
28145 \begin_layout Itemize
28146 When both sides of the equation are too long, the command
28156 \begin_layout Plain Layout
28165 It is inserted to the first column of the first line and effects that all
28166 further insertions overwrite the following columns:
28167 \begin_inset Formula \begin{eqnarray}
28168 \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 \\
28169 & & -\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 \\
28170 & & =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}
28174 After the insertion of
28180 , the cursor is in a purple box that is a bit shifted to the left from the
28182 In this the formula is inserted.
28183 \begin_inset Newline newline
28186 The content of the further lines is inserted to the second or another formula
28188 The greater the column number where it was inserted, the larger the indentation.
28189 \begin_inset VSpace medskip
28193 \begin_inset Newline newline
28197 \begin_inset Note Greyedout
28200 \begin_layout Plain Layout
28201 Note the following when using
28210 \begin_layout Itemize
28211 The formula doesn't use the full page width.
28213 \begin_inset space \thinspace{}
28217 \begin_inset space \space{}
28221 \begin_inset Formula $-B^{2}$
28224 is added to the first line in the above example, it would have been outside
28226 To better use the width, negative space can be inserted at the beginning
28230 \begin_layout Itemize
28231 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28236 \begin_layout Plain Layout
28237 \begin_inset CommandInset href
28239 name "LyX-bug #1429"
28240 target "http://www.lyx.org/trac/ticket/1429"
28249 One can only set the cursor at the beginning of the line and move it with
28258 \begin_layout Itemize
28259 Other methods to set long formulas are offered by the environments described
28261 \begin_inset CommandInset ref
28263 reference "sub:Multline-Environment"
28268 \begin_inset CommandInset ref
28270 reference "sub:Multiline-Formula-Parts"
28277 \begin_layout Subsubsection
28279 \begin_inset CommandInset label
28281 name "sub:Multiline-Brackets"
28289 \begin_layout Plain Layout
28290 Brackets ! for multiline expressions
28298 \begin_layout Standard
28299 For brackets spanning multiple lines the following problem occurs:
28300 \begin_inset Formula \begin{eqnarray*}
28301 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28302 & & \left.\cdots+B-D\right]\end{eqnarray*}
28309 \begin_layout Standard
28310 The closing bracket is smaller than the opening bracket because brackets
28311 with variable size may not span multiple lines.
28314 \begin_layout Standard
28315 To set the bracket size for the second line correctly, the first line is
28326 \begin_layout Plain Layout
28334 and the second line with
28342 \begin_layout Plain Layout
28356 \begin_inset CommandInset ref
28358 reference "sub:Automatic-Bracket-Size"
28373 \begin_layout Plain Layout
28399 \begin_layout Plain Layout
28418 \begin_layout Plain Layout
28437 \begin_layout Plain Layout
28449 \begin_inset Formula $\downarrow$
28458 \begin_layout Plain Layout
28466 is inserted, because the multiplication operator with its limits is the
28467 largest symbol in the first line and this should be the size for the bracket
28468 in the second line.
28471 \begin_layout Standard
28472 The result is this:
28473 \begin_inset Formula \begin{eqnarray*}
28474 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28475 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28482 \begin_layout Subsection
28486 \begin_layout Standard
28487 Align environments can be used for every kind of multiline formulas.
28488 They are specially useful to set several formulas side by side.
28491 \begin_layout Standard
28492 Align environments consist of columns.
28493 The odd columns are right aligned, the even ones left aligned.
28494 Every line in an Align environment can be numbered.
28497 \begin_layout Standard
28498 Align environments are created via the menu
28500 Insert\SpecialChar \menuseparator
28506 Edit\SpecialChar \menuseparator
28507 Math\SpecialChar \menuseparator
28508 Change Formula Type
28510 already existing formulas can be converted to Align environments.
28513 \begin_layout Standard
28514 To add or delete columns, the math toolbar buttons
28515 \begin_inset Graphics
28516 filename ../images/tabular-feature_append-column.png
28522 \begin_inset Graphics
28523 filename ../images/tabular-feature_delete-column.png
28528 , respectively, or the menu
28530 Edit\SpecialChar \menuseparator
28536 \begin_layout Subsubsection
28537 Standard align Environment
28538 \begin_inset CommandInset label
28540 name "sub:Standard-align-Environment"
28548 \begin_layout Plain Layout
28549 Formula ! multiline ! align environment
28557 \begin_layout Standard
28558 This Align environment is created by presssing
28561 arg "newline-insert newline"
28564 in a formula or by the menu
28566 Insert\SpecialChar \menuseparator
28567 Math\SpecialChar \menuseparator
28568 AMS align Environment
28573 \begin_layout Standard
28574 An example for two formulas set side by side, that are created with a four
28575 column align environment:
28576 \begin_inset Formula \begin{align*}
28577 A & =\sin(B) & C & =D\\
28578 C & \ne A & B & \ne D\end{align*}
28582 As it can be seen, the formulas in this environment are placed so as if
28591 \begin_layout Plain Layout
28599 \begin_inset CommandInset ref
28601 reference "sub:Variable-Space"
28612 before the first and after every even column.
28613 When the formula style
28619 \begin_layout Plain Layout
28621 \begin_inset CommandInset ref
28623 reference "sec:Formula-Styles"
28634 is used, the formula is set without the
28640 before the first column.
28643 \begin_layout Subsubsection
28644 Alignat Environment
28648 \begin_layout Plain Layout
28649 Formula ! multiline ! alignat environment
28657 \begin_layout Standard
28658 The alignat environment has no predefined column separation.
28659 It can be inserted manually with the spaces that are described
28660 \begin_inset CommandInset ref
28662 reference "sub:Space"
28669 \begin_layout Standard
28670 The above example in the alignat environment where 1
28671 \begin_inset space \thinspace{}
28674 cm space was inserted at the beginning of the second formula:
28675 \begin_inset Formula \begin{alignat*}{2}
28676 A & =\sin(B) & \hspace{1cm}C & =D\\
28677 C & \ne A & B & \ne D\end{alignat*}
28681 Because the column separation can be set separately for every column, this
28682 environment is especially suitable to set three and more formulas side
28686 \begin_layout Subsubsection
28687 Flalign Environment
28688 \begin_inset CommandInset label
28690 name "sub:Flalign-Environment"
28698 \begin_layout Plain Layout
28699 Formula ! multiline ! flalign environment
28707 \begin_layout Standard
28708 In this environment the first two columns are always set as much as possible
28709 to the left and the last two ones to the right.
28711 \begin_inset Formula \begin{flalign*}
28712 A & =1 & B & =2 & C & =3\\
28713 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28720 \begin_layout Standard
28721 By creating a flalign environment with an odd number of columns where an
28722 empty TeX-brace is inserted to the last column, several formulas in a document
28723 can be set to the left, although the formula style
28728 As example the indented formula
28729 \begin_inset CommandInset ref
28731 reference "eq:VolInt"
28736 \begin_inset Formula \begin{flalign}
28737 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28741 The first two columns contain the formula.
28742 To indent it as with the formula style
28747 \begin_inset space \thinspace{}
28750 pt space was inserted at the beginning of the first column.
28753 \begin_layout Subsection
28754 Eqnarray Environment
28755 \begin_inset CommandInset label
28757 name "sub:Eqnarray-Environment"
28765 \begin_layout Plain Layout
28766 Formula ! multiline ! eqnarray environment
28774 \begin_layout Standard
28775 When this environment has been created, three blue boxes appear.
28776 The content of the first box is right aligned, the content of the last
28778 The content of the middle box appears centered and a bit smaller, because
28779 it is designed to insert there only relation characters.
28780 \begin_inset Formula \begin{eqnarray*}
28781 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28783 A & = & A\end{eqnarray*}
28790 \begin_layout Subsection
28795 \begin_layout Plain Layout
28796 Formula ! multiline ! gather environment
28804 \begin_layout Standard
28805 This environment consists of only one centered column.
28806 Every line can be numbered.
28807 \begin_inset Formula \begin{gather}
28809 X=\textrm{-}1\end{gather}
28816 \begin_layout Subsection
28817 Multline Environment
28818 \begin_inset CommandInset label
28820 name "sub:Multline-Environment"
28828 \begin_layout Plain Layout
28829 Formula ! multiline ! multline environment
28837 \begin_layout Standard
28838 The multline environment consists, like the gather environment, of only
28840 But the first line is left aligned, the last one right aligned.
28841 All other lines are centered.
28842 Therefore this environment is suitable for long formulas.
28844 \begin_inset CommandInset ref
28846 reference "eq:lefteqn"
28850 in the multline environment:
28851 \begin_inset Formula \begin{multline}
28852 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}\\
28853 -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}\\
28854 =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}
28861 \begin_layout Standard
28862 In the output only the last (first) line of a multline environment appears
28863 numbered when the document numbering is right (left).
28867 \begin_layout Plain Layout
28868 numbering styles see
28869 \begin_inset CommandInset ref
28871 reference "sec:Formula-Styles"
28883 \begin_layout Standard
28892 \begin_layout Plain Layout
28910 \begin_layout Plain Layout
28920 a centered line can be right or left aligned, respectively.
28921 The commands are used as follows:
28924 \begin_layout Standard
28929 shoveright{line content}
28935 shoveleft{line content}
28938 \begin_layout Standard
28939 \begin_inset VSpace medskip
28950 \begin_layout Plain Layout
28960 specifies the distance of the first line from the left page margin.
28961 Predefined is the length 0
28962 \begin_inset space \thinspace{}
28968 \begin_layout Standard
28969 As example the above formula where the command
28972 \begin_layout Standard
28982 \begin_layout Standard
28983 was inserted in TeX-mode before:
28987 \begin_layout Plain Layout
28999 \begin_inset Formula \begin{multline}
29000 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}\\
29001 \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}}\\
29002 =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}
29010 \begin_layout Plain Layout
29021 The second line was left aligned using
29030 \begin_layout Subsection
29031 Multiline Formula Parts
29032 \begin_inset CommandInset label
29034 name "sub:Multiline-Formula-Parts"
29042 \begin_layout Plain Layout
29043 Formula ! multiline ! formula parts
29051 \begin_layout Standard
29052 To display only parts of a formula with multiple lines, one of the following
29053 environments are used:
29070 They can be inserted via the menu
29072 Insert\SpecialChar \menuseparator
29075 or by using the commands described in this section.
29078 \begin_layout Standard
29079 The first three have the same properties as the corresponding multiline
29080 formula environments, but it is possible to set further formula parts beside
29083 \begin_inset Formula \[
29084 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29085 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29086 \right\} \textrm{Uncertainty relations}\]
29093 \begin_layout Standard
29094 To get this formula, a displayed formula is created where the command
29102 \begin_layout Plain Layout
29113 A purple box appears around the blue formula box where now columns and
29114 lines can be added.
29115 Outside the multiline environment other formula parts can be set, like
29119 \begin_layout Standard
29120 The aligned environment is also suitable for long formulas whose lines are
29121 horizontally aligned.
29122 Using aligned in a displayed formula has the advantage that the formula
29123 number is vertically centered behind the lines.
29125 \begin_inset CommandInset ref
29127 reference "eq:shortlong"
29131 in the aligned environment:
29132 \begin_inset Formula \begin{equation}
29133 \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}|}\\
29134 & -\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}
29142 \begin_layout Standard
29143 To use the environments
29165 \begin_layout Plain Layout
29183 \begin_layout Plain Layout
29201 \begin_layout Plain Layout
29209 are inserted, respectively.
29210 The split environment has the same properties as the aligned environment
29211 but it can only have two columns.
29214 \begin_layout Subsection
29215 Text in multiline Formulas
29216 \begin_inset CommandInset label
29218 name "sub:Text-in-multiline"
29226 \begin_layout Plain Layout
29236 \begin_layout Plain Layout
29237 Formula ! multiline ! text
29245 \begin_layout Standard
29246 In the Align environments, and the multline and gather environment, text
29247 can be inserted that will appear in a separate line and doesn't affect
29248 the column alignment.
29249 To do this, the command
29257 \begin_layout Plain Layout
29267 is used in the following scheme:
29270 \begin_layout Standard
29278 \begin_layout Standard
29279 The text should not be longer than a line because it cannot be hyphenated.
29280 As LyX doesn't yet support
29286 directly, the text is written as mathematical text.
29293 must hereby be at the beginning of a line and appears in the output above
29295 An example where the text was inserted at the beginning of the second line:
29296 \begin_inset Formula \begin{align}
29297 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29298 \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}
29305 \begin_layout Section
29310 \begin_layout Plain Layout
29320 \begin_layout Plain Layout
29321 Formula ! numbering|see
29325 \begin_layout Plain Layout
29336 \begin_layout Plain Layout
29351 \begin_layout Subsection
29355 \begin_layout Standard
29356 Numbered formulas can be created with the menu
29358 Insert\SpecialChar \menuseparator
29359 Math\SpecialChar \menuseparator
29361 \begin_inset space ~
29369 \begin_inset space ~
29375 Existing formulas can be numbered with the menu
29377 Edit\SpecialChar \menuseparator
29378 Math\SpecialChar \menuseparator
29380 \begin_inset space ~
29388 arg "math-number-toggle"
29392 The formula number is displayed in LyX behind the formula as number sign
29394 The number sign is replaced in the output by the formula number.
29397 \begin_layout Standard
29398 When numbering is turned on in multiline formulas, all lines will be numbered.
29399 But the numbering can be controlled with the menu
29401 Edit\SpecialChar \menuseparator
29402 Math\SpecialChar \menuseparator
29404 \begin_inset space ~
29408 \begin_inset space ~
29412 \begin_inset space ~
29420 arg "math-number-line-toggle"
29426 \begin_layout Standard
29427 Except for inline formulas, all formulas can be numbered with two different
29429 \begin_inset CommandInset ref
29431 reference "sec:Formula-Styles"
29438 \begin_layout Subsection
29443 \begin_layout Plain Layout
29444 Cross-references ! to formulas
29452 \begin_layout Standard
29453 All labeled formulas can be cross-referenced.
29454 A label is added by the menu
29456 Insert\SpecialChar \menuseparator
29459 or the toolbar button
29460 \begin_inset Graphics
29461 filename ../images/label-insert.png
29467 The cursor must hereby be inside a displayed formula.
29468 A dialog pops up displaying the prefix
29473 The label is inserted there behind the prefix.
29474 The predefined prefix means
29475 \begin_inset Quotes eld
29479 \begin_inset Quotes erd
29482 and makes it easier to find labels in large documents because it marks
29483 it as formula label to divide it from e.
29484 \begin_inset space \thinspace{}
29488 \begin_inset space \space{}
29492 To change a label, the menu
29494 Insert\SpecialChar \menuseparator
29500 \begin_layout Standard
29501 The name of the label is displayed in LyX within two parentheses behind
29503 A formula with a label is always numbered.
29506 \begin_layout Standard
29507 Cross-references are inserted via the menu
29509 Insert\SpecialChar \menuseparator
29512 or with the toolbar button
29513 \begin_inset Graphics
29514 filename ../images/dialog-show-new-inset_ref.png
29520 A formula cross-reference appears in the output as formula number.
29521 When in the cross-reference dialog window the format
29525 is chosen, the cross-reference appears in the output as formula number
29527 \begin_inset Newline newline
29530 By right-clicking on a cross-reference in LyX, one jumps to the formula
29531 that is referenced.
29534 \begin_layout Standard
29535 Here are as examples cross-references to formulas of the following subsections:
29536 \begin_inset Note Note
29539 \begin_layout Plain Layout
29540 Note the different cross-reference types.
29548 \begin_layout Standard
29550 \begin_inset CommandInset ref
29557 \begin_inset CommandInset ref
29565 \begin_inset CommandInset ref
29571 ) big Latin letters are used for the numbering in contrary to (
29572 \begin_inset CommandInset ref
29581 \begin_layout Standard
29582 \begin_inset VSpace medskip
29585 When the argument of
29593 \begin_layout Plain Layout
29601 \begin_inset CommandInset ref
29603 reference "sub:User-defined-Numbering"
29614 contains a box like in
29615 \begin_inset CommandInset ref
29617 reference "sub:Paragraph-Boxes"
29621 , the formula cannot be referenced.
29624 \begin_layout Subsection
29629 \begin_layout Plain Layout
29630 Formula numbering ! subnumbering
29638 \begin_layout Standard
29639 With the help of the commands
29643 begin{subequations}
29651 formulas can be subnumbered.
29652 Both commands are inserted in TeX-mode.
29655 \begin_layout Standard
29657 \begin_inset Formula \begin{equation}
29658 A=C-B\label{eq:a}\end{equation}
29666 \begin_layout Plain Layout
29670 addtocounter{equation}{-1}
29679 \begin_layout Plain Layout
29683 begin{subequations}
29689 \begin_inset VSpace -5mm
29693 \begin_inset Formula \begin{equation}
29694 B=C-A\label{eq:b}\end{equation}
29699 \begin_inset Formula \begin{equation}
29700 C=A+B\label{eq:c}\end{equation}
29707 \begin_layout Standard
29711 \begin_layout Plain Layout
29723 \begin_layout Standard
29724 To create the example, the following is done:
29727 \begin_layout Enumerate
29728 first formula is inserted
29731 \begin_layout Enumerate
29736 addtocounter{equation}{-1}
29738 begin{subequations}
29742 \begin_layout Plain Layout
29751 \begin_inset Newline newline
29756 is inserted after the first formula
29759 \begin_layout Enumerate
29760 second formula is inserted
29763 \begin_layout Enumerate
29764 third formula is inserted
29767 \begin_layout Enumerate
29774 is inserted after the third formula
29777 \begin_layout Standard
29778 Every formula between the commands
29790 is subnumbered as a, b,
29791 \begin_inset Newline linebreak
29794 c, \SpecialChar \ldots{}
29795 For multiline formulas every line will be subnumbered.
29796 All subnumbered formulas are treated as
29801 But as every numbered formula increases the counter
29805 by one, the command
29811 is needed to decrease it.
29812 Otherwise the formulas
29813 \begin_inset CommandInset ref
29820 \begin_inset CommandInset ref
29827 \begin_inset CommandInset ref
29833 would be numbered as
29834 \begin_inset CommandInset ref
29841 \begin_inset CommandInset ref
29848 \begin_inset CommandInset ref
29857 \begin_layout Standard
29858 By inserting the commands in TeX-mode, a space is created between the first
29861 \begin_inset space \thinspace{}
29864 mm vertical space is inserted after the command
29868 begin{subequations}
29871 When the formula style
29877 \begin_layout Plain Layout
29879 \begin_inset CommandInset ref
29881 reference "sec:Formula-Styles"
29893 \begin_inset space \thinspace{}
29896 mm space is inserted instead.
29899 \begin_layout Standard
29900 Here is an example for a multiline formula where the numbering was turned
29901 off for the second line:
29905 \begin_layout Plain Layout
29909 begin{subequations}
29915 \begin_inset Formula \begin{eqnarray}
29916 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29917 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29918 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29926 \begin_layout Plain Layout
29938 \begin_layout Subsection
29939 User-defined Numbering
29940 \begin_inset CommandInset label
29942 name "sub:User-defined-Numbering"
29950 \begin_layout Plain Layout
29951 Formula numbering ! user-defined
29959 \begin_layout Standard
29963 \begin_layout Plain Layout
29964 Formula numbering ! self-defined delimiters
29969 With the standard numbering parentheses are set around the formula number.
29970 To replace the parentheses for example by vertical bars, the following
29971 line is added to the LaTeX-preamble:
29974 \begin_layout Standard
29986 \begin_inset Note Note
29989 \begin_layout Plain Layout
29990 This macro is already declared in the LaTeX-preamble for testing.
29991 To activate it, remove the percent sign at the beginning.
29999 \begin_layout Standard
30000 To use other characters, the vertical bars besides the
30004 are replaced by one ore more characters.
30005 To get only the formula number the vertical bars are omitted.
30008 \begin_layout Standard
30009 \begin_inset VSpace bigskip
30012 When there should be an expression of your choice instead of the consecutive
30013 formula number in parentheses behind the formula, the command
30023 \begin_layout Plain Layout
30032 \begin_inset Formula \begin{equation}
30033 A+B=C\tag{something}\label{eq:tag}\end{equation}
30037 In this example the command
30045 \begin_layout Plain Layout
30056 was inserted to the formula.
30059 \begin_layout Standard
30068 \begin_layout Plain Layout
30079 is inserted instead, the star prevents the parentheses around the expression:
30080 \begin_inset Formula \[
30081 A+B=C\tag*{something}\]
30088 \begin_layout Standard
30089 \begin_inset VSpace bigskip
30092 To restart the formula numbering with new document parts or sections, the
30093 following command is used:
30096 \begin_layout Standard
30101 @addtoreset{equation}{part}
30107 \begin_layout Plain Layout
30112 \begin_layout Plain Layout
30123 \begin_layout Plain Layout
30136 \begin_layout Plain Layout
30147 \begin_layout Plain Layout
30160 \begin_inset Newline newline
30164 \begin_inset Newline newline
30171 @addtoreset{equation}{section}
30174 \begin_layout Standard
30175 To be able to use these commands in TeX-mode, the
30176 \begin_inset Quotes eld
30180 \begin_inset Quotes erd
30183 character has to be made
30184 \begin_inset Quotes eld
30188 \begin_inset Quotes erd
30191 for LaTeX using the command
30205 So the command sequence in TeX-mode is:
30208 \begin_layout Standard
30214 \begin_inset Newline newline
30219 @addtoreset{equation}{section}
30220 \begin_inset Newline newline
30228 \begin_layout Standard
30229 In the LaTeX-preamble
30241 can be omitted as they are automatically internally inserted by LyX.
30244 \begin_layout Standard
30259 \begin_layout Plain Layout
30264 is part of the LaTeX-package
30272 \begin_layout Plain Layout
30273 Packages ! carlisle
30278 that is part of every LaTeX standard installation.
30287 \begin_layout Plain Layout
30288 Packages ! remreset
30293 has to be loaded in the LaTeX-preamble with the line
30296 \begin_layout Standard
30301 usepackage{remreset}
30304 \begin_layout Standard
30315 \begin_layout Plain Layout
30320 \begin_layout Plain Layout
30331 \begin_layout Plain Layout
30344 \begin_layout Plain Layout
30355 \begin_layout Plain Layout
30367 can be used with the same scheme as
30376 \begin_layout Standard
30377 \begin_inset VSpace bigskip
30380 Sometimes formulas should be numbered in the following form:
30383 \begin_layout Standard
30386 (section number.formula number)
30389 \begin_layout Standard
30390 The formula number should start with every section with
30391 \begin_inset Quotes eld
30395 \begin_inset Quotes erd
30401 \begin_layout Standard
30402 For this case there is the command
30412 \begin_layout Plain Layout
30420 , which is used with the following scheme:
30423 \begin_layout Standard
30428 numberwithin{counter}{sectioning}
30431 \begin_layout Standard
30432 Counter denotes what kind of numbering is affected, sectioning denotes what
30433 number is before the dot.
30436 \begin_layout Standard
30437 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30440 \begin_layout Standard
30445 numberwithin{equation}{section}
30448 \begin_layout Standard
30449 This is the result:
30453 \begin_layout Plain Layout
30457 numberwithin{equation}{section}
30463 \begin_inset Formula \begin{equation}
30464 A+B=C\end{equation}
30471 \begin_layout Standard
30473 \begin_inset space \thinspace{}
30477 \begin_inset space \space{}
30480 tables so that the number of the part is the sectioning,
30481 \begin_inset Newline newline
30488 numberwithin{table}{part}
30493 \begin_layout Standard
30494 To go back to the standard numbering or to prevent this kind of numbering
30495 when it is defined by the document class, the following command is inserted
30496 as TeX-Code or to the LaTeX-preamble:
30499 \begin_layout Standard
30512 \begin_layout Plain Layout
30526 \begin_layout Plain Layout
30542 \begin_inset Newline newline
30550 \begin_inset Newline newline
30562 \begin_layout Standard
30569 uses internally the command
30575 , described above, that also needs to be reverted.
30579 \begin_layout Plain Layout
30586 \begin_layout Plain Layout
30590 @removefromreset{equation}{section}
30593 \begin_layout Plain Layout
30605 \begin_layout Subsection
30606 Numbering with Roman Numbers and Letters
30610 \begin_layout Plain Layout
30611 Formula numbering ! with letters
30620 \begin_layout Plain Layout
30621 Formula numbering ! with Roman numbers
30629 \begin_layout Standard
30630 Formulas can also be numbered with Roman numbers and Latin letters.
30631 To number for example with small Roman numbers, the command
30634 \begin_layout Standard
30646 \begin_layout Standard
30647 is inserted before the formula in TeX-mode.
30658 \begin_layout Plain Layout
30666 redefines the predefined command
30682 \begin_layout Plain Layout
30689 has the same scheme like the command
30695 that is described in
30696 \begin_inset CommandInset ref
30698 reference "sub:The-Command-newcommand"
30711 is the formula counter.
30718 is used as prefix for a counter, the value of the counter is output as
30720 When a formula is numbered, LaTeX sets internally the command
30726 behind the formula.
30735 \begin_layout Plain Layout
30745 outputs the counter as small Roman number.
30748 \begin_layout Standard
30749 All formulas behind the command
30759 are now numbered Roman.
30760 To switch to numbering with big Roman numbers, the command is inserted
30777 \begin_layout Plain Layout
30789 \begin_inset Quotes eld
30793 \begin_inset Quotes erd
30796 with small Latin letters there is the command
30806 \begin_layout Plain Layout
30814 , for big ones there is the command
30824 \begin_layout Plain Layout
30837 \begin_layout Standard
30838 \begin_inset Note Greyedout
30841 \begin_layout Plain Layout
30846 Only maximal 26 formulas can be numbered with Latin letters in one document.
30854 \begin_layout Standard
30855 \begin_inset Newpage pagebreak
30861 \begin_layout Standard
30865 \begin_layout Plain Layout
30881 \begin_layout Standard
30882 \begin_inset Formula \begin{equation}
30883 A=\textrm{small roman}\end{equation}
30891 \begin_layout Plain Layout
30905 \begin_inset Formula \begin{equation}
30906 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30914 \begin_layout Plain Layout
30928 \begin_inset Formula \begin{equation}
30929 C=\textrm{small Latin}\end{equation}
30937 \begin_layout Plain Layout
30951 \begin_inset Formula \begin{equation}
30952 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30959 \begin_layout Standard
30960 To switch back to the default numbering, insert the command:
30963 \begin_layout Standard
30976 \begin_layout Plain Layout
30987 \begin_layout Standard
30991 \begin_layout Plain Layout
31005 \begin_inset Formula \begin{equation}
31006 E=\textrm{Arabic}\end{equation}
31013 \begin_layout Standard
31014 \begin_inset VSpace medskip
31017 As you see, formulas are numbered serially independent from the numbering
31019 When then numbering should start with
31020 \begin_inset Quotes eld
31024 \begin_inset Quotes erd
31027 when the style is changed, new equation counters have to be defined.
31028 A description about this can be found in the file
31029 \begin_inset CommandInset href
31031 name "Formula-numbering.lyx"
31032 target "run:Formula-numbering.lyx"
31039 \begin_layout Section
31040 Chemical Symbols and Equations
31041 \begin_inset CommandInset label
31043 name "sub:Chemical-Symbols-and"
31051 \begin_layout Plain Layout
31052 Chemical characters ! Symbols
31061 \begin_layout Plain Layout
31071 \begin_layout Plain Layout
31080 \begin_layout Standard
31081 An example text from chemistry:
31084 \begin_layout Quote
31086 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31089 -ion reacts with two
31090 \begin_inset Formula $\mathrm{Na^{+}}$
31093 -ions to sodium sulfate
31094 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31098 The chemical equation for this is:
31099 \begin_inset Formula \begin{equation}
31100 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31107 \begin_layout Standard
31108 This chemical equation can directly be created as formula.
31109 To avoid that the symbols appear italic, everything is highlighted and
31110 changed by the shortcut
31116 to the upright font style.
31120 \begin_layout Plain Layout
31126 \begin_inset CommandInset ref
31128 reference "sub:Font-Styles"
31140 \begin_layout Standard
31141 A more convenient way to typeset chemical formulas is to use the command
31152 \begin_layout Plain Layout
31160 that is available when the LaTeX-package
31168 \begin_layout Plain Layout
31181 to a formula a new blue box appears where chemical formulas can be inserted
31182 in an intuitive way.
31185 \begin_layout Standard
31187 \begin_inset Tabular
31188 <lyxtabular version="3" rows="9" columns="2">
31190 <column alignment="center" valignment="top" width="0">
31191 <column alignment="center" valignment="top" width="0">
31193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31196 \begin_layout Plain Layout
31202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31205 \begin_layout Plain Layout
31207 \begin_inset Note Note
31210 \begin_layout Plain Layout
31217 is only used as spacer.
31229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31232 \begin_layout Plain Layout
31239 \begin_layout Plain Layout
31253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31256 \begin_layout Plain Layout
31257 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31270 \begin_layout Plain Layout
31277 \begin_layout Plain Layout
31291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31294 \begin_layout Plain Layout
31295 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31308 \begin_layout Plain Layout
31315 \begin_layout Plain Layout
31329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31332 \begin_layout Plain Layout
31333 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31346 \begin_layout Plain Layout
31353 \begin_layout Plain Layout
31367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31370 \begin_layout Plain Layout
31371 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31384 \begin_layout Plain Layout
31391 \begin_layout Plain Layout
31406 \begin_layout Plain Layout
31421 \begin_layout Plain Layout
31435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31438 \begin_layout Plain Layout
31439 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31452 \begin_layout Plain Layout
31459 \begin_layout Plain Layout
31469 \begin_inset Formula $\downarrow$
31473 \begin_inset Formula $\to$
31481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31484 \begin_layout Plain Layout
31485 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31498 \begin_layout Plain Layout
31505 \begin_layout Plain Layout
31518 \begin_layout Plain Layout
31531 \begin_layout Plain Layout
31544 \begin_layout Plain Layout
31557 \begin_layout Plain Layout
31571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31574 \begin_layout Plain Layout
31575 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31588 \begin_layout Plain Layout
31595 \begin_layout Plain Layout
31608 \begin_layout Plain Layout
31621 \begin_layout Plain Layout
31634 \begin_layout Plain Layout
31651 \begin_layout Plain Layout
31665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31668 \begin_layout Plain Layout
31669 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
31685 \begin_layout Standard
31686 \begin_inset Note Greyedout
31689 \begin_layout Plain Layout
31694 Inserting a formula to a
31700 box will lead to LaTeX errors.
31701 In this case TeX code has to be used like for
31715 \begin_layout Plain Layout
31736 \begin_layout Standard
31743 the command for equation
31744 \begin_inset space ~
31748 \begin_inset CommandInset ref
31750 reference "eq:chem-reaction"
31755 \begin_inset Newline newline
31766 \begin_layout Plain Layout
31779 \begin_layout Plain Layout
31792 \begin_layout Plain Layout
31805 \begin_layout Plain Layout
31818 \begin_layout Plain Layout
31831 \begin_layout Plain Layout
31843 \begin_layout Standard
31844 To create multiline chemical equations first a multiline formula is created
31846 \begin_inset CommandInset ref
31848 reference "sec:Multiline-Formulas"
31853 Afterwards the command
31859 is used in every small blue box of the formula.
31861 \begin_inset CommandInset ref
31863 reference "eq:TEOS-reaction-1"
31868 \begin_inset CommandInset ref
31870 reference "eq:TEOS-reaction-2"
31874 are an example of a multi-stage chemical reaction where every equation
31875 has its own number.
31876 \begin_inset Formula \begin{eqnarray}
31877 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31878 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}\end{eqnarray}
31885 \begin_layout Standard
31896 package provides the command
31906 \begin_layout Plain Layout
31914 that has to be used for special cases.
31915 For more information about
31921 and more examples have a look at the documentation of
31926 \begin_inset CommandInset citation
31935 \begin_layout Section
31939 \begin_layout Standard
31940 LyX supports two types of commutative diagrams:
31948 that are explained in the following.
31951 \begin_layout Subsection
31956 \begin_layout Plain Layout
31965 \begin_layout Standard
31966 Diagrams of this type visualize relations by vertical and horizontal lines
31968 \begin_inset Formula \[
31969 \begin{CD}A@>>>B@>>>C\\
31971 F@<<<E@<<<D\end{CD}\]
31978 \begin_layout Standard
31979 To get them, the command
31987 \begin_layout Plain Layout
31997 is inserted to a formula.
31998 A blue box appears with two dashed lines where further commands can be
32003 arg "newline-insert newline"
32006 a new line is created.
32007 Horizontal relations are inserted in odd, vertical in even formula lines.
32010 \begin_layout Standard
32011 To create the relations there are the following commands:
32014 \begin_layout Itemize
32019 creates a left arrow,
32030 \begin_layout Itemize
32035 creates an up arrow,
32043 a vertical equal sign
32046 \begin_layout Itemize
32052 is a placeholder for non-existent relations
32055 \begin_layout Standard
32056 All arrows can be labeled as follows:
32059 \begin_layout Itemize
32060 Is text inserted between the first and second < or >, resp., it is placed
32062 When it is inserted between the second and third one, it appears under
32066 \begin_layout Itemize
32067 When text for vertical arrows is inserted between the first and second A
32068 or V, resp., it is placed left beside the arrow.
32069 When it is inserted between the second and third one, it appears right
32071 If the text contains an A or V, these letters must be set into a TeX-brace.
32074 \begin_layout Standard
32075 As example a diagram with all possible relations:
32078 \begin_layout Standard
32079 \begin_inset Formula \[
32080 \begin{CD}A@>j>>B@>>k>C@=F\\
32082 D@<<j<E@>k>>F@=C\end{CD}\]
32089 \begin_layout Standard
32090 The command for this is:
32091 \begin_inset Newline newline
32102 \begin_layout Plain Layout
32111 A@>j>>B@>>k>C@=F Ctrl+Return
32112 \begin_inset Newline newline
32119 \begin_layout Plain Layout
32134 \begin_layout Plain Layout
32147 \begin_layout Plain Layout
32159 \begin_inset Formula $\to$
32165 \begin_inset Newline newline
32172 \begin_layout Plain Layout
32187 \begin_layout Plain Layout
32200 \begin_layout Plain Layout
32210 \begin_layout Subsection
32215 \begin_layout Plain Layout
32216 Diagrams ! xymatrix
32224 \begin_layout Standard
32225 To be able to use xymatrices, the LaTeX-package
32230 A xymatrix is created by inserting the command
32237 Then you are able to add new matrix columns and rows like for normal matrices,
32239 \begin_inset CommandInset ref
32241 reference "sec:Matrices"
32248 \begin_layout Standard
32249 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32251 All possibilities to create commutative diagrams and decorations are explained
32256 that you find in the menu
32258 Help\SpecialChar \menuseparator
32260 \begin_inset space ~
32263 Manuals\SpecialChar \menuseparator
32265 \begin_inset space ~
32273 \begin_layout Standard
32274 \begin_inset Newpage newpage
32280 \begin_layout Section
32281 User-defined Commands
32285 \begin_layout Plain Layout
32286 User-defined commands
32294 \begin_layout Standard
32295 \begin_inset Note Greyedout
32298 \begin_layout Plain Layout
32303 The names of user-defined commands and macros may only consist of Latin
32312 \begin_layout Subsection
32316 \begin_inset CommandInset label
32318 name "sub:The-Command-newcommand"
32326 \begin_layout Plain Layout
32327 User-defined commands !
32338 \begin_layout Plain Layout
32349 \begin_layout Standard
32350 Many LaTeX-commands are too long to be used frequently.
32351 But it is possible to define with the command
32357 new shorter commands.
32360 \begin_layout Standard
32361 The command scheme of
32370 \begin_layout Standard
32375 newcommand{new command name}[number of arguments][optional
32380 \begin_inset Newline newline
32387 \begin_layout Plain Layout
32402 \begin_layout Plain Layout
32409 {command definition}
32412 \begin_layout Standard
32413 \begin_inset Note Greyedout
32416 \begin_layout Plain Layout
32421 Assure that the name of the new command is not already used in your document
32422 or by LaTeX-packages that you use.
32423 When you for example define the command
32435 , you get an error message because
32441 is already defined as command for
32442 \begin_inset Quotes eld
32446 \begin_inset Formula $\le$
32450 \begin_inset Quotes erd
32461 \begin_layout Standard
32462 The number of arguments is an integer in the range 0
32463 \begin_inset space \thinspace{}
32467 \begin_inset space \thinspace{}
32470 9 and specifies how many arguments the new command should have.
32471 With the optional value a value for an optional argument can be predefined.
32472 When this is done, the
32480 rgument of the new command is automatically an optional one.
32483 \begin_layout Standard
32484 Here are some examples:
32487 \begin_layout Itemize
32488 To define the command
32500 , the LaTeX-preamble line is:
32501 \begin_inset VSpace medskip
32505 \begin_inset Newline newline
32519 \begin_layout Itemize
32520 To define the command
32532 , the argument (that should be underlined) must be taken into account.
32533 For this the preamble line is:
32534 \begin_inset VSpace medskip
32538 \begin_inset Newline newline
32552 \begin_inset VSpace medskip
32556 \begin_inset Newline newline
32563 acts as argument placeholder, the
32567 behind it denotes that it is the placeholder for the first argument.
32570 \begin_layout Itemize
32578 \begin_inset space \thinspace{}
32582 \begin_inset space \space{}
32592 \begin_inset VSpace medskip
32596 \begin_inset Newline newline
32607 framebox#1#2{$#3$}}
32610 \begin_inset VSpace medskip
32614 \begin_inset Newline newline
32617 The two Dollar signs creates the extra formula needed for
32624 \begin_inset CommandInset ref
32626 reference "sub:Boxes-with-Frame"
32633 \begin_layout Itemize
32634 To create a new command for
32640 where the color for the box needn't to be specified, the argument for the
32641 color is defined optional:
32642 \begin_inset VSpace medskip
32646 \begin_inset Newline newline
32657 fcolorbox{#2}{#1}{$#3$}}
32660 \begin_inset VSpace medskip
32664 \begin_inset Newline newline
32667 When the color is not specified when using
32673 , the predefined color
32680 \begin_layout Standard
32681 A test of the new defined commands:
32684 \begin_layout Standard
32686 \begin_inset Tabular
32687 <lyxtabular version="3" rows="6" columns="2">
32689 <column alignment="center" valignment="top" width="0">
32690 <column alignment="center" valignment="top" width="0">
32692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32695 \begin_layout Plain Layout
32701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32704 \begin_layout Plain Layout
32706 \begin_inset Note Note
32709 \begin_layout Plain Layout
32716 is only used as spacer.
32728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32731 \begin_layout Plain Layout
32738 \begin_layout Plain Layout
32752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32755 \begin_layout Plain Layout
32756 \begin_inset Formula $A\gr B$
32766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32769 \begin_layout Plain Layout
32777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32780 \begin_layout Plain Layout
32781 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32794 \begin_layout Plain Layout
32798 \begin_inset Formula $\to$
32804 \begin_inset Formula $\to$
32815 \begin_layout Plain Layout
32829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32832 \begin_layout Plain Layout
32833 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
32843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32846 \begin_layout Plain Layout
32850 \begin_inset Formula $\to$
32861 \begin_layout Plain Layout
32875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32878 \begin_layout Plain Layout
32879 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32892 \begin_layout Plain Layout
32898 \begin_inset Formula $\to$
32909 \begin_layout Plain Layout
32923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32926 \begin_layout Plain Layout
32927 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
32943 \begin_layout Subsection
32948 \begin_layout Plain Layout
32949 User-defined commands! Math macros
32958 \begin_layout Plain Layout
32967 \begin_layout Standard
32968 User-defined commands are especially convenient for complex expressions.
32969 When you are for example dealing in a document with quadratic equations,
32970 the same solution type occurs several times.
32971 The general form of a quadratic equation is
32972 \begin_inset Formula \[
32973 0=\lambda^{2}+p\lambda+q\]
32977 The general form of the solution is
32978 \begin_inset Formula \[
32979 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
32986 \begin_layout Standard
32987 To define a command for the solution formula where only the three parameters
32989 \begin_inset Formula $\lambda$
32993 \begin_inset Formula $p$
32997 \begin_inset Formula $q$
33000 need to be specified and the index of
33001 \begin_inset Formula $\lambda$
33004 can be given optionally, the LaTeX-preamble line is
33005 \begin_inset Newline newline
33021 \begin_inset Newline newline
33028 \begin_layout Plain Layout
33043 \begin_layout Plain Layout
33054 frac{#3^{2}}{4}-#4}}
33057 \begin_layout Standard
33058 To create with this the solution formula, the command
33059 \begin_inset Newline newline
33069 \begin_inset Formula $\to$
33075 \begin_inset Formula $\to$
33082 is inserted to a formula
33087 \begin_layout Standard
33088 The definition of the new command is unintuitive because one has to know
33089 the schemes of all used LaTeX commands, e.
33090 \begin_inset space \thinspace{}
33094 \begin_inset space \space{}
33097 that a fraction is inserted in LaTeX as
33101 frac{numerator}{denominator}
33104 Furthermore one can easily forget a brace in the definition and cannot
33105 see in LyX what the new command is doing.
33106 To avoid these problems LyX offers the possibility to use math macros instead
33116 \begin_layout Standard
33117 A math macro is created by using the menu
33119 Insert\SpecialChar \menuseparator
33120 Math\SpecialChar \menuseparator
33123 or the toolbar button
33124 \begin_inset Graphics
33125 filename ../images/math-macro_newmacroname_newcommand.png
33131 The math macro toolbar appears together with the following box where the
33133 \begin_inset Newline newline
33137 \begin_inset space \hspace*{\fill}
33141 \begin_inset Graphics
33142 filename clipart/macrobox.png
33147 \begin_inset space \hspace*{\fill}
33151 \begin_inset Newline newline
33155 \begin_inset FormulaMacro
33156 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33161 newmacroname is the default name of the macro that should be changed to
33162 something sensible.
33163 The wanted formula is inserted in the first blue box.
33164 An argument placeholder is inserted with the command
33171 \begin_inset space \thinspace{}
33175 \begin_inset space \space{}
33184 or by using the macro toolbar button
33185 \begin_inset Graphics
33186 filename ../images/math-macro-add-param.png
33192 Argument placeholders are displayed red.
33193 Maximum 9 arguments are possible.
33194 Optional arguments are created with the toolbar button
33195 \begin_inset Graphics
33196 filename ../images/math-macro-add-optional-param.png
33202 The first non-optional argument can be transformed to an optional one with
33204 \begin_inset Graphics
33205 filename ../images/math-macro-make-optional.png
33211 In the second blue box the appearance of the macro in LyX can be defined.
33212 Normally you want to see it as it is defined, so the box is kept empty.
33213 But when you have created a macro that needs lot of space on the screen,
33214 you can insert in the box for example
33215 \begin_inset Newline newline
33245 \begin_inset Newline newline
33250 For the macro only the arguments with the macro name in front of them will
33251 then be displayed in LyX, leading to a better overview.
33252 The formula appears in the output as defined in the first box.
33253 \begin_inset Newline newline
33256 The appearance of macros in formulas can furthermore be changed for single
33257 macros by setting the cursor in the macro and using the menu
33259 View\SpecialChar \menuseparator
33261 \begin_inset space ~
33265 \begin_inset space ~
33273 \begin_layout Standard
33274 To use a macro, the macro name is inserted as command to a formula, in our
33282 Our macro looks in LyX like this:
33283 \begin_inset Newline newline
33287 \begin_inset space \hspace*{\fill}
33291 \begin_inset Graphics
33292 filename clipart/macrouse.png
33297 \begin_inset space \hspace*{\fill}
33301 \begin_inset Newline newline
33304 Here is our macro example with the arguments
33305 \begin_inset Formula $x$
33309 \begin_inset Formula $\ln(x)$
33313 \begin_inset Formula $B$
33319 \begin_layout Standard
33320 \begin_inset Formula \[
33328 \begin_layout Standard
33329 LyX offers in the menu
33331 Tools\SpecialChar \menuseparator
33332 Preferences\SpecialChar \menuseparator
33333 Editing\SpecialChar \menuseparator
33336 different styles to edit macros.
33337 To find the style that suits you the most, choose a style and set the cursor
33338 in a macro formula to see the difference.
33341 \begin_layout Standard
33342 A math macro is transformed internally to a
33348 command when exporting the document.
33355 command is not placed in the LaTeX-preamble, therefore macros can only
33356 be used in formulas that are in the document below the macro definition
33360 \begin_layout Standard
33361 Math macros can also be directly be created from a
33368 When writing for example the command
33371 \begin_inset Newline newline
33380 xleftarrow[#2]{#1}}
33381 \begin_inset Newline newline
33386 in LyX as normal text, highlighting it completely and using then the shortcut
33391 , the command will be transformed to a math macro.
33392 Using this method you need to be careful that the
33398 command is typed correctly, otherwise you get a faulty macro leading to
33402 \begin_layout Standard
33403 Math macros currently yet have the problem that further formulas in macro
33404 definitions are handled wrongly.
33405 Therefore the example
33412 \begin_inset CommandInset ref
33414 reference "sub:The-Command-newcommand"
33418 cannot be created as macro.
33421 \begin_layout Standard
33422 When the cursor is in a macro definition box, you will see the macro toolbar
33426 \begin_layout Standard
33427 \begin_inset VSpace defskip
33433 \begin_layout Standard
33434 \begin_inset Graphics
33435 filename clipart/MacroToolbar.png
33443 \begin_layout Plain Layout
33452 \begin_layout Standard
33453 \begin_inset VSpace defskip
33459 \begin_layout Standard
33460 The macro toolbar contains from left to right the following buttons:
33463 \begin_layout Standard
33464 \begin_inset VSpace defskip
33470 \begin_layout Standard
33471 \begin_inset Tabular
33472 <lyxtabular version="3" rows="9" columns="2">
33473 <features islongtable="true">
33474 <column alignment="left" valignment="top" width="0">
33475 <column alignment="left" valignment="top" width="85col%">
33476 <row interlinespace="2.5mm">
33477 <cell alignment="center" valignment="top" usebox="none">
33480 \begin_layout Plain Layout
33481 \begin_inset Graphics
33482 filename ../images/math-macro-remove-param.png
33483 BoundingBox 0bp 5bp 20bp 25bp
33484 rotateOrigin center
33493 <cell alignment="center" valignment="top" usebox="none">
33496 \begin_layout Plain Layout
33499 Edit\SpecialChar \menuseparator
33500 Math\SpecialChar \menuseparator
33502 \begin_inset space ~
33505 Definition\SpecialChar \menuseparator
33506 Remove Last Argument
33512 <row interlinespace="2.5mm">
33513 <cell alignment="center" valignment="top" usebox="none">
33516 \begin_layout Plain Layout
33517 \begin_inset Graphics
33518 filename ../images/math-macro-add-param.png
33519 BoundingBox 0bp 5bp 20bp 25bp
33520 rotateOrigin center
33529 <cell alignment="center" valignment="top" usebox="none">
33532 \begin_layout Plain Layout
33535 Edit\SpecialChar \menuseparator
33536 Math\SpecialChar \menuseparator
33538 \begin_inset space ~
33541 Definition\SpecialChar \menuseparator
33548 <row interlinespace="2.5mm">
33549 <cell alignment="center" valignment="top" usebox="none">
33552 \begin_layout Plain Layout
33553 \begin_inset Graphics
33554 filename ../images/math-macro-make-optional.png
33555 BoundingBox 0bp 5bp 20bp 25bp
33556 rotateOrigin center
33565 <cell alignment="center" valignment="top" usebox="none">
33568 \begin_layout Plain Layout
33571 Edit\SpecialChar \menuseparator
33572 Math\SpecialChar \menuseparator
33574 \begin_inset space ~
33577 Definition\SpecialChar \menuseparator
33578 Make First Non-Optional into
33579 \begin_inset Newline newline
33586 \begin_layout Plain Layout
33595 Edit\SpecialChar \menuseparator
33596 Math\SpecialChar \menuseparator
33598 \begin_inset space ~
33601 Definition\SpecialChar \menuseparator
33606 \begin_layout Plain Layout
33619 <row interlinespace="2.5mm">
33620 <cell alignment="center" valignment="top" usebox="none">
33623 \begin_layout Plain Layout
33624 \begin_inset Graphics
33625 filename ../images/math-macro-make-nonoptional.png
33626 BoundingBox 0bp 5bp 20bp 25bp
33627 rotateOrigin center
33636 <cell alignment="center" valignment="top" usebox="none">
33639 \begin_layout Plain Layout
33642 Edit\SpecialChar \menuseparator
33643 Math\SpecialChar \menuseparator
33645 \begin_inset space ~
33648 Definition\SpecialChar \menuseparator
33649 Make Last Optional into
33650 \begin_inset Newline newline
33657 \begin_layout Plain Layout
33666 Edit\SpecialChar \menuseparator
33667 Math\SpecialChar \menuseparator
33669 \begin_inset space ~
33672 Definition\SpecialChar \menuseparator
33677 \begin_layout Plain Layout
33684 Non-Optional Argument
33690 <row interlinespace="2.5mm">
33691 <cell alignment="center" valignment="top" usebox="none">
33694 \begin_layout Plain Layout
33695 \begin_inset Graphics
33696 filename ../images/math-macro-remove-optional-param.png
33697 BoundingBox 0bp 5bp 20bp 25bp
33698 rotateOrigin center
33707 <cell alignment="center" valignment="top" usebox="none">
33710 \begin_layout Plain Layout
33713 Edit\SpecialChar \menuseparator
33714 Math\SpecialChar \menuseparator
33716 \begin_inset space ~
33719 Definition\SpecialChar \menuseparator
33720 Remove Optional Argument
33726 <row interlinespace="2.5mm">
33727 <cell alignment="center" valignment="top" usebox="none">
33730 \begin_layout Plain Layout
33731 \begin_inset Graphics
33732 filename ../images/math-macro-add-optional-param.png
33733 BoundingBox 0bp 5bp 20bp 25bp
33734 rotateOrigin center
33743 <cell alignment="center" valignment="top" usebox="none">
33746 \begin_layout Plain Layout
33749 Edit\SpecialChar \menuseparator
33750 Math\SpecialChar \menuseparator
33752 \begin_inset space ~
33755 Definition\SpecialChar \menuseparator
33756 Insert Optional Argument
33762 <row interlinespace="2.5mm">
33763 <cell alignment="center" valignment="top" usebox="none">
33766 \begin_layout Plain Layout
33767 \begin_inset Graphics
33768 filename ../images/math-macro-remove-greedy-param.png
33769 BoundingBox 0bp 5bp 20bp 25bp
33770 rotateOrigin center
33779 <cell alignment="center" valignment="top" usebox="none">
33782 \begin_layout Plain Layout
33785 Edit\SpecialChar \menuseparator
33786 Math\SpecialChar \menuseparator
33788 \begin_inset space ~
33791 Definition\SpecialChar \menuseparator
33792 Remove Last Argument
33793 \begin_inset Newline newline
33800 \begin_layout Plain Layout
33809 Edit\SpecialChar \menuseparator
33810 Math\SpecialChar \menuseparator
33812 \begin_inset space ~
33815 Definition\SpecialChar \menuseparator
33820 \begin_layout Plain Layout
33827 Spitting Out To The Right
33833 <row interlinespace="2.5mm">
33834 <cell alignment="center" valignment="top" usebox="none">
33837 \begin_layout Plain Layout
33838 \begin_inset Graphics
33839 filename ../images/math-macro-append-greedy-param.png
33840 BoundingBox 0bp 5bp 20bp 25bp
33841 rotateOrigin center
33850 <cell alignment="center" valignment="top" usebox="none">
33853 \begin_layout Plain Layout
33856 Edit\SpecialChar \menuseparator
33857 Math\SpecialChar \menuseparator
33859 \begin_inset space ~
33862 Definition\SpecialChar \menuseparator
33864 \begin_inset Newline newline
33871 \begin_layout Plain Layout
33880 Edit\SpecialChar \menuseparator
33881 Math\SpecialChar \menuseparator
33883 \begin_inset space ~
33886 Definition\SpecialChar \menuseparator
33891 \begin_layout Plain Layout
33898 Eating From The Right
33904 <row interlinespace="2.5mm">
33905 <cell alignment="center" valignment="top" usebox="none">
33908 \begin_layout Plain Layout
33909 \begin_inset Graphics
33910 filename ../images/math-macro-add-greedy-optional-param.png
33911 BoundingBox 0bp 5bp 20bp 25bp
33912 rotateOrigin center
33921 <cell alignment="center" valignment="top" usebox="none">
33924 \begin_layout Plain Layout
33927 Edit\SpecialChar \menuseparator
33928 Math\SpecialChar \menuseparator
33930 \begin_inset space ~
33933 Definition\SpecialChar \menuseparator
33934 Append Optional Argument
33935 \begin_inset Newline newline
33942 \begin_layout Plain Layout
33951 Edit\SpecialChar \menuseparator
33952 Math\SpecialChar \menuseparator
33954 \begin_inset space ~
33957 Definition\SpecialChar \menuseparator
33962 \begin_layout Plain Layout
33969 Eating From The Right
33982 \begin_layout Standard
33983 \begin_inset Newpage newpage
33989 \begin_layout Section
33994 \begin_layout Plain Layout
34003 \begin_layout Subsection
34008 \begin_layout Plain Layout
34017 \begin_layout Standard
34018 Negative numbers often look ugly in formulas because the minus sign before
34019 the number is set with the same length as the minus operator sign.
34020 When writing the negative number in normal text, the minus sign appears
34024 \begin_layout Standard
34025 Thus, the problem disappears when converting the minus sign to mathematical
34029 \begin_layout Standard
34030 An example to visualize the problem:
34033 \begin_layout Standard
34035 \begin_inset Tabular
34036 <lyxtabular version="3" rows="3" columns="2">
34038 <column alignment="right" valignment="top" width="0">
34039 <column alignment="left" valignment="top" width="0">
34041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34044 \begin_layout Plain Layout
34050 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34053 \begin_layout Plain Layout
34061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34064 \begin_layout Plain Layout
34070 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34073 \begin_layout Plain Layout
34074 \begin_inset Formula $x=-2$
34084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34087 \begin_layout Plain Layout
34093 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34096 \begin_layout Plain Layout
34097 \begin_inset Formula $x=\textrm{-}2$
34113 \begin_layout Subsection
34114 Comma as decimal Separator
34118 \begin_layout Plain Layout
34127 \begin_layout Standard
34128 In LaTeX a comma inside a formula is used, according to the English convention,
34129 as number group separator.
34130 So there will be space added behind all commas in formulas.
34133 \begin_layout Standard
34134 To avoid this, the comma is highlighted and changed to mathematical text
34144 \begin_layout Standard
34145 To use all formula commas in the document as decimal separator, the file
34154 \begin_layout Plain Layout
34159 is part of the LaTeX-package
34167 \begin_layout Plain Layout
34172 \begin_layout Plain Layout
34195 \begin_layout Plain Layout
34201 is loaded with the LaTeX-preamble line
34204 \begin_layout Standard
34212 \begin_layout Subsection
34214 \begin_inset CommandInset label
34216 name "sub:Physical-Vectors"
34224 \begin_layout Plain Layout
34233 \begin_layout Standard
34234 Predefined vectors are offered by the LaTeX-package
34242 \begin_layout Plain Layout
34247 should be part of every LaTeX standard installation.
34256 \begin_layout Plain Layout
34262 that is loaded with the LaTeX-preamble line
34265 \begin_layout Standard
34273 \begin_layout Standard
34277 \begin_layout Plain Layout
34287 \begin_inset Note Note
34290 \begin_layout Plain Layout
34291 The following table will only be displayed when the LaTeX-package
34300 The following commands are defined:
34303 \begin_layout Standard
34305 \begin_inset Tabular
34306 <lyxtabular version="3" rows="4" columns="2">
34308 <column alignment="center" valignment="top" width="0">
34309 <column alignment="center" valignment="top" width="0">
34311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34314 \begin_layout Plain Layout
34320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34323 \begin_layout Plain Layout
34331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34334 \begin_layout Plain Layout
34344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34347 \begin_layout Plain Layout
34348 \begin_inset Formula $\Bra{\psi}$
34358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34361 \begin_layout Plain Layout
34371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34374 \begin_layout Plain Layout
34375 \begin_inset Formula $\Ket{\psi}$
34385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34388 \begin_layout Plain Layout
34400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34403 \begin_layout Plain Layout
34404 \begin_inset Formula $\Braket{\psi|\phi}$
34420 \begin_layout Standard
34427 assures that all vertical bars are set in the size of the surrounding brackets:
34428 \begin_inset Formula \[
34429 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34437 \begin_layout Plain Layout
34447 \begin_inset Note Note
34450 \begin_layout Plain Layout
34451 The following will be displayed when the LaTeX-package
34463 \begin_layout Standard
34464 You need to install the LaTeX-package
34468 to see the rest of this subsection in the output.
34471 \begin_layout Standard
34475 \begin_layout Plain Layout
34487 \begin_layout Standard
34494 can also be achieved using the command
34500 , that is described in
34501 \begin_inset CommandInset ref
34503 reference "sub:Automatic-Bracket-Size"
34510 \begin_layout Subsection
34511 Self-defined Fractions
34512 \begin_inset CommandInset label
34514 name "sub:Self-defined-Fractions"
34522 \begin_layout Plain Layout
34523 Fractions ! self-defined
34531 \begin_layout Standard
34532 To define custom commands for fractions, the command
34542 \begin_layout Plain Layout
34550 is used in the following scheme:
34553 \begin_layout Standard
34566 bracket}{fraction bar thickness}{style}
34567 \begin_inset Newline newline
34574 \begin_layout Plain Layout
34589 \begin_layout Plain Layout
34596 {numerator}{denominator}
34599 \begin_layout Standard
34600 The style is a number in the range of 0
34601 \begin_inset space \thinspace{}
34605 \begin_inset space \thinspace{}
34611 \begin_layout Standard
34613 \begin_inset Tabular
34614 <lyxtabular version="3" rows="5" columns="2">
34616 <column alignment="center" valignment="top" width="0">
34617 <column alignment="center" valignment="top" width="0">
34619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34622 \begin_layout Plain Layout
34628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34631 \begin_layout Plain Layout
34639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34642 \begin_layout Plain Layout
34648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34651 \begin_layout Plain Layout
34652 display style formula
34659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34662 \begin_layout Plain Layout
34668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34671 \begin_layout Plain Layout
34679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34682 \begin_layout Plain Layout
34688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34691 \begin_layout Plain Layout
34699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34702 \begin_layout Plain Layout
34708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34711 \begin_layout Plain Layout
34725 \begin_layout Standard
34726 When no style is given, the size is adjusted to the surrounding environment
34727 like for the command
34736 \begin_layout Standard
34737 When no fraction bar thickness is given, the predefined value of 0.4
34738 \begin_inset space \thinspace{}
34744 \begin_layout Standard
34745 \begin_inset VSpace medskip
34748 For example, the commands
34761 \begin_inset CommandInset ref
34763 reference "sub:Fractions"
34767 are defined with the commands
34770 \begin_layout Standard
34779 genfrac{}{}{}{0}{#1}{#2}}
34782 \begin_layout Standard
34786 \begin_layout Standard
34795 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34798 \begin_layout Standard
34799 \begin_inset VSpace medskip
34802 To define a fraction where the fraction bar thickness can be given as optional
34803 argument, the following line is inserted to the LaTeX-preamble:
34806 \begin_layout Standard
34815 genfrac{}{}{#1}{}{#2}{#3}}
34818 \begin_layout Standard
34820 \begin_inset Formula \begin{align*}
34821 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34822 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34826 As one can see, the distance of the numerator and the denominator to the
34827 fraction bar is round about three times the bar thickness.
34830 \begin_layout Subsection
34835 \begin_layout Plain Layout
34844 \begin_layout Standard
34845 To cancel formulas or formula parts, the LaTeX-package
34853 \begin_layout Plain Layout
34858 is part of every LaTeX standard installation.
34867 \begin_layout Plain Layout
34873 has to be loaded with the LaTeX-preamble line
34876 \begin_layout Standard
34881 usepackage[samesize]{cancel}
34884 \begin_layout Standard
34885 There are four ways to cancel formulas:
34888 \begin_layout Standard
34890 \begin_inset Tabular
34891 <lyxtabular version="3" rows="5" columns="2">
34893 <column alignment="center" valignment="top" width="0">
34894 <column alignment="center" valignment="top" width="0">
34896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34899 \begin_layout Plain Layout
34905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34908 \begin_layout Plain Layout
34910 \begin_inset Note Note
34913 \begin_layout Plain Layout
34920 are used here as spacer.
34932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34935 \begin_layout Plain Layout
34944 \begin_layout Plain Layout
34958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34961 \begin_layout Plain Layout
34962 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34975 \begin_layout Plain Layout
34984 \begin_layout Plain Layout
34998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35001 \begin_layout Plain Layout
35002 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35015 \begin_layout Plain Layout
35024 \begin_layout Plain Layout
35038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35041 \begin_layout Plain Layout
35042 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35055 \begin_layout Plain Layout
35059 \begin_inset Formula $\to$
35070 \begin_layout Plain Layout
35084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35087 \begin_layout Plain Layout
35088 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35104 \begin_layout Standard
35111 is especially suitable to visualize the reduction of fractions within formulas:
35112 \begin_inset Formula \[
35113 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35120 \begin_layout Subsection
35121 Formulas in Section Headings
35122 \begin_inset CommandInset label
35124 name "sub:Formulas-in-Section"
35132 \begin_layout Plain Layout
35133 Formula ! in section headings
35141 \begin_layout Standard
35142 When formulas are used in section headings, the following has to be taken
35146 \begin_layout Standard
35147 \begin_inset Note Greyedout
35150 \begin_layout Plain Layout
35159 \begin_layout Plain Layout
35160 Packages ! hyperref
35165 support is enabled in the document settings dialog under
35168 \begin_inset space ~
35173 , PDF-bookmarks are created for every section heading in the table of contents.
35174 If a section heading contains formulas, they are incorrectly displayed
35175 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35184 \begin_layout Standard
35185 Both problems can be solved by inserting at the end of the section heading
35186 a short title with the menu
35188 Insert\SpecialChar \menuseparator
35190 \begin_inset space ~
35196 Short titles are used as alternative for multiline section headings to
35197 keep the table of contents clearly arranged.
35198 Only the short title appears in the table of contents and therefore also
35199 in the PDF-bookmark.
35202 \begin_layout Standard
35203 When formulas should be used in the table of contents but
35207 is used, one can use the following command in TeX-mode:
35210 \begin_layout Standard
35215 texorpdfstring{part}{alternative}
35219 \begin_layout Plain Layout
35230 \begin_layout Standard
35231 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35232 This can be characters, formulas, footnotes, but also cross-references.
35233 The alternative is used instead of the part for the bookmark.
35236 \begin_layout Standard
35237 Here are two example headings:
35238 \begin_inset VSpace -3mm
35245 \begin_layout Plain Layout
35257 \begin_layout Subsubsection
35258 Heading without formula in table of contents
35259 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35263 \begin_inset OptArg
35266 \begin_layout Plain Layout
35267 Heading without formula in table of contents
35275 \begin_layout Subsubsection
35276 Heading with formula in table of contents
35280 \begin_layout Plain Layout
35290 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35297 \begin_layout Plain Layout
35307 \begin_layout Standard
35311 \begin_layout Plain Layout
35320 In the first heading a short title was used, in the second one
35329 \begin_layout Standard
35330 To get the same formatting as for the other headings, the complete heading
35339 \begin_layout Plain Layout
35341 \begin_inset CommandInset ref
35343 reference "sub:Bold-Formulas"
35355 \begin_layout Subsection
35356 Formulas in multi-column Text
35360 \begin_layout Plain Layout
35361 Formula ! in multi-column text
35369 \begin_layout Standard
35370 Formulas in multi-column text are often too wide to fit into a column and
35371 thus need to be set over the whole page width.
35372 This is done by using the LaTeX-package
35380 \begin_layout Plain Layout
35385 is part of every LaTeX standard installation.
35394 \begin_layout Plain Layout
35395 Packages ! multicol
35400 , that is loaded with the LaTeX-preamble line
35403 \begin_layout Standard
35408 usepackage{multicol}
35411 \begin_layout Standard
35412 \begin_inset Note Greyedout
35415 \begin_layout Plain Layout
35416 Note herby that the setting
35419 \begin_inset space ~
35426 Document\SpecialChar \menuseparator
35432 \begin_inset space ~
35452 \begin_layout Standard
35453 Before the multi-column text the command
35456 \begin_layout Standard
35461 begin{multicols}{column number}
35464 \begin_layout Standard
35465 is written in TeX-mode.
35466 The column number is a number in the range of 2
35467 \begin_inset space \thinspace{}
35471 \begin_inset space \thinspace{}
35475 Before the formula the multi-column text is ended by inserting the command
35478 \begin_layout Standard
35486 \begin_layout Standard
35490 \begin_layout Standard
35491 Due to the command some space is automatically added before the formula.
35493 \begin_inset space \thinspace{}
35496 mm vertical space is inserted before the formula.
35497 When the formula style
35503 \begin_layout Plain Layout
35505 \begin_inset CommandInset ref
35507 reference "sec:Formula-Styles"
35519 \begin_inset space \thinspace{}
35522 mm space is inserted instead.
35525 \begin_layout Standard
35526 As example a multi-column text with a displayed formula:
35529 \begin_layout Standard
35535 \begin_layout Plain Layout
35539 begin{multicols}{2}
35544 Das Spektrum wird fouriertransformiert.
35545 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35546 , Lösungsmittel) zu trennen.
35547 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35548 nun das Aussehen des Ausgangssignals.
35549 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35550 über alle Phasen integrieren muss.
35552 \begin_inset Formula $S$
35555 unser normiertes Ausgangssignal und
35556 \begin_inset Formula $P$
35559 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35563 \begin_layout Plain Layout
35573 \begin_inset VSpace -6mm
35577 \begin_inset Formula \begin{equation}
35578 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35586 \begin_layout Plain Layout
35590 begin{multicols}{2}
35596 \begin_inset Formula $S_{0}$
35599 das Signal ohne Gradient ist und die Normierungsbedingung
35600 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35604 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35606 \begin_inset Formula $\nicefrac{\pi}{2}$
35610 \begin_inset space \thinspace{}
35613 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35614 das Signal zusätzlich abschwächt.
35615 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35617 \begin_inset Formula $T_{2}$
35623 \begin_layout Standard
35629 \begin_layout Plain Layout
35641 \begin_layout Subsection
35642 Formulas with Description of Variables
35646 \begin_layout Plain Layout
35647 Formula ! with description of variables
35655 \begin_layout Standard
35656 To describe variables within a formula, like in formula
35657 \begin_inset CommandInset ref
35659 reference "eq:within"
35668 \begin_inset Formula $n$
35672 \begin_inset space ~
35675 matrix is used with left aligned columns for the
35676 \begin_inset Formula $n$
35683 \begin_layout Plain Layout
35685 \begin_inset CommandInset ref
35687 reference "sec:Matrices"
35696 To set the description in a smaller size, before the matrix e.
35697 \begin_inset space \thinspace{}
35701 \begin_inset space \space{}
35714 \begin_layout Plain Layout
35716 \begin_inset CommandInset ref
35718 reference "sub:Font-Sizes"
35730 \begin_layout Standard
35731 When the formula style
35737 \begin_layout Plain Layout
35739 \begin_inset CommandInset ref
35741 reference "sec:Formula-Styles"
35762 \begin_layout Plain Layout
35769 only works in formulas with the style
35774 \begin_inset CommandInset ref
35776 reference "sub:Variable-Space"
35785 is inserted before and after the matrix to have the same separation of
35786 the matrix from the equation and the side margin.
35789 \begin_layout Standard
35790 When the formula style
35794 is used, the method described in
35795 \begin_inset CommandInset ref
35797 reference "sub:Flalign-Environment"
35801 is used to indent formulas.
35803 \begin_inset CommandInset ref
35805 reference "eq:within"
35809 consists of five columns whereas in the first two columns contain the equation,
35810 the third the matrix, and the last one an empty TeX-brace.
35811 \begin_inset Formula \begin{flalign}
35812 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35813 \rho & \textrm{density}\\
35814 V & \textrm{volume}\\
35815 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35822 \begin_layout Subsection
35823 Upright small Greek Letters
35824 \begin_inset CommandInset label
35826 name "sub:Upright-small-Greek"
35834 \begin_layout Plain Layout
35835 Greek letters ! upright
35843 \begin_layout Standard
35844 Most of the math fonts only provide italic small Greek letters.
35845 But for symbols of elementary particles like pions and neutrinos, upright
35846 Greek letters are needed.
35855 \begin_layout Plain Layout
35860 is part of the LaTeX-package
35868 \begin_layout Plain Layout
35873 \begin_layout Plain Layout
35896 \begin_layout Plain Layout
35902 that is loaded with the LaTeX-preamble line
35905 \begin_layout Standard
35910 usepackage{upgreek}
35913 \begin_layout Standard
35919 \begin_layout Plain Layout
35929 \begin_inset Note Note
35932 \begin_layout Plain Layout
35933 The following table will only be displayed when the LaTeX-package
35942 They are created when the command for a small Greek letters is started
35948 For example the command
35955 \begin_inset Formula $\uptau$
35961 \begin_layout Standard
35962 With these commands reactions of elementary particles can be typeset:
35963 \begin_inset Formula \[
35964 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
35971 \begin_layout Standard
35972 The upright letters are more bold and wider than the italic ones.
35973 They should therefore not be used for units like
35974 \begin_inset Quotes eld
35978 \begin_inset Quotes erd
35984 \begin_layout Standard
35988 \begin_layout Plain Layout
35998 \begin_inset Note Note
36001 \begin_layout Plain Layout
36002 The following will be displayed when the LaTeX-package
36014 \begin_layout Standard
36015 You need to install the LaTeX-package
36019 to see the rest of this subsection in the output.
36022 \begin_layout Standard
36026 \begin_layout Plain Layout
36038 \begin_layout Subsection
36039 Text Characters in Formulas
36040 \begin_inset CommandInset label
36042 name "sub:Text-Characters-in"
36050 \begin_layout Plain Layout
36059 \begin_layout Standard
36060 In some cases you might want to insert text characters directly into formulas.
36061 When for example the centered dot · is often used in formulas like
36062 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36065 , one would have to insert the command
36075 \begin_layout Plain Layout
36077 \begin_inset CommandInset ref
36079 reference "sub:Binary-Operators"
36088 all the time, because this character is defined in all encodings as text
36090 But the encoding can be changed by this LaTeX-preamble line:
36093 \begin_layout Standard
36098 Declare Inputtext{183}{
36108 f\SpecialChar \textcompwordmark{}
36112 \begin_layout Standard
36113 The character encoding (menu
36115 Document\SpecialChar \menuseparator
36116 Settings\SpecialChar \menuseparator
36119 ) specifies what character appears when a keyboard key is pressed.
36120 When the key for the character '·' is pressed, internally the command
36127 But this command is not available in a formula so that you would get LaTeX-erro
36129 With the changed encoding the right command is chosen automatically, depending
36130 on if the character was inserted into a formula or not.
36133 \begin_layout Standard
36134 The encoding of several characters is saved in definition files.
36135 Fore example the encoding
36139 is defined in the file
36143 that is in the installation folder of LaTeX.
36144 Encodings should only be changed via the LaTeX-preamble and not in the
36146 Otherwise own documents could not be edited by other LyX users working
36147 on other computers.
36150 \begin_layout Standard
36151 \begin_inset VSpace medskip
36154 Besides the centered dot, in this document the degree sign ° is defined
36155 with the following LaTeX-preamble line so that it can directly be inserted
36159 \begin_layout Standard
36164 DeclareInputtext{176}{
36174 f\SpecialChar \textcompwordmark{}
36178 \begin_layout Standard
36179 \begin_inset Newpage newpage
36185 \begin_layout Section
36191 \begin_layout Plain Layout
36200 \begin_layout Standard
36201 This section is a summary of the most important typographic rules, listed
36206 \begin_layout Plain Layout
36207 This collection was partly taken from the German semi-official dictionary
36209 \begin_inset Quotes eld
36213 \begin_inset Quotes erd
36217 \begin_inset CommandInset citation
36223 that lists some of the ISO rules.
36231 \begin_layout Itemize
36240 \begin_layout Plain Layout
36241 done with font styles, see
36242 \begin_inset CommandInset ref
36244 reference "sub:Font-Styles"
36254 \begin_inset space \thinspace{}
36258 \begin_inset Newline newline
36261 Between the value and the unit is the smallest space, see
36262 \begin_inset CommandInset ref
36264 reference "sub:Predefined-Space"
36269 \begin_inset Newline newline
36272 This convention is automatically fulfilled when the command
36279 When it is entered to a formula, two boxes appear.
36280 In the first one the value is inserted, in the second one the unit, and
36282 \begin_inset Formula $\unit[30]{km/h}$
36286 \begin_inset space \thinspace{}
36296 is not a real LaTeX command but the command
36302 , therefore you cannot use it in TeX code.
36305 \begin_layout Itemize
36306 Percent and perthousand signs are set like physical units:
36307 \begin_inset Newline newline
36311 \begin_inset space \thinspace{}
36317 \begin_layout Itemize
36318 The degree sign follows directly on the value: 15°, but not when it is used
36320 \begin_inset space \thinspace{}
36326 \begin_layout Itemize
36327 In numbers with more than four digits the smallest space is inserted before
36328 every third digit to group them:
36338 \begin_inset space \thinspace{}
36342 \begin_inset space \thinspace{}
36348 \begin_layout Itemize
36349 For dimensions like 120×90×40
36350 \begin_inset space \thinspace{}
36353 cm the multiplication sign
36354 \begin_inset Quotes eld
36358 \begin_inset Quotes erd
36362 It is available either via the command
36370 Insert\SpecialChar \menuseparator
36371 Special Character\SpecialChar \menuseparator
36377 \begin_layout Itemize
36378 Functions with names consisting of several letters are set upright to avoid
36380 \begin_inset CommandInset ref
36382 reference "sub:Predefined-Functions"
36389 \begin_layout Itemize
36390 Indices consisting of several letters, are set upright:
36391 \begin_inset Formula $E_{\mathrm{kin}}$
36395 \begin_inset Newline newline
36398 Components of matrices are set italic:
36399 \begin_inset Formula $\hat{H}_{kl}$
36405 \begin_layout Itemize
36406 The differentiation/integration operator 'd', the Euler's number 'e', and
36407 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36411 \begin_layout Itemize
36412 The character that denotes a
36416 transformation is inserted either by the command
36424 \begin_layout Plain Layout
36441 \begin_layout Plain Layout
36451 Insert\SpecialChar \menuseparator
36452 Special Character\SpecialChar \menuseparator
36453 Symbols\SpecialChar \menuseparator
36455 \begin_inset space ~
36461 \begin_inset Formula $\mathscr{F}$
36465 \begin_inset Newline newline
36468 To be able to use the command
36474 , the LaTeX package
36482 \begin_layout Plain Layout
36483 Packages ! mathrsfs
36488 needs to be loaded with the LaTeX-preamble line
36492 usepackage{mathrsfs}
36497 \begin_layout Standard
36498 \begin_inset Newpage newpage
36504 \begin_layout Section
36509 \begin_layout Plain Layout
36518 \begin_layout Standard
36519 Some characters and symbols can be created with several commands.
36520 Here is a list of the synonym commands:
36523 \begin_layout Standard
36524 \begin_inset VSpace bigskip
36528 \begin_inset space \hfill{}
36532 \begin_inset Tabular
36533 <lyxtabular version="3" rows="12" columns="2">
36535 <column alignment="center" valignment="top" width="0pt">
36536 <column alignment="center" valignment="top" width="0pt">
36538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36541 \begin_layout Plain Layout
36547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36550 \begin_layout Plain Layout
36552 \begin_inset Note Note
36555 \begin_layout Plain Layout
36562 is only used as spacer.
36574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36577 \begin_layout Plain Layout
36585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36588 \begin_layout Plain Layout
36592 \begin_layout Plain Layout
36605 \begin_layout Plain Layout
36619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36622 \begin_layout Plain Layout
36630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36633 \begin_layout Plain Layout
36643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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