1 #LyX 2.1 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 % solves the following problem:
27 % If the dection number consits of too many numerals the section heading
28 % will be printed in the TOC without a space between it and the section number.
29 % As solution more space between the number and the heading is inserted:
30 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
31 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
33 % increase link area for cross-references and autoname them,
34 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
35 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
36 \addto\extrasenglish{%
37 \renewcommand*{\equationautorefname}[1]{}%
38 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
39 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
40 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
43 % don't load packages twice
44 % see first footnote in sec. 9.3
45 \@ifundefined{textcolor}{\usepackage{color}}{}
47 % the pages of the TOC are numbered roman
48 % and a PDF-bookmark for the TOC is added
50 \let\myTOC\tableofcontents
51 \renewcommand{\tableofcontents}{%
53 \pdfbookmark[1]{\contentsname}{}
56 \pagenumbering{arabic}}
58 % insert additional vertical space of 1.5 mm between footnotes,
60 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
62 % provides caption formatting
63 \setkomafont{captionlabel}{\bfseries}
65 % enables calculation of values
68 % for multiple columns used in sec. 24.7
74 % for the Fourier transformation symbol
77 % define a color, used in sec.9.3
78 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
80 % declare operators (see sec. 10.4 and sec. 15.2)
81 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
82 \DeclareMathOperator{\sgn}{sgn}
84 % example definitions for sec. 20.1
85 \newcommand{\gr}{\Longrightarrow}
86 \newcommand{\us}[1]{\underline{#1}}
87 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
88 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
89 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
91 % example macro from sec. 19.4
92 %\def\tagform@#1{\maketag@@@{|#1|}}
94 % macro from sec. 10.2
95 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
96 \def\mathclap {\mathpalette \mathclapinternal}
97 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
100 % ------------------------------------
101 % used to check for needed LaTeX packages
104 % check for package undertilde
105 % used for the command \utilde
106 \newboolean{undertilde}
107 \IfFileExists{undertilde.sty}
108 {\setboolean{undertilde}{true}}
109 {\setboolean{undertilde}{false}}
111 % check for package eurosym
112 % used for the Euro symbol
114 \IfFileExists{eurosym.sty}
115 {\usepackage[gennarrow]{eurosym}
116 \setboolean{eurosym}{true}}
117 {\setboolean{eurosym}{false}}
119 % check for package braket
120 % used for physical vectors
122 \IfFileExists{braket.sty}
124 \setboolean{braket}{true}}
125 {\setboolean{braket}{false}}
127 % check for package cancel
129 \IfFileExists{cancel.sty}
130 {\setboolean{cancel}{true}}
131 {\setboolean{cancel}{false}}
133 % check for package upgreek
135 \IfFileExists{upgreek.sty}
136 {\usepackage{upgreek}
137 \setboolean{upgreek}{true}}
138 {\setboolean{upgreek}{false}}
140 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
141 \use_default_options false
142 \maintain_unincluded_children false
144 \language_package default
149 \font_typewriter default
151 \font_default_family default
152 \use_non_tex_fonts false
158 \default_output_format default
160 \bibtex_command default
161 \index_command default
165 \pdf_title "LyX's Math Manual"
166 \pdf_author "LyX Team, Uwe Stöhr"
167 \pdf_subject "LyX-documentation about math"
168 \pdf_keywords "LyX, Mathed"
170 \pdf_bookmarksnumbered true
171 \pdf_bookmarksopen true
172 \pdf_bookmarksopenlevel 1
173 \pdf_breaklinks false
177 \pdf_pdfusetitle false
178 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
181 \use_package amsmath 2
182 \use_package amssymb 2
183 \use_package cancel 1
185 \use_package mathdots 1
186 \use_package mathtools 0
187 \use_package mhchem 1
188 \use_package stackrel 0
189 \use_package stmaryrd 0
190 \use_package undertilde 1
192 \cite_engine_type default
196 \paperorientation portrait
200 \notefontcolor #0000ff
207 \paragraph_separation skip
209 \quotes_language english
212 \paperpagestyle plain
216 \tracking_changes false
217 \output_changes false
220 \html_be_strict false
226 LyX's detailed Math manual
234 \begin_layout Plain Layout
236 If you have comments or error corrections, please send them to the LyX Documenta
240 \begin_inset CommandInset href
242 name "lyx-docs@lists.lyx.org"
243 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
254 \begin_inset Note Note
257 \begin_layout Plain Layout
264 \begin_inset Newline newline
268 \begin_inset Newline newline
276 \begin_layout Standard
277 \begin_inset CommandInset toc
278 LatexCommand tableofcontents
285 \begin_layout Standard
286 \begin_inset Note Note
289 \begin_layout Plain Layout
290 To export this document to PDF, PS or DVI the LaTeX-packages
292 braket, cancel, eurosym, mathdots, mhchem, undertilde
299 If they are not installed the document can be exported anyway but the sections
300 where the packages are required will not appear in the output.
305 ; if it is not installed, this file cannot be exported.
308 \begin_layout Plain Layout
309 The latest PDF-version of this document can be found here:
310 \begin_inset Newline newline
315 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
323 \begin_layout Standard
324 \begin_inset Newpage newpage
330 \begin_layout Section
334 \begin_layout Standard
335 This document explains LyX's math features and is furthermore a collection
336 of LaTeX-commands used for mathematical characters and constructs.
337 The explanations are designed for the usage of commands.
338 It is therefore required that you have read the section
349 \begin_layout Standard
350 Most of the characters and many constructs explained in this manual are
351 also accessible via the menu
355 \SpecialChar \menuseparator
371 But everybody who has to write lots of formulas will notice that it is
372 much faster to use commands instead of the math toolbar.
373 Therefore this manual is focused on commands but also mentions the correspondin
374 g toolbar buttons when available.
377 \begin_layout Standard
378 If not specially mentioned the commands are only available within formulas.
379 To be able to use all commands explained in this document, the option
383 must be checked in the document settings (menu
385 Document\SpecialChar \menuseparator
386 Settings\SpecialChar \menuseparator
397 \begin_layout Plain Layout
400 Use AMS math package automatically
406 \begin_layout Plain Layout
415 -math when math constructs are found that are supported by LyX.
423 \begin_layout Standard
424 This document doesn't list all
428 \begin_layout Plain Layout
441 \begin_layout Plain Layout
446 \begin_layout Plain Layout
455 -math commands is in the file
458 \begin_inset CommandInset href
461 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
467 , which is part of every LaTeX standard installation.
472 for lucidity reasons.
475 \begin_layout Section
479 \begin_layout Standard
480 To create an inline formula
481 \begin_inset Index idx
484 \begin_layout Plain Layout
490 that is embedded into a text line, use one of the shortcuts
496 or the toolbar button
497 \begin_inset Graphics
498 filename ../images/math-mode.png
504 \begin_inset Newline newline
507 To create a display style formula
508 \begin_inset Index idx
511 \begin_layout Plain Layout
512 Formula ! display style
517 which will appear bigger, has a different format, and will be in a separate
518 paragraph, use one of these shortcuts:
527 \begin_layout Standard
528 To change a display style formula to an inline formula, set the cursor into
529 the formula and use one of the shortcuts
537 Edit\SpecialChar \menuseparator
538 Math\SpecialChar \menuseparator
542 The same way is used to change an inline formula to a display style formula.
545 \begin_layout Standard
546 To display parts of an inline formula in the size of a display style formula,
554 \begin_inset Index idx
557 \begin_layout Plain Layout
566 Then a new blue box appears in which the desired formula part is inserted.
569 \begin_layout Standard
570 Only inline formulas are allowed inside tables.
573 \begin_layout Standard
578 can be turned on in the menu
580 View\SpecialChar \menuseparator
584 When you click there on
585 \begin_inset Quotes eld
589 \begin_inset Quotes erd
592 the toolbar will be shown permanently at the bottom; this state is visualized
597 menu with a checkmark.
598 When you click in this state again on
599 \begin_inset Quotes eld
603 \begin_inset Quotes erd
614 is only shown when the cursor is within a formula; this state is visualized
615 by the renaming of the menu entry from
616 \begin_inset Quotes eld
620 \begin_inset Quotes erd
624 \begin_inset Quotes eld
632 \begin_inset Quotes erd
638 \begin_layout Standard
640 \begin_inset Index idx
643 \begin_layout Plain Layout
649 is invoked by pressing the toolbar button
650 \begin_inset Graphics
651 filename ../images/ert-insert.png
658 Insert\SpecialChar \menuseparator
663 \begin_layout Plain Layout
679 \begin_inset Note Note
682 \begin_layout Plain Layout
683 In LyX there are three
684 \begin_inset Quotes eld
688 \begin_inset Quotes erd
691 that appear in the output with sub- and superscript letters: TeX, LaTeX
695 \begin_layout Plain Layout
696 To avoid that these names are recognized as proper names, a TeX-brace pair
705 \begin_layout Standard
706 To change the LaTeX-preamble
707 \begin_inset Index idx
710 \begin_layout Plain Layout
718 Document\SpecialChar \menuseparator
719 Settings\SpecialChar \menuseparator
724 \begin_layout Plain Layout
740 \begin_layout Standard
741 To edit matrices, case differentiations and multiline formulas subsequently,
744 Edit\SpecialChar \menuseparator
749 Edit\SpecialChar \menuseparator
751 \begin_inset space \thinspace{}
755 \begin_inset space \thinspace{}
765 When lines and columns are swapped via the menu, the column or line where
766 the cursor is in is exchanged with the column to the right or the line
768 Is the cursor in the last column or row, the exchange is done with the
769 column to the left or the line above.
772 \begin_layout Standard
773 To write text in formulas
777 \begin_layout Plain Layout
778 For multiline formulas the command
785 \begin_inset CommandInset ref
787 reference "sub:Text-in-multiline"
801 \begin_inset Index idx
804 \begin_layout Plain Layout
811 \begin_inset Index idx
814 \begin_layout Plain Layout
821 This mode is invoked with the shortcut
827 or by the insertion of the command
834 \begin_inset Index idx
837 \begin_layout Plain Layout
846 The text appears black in LyX and can therefore be distinguished from the
847 other formula parts which appear blue.
848 In the output mathematical text is set upright, in contrary to other formula
852 \begin_layout Subsection*
856 \begin_layout Standard
857 Most of the LaTeX-commands for math constructs have the following scheme:
860 \begin_layout Standard
876 \begin_layout Standard
877 A command always starts with a backslash
878 \begin_inset Quotes gld
888 \begin_inset Quotes grd
892 To omit optional arguments, also omit the associated brackets.
893 The braces around the required arguments are named in this document as
895 \begin_inset Index idx
898 \begin_layout Plain Layout
905 If you add in a formula a left brace to a command name, LyX automatically
907 In all other cases TeX-braces are created in formulas with the command
915 TeX-braces appear red in LyX, in contrary to normal braces which appear
917 In TeX-mode no command is needed to get TeX-braces.
918 TeX-braces don't appear in the output.
921 \begin_layout Standard
922 When commands without arguments, like commands for symbols are entered in
923 TeX-mode, a space character must
927 be behind the command to end it.
928 This space doesn't appear in the output.
929 When the space should appear in the output, the space must be followed
930 by a protected space in normal text.
933 \begin_layout Standard
934 A protected space is inserted with
937 arg "command-alternatives space-insert protected ; math-space"
943 \begin_layout Subsection*
944 \begin_inset Newpage newpage
950 \begin_layout Itemize
952 \begin_inset space \textvisiblespace{}
955 denotes a space character to be input.
958 \begin_layout Itemize
960 \begin_inset Formula $\to$
963 denotes the usage of the corresponding arrow key on the keyboard.
968 key can often be used instead of
969 \begin_inset Formula $\to$
973 \begin_inset Formula $\downarrow$
981 \begin_inset Formula $\leftarrow$
985 \begin_inset Formula $\uparrow$
991 \begin_layout Subsection*
995 \begin_layout Standard
997 \begin_inset Float table
1003 \begin_layout Plain Layout
1005 \begin_inset Caption Standard
1007 \begin_layout Plain Layout
1008 \begin_inset CommandInset label
1010 name "tab:Available-units"
1022 \begin_layout Plain Layout
1024 \begin_inset Tabular
1025 <lyxtabular version="3" rows="13" columns="2">
1026 <features rotate="0" tabularvalignment="middle">
1027 <column alignment="center" valignment="top">
1028 <column alignment="center" valignment="top">
1030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1033 \begin_layout Plain Layout
1039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1042 \begin_layout Plain Layout
1050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1053 \begin_layout Plain Layout
1059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1062 \begin_layout Plain Layout
1070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1073 \begin_layout Plain Layout
1079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1082 \begin_layout Plain Layout
1090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1093 \begin_layout Plain Layout
1099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1102 \begin_layout Plain Layout
1104 \begin_inset space \thinspace{}
1108 \begin_inset space \thinspace{}
1118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1121 \begin_layout Plain Layout
1127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1130 \begin_layout Plain Layout
1132 \begin_inset space \thinspace{}
1136 \begin_inset space \thinspace{}
1146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1149 \begin_layout Plain Layout
1155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1158 \begin_layout Plain Layout
1160 \begin_inset space \thinspace{}
1164 \begin_inset space \thinspace{}
1174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1177 \begin_layout Plain Layout
1183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1186 \begin_layout Plain Layout
1188 \begin_inset space \thinspace{}
1192 \begin_inset space \thinspace{}
1202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1205 \begin_layout Plain Layout
1211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1214 \begin_layout Plain Layout
1216 \begin_inset space \thinspace{}
1220 \begin_inset space \thinspace{}
1230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1233 \begin_layout Plain Layout
1239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1242 \begin_layout Plain Layout
1244 \begin_inset space \thinspace{}
1248 \begin_inset Formula $\approx$
1252 \begin_inset space \thinspace{}
1262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1265 \begin_layout Plain Layout
1271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1274 \begin_layout Plain Layout
1276 \begin_inset space \thinspace{}
1280 \begin_inset space \thinspace{}
1290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1293 \begin_layout Plain Layout
1299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1302 \begin_layout Plain Layout
1306 \begin_inset Quotes eld
1312 \begin_inset Quotes erd
1322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1325 \begin_layout Plain Layout
1331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1334 \begin_layout Plain Layout
1336 \begin_inset Quotes eld
1344 \begin_inset Quotes erd
1354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1357 \begin_layout Plain Layout
1363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1366 \begin_layout Plain Layout
1368 \begin_inset space \thinspace{}
1372 \begin_inset Formula $\nicefrac{1}{18}$
1376 \begin_inset space \thinspace{}
1397 \begin_layout Standard
1398 \begin_inset Newpage newpage
1404 \begin_layout Section
1408 \begin_layout Subsection
1410 \begin_inset Index idx
1413 \begin_layout Plain Layout
1420 \begin_inset Index idx
1423 \begin_layout Plain Layout
1430 \begin_inset Index idx
1433 \begin_layout Plain Layout
1438 \begin_layout Plain Layout
1449 \begin_layout Plain Layout
1462 \begin_inset Index idx
1465 \begin_layout Plain Layout
1470 \begin_layout Plain Layout
1481 \begin_layout Plain Layout
1496 \begin_layout Standard
1497 Indices are created with an underscore
1498 \begin_inset Quotes eld
1502 \begin_inset Quotes erd
1505 or via the math toolbar button
1506 \begin_inset Graphics
1507 filename ../images/math-subscript.png
1512 , exponents with a caret
1513 \begin_inset Quotes eld
1517 \begin_inset Quotes erd
1520 or via the math toolbar button
1521 \begin_inset Graphics
1522 filename ../images/math-superscript.png
1530 \begin_layout Standard
1532 \begin_inset Tabular
1533 <lyxtabular version="3" rows="4" columns="2">
1534 <features rotate="0" tabularvalignment="middle">
1535 <column alignment="center" valignment="top" width="0pt">
1536 <column alignment="center" valignment="top" width="0pt">
1538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1541 \begin_layout Plain Layout
1547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1550 \begin_layout Plain Layout
1552 \begin_inset Note Note
1555 \begin_layout Plain Layout
1562 is only used as spacer.
1574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1577 \begin_layout Plain Layout
1583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1586 \begin_layout Plain Layout
1587 \begin_inset Formula $B_{V}$
1597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1600 \begin_layout Plain Layout
1606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1609 \begin_layout Plain Layout
1610 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1623 \begin_layout Plain Layout
1625 \begin_inset space \textvisiblespace{}
1633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1636 \begin_layout Plain Layout
1637 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1653 \begin_layout Standard
1654 As the caret is in some languages an accent, vowels will be accentuated
1655 in this case and not set as exponents
1659 \begin_layout Plain Layout
1660 Depending on the used keyboard settings this can also happen for characters
1667 To get exponents in this case, press
1671 after the caret as in the last example.
1674 \begin_layout Subsection
1676 \begin_inset CommandInset label
1678 name "sub:Fractions"
1683 \begin_inset Index idx
1686 \begin_layout Plain Layout
1695 \begin_layout Standard
1696 Fractions are generated with the command
1703 \begin_inset Index idx
1706 \begin_layout Plain Layout
1714 or via the math toolbar button
1715 \begin_inset Graphics
1716 filename ../images/math/frac.png
1722 The font size is adjusted automatically, depending on whether the fraction
1723 is in an inline or display style formula.
1724 With the math toolbar button
1725 \begin_inset Graphics
1726 filename ../images/math/frac-square.png
1731 you can select different fraction types.
1734 \begin_layout Standard
1742 \begin_inset Index idx
1745 \begin_layout Plain Layout
1753 a fraction can be created that always has the size of a display style formula.
1761 \begin_inset Index idx
1764 \begin_layout Plain Layout
1772 the fraction appears always with the size of an inline formula.
1776 \begin_layout Standard
1777 A line with the fraction
1778 \begin_inset Formula $\frac{1}{2}$
1781 that was created with the command
1790 \begin_layout Standard
1791 A line with the fraction
1792 \begin_inset Formula $\dfrac{1}{2}$
1795 that was created with the command
1804 \begin_layout Standard
1806 \begin_inset Tabular
1807 <lyxtabular version="3" rows="4" columns="2">
1808 <features rotate="0" tabularvalignment="middle">
1809 <column alignment="center" valignment="top" width="0pt">
1810 <column alignment="center" valignment="top" width="0pt">
1812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1815 \begin_layout Plain Layout
1821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1824 \begin_layout Plain Layout
1826 \begin_inset Note Note
1829 \begin_layout Plain Layout
1836 is only used as spacer.
1848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1851 \begin_layout Plain Layout
1855 \begin_inset space \textvisiblespace{}
1859 \begin_inset Formula $\downarrow$
1867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1870 \begin_layout Plain Layout
1871 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1884 \begin_layout Plain Layout
1888 \begin_inset space \textvisiblespace{}
1892 \begin_inset Formula $\downarrow$
1900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1903 \begin_layout Plain Layout
1904 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1917 \begin_layout Plain Layout
1921 \begin_inset space \textvisiblespace{}
1927 \begin_inset space \textvisiblespace{}
1931 \begin_inset Formula $\downarrow$
1935 \begin_inset Formula $\downarrow\downarrow$
1943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1946 \begin_layout Plain Layout
1947 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1963 \begin_layout Standard
1964 \begin_inset VSpace bigskip
1968 \begin_inset Newpage newpage
1971 For nested fractions the command
1978 \begin_inset Index idx
1981 \begin_layout Plain Layout
1991 \begin_inset VSpace -3mm
1997 \begin_layout Standard
1998 \begin_inset Formula
2000 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2001 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2009 \begin_layout Standard
2010 The command for the example above is:
2013 \begin_layout Standard
2019 \begin_inset space \textvisiblespace{}
2023 \begin_inset Formula $\downarrow$
2029 \begin_inset space \textvisiblespace{}
2035 \begin_inset space \textvisiblespace{}
2039 \begin_inset Formula $\downarrow$
2043 \begin_inset Formula $\downarrow$
2049 \begin_layout Standard
2050 \begin_inset VSpace medskip
2056 \begin_layout Standard
2063 sets the fraction always in the size of a displayed formula, also when
2064 it is part of another fraction.
2067 \begin_layout Standard
2068 It is possible to specify the alignment of the numerator.
2075 is used to left align it, the command
2088 centers the numerator.
2089 These fractions demonstrate the different alignments:
2092 \begin_layout Standard
2095 \begin_inset Formula
2097 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2105 \begin_layout Standard
2106 \begin_inset Note Greyedout
2109 \begin_layout Plain Layout
2126 are no real LaTeX commands but represent the command
2130 cfrac[alignment]{numerator}{denominator}
2133 Therefore you cannot use them in TeX code.
2141 \begin_layout Standard
2142 \begin_inset VSpace medskip
2145 It is often advantageous to combine
2158 \begin_inset Formula
2160 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2168 \begin_layout Standard
2169 For inline fractions with a sloped fraction stroke you can use the command
2177 \begin_inset Index idx
2180 \begin_layout Plain Layout
2189 \begin_inset Formula $\nicefrac{5}{31}$
2199 \begin_inset Index idx
2202 \begin_layout Plain Layout
2211 \begin_inset Formula $\unitfrac{5}{31}$
2214 There is furthermore the command
2220 that offers to write a fraction in combination with a number:
2221 \begin_inset Formula $\unitfrac[2]{1}{3}$
2227 \begin_layout Standard
2228 \begin_inset Note Greyedout
2231 \begin_layout Plain Layout
2242 is not a real LaTeX command but the command
2243 \begin_inset Newline newline
2250 unitfrac[number]{numerator}{denominator}
2253 Therefore you cannot use it in TeX code.
2261 \begin_layout Standard
2262 How to define own fractions where the fraction stroke can be changed, is
2264 \begin_inset CommandInset ref
2266 reference "sub:Self-defined-Fractions"
2273 \begin_layout Standard
2274 \begin_inset Newpage newpage
2280 \begin_layout Subsection
2282 \begin_inset Index idx
2285 \begin_layout Plain Layout
2294 \begin_layout Standard
2295 Square roots are created with
2302 \begin_inset Index idx
2305 \begin_layout Plain Layout
2313 or the math toolbar button
2314 \begin_inset Graphics
2315 filename ../images/math/sqrt.png
2320 , all other roots with the command
2327 \begin_inset Index idx
2330 \begin_layout Plain Layout
2338 or with the math toolbar button
2339 \begin_inset Graphics
2340 filename ../images/math/root.png
2348 \begin_layout Standard
2350 \begin_inset Tabular
2351 <lyxtabular version="3" rows="3" columns="2">
2352 <features rotate="0" tabularvalignment="middle">
2353 <column alignment="center" valignment="top" width="0pt">
2354 <column alignment="center" valignment="top" width="0pt">
2356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2359 \begin_layout Plain Layout
2365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2368 \begin_layout Plain Layout
2370 \begin_inset Note Note
2373 \begin_layout Plain Layout
2380 is only used as spacer.
2392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2395 \begin_layout Plain Layout
2399 \begin_inset space \textvisiblespace{}
2407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2410 \begin_layout Plain Layout
2411 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2421 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2424 \begin_layout Plain Layout
2428 \begin_inset space \textvisiblespace{}
2432 \begin_inset Formula $\downarrow$
2440 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2443 \begin_layout Plain Layout
2444 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2460 \begin_layout Standard
2461 A square root can also be created with
2467 when the root index field is left empty.
2470 \begin_layout Standard
2471 With certain indices the distance to the root is too small, like in this
2473 \begin_inset Formula $\sqrt[\beta]{B}$
2477 \begin_inset Newline newline
2481 \begin_inset Formula $\beta$
2485 To avoid this, the commands
2492 \begin_inset Index idx
2495 \begin_layout Plain Layout
2510 \begin_inset Index idx
2513 \begin_layout Plain Layout
2521 are used with the following scheme:
2524 \begin_layout Standard
2538 \begin_layout Standard
2539 Distance is the number of Big Points (unit bp;
2540 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2543 ), that the index should be moved to the left or top, resp..
2544 The commands are written to the index.
2545 This way the command
2546 \begin_inset Newline newline
2556 \begin_inset Formula $\to$
2562 \begin_inset Formula $\to$
2568 \begin_inset space \textvisiblespace{}
2572 \begin_inset Formula $\to$
2576 \begin_inset Newline newline
2581 produces a correct typeset formula:
2582 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2588 \begin_layout Subsection
2589 Binomial Coefficients
2590 \begin_inset Index idx
2593 \begin_layout Plain Layout
2594 Binomial coefficients
2602 \begin_layout Standard
2603 Binomial coefficients are inserted with the command
2610 \begin_inset Index idx
2613 \begin_layout Plain Layout
2621 or with the submenu of the math toolbar button
2622 \begin_inset Graphics
2623 filename ../images/math/frac-square.png
2641 there are the commands
2648 \begin_inset Index idx
2651 \begin_layout Plain Layout
2666 \begin_inset Index idx
2669 \begin_layout Plain Layout
2678 For other brackets around binomial coeficients there are the commands
2685 \begin_inset Index idx
2688 \begin_layout Plain Layout
2703 \begin_inset Index idx
2706 \begin_layout Plain Layout
2717 \begin_layout Standard
2719 \begin_inset Tabular
2720 <lyxtabular version="3" rows="6" columns="2">
2721 <features rotate="0" tabularvalignment="middle">
2722 <column alignment="center" valignment="top" width="0pt">
2723 <column alignment="center" valignment="top" width="0pt">
2725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2728 \begin_layout Plain Layout
2734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2737 \begin_layout Plain Layout
2739 \begin_inset Note Note
2742 \begin_layout Plain Layout
2749 is only used as spacer.
2761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2764 \begin_layout Plain Layout
2768 \begin_inset space \textvisiblespace{}
2772 \begin_inset Formula $\downarrow$
2780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2783 \begin_layout Plain Layout
2784 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2797 \begin_layout Plain Layout
2801 \begin_inset space \textvisiblespace{}
2805 \begin_inset Formula $\downarrow$
2813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2816 \begin_layout Plain Layout
2817 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2830 \begin_layout Plain Layout
2834 \begin_inset space \textvisiblespace{}
2838 \begin_inset Formula $\downarrow$
2846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2849 \begin_layout Plain Layout
2850 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2863 \begin_layout Plain Layout
2867 \begin_inset space \textvisiblespace{}
2871 \begin_inset Formula $\downarrow$
2879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2882 \begin_layout Plain Layout
2883 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2896 \begin_layout Plain Layout
2900 \begin_inset space \textvisiblespace{}
2904 \begin_inset Formula $\downarrow$
2912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2915 \begin_layout Plain Layout
2916 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2932 \begin_layout Subsection
2933 Case Differentiations
2934 \begin_inset Index idx
2937 \begin_layout Plain Layout
2938 Case differentiations
2946 \begin_layout Standard
2948 \begin_inset Tabular
2949 <lyxtabular version="3" rows="3" columns="2">
2950 <features rotate="0" tabularvalignment="middle">
2951 <column alignment="center" valignment="top" width="0pt">
2952 <column alignment="center" valignment="top" width="0pt">
2954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2957 \begin_layout Plain Layout
2963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2966 \begin_layout Plain Layout
2974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2977 \begin_layout Plain Layout
2981 \begin_inset space \textvisiblespace{}
2985 \begin_inset Formula $\to$
2989 \begin_inset Index idx
2992 \begin_layout Plain Layout
3005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3008 \begin_layout Plain Layout
3009 \begin_inset Formula $\begin{cases}
3020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3023 \begin_layout Plain Layout
3027 \begin_inset space \textvisiblespace{}
3033 arg "newline-insert newline"
3041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3044 \begin_layout Plain Layout
3045 \begin_inset Formula $\begin{cases}
3046 A & \textrm{for }x>0\\
3047 B & \textrm{for }x=0
3064 \begin_layout Standard
3071 or pressing the math toolbar button
3072 \begin_inset Graphics
3073 filename ../images/math/cases.png
3078 you can create new lines with the shortcut
3081 arg "newline-insert newline"
3084 or the table toolbar button
3085 \begin_inset Graphics
3086 filename ../images/tabular-feature_append-row.png
3094 \begin_layout Standard
3101 is also available via the menu
3103 Insert\SpecialChar \menuseparator
3104 Math\SpecialChar \menuseparator
3110 \begin_layout Subsection
3112 \begin_inset Index idx
3115 \begin_layout Plain Layout
3124 \begin_layout Standard
3132 \begin_inset Index idx
3135 \begin_layout Plain Layout
3143 every character can be displayed canceled.
3144 The characters are quasi accentuated by a slash.
3147 \begin_layout Standard
3149 \begin_inset Tabular
3150 <lyxtabular version="3" rows="4" columns="2">
3151 <features rotate="0" tabularvalignment="middle">
3152 <column alignment="center" valignment="top" width="0pt">
3153 <column alignment="center" valignment="top" width="0pt">
3155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3158 \begin_layout Plain Layout
3164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3167 \begin_layout Plain Layout
3175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3178 \begin_layout Plain Layout
3186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3189 \begin_layout Plain Layout
3190 \begin_inset Formula $\not=$
3200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3203 \begin_layout Plain Layout
3213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3216 \begin_layout Plain Layout
3217 \begin_inset Formula $\not\le$
3227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3230 \begin_layout Plain Layout
3240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3243 \begin_layout Plain Layout
3244 \begin_inset Formula $\not\parallel$
3260 \begin_layout Standard
3261 The last example shows that not all negations look good.
3262 Therefore there are special commands for some negations (see
3263 \begin_inset CommandInset ref
3265 reference "sub:Mathematical-Symbols"
3270 \begin_inset CommandInset ref
3272 reference "sec:Relations"
3279 \begin_layout Subsection
3281 \begin_inset CommandInset label
3283 name "sub:Placeholders"
3288 \begin_inset Index idx
3291 \begin_layout Plain Layout
3298 \begin_inset Index idx
3301 \begin_layout Plain Layout
3302 Chemical characters ! Isotopes
3308 \begin_inset Index idx
3311 \begin_layout Plain Layout
3316 \begin_layout Plain Layout
3327 \begin_layout Plain Layout
3342 \begin_layout Standard
3344 \begin_inset space \thinspace{}
3348 \begin_inset space \space{}
3355 \begin_layout Plain Layout
3356 Typesetting isotopes and chemical symbols is described in
3357 \begin_inset CommandInset ref
3359 reference "sub:Chemical-Symbols-and"
3368 the following problem occurs:
3371 \begin_layout Standard
3373 \begin_inset Tabular
3374 <lyxtabular version="3" rows="2" columns="2">
3375 <features rotate="0" tabularvalignment="middle">
3376 <column alignment="center" valignment="top" width="0pt">
3377 <column alignment="center" valignment="top" width="0pt">
3379 <cell alignment="center" valignment="top" usebox="none">
3382 \begin_layout Plain Layout
3383 Indices created with sub- and superscripts:
3388 <cell alignment="center" valignment="top" usebox="none">
3391 \begin_layout Plain Layout
3392 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3402 <cell alignment="center" valignment="top" usebox="none">
3405 \begin_layout Plain Layout
3411 <cell alignment="center" valignment="top" usebox="none">
3414 \begin_layout Plain Layout
3415 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3429 \begin_inset Note Note
3432 \begin_layout Plain Layout
3439 is only used as spacer.
3447 \begin_layout Standard
3448 The shorter index is by default placed below or above the first character
3449 of the longer index.
3450 To avoid this there is the command
3457 \begin_inset Index idx
3460 \begin_layout Plain Layout
3468 or the math toolbar button
3469 \begin_inset space \thinspace{}
3476 \begin_layout Plain Layout
3477 can be found in the submenu of the toolbar button
3478 \begin_inset Graphics
3479 filename ../images/math/space.png
3490 \begin_inset Graphics
3491 filename ../images/math/phantom.png
3496 that creates one or more phantom characters.
3503 a small blue box appears that is superposed with two red arrows.
3504 The arrows indicate that the complete width and height of the box content
3505 will be created as placeholder.
3506 Phantom characters are accordingly placeholders with the size of the characters.
3509 \begin_layout Standard
3511 \begin_inset Tabular
3512 <lyxtabular version="3" rows="4" columns="2">
3513 <features rotate="0" tabularvalignment="middle">
3514 <column alignment="center" valignment="top">
3515 <column alignment="center" valignment="top">
3517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3520 \begin_layout Plain Layout
3526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3529 \begin_layout Plain Layout
3531 \begin_inset Note Note
3534 \begin_layout Plain Layout
3541 is only used as spacer.
3553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3556 \begin_layout Plain Layout
3558 \begin_inset space \textvisiblespace{}
3564 \begin_inset space \textvisiblespace{}
3568 \begin_inset Formula $\to$
3572 \begin_inset space \textvisiblespace{}
3580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3583 \begin_layout Plain Layout
3584 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3597 \begin_layout Plain Layout
3599 \begin_inset space \textvisiblespace{}
3605 \begin_inset space \textvisiblespace{}
3609 \begin_inset Formula $\to$
3613 \begin_inset space \textvisiblespace{}
3621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3624 \begin_layout Plain Layout
3625 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3638 \begin_layout Plain Layout
3642 \begin_inset space \textvisiblespace{}
3648 \begin_inset space \textvisiblespace{}
3652 \begin_inset Formula $\to$
3656 \begin_inset space \textvisiblespace{}
3664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3667 \begin_layout Plain Layout
3668 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3684 \begin_layout Standard
3685 Furthermore there are the commands
3692 \begin_inset Index idx
3695 \begin_layout Plain Layout
3704 \begin_inset space ~
3708 \begin_inset Graphics
3709 filename ../images/math/vphantom.png
3721 \begin_inset Index idx
3724 \begin_layout Plain Layout
3733 \begin_inset space ~
3737 \begin_inset Graphics
3738 filename ../images/math/hphantom.png
3750 creates only space for the maximal height of the characters in the box
3751 but not for its width.
3758 creates only space for the width of the box content.
3759 Therefore the boxes of both commands have only one red arrow.
3762 \begin_layout Standard
3763 For example the command
3768 \begin_inset space \textvisiblespace{}
3775 creates space for the height of the integral sign,
3779 \begin_layout Plain Layout
3786 creates an integral sign, see
3787 \begin_inset CommandInset ref
3789 reference "sub:Big-Operators"
3798 because this is the larger character.
3799 An example application is in
3800 \begin_inset CommandInset ref
3802 reference "sub:Multiline-Brackets"
3809 \begin_layout Standard
3810 Placeholders can also be used for text when they are inserted via the menu
3813 Insert\SpecialChar \menuseparator
3814 Formatting\SpecialChar \menuseparator
3820 \begin_layout Standard
3822 \begin_inset Newline newline
3826 \begin_inset Phantom Phantom
3829 \begin_layout Plain Layout
3838 \begin_layout Subsection
3840 \begin_inset Index idx
3843 \begin_layout Plain Layout
3850 \begin_inset Index idx
3853 \begin_layout Plain Layout
3854 Formula ! underlined
3862 \begin_layout Standard
3864 \begin_inset Tabular
3865 <lyxtabular version="3" rows="4" columns="2">
3866 <features rotate="0" tabularvalignment="middle">
3867 <column alignment="center" valignment="top" width="0pt">
3868 <column alignment="center" valignment="top" width="0pt">
3870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3873 \begin_layout Plain Layout
3879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3882 \begin_layout Plain Layout
3884 \begin_inset Note Note
3887 \begin_layout Plain Layout
3894 is only used as spacer.
3906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3909 \begin_layout Plain Layout
3913 \begin_inset space \textvisiblespace{}
3917 \begin_inset Index idx
3920 \begin_layout Plain Layout
3933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3936 \begin_layout Plain Layout
3937 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3950 \begin_layout Plain Layout
3954 \begin_inset space \textvisiblespace{}
3958 \begin_inset Index idx
3961 \begin_layout Plain Layout
3974 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3977 \begin_layout Plain Layout
3978 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3991 \begin_layout Plain Layout
3995 \begin_inset space \textvisiblespace{}
4001 \begin_inset space \textvisiblespace{}
4009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4012 \begin_layout Plain Layout
4013 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4029 \begin_layout Standard
4030 In the last example it doesn't matter if first
4045 \begin_layout Standard
4046 To double underline use
4055 \begin_layout Standard
4056 It is possible to place up to 6 lines above or below characters.
4059 \begin_layout Standard
4060 \begin_inset VSpace bigskip
4063 Custom lines can be created using the command
4070 \begin_inset Index idx
4073 \begin_layout Plain Layout
4081 which has the following scheme:
4084 \begin_layout Standard
4089 rule[vertical offset]{length}{thickness}
4092 \begin_layout Standard
4093 The optional vertical offset shifts the line upwards (or downwards, when
4094 the value is negative).
4096 \begin_inset CommandInset ref
4098 reference "tab:Available-units"
4102 can be used for the values.
4103 Here are two example lines created with the commands
4104 \begin_inset Newline newline
4111 rule[-2ex]{3cm}{2pt}
4122 \begin_layout Standard
4124 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4130 \begin_layout Standard
4137 can also be used for text when a line is inserted via the menu
4139 Insert\SpecialChar \menuseparator
4140 Formatting\SpecialChar \menuseparator
4142 \begin_inset space ~
4150 \begin_layout Standard
4152 \begin_inset CommandInset line
4163 \begin_layout Subsection
4165 \begin_inset CommandInset label
4172 \begin_inset Index idx
4175 \begin_layout Plain Layout
4184 \begin_layout Standard
4185 There are different types of ellipses available.
4189 \begin_layout Plain Layout
4190 In the math toolbar in the submenu of the button
4191 \begin_inset Graphics
4192 filename ../images/math/ldots.png
4202 For listings dots at the baseline are used (
4209 \begin_inset Index idx
4212 \begin_layout Plain Layout
4220 ), while for operations dots are needed that are on the same height as the
4228 \begin_inset Index idx
4231 \begin_layout Plain Layout
4240 When using the command
4247 \begin_inset Index idx
4250 \begin_layout Plain Layout
4258 , LaTeX decides on the basis of the next character what type is used.
4261 \begin_layout Standard
4263 \begin_inset Tabular
4264 <lyxtabular version="3" rows="9" columns="2">
4265 <features rotate="0" tabularvalignment="middle">
4266 <column alignment="center" valignment="top" width="0pt">
4267 <column alignment="center" valignment="top" width="0pt">
4269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4272 \begin_layout Plain Layout
4278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4281 \begin_layout Plain Layout
4289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4292 \begin_layout Plain Layout
4294 \begin_inset space \textvisiblespace{}
4300 \begin_inset space \textvisiblespace{}
4308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4311 \begin_layout Plain Layout
4312 \begin_inset Formula $A_{1},\dots,A_{n}$
4322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4325 \begin_layout Plain Layout
4327 \begin_inset space \textvisiblespace{}
4333 \begin_inset space \textvisiblespace{}
4341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4344 \begin_layout Plain Layout
4345 \begin_inset Formula $A_{1}+\dots+A_{n}$
4355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4358 \begin_layout Plain Layout
4360 \begin_inset space \textvisiblespace{}
4366 \begin_inset space \textvisiblespace{}
4374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4377 \begin_layout Plain Layout
4378 \begin_inset Formula $A_{1},\ldots,A_{n}$
4388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4391 \begin_layout Plain Layout
4393 \begin_inset space \textvisiblespace{}
4399 \begin_inset space \textvisiblespace{}
4407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4410 \begin_layout Plain Layout
4411 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4424 \begin_layout Plain Layout
4432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4435 \begin_layout Plain Layout
4436 \begin_inset Formula $\vdots$
4446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4449 \begin_layout Plain Layout
4457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4460 \begin_layout Plain Layout
4461 \begin_inset Formula $\ddots$
4471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4474 \begin_layout Plain Layout
4482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4485 \begin_layout Plain Layout
4486 \begin_inset Formula $\iddots$
4496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4499 \begin_layout Plain Layout
4501 \begin_inset space \thinspace{}
4504 matrix with the different dots
4509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4512 \begin_layout Plain Layout
4513 \begin_inset Formula $\begin{array}{ccc}
4514 A_{11} & \cdots & A_{1m}\\
4515 \vdots & \ddots & \vdots\\
4516 A_{n1} & \cdots & A_{nm}
4533 \begin_layout Standard
4534 The ellipses available in menu
4536 Insert\SpecialChar \menuseparator
4538 \begin_inset space ~
4552 \begin_layout Standard
4553 \begin_inset VSpace medskip
4562 , one of the options
4564 Use mathdots package (automatically)
4566 must be set in the document settings under
4569 \begin_inset space ~
4575 \begin_inset Newline newline
4580 Use mathdots package
4582 will improve the appearance of all dots in the documents if their font
4583 style or size is not the default.
4586 \begin_layout Standard
4587 \begin_inset VSpace medskip
4590 Specially for matrices there are ellipses that span over several columns.
4591 They are created with the command
4598 \begin_inset Index idx
4601 \begin_layout Plain Layout
4609 , that has the following scheme:
4612 \begin_layout Standard
4617 hdotsfor[distance]{number of columns}
4620 \begin_layout Standard
4621 The number of columns specifies how many columns should be spanned.
4622 Distance is a factor for the distance between the dots.
4625 \begin_layout Standard
4626 In the following matrix the command
4632 was inserted in the first box of the second line, to get an ellipsis with
4633 a dot distance twice as long as with the command
4640 \begin_inset Formula
4642 \left(\begin{array}{cccc}
4651 Note that the matrix fields that should be spanned must be empty, otherwise
4652 you get LaTeX-errors.
4655 \begin_layout Standard
4656 \begin_inset VSpace bigskip
4659 Furthermore you can fill with the command
4666 \begin_inset Index idx
4669 \begin_layout Plain Layout
4677 the rest of a line with dots.
4678 The effect of these commands is the same as with
4685 \begin_inset CommandInset ref
4687 reference "sub:Variable-Space"
4694 \begin_layout Standard
4695 For example the command
4700 \begin_inset space \textvisiblespace{}
4708 \begin_layout Standard
4709 \begin_inset Formula $A\dotfill B$
4715 \begin_layout Standard
4722 there is for a line the command
4729 \begin_inset Index idx
4732 \begin_layout Plain Layout
4743 \begin_layout Standard
4744 \begin_inset Formula $A\hrulefill B$
4750 \begin_layout Standard
4751 To use the commands for text, they have to be inserted in TeX-mode.
4754 \begin_layout Section
4756 \begin_inset CommandInset label
4763 \begin_inset Index idx
4766 \begin_layout Plain Layout
4775 \begin_layout Standard
4776 Matrices can be inserted via the math toolbar button
4777 \begin_inset Graphics
4778 filename ../images/dialog-show_mathmatrix.png
4785 Insert\SpecialChar \menuseparator
4786 Math\SpecialChar \menuseparator
4790 In the matrix dialog you can specify the number of columns and rows, the
4791 alignment and the decoration.
4792 The vertical alignment is only of importance for matrices in inline formulas:
4795 \begin_layout Standard
4796 The first matrix is top
4797 \begin_inset Formula $\begin{array}[t]{cccc}
4805 \begin_inset Formula $\begin{array}{cccc}
4812 and the third bottom
4813 \begin_inset Formula $\begin{array}[b]{cccc}
4823 \begin_layout Standard
4824 The horizontal alignment specifies how the column entries should be aligned.
4825 It is set by entering a letter for every column.
4830 denotes left aligned,
4839 To create for example a 4
4844 \begin_inset space ~
4847 matrix where the first column is left aligned, the second and third are
4848 centered and the last one is right aligned, one enters for the horizontal
4854 Normally in a matrix all columns are centered, therefore the default for
4862 \begin_layout Standard
4863 Horizontal alignment:
4866 \begin_layout Standard
4872 \begin_inset Formula $\begin{array}{lll}
4884 \begin_inset Formula $\begin{array}{ccc}
4896 \begin_inset Formula $\begin{array}{rrr}
4906 \begin_layout Standard
4907 To add or delete rows and columns subsequently, the math toolbar buttons
4909 \begin_inset Graphics
4910 filename ../images/tabular-feature_append-row.png
4916 \begin_inset Graphics
4917 filename ../images/tabular-feature_delete-row.png
4923 \begin_inset space \thinspace{}
4928 Edit\SpecialChar \menuseparator
4932 New rows can also be created with
4935 arg "newline-insert newline"
4941 \begin_layout Standard
4942 \begin_inset VSpace bigskip
4949 adds parentheses in the selected style around the matrix.
4950 Alternatively, parentheses can can either be created with the commands
4958 \begin_inset Index idx
4961 \begin_layout Plain Layout
4976 \begin_inset Index idx
4979 \begin_layout Plain Layout
4990 \begin_inset space ~
4996 \begin_inset CommandInset ref
4998 reference "sub:Automatic-Bracket-Size"
5002 , or by using the following commands:
5003 \begin_inset VSpace medskip
5009 \begin_layout Standard
5010 \begin_inset space \hfill{}
5014 \begin_inset Tabular
5015 <lyxtabular version="3" rows="4" columns="2">
5016 <features rotate="0" tabularvalignment="middle">
5017 <column alignment="center" valignment="top">
5018 <column alignment="center" valignment="top">
5020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5023 \begin_layout Plain Layout
5029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5032 \begin_layout Plain Layout
5034 \begin_inset Note Note
5037 \begin_layout Plain Layout
5044 is only used as spacer.
5056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5059 \begin_layout Plain Layout
5063 \begin_inset space \textvisiblespace{}
5071 \begin_inset space \thinspace{}
5079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5082 \begin_layout Plain Layout
5083 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5084 0 & \textrm{-}\mathrm{i}\\
5086 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5099 \begin_layout Plain Layout
5103 \begin_inset space \textvisiblespace{}
5111 \begin_inset space \thinspace{}
5119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5122 \begin_layout Plain Layout
5123 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5124 0 & \textrm{-}\mathrm{i}\\
5126 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5139 \begin_layout Plain Layout
5143 \begin_inset space \textvisiblespace{}
5151 \begin_inset space \thinspace{}
5159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5162 \begin_layout Plain Layout
5163 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5164 0 & \textrm{-}\mathrm{i}\\
5166 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5180 \begin_inset space \hfill{}
5184 \begin_inset Tabular
5185 <lyxtabular version="3" rows="4" columns="2">
5186 <features rotate="0" tabularvalignment="middle">
5187 <column alignment="center" valignment="top">
5188 <column alignment="center" valignment="top">
5190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5193 \begin_layout Plain Layout
5199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5202 \begin_layout Plain Layout
5210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5213 \begin_layout Plain Layout
5217 \begin_inset space \textvisiblespace{}
5225 \begin_inset space \thinspace{}
5233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5236 \begin_layout Plain Layout
5237 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5238 0 & \textrm{-}\mathrm{i}\\
5240 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5253 \begin_layout Plain Layout
5257 \begin_inset space \textvisiblespace{}
5265 \begin_inset space \thinspace{}
5273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5276 \begin_layout Plain Layout
5277 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5278 0 & \textrm{-}\mathrm{i}\\
5280 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5293 \begin_layout Plain Layout
5297 \begin_inset space \textvisiblespace{}
5305 \begin_inset space \thinspace{}
5313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5316 \begin_layout Plain Layout
5317 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5318 0 & \textrm{-}\mathrm{i}\\
5320 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5334 \begin_inset space \hfill{}
5340 \begin_layout Standard
5341 \begin_inset VSpace medskip
5345 \begin_inset space \thinspace{}
5349 \begin_inset space \space{}
5358 is inserted, a blue box appears between two vertical lines where the matrix
5360 \begin_inset Newline newline
5363 Note that decorated matrices ignore the vertical alignment.
5366 \begin_layout Standard
5367 \begin_inset VSpace bigskip
5370 As all multiline formulas are matrices, the length
5377 \begin_inset Index idx
5380 \begin_layout Plain Layout
5388 that is described in
5389 \begin_inset CommandInset ref
5391 reference "sub:Column-Separation"
5395 can also be used to change the column separation of matrices.
5398 \begin_layout Standard
5399 To change the row separation, the command
5406 \begin_inset Index idx
5409 \begin_layout Plain Layout
5418 It is used as follows:
5421 \begin_layout Standard
5428 arraystretch}{stretch factor}
5429 \begin_inset Index idx
5432 \begin_layout Plain Layout
5443 \begin_layout Standard
5450 assigns the stretch factor to the predefined command
5458 \begin_inset space \thinspace{}
5462 \begin_inset space \space{}
5465 the row separation, use the factor 2.
5466 This is then used for all following matrices.
5467 To go back to the original separation, assign the factor 1 to
5476 \begin_layout Standard
5477 To set matrices into a text line, the command
5484 \begin_inset Index idx
5487 \begin_layout Plain Layout
5496 When it is inserted a blue box with two dashed lines appears.
5497 In this box the matrix is inserted.
5500 \begin_layout Standard
5502 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5504 \end{smallmatrix}\right)$
5510 \begin_layout Section
5511 Brackets and Delimiters
5512 \begin_inset Index idx
5515 \begin_layout Plain Layout
5522 \begin_inset Index idx
5525 \begin_layout Plain Layout
5534 \begin_layout Subsection
5535 Vertical Brackets and Delimiters
5536 \begin_inset Index idx
5539 \begin_layout Plain Layout
5548 \begin_layout Standard
5549 \begin_inset space \hfill{}
5553 \begin_inset Tabular
5554 <lyxtabular version="3" rows="9" columns="2">
5555 <features rotate="0" tabularvalignment="middle">
5556 <column alignment="center" valignment="top" width="0pt">
5557 <column alignment="center" valignment="top" width="0pt">
5559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5562 \begin_layout Plain Layout
5568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5571 \begin_layout Plain Layout
5579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5582 \begin_layout Plain Layout
5588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5591 \begin_layout Plain Layout
5592 \begin_inset Formula $($
5602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5605 \begin_layout Plain Layout
5611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5614 \begin_layout Plain Layout
5615 \begin_inset Formula $\{$
5625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5628 \begin_layout Plain Layout
5634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5637 \begin_layout Plain Layout
5638 \begin_inset Formula $[$
5648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5651 \begin_layout Plain Layout
5659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5662 \begin_layout Plain Layout
5663 \begin_inset Formula $\langle$
5673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5676 \begin_layout Plain Layout
5684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5687 \begin_layout Plain Layout
5688 \begin_inset Formula $\lceil$
5698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5701 \begin_layout Plain Layout
5709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5712 \begin_layout Plain Layout
5713 \begin_inset Formula $\lfloor$
5723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5726 \begin_layout Plain Layout
5732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5735 \begin_layout Plain Layout
5736 \begin_inset Formula $/$
5746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5749 \begin_layout Plain Layout
5755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5758 \begin_layout Plain Layout
5759 \begin_inset Formula $|$
5773 \begin_inset space \hfill{}
5777 \begin_inset Tabular
5778 <lyxtabular version="3" rows="9" columns="2">
5779 <features rotate="0" tabularvalignment="middle">
5780 <column alignment="center" valignment="top" width="0pt">
5781 <column alignment="center" valignment="top" width="0pt">
5783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5786 \begin_layout Plain Layout
5792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5795 \begin_layout Plain Layout
5803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5806 \begin_layout Plain Layout
5812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5815 \begin_layout Plain Layout
5816 \begin_inset Formula $)$
5826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5829 \begin_layout Plain Layout
5835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5838 \begin_layout Plain Layout
5839 \begin_inset Formula $\}$
5849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5852 \begin_layout Plain Layout
5858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5861 \begin_layout Plain Layout
5862 \begin_inset Formula $]$
5872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5875 \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 $\rangle$
5897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5900 \begin_layout Plain Layout
5908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5911 \begin_layout Plain Layout
5912 \begin_inset Formula $\rceil$
5922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5925 \begin_layout Plain Layout
5933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5936 \begin_layout Plain Layout
5937 \begin_inset Formula $\rfloor$
5947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5950 \begin_layout Plain Layout
5960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5963 \begin_layout Plain Layout
5964 \begin_inset Formula $\backslash$
5974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5977 \begin_layout Plain Layout
5985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5988 \begin_layout Plain Layout
5989 \begin_inset Formula $\|$
6003 \begin_inset space \hfill{}
6009 \begin_layout Standard
6012 \begin_inset Note Greyedout
6015 \begin_layout Plain Layout
6020 In TeX-mode the command
6027 \begin_inset Index idx
6030 \begin_layout Plain Layout
6038 must be used for the backslash, because the command
6046 produces a line break there.
6054 \begin_layout Standard
6055 For all characters listed above the size can be adjusted with the commands
6056 described in the following two subsections.
6057 When using these commands, the characters < and > can directly be used
6058 instead of the commands
6073 \begin_layout Subsubsection
6075 \begin_inset CommandInset label
6077 name "sub:Manual-Bracket-Size"
6082 \begin_inset Index idx
6085 \begin_layout Plain Layout
6086 Bracket size ! manual
6094 \begin_layout Standard
6095 The bracket size can be specified manually by the LaTeX-commands
6102 \begin_inset Index idx
6105 \begin_layout Plain Layout
6138 denotes the smallest and
6144 the largest bracket size.
6147 \begin_layout Standard
6148 These commands are used to emphasize levels of brackets:
6151 \begin_layout Standard
6153 \begin_inset Tabular
6154 <lyxtabular version="3" rows="2" columns="2">
6155 <features rotate="0" tabularvalignment="middle">
6156 <column alignment="center" valignment="top" width="0pt">
6157 <column alignment="center" valignment="top" width="0pt">
6159 <cell alignment="center" valignment="top" usebox="none">
6162 \begin_layout Plain Layout
6163 all brackets in the same size:
6168 <cell alignment="center" valignment="top" usebox="none">
6171 \begin_layout Plain Layout
6172 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6182 <cell alignment="center" valignment="top" usebox="none">
6185 \begin_layout Plain Layout
6191 <cell alignment="center" valignment="top" usebox="none">
6194 \begin_layout Plain Layout
6195 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6209 \begin_inset Note Note
6212 \begin_layout Plain Layout
6219 is only used as spacer.
6227 \begin_layout Standard
6228 For the second formula the command
6235 \begin_inset space \textvisiblespace{}
6243 \begin_layout Standard
6244 Here is an overview about all bracket sizes:
6247 \begin_layout Standard
6264 \begin_inset space \textvisiblespace{}
6272 \begin_inset space \textvisiblespace{}
6276 \begin_inset space \textvisiblespace{}
6286 \begin_layout Standard
6288 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6294 \begin_layout Standard
6301 -commands there is the variant
6308 \begin_inset Index idx
6311 \begin_layout Plain Layout
6319 that adds a bit more space between the bracket and its content, and the
6333 \begin_inset Index idx
6336 \begin_layout Plain Layout
6346 , that don't add additional space.
6351 at the end of the command
6357 is for a left bracket; for a right bracket this will be replaced by an
6363 A left or right bracket can each be an opening or closing bracket.
6366 \begin_layout Standard
6367 In the following table is a comparison of the variants:
6370 \begin_layout Standard
6372 \begin_inset Tabular
6373 <lyxtabular version="3" rows="5" columns="2">
6374 <features rotate="0" tabularvalignment="middle">
6375 <column alignment="center" valignment="middle">
6376 <column alignment="center" valignment="middle">
6378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6381 \begin_layout Plain Layout
6387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6390 \begin_layout Plain Layout
6392 \begin_inset Note Note
6395 \begin_layout Plain Layout
6402 is only used as spacer.
6414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6417 \begin_layout Plain Layout
6427 \begin_inset space \textvisiblespace{}
6437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6440 \begin_layout Plain Layout
6441 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6454 \begin_layout Plain Layout
6464 \begin_inset space \textvisiblespace{}
6474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6477 \begin_layout Plain Layout
6478 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6491 \begin_layout Plain Layout
6501 \begin_inset space \textvisiblespace{}
6511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6514 \begin_layout Plain Layout
6515 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6528 \begin_layout Plain Layout
6540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6543 \begin_layout Plain Layout
6544 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6560 \begin_layout Subsubsection
6561 Automatic Bracket Size
6562 \begin_inset CommandInset label
6564 name "sub:Automatic-Bracket-Size"
6569 \begin_inset Index idx
6572 \begin_layout Plain Layout
6573 Bracket size ! automatic
6581 \begin_layout Standard
6582 Brackets with variable size can be inserted with the commands
6589 \begin_inset Index idx
6592 \begin_layout Plain Layout
6607 \begin_inset Index idx
6610 \begin_layout Plain Layout
6618 or via the math toolbar button
6619 \begin_inset Graphics
6620 filename ../images/dialog-show_mathdelimiter.png
6638 the wanted bracket must be inserted.
6639 The bracket size will then automatically be calculated for the output.
6642 \begin_layout Standard
6644 normal bracket: The command
6651 \begin_inset space \textvisiblespace{}
6655 \begin_inset Formula $\downarrow$
6659 \begin_inset space \textvisiblespace{}
6665 \begin_inset Formula
6675 \begin_layout Standard
6677 multiline bracket: The command
6686 \begin_inset space \textvisiblespace{}
6690 \begin_inset Formula $\downarrow$
6694 \begin_inset space \textvisiblespace{}
6702 \begin_inset Formula
6704 \ln\left(\frac{A}{C}\right)
6712 \begin_layout Standard
6728 \begin_inset space ~
6734 This has the advantage that you can see in LyX immediately the real bracket
6735 size and that the matching right bracket will be created too.
6736 \begin_inset Newline newline
6739 The command for the last example would then be:
6750 \begin_inset space \textvisiblespace{}
6754 \begin_inset Formula $\downarrow$
6760 \begin_layout Standard
6761 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6762 For example the command
6769 \begin_inset space \textvisiblespace{}
6773 \begin_inset Formula $\downarrow$
6777 \begin_inset space \textvisiblespace{}
6787 \begin_inset Formula
6789 \left.\frac{A}{B}\right\}
6808 will be converted by LyX to brackets in the right size when the document
6809 is reloaded and an omitted bracket will appear as dashed line.
6812 \begin_layout Standard
6813 \begin_inset VSpace bigskip
6816 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6824 \begin_inset Index idx
6827 \begin_layout Plain Layout
6835 is additionally available for all brackets and limits.
6836 With this command the height of the following character is adapted to the
6837 one of the surrounding brackets, what is e.
6838 \begin_inset space \thinspace{}
6842 \begin_inset space \space{}
6845 needed for physical vectors:
6846 \begin_inset Formula
6848 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
6853 For physical vectors there is a special LaTeX-package, described in
6854 \begin_inset CommandInset ref
6856 reference "sub:Physical-Vectors"
6863 \begin_layout Subsection
6865 \begin_inset Index idx
6868 \begin_layout Plain Layout
6869 Brackets ! horizontal
6877 \begin_layout Standard
6879 \begin_inset Tabular
6880 <lyxtabular version="3" rows="4" columns="2">
6881 <features rotate="0" tabularvalignment="middle">
6882 <column alignment="center" valignment="top" width="0pt">
6883 <column alignment="center" valignment="top" width="0pt">
6885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6888 \begin_layout Plain Layout
6890 \begin_inset Note Note
6893 \begin_layout Plain Layout
6900 is only used as spacer.
6910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6913 \begin_layout Plain Layout
6921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6924 \begin_layout Plain Layout
6928 \begin_layout Plain Layout
6940 \begin_inset space \textvisiblespace{}
6944 \begin_inset space \textvisiblespace{}
6951 \begin_layout Plain Layout
6959 \begin_inset Index idx
6962 \begin_layout Plain Layout
6975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6978 \begin_layout Plain Layout
6979 \begin_inset Formula $\overbrace{A+B}^{3}$
6989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6992 \begin_layout Plain Layout
6996 \begin_layout Plain Layout
7008 \begin_inset space \textvisiblespace{}
7012 \begin_inset space \textvisiblespace{}
7019 \begin_layout Plain Layout
7027 \begin_inset Index idx
7030 \begin_layout Plain Layout
7043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7046 \begin_layout Plain Layout
7047 \begin_inset Formula $\underbrace{A+B}_{5}$
7057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7060 \begin_layout Plain Layout
7064 \begin_inset space \textvisiblespace{}
7070 \begin_inset space \textvisiblespace{}
7074 \begin_inset space \textvisiblespace{}
7078 \begin_inset space \textvisiblespace{}
7082 \begin_inset space \textvisiblespace{}
7086 \begin_inset space \textvisiblespace{}
7090 \begin_inset space \textvisiblespace{}
7098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7101 \begin_layout Plain Layout
7102 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7118 \begin_layout Standard
7119 In the last example it doesn't matter if
7131 is inserted at first.
7134 \begin_layout Standard
7135 \begin_inset VSpace bigskip
7138 When brackets are needed that overlap each other, multiline formulas, as
7140 \begin_inset CommandInset ref
7142 reference "sec:Multiline-Formulas"
7147 \begin_inset Formula
7149 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7150 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7155 In the first row the formula is inserted together with the first brace.
7156 It is hereby important that the space command
7160 \begin_layout Plain Layout
7161 Space commands are explained in
7162 \begin_inset CommandInset ref
7164 reference "sub:Predefined-Space"
7179 is inserted before the first
7180 \begin_inset Formula $d$
7183 , because the brace that ends behind the
7184 \begin_inset Formula $q$
7187 prevents that the following
7188 \begin_inset Quotes eld
7192 \begin_inset Quotes erd
7195 is surrounded by space.
7199 \begin_layout Plain Layout
7200 because a bracket is not handled as a character, see
7201 \begin_inset CommandInset ref
7203 reference "sub:Binary-Operators"
7212 In the second row the second brace is inserted.
7213 As it should begin before the
7214 \begin_inset Formula $b$
7229 \begin_layout Plain Layout
7237 \begin_inset CommandInset ref
7239 reference "sub:Placeholders"
7248 This space is needed because the
7249 \begin_inset Quotes eld
7253 \begin_inset Quotes erd
7256 is also surrounded by space in the formula.
7257 The brace is placed under the command
7266 \begin_layout Standard
7267 It gets more complicated when brackets overlap each other, like in the following
7272 \begin_layout Plain Layout
7284 \begin_inset Formula
7286 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7287 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7296 \begin_layout Plain Layout
7307 The first formula row is the same as the second row of the previous example,
7308 with the difference that the brace is above.
7309 The second row contains the formula together with the second brace.
7310 To avoid that there is space between the upper brace in the first row and
7311 the formula, the row spacing needs to be reduced.
7312 This is not easily possible due to a bug in LyX
7316 \begin_layout Plain Layout
7317 \begin_inset CommandInset href
7319 name "LyX-bug #1505"
7320 target "http://www.lyx.org/trac/ticket/1505"
7330 As a solution for the problem, the global formula row separation
7337 \begin_inset Index idx
7340 \begin_layout Plain Layout
7348 must be changed to -6
7349 \begin_inset space \thinspace{}
7352 pt before the formula with the command
7367 is set back after the formula to the standard value of 3
7368 \begin_inset space \thinspace{}
7371 pt using the same command.
7372 More about the row separation in formulas is explained in
7373 \begin_inset CommandInset ref
7375 reference "sub:Line-Separation"
7382 \begin_layout Section
7384 \begin_inset Index idx
7387 \begin_layout Plain Layout
7396 \begin_layout Standard
7397 Arrows can be inserted via the math toolbar button
7398 \begin_inset Graphics
7399 filename ../images/math/leftarrow.png
7404 or the commands listed in the following subsections.
7407 \begin_layout Subsection
7409 \begin_inset Index idx
7412 \begin_layout Plain Layout
7421 \begin_layout Standard
7422 \begin_inset space \hfill{}
7426 \begin_inset Tabular
7427 <lyxtabular version="3" rows="8" columns="2">
7428 <features rotate="0" tabularvalignment="middle">
7429 <column alignment="center" valignment="top" width="0pt">
7430 <column alignment="center" valignment="top" width="0pt">
7432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7435 \begin_layout Plain Layout
7441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7444 \begin_layout Plain Layout
7452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7455 \begin_layout Plain Layout
7463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7466 \begin_layout Plain Layout
7467 \begin_inset Formula $\gets$
7477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7480 \begin_layout Plain Layout
7488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7491 \begin_layout Plain Layout
7492 \begin_inset Formula $\Leftarrow$
7502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7505 \begin_layout Plain Layout
7513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7516 \begin_layout Plain Layout
7517 \begin_inset Formula $\longleftarrow$
7527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7530 \begin_layout Plain Layout
7538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7541 \begin_layout Plain Layout
7542 \begin_inset Formula $\Longleftarrow$
7552 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7555 \begin_layout Plain Layout
7563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7566 \begin_layout Plain Layout
7567 \begin_inset Formula $\leftharpoonup$
7577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7580 \begin_layout Plain Layout
7588 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7591 \begin_layout Plain Layout
7592 \begin_inset Formula $\leftharpoondown$
7602 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7605 \begin_layout Plain Layout
7613 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7616 \begin_layout Plain Layout
7617 \begin_inset Formula $\hookleftarrow$
7631 \begin_inset space \hfill{}
7635 \begin_inset Tabular
7636 <lyxtabular version="3" rows="8" columns="2">
7637 <features rotate="0" tabularvalignment="middle">
7638 <column alignment="center" valignment="top" width="0pt">
7639 <column alignment="center" valignment="top" width="0pt">
7641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7644 \begin_layout Plain Layout
7650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7653 \begin_layout Plain Layout
7661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7664 \begin_layout Plain Layout
7672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7675 \begin_layout Plain Layout
7676 \begin_inset Formula $\to$
7686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7689 \begin_layout Plain Layout
7697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7700 \begin_layout Plain Layout
7701 \begin_inset Formula $\Rightarrow$
7711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7714 \begin_layout Plain Layout
7722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7725 \begin_layout Plain Layout
7726 \begin_inset Formula $\longrightarrow$
7736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7739 \begin_layout Plain Layout
7747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7750 \begin_layout Plain Layout
7751 \begin_inset Formula $\Longrightarrow$
7761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7764 \begin_layout Plain Layout
7772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7775 \begin_layout Plain Layout
7776 \begin_inset Formula $\rightharpoonup$
7786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7789 \begin_layout Plain Layout
7797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7800 \begin_layout Plain Layout
7801 \begin_inset Formula $\rightharpoondown$
7811 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7814 \begin_layout Plain Layout
7822 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7825 \begin_layout Plain Layout
7826 \begin_inset Formula $\hookrightarrow$
7840 \begin_inset space \hfill{}
7846 \begin_layout Standard
7847 \begin_inset space \hfill{}
7851 \begin_inset Tabular
7852 <lyxtabular version="3" rows="6" columns="2">
7853 <features rotate="0" tabularvalignment="middle">
7854 <column alignment="center" valignment="top" width="0pt">
7855 <column alignment="center" valignment="top" width="0pt">
7857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7860 \begin_layout Plain Layout
7866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7869 \begin_layout Plain Layout
7877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7880 \begin_layout Plain Layout
7888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7891 \begin_layout Plain Layout
7892 \begin_inset Formula $\leftrightarrow$
7902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7905 \begin_layout Plain Layout
7913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7916 \begin_layout Plain Layout
7917 \begin_inset Formula $\Leftrightarrow$
7927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7930 \begin_layout Plain Layout
7938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7941 \begin_layout Plain Layout
7942 \begin_inset Formula $\longleftrightarrow$
7952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7955 \begin_layout Plain Layout
7963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7966 \begin_layout Plain Layout
7967 \begin_inset Formula $\Longleftrightarrow$
7977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7980 \begin_layout Plain Layout
7988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7991 \begin_layout Plain Layout
7992 \begin_inset Formula $\rightleftharpoons$
8006 \begin_inset space \hspace{}
8011 \begin_inset space \hfill{}
8015 \begin_inset Tabular
8016 <lyxtabular version="3" rows="5" columns="2">
8017 <features rotate="0" tabularvalignment="middle">
8018 <column alignment="center" valignment="top" width="0pt">
8019 <column alignment="center" valignment="top" width="0pt">
8021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8024 \begin_layout Plain Layout
8030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8033 \begin_layout Plain Layout
8041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8044 \begin_layout Plain Layout
8052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8055 \begin_layout Plain Layout
8056 \begin_inset Formula $\mapsto$
8066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8069 \begin_layout Plain Layout
8077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8080 \begin_layout Plain Layout
8081 \begin_inset Formula $\longmapsto$
8091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8094 \begin_layout Plain Layout
8102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8105 \begin_layout Plain Layout
8106 \begin_inset Formula $\leadsto$
8116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8119 \begin_layout Plain Layout
8127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8130 \begin_layout Plain Layout
8131 \begin_inset Formula $\dasharrow$
8145 \begin_inset space \hfill{}
8151 \begin_layout Standard
8152 \begin_inset VSpace medskip
8155 Arrows used as accents like e.
8156 \begin_inset space \thinspace{}
8160 \begin_inset space \space{}
8163 vector arrows are listed in
8164 \begin_inset CommandInset ref
8166 reference "sec:Accents"
8173 \begin_layout Standard
8174 \begin_inset VSpace bigskip
8177 Furthermore there are the labeled arrows
8178 \begin_inset Index idx
8181 \begin_layout Plain Layout
8194 \begin_inset Index idx
8197 \begin_layout Plain Layout
8212 \begin_inset Index idx
8215 \begin_layout Plain Layout
8222 \begin_layout Plain Layout
8237 When inserting one of these commands in a formula, an arrow with two blue
8238 boxes appear where the label can be inserted.
8239 The length of the arrow adapts to the label width.
8242 \begin_layout Standard
8244 \begin_inset Tabular
8245 <lyxtabular version="3" rows="3" columns="2">
8246 <features rotate="0" tabularvalignment="middle">
8247 <column alignment="center" valignment="top" width="0pt">
8248 <column alignment="center" valignment="top" width="0pt">
8250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8253 \begin_layout Plain Layout
8259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8262 \begin_layout Plain Layout
8264 \begin_inset Note Note
8267 \begin_layout Plain Layout
8274 is only used as spacer.
8286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8289 \begin_layout Plain Layout
8293 \begin_inset space \textvisiblespace{}
8297 \begin_inset Formula $\downarrow$
8301 \begin_inset Formula $\to$
8309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8312 \begin_layout Plain Layout
8313 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8326 \begin_layout Plain Layout
8330 \begin_inset space \textvisiblespace{}
8334 \begin_inset Formula $\downarrow$
8338 \begin_inset Formula $\to$
8346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8349 \begin_layout Plain Layout
8350 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8366 \begin_layout Subsection
8367 Vertical and diagonal Arrows
8368 \begin_inset Index idx
8371 \begin_layout Plain Layout
8378 \begin_inset Index idx
8381 \begin_layout Plain Layout
8390 \begin_layout Standard
8391 \begin_inset space \hfill{}
8395 \begin_inset Tabular
8396 <lyxtabular version="3" rows="7" columns="2">
8397 <features rotate="0" tabularvalignment="middle">
8398 <column alignment="center" valignment="top" width="0pt">
8399 <column alignment="center" valignment="top" width="0pt">
8401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8404 \begin_layout Plain Layout
8410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8413 \begin_layout Plain Layout
8421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8424 \begin_layout Plain Layout
8432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8435 \begin_layout Plain Layout
8436 \begin_inset Formula $\uparrow$
8446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8449 \begin_layout Plain Layout
8457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8460 \begin_layout Plain Layout
8461 \begin_inset Formula $\Uparrow$
8471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8474 \begin_layout Plain Layout
8482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8485 \begin_layout Plain Layout
8486 \begin_inset Formula $\updownarrow$
8496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8499 \begin_layout Plain Layout
8507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8510 \begin_layout Plain Layout
8511 \begin_inset Formula $\Updownarrow$
8521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8524 \begin_layout Plain Layout
8532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8535 \begin_layout Plain Layout
8536 \begin_inset Formula $\Downarrow$
8546 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8549 \begin_layout Plain Layout
8557 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8560 \begin_layout Plain Layout
8561 \begin_inset Formula $\downarrow$
8575 \begin_inset space \hfill{}
8579 \begin_inset Tabular
8580 <lyxtabular version="3" rows="5" columns="2">
8581 <features rotate="0" tabularvalignment="middle">
8582 <column alignment="center" valignment="top" width="0pt">
8583 <column alignment="center" valignment="top" width="0pt">
8585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8588 \begin_layout Plain Layout
8594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8597 \begin_layout Plain Layout
8605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8608 \begin_layout Plain Layout
8616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8619 \begin_layout Plain Layout
8620 \begin_inset Formula $\nearrow$
8630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8633 \begin_layout Plain Layout
8641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8644 \begin_layout Plain Layout
8645 \begin_inset Formula $\searrow$
8655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8658 \begin_layout Plain Layout
8666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8669 \begin_layout Plain Layout
8670 \begin_inset Formula $\swarrow$
8680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8683 \begin_layout Plain Layout
8691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8694 \begin_layout Plain Layout
8695 \begin_inset Formula $\nwarrow$
8709 \begin_inset space \hfill{}
8715 \begin_layout Standard
8716 \begin_inset VSpace medskip
8719 Vertical arrows can be used also as delimiters together with the commands
8721 \begin_inset CommandInset ref
8723 reference "sub:Manual-Bracket-Size"
8728 \begin_inset CommandInset ref
8730 reference "sub:Automatic-Bracket-Size"
8737 \begin_layout Section
8739 \begin_inset CommandInset label
8746 \begin_inset Index idx
8749 \begin_layout Plain Layout
8758 \begin_layout Standard
8759 Accents can be inserted via the math toolbar button
8760 \begin_inset Graphics
8761 filename ../images/math/hat.png
8766 or the commands listed in the following subsections.
8769 \begin_layout Subsection
8770 Accents for one Character
8774 \begin_layout Plain Layout
8787 \begin_layout Plain Layout
8789 \begin_inset CommandInset ref
8791 reference "sub:Accents-in-Text"
8804 \begin_layout Plain Layout
8812 \begin_inset Note Note
8815 \begin_layout Plain Layout
8822 is used to avoid that the footnote appears in the PDF-bookmark.
8825 \begin_layout Plain Layout
8833 \begin_inset CommandInset ref
8835 reference "sub:Formulas-in-Section"
8845 \begin_inset CommandInset label
8847 name "sub:Accents-for-one"
8852 \begin_inset Index idx
8855 \begin_layout Plain Layout
8856 Accents ! for one character
8864 \begin_layout Standard
8865 \begin_inset space \hfill{}
8869 \begin_inset Tabular
8870 <lyxtabular version="3" rows="8" columns="2">
8871 <features rotate="0" tabularvalignment="middle">
8872 <column alignment="center" valignment="top" width="0pt">
8873 <column alignment="center" valignment="top" width="0pt">
8875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8878 \begin_layout Plain Layout
8884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8887 \begin_layout Plain Layout
8889 \begin_inset Note Note
8892 \begin_layout Plain Layout
8899 is only used as spacer.
8911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8914 \begin_layout Plain Layout
8918 \begin_inset space \textvisiblespace{}
8926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8929 \begin_layout Plain Layout
8930 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8940 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8943 \begin_layout Plain Layout
8947 \begin_inset space \textvisiblespace{}
8955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8958 \begin_layout Plain Layout
8959 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8972 \begin_layout Plain Layout
8976 \begin_inset space \textvisiblespace{}
8984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8987 \begin_layout Plain Layout
8988 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9001 \begin_layout Plain Layout
9005 \begin_inset space \textvisiblespace{}
9013 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9016 \begin_layout Plain Layout
9017 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9027 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9030 \begin_layout Plain Layout
9034 \begin_inset space \textvisiblespace{}
9038 \begin_inset Index idx
9041 \begin_layout Plain Layout
9052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9055 \begin_layout Plain Layout
9056 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9069 \begin_layout Plain Layout
9073 \begin_inset space \textvisiblespace{}
9081 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9084 \begin_layout Plain Layout
9085 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9095 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9098 \begin_layout Plain Layout
9102 \begin_inset space \textvisiblespace{}
9110 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9113 \begin_layout Plain Layout
9114 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9128 \begin_inset space \hfill{}
9132 \begin_inset Tabular
9133 <lyxtabular version="3" rows="7" columns="2">
9134 <features rotate="0" tabularvalignment="middle">
9135 <column alignment="center" valignment="top" width="0pt">
9136 <column alignment="center" valignment="top" width="0pt">
9138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9141 \begin_layout Plain Layout
9147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9150 \begin_layout Plain Layout
9158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9161 \begin_layout Plain Layout
9165 \begin_inset space \textvisiblespace{}
9173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9176 \begin_layout Plain Layout
9177 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9187 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9190 \begin_layout Plain Layout
9194 \begin_inset space \textvisiblespace{}
9202 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9205 \begin_layout Plain Layout
9206 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9216 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9219 \begin_layout Plain Layout
9223 \begin_inset space \textvisiblespace{}
9231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9234 \begin_layout Plain Layout
9235 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9245 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9248 \begin_layout Plain Layout
9252 \begin_inset space \textvisiblespace{}
9260 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9263 \begin_layout Plain Layout
9264 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9274 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9277 \begin_layout Plain Layout
9281 \begin_inset space \textvisiblespace{}
9289 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9292 \begin_layout Plain Layout
9293 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9303 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9306 \begin_layout Plain Layout
9310 \begin_inset space \textvisiblespace{}
9318 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9321 \begin_layout Plain Layout
9322 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9336 \begin_inset space \hfill{}
9342 \begin_layout Standard
9343 \begin_inset VSpace bigskip
9349 \begin_layout Standard
9350 You can directly insert accents like é to formulas.
9351 LyX will transform them to the corresponding accent command.
9353 \begin_inset Index idx
9356 \begin_layout Plain Layout
9362 it is better to insert a quotation mark before the vowel.
9363 These two characters are then treated by LaTeX as
9367 character when the formula part with the umlaut is marked as German.
9375 \begin_inset Quotes eld
9379 \begin_inset Quotes erd
9382 umlauts are created as demonstrated in the following example:
9385 \begin_layout Standard
9386 \begin_inset VSpace -2mm
9392 \begin_layout Standard
9394 \begin_inset Tabular
9395 <lyxtabular version="3" rows="3" columns="2">
9396 <features rotate="0" tabularvalignment="middle">
9397 <column alignment="center" valignment="top">
9398 <column alignment="center" valignment="top">
9400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9403 \begin_layout Plain Layout
9409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9412 \begin_layout Plain Layout
9414 \begin_inset Note Note
9417 \begin_layout Plain Layout
9425 \begin_inset space \thinspace{}
9428 pt space are only used as spacer.
9440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9443 \begin_layout Plain Layout
9446 \begin_inset Quotes grd
9454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9457 \begin_layout Plain Layout
9458 \begin_inset space \hspace{}
9465 \begin_inset Formula $"i$
9475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9478 \begin_layout Plain Layout
9482 \begin_inset space \textvisiblespace{}
9490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9493 \begin_layout Plain Layout
9494 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9510 \begin_layout Standard
9511 Another advantage to
9517 is that umlauts can directly be converted to mathematical text because
9518 the accent commands above are
9524 in mathematical text
9527 To convert an accented character to mathematical text, only the character
9528 under the accent may be converted.
9529 This applies also for all other conversions, e.
9530 \begin_inset space \thinspace{}
9534 \begin_inset space \space{}
9540 \begin_layout Standard
9541 In mathematical text, umlauts and other accented characters can directly
9545 \begin_layout Standard
9546 \begin_inset VSpace bigskip
9552 \begin_layout Standard
9553 LyX also supports a tilde under the character if the LaTeX-package
9558 \begin_inset Index idx
9561 \begin_layout Plain Layout
9562 Packages ! undertilde
9567 is installed on your system:
9570 \begin_layout Standard
9574 \begin_layout Plain Layout
9584 \begin_inset Note Note
9587 \begin_layout Plain Layout
9588 The following table will only be displayed when the LaTeX-package
9600 \begin_layout Standard
9603 \begin_inset Tabular
9604 <lyxtabular version="3" rows="2" columns="2">
9605 <features rotate="0" tabularvalignment="middle">
9606 <column alignment="center" valignment="top" width="0pt">
9607 <column alignment="center" valignment="top" width="0pt">
9609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9612 \begin_layout Plain Layout
9618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9621 \begin_layout Plain Layout
9629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9632 \begin_layout Plain Layout
9636 \begin_inset space \textvisiblespace{}
9644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9647 \begin_layout Plain Layout
9648 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
9664 \begin_layout Standard
9668 \begin_layout Plain Layout
9678 \begin_inset Note Note
9681 \begin_layout Plain Layout
9682 The following will be displayed when the LaTeX-package
9694 \begin_layout Standard
9695 You need to install the LaTeX-package
9699 to see the rest of this subsection in the output.
9702 \begin_layout Standard
9706 \begin_layout Plain Layout
9718 \begin_layout Subsection
9719 Accents for several Characters
9720 \begin_inset Index idx
9723 \begin_layout Plain Layout
9724 Accents ! for several characters
9732 \begin_layout Standard
9733 \begin_inset space \hfill{}
9737 \begin_inset Tabular
9738 <lyxtabular version="3" rows="5" columns="2">
9739 <features rotate="0" tabularvalignment="middle">
9740 <column alignment="center" valignment="top" width="0pt">
9741 <column alignment="center" valignment="top" width="0pt">
9743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9746 \begin_layout Plain Layout
9752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9755 \begin_layout Plain Layout
9757 \begin_inset Note Note
9760 \begin_layout Plain Layout
9767 is only used as spacer.
9779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9782 \begin_layout Plain Layout
9786 \begin_inset space \textvisiblespace{}
9794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9797 \begin_layout Plain Layout
9798 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9811 \begin_layout Plain Layout
9815 \begin_inset space \textvisiblespace{}
9823 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9826 \begin_layout Plain Layout
9827 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9840 \begin_layout Plain Layout
9844 \begin_inset space \textvisiblespace{}
9852 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9855 \begin_layout Plain Layout
9856 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9869 \begin_layout Plain Layout
9873 \begin_inset space \textvisiblespace{}
9881 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9884 \begin_layout Plain Layout
9885 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9899 \begin_inset space \hfill{}
9903 \begin_inset Tabular
9904 <lyxtabular version="3" rows="5" columns="2">
9905 <features rotate="0" tabularvalignment="middle">
9906 <column alignment="center" valignment="top" width="0pt">
9907 <column alignment="center" valignment="top" width="0pt">
9909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9912 \begin_layout Plain Layout
9918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9921 \begin_layout Plain Layout
9929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9932 \begin_layout Plain Layout
9936 \begin_inset space \textvisiblespace{}
9944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9947 \begin_layout Plain Layout
9948 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9958 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9961 \begin_layout Plain Layout
9965 \begin_inset space \textvisiblespace{}
9973 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9976 \begin_layout Plain Layout
9977 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9987 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9990 \begin_layout Plain Layout
9994 \begin_inset space \textvisiblespace{}
10002 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10005 \begin_layout Plain Layout
10006 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10016 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10019 \begin_layout Plain Layout
10023 \begin_inset space \textvisiblespace{}
10031 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10034 \begin_layout Plain Layout
10035 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10049 \begin_inset space \hfill{}
10055 \begin_layout Standard
10056 \begin_inset VSpace medskip
10059 With these commands as many characters as you like can be accented.
10072 will only be set in the output with a length of three characters, as shown
10073 in the following example:
10074 \begin_inset Formula
10076 \widetilde{A+B=C-D}
10084 \begin_layout Standard
10092 \begin_inset Index idx
10095 \begin_layout Plain Layout
10110 \begin_inset Index idx
10113 \begin_layout Plain Layout
10121 described in the previous subsection it is also possible to accent several
10128 \begin_inset space \textvisiblespace{}
10132 \begin_inset Formula $\downarrow$
10138 \begin_inset Formula
10140 \underset{***}{A=B}
10148 \begin_layout Standard
10149 \begin_inset Newpage newpage
10155 \begin_layout Section
10157 \begin_inset CommandInset label
10164 \begin_inset Index idx
10167 \begin_layout Plain Layout
10176 \begin_layout Subsection
10178 \begin_inset CommandInset label
10180 name "sub:Predefined-Space"
10185 \begin_inset Index idx
10188 \begin_layout Plain Layout
10189 Space ! horizontal ! predefined
10197 \begin_layout Standard
10198 Sometimes it is necessary to insert horizontal space into a formula.
10199 This is done by inserting a protected space (shortcut
10202 arg "command-alternatives space-insert protected ; math-space"
10207 \begin_inset Quotes eld
10213 \begin_inset space \textvisiblespace{}
10219 \begin_inset Quotes erd
10222 appears and by pressing
10226 several times one can select one of eight different space sizes.
10227 The spaces can also be inserted using the math toolbar button
10228 \begin_inset Graphics
10229 filename ../images/math/space.png
10234 or special commands.
10235 Independent from the inserted command, one can select the size again by
10243 \begin_layout Standard
10246 \begin_inset VSpace -5mm
10250 \begin_inset Tabular
10251 <lyxtabular version="3" rows="3" columns="7">
10252 <features rotate="0" tabularvalignment="middle">
10253 <column alignment="center" valignment="middle" width="6.8cm">
10254 <column alignment="center" valignment="top">
10255 <column alignment="center" valignment="top">
10256 <column alignment="center" valignment="top">
10257 <column alignment="center" valignment="top">
10258 <column alignment="center" valignment="top">
10259 <column alignment="center" valignment="top">
10261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10264 \begin_layout Plain Layout
10270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10273 \begin_layout Plain Layout
10281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10284 \begin_layout Plain Layout
10292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10295 \begin_layout Plain Layout
10303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10306 \begin_layout Plain Layout
10314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10317 \begin_layout Plain Layout
10325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10328 \begin_layout Plain Layout
10338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10341 \begin_layout Plain Layout
10346 keystrokes after inserting the protected space
10351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10354 \begin_layout Plain Layout
10360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10363 \begin_layout Plain Layout
10369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10372 \begin_layout Plain Layout
10378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10381 \begin_layout Plain Layout
10387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10390 \begin_layout Plain Layout
10396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10399 \begin_layout Plain Layout
10407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10410 \begin_layout Plain Layout
10416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10419 \begin_layout Plain Layout
10420 \begin_inset Formula $A\, B$
10428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10431 \begin_layout Plain Layout
10432 \begin_inset Formula $A\: B$
10440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10443 \begin_layout Plain Layout
10444 \begin_inset Formula $A\; B$
10452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10455 \begin_layout Plain Layout
10456 \begin_inset Formula $A\quad B$
10464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10467 \begin_layout Plain Layout
10468 \begin_inset Formula $A\qquad B$
10476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10479 \begin_layout Plain Layout
10480 \begin_inset Formula $A\! B$
10496 \begin_layout Standard
10497 The last size seem to produce no space.
10498 It is displayed red in LyX contrary to the other sizes, because it is a
10500 There are two more negative spaces:
10503 \begin_layout Standard
10505 \begin_inset Tabular
10506 <lyxtabular version="3" rows="3" columns="3">
10507 <features rotate="0" tabularvalignment="middle">
10508 <column alignment="center" valignment="middle" width="6.8cm">
10509 <column alignment="center" valignment="top" width="0pt">
10510 <column alignment="center" valignment="top" width="0pt">
10512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10515 \begin_layout Plain Layout
10521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10524 \begin_layout Plain Layout
10532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10535 \begin_layout Plain Layout
10545 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10548 \begin_layout Plain Layout
10553 keystrokes after inserting the protected space
10558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10561 \begin_layout Plain Layout
10567 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10570 \begin_layout Plain Layout
10578 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10581 \begin_layout Plain Layout
10587 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10590 \begin_layout Plain Layout
10591 \begin_inset Formula $A\negmedspace B$
10599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10602 \begin_layout Plain Layout
10603 \begin_inset Formula $A\negthickspace B$
10619 \begin_layout Standard
10620 Negative spaces can lead to characters overlapping each other.
10621 Thus they can be used to enforce ligatures, which are e.
10622 \begin_inset space \thinspace{}
10626 \begin_inset space \space{}
10629 useful for summation operators:
10632 \begin_layout Standard
10634 \begin_inset Tabular
10635 <lyxtabular version="3" rows="3" columns="2">
10636 <features rotate="0" tabularvalignment="middle">
10637 <column alignment="center" valignment="top">
10638 <column alignment="center" valignment="top">
10640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10643 \begin_layout Plain Layout
10649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10652 \begin_layout Plain Layout
10654 \begin_inset Note Note
10657 \begin_layout Plain Layout
10664 is only used as spacer.
10676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10679 \begin_layout Plain Layout
10685 \begin_inset space \textvisiblespace{}
10693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10696 \begin_layout Plain Layout
10697 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10710 \begin_layout Plain Layout
10718 \begin_inset space \textvisiblespace{}
10726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10729 \begin_layout Plain Layout
10730 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10746 \begin_layout Standard
10747 Relations like for example equal signs, are always surrounded by space.
10748 To suppress this, the equal sign is placed into a TeX-brace.
10749 The following example demonstrates this:
10752 \begin_layout Standard
10754 \begin_inset Tabular
10755 <lyxtabular version="3" rows="2" columns="2">
10756 <features rotate="0" tabularvalignment="middle">
10757 <column alignment="center" valignment="top" width="0pt">
10758 <column alignment="center" valignment="top" width="0pt">
10760 <cell alignment="center" valignment="top" usebox="none">
10763 \begin_layout Plain Layout
10769 <cell alignment="center" valignment="top" usebox="none">
10772 \begin_layout Plain Layout
10773 \begin_inset Formula $A=B$
10783 <cell alignment="center" valignment="top" usebox="none">
10786 \begin_layout Plain Layout
10787 \begin_inset Note Note
10790 \begin_layout Plain Layout
10797 is only used as spacer.
10803 \begin_inset Formula $\raisebox{5mm}{}$
10806 equation without space
10811 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
10814 \begin_layout Plain Layout
10815 \begin_inset Formula $A{=}B$
10831 \begin_layout Standard
10833 The command for the last formula is:
10838 \begin_inset Formula $\to$
10844 \begin_layout Standard
10845 \begin_inset VSpace bigskip
10848 Spaces are needed for physical units, because the space between the value
10849 and the unit is the smallest one and not a normal space.
10850 For units in text, the smallest space is inserted via the menu
10852 Insert\SpecialChar \menuseparator
10853 Formatting\SpecialChar \menuseparator
10855 \begin_inset space ~
10863 arg "space-insert thin"
10869 \begin_layout Standard
10870 An example to visualize the difference:
10873 \begin_layout Standard
10874 \begin_inset Tabular
10875 <lyxtabular version="3" rows="2" columns="2">
10876 <features rotate="0" tabularvalignment="middle">
10877 <column alignment="left" valignment="top">
10878 <column alignment="left" valignment="top">
10880 <cell alignment="center" valignment="top" usebox="none">
10883 \begin_layout Plain Layout
10885 \begin_inset Formula $\cdot$
10893 <cell alignment="center" valignment="top" usebox="none">
10896 \begin_layout Plain Layout
10897 space between value and unit
10904 <cell alignment="center" valignment="top" usebox="none">
10907 \begin_layout Plain Layout
10909 \begin_inset space \thinspace{}
10913 \begin_inset Formula $\cdot$
10921 <cell alignment="center" valignment="top" usebox="none">
10924 \begin_layout Plain Layout
10925 smallest space between value and unit
10938 \begin_layout Subsection
10943 \begin_layout Plain Layout
10956 \begin_layout Plain Layout
10957 for vertical space in formulas see
10958 \begin_inset CommandInset ref
10960 reference "sub:Line-Separation"
10973 \begin_layout Plain Layout
10981 \begin_inset Note Note
10984 \begin_layout Plain Layout
10987 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
10990 \begin_layout Plain Layout
10993 texorpdfstring is in section
10994 \begin_inset CommandInset ref
10996 reference "sub:Formulas-in-Section"
11006 \begin_inset CommandInset label
11008 name "sub:Variable-Space"
11013 \begin_inset Index idx
11016 \begin_layout Plain Layout
11017 Space ! horizontal ! variable
11025 \begin_layout Standard
11026 Space with a defined length can be inserted with the command
11033 \begin_inset Index idx
11036 \begin_layout Plain Layout
11046 \begin_inset Quotes eld
11052 \begin_inset space \textvisiblespace{}
11058 \begin_inset Quotes erd
11062 The length can be specified by left-clicking on the
11063 \begin_inset Quotes eld
11069 \begin_inset space \textvisiblespace{}
11075 \begin_inset Quotes erd
11079 The length may also be negative.
11080 To insert as much space as is available, the command
11087 \begin_inset Index idx
11090 \begin_layout Plain Layout
11101 \begin_layout Standard
11102 \begin_inset VSpace -1mm
11108 \begin_layout Standard
11110 \begin_inset Tabular
11111 <lyxtabular version="3" rows="4" columns="2">
11112 <features rotate="0" tabularvalignment="middle">
11113 <column alignment="center" valignment="top">
11114 <column alignment="center" valignment="top">
11116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11119 \begin_layout Plain Layout
11127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11130 \begin_layout Plain Layout
11138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11141 \begin_layout Plain Layout
11145 \begin_inset space \textvisiblespace{}
11149 \begin_inset Formula $\to$
11155 \begin_inset space \thinspace{}
11163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11166 \begin_layout Plain Layout
11167 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11180 \begin_layout Plain Layout
11184 \begin_inset space \textvisiblespace{}
11188 \begin_inset Formula $\to$
11194 \begin_inset space \thinspace{}
11202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11205 \begin_layout Plain Layout
11206 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11219 \begin_layout Plain Layout
11223 \begin_inset space \textvisiblespace{}
11231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11234 \begin_layout Plain Layout
11235 \begin_inset Formula $A=A\hfill B=B$
11251 \begin_layout Standard
11252 In the last example the available space is given by the longest column entry
11254 In an inline formula the space depends on the length of the line in which
11262 Thus, when the line uses the full width, no space will be created.
11269 only has an effect on displayed formulas when the formula style
11274 (Formula styles are explained in
11275 \begin_inset CommandInset ref
11277 reference "sec:Formula-Styles"
11284 \begin_layout Standard
11291 , there are the commands
11303 that fill the space with a pattern, see
11304 \begin_inset CommandInset ref
11306 reference "sub:Ellipses"
11313 \begin_layout Standard
11314 For text, variable space can be inserted via the menu
11316 Insert\SpecialChar \menuseparator
11317 Formatting\SpecialChar \menuseparator
11319 \begin_inset space ~
11327 \begin_layout Standard
11328 This is a line with
11329 \begin_inset space \hspace{}
11334 \begin_inset space \thinspace{}
11340 \begin_layout Standard
11341 This is a line with
11342 \begin_inset space \hfill{}
11348 \begin_layout Subsection
11349 Space besides inline Formulas
11350 \begin_inset Index idx
11353 \begin_layout Plain Layout
11354 Space ! besides inline formulas
11362 \begin_layout Standard
11363 The space that surrounds inline formulas can be adjusted with the length
11371 \begin_inset Index idx
11374 \begin_layout Plain Layout
11383 The value of a length is set with the command
11390 \begin_inset Index idx
11393 \begin_layout Plain Layout
11401 which has the following scheme:
11404 \begin_layout Standard
11409 setlength{length name}{value}
11412 \begin_layout Standard
11420 \begin_inset space \thinspace{}
11426 \begin_layout Standard
11436 \begin_layout Standard
11437 is inserted in TeX-mode.
11439 \begin_inset space \thinspace{}
11442 mm space will now be set around all inline formulas:
11446 \begin_layout Plain Layout
11460 \begin_layout Standard
11461 This is a line with an inline formula
11462 \begin_inset Formula $A=B$
11466 \begin_inset space \thinspace{}
11469 mm surrounding space.
11473 \begin_layout Plain Layout
11487 \begin_layout Standard
11488 To return to the predefined value,
11494 is set to the value 0
11495 \begin_inset space \thinspace{}
11501 \begin_layout Section
11503 \begin_inset Index idx
11506 \begin_layout Plain Layout
11513 \begin_inset Index idx
11516 \begin_layout Plain Layout
11521 \begin_layout Plain Layout
11532 \begin_layout Plain Layout
11547 \begin_layout Standard
11548 Boxes for text are described in chapter
11555 \begin_inset space ~
11563 \begin_layout Subsection
11565 \begin_inset CommandInset label
11567 name "sub:Boxes-with-Frame"
11572 \begin_inset Index idx
11575 \begin_layout Plain Layout
11584 \begin_layout Standard
11585 It is possible to frame a formula or part of one with the commands
11592 \begin_inset Index idx
11595 \begin_layout Plain Layout
11610 \begin_inset Index idx
11613 \begin_layout Plain Layout
11624 \begin_layout Standard
11625 When one of these commands is inserted in a formula, a blue box appears
11626 within a frame to enter formula parts.
11633 an additional formula has to be created by
11637 within this box, because the box content will otherwise be treated as mathemati
11645 is used, a new formula is automatically created inside the frame.
11648 \begin_layout Standard
11655 is not suitable to frame displayed formulas because the formula will always
11656 be set in the size of the text.
11663 is in contrary not suitable to frame inline formulas, because the formula
11664 will always be set in the size of a displayed formula.
11667 \begin_layout Standard
11681 \begin_inset Index idx
11684 \begin_layout Plain Layout
11692 where additionally the frame width and the alignment can be specified.
11699 is used in the following scheme:
11702 \begin_layout Standard
11707 framebox[frame width][position]{box content}
11710 \begin_layout Standard
11711 The position can either be
11728 right aligns the formula in the box.
11729 When no position is given, the formula will be centered.
11730 \begin_inset Newline newline
11733 If no width is given, also no position can be given.
11734 In this case the frame width is adjusted to the box content like for
11743 \begin_layout Standard
11750 is inserted, a box appears containing three blue boxes.
11751 The first two boxes are surrounded by brackets and denote the two optional
11753 The third box is for formula parts like for
11762 \begin_layout Standard
11763 \begin_inset Newpage newpage
11769 \begin_layout Standard
11771 \begin_inset Tabular
11772 <lyxtabular version="3" rows="5" columns="2">
11773 <features rotate="0" tabularvalignment="middle">
11774 <column alignment="center" valignment="top">
11775 <column alignment="center" valignment="top">
11777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11780 \begin_layout Plain Layout
11786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11789 \begin_layout Plain Layout
11791 \begin_inset Note Note
11794 \begin_layout Plain Layout
11801 is only used as spacer.
11813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11816 \begin_layout Plain Layout
11820 \begin_inset space \textvisiblespace{}
11830 \begin_inset space \textvisiblespace{}
11838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11841 \begin_layout Plain Layout
11842 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
11852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11855 \begin_layout Plain Layout
11859 \begin_inset space \textvisiblespace{}
11865 \begin_inset space \textvisiblespace{}
11873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11876 \begin_layout Plain Layout
11877 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
11887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11890 \begin_layout Plain Layout
11894 \begin_inset space \textvisiblespace{}
11902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11905 \begin_layout Plain Layout
11906 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
11916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11919 \begin_layout Plain Layout
11923 \begin_inset space \textvisiblespace{}
11927 \begin_inset Formula $\to$
11931 \begin_inset Formula $\to$
11941 \begin_inset space \textvisiblespace{}
11945 \begin_inset Formula $\downarrow$
11953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11956 \begin_layout Plain Layout
11957 \begin_inset Formula $\raisebox{6mm}{}$
11961 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
11965 \begin_inset Formula $\raisebox{-4mm}{}$
11981 \begin_layout Standard
11982 The frame thickness can also be adjusted.
11983 To do this the following commands have to be inserted in TeX-mode before
11987 \begin_layout Standard
11997 \begin_inset Quotes eld
12001 \begin_inset Quotes erd
12015 \begin_inset Quotes eld
12019 \begin_inset Quotes erd
12025 \begin_layout Standard
12026 \begin_inset Quotes eld
12030 \begin_inset Quotes erd
12033 specifies the minimal distance between the frame and the first character
12035 An example for this is the following framed formula:
12039 \begin_layout Plain Layout
12051 \begin_inset Formula
12058 Before this formula the commands
12061 \begin_layout Standard
12083 \begin_layout Standard
12084 were inserted in TeX-mode.
12085 The given values are used for all following boxes.
12088 \begin_layout Standard
12089 To return to the standard frame size, the command
12092 \begin_layout Standard
12117 \begin_layout Plain Layout
12131 \begin_layout Standard
12132 is inserted in TeX-mode before the next formula.
12135 \begin_layout Subsection
12136 Boxes without Frame
12137 \begin_inset CommandInset label
12139 name "sub:Boxes-without-Frame"
12144 \begin_inset Index idx
12147 \begin_layout Plain Layout
12148 Boxes ! without frame
12156 \begin_layout Standard
12157 For boxes without a frame there are the following box commands:
12164 \begin_inset Index idx
12167 \begin_layout Plain Layout
12182 \begin_inset Index idx
12185 \begin_layout Plain Layout
12200 \begin_inset Index idx
12203 \begin_layout Plain Layout
12214 \begin_layout Standard
12221 a box can be super- or subscripted.
12222 But in contrary to normal super- and subscripting, the characters in the
12223 box keep their font size.
12230 is used in the following scheme:
12233 \begin_layout Standard
12238 raisebox{height}{box content}
12241 \begin_layout Standard
12242 When the box should contain a formula, an extra formula is needed like for
12253 \begin_inset Note Greyedout
12256 \begin_layout Plain Layout
12267 this extra formula is created by pressing
12271 twice instead of once because LyX doesn't yet support
12285 \begin_layout Standard
12287 \begin_inset Tabular
12288 <lyxtabular version="3" rows="4" columns="2">
12289 <features rotate="0" tabularvalignment="middle">
12290 <column alignment="center" valignment="top">
12291 <column alignment="center" valignment="top">
12293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12296 \begin_layout Plain Layout
12302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12305 \begin_layout Plain Layout
12313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12316 \begin_layout Plain Layout
12320 \begin_inset Formula $\to$
12326 \begin_inset Formula $\to$
12334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12337 \begin_layout Plain Layout
12338 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12351 \begin_layout Plain Layout
12355 \begin_inset Formula $\to$
12361 \begin_inset Formula $\to$
12369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12372 \begin_layout Plain Layout
12373 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12386 \begin_layout Plain Layout
12390 \begin_inset Formula $\to$
12406 \begin_inset space \textvisiblespace{}
12414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12417 \begin_layout Plain Layout
12418 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
12434 \begin_layout Standard
12459 , with the difference that there is no frame.
12462 \begin_layout Subsection
12464 \begin_inset CommandInset label
12466 name "sub:Colored-Boxes"
12471 \begin_inset Index idx
12474 \begin_layout Plain Layout
12483 \begin_layout Standard
12484 To be able to use all commands explained in this section, the LaTeX-package
12493 \begin_layout Plain Layout
12498 is part of every LaTeX standard installation.
12504 \begin_inset Index idx
12507 \begin_layout Plain Layout
12513 has to be loaded in the LaTeX-preamble with the line
12517 \begin_layout Plain Layout
12518 When text is colored somewhere in the document with a predefined color,
12519 LyX loads the LaTeX-package
12524 Thus it is possible that the package is loaded twice, but this does not
12531 \begin_inset Note Note
12534 \begin_layout Plain Layout
12535 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12544 \begin_layout Standard
12552 \begin_layout Standard
12553 \begin_inset VSpace medskip
12556 To color boxes, the command
12563 \begin_inset Index idx
12566 \begin_layout Plain Layout
12574 is used in the following scheme:
12577 \begin_layout Standard
12582 colorbox{color}{box content}
12585 \begin_layout Standard
12586 The box content can also be a box and a
12592 can also be part of another box (see the 2nd and 3rd example).
12593 When the box should contain a formula, an extra formula has to be created,
12594 the same way as for
12604 \begin_layout Plain Layout
12605 This also applies for the command
12619 \begin_layout Standard
12620 One of the following predefined colors can be chosen:
12623 \begin_layout Standard
12657 \begin_layout Standard
12659 \begin_inset Tabular
12660 <lyxtabular version="3" rows="4" columns="2">
12661 <features rotate="0" tabularvalignment="middle">
12662 <column alignment="center" valignment="top">
12663 <column alignment="center" valignment="top">
12665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12668 \begin_layout Plain Layout
12674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12677 \begin_layout Plain Layout
12679 \begin_inset Note Note
12682 \begin_layout Plain Layout
12689 is only used as spacer.
12701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12704 \begin_layout Plain Layout
12708 \begin_inset Formula $\to$
12718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12721 \begin_layout Plain Layout
12722 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12735 \begin_layout Plain Layout
12739 \begin_inset Formula $\to$
12747 \begin_inset space \textvisiblespace{}
12755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12758 \begin_layout Plain Layout
12759 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
12769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12772 \begin_layout Plain Layout
12776 \begin_inset space \textvisiblespace{}
12782 \begin_inset Formula $\to$
12798 \begin_inset space \textvisiblespace{}
12806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12809 \begin_layout Plain Layout
12810 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
12826 \begin_layout Standard
12833 only colors the box but not the characters in the box.
12834 To color all characters, the whole formula is highlighted and the desired
12835 color is chosen in the
12838 \begin_inset space ~
12844 The dialog can be called with the toolbar button
12845 \begin_inset Graphics
12846 filename ../images/dialog-show_character.png
12853 Edit\SpecialChar \menuseparator
12855 \begin_inset space ~
12858 Style\SpecialChar \menuseparator
12862 The formula number then has the same color as the formula.
12863 When the formula number should get another color than the formula characters,
12864 the color must be changed within the formula.
12867 \begin_layout Standard
12871 \begin_layout Standard
12874 \begin_inset Formula
12876 \int A=B\label{eq:red}
12884 \begin_inset Formula
12886 \textcolor{red}{\int A=B}\label{eq:redgreen}
12894 \begin_layout Standard
12896 \begin_inset CommandInset ref
12902 is completely colored red.
12903 \begin_inset Newline newline
12907 \begin_inset CommandInset ref
12909 reference "eq:redgreen"
12913 was first completely colored green to set the color for the formula number.
12914 Subsequently the formula characters were colored red.
12917 \begin_layout Standard
12918 \begin_inset VSpace bigskip
12921 To color the frame different than the rest of the box, the command
12928 \begin_inset Index idx
12931 \begin_layout Plain Layout
12939 is used in the following scheme:
12942 \begin_layout Standard
12947 fcolorbox{frame color}{color}{box content}
12950 \begin_layout Standard
12957 is an extension of the command
12964 The frame width is set, like for
12987 \begin_layout Plain Layout
12999 \begin_inset Formula
13001 \fcolorbox{cyan}{magenta}{A=B}
13010 \begin_layout Plain Layout
13024 \begin_layout Standard
13025 This formula was created with the command
13026 \begin_inset Newline newline
13034 \begin_inset Formula $\to$
13040 \begin_inset Formula $\to$
13050 \begin_layout Standard
13051 \begin_inset VSpace bigskip
13054 To use other colors than the predefined ones, they have to be defined first.
13057 \begin_layout Standard
13058 One can for example define the color
13059 \begin_inset Quotes eld
13067 \begin_inset Quotes erd
13070 with the LaTeX-preamble line:
13073 \begin_layout Standard
13078 definecolor{darkgreen}{cmyk}{0.5,
13093 \begin_inset Index idx
13096 \begin_layout Plain Layout
13107 \begin_layout Standard
13112 is the color space that denotes the colors
13129 The four comma separated numbers are the portion factor for the corresponding
13130 colors of the color space.
13131 The factors can be in the range of 0
13132 \begin_inset space \thinspace{}
13136 \begin_inset space \thinspace{}
13144 also the color space
13148 can be used for definitions.
13165 , so that there are in this case three portion factors for the corresponding
13167 Furthermore there is the color space
13171 with one portion factor for the gray value.
13174 \begin_layout Standard
13175 As example a framed box with the new defined color
13179 where the characters have been colored
13184 \begin_inset Formula
13186 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
13194 \begin_layout Standard
13195 Self-defined colors can also be used for text with the help of the command
13203 \begin_inset Index idx
13206 \begin_layout Plain Layout
13215 \begin_layout Standard
13219 \begin_layout Plain Layout
13223 textcolor{darkgreen}{
13229 \begin_inset Quotes eld
13233 \begin_inset Quotes erd
13240 \begin_layout Plain Layout
13250 \begin_layout Standard
13258 \begin_inset Index idx
13261 \begin_layout Plain Layout
13269 is used in the scheme
13273 textcolor{color}{characters to color}
13278 \begin_layout Subsection
13280 \begin_inset CommandInset label
13282 name "sub:Paragraph-Boxes"
13287 \begin_inset Index idx
13290 \begin_layout Plain Layout
13291 Boxes ! as paragraph
13299 \begin_layout Standard
13300 A box that can contain several lines and paragraphs, a so-called paragraph
13301 box (parbox), can be created with the menu
13303 Insert\SpecialChar \menuseparator
13306 or the toolbar button
13307 \begin_inset Graphics
13308 filename ../images/box-insert.png
13316 \begin_layout Standard
13317 The following example shows a framed parbox in a line:
13320 \begin_layout Standard
13321 \begin_inset VSpace medskip
13325 \begin_inset Box Boxed
13335 height_special "totalheight"
13338 \begin_layout Plain Layout
13339 This is a paragraph box.
13341 \begin_inset space \thinspace{}
13344 cm long and can also contain formulas:
13345 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13356 \begin_layout Standard
13357 \begin_inset VSpace medskip
13363 \begin_layout Standard
13364 Such a box is created by right-clicking on the gray box inset.
13365 A dialog pops up showing the box properties.
13379 \begin_inset space \thinspace{}
13384 Vertical Box Alignment
13389 \begin_layout Standard
13390 \begin_inset VSpace medskip
13393 In LaTeX a parbox is created with the command
13400 \begin_inset Index idx
13403 \begin_layout Plain Layout
13411 which has the following scheme:
13414 \begin_layout Standard
13419 parbox[position]{width}{box content}
13422 \begin_layout Standard
13437 \begin_inset Quotes eld
13441 \begin_inset Quotes erd
13444 means that the box is aligned within the surrounding text with its last
13451 \begin_inset Quotes eld
13455 \begin_inset Quotes erd
13458 this is done with the first line.
13459 When no position is given, the box will be vertically centered, see section
13467 \begin_inset space ~
13472 manual for examples.
13475 \begin_layout Standard
13476 \begin_inset VSpace bigskip
13479 To frame formulas completely, including the formula number, the formula
13480 must be set into a parbox.
13481 To do this, the command
13495 is inserted in TeX-mode before the formula.
13503 \begin_inset Index idx
13506 \begin_layout Plain Layout
13514 is hereby the line width set for the document.
13515 Because the frame is outside the parbox, 2
13516 \begin_inset space \thinspace{}
13519 times the frame separation and the frame thickness must be subtracted from
13521 As this is not automatically done by LyX due to a bug
13525 \begin_layout Plain Layout
13526 \begin_inset CommandInset href
13528 name "LyX-bug #4483"
13529 target "http://www.lyx.org/trac/ticket/4483"
13538 , TeX-mode has to be used.
13539 To be able to multiply and subtract in arguments, the LaTeX-package
13547 \begin_layout Plain Layout
13552 is part of every LaTeX standard installation.
13558 \begin_inset Index idx
13561 \begin_layout Plain Layout
13567 must be loaded in the LaTeX-preamble with the line
13570 \begin_layout Standard
13578 \begin_layout Standard
13579 Behind the formula both boxes are closed by entering
13584 Here is an example:
13588 \begin_layout Plain Layout
13602 \begin_layout Standard
13606 \begin_layout Plain Layout
13624 \begin_inset Formula
13626 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
13635 \begin_layout Plain Layout
13646 \begin_layout Plain Layout
13660 \begin_layout Standard
13661 \begin_inset VSpace medskip
13664 As a parbox is used as the argument of
13670 , there is in this case no difference between
13685 \begin_layout Standard
13686 \begin_inset VSpace bigskip
13689 Paragraph boxes are very useful to comment formulas directly.
13696 is used in combination with the command
13710 \begin_inset CommandInset ref
13712 reference "sub:User-defined-Numbering"
13719 \begin_layout Standard
13720 An example of a formula commented with
13729 \begin_layout Standard
13733 \begin_layout Plain Layout
13746 This is a description.
13747 It is distinctly separated from the formula and multiline.
13751 \begin_layout Plain Layout
13763 \begin_layout Standard
13764 Such a formula must be inserted completely in TeX-mode because LyX does
13765 not yet support the command
13772 The formula is created with the following command sequence:
13775 \begin_layout Standard
13788 is inserted in TeX-mode.
13792 \begin_layout Plain Layout
13793 When the formula style
13805 can also be replaced by
13812 (formula styles see
13813 \begin_inset CommandInset ref
13815 reference "sec:Formula-Styles"
13824 Then the description follows as normal text and finally
13830 is inserted in TeX-mode.
13843 hereby create a displayed formula.
13846 \begin_layout Standard
13853 can be seen in this example that was
13854 \begin_inset Quotes eld
13858 \begin_inset Quotes erd
13861 using the mathematical textmode:
13862 \begin_inset Formula
13864 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
13872 \begin_layout Section
13874 \begin_inset Index idx
13877 \begin_layout Plain Layout
13886 \begin_layout Subsection
13888 \begin_inset CommandInset label
13890 name "sub:Big-Operators"
13895 \begin_inset Index idx
13898 \begin_layout Plain Layout
13905 \begin_inset Index idx
13908 \begin_layout Plain Layout
13915 \begin_inset Index idx
13918 \begin_layout Plain Layout
13927 \begin_layout Standard
13928 To be able to use all integral operators listed here, the option
13930 Use esint package automatically
13932 must be set in the document settings under
13935 \begin_inset space ~
13943 \begin_layout Standard
13944 \begin_inset space \hfill{}
13948 \begin_inset Tabular
13949 <lyxtabular version="3" rows="11" columns="2">
13950 <features rotate="0" tabularvalignment="middle">
13951 <column alignment="center" valignment="top" width="0pt">
13952 <column alignment="center" valignment="top" width="0pt">
13954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13957 \begin_layout Plain Layout
13963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13966 \begin_layout Plain Layout
13974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13977 \begin_layout Plain Layout
13981 \begin_inset Index idx
13984 \begin_layout Plain Layout
13997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14000 \begin_layout Plain Layout
14001 \begin_inset Formula $\int$
14011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14014 \begin_layout Plain Layout
14022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14025 \begin_layout Plain Layout
14026 \begin_inset Formula $\oint$
14036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14039 \begin_layout Plain Layout
14047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14050 \begin_layout Plain Layout
14051 \begin_inset Formula $\ointctrclockwise$
14061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14064 \begin_layout Plain Layout
14072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14075 \begin_layout Plain Layout
14076 \begin_inset Formula $\ointclockwise$
14086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14089 \begin_layout Plain Layout
14097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14100 \begin_layout Plain Layout
14101 \begin_inset Formula $\sqint$
14111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14114 \begin_layout Plain Layout
14122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14125 \begin_layout Plain Layout
14127 \begin_inset Formula $\fint$
14137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14140 \begin_layout Plain Layout
14148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14151 \begin_layout Plain Layout
14153 \begin_inset Formula $\landupint$
14163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14166 \begin_layout Plain Layout
14174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14177 \begin_layout Plain Layout
14179 \begin_inset Formula $\landdownint$
14189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14192 \begin_layout Plain Layout
14200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14203 \begin_layout Plain Layout
14204 \begin_inset Formula $\bigcap$
14214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14217 \begin_layout Plain Layout
14225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14228 \begin_layout Plain Layout
14229 \begin_inset Formula $\bigcup$
14243 \begin_inset space \hfill{}
14247 \begin_inset Tabular
14248 <lyxtabular version="3" rows="11" columns="2">
14249 <features rotate="0" tabularvalignment="middle">
14250 <column alignment="center" valignment="top" width="0pt">
14251 <column alignment="center" valignment="top" width="0pt">
14253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14256 \begin_layout Plain Layout
14262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14265 \begin_layout Plain Layout
14273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14276 \begin_layout Plain Layout
14280 \begin_inset Index idx
14283 \begin_layout Plain Layout
14296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14299 \begin_layout Plain Layout
14300 \begin_inset Formula $\sum$
14310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14313 \begin_layout Plain Layout
14317 \begin_inset Index idx
14320 \begin_layout Plain Layout
14327 \begin_layout Plain Layout
14346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14349 \begin_layout Plain Layout
14350 \begin_inset Formula $\prod$
14360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14363 \begin_layout Plain Layout
14371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14374 \begin_layout Plain Layout
14375 \begin_inset Formula $\coprod$
14385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14388 \begin_layout Plain Layout
14396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14399 \begin_layout Plain Layout
14400 \begin_inset Formula $\bigodot$
14410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14413 \begin_layout Plain Layout
14421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14424 \begin_layout Plain Layout
14425 \begin_inset Formula $\bigotimes$
14435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14438 \begin_layout Plain Layout
14446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14449 \begin_layout Plain Layout
14450 \begin_inset Formula $\bigoplus$
14460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14463 \begin_layout Plain Layout
14471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14474 \begin_layout Plain Layout
14475 \begin_inset Formula $\bigwedge$
14485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14488 \begin_layout Plain Layout
14496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14499 \begin_layout Plain Layout
14500 \begin_inset Formula $\bigvee$
14510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14513 \begin_layout Plain Layout
14521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14524 \begin_layout Plain Layout
14525 \begin_inset Formula $\bigsqcup$
14535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14538 \begin_layout Plain Layout
14546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14549 \begin_layout Plain Layout
14550 \begin_inset Formula $\biguplus$
14564 \begin_inset space \hfill{}
14570 \begin_layout Standard
14571 All big operators can also be inserted via the math toolbar button
14572 \begin_inset Graphics
14573 filename ../images/math/intop.png
14581 \begin_layout Standard
14582 The operators are called big because they are bigger than the sometimes
14583 equal looking binary operators.
14584 All big operators can have limits as described in the next subsection.
14587 \begin_layout Standard
14588 For all integral operators there is a second version available, ending in
14606 These operators are different from
14613 \begin_inset space \space{}
14616 in the style the operator limits are displayed, see
14617 \begin_inset CommandInset ref
14619 reference "sub:Operator-Limits"
14627 \begin_layout Subsubsection*
14628 Advice for Integrals
14631 \begin_layout Standard
14636 in an integral is an operator, that therefore has to be set upright.
14637 This is done by highlighting the
14641 and using the keyboard shortcut
14651 \begin_layout Plain Layout
14657 \begin_inset CommandInset ref
14659 reference "sub:Font-Styles"
14669 Finally the smallest space is inserted before the
14673 , as this is usual for operators.
14677 \begin_layout Standard
14679 \begin_inset Formula $\int A(x)dx$
14683 \begin_inset Newline newline
14687 \begin_inset Phantom HPhantom
14690 \begin_layout Plain Layout
14697 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14703 \begin_layout Standard
14704 For multiple integrals there are the following commands:
14705 \begin_inset VSpace medskip
14711 \begin_layout Standard
14712 \begin_inset space \hfill{}
14716 \begin_inset Tabular
14717 <lyxtabular version="3" rows="4" columns="2">
14718 <features rotate="0" tabularvalignment="middle">
14719 <column alignment="center" valignment="top">
14720 <column alignment="center" valignment="top">
14722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14725 \begin_layout Plain Layout
14731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14734 \begin_layout Plain Layout
14736 \begin_inset Note Note
14739 \begin_layout Plain Layout
14746 is only used as spacer.
14758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14761 \begin_layout Plain Layout
14769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14772 \begin_layout Plain Layout
14773 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
14783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14786 \begin_layout Plain Layout
14794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14797 \begin_layout Plain Layout
14798 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
14808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14811 \begin_layout Plain Layout
14819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14822 \begin_layout Plain Layout
14823 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
14837 \begin_inset space \hfill{}
14841 \begin_inset Tabular
14842 <lyxtabular version="3" rows="4" columns="2">
14843 <features rotate="0" tabularvalignment="middle">
14844 <column alignment="center" valignment="top">
14845 <column alignment="center" valignment="top">
14847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14850 \begin_layout Plain Layout
14856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14859 \begin_layout Plain Layout
14867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14870 \begin_layout Plain Layout
14878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14881 \begin_layout Plain Layout
14882 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
14892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14895 \begin_layout Plain Layout
14903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14906 \begin_layout Plain Layout
14907 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
14917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14920 \begin_layout Plain Layout
14928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14931 \begin_layout Plain Layout
14932 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
14946 \begin_inset space \hfill{}
14952 \begin_layout Standard
14953 \begin_inset Newpage newpage
14959 \begin_layout Subsection
14961 \begin_inset CommandInset label
14963 name "sub:Operator-Limits"
14968 \begin_inset Index idx
14971 \begin_layout Plain Layout
14980 \begin_layout Standard
14981 Limits are created by super- and subscripts:
14984 \begin_layout Standard
14986 \begin_inset Tabular
14987 <lyxtabular version="3" rows="2" columns="2">
14988 <features rotate="0" tabularvalignment="middle">
14989 <column alignment="center" valignment="top" width="0pt">
14990 <column alignment="center" valignment="top" width="0pt">
14992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14995 \begin_layout Plain Layout
15001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15004 \begin_layout Plain Layout
15006 \begin_inset Note Note
15009 \begin_layout Plain Layout
15016 is only used as spacer.
15028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15031 \begin_layout Plain Layout
15037 \begin_inset space \textvisiblespace{}
15041 \begin_inset Formula $\to$
15045 \begin_inset Formula $\to$
15053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15056 \begin_layout Plain Layout
15057 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15073 \begin_layout Standard
15074 Limits of inline formulas are set right beside the operator.
15075 Limits in displayed formulas are set above or below the operator, except
15076 for integral limits.
15079 \begin_layout Standard
15080 To force that the limits are set beside the operator, the cursor is set
15081 directly behind the operator and the limits type is changed with the menu
15084 Edit\SpecialChar \menuseparator
15085 Math\SpecialChar \menuseparator
15104 \begin_layout Standard
15105 The default limits type is this:
15106 \begin_inset Formula
15108 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15113 This is how it looks when the limits type was changed to
15120 \begin_inset Formula
15122 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
15127 For integrals, except those ending with
15143 etc., the limits are by default set beside the operator.
15144 But for multiple integrals the limits are often set below the operator.
15145 In the following example the limits type was therefore set to
15149 and so set below the integrals:
15150 \begin_inset Formula
15152 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
15160 \begin_layout Standard
15161 \begin_inset VSpace medskip
15164 To specify conditions for limits, the commands
15171 \begin_inset Index idx
15174 \begin_layout Plain Layout
15189 \begin_inset Index idx
15192 \begin_layout Plain Layout
15201 To create for example this expression
15202 \begin_inset Formula
15204 \sum_{\begin{subarray}{c}
15208 \end{subarray}}^{n}k^{-2}\label{eq:substack}
15216 \begin_layout Standard
15217 the following has to be done:
15218 \begin_inset Newline newline
15230 \begin_inset space \textvisiblespace{}
15236 One is now in a blue box under the summation operator and insert there
15242 \begin_inset space \textvisiblespace{}
15248 The blue box is now within a purple box and now several lines can be written
15250 A new line is created by inserting a line break (
15253 arg "newline-insert newline"
15258 \begin_inset Newline newline
15263 0<k<1000 Ctrl+Return
15264 \begin_inset Newline newline
15269 is typed in, a new box appears below for the new line.
15272 \begin_layout Standard
15273 The alignment of the lines can be changed to left aligned with the
15283 Edit\SpecialChar \menuseparator
15287 To get right alignment,
15292 \begin_inset space \textvisiblespace{}
15297 is inserted at the beginning of the line.
15300 \begin_layout Standard
15313 with the difference that the lines are always centered.
15316 \begin_layout Standard
15317 \begin_inset VSpace bigskip
15321 \begin_inset CommandInset ref
15323 reference "eq:substack"
15327 there can be too much space beside an operator, because the characters
15328 following the operator are set beside the limits.
15331 \begin_layout Standard
15332 To avoid this, the following macro can be used in the LaTeX-preamble:
15335 \begin_layout Standard
15349 \begin_inset Newline newline
15361 \begin_inset Newline newline
15368 mathclapinternal #1#2{
15372 mathsurround =0pt #1{#2}$}}
15375 \begin_layout Standard
15376 This defines the command
15383 \begin_inset Index idx
15386 \begin_layout Plain Layout
15394 that sets the width of the limit to 0
15395 \begin_inset space \thinspace{}
15399 The command scheme is
15402 \begin_layout Standard
15410 \begin_layout Standard
15411 where the limit can consist of several conditions.
15414 \begin_layout Standard
15416 \begin_inset CommandInset ref
15418 reference "eq:substack"
15422 , one uses the command
15425 \begin_layout Standard
15435 \begin_inset space \textvisiblespace{}
15438 0<k<1000 Ctrl+Return
15441 \begin_layout Standard
15442 to create the lower limit.
15443 The summand is now directly behind the summation operator:
15444 \begin_inset Formula
15446 \sum_{\mathclap{\substack{0<k<1000\\
15458 \begin_layout Standard
15459 \begin_inset VSpace bigskip
15462 How to use one limit for several operators is described in
15463 \begin_inset CommandInset ref
15465 reference "sub:Self-defined-Operators"
15472 \begin_layout Subsection
15473 Decoration for Operators
15474 \begin_inset Index idx
15477 \begin_layout Plain Layout
15478 Operators ! Decoration
15486 \begin_layout Standard
15494 \begin_inset Index idx
15497 \begin_layout Plain Layout
15512 \begin_inset Index idx
15515 \begin_layout Plain Layout
15523 characters can be placed above or below an operator, respectively.
15531 \begin_inset Index idx
15534 \begin_layout Plain Layout
15542 characters can be set before and behind a big operator.
15543 The command scheme is:
15546 \begin_layout Standard
15562 \begin_layout Standard
15569 must always be before the operator.
15570 You can decorate with several characters and even with other operators
15572 To place for example only characters behind a big operator, write nothing
15573 between the first braces but don't omit the braces.
15576 \begin_layout Standard
15577 For example the command
15582 \begin_inset Formula $\to$
15592 \begin_inset Formula $\to$
15598 \begin_inset space \textvisiblespace{}
15608 \begin_inset Formula
15610 \sideset{}{'}\sum_{k=1}^{n}
15618 \begin_layout Standard
15619 \begin_inset Note Greyedout
15622 \begin_layout Plain Layout
15629 can only be used to decorate big operators, binary operators are not allowed.
15637 \begin_layout Standard
15650 can also be used to decorate symbols and characters.
15651 For example, the command
15656 \begin_inset space \textvisiblespace{}
15662 \begin_inset space \textvisiblespace{}
15668 \begin_inset Formula $\uparrow$
15676 \begin_inset Formula
15678 \overset{a}{\maltese}
15686 \begin_layout Subsection
15688 \begin_inset CommandInset label
15690 name "sub:Binary-Operators"
15695 \begin_inset Index idx
15698 \begin_layout Plain Layout
15707 \begin_layout Standard
15708 Binary operators are surrounded by space when there is a character before
15710 \begin_inset VSpace medskip
15716 \begin_layout Standard
15717 \begin_inset space \hfill{}
15721 \begin_inset Tabular
15722 <lyxtabular version="3" rows="13" columns="2">
15723 <features rotate="0" tabularvalignment="middle">
15724 <column alignment="center" valignment="top" width="0pt">
15725 <column alignment="center" valignment="top" width="0pt">
15727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15730 \begin_layout Plain Layout
15732 \begin_inset Note Note
15735 \begin_layout Plain Layout
15742 is only used as spacer.
15752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15755 \begin_layout Plain Layout
15763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15766 \begin_layout Plain Layout
15772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15775 \begin_layout Plain Layout
15776 \begin_inset Formula $+$
15786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15789 \begin_layout Plain Layout
15795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15798 \begin_layout Plain Layout
15799 \begin_inset Formula $-$
15809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15812 \begin_layout Plain Layout
15820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15823 \begin_layout Plain Layout
15824 \begin_inset Formula $\pm$
15834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15837 \begin_layout Plain Layout
15845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15848 \begin_layout Plain Layout
15849 \begin_inset Formula $\mp$
15859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15862 \begin_layout Plain Layout
15870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15873 \begin_layout Plain Layout
15874 \begin_inset Formula $\cdot$
15884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15887 \begin_layout Plain Layout
15895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15898 \begin_layout Plain Layout
15899 \begin_inset Formula $\times$
15909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15912 \begin_layout Plain Layout
15920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15923 \begin_layout Plain Layout
15924 \begin_inset Formula $\div$
15934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15937 \begin_layout Plain Layout
15941 \begin_layout Plain Layout
15954 \begin_layout Plain Layout
15966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15969 \begin_layout Plain Layout
15970 \begin_inset Formula $*$
15980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15983 \begin_layout Plain Layout
15991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15994 \begin_layout Plain Layout
15995 \begin_inset Formula $\star$
16005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16008 \begin_layout Plain Layout
16016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16019 \begin_layout Plain Layout
16020 \begin_inset Formula $\circ$
16030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16033 \begin_layout Plain Layout
16041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16044 \begin_layout Plain Layout
16045 \begin_inset Formula $\diamond$
16055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16058 \begin_layout Plain Layout
16066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16069 \begin_layout Plain Layout
16070 \begin_inset Formula $\bullet$
16084 \begin_inset space \hfill{}
16088 \begin_inset Tabular
16089 <lyxtabular version="3" rows="13" columns="2">
16090 <features rotate="0" tabularvalignment="middle">
16091 <column alignment="center" valignment="top" width="0pt">
16092 <column alignment="center" valignment="top" width="0pt">
16094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16097 \begin_layout Plain Layout
16103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16106 \begin_layout Plain Layout
16114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16117 \begin_layout Plain Layout
16125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16128 \begin_layout Plain Layout
16129 \begin_inset Formula $\nabla$
16139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16142 \begin_layout Plain Layout
16150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16153 \begin_layout Plain Layout
16154 \begin_inset Formula $\bigtriangledown$
16164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16167 \begin_layout Plain Layout
16175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16178 \begin_layout Plain Layout
16179 \begin_inset Formula $\bigtriangleup$
16189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16192 \begin_layout Plain Layout
16200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16203 \begin_layout Plain Layout
16204 \begin_inset Formula $\Box$
16214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16217 \begin_layout Plain Layout
16225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16228 \begin_layout Plain Layout
16229 \begin_inset Formula $\cap$
16239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16242 \begin_layout Plain Layout
16250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16253 \begin_layout Plain Layout
16254 \begin_inset Formula $\cup$
16264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16267 \begin_layout Plain Layout
16275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16278 \begin_layout Plain Layout
16279 \begin_inset Formula $\dagger$
16289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16292 \begin_layout Plain Layout
16300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16303 \begin_layout Plain Layout
16304 \begin_inset Formula $\ddagger$
16314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16317 \begin_layout Plain Layout
16325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16328 \begin_layout Plain Layout
16329 \begin_inset Formula $\wr$
16339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16342 \begin_layout Plain Layout
16350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16353 \begin_layout Plain Layout
16354 \begin_inset Formula $\bigcirc$
16364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16367 \begin_layout Plain Layout
16375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16378 \begin_layout Plain Layout
16379 \begin_inset Formula $\wedge$
16389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16392 \begin_layout Plain Layout
16400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16403 \begin_layout Plain Layout
16404 \begin_inset Formula $\vee$
16418 \begin_inset space \hfill{}
16422 \begin_inset Tabular
16423 <lyxtabular version="3" rows="13" columns="2">
16424 <features rotate="0" tabularvalignment="middle">
16425 <column alignment="center" valignment="top" width="0pt">
16426 <column alignment="center" valignment="top" width="0pt">
16428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16431 \begin_layout Plain Layout
16437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16440 \begin_layout Plain Layout
16448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16451 \begin_layout Plain Layout
16459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16462 \begin_layout Plain Layout
16463 \begin_inset Formula $\oplus$
16473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16476 \begin_layout Plain Layout
16484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16487 \begin_layout Plain Layout
16488 \begin_inset Formula $\ominus$
16498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16501 \begin_layout Plain Layout
16509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16512 \begin_layout Plain Layout
16513 \begin_inset Formula $\otimes$
16523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16526 \begin_layout Plain Layout
16534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16537 \begin_layout Plain Layout
16538 \begin_inset Formula $\oslash$
16548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16551 \begin_layout Plain Layout
16559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16562 \begin_layout Plain Layout
16563 \begin_inset Formula $\odot$
16573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16576 \begin_layout Plain Layout
16584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16587 \begin_layout Plain Layout
16588 \begin_inset Formula $\amalg$
16598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16601 \begin_layout Plain Layout
16609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16612 \begin_layout Plain Layout
16613 \begin_inset Formula $\uplus$
16623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16626 \begin_layout Plain Layout
16634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16637 \begin_layout Plain Layout
16638 \begin_inset Formula $\setminus$
16648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16651 \begin_layout Plain Layout
16659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16662 \begin_layout Plain Layout
16663 \begin_inset Formula $\sqcap$
16673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16676 \begin_layout Plain Layout
16684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16687 \begin_layout Plain Layout
16688 \begin_inset Formula $\sqcup$
16698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16701 \begin_layout Plain Layout
16709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16712 \begin_layout Plain Layout
16713 \begin_inset Formula $\triangleleft$
16723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16726 \begin_layout Plain Layout
16734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16737 \begin_layout Plain Layout
16738 \begin_inset Formula $\triangleright$
16752 \begin_inset space \hfill{}
16758 \begin_layout Standard
16759 All binary operators can also be inserted via the math toolbar button
16760 \begin_inset Graphics
16761 filename ../images/math/pm.png
16769 \begin_layout Standard
16770 To typeset the Laplace operator also
16787 \begin_inset Formula $\nabla^{2}$
16790 ) can be used instead of
16799 \begin_layout Standard
16806 Insert\SpecialChar \menuseparator
16818 \begin_layout Subsection
16819 Self-defined Operators
16820 \begin_inset CommandInset label
16822 name "sub:Self-defined-Operators"
16827 \begin_inset Index idx
16830 \begin_layout Plain Layout
16831 Operators ! self-defined
16839 \begin_layout Standard
16840 With the help of the command
16844 DeclareMathOperator
16847 \begin_inset Index idx
16850 \begin_layout Plain Layout
16855 DeclareMathOperator
16860 custom operators can be defined in the LaTeX-preamble.
16861 Its command scheme is:
16864 \begin_layout Standard
16869 DeclareMathOperator{new command}{display}
16872 \begin_layout Standard
16873 Display can be characters or symbols that define how the operator looks
16875 To define a big operator a * is set behind the command.
16876 All self-defined big operators can have limits as described in
16877 \begin_inset CommandInset ref
16879 reference "sub:Operator-Limits"
16886 \begin_layout Standard
16887 For example the LaTeX-preamble line
16890 \begin_layout Standard
16895 DeclareMathOperator*{
16902 \begin_layout Standard
16903 defines the command
16909 , that inserts a big operator consisting of the lozenge symbol from
16910 \begin_inset CommandInset ref
16912 reference "sub:Miscellaneous-Symbols"
16917 \begin_inset Formula
16919 \Lozenge_{n=1}^{\infty}
16924 The command for this formula is:
16935 \begin_inset Formula $\to$
16941 \begin_layout Standard
16942 \begin_inset VSpace bigskip
16945 When self-defined operators are not used several times in the document,
16946 they can also be defined with the commands
16953 \begin_inset Index idx
16956 \begin_layout Plain Layout
16971 \begin_inset Index idx
16974 \begin_layout Plain Layout
16982 , which have the following scheme:
16985 \begin_layout Standard
16999 \begin_layout Standard
17006 defines big operators,
17015 \begin_layout Standard
17023 \begin_inset space \thinspace{}
17027 \begin_inset space \space{}
17030 be used to use one limit for several operators:
17033 \begin_layout Standard
17034 \begin_inset Formula
17036 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17044 \begin_layout Standard
17045 The command for the formula above is:
17046 \begin_inset Newline newline
17062 \begin_inset space \textvisiblespace{}
17068 \begin_inset Formula $\to$
17074 \begin_inset space \textvisiblespace{}
17082 \begin_layout Section
17084 \begin_inset Index idx
17087 \begin_layout Plain Layout
17096 \begin_layout Subsection
17098 \begin_inset CommandInset label
17100 name "sub:Font-Styles"
17105 \begin_inset Index idx
17108 \begin_layout Plain Layout
17117 \begin_layout Standard
17118 Latin letters in formulas can be set in one of the following font styles:
17119 \begin_inset VSpace -2mm
17125 \begin_layout Standard
17127 \begin_inset Tabular
17128 <lyxtabular version="3" rows="7" columns="3">
17129 <features rotate="0" tabularvalignment="middle">
17130 <column alignment="center" valignment="top">
17131 <column alignment="center" valignment="top">
17132 <column alignment="center" valignment="top">
17134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17137 \begin_layout Plain Layout
17143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17146 \begin_layout Plain Layout
17152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17155 \begin_layout Plain Layout
17163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17166 \begin_layout Plain Layout
17172 \begin_inset space \textvisiblespace{}
17182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17185 \begin_layout Plain Layout
17186 \begin_inset Formula $\mathbb{ABC}$
17194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17197 \begin_layout Plain Layout
17210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17213 \begin_layout Plain Layout
17219 \begin_inset space \textvisiblespace{}
17229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17232 \begin_layout Plain Layout
17233 \begin_inset Formula $\mathbf{AbC}$
17241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17244 \begin_layout Plain Layout
17257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17260 \begin_layout Plain Layout
17266 \begin_inset space \textvisiblespace{}
17276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17279 \begin_layout Plain Layout
17280 \begin_inset Formula $\boldsymbol{AbC}$
17288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17291 \begin_layout Plain Layout
17294 arg "font-boldsymbol"
17304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17307 \begin_layout Plain Layout
17313 \begin_inset space \textvisiblespace{}
17323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17326 \begin_layout Plain Layout
17327 \begin_inset Formula $\mathcal{ABC}$
17335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17338 \begin_layout Plain Layout
17351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17354 \begin_layout Plain Layout
17360 \begin_inset space \textvisiblespace{}
17370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17373 \begin_layout Plain Layout
17374 \begin_inset Formula $\mathfrak{AbC}$
17382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17385 \begin_layout Plain Layout
17393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17396 \begin_layout Plain Layout
17402 \begin_inset space \textvisiblespace{}
17412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17415 \begin_layout Plain Layout
17416 \begin_inset Formula $\mathscr{AbC}$
17424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17427 \begin_layout Plain Layout
17441 \begin_layout Standard
17443 \begin_inset Tabular
17444 <lyxtabular version="3" rows="5" columns="3">
17445 <features rotate="0" tabularvalignment="middle">
17446 <column alignment="center" valignment="top">
17447 <column alignment="center" valignment="top">
17448 <column alignment="center" valignment="top">
17450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17453 \begin_layout Plain Layout
17459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17462 \begin_layout Plain Layout
17468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17471 \begin_layout Plain Layout
17479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17482 \begin_layout Plain Layout
17488 \begin_inset space \textvisiblespace{}
17498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17501 \begin_layout Plain Layout
17502 \begin_inset Formula $\mathit{AbC}$
17510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17513 \begin_layout Plain Layout
17521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17524 \begin_layout Plain Layout
17530 \begin_inset space \textvisiblespace{}
17540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17543 \begin_layout Plain Layout
17544 \begin_inset Formula $\mathrm{AbC}$
17552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17555 \begin_layout Plain Layout
17568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17571 \begin_layout Plain Layout
17577 \begin_inset space \textvisiblespace{}
17587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17590 \begin_layout Plain Layout
17591 \begin_inset Formula $\mathsf{AbC}$
17599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17602 \begin_layout Plain Layout
17615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17618 \begin_layout Plain Layout
17624 \begin_inset space \textvisiblespace{}
17634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17637 \begin_layout Plain Layout
17638 \begin_inset Formula $\mathtt{AbC}$
17646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17649 \begin_layout Plain Layout
17652 arg "font-typewriter"
17668 \begin_layout Standard
17669 \begin_inset Note Greyedout
17672 \begin_layout Plain Layout
17689 can only be used for big letters.
17697 \begin_layout Standard
17698 Predefined is the style
17707 \begin_layout Standard
17708 The style commands work also for letters in mathematical constructs:
17709 \begin_inset Formula
17711 \mathfrak{A=\frac{b}{C}}
17719 \begin_layout Standard
17720 Characters in mathematical text don't appear in a math font style but in
17721 the text font style
17728 That their style can't be set correctly via the text style dialog is a
17733 \begin_layout Plain Layout
17734 \begin_inset CommandInset href
17736 name "LyX-bug #4629"
17737 target "http://www.lyx.org/trac/ticket/4629"
17749 \begin_layout Standard
17750 Instead of the style commands the dialog
17752 Edit\SpecialChar \menuseparator
17753 Math\SpecialChar \menuseparator
17756 or the toolbar button
17757 \begin_inset Graphics
17758 filename ../images/math/font.png
17766 \begin_layout Subsection
17768 \begin_inset CommandInset label
17770 name "sub:Bold-Formulas"
17775 \begin_inset Index idx
17778 \begin_layout Plain Layout
17787 \begin_layout Standard
17788 To make a complete formula bold, the command
17794 from the previous subsection cannot be used, because it doesn't work for
17795 small Greek letters.
17796 Furthermore it prints Latin letters always upright, like in the following
17800 \begin_layout Standard
17801 \begin_inset Formula
17803 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
17811 \begin_layout Standard
17812 To display the formula correctly, the command
17819 \begin_inset Formula
17821 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
17826 It is also possible to set the formula in a
17828 boldmath environment
17831 This environment is created by inserting the command
17838 \begin_inset Index idx
17841 \begin_layout Plain Layout
17850 To end the environment, the command
17857 \begin_inset Index idx
17860 \begin_layout Plain Layout
17868 is inserted in TeX-mode.
17872 \begin_layout Plain Layout
17882 \begin_inset Formula
17884 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
17893 \begin_layout Plain Layout
17905 \begin_layout Subsection
17907 \begin_inset Index idx
17910 \begin_layout Plain Layout
17919 \begin_layout Standard
17920 Formulas can be colored like normal text: Highlight a formula or a formula
17926 Here is a formula in magenta:
17927 \begin_inset Formula
17929 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
17937 \begin_layout Standard
17938 You can also define your own colors as described in
17939 \begin_inset CommandInset ref
17941 reference "sub:Colored-Boxes"
17946 They can be used with the TeX code command
17953 \begin_inset Index idx
17956 \begin_layout Plain Layout
17967 \begin_layout Standard
17972 textcolor{color}{characters or formula}
17975 \begin_layout Standard
17976 The following example was colored completely dark green and partly red:
17979 \begin_layout Standard
17983 \begin_layout Plain Layout
17987 textcolor{darkgreen}{
17993 \begin_inset Formula
17995 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18004 \begin_layout Plain Layout
18014 \begin_layout Standard
18015 Due to a bug in LyX only complete formulas can be colored with self-defined
18020 \begin_layout Plain Layout
18021 \begin_inset CommandInset href
18023 name "LyX-bug #5269"
18024 target "http://www.lyx.org/trac/ticket/5269"
18036 \begin_layout Subsection
18038 \begin_inset CommandInset label
18040 name "sub:Font-Sizes"
18045 \begin_inset Index idx
18048 \begin_layout Plain Layout
18057 \begin_layout Standard
18058 For characters in formulas there are, analog to characters in text, the
18059 following size commands:
18062 \begin_layout Standard
18106 \begin_inset Newline newline
18128 \begin_layout Standard
18129 The size produced by the commands depends on the document font size, which
18130 corresponds to the command
18137 The other commands produce smaller or larger sizes than
18144 The font size can however not exceed a certain value.
18145 Is for example the document font size 12
18146 \begin_inset space \thinspace{}
18155 switches to the same size as
18165 \begin_layout Standard
18166 A size command is inserted in TeX-mode before the formula and sets the size
18167 for all following formula and text characters.
18168 To switch back to the initial size, the command
18174 is inserted behind the formula in TeX-mode.
18177 \begin_layout Standard
18178 Within a formula the size can be changed using the following size commands:
18181 \begin_layout Standard
18184 \begin_inset Tabular
18185 <lyxtabular version="3" rows="5" columns="2">
18186 <features rotate="0" tabularvalignment="middle">
18187 <column alignment="center" valignment="top">
18188 <column alignment="center" valignment="top">
18190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18193 \begin_layout Plain Layout
18199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18202 \begin_layout Plain Layout
18204 \begin_inset Note Note
18207 \begin_layout Plain Layout
18214 is only used as spacer.
18226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18229 \begin_layout Plain Layout
18233 \begin_inset Index idx
18236 \begin_layout Plain Layout
18249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18252 \begin_layout Plain Layout
18253 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
18263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18266 \begin_layout Plain Layout
18274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18277 \begin_layout Plain Layout
18278 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
18288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18291 \begin_layout Plain Layout
18299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18302 \begin_layout Plain Layout
18303 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18316 \begin_layout Plain Layout
18324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18327 \begin_layout Plain Layout
18328 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18344 \begin_layout Standard
18345 After entering these commands, a blue box appears in which the formula parts
18349 \begin_layout Standard
18350 There is a further method to change the font size, that though only works
18351 for symbols or letters in mathematical text.
18352 To use it, one of the above text size commands is inserted in mathematical
18354 All following characters until the end of the mathematical text or until
18355 another size command will have the selected size.
18357 \begin_inset VSpace -2mm
18363 \begin_layout Standard
18367 \begin_layout Plain Layout
18377 \begin_inset Formula
18379 A=\frac{B}{c}\cdot\maltese
18385 \begin_inset Formula
18387 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
18396 \begin_layout Plain Layout
18408 \begin_layout Standard
18409 \begin_inset VSpace medskip
18412 Before both formulas the command
18419 The command for the second formula is:
18420 \begin_inset Newline newline
18428 \begin_inset space \textvisiblespace{}
18434 \begin_inset space \textvisiblespace{}
18440 \begin_inset space \textvisiblespace{}
18446 \begin_inset space \textvisiblespace{}
18450 \begin_inset Formula $\to$
18454 \begin_inset Formula $\to$
18458 \begin_inset Newline newline
18462 \begin_inset space \hspace*{}
18473 \begin_inset space \textvisiblespace{}
18479 \begin_inset space \textvisiblespace{}
18485 \begin_inset space \textvisiblespace{}
18491 \begin_layout Standard
18492 If a symbol cannot be displayed in different sizes, it will always be displayed
18493 in the default size.
18496 \begin_layout Section
18498 \begin_inset Index idx
18501 \begin_layout Plain Layout
18510 \begin_layout Standard
18511 Greek letters can also be inserted via the toolbar button
18512 \begin_inset Graphics
18513 filename ../images/math/alpha.png
18519 All international typesetting norms purport that Greek letters in math
18520 have to be typeset italic/slanted.
18521 In some languages, like French or Russian, they are nevertheless sometimes
18525 \begin_layout Subsection
18527 \begin_inset Index idx
18530 \begin_layout Plain Layout
18531 Greek letters ! small
18539 \begin_layout Standard
18540 \begin_inset space \hfill{}
18544 \begin_inset Tabular
18545 <lyxtabular version="3" rows="11" columns="2">
18546 <features rotate="0" tabularvalignment="middle">
18547 <column alignment="center" valignment="top" width="0pt">
18548 <column alignment="center" valignment="top" width="0pt">
18550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18553 \begin_layout Plain Layout
18559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18562 \begin_layout Plain Layout
18570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18573 \begin_layout Plain Layout
18581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18584 \begin_layout Plain Layout
18585 \begin_inset Formula $\alpha$
18595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18598 \begin_layout Plain Layout
18606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18609 \begin_layout Plain Layout
18610 \begin_inset Formula $\beta$
18620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18623 \begin_layout Plain Layout
18631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18634 \begin_layout Plain Layout
18635 \begin_inset Formula $\gamma$
18645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18648 \begin_layout Plain Layout
18656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18659 \begin_layout Plain Layout
18660 \begin_inset Formula $\delta$
18670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18673 \begin_layout Plain Layout
18681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18684 \begin_layout Plain Layout
18685 \begin_inset Formula $\epsilon$
18695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18698 \begin_layout Plain Layout
18706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18709 \begin_layout Plain Layout
18710 \begin_inset Formula $\varepsilon$
18720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18723 \begin_layout Plain Layout
18731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18734 \begin_layout Plain Layout
18735 \begin_inset Formula $\zeta$
18745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18748 \begin_layout Plain Layout
18756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18759 \begin_layout Plain Layout
18760 \begin_inset Formula $\eta$
18770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18773 \begin_layout Plain Layout
18781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18784 \begin_layout Plain Layout
18785 \begin_inset Formula $\theta$
18795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18798 \begin_layout Plain Layout
18806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18809 \begin_layout Plain Layout
18810 \begin_inset Formula $\vartheta$
18824 \begin_inset space \hfill{}
18828 \begin_inset Tabular
18829 <lyxtabular version="3" rows="12" columns="2">
18830 <features rotate="0" tabularvalignment="middle">
18831 <column alignment="center" valignment="top" width="0pt">
18832 <column alignment="center" valignment="top" width="0pt">
18834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18837 \begin_layout Plain Layout
18843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18846 \begin_layout Plain Layout
18854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18857 \begin_layout Plain Layout
18865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18868 \begin_layout Plain Layout
18869 \begin_inset Formula $\iota$
18879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18882 \begin_layout Plain Layout
18890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18893 \begin_layout Plain Layout
18894 \begin_inset Formula $\kappa$
18904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18907 \begin_layout Plain Layout
18915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18918 \begin_layout Plain Layout
18919 \begin_inset Formula $\varkappa$
18929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18932 \begin_layout Plain Layout
18940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18943 \begin_layout Plain Layout
18944 \begin_inset Formula $\lambda$
18954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18957 \begin_layout Plain Layout
18965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18968 \begin_layout Plain Layout
18969 \begin_inset Formula $\mu$
18979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18982 \begin_layout Plain Layout
18990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18993 \begin_layout Plain Layout
18994 \begin_inset Formula $\nu$
19004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19007 \begin_layout Plain Layout
19015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19018 \begin_layout Plain Layout
19019 \begin_inset Formula $\xi$
19029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19032 \begin_layout Plain Layout
19038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19041 \begin_layout Plain Layout
19042 \begin_inset Formula $o$
19052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19055 \begin_layout Plain Layout
19063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19066 \begin_layout Plain Layout
19067 \begin_inset Formula $\pi$
19077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19080 \begin_layout Plain Layout
19088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19091 \begin_layout Plain Layout
19092 \begin_inset Formula $\varpi$
19102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19105 \begin_layout Plain Layout
19113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19116 \begin_layout Plain Layout
19117 \begin_inset Formula $\rho$
19131 \begin_inset space \hfill{}
19135 \begin_inset Tabular
19136 <lyxtabular version="3" rows="11" columns="2">
19137 <features rotate="0" tabularvalignment="middle">
19138 <column alignment="center" valignment="top" width="0pt">
19139 <column alignment="center" valignment="top" width="0pt">
19141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19144 \begin_layout Plain Layout
19150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19153 \begin_layout Plain Layout
19161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19164 \begin_layout Plain Layout
19172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19175 \begin_layout Plain Layout
19176 \begin_inset Formula $\varrho$
19186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19189 \begin_layout Plain Layout
19197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19200 \begin_layout Plain Layout
19201 \begin_inset Formula $\sigma$
19211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19214 \begin_layout Plain Layout
19222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19225 \begin_layout Plain Layout
19226 \begin_inset Formula $\varsigma$
19236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19239 \begin_layout Plain Layout
19247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19250 \begin_layout Plain Layout
19251 \begin_inset Formula $\tau$
19261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19264 \begin_layout Plain Layout
19272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19275 \begin_layout Plain Layout
19276 \begin_inset Formula $\upsilon$
19286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19289 \begin_layout Plain Layout
19297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19300 \begin_layout Plain Layout
19301 \begin_inset Formula $\phi$
19311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19314 \begin_layout Plain Layout
19322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19325 \begin_layout Plain Layout
19326 \begin_inset Formula $\varphi$
19336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19339 \begin_layout Plain Layout
19347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19350 \begin_layout Plain Layout
19351 \begin_inset Formula $\chi$
19361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19364 \begin_layout Plain Layout
19372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19375 \begin_layout Plain Layout
19376 \begin_inset Formula $\psi$
19386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19389 \begin_layout Plain Layout
19397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19400 \begin_layout Plain Layout
19401 \begin_inset Formula $\omega$
19415 \begin_inset space \hfill{}
19421 \begin_layout Standard
19422 \begin_inset VSpace medskip
19428 \begin_layout Standard
19429 How to create special upright Greek letters is explained in
19430 \begin_inset CommandInset ref
19432 reference "sub:Upright-small-Greek"
19439 \begin_layout Subsection
19441 \begin_inset Index idx
19444 \begin_layout Plain Layout
19445 Greek letters ! big
19453 \begin_layout Standard
19454 \begin_inset space \hfill{}
19458 \begin_inset Tabular
19459 <lyxtabular version="3" rows="7" columns="2">
19460 <features rotate="0" tabularvalignment="middle">
19461 <column alignment="center" valignment="top" width="0pt">
19462 <column alignment="center" valignment="top" width="0pt">
19464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19467 \begin_layout Plain Layout
19473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19476 \begin_layout Plain Layout
19484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19487 \begin_layout Plain Layout
19495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19498 \begin_layout Plain Layout
19499 \begin_inset Formula $\Gamma$
19509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19512 \begin_layout Plain Layout
19520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19523 \begin_layout Plain Layout
19524 \begin_inset Formula $\Delta$
19534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19537 \begin_layout Plain Layout
19545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19548 \begin_layout Plain Layout
19549 \begin_inset Formula $\Theta$
19559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19562 \begin_layout Plain Layout
19570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19573 \begin_layout Plain Layout
19574 \begin_inset Formula $\Lambda$
19584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19587 \begin_layout Plain Layout
19595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19598 \begin_layout Plain Layout
19599 \begin_inset Formula $\Xi$
19609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19612 \begin_layout Plain Layout
19620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19623 \begin_layout Plain Layout
19624 \begin_inset Formula $\Pi$
19638 \begin_inset space \hfill{}
19642 \begin_inset Tabular
19643 <lyxtabular version="3" rows="6" columns="2">
19644 <features rotate="0" tabularvalignment="middle">
19645 <column alignment="center" valignment="top" width="0pt">
19646 <column alignment="center" valignment="top" width="0pt">
19648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19651 \begin_layout Plain Layout
19657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19660 \begin_layout Plain Layout
19668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19671 \begin_layout Plain Layout
19679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19682 \begin_layout Plain Layout
19683 \begin_inset Formula $\Sigma$
19693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19696 \begin_layout Plain Layout
19704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19707 \begin_layout Plain Layout
19708 \begin_inset Formula $\Upsilon$
19718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19721 \begin_layout Plain Layout
19729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19732 \begin_layout Plain Layout
19733 \begin_inset Formula $\Phi$
19743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19746 \begin_layout Plain Layout
19754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19757 \begin_layout Plain Layout
19758 \begin_inset Formula $\Psi$
19768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19771 \begin_layout Plain Layout
19779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19782 \begin_layout Plain Layout
19783 \begin_inset Formula $\Omega$
19797 \begin_inset space \hfill{}
19803 \begin_layout Standard
19804 \begin_inset VSpace medskip
19807 That the big Greek letters appear upright is caused by a design bug when
19809 To get correct italic big letters, begin every command with
19814 For example the command
19821 \begin_inset Formula $\varGamma$
19825 Another way is to load the package
19833 \begin_layout Plain Layout
19838 is part of the LaTeX-package
19843 \begin_inset Index idx
19846 \begin_layout Plain Layout
19851 \begin_layout Plain Layout
19871 \begin_inset Index idx
19874 \begin_layout Plain Layout
19880 with the LaTeX-preamble line
19883 \begin_layout Standard
19888 usepackage{fixmath}
19891 \begin_layout Standard
19892 Then all big Greek letters in a document will automatically be typeset italic.
19895 \begin_layout Subsection
19897 \begin_inset Index idx
19900 \begin_layout Plain Layout
19901 Greek letters ! bold
19909 \begin_layout Standard
19910 Greek letters cannot be set with different font styles like Latin letters.
19911 They can only be made bold with the command
19918 \begin_inset Index idx
19921 \begin_layout Plain Layout
19932 \begin_layout Standard
19934 \begin_inset Tabular
19935 <lyxtabular version="3" rows="3" columns="2">
19936 <features rotate="0" tabularvalignment="middle">
19937 <column alignment="center" valignment="top">
19938 <column alignment="center" valignment="top">
19940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19943 \begin_layout Plain Layout
19949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19952 \begin_layout Plain Layout
19960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19963 \begin_layout Plain Layout
19975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19978 \begin_layout Plain Layout
19979 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
19989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19992 \begin_layout Plain Layout
20004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20007 \begin_layout Plain Layout
20008 \begin_inset Formula $\theta\boldsymbol{\theta}$
20024 \begin_layout Section
20029 \begin_layout Plain Layout
20042 \begin_layout Plain Layout
20043 A list with all symbols of most of the LaTeX-packages can be found in
20044 \begin_inset CommandInset citation
20059 \begin_layout Plain Layout
20067 \begin_inset Note Note
20070 \begin_layout Plain Layout
20073 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20076 \begin_layout Plain Layout
20079 texorpdfstring is in section
20080 \begin_inset CommandInset ref
20082 reference "sub:Formulas-in-Section"
20092 \begin_inset Index idx
20095 \begin_layout Plain Layout
20104 \begin_layout Standard
20105 Many of the symbols listed in this section can also be inserted via the
20107 \begin_inset Graphics
20108 filename ../images/math/nabla.png
20114 \begin_inset Graphics
20115 filename ../images/math/digamma.png
20123 \begin_layout Subsection
20124 Mathematical Symbols
20125 \begin_inset CommandInset label
20127 name "sub:Mathematical-Symbols"
20132 \begin_inset Index idx
20135 \begin_layout Plain Layout
20136 Symbols ! mathematical
20144 \begin_layout Standard
20145 \begin_inset space \hfill{}
20149 \begin_inset Tabular
20150 <lyxtabular version="3" rows="10" columns="2">
20151 <features rotate="0" tabularvalignment="middle">
20152 <column alignment="center" valignment="top" width="0pt">
20153 <column alignment="center" valignment="top" width="0pt">
20155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20158 \begin_layout Plain Layout
20164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20167 \begin_layout Plain Layout
20175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20178 \begin_layout Plain Layout
20186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20189 \begin_layout Plain Layout
20190 \begin_inset Formula $\neg$
20200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20203 \begin_layout Plain Layout
20211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20214 \begin_layout Plain Layout
20215 \begin_inset Formula $\Im$
20225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20228 \begin_layout Plain Layout
20236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20239 \begin_layout Plain Layout
20240 \begin_inset Formula $\Re$
20250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20253 \begin_layout Plain Layout
20261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20264 \begin_layout Plain Layout
20265 \begin_inset Formula $\aleph$
20275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20278 \begin_layout Plain Layout
20286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20289 \begin_layout Plain Layout
20290 \begin_inset Formula $\partial$
20300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20303 \begin_layout Plain Layout
20311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20314 \begin_layout Plain Layout
20315 \begin_inset Formula $\infty$
20325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20328 \begin_layout Plain Layout
20336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20339 \begin_layout Plain Layout
20340 \begin_inset Formula $\wp$
20350 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20353 \begin_layout Plain Layout
20361 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20364 \begin_layout Plain Layout
20365 \begin_inset Formula $\imath$
20375 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20378 \begin_layout Plain Layout
20386 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20389 \begin_layout Plain Layout
20390 \begin_inset Formula $\jmath$
20404 \begin_inset space \hfill{}
20408 \begin_inset Tabular
20409 <lyxtabular version="3" rows="10" columns="2">
20410 <features rotate="0" tabularvalignment="middle">
20411 <column alignment="center" valignment="top" width="0pt">
20412 <column alignment="center" valignment="top" width="0pt">
20414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20417 \begin_layout Plain Layout
20423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20426 \begin_layout Plain Layout
20428 \begin_inset Note Note
20431 \begin_layout Plain Layout
20438 is only used as spacer.
20450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20453 \begin_layout Plain Layout
20461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20464 \begin_layout Plain Layout
20465 \begin_inset Formula $\forall$
20475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20478 \begin_layout Plain Layout
20486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20489 \begin_layout Plain Layout
20490 \begin_inset Formula $\exists$
20500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20503 \begin_layout Plain Layout
20511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20514 \begin_layout Plain Layout
20515 \begin_inset Formula $\nexists$
20525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20528 \begin_layout Plain Layout
20536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20539 \begin_layout Plain Layout
20540 \begin_inset Formula $\emptyset$
20550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20553 \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 $\varnothing$
20575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20578 \begin_layout Plain Layout
20586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20589 \begin_layout Plain Layout
20590 \begin_inset Formula $\dag$
20600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20603 \begin_layout Plain Layout
20611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20614 \begin_layout Plain Layout
20615 \begin_inset Formula $\ddag$
20625 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20628 \begin_layout Plain Layout
20636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20639 \begin_layout Plain Layout
20643 \begin_layout Plain Layout
20653 \begin_inset Formula $\complement$
20660 \begin_layout Plain Layout
20674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20677 \begin_layout Plain Layout
20685 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20688 \begin_layout Plain Layout
20689 \begin_inset Formula $\Bbbk$
20703 \begin_inset space \hfill{}
20707 \begin_inset Tabular
20708 <lyxtabular version="3" rows="10" columns="2">
20709 <features rotate="0" tabularvalignment="middle">
20710 <column alignment="center" valignment="top" width="0pt">
20711 <column alignment="center" valignment="top" width="0pt">
20713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20716 \begin_layout Plain Layout
20722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20725 \begin_layout Plain Layout
20733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20736 \begin_layout Plain Layout
20744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20747 \begin_layout Plain Layout
20748 \begin_inset Formula $\prime$
20758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20761 \begin_layout Plain Layout
20769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20772 \begin_layout Plain Layout
20773 \begin_inset Formula $\backprime$
20783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20786 \begin_layout Plain Layout
20794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20797 \begin_layout Plain Layout
20798 \begin_inset Formula $\mho$
20808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20811 \begin_layout Plain Layout
20819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20822 \begin_layout Plain Layout
20823 \begin_inset Formula $\triangle$
20833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20836 \begin_layout Plain Layout
20844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20847 \begin_layout Plain Layout
20848 \begin_inset Formula $\angle$
20858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20861 \begin_layout Plain Layout
20869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20872 \begin_layout Plain Layout
20873 \begin_inset Formula $\measuredangle$
20883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20886 \begin_layout Plain Layout
20894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20897 \begin_layout Plain Layout
20898 \begin_inset Formula $\sphericalangle$
20908 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20911 \begin_layout Plain Layout
20919 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20922 \begin_layout Plain Layout
20923 \begin_inset Formula $\top$
20933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20936 \begin_layout Plain Layout
20944 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20947 \begin_layout Plain Layout
20948 \begin_inset Formula $\bot$
20962 \begin_inset space \hfill{}
20968 \begin_layout Subsection
20969 Miscellaneous Symbols
20970 \begin_inset CommandInset label
20972 name "sub:Miscellaneous-Symbols"
20977 \begin_inset Index idx
20980 \begin_layout Plain Layout
20981 Symbols ! miscellaneous
20989 \begin_layout Standard
20992 \begin_inset Tabular
20993 <lyxtabular version="3" rows="10" columns="2">
20994 <features rotate="0" tabularvalignment="middle">
20995 <column alignment="center" valignment="top" width="0pt">
20996 <column alignment="center" valignment="top" width="0pt">
20998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21001 \begin_layout Plain Layout
21007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21010 \begin_layout Plain Layout
21018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21021 \begin_layout Plain Layout
21029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21032 \begin_layout Plain Layout
21033 \begin_inset Formula $\flat$
21043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21046 \begin_layout Plain Layout
21054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21057 \begin_layout Plain Layout
21058 \begin_inset Formula $\natural$
21068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21071 \begin_layout Plain Layout
21079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21082 \begin_layout Plain Layout
21083 \begin_inset Formula $\sharp$
21093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21096 \begin_layout Plain Layout
21104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21107 \begin_layout Plain Layout
21108 \begin_inset Formula $\surd$
21118 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21121 \begin_layout Plain Layout
21129 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21132 \begin_layout Plain Layout
21133 \begin_inset Formula $\checkmark$
21143 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21146 \begin_layout Plain Layout
21154 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21157 \begin_layout Plain Layout
21158 \begin_inset Formula $\yen$
21168 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21171 \begin_layout Plain Layout
21179 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21182 \begin_layout Plain Layout
21183 \begin_inset Formula $\pounds$
21193 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21196 \begin_layout Plain Layout
21202 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21205 \begin_layout Plain Layout
21206 \begin_inset Formula $\$$
21216 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21219 \begin_layout Plain Layout
21225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21228 \begin_layout Plain Layout
21229 \begin_inset Formula $§$
21243 \begin_inset Tabular
21244 <lyxtabular version="3" rows="10" columns="2">
21245 <features rotate="0" tabularvalignment="middle">
21246 <column alignment="center" valignment="top">
21247 <column alignment="center" valignment="top">
21249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21252 \begin_layout Plain Layout
21258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21261 \begin_layout Plain Layout
21269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21272 \begin_layout Plain Layout
21280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21283 \begin_layout Plain Layout
21284 \begin_inset Formula $\hbar$
21294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21297 \begin_layout Plain Layout
21305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21308 \begin_layout Plain Layout
21309 \begin_inset Formula $\hslash$
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 $\clubsuit$
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 $\spadesuit$
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 $\bigstar$
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 $\blacklozenge$
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 $\blacktriangle$
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 $\blacktriangledown$
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 $\bullet$
21498 \begin_inset Tabular
21499 <lyxtabular version="3" rows="10" columns="2">
21500 <features rotate="0" tabularvalignment="middle">
21501 <column alignment="center" valignment="top" width="0pt">
21502 <column alignment="center" valignment="top" width="0pt">
21504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21507 \begin_layout Plain Layout
21513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21516 \begin_layout Plain Layout
21524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21527 \begin_layout Plain Layout
21535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21538 \begin_layout Plain Layout
21539 \begin_inset Formula $\diamondsuit$
21549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21552 \begin_layout Plain Layout
21560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21563 \begin_layout Plain Layout
21564 \begin_inset Formula $\Diamond$
21574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21577 \begin_layout Plain Layout
21585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21588 \begin_layout Plain Layout
21589 \begin_inset Formula $\heartsuit$
21599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21602 \begin_layout Plain Layout
21610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21613 \begin_layout Plain Layout
21614 \begin_inset Formula $\P$
21624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21627 \begin_layout Plain Layout
21635 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21638 \begin_layout Plain Layout
21639 \begin_inset Formula $\copyright$
21649 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21652 \begin_layout Plain Layout
21660 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21663 \begin_layout Plain Layout
21664 \begin_inset Formula $\circledR$
21674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21677 \begin_layout Plain Layout
21685 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21688 \begin_layout Plain Layout
21689 \begin_inset Formula $\maltese$
21699 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21702 \begin_layout Plain Layout
21710 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21713 \begin_layout Plain Layout
21714 \begin_inset Formula $\diagup$
21724 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21727 \begin_layout Plain Layout
21735 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21738 \begin_layout Plain Layout
21739 \begin_inset Formula $\diagdown$
21755 \begin_layout Standard
21756 \begin_inset VSpace medskip
21762 \begin_layout Standard
21763 Some symbols can be displayed in different sizes, see
21764 \begin_inset CommandInset ref
21766 reference "sub:Font-Sizes"
21773 \begin_layout Subsection
21775 \begin_inset Index idx
21778 \begin_layout Plain Layout
21779 Symbols ! Euro-symbol
21785 \begin_inset Index idx
21788 \begin_layout Plain Layout
21795 \begin_layout Plain Layout
21812 \begin_layout Standard
21813 To use the Euro symbol in formulas, the LaTeX-package
21818 \begin_inset Index idx
21821 \begin_layout Plain Layout
21827 must be installed and loaded with the LaTeX-preamble line
21830 \begin_layout Standard
21835 usepackage[gennarrow]{eurosym}
21838 \begin_layout Standard
21839 The Euro symbol can now be inserted with the command
21846 \begin_inset Index idx
21849 \begin_layout Plain Layout
21860 \begin_layout Standard
21861 The Euro symbol can directly be inserted with the € key in mathematical
21862 text, without having
21877 can also be inserted in TeX-mode.
21878 The official currency symbol can then be inserted with the command
21885 \begin_inset Index idx
21888 \begin_layout Plain Layout
21896 , that is only available in TeX-mode.
21899 \begin_layout Standard
21903 \begin_layout Plain Layout
21913 \begin_inset Note Note
21916 \begin_layout Plain Layout
21917 The following table will only be displayed when the LaTeX-package
21929 \begin_layout Standard
21930 An overview about the different Euro symbols:
21933 \begin_layout Standard
21935 \begin_inset Tabular
21936 <lyxtabular version="3" rows="4" columns="3">
21937 <features rotate="0" tabularvalignment="middle">
21938 <column alignment="center" valignment="top" width="0pt">
21939 <column alignment="center" valignment="top" width="0pt">
21940 <column alignment="center" valignment="top" width="0pt">
21942 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
21945 \begin_layout Plain Layout
21951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21954 \begin_layout Plain Layout
21960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21963 \begin_layout Plain Layout
21971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21974 \begin_layout Plain Layout
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 $\euro$
22005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22008 \begin_layout Plain Layout
22014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22017 \begin_layout Plain Layout
22023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22026 \begin_layout Plain Layout
22027 \begin_inset Formula $\mbox{€}$
22037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22040 \begin_layout Plain Layout
22046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22049 \begin_layout Plain Layout
22057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22060 \begin_layout Plain Layout
22064 \begin_layout Plain Layout
22086 \begin_layout Standard
22090 \begin_layout Plain Layout
22100 \begin_inset Note Note
22103 \begin_layout Plain Layout
22104 The following will be displayed when the LaTeX-package
22116 \begin_layout Standard
22117 You need to install the LaTeX-package
22121 to see the rest of this subsection in the output.
22124 \begin_layout Standard
22128 \begin_layout Plain Layout
22140 \begin_layout Section
22142 \begin_inset CommandInset label
22144 name "sec:Relations"
22149 \begin_inset Index idx
22152 \begin_layout Plain Layout
22159 \begin_inset Index idx
22162 \begin_layout Plain Layout
22167 \begin_layout Plain Layout
22178 \begin_layout Plain Layout
22193 \begin_layout Standard
22194 All relations can also be inserted via the toolbar button
22195 \begin_inset Graphics
22196 filename ../images/math/leq.png
22204 \begin_layout Standard
22205 \begin_inset space \hfill{}
22209 \begin_inset Tabular
22210 <lyxtabular version="3" rows="17" columns="2">
22211 <features rotate="0" tabularvalignment="middle">
22212 <column alignment="center" valignment="top" width="0pt">
22213 <column alignment="center" valignment="top" width="0pt">
22215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22218 \begin_layout Plain Layout
22224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22227 \begin_layout Plain Layout
22235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22238 \begin_layout Plain Layout
22244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22247 \begin_layout Plain Layout
22248 \begin_inset Formula $<$
22258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22261 \begin_layout Plain Layout
22269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22272 \begin_layout Plain Layout
22273 \begin_inset Formula $\le$
22283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22286 \begin_layout Plain Layout
22294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22297 \begin_layout Plain Layout
22298 \begin_inset Formula $\ll$
22308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22311 \begin_layout Plain Layout
22319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22322 \begin_layout Plain Layout
22323 \begin_inset Formula $\prec$
22333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22336 \begin_layout Plain Layout
22344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22347 \begin_layout Plain Layout
22348 \begin_inset Formula $\preceq$
22358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22361 \begin_layout Plain Layout
22369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22372 \begin_layout Plain Layout
22373 \begin_inset Formula $\subset$
22383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22386 \begin_layout Plain Layout
22394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22397 \begin_layout Plain Layout
22398 \begin_inset Formula $\subseteq$
22408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22411 \begin_layout Plain Layout
22419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22422 \begin_layout Plain Layout
22423 \begin_inset Formula $\sqsubseteq$
22433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22436 \begin_layout Plain Layout
22444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22447 \begin_layout Plain Layout
22448 \begin_inset Formula $\in$
22458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22461 \begin_layout Plain Layout
22469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22472 \begin_layout Plain Layout
22473 \begin_inset Formula $\vdash$
22483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22486 \begin_layout Plain Layout
22494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22497 \begin_layout Plain Layout
22498 \begin_inset Formula $\smile$
22508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22511 \begin_layout Plain Layout
22519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22522 \begin_layout Plain Layout
22523 \begin_inset Formula $\lhd$
22533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22536 \begin_layout Plain Layout
22544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22547 \begin_layout Plain Layout
22548 \begin_inset Formula $\unlhd$
22558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22561 \begin_layout Plain Layout
22569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22572 \begin_layout Plain Layout
22573 \begin_inset Formula $\gtrless$
22583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22586 \begin_layout Plain Layout
22594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22597 \begin_layout Plain Layout
22598 \begin_inset Formula $\mid$
22608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22611 \begin_layout Plain Layout
22619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22622 \begin_layout Plain Layout
22623 \begin_inset Formula $\nmid$
22637 \begin_inset space \hfill{}
22641 \begin_inset Tabular
22642 <lyxtabular version="3" rows="17" columns="2">
22643 <features rotate="0" tabularvalignment="middle">
22644 <column alignment="center" valignment="top" width="0pt">
22645 <column alignment="center" valignment="top" width="0pt">
22647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22650 \begin_layout Plain Layout
22656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22659 \begin_layout Plain Layout
22667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22670 \begin_layout Plain Layout
22676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22679 \begin_layout Plain Layout
22680 \begin_inset Formula $=$
22690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22693 \begin_layout Plain Layout
22701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22704 \begin_layout Plain Layout
22705 \begin_inset Formula $\not=$
22715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22718 \begin_layout Plain Layout
22726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22729 \begin_layout Plain Layout
22730 \begin_inset Formula $\equiv$
22740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22743 \begin_layout Plain Layout
22751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22754 \begin_layout Plain Layout
22755 \begin_inset Formula $\sim$
22765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22768 \begin_layout Plain Layout
22776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22779 \begin_layout Plain Layout
22780 \begin_inset Formula $\simeq$
22790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22793 \begin_layout Plain Layout
22801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22804 \begin_layout Plain Layout
22805 \begin_inset Formula $\approx$
22815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22818 \begin_layout Plain Layout
22826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22829 \begin_layout Plain Layout
22830 \begin_inset Formula $\cong$
22840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22843 \begin_layout Plain Layout
22851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22854 \begin_layout Plain Layout
22855 \begin_inset Formula $\bowtie$
22865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22868 \begin_layout Plain Layout
22876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22879 \begin_layout Plain Layout
22880 \begin_inset Formula $\notin$
22890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22893 \begin_layout Plain Layout
22901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22904 \begin_layout Plain Layout
22905 \begin_inset Formula $\perp$
22915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22918 \begin_layout Plain Layout
22926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22929 \begin_layout Plain Layout
22930 \begin_inset Formula $\propto$
22940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22943 \begin_layout Plain Layout
22951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22954 \begin_layout Plain Layout
22955 \begin_inset Formula $\asymp$
22965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22968 \begin_layout Plain Layout
22976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22979 \begin_layout Plain Layout
22980 \begin_inset Formula $\doteq$
22990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22993 \begin_layout Plain Layout
23001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23004 \begin_layout Plain Layout
23005 \begin_inset Formula $\circeq$
23015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23018 \begin_layout Plain Layout
23026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23029 \begin_layout Plain Layout
23030 \begin_inset Formula $\models$
23040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23043 \begin_layout Plain Layout
23051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23054 \begin_layout Plain Layout
23055 \begin_inset Formula $\widehat{=}$
23069 \begin_inset space \hfill{}
23073 \begin_inset Tabular
23074 <lyxtabular version="3" rows="17" columns="2">
23075 <features rotate="0" tabularvalignment="middle">
23076 <column alignment="center" valignment="top" width="0pt">
23077 <column alignment="center" valignment="top" width="0pt">
23079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23082 \begin_layout Plain Layout
23088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23091 \begin_layout Plain Layout
23099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23102 \begin_layout Plain Layout
23108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23111 \begin_layout Plain Layout
23112 \begin_inset Formula $>$
23122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23125 \begin_layout Plain Layout
23133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23136 \begin_layout Plain Layout
23137 \begin_inset Formula $\ge$
23147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23150 \begin_layout Plain Layout
23158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23161 \begin_layout Plain Layout
23162 \begin_inset Formula $\gg$
23172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23175 \begin_layout Plain Layout
23183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23186 \begin_layout Plain Layout
23187 \begin_inset Formula $\succ$
23197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23200 \begin_layout Plain Layout
23208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23211 \begin_layout Plain Layout
23212 \begin_inset Formula $\succeq$
23222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23225 \begin_layout Plain Layout
23233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23236 \begin_layout Plain Layout
23237 \begin_inset Formula $\supset$
23247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23250 \begin_layout Plain Layout
23258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23261 \begin_layout Plain Layout
23262 \begin_inset Formula $\supseteq$
23272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23275 \begin_layout Plain Layout
23283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23286 \begin_layout Plain Layout
23287 \begin_inset Formula $\sqsupseteq$
23297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23300 \begin_layout Plain Layout
23308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23311 \begin_layout Plain Layout
23312 \begin_inset Formula $\ni$
23322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23325 \begin_layout Plain Layout
23333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23336 \begin_layout Plain Layout
23337 \begin_inset Formula $\dashv$
23347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23350 \begin_layout Plain Layout
23358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23361 \begin_layout Plain Layout
23362 \begin_inset Formula $\frown$
23372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23375 \begin_layout Plain Layout
23383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23386 \begin_layout Plain Layout
23387 \begin_inset Formula $\rhd$
23397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23400 \begin_layout Plain Layout
23408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23411 \begin_layout Plain Layout
23412 \begin_inset Formula $\unrhd$
23422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23425 \begin_layout Plain Layout
23433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23436 \begin_layout Plain Layout
23437 \begin_inset Formula $\lessgtr$
23447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23450 \begin_layout Plain Layout
23458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23461 \begin_layout Plain Layout
23462 \begin_inset Formula $\parallel$
23472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23475 \begin_layout Plain Layout
23483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23486 \begin_layout Plain Layout
23487 \begin_inset Formula $\nparallel$
23501 \begin_inset space \hfill{}
23507 \begin_layout Standard
23508 \begin_inset VSpace medskip
23523 are bigger than the equal looking operators
23538 \begin_layout Standard
23539 Relations are, in contrary to symbols, always surrounded by space.
23542 \begin_layout Standard
23543 Relations with labels can be created with the command
23550 \begin_inset Index idx
23553 \begin_layout Plain Layout
23564 \begin_layout Standard
23566 \begin_inset Tabular
23567 <lyxtabular version="3" rows="2" columns="2">
23568 <features rotate="0" tabularvalignment="middle">
23569 <column alignment="center" valignment="top">
23570 <column alignment="center" valignment="top">
23572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23575 \begin_layout Plain Layout
23581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23584 \begin_layout Plain Layout
23586 \begin_inset Note Note
23589 \begin_layout Plain Layout
23596 is only used as spacer.
23608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23611 \begin_layout Plain Layout
23615 \begin_inset space \textvisiblespace{}
23623 \begin_inset space \textvisiblespace{}
23627 \begin_inset Formula $\downarrow$
23633 \begin_inset space \textvisiblespace{}
23637 \begin_inset space \textvisiblespace{}
23645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23648 \begin_layout Plain Layout
23649 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23665 \begin_layout Section
23669 \begin_layout Subsection
23670 Predefined Functions
23671 \begin_inset CommandInset label
23673 name "sub:Predefined-Functions"
23678 \begin_inset Index idx
23681 \begin_layout Plain Layout
23682 Functions ! predefined
23690 \begin_layout Standard
23691 In general, variables are set
23695 in mathematical expressions, but not function names, because
23696 \begin_inset Formula $sin$
23699 could be misunderstood as
23700 \begin_inset Formula $s\cdot i\cdot n$
23704 Therefore there are predefined functionswhich are additionally a bit separated
23706 They are inserted as commands starting with a backslash before their name.
23709 \begin_layout Standard
23711 \begin_inset Tabular
23712 <lyxtabular version="3" rows="2" columns="4">
23713 <features rotate="0" tabularvalignment="middle">
23714 <column alignment="center" valignment="top" width="0pt">
23715 <column alignment="center" valignment="top" width="0pt">
23716 <column alignment="center" valignment="top" width="0pt">
23717 <column alignment="center" valignment="top" width="0pt">
23719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23722 \begin_layout Plain Layout
23728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23731 \begin_layout Plain Layout
23737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23740 \begin_layout Plain Layout
23746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23749 \begin_layout Plain Layout
23757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23760 \begin_layout Plain Layout
23766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23769 \begin_layout Plain Layout
23770 \begin_inset Formula $Asin(x)+B$
23778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23781 \begin_layout Plain Layout
23789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23792 \begin_layout Plain Layout
23793 \begin_inset Formula $A\sin(x)+B$
23809 \begin_layout Standard
23810 The following functions are predefined:
23813 \begin_layout Standard
23814 \begin_inset VSpace -2mm
23820 \begin_layout Standard
23822 \begin_inset Tabular
23823 <lyxtabular version="3" rows="9" columns="4">
23824 <features rotate="0" tabularvalignment="middle">
23825 <column alignment="center" valignment="top" width="0pt">
23826 <column alignment="center" valignment="top" width="0pt">
23827 <column alignment="center" valignment="top" width="0pt">
23828 <column alignment="center" valignment="top" width="0pt">
23830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23833 \begin_layout Plain Layout
23839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23842 \begin_layout Plain Layout
23848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23851 \begin_layout Plain Layout
23857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23860 \begin_layout Plain Layout
23868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23871 \begin_layout Plain Layout
23879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23882 \begin_layout Plain Layout
23890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23893 \begin_layout Plain Layout
23901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23904 \begin_layout Plain Layout
23914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23917 \begin_layout Plain Layout
23925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23928 \begin_layout Plain Layout
23936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23939 \begin_layout Plain Layout
23947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23950 \begin_layout Plain Layout
23960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23963 \begin_layout Plain Layout
23971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23974 \begin_layout Plain Layout
23982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23985 \begin_layout Plain Layout
23993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23996 \begin_layout Plain Layout
24006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24009 \begin_layout Plain Layout
24017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24020 \begin_layout Plain Layout
24028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24031 \begin_layout Plain Layout
24039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24042 \begin_layout Plain Layout
24052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24055 \begin_layout Plain Layout
24063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24066 \begin_layout Plain Layout
24074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24077 \begin_layout Plain Layout
24085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24088 \begin_layout Plain Layout
24098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24101 \begin_layout Plain Layout
24109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24112 \begin_layout Plain Layout
24120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24123 \begin_layout Plain Layout
24131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24134 \begin_layout Plain Layout
24144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24147 \begin_layout Plain Layout
24155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24158 \begin_layout Plain Layout
24166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24169 \begin_layout Plain Layout
24177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24180 \begin_layout Plain Layout
24190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24193 \begin_layout Plain Layout
24201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24204 \begin_layout Plain Layout
24212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24215 \begin_layout Plain Layout
24223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24226 \begin_layout Plain Layout
24242 \begin_layout Standard
24243 They can also be inserted with the math toolbar button
24244 \begin_inset Graphics
24245 filename ../images/math/functions.png
24253 \begin_layout Subsection
24254 Self-defined Functions
24255 \begin_inset Index idx
24258 \begin_layout Plain Layout
24259 Functions ! self-defined
24267 \begin_layout Standard
24268 To use a function that is not predefined, like for example the sign function
24269 sgn(x), there are two possibilities:
24272 \begin_layout Itemize
24273 Define the function by inserting the following line to the LaTeX-preamble
24277 \begin_layout Plain Layout
24282 DeclareMathOperator
24285 \begin_inset CommandInset ref
24287 reference "sub:Self-defined-Operators"
24297 \begin_inset Newline newline
24301 \begin_inset VSpace -3mm
24305 \begin_inset Newline newline
24312 DeclareMathOperator{
24317 \begin_inset Index idx
24320 \begin_layout Plain Layout
24325 DeclareMathOperator
24331 \begin_inset Newline newline
24335 \begin_inset VSpace -2mm
24339 \begin_inset Newline newline
24342 Now the new defined function can be called with the command
24351 \begin_layout Itemize
24352 Write the formula as usual, mark the formula name, in our example the letters
24357 , and change it to mathematical text.
24358 Finally, a space is inserted between prefactor and function.
24361 \begin_layout Standard
24362 The result is the same with both methods as with a predefined function
24366 \begin_layout Plain Layout
24367 In LyX self-defined functions are displayed red, predefined ones black.
24375 \begin_layout Standard
24377 \begin_inset Tabular
24378 <lyxtabular version="3" rows="3" columns="2">
24379 <features rotate="0" tabularvalignment="middle">
24380 <column alignment="center" valignment="top" width="0pt">
24381 <column alignment="center" valignment="top" width="0pt">
24383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24386 \begin_layout Plain Layout
24392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24395 \begin_layout Plain Layout
24403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24406 \begin_layout Plain Layout
24414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24417 \begin_layout Plain Layout
24418 \begin_inset Formula $A\sgn(x)+B$
24428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24431 \begin_layout Plain Layout
24435 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
24443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24446 \begin_layout Plain Layout
24447 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24463 \begin_layout Standard
24464 The first method is more suitable when the self-defined function should
24465 be used several times.
24468 \begin_layout Subsection
24470 \begin_inset Index idx
24473 \begin_layout Plain Layout
24482 \begin_layout Standard
24483 For limits, in addition to the commands
24490 \begin_inset Index idx
24493 \begin_layout Plain Layout
24513 the following functions are defined:
24516 \begin_layout Standard
24518 \begin_inset Tabular
24519 <lyxtabular version="3" rows="5" columns="2">
24520 <features rotate="0" tabularvalignment="middle">
24521 <column alignment="center" valignment="top">
24522 <column alignment="center" valignment="top">
24524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24527 \begin_layout Plain Layout
24533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24536 \begin_layout Plain Layout
24538 \begin_inset Note Note
24541 \begin_layout Plain Layout
24548 is only used as spacer.
24560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24563 \begin_layout Plain Layout
24571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24574 \begin_layout Plain Layout
24575 \begin_inset Formula $\varliminf$
24585 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24588 \begin_layout Plain Layout
24596 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24599 \begin_layout Plain Layout
24600 \begin_inset Formula $\varlimsup$
24610 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24613 \begin_layout Plain Layout
24621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24624 \begin_layout Plain Layout
24625 \begin_inset Formula $\varprojlim$
24635 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24638 \begin_layout Plain Layout
24646 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24649 \begin_layout Plain Layout
24650 \begin_inset Formula $\varinjlim$
24654 \begin_inset Formula $\raisebox{-2.5mm}{}$
24670 \begin_layout Standard
24671 \begin_inset VSpace medskip
24674 The limit is created by inserting a subscript.
24675 It is set right beside the function in an inline formula:
24678 \begin_layout Standard
24680 \begin_inset Tabular
24681 <lyxtabular version="3" rows="2" columns="2">
24682 <features rotate="0" tabularvalignment="middle">
24683 <column alignment="center" valignment="top" width="0pt">
24684 <column alignment="center" valignment="top" width="0pt">
24686 <cell alignment="center" valignment="top" usebox="none">
24689 \begin_layout Plain Layout
24695 <cell alignment="center" valignment="top" usebox="none">
24698 \begin_layout Plain Layout
24699 \begin_inset space \hspace{}
24704 \begin_inset Note Note
24707 \begin_layout Plain Layout
24714 are used here as spacer.
24726 <cell alignment="center" valignment="top" usebox="none">
24729 \begin_layout Plain Layout
24735 \begin_inset space \textvisiblespace{}
24739 \begin_inset space \textvisiblespace{}
24747 <cell alignment="center" valignment="top" usebox="none">
24750 \begin_layout Plain Layout
24751 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
24767 \begin_layout Standard
24768 In a displayed formula the limit is set below the formula, as usual:
24769 \begin_inset Formula
24779 \begin_layout Subsection
24781 \begin_inset Index idx
24784 \begin_layout Plain Layout
24785 Functions ! modulo-
24793 \begin_layout Standard
24794 The modulo-function is special, because it exists in four variants.
24795 The variants in a displayed formula are:
24796 \begin_inset Formula
24798 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
24799 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
24800 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
24801 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
24802 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
24810 \begin_layout Standard
24811 In an inline formula less space is set before the function names for all
24813 By default the modulo-functions take only the first following character
24815 To use more than one character, one has to put them into TeX-braces:
24816 \begin_inset Formula
24818 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
24819 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
24820 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
24828 \begin_layout Section
24830 \begin_inset Index idx
24833 \begin_layout Plain Layout
24842 \begin_layout Subsection
24843 Special Characters in Mathematical Text
24846 \begin_layout Standard
24847 The following commands can only be used in mathematical text or in TeX-mode:
24850 \begin_layout Standard
24851 \begin_inset space \hfill{}
24855 \begin_inset Tabular
24856 <lyxtabular version="3" rows="8" columns="2">
24857 <features rotate="0" tabularvalignment="middle">
24858 <column alignment="block" valignment="top">
24859 <column alignment="block" valignment="top">
24861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24864 \begin_layout Plain Layout
24870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24873 \begin_layout Plain Layout
24881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24884 \begin_layout Plain Layout
24892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24895 \begin_layout Plain Layout
24896 \begin_inset Formula $\textrm{œ}$
24906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24909 \begin_layout Plain Layout
24917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24920 \begin_layout Plain Layout
24921 \begin_inset Formula $\textrm{Œ}$
24931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24934 \begin_layout Plain Layout
24942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24945 \begin_layout Plain Layout
24946 \begin_inset Formula $\textrm{æ}$
24956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24959 \begin_layout Plain Layout
24967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24970 \begin_layout Plain Layout
24971 \begin_inset Formula $\textrm{Æ}$
24981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24984 \begin_layout Plain Layout
24992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24995 \begin_layout Plain Layout
24996 \begin_inset Formula $\textrm{\aa}$
25006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25009 \begin_layout Plain Layout
25013 \begin_inset Index idx
25016 \begin_layout Plain Layout
25023 \begin_layout Plain Layout
25044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25047 \begin_layout Plain Layout
25048 \begin_inset Formula $\textrm{Å}$
25058 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25061 \begin_layout Plain Layout
25069 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25072 \begin_layout Plain Layout
25073 \begin_inset Formula $\textrm{ı}$
25087 \begin_inset space \hfill{}
25091 \begin_inset Tabular
25092 <lyxtabular version="3" rows="8" columns="2">
25093 <features rotate="0" tabularvalignment="middle">
25094 <column alignment="block" valignment="top">
25095 <column alignment="center" valignment="top">
25097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25100 \begin_layout Plain Layout
25102 \begin_inset Note Note
25105 \begin_layout Plain Layout
25107 \begin_inset space \thinspace{}
25110 mm is used for separation, because otherwise the output will be ¡ and ¿
25121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25124 \begin_layout Plain Layout
25132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25135 \begin_layout Plain Layout
25143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25146 \begin_layout Plain Layout
25147 \begin_inset Formula $\textrm{ø}$
25157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25160 \begin_layout Plain Layout
25168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25171 \begin_layout Plain Layout
25172 \begin_inset Formula $\textrm{Ø}$
25182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25185 \begin_layout Plain Layout
25193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25196 \begin_layout Plain Layout
25197 \begin_inset Formula $\textrm{ł}$
25207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25210 \begin_layout Plain Layout
25218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25221 \begin_layout Plain Layout
25222 \begin_inset Formula $\textrm{Ł}$
25232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25235 \begin_layout Plain Layout
25237 \begin_inset space \hspace{}
25242 \begin_inset space \textvisiblespace{}
25250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25253 \begin_layout Plain Layout
25254 \begin_inset Formula $\textrm{!`}$
25264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25267 \begin_layout Plain Layout
25269 \begin_inset space \hspace{}
25274 \begin_inset space \textvisiblespace{}
25282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25285 \begin_layout Plain Layout
25286 \begin_inset Formula $\textrm{?`}$
25296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25299 \begin_layout Plain Layout
25307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25310 \begin_layout Plain Layout
25311 \begin_inset Formula $\textrm{ȷ}$
25325 \begin_inset space \hfill{}
25331 \begin_layout Standard
25333 \begin_inset Formula $\textrm{\textrm{Å}}$
25337 \begin_inset Formula $\textrm{\textrm{Ø}}$
25340 can also be inserted via the math toolbar button
25341 \begin_inset Graphics
25342 filename ../images/math/digamma.png
25350 \begin_layout Standard
25351 An exception are the commands
25354 \begin_inset space \hspace{}
25363 \begin_inset space \hspace{}
25369 , because they can be inserted in LyX directly to text.
25372 \begin_layout Subsection
25374 \begin_inset CommandInset label
25376 name "sub:Accents-in-Text"
25381 \begin_inset Index idx
25384 \begin_layout Plain Layout
25393 \begin_layout Standard
25394 With the following commands all letters can be accented.
25395 The commands must be inserted in TeX-mode.
25398 \begin_layout Standard
25399 \begin_inset space \hfill{}
25403 \begin_inset Tabular
25404 <lyxtabular version="3" rows="8" columns="2">
25405 <features rotate="0" tabularvalignment="middle">
25406 <column alignment="block" valignment="top">
25407 <column alignment="block" valignment="top">
25409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25412 \begin_layout Plain Layout
25418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25421 \begin_layout Plain Layout
25429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25432 \begin_layout Plain Layout
25436 \begin_inset Quotes grd
25444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25447 \begin_layout Plain Layout
25451 \begin_layout Plain Layout
25467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25470 \begin_layout Plain Layout
25478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25481 \begin_layout Plain Layout
25485 \begin_layout Plain Layout
25501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25504 \begin_layout Plain Layout
25508 \begin_inset space \textvisiblespace{}
25516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25519 \begin_layout Plain Layout
25523 \begin_layout Plain Layout
25539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25542 \begin_layout Plain Layout
25550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25553 \begin_layout Plain Layout
25557 \begin_layout Plain Layout
25573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25576 \begin_layout Plain Layout
25580 \begin_inset space \textvisiblespace{}
25588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25591 \begin_layout Plain Layout
25595 \begin_layout Plain Layout
25611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25614 \begin_layout Plain Layout
25618 \begin_inset space \textvisiblespace{}
25626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25629 \begin_layout Plain Layout
25633 \begin_layout Plain Layout
25649 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25652 \begin_layout Plain Layout
25656 \begin_inset space \textvisiblespace{}
25664 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25667 \begin_layout Plain Layout
25671 \begin_layout Plain Layout
25691 \begin_inset space \hfill{}
25695 \begin_inset Tabular
25696 <lyxtabular version="3" rows="8" columns="2">
25697 <features rotate="0" tabularvalignment="middle">
25698 <column alignment="block" valignment="top">
25699 <column alignment="center" valignment="top">
25701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25704 \begin_layout Plain Layout
25710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25713 \begin_layout Plain Layout
25721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25724 \begin_layout Plain Layout
25728 \begin_inset space \textvisiblespace{}
25736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25739 \begin_layout Plain Layout
25743 \begin_layout Plain Layout
25759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25762 \begin_layout Plain Layout
25770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25773 \begin_layout Plain Layout
25777 \begin_layout Plain Layout
25793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25796 \begin_layout Plain Layout
25800 \begin_inset Index idx
25803 \begin_layout Plain Layout
25814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25817 \begin_layout Plain Layout
25821 \begin_layout Plain Layout
25837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25840 \begin_layout Plain Layout
25848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25851 \begin_layout Plain Layout
25855 \begin_layout Plain Layout
25871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25874 \begin_layout Plain Layout
25878 \begin_inset space \textvisiblespace{}
25886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25889 \begin_layout Plain Layout
25893 \begin_layout Plain Layout
25909 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25912 \begin_layout Plain Layout
25916 \begin_inset space \textvisiblespace{}
25924 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25927 \begin_layout Plain Layout
25931 \begin_layout Plain Layout
25947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25950 \begin_layout Plain Layout
25954 \begin_inset space \textvisiblespace{}
25962 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25965 \begin_layout Plain Layout
25969 \begin_layout Plain Layout
25989 \begin_inset space \hfill{}
25995 \begin_layout Standard
25996 \begin_inset VSpace medskip
26005 also two different characters can be accented.
26011 \begin_inset space \textvisiblespace{}
26020 \begin_layout Plain Layout
26032 \begin_layout Standard
26045 can in combination with vowels directly be inserted with the keyboard without
26047 The same applies for the tilde
26051 \begin_layout Plain Layout
26052 This only applies for keyboards where the tilde is defined as accent.
26061 in combination with
26076 \begin_layout Standard
26119 and accents that are inserted directly with the keyboard are also available
26120 in mathematical text.
26121 For the other accents there are special math commands to be used in formulas,
26123 \begin_inset CommandInset ref
26125 reference "sub:Accents-for-one"
26132 \begin_layout Standard
26133 \begin_inset VSpace bigskip
26136 Furthermore, with the command
26143 \begin_inset Index idx
26146 \begin_layout Plain Layout
26154 all numbers and letters can be set into a circle, quasi accented with a
26155 circle, similar to the copyright symbol.
26158 \begin_layout Standard
26160 \begin_inset Tabular
26161 <lyxtabular version="3" rows="3" columns="2">
26162 <features rotate="0" tabularvalignment="middle">
26163 <column alignment="center" valignment="top">
26164 <column alignment="center" valignment="top">
26166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26169 \begin_layout Plain Layout
26175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26178 \begin_layout Plain Layout
26180 \begin_inset Note Note
26183 \begin_layout Plain Layout
26190 is only used as spacer.
26202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26205 \begin_layout Plain Layout
26213 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26216 \begin_layout Plain Layout
26220 \begin_layout Plain Layout
26236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26239 \begin_layout Plain Layout
26250 raisebox{-1.5pt}{W}}
26255 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26258 \begin_layout Plain Layout
26259 \begin_inset Formula $\raisebox{4.5mm}{}$
26266 \begin_layout Plain Layout
26284 \begin_inset Formula $\raisebox{-2mm}{}$
26300 \begin_layout Standard
26301 One has to take care that the character fits in the circle.
26312 \begin_layout Plain Layout
26314 \begin_inset CommandInset ref
26316 reference "sub:Font-Sizes"
26325 specifies thereby the size of the circle.
26336 \begin_layout Plain Layout
26338 \begin_inset CommandInset ref
26340 reference "sub:Boxes-without-Frame"
26349 the character can be centered.
26352 \begin_layout Subsection
26354 \begin_inset Index idx
26357 \begin_layout Plain Layout
26366 \begin_layout Standard
26367 Old-style figures (also known as old-style numerals) are created with the
26375 \begin_inset Index idx
26378 \begin_layout Plain Layout
26387 The command can be used in formulas and in TeX-mode.
26388 The command scheme is:
26391 \begin_layout Standard
26396 oldstylenums{number}
26399 \begin_layout Standard
26404 oldstylenums{0123456789
26407 \begin_inset Formula $\oldstylenums{0123456789}$
26413 \begin_layout Section
26415 \begin_inset CommandInset label
26417 name "sec:Formula-Styles"
26422 \begin_inset Index idx
26425 \begin_layout Plain Layout
26434 \begin_layout Itemize
26435 There are two different alignment styles:
26439 \begin_layout Description
26440 Centered is the predefined standard
26443 \begin_layout Description
26444 Indented for this the option
26448 must be inserted in the menu
26450 Document\SpecialChar \menuseparator
26456 \begin_inset space ~
26462 \begin_layout Standard
26467 is used, the indentation can be adjusted with the length
26474 \begin_inset Index idx
26477 \begin_layout Plain Layout
26486 Should the distance be 15
26487 \begin_inset space \thinspace{}
26490 mm, the following command line is inserted in the LaTeX-preamble
26493 \begin_layout Standard
26503 \begin_layout Standard
26504 When no length is specified, the predefined value of 30
26505 \begin_inset space \thinspace{}
26512 \begin_layout Itemize
26513 And two different numbering styles:
26517 \begin_layout Description
26518 Right is the predefined standard
26521 \begin_layout Description
26522 Left for this the option
26526 must be inserted in the menu
26528 Document\SpecialChar \menuseparator
26534 \begin_inset space ~
26541 \begin_layout Standard
26550 can also be used together.
26551 In this case both options are inserted, separated by a comma.
26554 \begin_layout Standard
26555 The chosen styles are used for all displayed formulas of the document.
26556 When both, centered and indented formulas should be created in a document,
26562 The indented formulas are then set in a flalign environment, see
26563 \begin_inset CommandInset ref
26565 reference "sub:Flalign-Environment"
26572 \begin_layout Section
26574 \begin_inset CommandInset label
26576 name "sec:Multiline-Formulas"
26581 \begin_inset Index idx
26584 \begin_layout Plain Layout
26585 Formula ! multiline
26593 \begin_layout Subsection
26597 \begin_layout Standard
26598 In LyX multiline formulas are created by pressing
26603 arg "newline-insert newline"
26609 This creates either an
26611 eqnarray environment
26613 that is described in
26614 \begin_inset CommandInset ref
26616 reference "sub:Eqnarray-Environment"
26620 or, when the option
26622 Use AMS math package
26624 in the document settings is selected, an
26628 that is described in
26629 \begin_inset CommandInset ref
26631 reference "sub:Standard-align-Environment"
26636 The align environment is recommended because it provides in any case a
26637 typographically correct output.
26640 \begin_layout Standard
26641 There are other multiline formula environments that can be created via the
26644 Insert\SpecialChar \menuseparator
26648 These environments are described in the following sections.
26651 \begin_layout Standard
26652 In all multiline formula environments a new line is created by pressing
26656 arg "newline-insert newline"
26660 To add or delete lines, the math toolbar buttons
26661 \begin_inset Graphics
26662 filename ../images/tabular-feature_append-row.png
26668 \begin_inset Graphics
26669 filename ../images/tabular-feature_delete-row.png
26674 , respectively, or the menu
26676 Edit\SpecialChar \menuseparator
26682 \begin_layout Subsubsection
26684 \begin_inset CommandInset label
26686 name "sub:Line-Separation"
26691 \begin_inset Index idx
26694 \begin_layout Plain Layout
26695 Formula ! multiline ! Line separation
26703 \begin_layout Standard
26704 There is sometimes not enough space in multiline formulas between the lines:
26705 \begin_inset Formula
26707 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}\\
26708 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
26716 \begin_layout Standard
26717 In LaTeX additional line space is specified as optional argument of the
26719 This is not yet possible in LyX
26723 \begin_layout Plain Layout
26725 \begin_inset CommandInset href
26727 name "LyX-bug #1505"
26728 target "http://www.lyx.org/trac/ticket/1505"
26737 , therefore the whole formula must be inserted in TeX-mode.
26738 To add in our example space, the command
26746 is inserted at the end of the first line.
26751 \begin_layout Plain Layout
26758 \begin_layout Plain Layout
26760 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26763 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26770 \begin_layout Plain Layout
26774 left(B^{2}+x_{0}^{2}
26782 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26787 \begin_layout Plain Layout
26799 \begin_layout Standard
26800 \begin_inset VSpace bigskip
26803 To set the line separation for all lines in a formula, the length
26810 \begin_inset Index idx
26813 \begin_layout Plain Layout
26823 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26834 \begin_inset space \thinspace{}
26839 \begin_inset space \thinspace{}
26842 mm additional line separation as in the previous example, the command
26845 \begin_layout Standard
26855 \begin_layout Standard
26856 is inserted in TeX-mode before the formula.
26857 This requires that the LaTeX-package
26865 \begin_layout Plain Layout
26870 is part of every LaTeX standard installation.
26876 \begin_inset Index idx
26879 \begin_layout Plain Layout
26885 was loaded in LaTeX-preamble with the line
26888 \begin_layout Standard
26896 \begin_layout Standard
26901 \begin_layout Plain Layout
26913 \begin_inset Formula
26915 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}\\
26916 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
26924 \begin_layout Standard
26928 \begin_layout Plain Layout
26939 To get back to the predefined distance,
26945 is set to the value 3
26946 \begin_inset space \thinspace{}
26952 \begin_layout Subsubsection
26954 \begin_inset CommandInset label
26956 name "sub:Column-Separation"
26961 \begin_inset Index idx
26964 \begin_layout Plain Layout
26965 Formula ! multiline ! Column separation
26973 \begin_layout Standard
26974 Multiline formulas form a matrix.
26975 A formula in the eqnarray environment is for example a matrix with three
26977 By changing the column separation in this environment, the space beside
26978 the relation sign can be changed.
26981 \begin_layout Standard
26982 The column separation is specified with the length
26989 \begin_inset Index idx
26992 \begin_layout Plain Layout
27001 \begin_inset Newline newline
27004 column separation = 2
27005 \begin_inset space \thinspace{}
27015 \begin_inset Newline newline
27021 \begin_layout Standard
27031 \begin_layout Standard
27032 inserted in TeX-mode, sets for all following formulas a column separation
27034 \begin_inset space \thinspace{}
27038 To get back to the predefined distance,
27045 \begin_inset space \thinspace{}
27051 \begin_layout Standard
27053 \begin_inset space \thinspace{}
27056 cm column separation:
27060 \begin_layout Plain Layout
27072 \begin_inset Formula
27080 A formula with the predefined column separation for matrices of 10
27081 \begin_inset space \thinspace{}
27088 \begin_layout Plain Layout
27100 \begin_inset Formula
27111 \begin_layout Subsubsection
27113 \begin_inset Index idx
27116 \begin_layout Plain Layout
27125 \begin_layout Standard
27126 Long formulas can be typeset using these methods:
27129 \begin_layout Itemize
27130 When one side of the equation is much shorter than the line width, this
27131 one is chosen for the left side and the right side is typeset over two
27133 \begin_inset Formula
27135 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 \\
27136 & & -\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}
27141 The minus sign at the beginning of the second line does normally not appear
27142 as an operator because it is the first character of the line.
27143 Thus it would not be surrounded by space and could not be distinguished
27144 from the fraction bar.
27146 \begin_inset space \thinspace{}
27149 pt space was inserted behind the minus sign with the command
27159 \begin_layout Plain Layout
27167 \begin_inset CommandInset ref
27169 reference "sub:Variable-Space"
27179 \begin_inset Index idx
27182 \begin_layout Plain Layout
27193 \begin_layout Itemize
27194 When both sides of the equation are too long, the command
27201 \begin_inset Index idx
27204 \begin_layout Plain Layout
27213 It is inserted in the first column of the first line and causes all further
27214 insertions to overwrite the following columns:
27215 \begin_inset Formula
27217 \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 \\
27218 & & -\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 \\
27219 & & =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}
27224 After the insertion of
27230 , the cursor is in a purple box that is a bit shifted to the left from the
27232 In this the formula is inserted.
27233 \begin_inset Newline newline
27236 The content of the further lines is inserted to the second or another formula
27238 The greater the column number where it was inserted, the larger the indentation.
27239 \begin_inset VSpace medskip
27243 \begin_inset Newline newline
27247 \begin_inset Note Greyedout
27250 \begin_layout Plain Layout
27251 Note the following when using
27260 \begin_layout Itemize
27261 The formula doesn't use the full page width.
27263 \begin_inset space \thinspace{}
27267 \begin_inset space \space{}
27271 \begin_inset Formula $-B^{2}$
27274 is added to the first line in the above example, it would have been outside
27276 To better use the width, negative space can be inserted at the beginning
27280 \begin_layout Itemize
27281 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27286 \begin_layout Plain Layout
27287 \begin_inset CommandInset href
27289 name "LyX-bug #1429"
27290 target "http://www.lyx.org/trac/ticket/1429"
27299 One can only set the cursor at the beginning of the line and move it with
27308 \begin_layout Itemize
27309 Other methods to set long formulas are offered by the environments described
27311 \begin_inset CommandInset ref
27313 reference "sub:Multline-Environment"
27318 \begin_inset CommandInset ref
27320 reference "sub:Multiline-Formula-Parts"
27327 \begin_layout Subsubsection
27329 \begin_inset CommandInset label
27331 name "sub:Multiline-Brackets"
27336 \begin_inset Index idx
27339 \begin_layout Plain Layout
27340 Brackets ! for multiline expressions
27348 \begin_layout Standard
27349 For brackets spanning multiple lines the following problem occurs:
27350 \begin_inset Formula
27352 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27353 & & \left.\cdots+B-D\right]
27361 \begin_layout Standard
27362 The closing bracket is smaller than the opening bracket because brackets
27363 with variable size may not span multiple lines.
27366 \begin_layout Standard
27367 To set the bracket size for the second line correctly, the first line is
27375 \begin_inset Index idx
27378 \begin_layout Plain Layout
27386 and the second line with
27394 \begin_layout Plain Layout
27408 \begin_inset CommandInset ref
27410 reference "sub:Automatic-Bracket-Size"
27422 \begin_inset Index idx
27425 \begin_layout Plain Layout
27448 \begin_inset space \textvisiblespace{}
27458 \begin_inset space \textvisiblespace{}
27468 \begin_inset space \textvisiblespace{}
27474 \begin_inset Formula $\downarrow$
27480 \begin_inset Index idx
27483 \begin_layout Plain Layout
27491 is inserted, because the multiplication operator with its limits is the
27492 largest symbol in the first line and this should be the size for the bracket
27493 in the second line.
27496 \begin_layout Standard
27497 The result is this:
27498 \begin_inset Formula
27500 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27501 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
27509 \begin_layout Subsection
27513 \begin_layout Standard
27514 Align environments can be used for every kind of multiline formulas.
27515 They are especially useful to set several formulas side by side.
27518 \begin_layout Standard
27519 Align environments consist of columns.
27520 The odd columns are right aligned, the even ones left aligned.
27521 Every line in an Align environment can be numbered.
27524 \begin_layout Standard
27525 Align environments are created via the menu
27527 Insert\SpecialChar \menuseparator
27533 Edit\SpecialChar \menuseparator
27534 Math\SpecialChar \menuseparator
27535 Change Formula Type
27537 already existing formulas can be converted to Align environments.
27540 \begin_layout Standard
27541 To add or delete columns, the math toolbar buttons
27542 \begin_inset Graphics
27543 filename ../images/tabular-feature_append-column.png
27549 \begin_inset Graphics
27550 filename ../images/tabular-feature_delete-column.png
27555 , respectively, or the menu
27557 Edit\SpecialChar \menuseparator
27563 \begin_layout Subsubsection
27564 Standard align Environment
27565 \begin_inset CommandInset label
27567 name "sub:Standard-align-Environment"
27572 \begin_inset Index idx
27575 \begin_layout Plain Layout
27576 Formula ! multiline ! align environment
27584 \begin_layout Standard
27585 This Align environment is created by pressing
27588 arg "newline-insert newline"
27591 in a formula or by the menu
27593 Insert\SpecialChar \menuseparator
27594 Math\SpecialChar \menuseparator
27595 AMS align Environment
27600 \begin_layout Standard
27601 An example for two formulas set side by side, that are created with a four
27602 column align environment:
27603 \begin_inset Formula
27605 A & =\sin(B) & C & =D\\
27606 C & \ne A & B & \ne D
27611 As it can be seen, the formulas in this environment are placed so as if
27620 \begin_layout Plain Layout
27628 \begin_inset CommandInset ref
27630 reference "sub:Variable-Space"
27641 before the first and after every even column.
27642 When the formula style
27648 \begin_layout Plain Layout
27650 \begin_inset CommandInset ref
27652 reference "sec:Formula-Styles"
27663 is used, the formula is set without the
27669 before the first column.
27672 \begin_layout Subsubsection
27673 Alignat Environment
27674 \begin_inset Index idx
27677 \begin_layout Plain Layout
27678 Formula ! multiline ! alignat environment
27686 \begin_layout Standard
27687 The alignat environment has no predefined column separation.
27688 It can be inserted manually with the spaces that are described
27689 \begin_inset CommandInset ref
27691 reference "sub:Space"
27698 \begin_layout Standard
27699 The above example in the alignat environment where 1
27700 \begin_inset space \thinspace{}
27703 cm space was inserted at the beginning of the second formula:
27704 \begin_inset Formula
27705 \begin{alignat*}{2}
27706 A & =\sin(B) & \hspace{1cm}C & =D\\
27707 C & \ne A & B & \ne D
27712 Because the column separation can be set separately for every column, this
27713 environment is especially suitable to set three and more formulas side
27717 \begin_layout Subsubsection
27718 Flalign Environment
27719 \begin_inset CommandInset label
27721 name "sub:Flalign-Environment"
27726 \begin_inset Index idx
27729 \begin_layout Plain Layout
27730 Formula ! multiline ! flalign environment
27738 \begin_layout Standard
27739 In this environment the first two columns are always set as much as possible
27740 to the left and the last two ones to the right.
27742 \begin_inset Formula
27744 A & =1 & B & =2 & C & =3\\
27745 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
27753 \begin_layout Standard
27754 By creating a flalign environment with an odd number of columns where an
27755 empty TeX-brace is inserted to the last column, several formulas in a document
27756 can be set to the left, although the formula style
27761 As example the indented formula
27762 \begin_inset CommandInset ref
27764 reference "eq:VolInt"
27769 \begin_inset Formula
27771 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
27776 The first two columns contain the formula.
27777 To indent it as with the formula style
27782 \begin_inset space \thinspace{}
27785 pt space was inserted at the beginning of the first column.
27788 \begin_layout Subsection
27789 Eqnarray Environment
27790 \begin_inset CommandInset label
27792 name "sub:Eqnarray-Environment"
27797 \begin_inset Index idx
27800 \begin_layout Plain Layout
27801 Formula ! multiline ! eqnarray environment
27809 \begin_layout Standard
27810 When this environment has been created, three blue boxes appear.
27811 The content of the first box is right aligned, the content of the last
27813 The content of the middle box appears centered and a bit smaller, because
27814 it is designed to insert there only relation characters.
27815 \begin_inset Formula
27817 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27827 \begin_layout Subsection
27829 \begin_inset Index idx
27832 \begin_layout Plain Layout
27833 Formula ! multiline ! gather environment
27841 \begin_layout Standard
27842 This environment consists of only one centered column.
27843 Every line can be numbered.
27844 \begin_inset Formula
27855 \begin_layout Subsection
27856 Multline Environment
27857 \begin_inset CommandInset label
27859 name "sub:Multline-Environment"
27864 \begin_inset Index idx
27867 \begin_layout Plain Layout
27868 Formula ! multiline ! multline environment
27876 \begin_layout Standard
27877 The multline environment consists, like the gather environment, of only
27879 But the first line is left aligned, the last one right aligned.
27880 All other lines are centered.
27881 Therefore this environment is suitable for long formulas.
27883 \begin_inset CommandInset ref
27885 reference "eq:lefteqn"
27889 in the multline environment:
27890 \begin_inset Formula
27892 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}\\
27893 -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}\\
27894 =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}}
27902 \begin_layout Standard
27903 In the output only the last (first) line of a multline environment appears
27904 numbered when the document numbering is right (left).
27908 \begin_layout Plain Layout
27909 numbering styles see
27910 \begin_inset CommandInset ref
27912 reference "sec:Formula-Styles"
27924 \begin_layout Standard
27932 \begin_inset Index idx
27935 \begin_layout Plain Layout
27950 \begin_inset Index idx
27953 \begin_layout Plain Layout
27961 a centered line can be right or left aligned, respectively.
27962 The commands are used as follows:
27965 \begin_layout Standard
27970 shoveright{line content}
27976 shoveleft{line content}
27979 \begin_layout Standard
27980 \begin_inset VSpace medskip
27990 \begin_inset Index idx
27993 \begin_layout Plain Layout
28001 specifies the distance of the first line from the left page margin.
28002 Predefined is the length 0
28003 \begin_inset space \thinspace{}
28009 \begin_layout Standard
28010 As example the above formula where the command
28013 \begin_layout Standard
28023 \begin_layout Standard
28024 was inserted in TeX-mode before:
28028 \begin_layout Plain Layout
28040 \begin_inset Formula
28042 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}\\
28043 \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}}\\
28044 =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}}
28053 \begin_layout Plain Layout
28064 The second line was left aligned using
28073 \begin_layout Subsection
28074 Multiline Formula Parts
28075 \begin_inset CommandInset label
28077 name "sub:Multiline-Formula-Parts"
28082 \begin_inset Index idx
28085 \begin_layout Plain Layout
28086 Formula ! multiline ! formula parts
28094 \begin_layout Standard
28095 To display only parts of a formula with multiple lines, one of the following
28096 environments is used:
28113 They can be inserted via the menu
28115 Insert\SpecialChar \menuseparator
28118 or by using the commands described in this section.
28121 \begin_layout Standard
28122 The first three have the same properties as the corresponding multiline
28123 formula environments, but it is possible to set further formula parts beside
28126 \begin_inset Formula
28128 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28129 \Delta E\Delta t & \ge\frac{\hbar}{2}
28131 \right\} \textrm{Uncertainty relations}
28139 \begin_layout Standard
28140 To get this formula, a displayed formula is created where the command
28147 \begin_inset Index idx
28150 \begin_layout Plain Layout
28159 A purple box appears around the blue formula box where now columns and
28160 lines can be added.
28161 Outside the multiline environment other formula parts can be set, like
28165 \begin_layout Standard
28166 The aligned environment is also suitable for long formulas whose lines are
28167 horizontally aligned.
28168 Using aligned in a displayed formula has the advantage that the formula
28169 number is vertically centered behind the lines.
28171 \begin_inset CommandInset ref
28173 reference "eq:shortlong"
28177 in the aligned environment:
28178 \begin_inset Formula
28180 \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}|}\\
28181 & -\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}|}
28190 \begin_layout Standard
28191 To use the environments
28210 \begin_inset Index idx
28213 \begin_layout Plain Layout
28228 \begin_inset Index idx
28231 \begin_layout Plain Layout
28246 \begin_inset Index idx
28249 \begin_layout Plain Layout
28257 are inserted, respectively.
28258 The split environment has the same properties as the aligned environment
28259 but it can only have two columns.
28262 \begin_layout Subsection
28263 Text in multiline Formulas
28264 \begin_inset CommandInset label
28266 name "sub:Text-in-multiline"
28271 \begin_inset Index idx
28274 \begin_layout Plain Layout
28281 \begin_inset Index idx
28284 \begin_layout Plain Layout
28285 Formula ! multiline ! text
28293 \begin_layout Standard
28294 In the Align environments, and the multline and gather environment, text
28295 can be inserted that will appear in a separate line and doesn't affect
28296 the column alignment.
28297 To do this, the command
28304 \begin_inset Index idx
28307 \begin_layout Plain Layout
28315 is used in the following scheme:
28318 \begin_layout Standard
28326 \begin_layout Standard
28327 The text should not be longer than a line because it cannot be hyphenated.
28328 As LyX doesn't yet support
28334 directly, the text is written as mathematical text.
28341 must hereby be at the beginning of a line and appears in the output above
28343 An example where the text was inserted at the beginning of the second line:
28344 \begin_inset Formula
28346 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28347 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28355 \begin_layout Section
28357 \begin_inset Index idx
28360 \begin_layout Plain Layout
28367 \begin_inset Index idx
28370 \begin_layout Plain Layout
28371 Formula ! numbering|see
28375 \begin_layout Plain Layout
28386 \begin_layout Plain Layout
28401 \begin_layout Subsection
28405 \begin_layout Standard
28406 Numbered formulas can be created with the menu
28408 Insert\SpecialChar \menuseparator
28409 Math\SpecialChar \menuseparator
28411 \begin_inset space ~
28419 \begin_inset space ~
28425 Existing formulas can be numbered with the menu
28427 Edit\SpecialChar \menuseparator
28428 Math\SpecialChar \menuseparator
28430 \begin_inset space ~
28438 arg "math-number-toggle"
28442 The formula number is displayed in LyX behind the formula as a number sign
28444 The number sign is replaced in the output by the formula number.
28447 \begin_layout Standard
28448 When numbering is turned on in multiline formulas, all lines will be numbered.
28449 But the numbering can be controlled with the menu
28451 Edit\SpecialChar \menuseparator
28452 Math\SpecialChar \menuseparator
28454 \begin_inset space ~
28458 \begin_inset space ~
28462 \begin_inset space ~
28470 arg "math-number-line-toggle"
28476 \begin_layout Standard
28477 Except for inline formulas, all formulas can be numbered with two different
28479 \begin_inset CommandInset ref
28481 reference "sec:Formula-Styles"
28488 \begin_layout Subsection
28490 \begin_inset Index idx
28493 \begin_layout Plain Layout
28494 Cross-references ! to formulas
28502 \begin_layout Standard
28503 All labeled formulas can be cross-referenced.
28504 A label is added by the menu
28506 Insert\SpecialChar \menuseparator
28509 or the toolbar button
28510 \begin_inset Graphics
28511 filename ../images/label-insert.png
28517 The cursor must hereby be inside a displayed formula.
28518 Alternatively you can right-click on the formula and choose
28523 A dialog pops up displaying the prefix
28528 The label is inserted there behind the prefix.
28529 The predefined prefix means
28530 \begin_inset Quotes eld
28534 \begin_inset Quotes erd
28537 and makes it easier to find labels in large documents because it marks
28538 it as formula label to divide it from e.
28539 \begin_inset space \thinspace{}
28543 \begin_inset space \space{}
28547 To change a label, the menu
28549 Insert\SpecialChar \menuseparator
28552 is used again or you right-click on a formula and then on
28559 \begin_layout Standard
28560 The name of the label is displayed in LyX within two parentheses behind
28562 A formula with a label is always numbered.
28565 \begin_layout Standard
28566 Cross-references are inserted via the menu
28568 Insert\SpecialChar \menuseparator
28571 or with the toolbar button
28572 \begin_inset Graphics
28573 filename ../images/dialog-show-new-inset_ref.png
28579 A formula cross-reference appears in the output as formula number.
28580 When in the cross-reference dialog window the format
28584 is chosen, the cross-reference appears in the output as formula number
28586 \begin_inset Newline newline
28589 By right-clicking on a cross-reference in LyX, one jumps to the formula
28590 that is referenced.
28593 \begin_layout Standard
28594 Here are as examples cross-references to formulas of the following subsections:
28595 \begin_inset Note Note
28598 \begin_layout Plain Layout
28599 Note the different cross-reference types.
28607 \begin_layout Standard
28609 \begin_inset CommandInset ref
28616 \begin_inset CommandInset ref
28624 \begin_inset CommandInset ref
28630 ) big Latin letters are used for the numbering in contrary to (
28631 \begin_inset CommandInset ref
28640 \begin_layout Standard
28641 \begin_inset VSpace medskip
28644 When the argument of
28652 \begin_layout Plain Layout
28660 \begin_inset CommandInset ref
28662 reference "sub:User-defined-Numbering"
28673 contains a box like in
28674 \begin_inset CommandInset ref
28676 reference "sub:Paragraph-Boxes"
28680 , the formula cannot be referenced.
28683 \begin_layout Subsection
28685 \begin_inset Index idx
28688 \begin_layout Plain Layout
28689 Formula numbering ! subnumbering
28697 \begin_layout Standard
28698 With the help of the commands
28702 begin{subequations}
28710 formulas can be subnumbered.
28711 Both commands are inserted in TeX-mode.
28714 \begin_layout Standard
28716 \begin_inset Formula
28727 \begin_layout Plain Layout
28731 addtocounter{equation}{-1}
28740 \begin_layout Plain Layout
28744 begin{subequations}
28750 \begin_inset VSpace -5mm
28754 \begin_inset Formula
28762 \begin_inset Formula
28772 \begin_layout Standard
28776 \begin_layout Plain Layout
28788 \begin_layout Standard
28789 To create the example, the following is done:
28792 \begin_layout Enumerate
28793 first formula is inserted
28796 \begin_layout Enumerate
28801 addtocounter{equation}{-1}
28803 begin{subequations}
28804 \begin_inset Index idx
28807 \begin_layout Plain Layout
28816 \begin_inset Newline newline
28821 is inserted after the first formula
28824 \begin_layout Enumerate
28825 second formula is inserted
28828 \begin_layout Enumerate
28829 third formula is inserted
28832 \begin_layout Enumerate
28839 is inserted after the third formula
28842 \begin_layout Standard
28843 Every formula between the commands
28855 is subnumbered as a, b,
28856 \begin_inset Newline linebreak
28859 c, \SpecialChar \ldots{}
28860 For multiline formulas every line will be subnumbered.
28861 All subnumbered formulas are treated as
28866 But as every numbered formula increases the counter
28870 by one, the command
28876 is needed to decrease it.
28877 Otherwise the formulas
28878 \begin_inset CommandInset ref
28885 \begin_inset CommandInset ref
28892 \begin_inset CommandInset ref
28898 would be numbered as
28899 \begin_inset CommandInset ref
28906 \begin_inset CommandInset ref
28913 \begin_inset CommandInset ref
28922 \begin_layout Standard
28923 By inserting the commands in TeX-mode, a space is created between the first
28926 \begin_inset space \thinspace{}
28929 mm vertical space is inserted after the command
28933 begin{subequations}
28936 When the formula style
28942 \begin_layout Plain Layout
28944 \begin_inset CommandInset ref
28946 reference "sec:Formula-Styles"
28958 \begin_inset space \thinspace{}
28961 mm space is inserted instead.
28964 \begin_layout Standard
28965 Here is an example for a multiline formula where the numbering was turned
28966 off for the second line:
28970 \begin_layout Plain Layout
28974 begin{subequations}
28980 \begin_inset Formula
28982 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
28983 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
28984 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
28993 \begin_layout Plain Layout
29005 \begin_layout Subsection
29006 User-defined Numbering
29007 \begin_inset CommandInset label
29009 name "sub:User-defined-Numbering"
29014 \begin_inset Index idx
29017 \begin_layout Plain Layout
29018 Formula numbering ! user-defined
29026 \begin_layout Standard
29027 \begin_inset Index idx
29030 \begin_layout Plain Layout
29031 Formula numbering ! self-defined delimiters
29036 With the standard numbering parentheses are set around the formula number.
29037 To replace the parentheses for example by vertical bars, the following
29038 line is added to the LaTeX-preamble:
29041 \begin_layout Standard
29053 \begin_inset Note Note
29056 \begin_layout Plain Layout
29057 This macro is already declared in the LaTeX-preamble for testing.
29058 To activate it, remove the percent sign at the beginning.
29066 \begin_layout Standard
29067 To use other characters, the vertical bars besides the
29071 are replaced by one ore more characters.
29072 To get only the formula number the vertical bars are omitted.
29075 \begin_layout Standard
29076 \begin_inset VSpace bigskip
29079 When there should be an expression of your choice instead of the consecutive
29080 formula number in parentheses behind the formula, the command
29087 \begin_inset Index idx
29090 \begin_layout Plain Layout
29099 \begin_inset Formula
29101 A+B=C\tag{something}\label{eq:tag}
29106 In this example the command
29111 \begin_inset space \textvisiblespace{}
29116 was inserted in the formula.
29119 \begin_layout Standard
29125 \begin_inset space \textvisiblespace{}
29130 is inserted instead, the star prevents the parentheses around the expression:
29131 \begin_inset Formula
29133 A+B=C\tag*{something}
29141 \begin_layout Standard
29142 \begin_inset VSpace bigskip
29145 To restart the formula numbering with new document parts or sections, the
29146 following command is used:
29149 \begin_layout Standard
29154 @addtoreset{equation}{part}
29157 \begin_inset Index idx
29160 \begin_layout Plain Layout
29165 \begin_layout Plain Layout
29176 \begin_layout Plain Layout
29189 \begin_layout Plain Layout
29200 \begin_layout Plain Layout
29213 \begin_inset Newline newline
29217 \begin_inset Newline newline
29224 @addtoreset{equation}{section}
29227 \begin_layout Standard
29228 To be able to use these commands in TeX-mode, the
29229 \begin_inset Quotes eld
29233 \begin_inset Quotes erd
29236 character has to be made
29237 \begin_inset Quotes eld
29241 \begin_inset Quotes erd
29244 for LaTeX using the command
29258 So the command sequence in TeX-mode is:
29261 \begin_layout Standard
29267 \begin_inset Newline newline
29272 @addtoreset{equation}{section}
29273 \begin_inset Newline newline
29281 \begin_layout Standard
29282 In the LaTeX-preamble
29294 can be omitted as they are automatically internally inserted by LyX.
29297 \begin_layout Standard
29312 \begin_layout Plain Layout
29317 is part of the LaTeX-package
29322 \begin_inset Index idx
29325 \begin_layout Plain Layout
29326 Packages ! carlisle
29331 that is part of every LaTeX standard installation.
29337 \begin_inset Index idx
29340 \begin_layout Plain Layout
29341 Packages ! remreset
29346 has to be loaded in the LaTeX-preamble with the line
29349 \begin_layout Standard
29354 usepackage{remreset}
29357 \begin_layout Standard
29365 \begin_inset Index idx
29368 \begin_layout Plain Layout
29373 \begin_layout Plain Layout
29384 \begin_layout Plain Layout
29397 \begin_layout Plain Layout
29408 \begin_layout Plain Layout
29420 can be used with the same scheme as
29429 \begin_layout Standard
29430 \begin_inset VSpace bigskip
29433 Sometimes formulas should be numbered in the following form:
29436 \begin_layout Standard
29439 (section number.formula number)
29442 \begin_layout Standard
29443 The formula number should start with every section with
29444 \begin_inset Quotes eld
29448 \begin_inset Quotes erd
29454 \begin_layout Standard
29455 For this case there is the command
29462 \begin_inset Index idx
29465 \begin_layout Plain Layout
29473 , which is used with the following scheme:
29476 \begin_layout Standard
29481 numberwithin{counter}{sectioning}
29484 \begin_layout Standard
29485 Counter denotes what kind of numbering is affected, sectioning denotes what
29486 number is before the dot.
29489 \begin_layout Standard
29490 Thus in our case the following LaTeX-preamble or TeX code line is used:
29493 \begin_layout Standard
29498 numberwithin{equation}{section}
29501 \begin_layout Standard
29502 This is the result:
29506 \begin_layout Plain Layout
29510 numberwithin{equation}{section}
29516 \begin_inset Formula
29526 \begin_layout Standard
29528 \begin_inset space \thinspace{}
29532 \begin_inset space \space{}
29535 tables so that the number of the part is the sectioning,
29536 \begin_inset Newline newline
29543 numberwithin{table}{part}
29548 \begin_layout Standard
29549 To go back to the standard numbering or to prevent this kind of numbering
29550 when it is defined by the document class, the following command is inserted
29551 as TeX code or to the LaTeX-preamble:
29554 \begin_layout Standard
29564 \begin_inset Index idx
29567 \begin_layout Plain Layout
29581 \begin_layout Plain Layout
29597 \begin_inset Newline newline
29605 \begin_inset Newline newline
29617 \begin_layout Standard
29624 uses internally the command
29630 , described above, that also needs to be reverted.
29634 \begin_layout Plain Layout
29641 \begin_layout Plain Layout
29645 @removefromreset{equation}{section}
29648 \begin_layout Plain Layout
29660 \begin_layout Subsection
29661 Numbering with Roman Numbers and Letters
29662 \begin_inset Index idx
29665 \begin_layout Plain Layout
29666 Formula numbering ! with letters
29672 \begin_inset Index idx
29675 \begin_layout Plain Layout
29676 Formula numbering ! with Roman numbers
29684 \begin_layout Standard
29685 Formulas can also be numbered with Roman numbers and Latin letters.
29686 To number for example with small Roman numbers, the command
29689 \begin_layout Standard
29701 \begin_layout Standard
29702 is inserted before the formula in TeX-mode.
29710 \begin_inset Index idx
29713 \begin_layout Plain Layout
29721 redefines the predefined command
29737 \begin_layout Plain Layout
29744 has the same scheme like the command
29750 that is described in
29751 \begin_inset CommandInset ref
29753 reference "sub:The-Command-newcommand"
29766 is the formula counter.
29773 is used as prefix for a counter, the value of the counter is output as
29775 When a formula is numbered, LaTeX sets internally the command
29781 behind the formula.
29787 \begin_inset Index idx
29790 \begin_layout Plain Layout
29800 outputs the counter as small Roman number.
29803 \begin_layout Standard
29804 All formulas behind the command
29814 are now numbered Roman.
29815 To switch to numbering with big Roman numbers, the command is inserted
29829 \begin_inset Index idx
29832 \begin_layout Plain Layout
29844 \begin_inset Quotes eld
29848 \begin_inset Quotes erd
29851 with small Latin letters there is the command
29858 \begin_inset Index idx
29861 \begin_layout Plain Layout
29869 , for big ones there is the command
29876 \begin_inset Index idx
29879 \begin_layout Plain Layout
29892 \begin_layout Standard
29893 \begin_inset Note Greyedout
29896 \begin_layout Plain Layout
29903 \begin_inset space ~
29906 formulas can be numbered with Latin letters in one document.
29914 \begin_layout Standard
29918 \begin_layout Plain Layout
29934 \begin_layout Standard
29935 \begin_inset Formula
29937 A=\textrm{small roman}
29946 \begin_layout Plain Layout
29960 \begin_inset Formula
29962 B=\textrm{big Roman}\label{eq:Rom}
29971 \begin_layout Plain Layout
29985 \begin_inset Formula
29987 C=\textrm{small Latin}
29996 \begin_layout Plain Layout
30010 \begin_inset Formula
30012 D=\textrm{big Latin}\label{eq:Lat}
30020 \begin_layout Standard
30021 To switch back to the default numbering, insert the command:
30024 \begin_layout Standard
30034 \begin_inset Index idx
30037 \begin_layout Plain Layout
30048 \begin_layout Standard
30052 \begin_layout Plain Layout
30066 \begin_inset Formula
30076 \begin_layout Standard
30077 \begin_inset VSpace medskip
30080 As you see, formulas are numbered serially independent from the numbering
30082 When then numbering should start with
30083 \begin_inset Quotes eld
30087 \begin_inset Quotes erd
30090 when the style is changed, new equation counters have to be defined.
30091 A description about this can be found in the file
30092 \begin_inset CommandInset href
30094 name "Formula-numbering.lyx"
30095 target "run:Formula-numbering.lyx"
30102 \begin_layout Standard
30103 \begin_inset Newpage newpage
30109 \begin_layout Section
30110 Chemical Symbols and Equations
30111 \begin_inset CommandInset label
30113 name "sub:Chemical-Symbols-and"
30118 \begin_inset Index idx
30121 \begin_layout Plain Layout
30122 Chemical characters ! Symbols
30128 \begin_inset Index idx
30131 \begin_layout Plain Layout
30138 \begin_inset Index idx
30141 \begin_layout Plain Layout
30150 \begin_layout Standard
30151 An example text from chemistry:
30154 \begin_layout Quote
30156 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30159 -ion reacts with two
30160 \begin_inset Formula $\mathrm{Na^{+}}$
30163 -ions to sodium sulfate
30164 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30168 The chemical equation for this is:
30169 \begin_inset Formula
30171 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
30179 \begin_layout Standard
30180 This chemical equation can directly be created as formula.
30181 To avoid that the symbols appear italic, everything is highlighted and
30182 changed by the shortcut
30188 to the upright font style.
30192 \begin_layout Plain Layout
30198 \begin_inset CommandInset ref
30200 reference "sub:Font-Styles"
30212 \begin_layout Standard
30213 A more convenient way to typeset chemical formulas is to use the command
30221 \begin_inset Index idx
30224 \begin_layout Plain Layout
30232 that is available when the LaTeX-package
30237 \begin_inset Index idx
30240 \begin_layout Plain Layout
30253 to a formula a new blue box appears where chemical formulas can be inserted
30254 in an intuitive way.
30257 \begin_layout Standard
30259 \begin_inset Tabular
30260 <lyxtabular version="3" rows="9" columns="2">
30261 <features rotate="0" tabularvalignment="middle">
30262 <column alignment="center" valignment="top">
30263 <column alignment="center" valignment="top">
30265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30268 \begin_layout Plain Layout
30274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30277 \begin_layout Plain Layout
30279 \begin_inset Note Note
30282 \begin_layout Plain Layout
30289 is only used as spacer.
30301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30304 \begin_layout Plain Layout
30308 \begin_inset space \textvisiblespace{}
30316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30319 \begin_layout Plain Layout
30320 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
30330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30333 \begin_layout Plain Layout
30337 \begin_inset space \textvisiblespace{}
30345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30348 \begin_layout Plain Layout
30349 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
30359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30362 \begin_layout Plain Layout
30366 \begin_inset space \textvisiblespace{}
30374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30377 \begin_layout Plain Layout
30378 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
30388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30391 \begin_layout Plain Layout
30395 \begin_inset space \textvisiblespace{}
30403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30406 \begin_layout Plain Layout
30407 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
30417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30420 \begin_layout Plain Layout
30424 \begin_inset space \textvisiblespace{}
30430 \begin_inset space \textvisiblespace{}
30436 \begin_inset space \textvisiblespace{}
30444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30447 \begin_layout Plain Layout
30448 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
30458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30461 \begin_layout Plain Layout
30465 \begin_inset space \textvisiblespace{}
30469 \begin_inset Formula $\downarrow$
30473 \begin_inset Formula $\to$
30481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30484 \begin_layout Plain Layout
30485 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
30495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30498 \begin_layout Plain Layout
30502 \begin_inset space \textvisiblespace{}
30506 \begin_inset space \textvisiblespace{}
30510 \begin_inset space \textvisiblespace{}
30514 \begin_inset space \textvisiblespace{}
30518 \begin_inset space \textvisiblespace{}
30526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30529 \begin_layout Plain Layout
30530 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
30540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30543 \begin_layout Plain Layout
30547 \begin_inset space \textvisiblespace{}
30551 \begin_inset space \textvisiblespace{}
30555 \begin_inset space \textvisiblespace{}
30559 \begin_inset space \textvisiblespace{}
30567 \begin_inset space \textvisiblespace{}
30575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30578 \begin_layout Plain Layout
30579 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
30595 \begin_layout Standard
30596 \begin_inset Note Greyedout
30599 \begin_layout Plain Layout
30605 Inserting a formula to a
30611 box will lead to LaTeX errors due to a LyX bug.
30617 \begin_layout Plain Layout
30618 \begin_inset CommandInset href
30620 name "LyX-bug #8566"
30621 target "http://www.lyx.org/trac/ticket/8566"
30632 In this case TeX code has to be used like for
30646 \begin_layout Plain Layout
30667 \begin_layout Standard
30668 \begin_inset Note Greyedout
30671 \begin_layout Plain Layout
30677 It is not possible in LyX to use the character ^ to get an up-arrow as
30683 One instead uses a negative thin space followed by the command
30690 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
30701 \begin_layout Standard
30708 the command for equation
30709 \begin_inset space ~
30713 \begin_inset CommandInset ref
30715 reference "eq:chem-reaction"
30720 \begin_inset Newline newline
30728 \begin_inset space \textvisiblespace{}
30732 \begin_inset space \textvisiblespace{}
30736 \begin_inset space \textvisiblespace{}
30740 \begin_inset space \textvisiblespace{}
30744 \begin_inset space \textvisiblespace{}
30748 \begin_inset space \textvisiblespace{}
30754 \begin_layout Standard
30755 To create multiline chemical equations first a multiline formula is created
30757 \begin_inset CommandInset ref
30759 reference "sec:Multiline-Formulas"
30764 Afterwards the command
30770 is used in every small blue box of the formula.
30772 \begin_inset CommandInset ref
30774 reference "eq:TEOS-reaction-1"
30779 \begin_inset CommandInset ref
30781 reference "eq:TEOS-reaction-2"
30785 are an example of a multi-stage chemical reaction where every equation
30786 has its own number.
30787 \begin_inset Formula
30789 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
30790 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
30798 \begin_layout Standard
30809 package provides the command
30816 \begin_inset Index idx
30819 \begin_layout Plain Layout
30827 that has to be used for special cases.
30828 For more information about
30834 and more examples have a look at the documentation of
30839 \begin_inset CommandInset citation
30848 \begin_layout Section
30852 \begin_layout Standard
30853 LyX supports two types of commutative diagrams:
30861 that are explained in the following.
30864 \begin_layout Subsection
30866 \begin_inset Index idx
30869 \begin_layout Plain Layout
30878 \begin_layout Standard
30879 Diagrams of this type visualize relations by vertical and horizontal lines
30881 \begin_inset Formula
30883 \begin{CD}A@>>>B@>>>C\\
30894 \begin_layout Standard
30895 To get them, the command
30900 \begin_inset Index idx
30903 \begin_layout Plain Layout
30913 is inserted to a formula.
30914 A blue box appears with two dashed lines where further commands can be
30919 arg "newline-insert newline"
30922 a new line is created.
30923 Horizontal relations are inserted in odd, vertical in even formula lines.
30926 \begin_layout Standard
30927 To create the relations there are the following commands:
30930 \begin_layout Itemize
30935 creates a left arrow,
30946 \begin_layout Itemize
30951 creates an up arrow,
30959 a vertical equal sign
30962 \begin_layout Itemize
30968 is a placeholder for non-existent relations
30971 \begin_layout Standard
30972 All arrows can be labeled as follows:
30975 \begin_layout Itemize
30976 If text inserted between the first and second < or >, resp., it is placed
30978 When it is inserted between the second and third one, it appears under
30982 \begin_layout Itemize
30983 When text for vertical arrows is inserted between the first and second A
30984 or V, resp., it is placed left beside the arrow.
30985 When it is inserted between the second and third one, it appears right
30987 If the text contains an A or V, these letters must be set into a TeX-brace.
30990 \begin_layout Standard
30991 As example a diagram with all possible relations:
30994 \begin_layout Standard
30995 \begin_inset Formula
30997 \begin{CD}A@>j>>B@>>k>C@=F\\
31008 \begin_layout Standard
31009 The command for this is:
31010 \begin_inset Newline newline
31018 \begin_inset space \textvisiblespace{}
31021 A@>j>>B@>>k>C@=F Ctrl+Return
31022 \begin_inset Newline newline
31026 \begin_inset Phantom HPhantom
31029 \begin_layout Plain Layout
31035 \begin_inset space \textvisiblespace{}
31048 \begin_inset Formula $\to$
31054 \begin_inset Newline newline
31058 \begin_inset Phantom HPhantom
31061 \begin_layout Plain Layout
31067 \begin_inset space \textvisiblespace{}
31078 \begin_layout Subsection
31080 \begin_inset Index idx
31083 \begin_layout Plain Layout
31084 Diagrams ! xymatrix
31092 \begin_layout Standard
31093 To be able to use xymatrices, the LaTeX-package
31098 A xymatrix is created by inserting the command
31105 Then you are able to add new matrix columns and rows like for normal matrices,
31107 \begin_inset CommandInset ref
31109 reference "sec:Matrices"
31116 \begin_layout Standard
31117 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31119 All possibilities to create commutative diagrams and decorations are explained
31124 that you find in the menu
31126 Help\SpecialChar \menuseparator
31128 \begin_inset space ~
31136 \begin_layout Subsection
31142 \begin_inset Index idx
31145 \begin_layout Plain Layout
31154 \begin_layout Standard
31159 -diagrams, the LaTeX-package
31168 -diagram is created by inserting the command
31175 Then you are able to add new matrix columns and rows like for normal matrices,
31177 \begin_inset CommandInset ref
31179 reference "sec:Matrices"
31186 \begin_layout Standard
31187 Examples how to create
31191 diagrams in LyX is given in the
31193 Feynman-diagram manual
31195 that you find in the menu
31197 Help\SpecialChar \menuseparator
31199 \begin_inset space ~
31207 \begin_layout Standard
31208 \begin_inset Newpage newpage
31214 \begin_layout Section
31215 User-defined Commands
31216 \begin_inset Index idx
31219 \begin_layout Plain Layout
31220 User-defined commands
31228 \begin_layout Standard
31229 \begin_inset Note Greyedout
31232 \begin_layout Plain Layout
31237 The names of user-defined commands and macros may only consist of Latin
31246 \begin_layout Subsection
31250 \begin_inset CommandInset label
31252 name "sub:The-Command-newcommand"
31257 \begin_inset Index idx
31260 \begin_layout Plain Layout
31261 User-defined commands !
31269 \begin_inset Index idx
31272 \begin_layout Plain Layout
31283 \begin_layout Standard
31284 Many LaTeX-commands are too long to be used frequently.
31285 But it is possible to define with the command
31291 new shorter commands.
31294 \begin_layout Standard
31295 The command scheme of
31304 \begin_layout Standard
31309 newcommand{new command name}[number of arguments][optional
31314 \begin_inset Newline newline
31318 \begin_inset Phantom HPhantom
31321 \begin_layout Plain Layout
31331 {command definition}
31334 \begin_layout Standard
31335 \begin_inset Note Greyedout
31338 \begin_layout Plain Layout
31343 Assure that the name of the new command is not already used in your document
31344 or by LaTeX-packages that you use.
31345 When you for example define the command
31357 , you get an error message because
31363 is already defined as command for
31364 \begin_inset Quotes eld
31368 \begin_inset Formula $\le$
31372 \begin_inset Quotes erd
31383 \begin_layout Standard
31384 The number of arguments is an integer in the range 0
31385 \begin_inset space \thinspace{}
31389 \begin_inset space \thinspace{}
31392 9 and specifies how many arguments the new command should have.
31393 With the optional value a value for an optional argument can be predefined.
31394 When this is done, the
31402 rgument of the new command is automatically an optional one.
31405 \begin_layout Standard
31406 Here are some examples:
31409 \begin_layout Itemize
31410 To define the command
31422 , the LaTeX-preamble line is:
31423 \begin_inset VSpace medskip
31427 \begin_inset Newline newline
31441 \begin_layout Itemize
31442 To define the command
31454 , the argument (that should be underlined) must be taken into account.
31455 For this the preamble line is:
31456 \begin_inset VSpace medskip
31460 \begin_inset Newline newline
31474 \begin_inset VSpace medskip
31478 \begin_inset Newline newline
31485 acts as argument placeholder, the
31489 behind it denotes that it is the placeholder for the first argument.
31492 \begin_layout Itemize
31500 \begin_inset space \thinspace{}
31504 \begin_inset space \space{}
31514 \begin_inset VSpace medskip
31518 \begin_inset Newline newline
31529 framebox#1#2{$#3$}}
31532 \begin_inset VSpace medskip
31536 \begin_inset Newline newline
31539 The two Dollar signs creates the extra formula needed for
31546 \begin_inset CommandInset ref
31548 reference "sub:Boxes-with-Frame"
31555 \begin_layout Itemize
31556 To create a new command for
31562 where the color for the box need not be specified, the argument for the
31563 color is defined optional:
31564 \begin_inset VSpace medskip
31568 \begin_inset Newline newline
31579 fcolorbox{#2}{#1}{$#3$}}
31582 \begin_inset VSpace medskip
31586 \begin_inset Newline newline
31589 When the color is not specified when using
31595 , the predefined color
31602 \begin_layout Standard
31603 A test of the new defined commands:
31606 \begin_layout Standard
31608 \begin_inset Tabular
31609 <lyxtabular version="3" rows="6" columns="2">
31610 <features rotate="0" tabularvalignment="middle">
31611 <column alignment="center" valignment="top">
31612 <column alignment="center" valignment="top">
31614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31617 \begin_layout Plain Layout
31623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31626 \begin_layout Plain Layout
31628 \begin_inset Note Note
31631 \begin_layout Plain Layout
31638 is only used as spacer.
31650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31653 \begin_layout Plain Layout
31657 \begin_inset space \textvisiblespace{}
31665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31668 \begin_layout Plain Layout
31669 \begin_inset Formula $A\gr B$
31679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31682 \begin_layout Plain Layout
31690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31693 \begin_layout Plain Layout
31694 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31707 \begin_layout Plain Layout
31711 \begin_inset Formula $\to$
31717 \begin_inset Formula $\to$
31725 \begin_inset space \textvisiblespace{}
31733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31736 \begin_layout Plain Layout
31737 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31750 \begin_layout Plain Layout
31754 \begin_inset Formula $\to$
31762 \begin_inset space \textvisiblespace{}
31770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31773 \begin_layout Plain Layout
31774 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31787 \begin_layout Plain Layout
31793 \begin_inset Formula $\to$
31801 \begin_inset space \textvisiblespace{}
31809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31812 \begin_layout Plain Layout
31813 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31829 \begin_layout Subsection
31831 \begin_inset Index idx
31834 \begin_layout Plain Layout
31835 User-defined commands! Math macros
31841 \begin_inset Index idx
31844 \begin_layout Plain Layout
31853 \begin_layout Standard
31854 User-defined commands are especially convenient for complex expressions.
31855 When you are for example dealing with a document that has quadratic equations,
31856 the same solution type occurs several times.
31857 The general form of a quadratic equation is
31858 \begin_inset Formula
31860 0=\lambda^{2}+p\lambda+q
31865 The general form of the solution is
31866 \begin_inset Formula
31868 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
31876 \begin_layout Standard
31877 To define a command for the solution formula where only the three parameters
31879 \begin_inset Formula $\lambda$
31883 \begin_inset Formula $p$
31887 \begin_inset Formula $q$
31890 need to be specified and the index of
31891 \begin_inset Formula $\lambda$
31894 can be given optionally, the LaTeX-preamble line is
31895 \begin_inset Newline newline
31911 \begin_inset Newline newline
31915 \begin_inset Phantom HPhantom
31918 \begin_layout Plain Layout
31932 frac{#3^{2}}{4}-#4}}
31935 \begin_layout Standard
31936 To create with this the solution formula, the command
31937 \begin_inset Newline newline
31947 \begin_inset Formula $\to$
31953 \begin_inset Formula $\to$
31960 is inserted to a formula
31965 \begin_layout Standard
31966 The definition of the new command is unintuitive because one has to know
31967 the schemes of all used LaTeX commands, e.
31968 \begin_inset space \thinspace{}
31972 \begin_inset space \space{}
31975 that a fraction is inserted in LaTeX as
31979 frac{numerator}{denominator}
31982 Furthermore one can easily forget a brace in the definition and cannot
31983 see in LyX what the new command is doing.
31984 To avoid these problems LyX offers the possibility to use math macros instead
31994 \begin_layout Standard
31995 A math macro is created by using the menu
31997 Insert\SpecialChar \menuseparator
31998 Math\SpecialChar \menuseparator
32001 or the toolbar button
32002 \begin_inset Graphics
32003 filename ../images/math-macro_newmacroname_newcommand.png
32009 The math macro toolbar appears together with the following box where the
32011 \begin_inset Newline newline
32015 \begin_inset space \hspace*{\fill}
32019 \begin_inset Graphics
32020 filename clipart/macrobox.png
32025 \begin_inset space \hspace*{\fill}
32029 \begin_inset Newline newline
32033 \begin_inset FormulaMacro
32034 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
32039 newmacroname is the default name of the macro that should be changed to
32040 something sensible.
32041 The wanted formula is inserted in the first blue box.
32042 An argument placeholder is inserted with the command
32049 \begin_inset space \thinspace{}
32053 \begin_inset space \space{}
32062 or by using the macro toolbar button
32063 \begin_inset Graphics
32064 filename ../images/math-macro-add-param.png
32070 Argument placeholders are displayed red.
32072 \begin_inset space ~
32075 arguments are possible.
32076 Optional arguments are created with the toolbar button
32077 \begin_inset Graphics
32078 filename ../images/math-macro-add-optional-param.png
32084 The first non-optional argument can be transformed to an optional one with
32086 \begin_inset Graphics
32087 filename ../images/math-macro-make-optional.png
32093 In the second blue box the appearance of the macro in LyX can be defined.
32094 Normally you want to see it as it is defined, so the box is kept empty.
32095 But when you have created a macro that needs lot of space on the screen,
32096 you can insert in the box for example
32097 \begin_inset Newline newline
32127 \begin_inset Newline newline
32132 For the macro only the arguments with the macro name in front of them will
32133 then be displayed in LyX, leading to a better overview.
32134 The formula appears in the output as defined in the first box.
32135 \begin_inset Newline newline
32138 The appearance of macros in formulas can furthermore be changed for single
32139 macros by setting the cursor in the macro and using the menu
32141 View\SpecialChar \menuseparator
32143 \begin_inset space ~
32147 \begin_inset space ~
32155 \begin_layout Standard
32156 To use a macro, the macro name is inserted as command to a formula, in our
32164 Our macro looks in LyX like this:
32165 \begin_inset Newline newline
32169 \begin_inset space \hspace*{\fill}
32173 \begin_inset Graphics
32174 filename clipart/macrouse.png
32179 \begin_inset space \hspace*{\fill}
32183 \begin_inset Newline newline
32186 Here is our macro example with the arguments
32187 \begin_inset Formula $x$
32191 \begin_inset Formula $\ln(x)$
32195 \begin_inset Formula $B$
32201 \begin_layout Standard
32202 \begin_inset Formula
32212 \begin_layout Standard
32213 LyX offers in the menu
32215 Tools\SpecialChar \menuseparator
32216 Preferences\SpecialChar \menuseparator
32217 Editing\SpecialChar \menuseparator
32220 different styles to edit macros.
32221 To find the style that suits you the most, choose a style and set the cursor
32222 in a macro formula to see the difference.
32225 \begin_layout Standard
32226 A math macro is transformed internally to a
32232 command when exporting the document.
32239 command is not placed in the LaTeX-preamble, therefore macros can only
32240 be used in formulas that are in the document below the macro definition
32244 \begin_layout Standard
32245 Math macros can also be directly created from a
32252 When writing for example the command
32255 \begin_inset Newline newline
32264 xleftarrow[#2]{#1}}
32265 \begin_inset Newline newline
32270 in LyX as normal text, highlighting it completely and using then the shortcut
32275 , the command will be transformed to a math macro.
32276 Using this method you need to be careful that the
32282 command is typed correctly, otherwise you get a faulty macro leading to
32286 \begin_layout Standard
32287 Math macros currently have the problem that further formulas in macro definition
32288 s are handled wrongly.
32289 Therefore the example
32296 \begin_inset CommandInset ref
32298 reference "sub:The-Command-newcommand"
32302 cannot be created as macro.
32305 \begin_layout Standard
32306 When the cursor is in a macro definition box, you will see the macro toolbar
32310 \begin_layout Standard
32311 \begin_inset VSpace defskip
32317 \begin_layout Standard
32318 \begin_inset Graphics
32319 filename clipart/MacroToolbar.png
32324 \begin_inset Index idx
32327 \begin_layout Plain Layout
32336 \begin_layout Standard
32337 \begin_inset VSpace defskip
32343 \begin_layout Standard
32344 The macro toolbar contains from left to right the following buttons:
32347 \begin_layout Standard
32348 \begin_inset VSpace defskip
32354 \begin_layout Standard
32355 \begin_inset Tabular
32356 <lyxtabular version="3" rows="9" columns="2">
32357 <features rotate="0" islongtable="true" longtabularalignment="center">
32358 <column alignment="left" valignment="top">
32359 <column alignment="left" valignment="top" width="85col%">
32360 <row interlinespace="2.5mm">
32361 <cell alignment="center" valignment="top" usebox="none">
32364 \begin_layout Plain Layout
32365 \begin_inset Graphics
32366 filename ../images/math-macro-remove-param.png
32367 rotateOrigin center
32376 <cell alignment="center" valignment="top" usebox="none">
32379 \begin_layout Plain Layout
32382 Edit\SpecialChar \menuseparator
32383 Math\SpecialChar \menuseparator
32385 \begin_inset space ~
32388 Definition\SpecialChar \menuseparator
32389 Remove Last Argument
32395 <row interlinespace="2.5mm">
32396 <cell alignment="center" valignment="top" usebox="none">
32399 \begin_layout Plain Layout
32400 \begin_inset Graphics
32401 filename ../images/math-macro-add-param.png
32402 rotateOrigin center
32411 <cell alignment="center" valignment="top" usebox="none">
32414 \begin_layout Plain Layout
32417 Edit\SpecialChar \menuseparator
32418 Math\SpecialChar \menuseparator
32420 \begin_inset space ~
32423 Definition\SpecialChar \menuseparator
32430 <row interlinespace="2.5mm">
32431 <cell alignment="center" valignment="top" usebox="none">
32434 \begin_layout Plain Layout
32435 \begin_inset Graphics
32436 filename ../images/math-macro-make-optional.png
32437 rotateOrigin center
32446 <cell alignment="center" valignment="top" usebox="none">
32449 \begin_layout Plain Layout
32452 Edit\SpecialChar \menuseparator
32453 Math\SpecialChar \menuseparator
32455 \begin_inset space ~
32458 Definition\SpecialChar \menuseparator
32459 Make First Non-Optional into
32460 \begin_inset Newline newline
32464 \begin_inset Phantom HPhantom
32467 \begin_layout Plain Layout
32470 Edit\SpecialChar \menuseparator
32471 Math\SpecialChar \menuseparator
32473 \begin_inset space ~
32476 Definition\SpecialChar \menuseparator
32488 <row interlinespace="2.5mm">
32489 <cell alignment="center" valignment="top" usebox="none">
32492 \begin_layout Plain Layout
32493 \begin_inset Graphics
32494 filename ../images/math-macro-make-nonoptional.png
32495 rotateOrigin center
32504 <cell alignment="center" valignment="top" usebox="none">
32507 \begin_layout Plain Layout
32510 Edit\SpecialChar \menuseparator
32511 Math\SpecialChar \menuseparator
32513 \begin_inset space ~
32516 Definition\SpecialChar \menuseparator
32517 Make Last Optional into
32518 \begin_inset Newline newline
32522 \begin_inset Phantom HPhantom
32525 \begin_layout Plain Layout
32528 Edit\SpecialChar \menuseparator
32529 Math\SpecialChar \menuseparator
32531 \begin_inset space ~
32534 Definition\SpecialChar \menuseparator
32540 Non-Optional Argument
32546 <row interlinespace="2.5mm">
32547 <cell alignment="center" valignment="top" usebox="none">
32550 \begin_layout Plain Layout
32551 \begin_inset Graphics
32552 filename ../images/math-macro-remove-optional-param.png
32553 rotateOrigin center
32562 <cell alignment="center" valignment="top" usebox="none">
32565 \begin_layout Plain Layout
32568 Edit\SpecialChar \menuseparator
32569 Math\SpecialChar \menuseparator
32571 \begin_inset space ~
32574 Definition\SpecialChar \menuseparator
32575 Remove Optional Argument
32581 <row interlinespace="2.5mm">
32582 <cell alignment="center" valignment="top" usebox="none">
32585 \begin_layout Plain Layout
32586 \begin_inset Graphics
32587 filename ../images/math-macro-add-optional-param.png
32588 rotateOrigin center
32597 <cell alignment="center" valignment="top" usebox="none">
32600 \begin_layout Plain Layout
32603 Edit\SpecialChar \menuseparator
32604 Math\SpecialChar \menuseparator
32606 \begin_inset space ~
32609 Definition\SpecialChar \menuseparator
32610 Insert Optional Argument
32616 <row interlinespace="2.5mm">
32617 <cell alignment="center" valignment="top" usebox="none">
32620 \begin_layout Plain Layout
32621 \begin_inset Graphics
32622 filename ../images/math-macro-remove-greedy-param.png
32623 rotateOrigin center
32632 <cell alignment="center" valignment="top" usebox="none">
32635 \begin_layout Plain Layout
32638 Edit\SpecialChar \menuseparator
32639 Math\SpecialChar \menuseparator
32641 \begin_inset space ~
32644 Definition\SpecialChar \menuseparator
32645 Remove Last Argument
32646 \begin_inset Newline newline
32650 \begin_inset Phantom HPhantom
32653 \begin_layout Plain Layout
32656 Edit\SpecialChar \menuseparator
32657 Math\SpecialChar \menuseparator
32659 \begin_inset space ~
32662 Definition\SpecialChar \menuseparator
32668 Spitting Out To The Right
32674 <row interlinespace="2.5mm">
32675 <cell alignment="center" valignment="top" usebox="none">
32678 \begin_layout Plain Layout
32679 \begin_inset Graphics
32680 filename ../images/math-macro-append-greedy-param.png
32681 rotateOrigin center
32690 <cell alignment="center" valignment="top" usebox="none">
32693 \begin_layout Plain Layout
32696 Edit\SpecialChar \menuseparator
32697 Math\SpecialChar \menuseparator
32699 \begin_inset space ~
32702 Definition\SpecialChar \menuseparator
32704 \begin_inset Newline newline
32708 \begin_inset Phantom HPhantom
32711 \begin_layout Plain Layout
32714 Edit\SpecialChar \menuseparator
32715 Math\SpecialChar \menuseparator
32717 \begin_inset space ~
32720 Definition\SpecialChar \menuseparator
32726 Eating From The Right
32732 <row interlinespace="2.5mm">
32733 <cell alignment="center" valignment="top" usebox="none">
32736 \begin_layout Plain Layout
32737 \begin_inset Graphics
32738 filename ../images/math-macro-add-greedy-optional-param.png
32739 rotateOrigin center
32748 <cell alignment="center" valignment="top" usebox="none">
32751 \begin_layout Plain Layout
32754 Edit\SpecialChar \menuseparator
32755 Math\SpecialChar \menuseparator
32757 \begin_inset space ~
32760 Definition\SpecialChar \menuseparator
32761 Append Optional Argument
32762 \begin_inset Newline newline
32766 \begin_inset Phantom HPhantom
32769 \begin_layout Plain Layout
32772 Edit\SpecialChar \menuseparator
32773 Math\SpecialChar \menuseparator
32775 \begin_inset space ~
32778 Definition\SpecialChar \menuseparator
32784 Eating From The Right
32797 \begin_layout Section
32798 Computer Algebra Systems
32801 \begin_layout Standard
32802 LyX offers the exchange between mathematical expressions written in LyX's
32803 math editor and external applications or user defined scripts.
32804 Currently supported applications are
32821 Note that the set of supported mathematical constructs is limited only
32822 to very simple cases.
32825 \begin_layout Subsection
32829 \begin_layout Standard
32830 Write some expression in a formula, go to the
32832 Edit\SpecialChar \menuseparator
32833 Math\SpecialChar \menuseparator
32834 Use Computer Algebra System
32836 menu and choose the application you have installed on the computer.
32837 After that the result of computation should show on the right side of the
32838 expression together with the
32839 \begin_inset Quotes eld
32843 \begin_inset Quotes erd
32849 \begin_layout Standard
32850 Here are few simple examples (with results from
32854 ) to show what kind of computations can be performed:
32857 \begin_layout Itemize
32858 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
32864 \begin_layout Itemize
32865 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
32871 \begin_layout Itemize
32872 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
32878 \begin_layout Itemize
32879 \begin_inset Formula $\det\left[\begin{array}{ccc}
32883 \end{array}\right]=-56$
32889 \begin_layout Itemize
32890 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
32896 \begin_layout Subsection
32900 \begin_layout Standard
32901 Currently there is no keyboard shortcut for calling the algebra applications.
32902 One can easily bind a shortcut to the
32906 LyX function (see the
32914 \begin_inset space \thinspace{}
32918 \begin_inset space \space{}
32925 key inside the math editor.
32930 one would use this shortcut definition command:
32933 \begin_layout Standard
32936 command-alternatives break-paragraph;math-extern maxima
32939 \begin_layout Section
32941 \begin_inset Index idx
32944 \begin_layout Plain Layout
32953 \begin_layout Subsection
32955 \begin_inset Index idx
32958 \begin_layout Plain Layout
32967 \begin_layout Standard
32968 Negative numbers often look ugly in formulas because the minus sign before
32969 the number is set with the same length as the minus operator sign.
32970 When writing the negative number in normal text, the minus sign appears
32974 \begin_layout Standard
32975 Thus, the problem disappears when converting the minus sign to mathematical
32979 \begin_layout Standard
32980 An example to visualize the problem:
32983 \begin_layout Standard
32985 \begin_inset Tabular
32986 <lyxtabular version="3" rows="3" columns="2">
32987 <features rotate="0" tabularvalignment="middle">
32988 <column alignment="right" valignment="top">
32989 <column alignment="left" valignment="top">
32991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32994 \begin_layout Plain Layout
33000 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33003 \begin_layout Plain Layout
33011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33014 \begin_layout Plain Layout
33020 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33023 \begin_layout Plain Layout
33024 \begin_inset Formula $x=-2$
33034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33037 \begin_layout Plain Layout
33043 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33046 \begin_layout Plain Layout
33047 \begin_inset Formula $x=\textrm{-}2$
33063 \begin_layout Subsection
33064 Comma as decimal Separator
33065 \begin_inset Index idx
33068 \begin_layout Plain Layout
33077 \begin_layout Standard
33078 In LaTeX a comma inside a formula is used, according to the English convention,
33079 as number group separator.
33080 So there will be space added behind all commas in formulas.
33083 \begin_layout Standard
33084 To avoid this, the comma is highlighted and changed to mathematical text
33094 \begin_layout Standard
33095 To use all formula commas in the document as decimal separator, the file
33104 \begin_layout Plain Layout
33109 is part of the LaTeX-package
33114 \begin_inset Index idx
33117 \begin_layout Plain Layout
33122 \begin_layout Plain Layout
33142 \begin_inset Index idx
33145 \begin_layout Plain Layout
33151 is loaded with the LaTeX-preamble line
33154 \begin_layout Standard
33162 \begin_layout Subsection
33164 \begin_inset CommandInset label
33166 name "sub:Physical-Vectors"
33171 \begin_inset Index idx
33174 \begin_layout Plain Layout
33183 \begin_layout Standard
33184 Predefined vectors are offered by the LaTeX-package
33189 \begin_inset Index idx
33192 \begin_layout Plain Layout
33198 that is loaded with the LaTeX-preamble line
33201 \begin_layout Standard
33209 \begin_layout Standard
33213 \begin_layout Plain Layout
33223 \begin_inset Note Note
33226 \begin_layout Plain Layout
33227 The following table will only be displayed when the LaTeX-package
33239 \begin_layout Standard
33240 The following commands are defined:
33243 \begin_layout Standard
33245 \begin_inset Tabular
33246 <lyxtabular version="3" rows="4" columns="2">
33247 <features rotate="0" tabularvalignment="middle">
33248 <column alignment="center" valignment="top">
33249 <column alignment="center" valignment="top">
33251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33254 \begin_layout Plain Layout
33260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33263 \begin_layout Plain Layout
33271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33274 \begin_layout Plain Layout
33284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33287 \begin_layout Plain Layout
33288 \begin_inset Formula $\Bra{\psi}$
33298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33301 \begin_layout Plain Layout
33311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33314 \begin_layout Plain Layout
33315 \begin_inset Formula $\Ket{\psi}$
33325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33328 \begin_layout Plain Layout
33340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33343 \begin_layout Plain Layout
33344 \begin_inset Formula $\Braket{\psi|\phi}$
33360 \begin_layout Standard
33367 assures that all vertical bars are set in the size of the surrounding brackets:
33368 \begin_inset Formula
33370 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
33379 \begin_layout Plain Layout
33389 \begin_inset Note Note
33392 \begin_layout Plain Layout
33393 The following will be displayed when the LaTeX-package
33405 \begin_layout Standard
33406 You need to install the LaTeX-package
33410 to see the rest of this subsection in the output.
33413 \begin_layout Standard
33417 \begin_layout Plain Layout
33429 \begin_layout Standard
33436 can also be achieved using the command
33442 , that is described in
33443 \begin_inset CommandInset ref
33445 reference "sub:Automatic-Bracket-Size"
33452 \begin_layout Subsection
33453 Self-defined Fractions
33454 \begin_inset CommandInset label
33456 name "sub:Self-defined-Fractions"
33461 \begin_inset Index idx
33464 \begin_layout Plain Layout
33465 Fractions ! self-defined
33473 \begin_layout Standard
33474 To define custom commands for fractions, the command
33481 \begin_inset Index idx
33484 \begin_layout Plain Layout
33491 \begin_layout Plain Layout
33505 is used in the following scheme:
33508 \begin_layout Standard
33521 bracket}{fraction bar thickness}{style}
33522 \begin_inset Newline newline
33526 \begin_inset Phantom HPhantom
33529 \begin_layout Plain Layout
33539 {numerator}{denominator}
33542 \begin_layout Standard
33543 The style is a number in the range of 0
33544 \begin_inset space \thinspace{}
33548 \begin_inset space \thinspace{}
33554 \begin_layout Standard
33556 \begin_inset Tabular
33557 <lyxtabular version="3" rows="5" columns="2">
33558 <features rotate="0" tabularvalignment="middle">
33559 <column alignment="center" valignment="top">
33560 <column alignment="center" valignment="top">
33562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33565 \begin_layout Plain Layout
33571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33574 \begin_layout Plain Layout
33582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33585 \begin_layout Plain Layout
33591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33594 \begin_layout Plain Layout
33595 display style formula
33602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33605 \begin_layout Plain Layout
33611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33614 \begin_layout Plain Layout
33622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33625 \begin_layout Plain Layout
33631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33634 \begin_layout Plain Layout
33642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33645 \begin_layout Plain Layout
33651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33654 \begin_layout Plain Layout
33668 \begin_layout Standard
33669 When no style is given, the size is adjusted to the surrounding environment
33670 like for the command
33679 \begin_layout Standard
33680 When no fraction bar thickness is given, the predefined value of 0.4
33681 \begin_inset space \thinspace{}
33687 \begin_layout Standard
33688 \begin_inset VSpace medskip
33691 For example, the commands
33704 \begin_inset CommandInset ref
33706 reference "sub:Fractions"
33710 are defined with the commands
33713 \begin_layout Standard
33722 genfrac{}{}{}{0}{#1}{#2}}
33725 \begin_layout Standard
33729 \begin_layout Standard
33738 genfrac{(}{)}{0pt}{1}{#1}{#2}}
33741 \begin_layout Standard
33742 \begin_inset VSpace medskip
33745 To define a fraction where the fraction bar thickness can be given as optional
33746 argument, the following line is inserted to the LaTeX-preamble:
33749 \begin_layout Standard
33758 genfrac{}{}{#1}{}{#2}{#3}}
33761 \begin_layout Standard
33763 \begin_inset Formula
33765 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33766 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
33771 As one can see, the distance of the numerator and the denominator to the
33772 fraction bar is round about three times the bar thickness.
33775 \begin_layout Subsection
33777 \begin_inset Index idx
33780 \begin_layout Plain Layout
33789 \begin_layout Standard
33790 There are four ways to cancel formulas or parts of formulas:
33793 \begin_layout Standard
33797 \begin_layout Plain Layout
33807 \begin_inset Note Note
33810 \begin_layout Plain Layout
33811 The following table will only be displayed when the LaTeX-package
33823 \begin_layout Standard
33825 \begin_inset Tabular
33826 <lyxtabular version="3" rows="5" columns="2">
33827 <features rotate="0" tabularvalignment="middle">
33828 <column alignment="center" valignment="top">
33829 <column alignment="center" valignment="top">
33831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33834 \begin_layout Plain Layout
33840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33843 \begin_layout Plain Layout
33845 \begin_inset Note Note
33848 \begin_layout Plain Layout
33855 are used here as spacer.
33867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33870 \begin_layout Plain Layout
33874 \begin_inset space \textvisiblespace{}
33880 \begin_inset space \textvisiblespace{}
33888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33891 \begin_layout Plain Layout
33892 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33905 \begin_layout Plain Layout
33909 \begin_inset space \textvisiblespace{}
33915 \begin_inset space \textvisiblespace{}
33923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33926 \begin_layout Plain Layout
33927 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33940 \begin_layout Plain Layout
33944 \begin_inset space \textvisiblespace{}
33950 \begin_inset space \textvisiblespace{}
33958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33961 \begin_layout Plain Layout
33962 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33975 \begin_layout Plain Layout
33979 \begin_inset space \textvisiblespace{}
33985 \begin_inset space \textvisiblespace{}
33989 \begin_inset Formula $\to$
33997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34000 \begin_layout Plain Layout
34001 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34017 \begin_layout Standard
34024 is especially suitable to visualize the reduction of fractions within formulas:
34025 \begin_inset Formula
34027 \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}}}
34035 \begin_layout Standard
34036 To change the size of
34043 \begin_inset Quotes eld
34047 \begin_inset Quotes erd
34050 value one can add the LaTeX-preamble line
34053 \begin_layout Standard
34058 PassOptionsToPackage{option}{cancel}
34061 \begin_layout Standard
34070 which leads to the same size as for the canceled value, or
34074 which makes is it a bit smaller than normal.
34077 \begin_layout Standard
34078 To color the cancellation bar one adds this command as TeX code:
34081 \begin_layout Standard
34093 \begin_layout Standard
34098 can be replaced by a color of your choice.
34101 \begin_layout Standard
34105 \begin_layout Plain Layout
34121 \begin_layout Standard
34122 \begin_inset Formula
34124 \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}}}
34132 \begin_layout Standard
34136 \begin_layout Plain Layout
34150 \begin_inset Note Note
34153 \begin_layout Plain Layout
34162 \begin_layout Standard
34163 For further customizations, see the documentation of the package
34168 \begin_inset CommandInset citation
34175 \begin_inset Index idx
34178 \begin_layout Plain Layout
34187 \begin_layout Standard
34191 \begin_layout Plain Layout
34201 \begin_inset Note Note
34204 \begin_layout Plain Layout
34205 The following will be displayed when the LaTeX-package
34217 \begin_layout Standard
34218 You need to install the LaTeX-package
34222 to see the rest of this subsection in the output.
34225 \begin_layout Standard
34229 \begin_layout Plain Layout
34241 \begin_layout Standard
34242 \begin_inset Newpage newpage
34248 \begin_layout Subsection
34249 Formulas in Section Headings
34250 \begin_inset CommandInset label
34252 name "sub:Formulas-in-Section"
34257 \begin_inset Index idx
34260 \begin_layout Plain Layout
34261 Formula ! in section headings
34269 \begin_layout Standard
34270 When formulas are used in section headings, the following has to be taken
34274 \begin_layout Standard
34275 \begin_inset Note Greyedout
34278 \begin_layout Plain Layout
34284 \begin_inset Index idx
34287 \begin_layout Plain Layout
34288 Packages ! hyperref
34293 support is enabled in the document settings dialog under
34296 \begin_inset space ~
34301 , PDF-bookmarks are created for every section heading in the table of contents.
34302 If a section heading contains formulas, they are incorrectly displayed
34303 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34312 \begin_layout Standard
34313 Both problems can be solved by inserting at the end of the section heading
34314 a short title with the menu
34316 Insert\SpecialChar \menuseparator
34318 \begin_inset space ~
34324 Short titles are used as alternative for multiline section headings to
34325 keep the table of contents clearly arranged.
34326 Only the short title appears in the table of contents and therefore also
34327 in the PDF-bookmark.
34330 \begin_layout Standard
34331 When formulas should be used in the table of contents but
34335 is used, one can use the following command in TeX-mode:
34338 \begin_layout Standard
34343 texorpdfstring{part}{alternative}
34344 \begin_inset Index idx
34347 \begin_layout Plain Layout
34358 \begin_layout Standard
34359 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34360 This can be characters, formulas, footnotes, but also cross-references.
34361 The alternative is used instead of the part for the bookmark.
34364 \begin_layout Standard
34365 Here are two example headings:
34366 \begin_inset VSpace -3mm
34373 \begin_layout Plain Layout
34385 \begin_layout Subsubsection
34386 Heading without formula in table of contents
34387 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34391 \begin_inset Argument 1
34394 \begin_layout Plain Layout
34395 Heading without formula in table of contents
34403 \begin_layout Subsubsection
34404 Heading with formula in table of contents
34408 \begin_layout Plain Layout
34418 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34425 \begin_layout Plain Layout
34435 \begin_layout Standard
34439 \begin_layout Plain Layout
34448 In the first heading a short title was used, in the second one
34457 \begin_layout Standard
34458 To get the same formatting as for the other headings, the complete heading
34467 \begin_layout Plain Layout
34469 \begin_inset CommandInset ref
34471 reference "sub:Bold-Formulas"
34483 \begin_layout Subsection
34484 Formulas in multi-column Text
34485 \begin_inset Index idx
34488 \begin_layout Plain Layout
34489 Formula ! in multi-column text
34497 \begin_layout Standard
34498 Formulas in multi-column text are often too wide to fit into a column and
34499 thus need to be set over the whole page width.
34500 This is done by using the LaTeX-package
34508 \begin_layout Plain Layout
34513 is part of every LaTeX standard installation.
34519 \begin_inset Index idx
34522 \begin_layout Plain Layout
34523 Packages ! multicol
34528 , that is loaded with the LaTeX-preamble line
34531 \begin_layout Standard
34536 usepackage{multicol}
34539 \begin_layout Standard
34540 \begin_inset Note Greyedout
34543 \begin_layout Plain Layout
34544 Note that in this case the setting
34547 \begin_inset space ~
34554 Document\SpecialChar \menuseparator
34560 \begin_inset space ~
34580 \begin_layout Standard
34581 Before the multi-column text the command
34584 \begin_layout Standard
34589 begin{multicols}{column number}
34592 \begin_layout Standard
34593 is written in TeX-mode.
34594 The column number is a number in the range of 2
34595 \begin_inset space \thinspace{}
34599 \begin_inset space \thinspace{}
34603 Before the formula the multi-column text is ended by inserting the command
34606 \begin_layout Standard
34614 \begin_layout Standard
34618 \begin_layout Standard
34619 Due to the command some space is automatically added before the formula.
34621 \begin_inset space \thinspace{}
34624 mm vertical space is inserted before the formula.
34625 When the formula style
34631 \begin_layout Plain Layout
34633 \begin_inset CommandInset ref
34635 reference "sec:Formula-Styles"
34647 \begin_inset space \thinspace{}
34650 mm space is inserted instead.
34653 \begin_layout Standard
34654 As example a multi-column text with a displayed formula:
34657 \begin_layout Standard
34663 \begin_layout Plain Layout
34667 begin{multicols}{2}
34672 Das Spektrum wird fouriertransformiert.
34673 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
34674 , Lösungsmittel) zu trennen.
34675 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
34676 nun das Aussehen des Ausgangssignals.
34677 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
34678 über alle Phasen integrieren muss.
34680 \begin_inset Formula $S$
34683 unser normiertes Ausgangssignal und
34684 \begin_inset Formula $P$
34687 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
34691 \begin_layout Plain Layout
34701 \begin_inset VSpace -6mm
34705 \begin_inset Formula
34707 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
34716 \begin_layout Plain Layout
34720 begin{multicols}{2}
34726 \begin_inset Formula $S_{0}$
34729 das Signal ohne Gradient ist und die Normierungsbedingung
34730 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34734 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
34736 \begin_inset Formula $\nicefrac{\pi}{2}$
34740 \begin_inset space \thinspace{}
34743 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
34744 das Signal zusätzlich abschwächt.
34745 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
34747 \begin_inset Formula $T_{2}$
34753 \begin_layout Standard
34759 \begin_layout Plain Layout
34771 \begin_layout Subsection
34772 Formulas with Description of Variables
34773 \begin_inset Index idx
34776 \begin_layout Plain Layout
34777 Formula ! with description of variables
34785 \begin_layout Standard
34786 To describe variables within a formula, like in formula
34787 \begin_inset CommandInset ref
34789 reference "eq:within"
34798 \begin_inset Formula $n$
34802 \begin_inset space ~
34805 matrix is used with left aligned columns for the
34806 \begin_inset Formula $n$
34813 \begin_layout Plain Layout
34815 \begin_inset CommandInset ref
34817 reference "sec:Matrices"
34826 To set the description in a smaller size, before the matrix e.
34827 \begin_inset space \thinspace{}
34831 \begin_inset space \space{}
34844 \begin_layout Plain Layout
34846 \begin_inset CommandInset ref
34848 reference "sub:Font-Sizes"
34860 \begin_layout Standard
34861 When the formula style
34867 \begin_layout Plain Layout
34869 \begin_inset CommandInset ref
34871 reference "sec:Formula-Styles"
34892 \begin_layout Plain Layout
34899 only works in formulas with the style
34904 \begin_inset CommandInset ref
34906 reference "sub:Variable-Space"
34915 is inserted before and after the matrix to have the same separation of
34916 the matrix from the equation and the side margin.
34919 \begin_layout Standard
34920 When the formula style
34924 is used, the method described in
34925 \begin_inset CommandInset ref
34927 reference "sub:Flalign-Environment"
34931 is used to indent formulas.
34933 \begin_inset CommandInset ref
34935 reference "eq:within"
34939 consists of five columns where in the first two columns contain the equation,
34940 the third the matrix and the last one an empty TeX-brace.
34941 \begin_inset Formula
34943 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
34944 \rho & \textrm{density}\\
34945 V & \textrm{volume}\\
34946 g & \textrm{gravitational acceleration}
34947 \end{array} & & {}\label{eq:within}
34955 \begin_layout Subsection
34956 Upright small Greek Letters
34957 \begin_inset CommandInset label
34959 name "sub:Upright-small-Greek"
34964 \begin_inset Index idx
34967 \begin_layout Plain Layout
34968 Greek letters ! upright
34976 \begin_layout Standard
34977 Most of the math fonts only provide italic small Greek letters.
34978 But for symbols of elementary particles like pions and neutrinos, upright
34979 Greek letters are needed.
34988 \begin_layout Plain Layout
34993 is part of the LaTeX-package
34998 \begin_inset Index idx
35001 \begin_layout Plain Layout
35006 \begin_layout Plain Layout
35026 \begin_inset Index idx
35029 \begin_layout Plain Layout
35035 that is loaded with the LaTeX-preamble line
35038 \begin_layout Standard
35043 usepackage{upgreek}
35046 \begin_layout Standard
35052 \begin_layout Plain Layout
35062 \begin_inset Note Note
35065 \begin_layout Plain Layout
35066 The following table will only be displayed when the LaTeX-package
35075 They are created when the command for a small Greek letter is started with
35081 For example the command
35088 \begin_inset Formula $\uptau$
35094 \begin_layout Standard
35095 With these commands reactions of elementary particles can be typeset:
35096 \begin_inset Formula
35098 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
35106 \begin_layout Standard
35107 The upright letters are more bold and wider than the italic ones.
35108 They should therefore not be used for units like
35109 \begin_inset Quotes eld
35113 \begin_inset Quotes erd
35119 \begin_layout Standard
35123 \begin_layout Plain Layout
35133 \begin_inset Note Note
35136 \begin_layout Plain Layout
35137 The following will be displayed when the LaTeX-package
35149 \begin_layout Standard
35150 You need to install the LaTeX-package
35154 to see the rest of this subsection in the output.
35157 \begin_layout Standard
35161 \begin_layout Plain Layout
35173 \begin_layout Subsection
35174 Text Characters in Formulas
35175 \begin_inset CommandInset label
35177 name "sub:Text-Characters-in"
35182 \begin_inset Index idx
35185 \begin_layout Plain Layout
35194 \begin_layout Standard
35195 In some cases you might want to insert text characters directly into formulas.
35196 When for example the centered dot · is often used in formulas like
35197 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35200 , one would have to insert the command
35210 \begin_layout Plain Layout
35212 \begin_inset CommandInset ref
35214 reference "sub:Binary-Operators"
35223 all the time, because this character is defined in all encodings as text
35225 But the encoding can be changed by this LaTeX-preamble line:
35228 \begin_layout Standard
35233 Declare Inputtext{183}{
35243 f\SpecialChar \textcompwordmark{}
35247 \begin_layout Standard
35248 The character encoding (menu
35250 Document\SpecialChar \menuseparator
35251 Settings\SpecialChar \menuseparator
35254 ) specifies what character appears when a keyboard key is pressed.
35255 When the key for the character '·' is pressed, internally the command
35262 But this command is not available in a formula so that you would get LaTeX-erro
35264 With the changed encoding the right command is chosen automatically, depending
35265 on if the character was inserted into a formula or not.
35268 \begin_layout Standard
35269 The encoding of several characters is saved in definition files.
35270 For example the encoding
35274 is defined in the file
35278 which is in the installation folder of LaTeX.
35279 Encodings should only be changed via the LaTeX-preamble and not in the
35281 Otherwise documents could not be edited by other LyX users working on other
35285 \begin_layout Standard
35286 \begin_inset VSpace medskip
35289 Besides the centered dot, in this document the degree sign ° is defined
35290 with the following LaTeX-preamble line so that it can be directly inserted
35294 \begin_layout Standard
35299 DeclareInputtext{176}{
35309 f\SpecialChar \textcompwordmark{}
35313 \begin_layout Standard
35314 \begin_inset Newpage newpage
35320 \begin_layout Section
35323 \begin_inset Index idx
35326 \begin_layout Plain Layout
35335 \begin_layout Standard
35336 This section is a summary of the most important typographic rules, listed
35341 \begin_layout Plain Layout
35342 This collection was partly taken from the German semi-official dictionary
35344 \begin_inset Quotes eld
35348 \begin_inset Quotes erd
35352 \begin_inset CommandInset citation
35358 that lists some of the ISO rules.
35359 More rules are listed in
35360 \begin_inset CommandInset citation
35374 \begin_layout Itemize
35383 \begin_layout Plain Layout
35384 done with font styles, see
35385 \begin_inset CommandInset ref
35387 reference "sub:Font-Styles"
35396 , no matter if they appear in italic text: 30
35397 \begin_inset space \thinspace{}
35401 \begin_inset Newline newline
35404 Between the value and the unit is the smallest space, see
35405 \begin_inset CommandInset ref
35407 reference "sub:Predefined-Space"
35412 \begin_inset Newline newline
35415 This convention is automatically fulfilled when the command
35422 When it is entered to a formula, two boxes appear.
35423 In the first one the value is inserted, in the second one the unit, and
35425 \begin_inset Formula $\unit[30]{km/h}$
35429 \begin_inset space \thinspace{}
35439 is not a real LaTeX command but the command
35445 , therefore you cannot use it in TeX code.
35448 \begin_layout Itemize
35449 Percent and perthousand signs are set like physical units:
35450 \begin_inset Newline newline
35454 \begin_inset space \thinspace{}
35460 \begin_layout Itemize
35461 The degree sign follows directly on the value: 15°, but not when it is used
35463 \begin_inset space \thinspace{}
35469 \begin_layout Itemize
35470 In numbers with more than four digits the smallest space is inserted before
35471 every third digit to group them:
35481 \begin_inset space \thinspace{}
35485 \begin_inset space \thinspace{}
35491 \begin_layout Itemize
35492 For dimensions like 120×90×40
35493 \begin_inset space \thinspace{}
35496 cm the multiplication sign
35497 \begin_inset Quotes eld
35501 \begin_inset Quotes erd
35505 It is available either via the command
35513 Insert\SpecialChar \menuseparator
35514 Special Character\SpecialChar \menuseparator
35520 \begin_layout Itemize
35521 Functions with names consisting of several letters are set upright to avoid
35523 \begin_inset CommandInset ref
35525 reference "sub:Predefined-Functions"
35532 \begin_layout Itemize
35533 Indices consisting of several letters, are set upright:
35534 \begin_inset Formula $E_{\mathrm{kin}}$
35538 \begin_inset Newline newline
35541 Components of matrices are set italic:
35542 \begin_inset Formula $\hat{H}_{kl}$
35548 \begin_layout Itemize
35549 The differentiation/integration operator 'd', the Euler's number 'e' and
35550 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35554 \begin_layout Itemize
35555 The character that denotes a
35559 transformation is inserted either by the command
35564 \begin_inset space \textvisiblespace{}
35571 Insert\SpecialChar \menuseparator
35572 Special Character\SpecialChar \menuseparator
35573 Symbols\SpecialChar \menuseparator
35575 \begin_inset space ~
35581 \begin_inset Formula $\mathscr{F}$
35587 \begin_layout Standard
35588 \begin_inset Newpage newpage
35594 \begin_layout Section
35596 \begin_inset Index idx
35599 \begin_layout Plain Layout
35608 \begin_layout Standard
35609 Some characters and symbols can be created with several commands.
35610 Here is a list of the synonym commands:
35613 \begin_layout Standard
35614 \begin_inset VSpace bigskip
35618 \begin_inset space \hfill{}
35622 \begin_inset Tabular
35623 <lyxtabular version="3" rows="12" columns="2">
35624 <features rotate="0" tabularvalignment="middle">
35625 <column alignment="center" valignment="top" width="0pt">
35626 <column alignment="center" valignment="top" width="0pt">
35628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35631 \begin_layout Plain Layout
35637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35640 \begin_layout Plain Layout
35642 \begin_inset Note Note
35645 \begin_layout Plain Layout
35652 is only used as spacer.
35664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35667 \begin_layout Plain Layout
35675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35678 \begin_layout Plain Layout
35682 \begin_layout Plain Layout
35695 \begin_layout Plain Layout
35709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35712 \begin_layout Plain Layout
35720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35723 \begin_layout Plain Layout
35733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35736 \begin_layout Plain Layout
35744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35747 \begin_layout Plain Layout
35757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35760 \begin_layout Plain Layout
35768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35771 \begin_layout Plain Layout
35779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35782 \begin_layout Plain Layout
35790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35793 \begin_layout Plain Layout
35801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35804 \begin_layout Plain Layout
35812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35815 \begin_layout Plain Layout
35825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35828 \begin_layout Plain Layout
35836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35839 \begin_layout Plain Layout
35849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35852 \begin_layout Plain Layout
35860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35863 \begin_layout Plain Layout
35873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35876 \begin_layout Plain Layout
35884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35887 \begin_layout Plain Layout
35897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35900 \begin_layout Plain Layout
35908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35911 \begin_layout Plain Layout
35919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35922 \begin_layout Plain Layout
35930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35933 \begin_layout Plain Layout
35945 \begin_inset space \hfill{}
35949 \begin_inset Tabular
35950 <lyxtabular version="3" rows="12" columns="2">
35951 <features rotate="0" tabularvalignment="middle">
35952 <column alignment="center" valignment="top" width="0pt">
35953 <column alignment="center" valignment="top" width="0pt">
35955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35958 \begin_layout Plain Layout
35964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35967 \begin_layout Plain Layout
35975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35978 \begin_layout Plain Layout
35986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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36493 Auflage, Duden 2001
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