1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
5 \origin /systemlyxdir/doc/
8 % DO NOT ALTER THIS PREAMBLE!!!
10 % This preamble is designed to ensure that the file prints
11 % out as advertised. If you mess with this preamble,
12 % parts of this document may not print out as expected. If you
13 % have problems LaTeXing this file, please contact
14 % the documentation team
15 % email: lyx-docs@lists.lyx.org
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 \fi % end if pdflatex is used
27 % solves the following problem:
28 % If the dection number consits of too many numerals the section heading
29 % will be printed in the TOC without a space between it and the section number.
30 % As solution more space between the number and the heading is inserted:
31 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
32 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
34 % increase link area for cross-references and autoname them,
35 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
36 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
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42 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
46 % don't load packages twice
47 % see first footnote in sec. 9.3
48 \@ifundefined{textcolor}{\usepackage{color}}{}
50 % the pages of the TOC are numbered roman
51 % and a PDF-bookmark for the TOC is added
53 \let\myTOC\tableofcontents
54 \renewcommand{\tableofcontents}{%
56 \pdfbookmark[1]{\contentsname}{}
59 \pagenumbering{arabic}}
61 % add 0.5 mm vertical space for table rows
62 \@ifundefined{extrarowheight} {\usepackage{array}}{}
63 \setlength{\extrarowheight}{0.5mm}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % makes caption labels bold
70 \setkomafont{captionlabel}{\bfseries}
72 % enables calculation of values
75 % for multiple columns used in sec. 24.7
81 % for the Fourier transformation symbol
84 % define a color, used in sec.9.3
85 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
87 % declare operators (see sec. 10.4 and sec. 15.2)
88 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
89 \DeclareMathOperator{\sgn}{sgn}
91 % example definitions for sec. 20.1
92 \newcommand{\gr}{\Longrightarrow}
93 \newcommand{\us}[1]{\underline{#1}}
94 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
95 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
96 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
98 % example macro from sec. 19.4
99 %\def\tagform@#1{\maketag@@@{|#1|}}
102 % ------------------------------------
103 % used to check for needed LaTeX packages
106 % check for package undertilde
107 % used for the command \utilde
108 \newboolean{undertilde}
109 \IfFileExists{undertilde.sty}
110 {\usepackage{undertilde}
111 \setboolean{undertilde}{true}}
112 {\setboolean{undertilde}{false}}
114 % check for package eurosym
115 % used for the Euro symbol
117 \IfFileExists{eurosym.sty}
118 {\usepackage[gennarrow]{eurosym}
119 \setboolean{eurosym}{true}}
120 {\setboolean{eurosym}{false}}
122 % check for package braket
123 % used for physical vectors
125 \IfFileExists{braket.sty}
127 \setboolean{braket}{true}}
128 {\setboolean{braket}{false}}
130 % check for package cancel
132 \IfFileExists{cancel.sty}
134 \setboolean{cancel}{true}}
135 {\setboolean{cancel}{false}}
137 % check for package upgreek
139 \IfFileExists{upgreek.sty}
140 {\usepackage{upgreek}
141 \setboolean{upgreek}{true}}
142 {\setboolean{upgreek}{false}}
144 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
145 \use_default_options false
146 \maintain_unincluded_children false
148 \language_package default
151 \font_roman "default" "default"
152 \font_sans "default" "default"
153 \font_typewriter "default" "default"
154 \font_math "auto" "auto"
155 \font_default_family default
156 \use_non_tex_fonts false
159 \font_sf_scale 100 100
160 \font_tt_scale 100 100
162 \default_output_format default
164 \bibtex_command default
165 \index_command default
169 \pdf_title "LyX's Math Manual"
170 \pdf_author "LyX Team, Uwe Stöhr"
171 \pdf_subject "LyX-documentation about math"
172 \pdf_keywords "LyX, Mathed"
174 \pdf_bookmarksnumbered true
175 \pdf_bookmarksopen true
176 \pdf_bookmarksopenlevel 1
177 \pdf_breaklinks false
181 \pdf_pdfusetitle false
182 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
185 \use_package amsmath 2
186 \use_package amssymb 2
187 \use_package cancel 0
189 \use_package mathdots 1
190 \use_package mathtools 2
191 \use_package mhchem 1
192 \use_package stackrel 0
193 \use_package stmaryrd 0
194 \use_package undertilde 0
196 \cite_engine_type default
200 \paperorientation portrait
204 \notefontcolor #0000ff
211 \paragraph_separation skip
213 \quotes_language english
216 \paperpagestyle plain
220 \tracking_changes false
221 \output_changes false
224 \html_be_strict false
231 's detailed Math manual
235 by the \SpecialChar LyX
240 \begin_layout Plain Layout
242 If you have comments or error corrections, please send them to the \SpecialChar LyX
247 \begin_inset CommandInset href
249 name "lyx-docs@lists.lyx.org"
250 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
261 \begin_inset Note Note
264 \begin_layout Plain Layout
271 \begin_inset Newline newline
275 \begin_inset Newline newline
283 \begin_layout Standard
284 \begin_inset CommandInset toc
285 LatexCommand tableofcontents
292 \begin_layout Standard
293 \begin_inset Note Note
296 \begin_layout Plain Layout
297 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
300 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
307 If they are not installed the document can be exported anyway but the sections
308 where the packages are required will not appear in the output.
313 ; if it is not installed, this file cannot be exported.
316 \begin_layout Plain Layout
317 The latest PDF-version of this document can be found here:
318 \begin_inset Newline newline
323 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
331 \begin_layout Standard
332 \begin_inset Newpage newpage
338 \begin_layout Section
342 \begin_layout Standard
343 This document explains \SpecialChar LyX
344 's math features and is furthermore a collection
345 of \SpecialChar LaTeX
346 -commands used for mathematical characters and constructs.
347 The explanations are designed for the usage of commands.
348 It is therefore required that you have read the section
359 \begin_layout Standard
360 Most of the characters and many constructs explained in this manual are
361 also accessible via the menu
365 \SpecialChar menuseparator
381 But everybody who has to write lots of formulas will notice that it is
382 much faster to use commands instead of the math toolbar.
383 Therefore this manual is focused on commands but also mentions the correspondin
384 g toolbar buttons when available.
387 \begin_layout Standard
388 If not specially mentioned the commands are only available within formulas.
389 To be able to use all commands explained in this document, the option
393 must be checked in the document settings (menu
395 Document\SpecialChar menuseparator
396 Settings\SpecialChar menuseparator
407 \begin_layout Plain Layout
410 Use AMS math package automatically
416 \begin_layout Plain Layout
425 -math when math constructs are found that are supported by \SpecialChar LyX
434 \begin_layout Standard
435 This document doesn't list all
439 \begin_layout Plain Layout
452 \begin_layout Plain Layout
457 \begin_layout Plain Layout
466 -math commands is in the file
469 \begin_inset CommandInset href
472 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
478 , which is part of every \SpecialChar LaTeX
479 standard installation.
484 for lucidity reasons.
487 \begin_layout Section
491 \begin_layout Standard
492 To create an inline formula
493 \begin_inset Index idx
496 \begin_layout Plain Layout
502 that is embedded into a text line, use one of the shortcuts
508 or the toolbar button
515 \begin_inset Newline newline
518 To create a display style formula
519 \begin_inset Index idx
522 \begin_layout Plain Layout
523 Formula ! display style
528 which will appear bigger, has a different format, and will be in a separate
529 paragraph, use one of these shortcuts:
538 \begin_layout Standard
539 To change a display style formula to an inline formula, set the cursor into
540 the formula and use one of the shortcuts
548 Edit\SpecialChar menuseparator
549 Math\SpecialChar menuseparator
553 The same way is used to change an inline formula to a display style formula.
556 \begin_layout Standard
557 To display parts of an inline formula in the size of a display style formula,
565 \begin_inset Index idx
568 \begin_layout Plain Layout
577 Then a new blue box appears in which the desired formula part is inserted.
580 \begin_layout Standard
581 Only inline formulas are allowed inside tables.
584 \begin_layout Standard
589 can be turned on in the menu
591 View\SpecialChar menuseparator
595 When you click there on
596 \begin_inset Quotes eld
600 \begin_inset Quotes erd
603 the toolbar will be shown permanently at the bottom; this state is visualized
608 menu with a checkmark.
609 When you click in this state again on
610 \begin_inset Quotes eld
614 \begin_inset Quotes erd
625 is only shown when the cursor is within a formula; this state is visualized
626 by the renaming of the menu entry from
627 \begin_inset Quotes eld
631 \begin_inset Quotes erd
635 \begin_inset Quotes eld
643 \begin_inset Quotes erd
649 \begin_layout Standard
652 \begin_inset Index idx
655 \begin_layout Plain Layout
662 is invoked by pressing the toolbar button
670 Insert\SpecialChar menuseparator
682 \begin_layout Standard
683 To change the \SpecialChar LaTeX
685 \begin_inset Index idx
688 \begin_layout Plain Layout
697 Document\SpecialChar menuseparator
698 Settings\SpecialChar menuseparator
708 \begin_layout Standard
709 To edit matrices, case differentiations and multiline formulas subsequently,
712 Edit\SpecialChar menuseparator
717 Edit\SpecialChar menuseparator
719 \begin_inset space \thinspace{}
723 \begin_inset space \thinspace{}
733 When lines and columns are swapped via the menu, the column or line where
734 the cursor is in is exchanged with the column to the right or the line
736 Is the cursor in the last column or row, the exchange is done with the
737 column to the left or the line above.
740 \begin_layout Standard
741 To write text in formulas
745 \begin_layout Plain Layout
746 For multiline formulas the command
753 \begin_inset CommandInset ref
755 reference "subsec:Text-in-multiline"
769 \begin_inset Index idx
772 \begin_layout Plain Layout
779 \begin_inset Index idx
782 \begin_layout Plain Layout
789 This mode is invoked with the shortcut
795 or by the insertion of the command
802 \begin_inset Index idx
805 \begin_layout Plain Layout
814 The text appears black in \SpecialChar LyX
815 and can therefore be distinguished from the
816 other formula parts which appear blue.
817 In the output mathematical text is set upright, in contrary to other formula
821 \begin_layout Subsection*
825 \begin_layout Standard
826 Most of the \SpecialChar LaTeX
827 -commands for math constructs have the following scheme:
830 \begin_layout Standard
846 \begin_layout Standard
847 A command always starts with a backslash
848 \begin_inset Quotes gld
858 \begin_inset Quotes grd
862 To omit optional arguments, also omit the associated brackets.
863 The braces around the required arguments are named in this document as
866 \begin_inset Index idx
869 \begin_layout Plain Layout
877 If you add in a formula a left brace to a command name, \SpecialChar LyX
879 creates a \SpecialChar TeX
881 In all other cases \SpecialChar TeX
882 braces are created in formulas with the command
890 braces appear red in \SpecialChar LyX
891 , in contrary to normal braces which appear blue.
893 mode no command is needed to get \SpecialChar TeX
896 braces don't appear in the output.
899 \begin_layout Standard
900 When commands without arguments, like commands for symbols are entered in
902 mode, a space character must
906 be behind the command to end it.
907 This space doesn't appear in the output.
908 When the space should appear in the output, the space must be followed
909 by a protected space in normal text.
912 \begin_layout Standard
913 A protected space is inserted with
916 arg "command-alternatives space-insert protected ; math-space"
922 \begin_layout Subsection*
923 \begin_inset Newpage newpage
929 \begin_layout Itemize
931 \begin_inset space \textvisiblespace{}
934 denotes a space character to be input.
937 \begin_layout Itemize
939 \begin_inset Formula $\to$
942 denotes the usage of the corresponding arrow key on the keyboard.
947 key can often be used instead of
948 \begin_inset Formula $\to$
952 \begin_inset Formula $\downarrow$
960 \begin_inset Formula $\leftarrow$
964 \begin_inset Formula $\uparrow$
970 \begin_layout Subsection*
974 \begin_layout Standard
976 \begin_inset Float table
982 \begin_layout Plain Layout
984 \begin_inset Caption Standard
986 \begin_layout Plain Layout
987 \begin_inset CommandInset label
989 name "tab:Available-units"
1001 \begin_layout Plain Layout
1003 \begin_inset Tabular
1004 <lyxtabular version="3" rows="13" columns="2">
1005 <features booktabs="true" tabularvalignment="middle">
1006 <column alignment="center" valignment="top">
1007 <column alignment="center" valignment="top" width="0pt">
1009 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1012 \begin_layout Plain Layout
1018 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1021 \begin_layout Plain Layout
1029 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1032 \begin_layout Plain Layout
1038 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1041 \begin_layout Plain Layout
1049 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1052 \begin_layout Plain Layout
1058 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1061 \begin_layout Plain Layout
1069 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1072 \begin_layout Plain Layout
1078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1081 \begin_layout Plain Layout
1083 \begin_inset space \thinspace{}
1087 \begin_inset space \thinspace{}
1097 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1100 \begin_layout Plain Layout
1106 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1109 \begin_layout Plain Layout
1111 \begin_inset space \thinspace{}
1115 \begin_inset space \thinspace{}
1125 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1128 \begin_layout Plain Layout
1134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1137 \begin_layout Plain Layout
1139 \begin_inset space \thinspace{}
1143 \begin_inset space \thinspace{}
1153 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1156 \begin_layout Plain Layout
1162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1165 \begin_layout Plain Layout
1167 \begin_inset space \thinspace{}
1171 \begin_inset space \thinspace{}
1181 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1184 \begin_layout Plain Layout
1190 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1193 \begin_layout Plain Layout
1195 \begin_inset space \thinspace{}
1199 \begin_inset space \thinspace{}
1209 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1212 \begin_layout Plain Layout
1218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1221 \begin_layout Plain Layout
1223 \begin_inset space \thinspace{}
1227 \begin_inset Formula $\approx$
1231 \begin_inset space \thinspace{}
1241 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1244 \begin_layout Plain Layout
1250 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1253 \begin_layout Plain Layout
1255 \begin_inset space \thinspace{}
1259 \begin_inset space \thinspace{}
1269 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1272 \begin_layout Plain Layout
1278 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1281 \begin_layout Plain Layout
1285 \begin_inset Quotes eld
1291 \begin_inset Quotes erd
1301 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1304 \begin_layout Plain Layout
1310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1313 \begin_layout Plain Layout
1315 \begin_inset Quotes eld
1323 \begin_inset Quotes erd
1333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1336 \begin_layout Plain Layout
1342 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1345 \begin_layout Plain Layout
1347 \begin_inset space \thinspace{}
1351 \begin_inset Formula $\nicefrac{1}{18}$
1355 \begin_inset space \thinspace{}
1376 \begin_layout Standard
1377 \begin_inset Newpage newpage
1383 \begin_layout Section
1387 \begin_layout Subsection
1389 \begin_inset Index idx
1392 \begin_layout Plain Layout
1399 \begin_inset Index idx
1402 \begin_layout Plain Layout
1409 \begin_inset Index idx
1412 \begin_layout Plain Layout
1417 \begin_layout Plain Layout
1428 \begin_layout Plain Layout
1441 \begin_inset Index idx
1444 \begin_layout Plain Layout
1449 \begin_layout Plain Layout
1460 \begin_layout Plain Layout
1475 \begin_layout Standard
1476 Indices are created with an underscore
1477 \begin_inset Quotes eld
1481 \begin_inset Quotes erd
1484 or via the math toolbar button
1487 arg "math-subscript"
1490 , exponents with a caret
1491 \begin_inset Quotes eld
1495 \begin_inset Quotes erd
1498 or via the math toolbar button
1501 arg "math-superscript"
1505 \begin_inset Separator parbreak
1511 \begin_layout Standard
1513 \begin_inset Tabular
1514 <lyxtabular version="3" rows="4" columns="2">
1515 <features booktabs="true" tabularvalignment="middle">
1516 <column alignment="center" valignment="top" width="0pt">
1517 <column alignment="center" valignment="top" width="0pt">
1519 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1522 \begin_layout Plain Layout
1528 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1531 \begin_layout Plain Layout
1539 <cell alignment="center" valignment="top" usebox="none">
1542 \begin_layout Plain Layout
1548 <cell alignment="center" valignment="top" usebox="none">
1551 \begin_layout Plain Layout
1552 \begin_inset Formula $B_{V}$
1561 <row topspace="1.5mm">
1562 <cell alignment="center" valignment="top" usebox="none">
1565 \begin_layout Plain Layout
1571 <cell alignment="center" valignment="top" usebox="none">
1574 \begin_layout Plain Layout
1575 \begin_inset Formula $B^{V}$
1584 <row topspace="1.5mm">
1585 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1588 \begin_layout Plain Layout
1590 \begin_inset space \textvisiblespace{}
1598 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1601 \begin_layout Plain Layout
1602 \begin_inset Formula $B^{A}$
1618 \begin_layout Standard
1619 As the caret is in some languages an accent, vowels will be accentuated
1620 in this case and not set as exponents
1624 \begin_layout Plain Layout
1625 Depending on the used keyboard settings this can also happen for characters
1632 To get exponents in this case, press
1636 after the caret as in the last example.
1639 \begin_layout Subsection
1641 \begin_inset CommandInset label
1643 name "subsec:Fractions"
1648 \begin_inset Index idx
1651 \begin_layout Plain Layout
1660 \begin_layout Standard
1661 Fractions are generated with the command
1668 \begin_inset Index idx
1671 \begin_layout Plain Layout
1679 or via the math toolbar button
1682 arg "math-insert \\frac"
1686 The font size is adjusted automatically, depending on whether the fraction
1687 is in an inline or display style formula.
1688 With the math toolbar button
1691 arg "math-insert \\frac-square"
1694 you can select different fraction types.
1697 \begin_layout Standard
1705 \begin_inset Index idx
1708 \begin_layout Plain Layout
1716 a fraction can be created that always has the size of a display style formula.
1724 \begin_inset Index idx
1727 \begin_layout Plain Layout
1735 the fraction appears always with the size of an inline formula.
1739 \begin_layout Standard
1740 A line with the fraction
1741 \begin_inset Formula $\frac{1}{2}$
1744 that was created with the command
1753 \begin_layout Standard
1754 A line with the fraction
1755 \begin_inset Formula $\dfrac{1}{2}$
1758 that was created with the command
1765 \begin_inset Separator parbreak
1771 \begin_layout Standard
1773 \begin_inset Tabular
1774 <lyxtabular version="3" rows="4" columns="2">
1775 <features booktabs="true" tabularvalignment="middle">
1776 <column alignment="center" valignment="top" width="0pt">
1777 <column alignment="center" valignment="top" width="0pt">
1779 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1782 \begin_layout Plain Layout
1788 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1791 \begin_layout Plain Layout
1798 <row topspace="1.5mm">
1799 <cell alignment="center" valignment="top" usebox="none">
1802 \begin_layout Plain Layout
1806 \begin_inset space \textvisiblespace{}
1810 \begin_inset Formula $\downarrow$
1818 <cell alignment="center" valignment="top" usebox="none">
1821 \begin_layout Plain Layout
1822 \begin_inset Formula $\frac{A}{B}$
1831 <row topspace="2mm">
1832 <cell alignment="center" valignment="top" usebox="none">
1835 \begin_layout Plain Layout
1839 \begin_inset space \textvisiblespace{}
1843 \begin_inset Formula $\downarrow$
1851 <cell alignment="center" valignment="top" usebox="none">
1854 \begin_layout Plain Layout
1855 \begin_inset Formula $\dfrac{A}{B}$
1864 <row topspace="2mm" bottomspace="1mm">
1865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1868 \begin_layout Plain Layout
1872 \begin_inset space \textvisiblespace{}
1878 \begin_inset space \textvisiblespace{}
1882 \begin_inset Formula $\downarrow$
1886 \begin_inset Formula $\downarrow\downarrow$
1894 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1897 \begin_layout Plain Layout
1898 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1914 \begin_layout Standard
1915 \begin_inset VSpace bigskip
1919 \begin_inset Newpage newpage
1922 For nested fractions the command
1929 \begin_inset Index idx
1932 \begin_layout Plain Layout
1942 \begin_inset VSpace -3mm
1948 \begin_layout Standard
1949 \begin_inset Formula
1951 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1952 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1960 \begin_layout Standard
1961 The command for the example above is:
1964 \begin_layout Standard
1970 \begin_inset space \textvisiblespace{}
1974 \begin_inset Formula $\downarrow$
1980 \begin_inset space \textvisiblespace{}
1986 \begin_inset space \textvisiblespace{}
1990 \begin_inset Formula $\downarrow$
1994 \begin_inset Formula $\downarrow$
2000 \begin_layout Standard
2001 \begin_inset VSpace medskip
2007 \begin_layout Standard
2014 sets the fraction always in the size of a displayed formula, also when
2015 it is part of another fraction.
2018 \begin_layout Standard
2019 It is possible to specify the alignment of the numerator.
2026 is used to left align it, the command
2039 centers the numerator.
2040 These fractions demonstrate the different alignments:
2043 \begin_layout Standard
2046 \begin_inset Formula
2048 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2056 \begin_layout Standard
2057 \begin_inset Note Greyedout
2060 \begin_layout Plain Layout
2077 are no real \SpecialChar LaTeX
2078 commands but represent the command
2082 cfrac[alignment]{numerator}{denominator}
2085 Therefore you cannot use them in \SpecialChar TeX
2094 \begin_layout Standard
2095 \begin_inset VSpace medskip
2098 It is often advantageous to combine
2111 \begin_inset Formula
2113 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2121 \begin_layout Standard
2122 For inline fractions with a sloped fraction stroke you can use the command
2130 \begin_inset Index idx
2133 \begin_layout Plain Layout
2142 \begin_inset Formula $\nicefrac{5}{31}$
2152 \begin_inset Index idx
2155 \begin_layout Plain Layout
2164 \begin_inset Formula $\unitfrac{5}{31}$
2167 There is furthermore the command
2173 that offers to write a fraction in combination with a number:
2174 \begin_inset Formula $\unitfrac[2]{1}{3}$
2180 \begin_layout Standard
2181 \begin_inset Note Greyedout
2184 \begin_layout Plain Layout
2195 is not a real \SpecialChar LaTeX
2196 command but the command
2197 \begin_inset Newline newline
2204 unitfrac[number]{numerator}{denominator}
2207 Therefore you cannot use it in \SpecialChar TeX
2216 \begin_layout Standard
2217 How to define own fractions where the fraction stroke can be changed, is
2219 \begin_inset CommandInset ref
2221 reference "subsec:Self-defined-Fractions"
2228 \begin_layout Standard
2229 Multiline fractions are explained in
2230 \begin_inset CommandInset ref
2232 reference "subsec:Multiline-Fractions"
2239 \begin_layout Subsection
2241 \begin_inset Index idx
2244 \begin_layout Plain Layout
2253 \begin_layout Standard
2254 Square roots are created with
2261 \begin_inset Index idx
2264 \begin_layout Plain Layout
2272 or the math toolbar button
2275 arg "math-insert \\sqrt"
2278 , all other roots with the command
2285 \begin_inset Index idx
2288 \begin_layout Plain Layout
2296 or with the math toolbar button
2299 arg "math-insert \\root"
2303 \begin_inset Separator parbreak
2309 \begin_layout Standard
2311 \begin_inset Tabular
2312 <lyxtabular version="3" rows="3" columns="2">
2313 <features booktabs="true" tabularvalignment="middle">
2314 <column alignment="center" valignment="top" width="0pt">
2315 <column alignment="center" valignment="top" width="0pt">
2317 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2320 \begin_layout Plain Layout
2326 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2329 \begin_layout Plain Layout
2336 <row topspace="1mm">
2337 <cell alignment="center" valignment="top" usebox="none">
2340 \begin_layout Plain Layout
2344 \begin_inset space \textvisiblespace{}
2352 <cell alignment="center" valignment="top" usebox="none">
2355 \begin_layout Plain Layout
2356 \begin_inset Formula $\sqrt{A-B}$
2365 <row topspace="1mm">
2366 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2369 \begin_layout Plain Layout
2373 \begin_inset space \textvisiblespace{}
2377 \begin_inset Formula $\downarrow$
2385 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2388 \begin_layout Plain Layout
2389 \begin_inset Formula $\sqrt[3]{A-B}$
2405 \begin_layout Standard
2406 A square root can also be created with
2412 when the root index field is left empty.
2415 \begin_layout Standard
2416 With certain indices the distance to the root is too small, like in this
2418 \begin_inset Formula $\sqrt[\beta]{B}$
2422 \begin_inset Newline newline
2426 \begin_inset Formula $\beta$
2430 To avoid this, the commands
2437 \begin_inset Index idx
2440 \begin_layout Plain Layout
2455 \begin_inset Index idx
2458 \begin_layout Plain Layout
2466 are used with the following scheme:
2469 \begin_layout Standard
2483 \begin_layout Standard
2484 Distance is the number of Big Points (unit bp;
2485 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2488 ), that the index should be moved to the left or top, resp..
2489 The commands are written to the index.
2490 This way the command
2491 \begin_inset Newline newline
2501 \begin_inset Formula $\to$
2507 \begin_inset Formula $\to$
2513 \begin_inset space \textvisiblespace{}
2517 \begin_inset Formula $\to$
2521 \begin_inset Newline newline
2526 produces a correct typeset formula:
2527 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2533 \begin_layout Subsection
2534 Binomial Coefficients
2535 \begin_inset Index idx
2538 \begin_layout Plain Layout
2539 Binomial coefficients
2547 \begin_layout Standard
2548 Binomial coefficients are inserted with the command
2555 \begin_inset Index idx
2558 \begin_layout Plain Layout
2566 or with the submenu of the math toolbar button
2569 arg "math-insert \\frac-square"
2585 there are the commands
2592 \begin_inset Index idx
2595 \begin_layout Plain Layout
2610 \begin_inset Index idx
2613 \begin_layout Plain Layout
2622 For other brackets around binomial coeficients there are the commands
2629 \begin_inset Index idx
2632 \begin_layout Plain Layout
2647 \begin_inset Index idx
2650 \begin_layout Plain Layout
2659 \begin_inset Separator parbreak
2665 \begin_layout Standard
2667 \begin_inset Tabular
2668 <lyxtabular version="3" rows="6" columns="2">
2669 <features booktabs="true" tabularvalignment="middle">
2670 <column alignment="center" valignment="top" width="0pt">
2671 <column alignment="center" valignment="top" width="0pt">
2673 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2676 \begin_layout Plain Layout
2682 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2685 \begin_layout Plain Layout
2692 <row topspace="1mm">
2693 <cell alignment="center" valignment="top" usebox="none">
2696 \begin_layout Plain Layout
2700 \begin_inset space \textvisiblespace{}
2704 \begin_inset Formula $\downarrow$
2712 <cell alignment="center" valignment="top" usebox="none">
2715 \begin_layout Plain Layout
2716 \begin_inset Formula $\binom{A}{B}$
2725 <row topspace="2mm">
2726 <cell alignment="center" valignment="top" usebox="none">
2729 \begin_layout Plain Layout
2733 \begin_inset space \textvisiblespace{}
2737 \begin_inset Formula $\downarrow$
2745 <cell alignment="center" valignment="top" usebox="none">
2748 \begin_layout Plain Layout
2749 \begin_inset Formula $\dbinom{A}{B}$
2758 <row topspace="2mm" bottomspace="0.5mm">
2759 <cell alignment="center" valignment="top" usebox="none">
2762 \begin_layout Plain Layout
2766 \begin_inset space \textvisiblespace{}
2770 \begin_inset Formula $\downarrow$
2778 <cell alignment="center" valignment="top" usebox="none">
2781 \begin_layout Plain Layout
2782 \begin_inset Formula $\tbinom{A}{B}$
2791 <row topspace="1mm">
2792 <cell alignment="center" valignment="top" topline="true" usebox="none">
2795 \begin_layout Plain Layout
2799 \begin_inset space \textvisiblespace{}
2803 \begin_inset Formula $\downarrow$
2811 <cell alignment="center" valignment="top" topline="true" usebox="none">
2814 \begin_layout Plain Layout
2815 \begin_inset Formula ${A \brack B}$
2824 <row topspace="2mm" bottomspace="0.5mm">
2825 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2828 \begin_layout Plain Layout
2832 \begin_inset space \textvisiblespace{}
2836 \begin_inset Formula $\downarrow$
2844 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2847 \begin_layout Plain Layout
2848 \begin_inset Formula ${A \brace B}$
2864 \begin_layout Subsection
2865 Case Differentiations
2866 \begin_inset Index idx
2869 \begin_layout Plain Layout
2870 Case differentiations
2878 \begin_layout Standard
2880 \begin_inset Tabular
2881 <lyxtabular version="3" rows="3" columns="2">
2882 <features booktabs="true" tabularvalignment="middle">
2883 <column alignment="center" valignment="top" width="0pt">
2884 <column alignment="center" valignment="top" width="0pt">
2886 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2889 \begin_layout Plain Layout
2895 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2898 \begin_layout Plain Layout
2906 <cell alignment="center" valignment="top" usebox="none">
2909 \begin_layout Plain Layout
2913 \begin_inset space \textvisiblespace{}
2917 \begin_inset Formula $\to$
2921 \begin_inset Index idx
2924 \begin_layout Plain Layout
2937 <cell alignment="center" valignment="top" usebox="none">
2940 \begin_layout Plain Layout
2941 \begin_inset Formula $\begin{cases}
2951 <row topspace="1.5mm">
2952 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2955 \begin_layout Plain Layout
2959 \begin_inset space \textvisiblespace{}
2965 arg "newline-insert newline"
2973 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2976 \begin_layout Plain Layout
2977 \begin_inset Formula $\begin{cases}
2978 A & \textrm{for }x>0\\
2979 B & \textrm{for }x=0
2996 \begin_layout Standard
3003 or pressing the math toolbar button
3006 arg "math-insert \\cases"
3009 you can create new lines with the shortcut
3012 arg "newline-insert newline"
3015 or the table toolbar button
3018 arg "inset-modify tabular append-row"
3024 \begin_layout Standard
3031 is also available via the menu
3033 Insert\SpecialChar menuseparator
3034 Math\SpecialChar menuseparator
3040 \begin_layout Subsection
3042 \begin_inset Index idx
3045 \begin_layout Plain Layout
3054 \begin_layout Standard
3062 \begin_inset Index idx
3065 \begin_layout Plain Layout
3073 every character can be displayed canceled.
3074 The characters are quasi accentuated by a slash.
3075 \begin_inset Separator parbreak
3081 \begin_layout Standard
3083 \begin_inset Tabular
3084 <lyxtabular version="3" rows="4" columns="2">
3085 <features booktabs="true" tabularvalignment="middle">
3086 <column alignment="center" valignment="top" width="0pt">
3087 <column alignment="center" valignment="top" width="0pt">
3089 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3092 \begin_layout Plain Layout
3098 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3101 \begin_layout Plain Layout
3109 <cell alignment="center" valignment="top" usebox="none">
3112 \begin_layout Plain Layout
3120 <cell alignment="center" valignment="top" usebox="none">
3123 \begin_layout Plain Layout
3124 \begin_inset Formula $\not=$
3134 <cell alignment="center" valignment="top" usebox="none">
3137 \begin_layout Plain Layout
3147 <cell alignment="center" valignment="top" usebox="none">
3150 \begin_layout Plain Layout
3151 \begin_inset Formula $\not\le$
3161 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3164 \begin_layout Plain Layout
3174 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3177 \begin_layout Plain Layout
3178 \begin_inset Formula $\not\parallel$
3194 \begin_layout Standard
3195 The last example shows that not all negations look good.
3196 Therefore there are special commands for some negations (see
3197 \begin_inset CommandInset ref
3199 reference "subsec:Mathematical-Symbols"
3204 \begin_inset CommandInset ref
3206 reference "sec:Relations"
3213 \begin_layout Subsection
3215 \begin_inset CommandInset label
3217 name "subsec:Placeholders"
3222 \begin_inset Index idx
3225 \begin_layout Plain Layout
3232 \begin_inset Index idx
3235 \begin_layout Plain Layout
3236 Chemical characters ! Isotopes
3242 \begin_inset Index idx
3245 \begin_layout Plain Layout
3250 \begin_layout Plain Layout
3261 \begin_layout Plain Layout
3276 \begin_layout Standard
3278 \begin_inset space \thinspace{}
3282 \begin_inset space \space{}
3289 \begin_layout Plain Layout
3290 Typesetting isotopes and chemical symbols is described in
3291 \begin_inset CommandInset ref
3293 reference "subsec:Chemical-Symbols-and"
3302 the following problem occurs:
3303 \begin_inset Separator parbreak
3309 \begin_layout Standard
3311 \begin_inset Tabular
3312 <lyxtabular version="3" rows="2" columns="2">
3313 <features booktabs="true" tabularvalignment="middle">
3314 <column alignment="center" valignment="top" width="0pt">
3315 <column alignment="center" valignment="top" width="0pt">
3317 <cell alignment="center" valignment="top" usebox="none">
3320 \begin_layout Plain Layout
3321 Indices created with sub- and superscripts:
3326 <cell alignment="center" valignment="top" usebox="none">
3329 \begin_layout Plain Layout
3330 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3339 <row topspace="1.5mm">
3340 <cell alignment="center" valignment="top" usebox="none">
3343 \begin_layout Plain Layout
3349 <cell alignment="center" valignment="top" usebox="none">
3352 \begin_layout Plain Layout
3353 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3369 \begin_layout Standard
3370 The shorter index is by default placed below or above the first character
3371 of the longer index.
3372 To avoid this there is the command
3379 \begin_inset Index idx
3382 \begin_layout Plain Layout
3390 or the math toolbar button
3391 \begin_inset space \thinspace{}
3398 \begin_layout Plain Layout
3399 can be found in the submenu of the toolbar button
3402 arg "math-insert \\space"
3411 \begin_inset Graphics
3412 filename ../images/math/phantom.png
3417 that creates one or more phantom characters.
3424 a small blue box appears that is superposed with two red arrows.
3425 The arrows indicate that the complete width and height of the box content
3426 will be created as placeholder.
3427 Phantom characters are accordingly placeholders with the size of the characters.
3428 \begin_inset Separator parbreak
3434 \begin_layout Standard
3436 \begin_inset Tabular
3437 <lyxtabular version="3" rows="4" columns="2">
3438 <features booktabs="true" tabularvalignment="middle">
3439 <column alignment="center" valignment="top" width="0pt">
3440 <column alignment="center" valignment="top" width="0pt">
3442 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3445 \begin_layout Plain Layout
3451 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3454 \begin_layout Plain Layout
3461 <row topspace="1.5mm">
3462 <cell alignment="center" valignment="top" usebox="none">
3465 \begin_layout Plain Layout
3467 \begin_inset space \textvisiblespace{}
3473 \begin_inset space \textvisiblespace{}
3477 \begin_inset Formula $\to$
3481 \begin_inset space \textvisiblespace{}
3489 <cell alignment="center" valignment="top" usebox="none">
3492 \begin_layout Plain Layout
3493 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3502 <row topspace="1.5mm" bottomspace="0.5mm">
3503 <cell alignment="center" valignment="top" usebox="none">
3506 \begin_layout Plain Layout
3508 \begin_inset space \textvisiblespace{}
3514 \begin_inset space \textvisiblespace{}
3518 \begin_inset Formula $\to$
3522 \begin_inset space \textvisiblespace{}
3530 <cell alignment="center" valignment="top" usebox="none">
3533 \begin_layout Plain Layout
3534 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3543 <row topspace="1.5mm" bottomspace="0.5mm">
3544 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3547 \begin_layout Plain Layout
3551 \begin_inset space \textvisiblespace{}
3557 \begin_inset space \textvisiblespace{}
3561 \begin_inset Formula $\to$
3565 \begin_inset space \textvisiblespace{}
3573 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3576 \begin_layout Plain Layout
3577 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3593 \begin_layout Standard
3594 Furthermore there are the commands
3601 \begin_inset Index idx
3604 \begin_layout Plain Layout
3613 \begin_inset space ~
3617 \begin_inset Graphics
3618 filename ../images/math/vphantom.png
3630 \begin_inset Index idx
3633 \begin_layout Plain Layout
3642 \begin_inset space ~
3646 \begin_inset Graphics
3647 filename ../images/math/hphantom.png
3659 creates only space for the maximal height of the characters in the box
3660 but not for its width.
3667 creates only space for the width of the box content.
3668 Therefore the boxes of both commands have only one red arrow.
3671 \begin_layout Standard
3672 For example the command
3677 \begin_inset space \textvisiblespace{}
3684 creates space for the height of the integral sign,
3688 \begin_layout Plain Layout
3695 creates an integral sign, see
3696 \begin_inset CommandInset ref
3698 reference "subsec:Big-Operators"
3707 because this is the larger character.
3708 An example application is in
3709 \begin_inset CommandInset ref
3711 reference "subsec:Multiline-Brackets"
3718 \begin_layout Standard
3719 Placeholders can also be used for text when they are inserted via the menu
3722 Insert\SpecialChar menuseparator
3723 Formatting\SpecialChar menuseparator
3729 \begin_layout Standard
3731 \begin_inset Newline newline
3735 \begin_inset Phantom Phantom
3738 \begin_layout Plain Layout
3747 \begin_layout Subsection
3749 \begin_inset Index idx
3752 \begin_layout Plain Layout
3759 \begin_inset Index idx
3762 \begin_layout Plain Layout
3763 Formula ! underlined
3771 \begin_layout Standard
3773 \begin_inset Tabular
3774 <lyxtabular version="3" rows="4" columns="2">
3775 <features booktabs="true" tabularvalignment="middle">
3776 <column alignment="center" valignment="top" width="0pt">
3777 <column alignment="center" valignment="top" width="0pt">
3779 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3782 \begin_layout Plain Layout
3788 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3791 \begin_layout Plain Layout
3798 <row topspace="2mm">
3799 <cell alignment="center" valignment="top" usebox="none">
3802 \begin_layout Plain Layout
3806 \begin_inset space \textvisiblespace{}
3810 \begin_inset Index idx
3813 \begin_layout Plain Layout
3826 <cell alignment="center" valignment="top" usebox="none">
3829 \begin_layout Plain Layout
3830 \begin_inset Formula $\overline{A+B}$
3839 <row bottomspace="1mm">
3840 <cell alignment="center" valignment="top" usebox="none">
3843 \begin_layout Plain Layout
3847 \begin_inset space \textvisiblespace{}
3851 \begin_inset Index idx
3854 \begin_layout Plain Layout
3867 <cell alignment="center" valignment="top" usebox="none">
3870 \begin_layout Plain Layout
3871 \begin_inset Formula $\underline{A+B}$
3880 <row topspace="2mm" bottomspace="1mm">
3881 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3884 \begin_layout Plain Layout
3888 \begin_inset space \textvisiblespace{}
3894 \begin_inset space \textvisiblespace{}
3902 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3905 \begin_layout Plain Layout
3906 \begin_inset Formula $\overline{\underline{A+B}}$
3922 \begin_layout Standard
3923 In the last example it doesn't matter if first
3938 \begin_layout Standard
3939 To double underline use
3948 \begin_layout Standard
3949 It is possible to place up to 6 lines above or below characters.
3952 \begin_layout Standard
3953 \begin_inset VSpace bigskip
3956 Custom lines can be created using the command
3963 \begin_inset Index idx
3966 \begin_layout Plain Layout
3974 which has the following scheme:
3977 \begin_layout Standard
3982 rule[vertical offset]{length}{thickness}
3985 \begin_layout Standard
3986 The optional vertical offset shifts the line upwards (or downwards, when
3987 the value is negative).
3989 \begin_inset CommandInset ref
3991 reference "tab:Available-units"
3995 can be used for the values.
3996 Here are two example lines created with the commands
3997 \begin_inset Newline newline
4004 rule[-2ex]{3cm}{2pt}
4015 \begin_layout Standard
4017 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4023 \begin_layout Standard
4030 can also be used for text when a line is inserted via the menu
4032 Insert\SpecialChar menuseparator
4033 Formatting\SpecialChar menuseparator
4035 \begin_inset space ~
4043 \begin_layout Standard
4045 \begin_inset CommandInset line
4056 \begin_layout Subsection
4058 \begin_inset CommandInset label
4060 name "subsec:Ellipses"
4065 \begin_inset Index idx
4068 \begin_layout Plain Layout
4077 \begin_layout Standard
4078 There are different types of ellipses available.
4082 \begin_layout Plain Layout
4083 In the math toolbar in the submenu of the button
4086 arg "math-insert \\ldots"
4094 For listings dots at the baseline are used (
4101 \begin_inset Index idx
4104 \begin_layout Plain Layout
4112 ), while for operations dots are needed that are on the same height as the
4120 \begin_inset Index idx
4123 \begin_layout Plain Layout
4132 When using the command
4139 \begin_inset Index idx
4142 \begin_layout Plain Layout
4150 , \SpecialChar LaTeX
4151 decides on the basis of the next character what type is used.
4152 \begin_inset Separator parbreak
4158 \begin_layout Standard
4160 \begin_inset Tabular
4161 <lyxtabular version="3" rows="9" columns="2">
4162 <features booktabs="true" tabularvalignment="middle">
4163 <column alignment="center" valignment="top" width="0pt">
4164 <column alignment="center" valignment="top" width="0pt">
4166 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4169 \begin_layout Plain Layout
4175 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4178 \begin_layout Plain Layout
4186 <cell alignment="center" valignment="top" usebox="none">
4189 \begin_layout Plain Layout
4191 \begin_inset space \textvisiblespace{}
4197 \begin_inset space \textvisiblespace{}
4205 <cell alignment="center" valignment="top" usebox="none">
4208 \begin_layout Plain Layout
4209 \begin_inset Formula $A_{1},\dots,A_{n}$
4219 <cell alignment="center" valignment="top" usebox="none">
4222 \begin_layout Plain Layout
4224 \begin_inset space \textvisiblespace{}
4230 \begin_inset space \textvisiblespace{}
4238 <cell alignment="center" valignment="top" usebox="none">
4241 \begin_layout Plain Layout
4242 \begin_inset Formula $A_{1}+\dots+A_{n}$
4252 <cell alignment="center" valignment="top" usebox="none">
4255 \begin_layout Plain Layout
4257 \begin_inset space \textvisiblespace{}
4263 \begin_inset space \textvisiblespace{}
4271 <cell alignment="center" valignment="top" usebox="none">
4274 \begin_layout Plain Layout
4275 \begin_inset Formula $A_{1},\ldots,A_{n}$
4285 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4288 \begin_layout Plain Layout
4290 \begin_inset space \textvisiblespace{}
4296 \begin_inset space \textvisiblespace{}
4304 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4307 \begin_layout Plain Layout
4308 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4318 <cell alignment="center" valignment="top" usebox="none">
4321 \begin_layout Plain Layout
4329 <cell alignment="center" valignment="top" usebox="none">
4332 \begin_layout Plain Layout
4333 \begin_inset Formula $\vdots$
4343 <cell alignment="center" valignment="top" usebox="none">
4346 \begin_layout Plain Layout
4354 <cell alignment="center" valignment="top" usebox="none">
4357 \begin_layout Plain Layout
4358 \begin_inset Formula $\ddots$
4368 <cell alignment="center" valignment="top" usebox="none">
4371 \begin_layout Plain Layout
4379 <cell alignment="center" valignment="top" usebox="none">
4382 \begin_layout Plain Layout
4383 \begin_inset Formula $\iddots$
4393 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4396 \begin_layout Plain Layout
4398 \begin_inset space \thinspace{}
4401 matrix with the different dots
4406 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4409 \begin_layout Plain Layout
4410 \begin_inset Formula $\begin{array}{ccc}
4411 A_{11} & \cdots & A_{1m}\\
4412 \vdots & \ddots & \vdots\\
4413 A_{n1} & \cdots & A_{nm}
4430 \begin_layout Standard
4431 The ellipses available in menu
4433 Insert\SpecialChar menuseparator
4435 \begin_inset space ~
4449 \begin_layout Standard
4450 \begin_inset VSpace medskip
4459 , one of the options
4461 Use mathdots package (automatically)
4463 must be set in the document settings under
4466 \begin_inset space ~
4472 \begin_inset Newline newline
4477 Use mathdots package
4479 will improve the appearance of all dots in the documents if their font
4480 style or size is not the default.
4483 \begin_layout Standard
4484 \begin_inset VSpace medskip
4487 Specially for matrices there are ellipses that span over several columns.
4488 They are created with the command
4495 \begin_inset Index idx
4498 \begin_layout Plain Layout
4506 , that has the following scheme:
4509 \begin_layout Standard
4514 hdotsfor[distance]{number of columns}
4517 \begin_layout Standard
4518 The number of columns specifies how many columns should be spanned.
4519 Distance is a factor for the distance between the dots.
4522 \begin_layout Standard
4523 In the following matrix the command
4529 was inserted in the first box of the second line, to get an ellipsis with
4530 a dot distance twice as long as with the command
4537 \begin_inset Formula
4539 \left(\begin{array}{cccc}
4548 Note that the matrix fields that should be spanned must be empty, otherwise
4549 you get \SpecialChar LaTeX
4553 \begin_layout Standard
4554 \begin_inset VSpace bigskip
4557 Furthermore you can fill with the command
4564 \begin_inset Index idx
4567 \begin_layout Plain Layout
4575 the rest of a line with dots.
4576 The effect of these commands is the same as with
4583 \begin_inset CommandInset ref
4585 reference "subsec:Variable-Space"
4592 \begin_layout Standard
4593 For example the command
4598 \begin_inset space \textvisiblespace{}
4606 \begin_layout Standard
4607 \begin_inset Formula $A\dotfill B$
4613 \begin_layout Standard
4620 there is for a line the command
4627 \begin_inset Index idx
4630 \begin_layout Plain Layout
4641 \begin_layout Standard
4642 \begin_inset Formula $A\hrulefill B$
4648 \begin_layout Standard
4649 To use the commands for text, they have to be inserted in \SpecialChar TeX
4653 \begin_layout Section
4655 \begin_inset CommandInset label
4662 \begin_inset Index idx
4665 \begin_layout Plain Layout
4674 \begin_layout Standard
4675 Matrices can be inserted via the math toolbar button
4678 arg "dialog-show mathmatrix"
4683 Insert\SpecialChar menuseparator
4684 Math\SpecialChar menuseparator
4688 In the matrix dialog you can specify the number of columns and rows, the
4689 alignment and the decoration.
4690 The vertical alignment is only of importance for matrices in inline formulas:
4693 \begin_layout Standard
4694 The first matrix is top
4695 \begin_inset Formula $\begin{array}[t]{cccc}
4703 \begin_inset Formula $\begin{array}{cccc}
4710 and the third bottom
4711 \begin_inset Formula $\begin{array}[b]{cccc}
4721 \begin_layout Standard
4722 The horizontal alignment specifies how the column entries should be aligned.
4723 It is set by entering a letter for every column.
4728 denotes left aligned,
4737 To create for example a 4
4742 \begin_inset space ~
4745 matrix where the first column is left aligned, the second and third are
4746 centered and the last one is right aligned, one enters for the horizontal
4752 Normally in a matrix all columns are centered, therefore the default for
4760 \begin_layout Standard
4761 Horizontal alignment:
4764 \begin_layout Standard
4770 \begin_inset Formula $\begin{array}{lll}
4782 \begin_inset Formula $\begin{array}{ccc}
4794 \begin_inset Formula $\begin{array}{rrr}
4804 \begin_layout Standard
4805 To add or delete rows and columns subsequently, the math toolbar buttons
4809 arg "inset-modify tabular append-row"
4815 arg "inset-modify tabular delete-row"
4819 \begin_inset space \thinspace{}
4824 Edit\SpecialChar menuseparator
4828 New rows can also be created with
4831 arg "newline-insert newline"
4837 \begin_layout Standard
4838 \begin_inset VSpace bigskip
4845 adds parentheses in the selected style around the matrix.
4846 Alternatively, parentheses can can either be created with the commands
4854 \begin_inset Index idx
4857 \begin_layout Plain Layout
4872 \begin_inset Index idx
4875 \begin_layout Plain Layout
4886 \begin_inset space ~
4892 \begin_inset CommandInset ref
4894 reference "subsec:Automatic-Bracket-Size"
4898 , or by using the following commands:
4899 \begin_inset VSpace medskip
4905 \begin_layout Standard
4906 \begin_inset space \hfill{}
4910 \begin_inset Tabular
4911 <lyxtabular version="3" rows="4" columns="2">
4912 <features booktabs="true" tabularvalignment="middle">
4913 <column alignment="center" valignment="top" width="0pt">
4914 <column alignment="center" valignment="top">
4916 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4919 \begin_layout Plain Layout
4925 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4928 \begin_layout Plain Layout
4935 <row topspace="1.5mm">
4936 <cell alignment="center" valignment="top" usebox="none">
4939 \begin_layout Plain Layout
4943 \begin_inset space \textvisiblespace{}
4951 \begin_inset space \thinspace{}
4959 <cell alignment="center" valignment="top" usebox="none">
4962 \begin_layout Plain Layout
4963 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4964 0 & \textrm{-}\mathrm{i}\\
4966 \end{array}\end{bmatrix}$
4975 <row topspace="1.5mm" bottomspace="0.5mm">
4976 <cell alignment="center" valignment="top" usebox="none">
4979 \begin_layout Plain Layout
4983 \begin_inset space \textvisiblespace{}
4991 \begin_inset space \thinspace{}
4999 <cell alignment="center" valignment="top" usebox="none">
5002 \begin_layout Plain Layout
5003 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
5004 0 & \textrm{-}\mathrm{i}\\
5006 \end{array}\end{Bmatrix}$
5016 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5019 \begin_layout Plain Layout
5023 \begin_inset space \textvisiblespace{}
5031 \begin_inset space \thinspace{}
5039 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5042 \begin_layout Plain Layout
5043 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5044 0 & \textrm{-}\mathrm{i}\\
5046 \end{array}\end{pmatrix}$
5060 \begin_inset space \hfill{}
5064 \begin_inset Tabular
5065 <lyxtabular version="3" rows="4" columns="2">
5066 <features booktabs="true" tabularvalignment="middle">
5067 <column alignment="center" valignment="top" width="0pt">
5068 <column alignment="center" valignment="top">
5070 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5073 \begin_layout Plain Layout
5079 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5082 \begin_layout Plain Layout
5089 <row topspace="1.5mm">
5090 <cell alignment="center" valignment="top" usebox="none">
5093 \begin_layout Plain Layout
5097 \begin_inset space \textvisiblespace{}
5105 \begin_inset space \thinspace{}
5113 <cell alignment="center" valignment="top" usebox="none">
5116 \begin_layout Plain Layout
5117 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5118 0 & \textrm{-}\mathrm{i}\\
5120 \end{array}\end{vmatrix}$
5129 <row topspace="1.5mm" bottomspace="0.5mm">
5130 <cell alignment="center" valignment="top" usebox="none">
5133 \begin_layout Plain Layout
5137 \begin_inset space \textvisiblespace{}
5145 \begin_inset space \thinspace{}
5153 <cell alignment="center" valignment="top" usebox="none">
5156 \begin_layout Plain Layout
5157 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5158 0 & \textrm{-}\mathrm{i}\\
5160 \end{array}\end{Vmatrix}$
5170 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5173 \begin_layout Plain Layout
5177 \begin_inset space \textvisiblespace{}
5185 \begin_inset space \thinspace{}
5193 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5196 \begin_layout Plain Layout
5197 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5198 0 & \textrm{-}\mathrm{i}\\
5200 \end{array}\end{matrix}$
5214 \begin_inset space \hfill{}
5220 \begin_layout Standard
5221 \begin_inset VSpace medskip
5225 \begin_inset space \thinspace{}
5229 \begin_inset space \space{}
5238 is inserted, a blue box appears between two vertical lines where the matrix
5240 \begin_inset Newline newline
5243 Note that decorated matrices ignore the vertical alignment.
5246 \begin_layout Standard
5247 \begin_inset VSpace bigskip
5250 As all multiline formulas are matrices, the length
5257 \begin_inset Index idx
5260 \begin_layout Plain Layout
5268 that is described in
5269 \begin_inset CommandInset ref
5271 reference "subsec:Column-Separation"
5275 can also be used to change the column separation of matrices.
5278 \begin_layout Standard
5279 To change the row separation, the command
5286 \begin_inset Index idx
5289 \begin_layout Plain Layout
5298 It is used as follows:
5301 \begin_layout Standard
5308 arraystretch}{stretch factor}
5309 \begin_inset Index idx
5312 \begin_layout Plain Layout
5323 \begin_layout Standard
5330 assigns the stretch factor to the predefined command
5338 \begin_inset space \thinspace{}
5342 \begin_inset space \space{}
5345 the row separation, use the factor 2.
5346 This is then used for all following matrices.
5347 To go back to the original separation, assign the factor 1 to
5356 \begin_layout Standard
5357 To set matrices into a text line, the command
5364 \begin_inset Index idx
5367 \begin_layout Plain Layout
5376 When it is inserted a blue box with two dashed lines appears.
5377 In this box the matrix is inserted.
5380 \begin_layout Standard
5382 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5384 \end{smallmatrix}\right)$
5390 \begin_layout Section
5391 Brackets and Delimiters
5392 \begin_inset Index idx
5395 \begin_layout Plain Layout
5402 \begin_inset Index idx
5405 \begin_layout Plain Layout
5414 \begin_layout Subsection
5415 Vertical Brackets and Delimiters
5416 \begin_inset Index idx
5419 \begin_layout Plain Layout
5428 \begin_layout Standard
5429 \begin_inset space \hfill{}
5433 \begin_inset Tabular
5434 <lyxtabular version="3" rows="9" columns="2">
5435 <features booktabs="true" tabularvalignment="middle">
5436 <column alignment="center" valignment="top" width="0pt">
5437 <column alignment="center" valignment="top" width="0pt">
5439 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5442 \begin_layout Plain Layout
5448 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5451 \begin_layout Plain Layout
5459 <cell alignment="center" valignment="top" usebox="none">
5462 \begin_layout Plain Layout
5468 <cell alignment="center" valignment="top" usebox="none">
5471 \begin_layout Plain Layout
5472 \begin_inset Formula $($
5482 <cell alignment="center" valignment="top" usebox="none">
5485 \begin_layout Plain Layout
5491 <cell alignment="center" valignment="top" usebox="none">
5494 \begin_layout Plain Layout
5495 \begin_inset Formula $\{$
5505 <cell alignment="center" valignment="top" usebox="none">
5508 \begin_layout Plain Layout
5514 <cell alignment="center" valignment="top" usebox="none">
5517 \begin_layout Plain Layout
5518 \begin_inset Formula $[$
5528 <cell alignment="center" valignment="top" usebox="none">
5531 \begin_layout Plain Layout
5539 <cell alignment="center" valignment="top" usebox="none">
5542 \begin_layout Plain Layout
5543 \begin_inset Formula $\langle$
5553 <cell alignment="center" valignment="top" usebox="none">
5556 \begin_layout Plain Layout
5564 <cell alignment="center" valignment="top" usebox="none">
5567 \begin_layout Plain Layout
5568 \begin_inset Formula $\lceil$
5578 <cell alignment="center" valignment="top" usebox="none">
5581 \begin_layout Plain Layout
5589 <cell alignment="center" valignment="top" usebox="none">
5592 \begin_layout Plain Layout
5593 \begin_inset Formula $\lfloor$
5603 <cell alignment="center" valignment="top" usebox="none">
5606 \begin_layout Plain Layout
5612 <cell alignment="center" valignment="top" usebox="none">
5615 \begin_layout Plain Layout
5616 \begin_inset Formula $/$
5626 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5629 \begin_layout Plain Layout
5635 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5638 \begin_layout Plain Layout
5639 \begin_inset Formula $|$
5653 \begin_inset space \hfill{}
5657 \begin_inset Tabular
5658 <lyxtabular version="3" rows="9" columns="2">
5659 <features booktabs="true" tabularvalignment="middle">
5660 <column alignment="center" valignment="top" width="0pt">
5661 <column alignment="center" valignment="top" width="0pt">
5663 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5666 \begin_layout Plain Layout
5672 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5675 \begin_layout Plain Layout
5683 <cell alignment="center" valignment="top" usebox="none">
5686 \begin_layout Plain Layout
5692 <cell alignment="center" valignment="top" usebox="none">
5695 \begin_layout Plain Layout
5696 \begin_inset Formula $)$
5706 <cell alignment="center" valignment="top" usebox="none">
5709 \begin_layout Plain Layout
5715 <cell alignment="center" valignment="top" usebox="none">
5718 \begin_layout Plain Layout
5719 \begin_inset Formula $\}$
5729 <cell alignment="center" valignment="top" usebox="none">
5732 \begin_layout Plain Layout
5738 <cell alignment="center" valignment="top" usebox="none">
5741 \begin_layout Plain Layout
5742 \begin_inset Formula $]$
5752 <cell alignment="center" valignment="top" usebox="none">
5755 \begin_layout Plain Layout
5763 <cell alignment="center" valignment="top" usebox="none">
5766 \begin_layout Plain Layout
5767 \begin_inset Formula $\rangle$
5777 <cell alignment="center" valignment="top" usebox="none">
5780 \begin_layout Plain Layout
5788 <cell alignment="center" valignment="top" usebox="none">
5791 \begin_layout Plain Layout
5792 \begin_inset Formula $\rceil$
5802 <cell alignment="center" valignment="top" usebox="none">
5805 \begin_layout Plain Layout
5813 <cell alignment="center" valignment="top" usebox="none">
5816 \begin_layout Plain Layout
5817 \begin_inset Formula $\rfloor$
5827 <cell alignment="center" valignment="top" usebox="none">
5830 \begin_layout Plain Layout
5840 <cell alignment="center" valignment="top" usebox="none">
5843 \begin_layout Plain Layout
5844 \begin_inset Formula $\backslash$
5854 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5857 \begin_layout Plain Layout
5865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5868 \begin_layout Plain Layout
5869 \begin_inset Formula $\|$
5883 \begin_inset space \hfill{}
5889 \begin_layout Standard
5892 \begin_inset Note Greyedout
5895 \begin_layout Plain Layout
5908 \begin_inset Index idx
5911 \begin_layout Plain Layout
5919 must be used for the backslash, because the command
5927 produces a line break there.
5935 \begin_layout Standard
5936 For all characters listed above the size can be adjusted with the commands
5937 described in the following two subsections.
5938 When using these commands, the characters < and > can directly be used
5939 instead of the commands
5954 \begin_layout Subsubsection
5956 \begin_inset CommandInset label
5958 name "subsec:Manual-Bracket-Size"
5963 \begin_inset Index idx
5966 \begin_layout Plain Layout
5967 Bracket size ! manual
5975 \begin_layout Standard
5976 The bracket size can be specified manually by the \SpecialChar LaTeX
5984 \begin_inset Index idx
5987 \begin_layout Plain Layout
6020 denotes the smallest and
6026 the largest bracket size.
6029 \begin_layout Standard
6030 These commands are used to emphasize levels of brackets:
6031 \begin_inset Separator parbreak
6037 \begin_layout Standard
6039 \begin_inset Tabular
6040 <lyxtabular version="3" rows="2" columns="2">
6041 <features booktabs="true" tabularvalignment="middle">
6042 <column alignment="center" valignment="top" width="0pt">
6043 <column alignment="center" valignment="top" width="0pt">
6045 <cell alignment="center" valignment="top" usebox="none">
6048 \begin_layout Plain Layout
6049 all brackets in the same size:
6054 <cell alignment="center" valignment="top" usebox="none">
6057 \begin_layout Plain Layout
6058 \begin_inset Formula $((A+B)(A-B))^{C}$
6067 <row topspace="2mm">
6068 <cell alignment="center" valignment="top" usebox="none">
6071 \begin_layout Plain Layout
6077 <cell alignment="center" valignment="top" usebox="none">
6080 \begin_layout Plain Layout
6081 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6097 \begin_layout Standard
6098 For the second formula the command
6105 \begin_inset space \textvisiblespace{}
6113 \begin_layout Standard
6114 Here is an overview about all bracket sizes:
6115 \begin_inset Separator parbreak
6121 \begin_layout Standard
6138 \begin_inset space \textvisiblespace{}
6146 \begin_inset space \textvisiblespace{}
6150 \begin_inset space \textvisiblespace{}
6160 \begin_layout Standard
6162 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6168 \begin_layout Standard
6175 -commands there is the variant
6182 \begin_inset Index idx
6185 \begin_layout Plain Layout
6193 that adds a bit more space between the bracket and its content, and the
6207 \begin_inset Index idx
6210 \begin_layout Plain Layout
6220 , that don't add additional space.
6225 at the end of the command
6231 is for a left bracket; for a right bracket this will be replaced by an
6237 A left or right bracket can each be an opening or closing bracket.
6240 \begin_layout Standard
6241 In the following table is a comparison of the variants:
6242 \begin_inset Separator parbreak
6248 \begin_layout Standard
6250 \begin_inset Tabular
6251 <lyxtabular version="3" rows="5" columns="2">
6252 <features booktabs="true" tabularvalignment="middle">
6253 <column alignment="center" valignment="top" width="0pt">
6254 <column alignment="center" valignment="middle">
6256 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6259 \begin_layout Plain Layout
6265 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6268 \begin_layout Plain Layout
6275 <row topspace="2mm">
6276 <cell alignment="center" valignment="top" usebox="none">
6279 \begin_layout Plain Layout
6289 \begin_inset space \textvisiblespace{}
6299 <cell alignment="center" valignment="top" usebox="none">
6302 \begin_layout Plain Layout
6303 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6312 <row topspace="2mm">
6313 <cell alignment="center" valignment="top" usebox="none">
6316 \begin_layout Plain Layout
6326 \begin_inset space \textvisiblespace{}
6336 <cell alignment="center" valignment="top" usebox="none">
6339 \begin_layout Plain Layout
6340 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6349 <row topspace="2mm" bottomspace="0.5mm">
6350 <cell alignment="center" valignment="top" usebox="none">
6353 \begin_layout Plain Layout
6363 \begin_inset space \textvisiblespace{}
6373 <cell alignment="center" valignment="top" usebox="none">
6376 \begin_layout Plain Layout
6377 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6386 <row topspace="1.5mm" bottomspace="0.5mm">
6387 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6390 \begin_layout Plain Layout
6402 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6405 \begin_layout Plain Layout
6406 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6422 \begin_layout Subsubsection
6423 Automatic Bracket Size
6424 \begin_inset CommandInset label
6426 name "subsec:Automatic-Bracket-Size"
6431 \begin_inset Index idx
6434 \begin_layout Plain Layout
6435 Bracket size ! automatic
6443 \begin_layout Standard
6444 Brackets with variable size can be inserted with the commands
6451 \begin_inset Index idx
6454 \begin_layout Plain Layout
6469 \begin_inset Index idx
6472 \begin_layout Plain Layout
6480 or via the math toolbar button
6483 arg "dialog-show mathdelimiter"
6499 the wanted bracket must be inserted.
6500 The bracket size will then automatically be calculated for the output.
6501 \begin_inset Separator parbreak
6507 \begin_layout Standard
6509 normal bracket: The command
6516 \begin_inset space \textvisiblespace{}
6520 \begin_inset Formula $\downarrow$
6524 \begin_inset space \textvisiblespace{}
6530 \begin_inset Formula
6540 \begin_layout Standard
6542 multiline bracket: The command
6551 \begin_inset space \textvisiblespace{}
6555 \begin_inset Formula $\downarrow$
6559 \begin_inset space \textvisiblespace{}
6567 \begin_inset Formula
6569 \ln\left(\frac{A}{C}\right)
6577 \begin_layout Standard
6593 \begin_inset space ~
6599 This has the advantage that you can see in \SpecialChar LyX
6600 immediately the real bracket
6601 size and that the matching right bracket will be created too.
6602 \begin_inset Newline newline
6605 The command for the last example would then be:
6616 \begin_inset space \textvisiblespace{}
6620 \begin_inset Formula $\downarrow$
6626 \begin_layout Standard
6627 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6628 For example the command
6635 \begin_inset space \textvisiblespace{}
6639 \begin_inset Formula $\downarrow$
6643 \begin_inset space \textvisiblespace{}
6653 \begin_inset Formula
6655 \left.\frac{A}{B}\right\}
6674 will be converted by \SpecialChar LyX
6675 to brackets in the right size when the document is
6676 reloaded and an omitted bracket will appear as dashed line.
6679 \begin_layout Standard
6680 \begin_inset VSpace bigskip
6683 Because all popular \SpecialChar LaTeX
6684 distributions use e\SpecialChar TeX
6685 , an extension to \SpecialChar LaTeX
6694 \begin_inset Index idx
6697 \begin_layout Plain Layout
6705 is additionally available for all brackets and limits.
6706 With this command the height of the following character is adapted to the
6707 one of the surrounding brackets, what is e.
6708 \begin_inset space \thinspace{}
6712 \begin_inset space \space{}
6715 needed for physical vectors:
6716 \begin_inset Formula
6718 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6723 For physical vectors there is a special \SpecialChar LaTeX
6724 -package, described in
6725 \begin_inset CommandInset ref
6727 reference "subsec:Physical-Vectors"
6734 \begin_layout Subsection
6736 \begin_inset Index idx
6739 \begin_layout Plain Layout
6740 Brackets ! horizontal
6748 \begin_layout Standard
6750 \begin_inset Tabular
6751 <lyxtabular version="3" rows="4" columns="2">
6752 <features booktabs="true" tabularvalignment="middle">
6753 <column alignment="center" valignment="top" width="0pt">
6754 <column alignment="center" valignment="top" width="0pt">
6756 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6759 \begin_layout Plain Layout
6765 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6768 \begin_layout Plain Layout
6776 <cell alignment="center" valignment="top" usebox="none">
6779 \begin_layout Plain Layout
6783 \begin_inset space \textvisiblespace{}
6787 \begin_inset space \textvisiblespace{}
6791 \begin_inset Index idx
6794 \begin_layout Plain Layout
6807 <cell alignment="center" valignment="top" usebox="none">
6810 \begin_layout Plain Layout
6811 \begin_inset Formula $\overbrace{A+B}^{3}$
6820 <row topspace="2mm">
6821 <cell alignment="center" valignment="top" usebox="none">
6824 \begin_layout Plain Layout
6828 \begin_inset space \textvisiblespace{}
6832 \begin_inset space \textvisiblespace{}
6836 \begin_inset Index idx
6839 \begin_layout Plain Layout
6852 <cell alignment="center" valignment="top" usebox="none">
6855 \begin_layout Plain Layout
6856 \begin_inset Formula $\underbrace{A+B}_{5}$
6866 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6869 \begin_layout Plain Layout
6873 \begin_inset space \textvisiblespace{}
6879 \begin_inset space \textvisiblespace{}
6883 \begin_inset space \textvisiblespace{}
6887 \begin_inset space \textvisiblespace{}
6891 \begin_inset space \textvisiblespace{}
6895 \begin_inset space \textvisiblespace{}
6899 \begin_inset space \textvisiblespace{}
6907 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6910 \begin_layout Plain Layout
6911 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6927 \begin_layout Standard
6928 In the last example it doesn't matter if
6940 is inserted at first.
6943 \begin_layout Standard
6944 \begin_inset VSpace medskip
6950 \begin_layout Standard
6951 If you set in the document settings under
6954 \begin_inset space ~
6964 \begin_inset Index idx
6967 \begin_layout Plain Layout
6968 Packages ! mathtools
6976 \begin_inset space ~
6981 , you have access to square backets:
6982 \begin_inset Separator parbreak
6988 \begin_layout Standard
6990 \begin_inset Tabular
6991 <lyxtabular version="3" rows="4" columns="2">
6992 <features booktabs="true" tabularvalignment="middle">
6993 <column alignment="center" valignment="top" width="0pt">
6994 <column alignment="center" valignment="top" width="0pt">
6996 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6999 \begin_layout Plain Layout
7005 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7008 \begin_layout Plain Layout
7016 <cell alignment="center" valignment="top" usebox="none">
7019 \begin_layout Plain Layout
7047 \begin_inset space \textvisiblespace{}
7051 \begin_inset Index idx
7054 \begin_layout Plain Layout
7067 <cell alignment="center" valignment="top" usebox="none">
7070 \begin_layout Plain Layout
7071 \begin_inset Formula $\overbracket{A+B}^{3}$
7080 <row topspace="2mm">
7081 <cell alignment="center" valignment="top" usebox="none">
7084 \begin_layout Plain Layout
7112 \begin_inset space \textvisiblespace{}
7116 \begin_inset Index idx
7119 \begin_layout Plain Layout
7144 <cell alignment="center" valignment="top" usebox="none">
7147 \begin_layout Plain Layout
7148 \begin_inset Formula $\underbracket{A+B}_{5}$
7158 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7161 \begin_layout Plain Layout
7167 \begin_inset space \textvisiblespace{}
7171 \begin_inset space \textvisiblespace{}
7175 \begin_inset space \textvisiblespace{}
7179 \begin_inset space \textvisiblespace{}
7183 \begin_inset space \textvisiblespace{}
7191 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7194 \begin_layout Plain Layout
7195 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7211 \begin_layout Standard
7224 you can change the thickness of the bracket's stroke by specifying the
7225 desired thickness in square brackets behind the command:
7226 \begin_inset Separator parbreak
7232 \begin_layout Standard
7234 \begin_inset Tabular
7235 <lyxtabular version="3" rows="3" columns="2">
7236 <features booktabs="true" tabularvalignment="middle">
7237 <column alignment="center" valignment="top" width="0pt">
7238 <column alignment="center" valignment="top" width="0pt">
7240 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7243 \begin_layout Plain Layout
7249 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7252 \begin_layout Plain Layout
7260 <cell alignment="center" valignment="top" usebox="none">
7263 \begin_layout Plain Layout
7293 \begin_inset space \textvisiblespace{}
7301 <cell alignment="center" valignment="top" usebox="none">
7304 \begin_layout Plain Layout
7305 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7314 <row topspace="2mm">
7315 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7318 \begin_layout Plain Layout
7348 \begin_inset space \textvisiblespace{}
7356 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7359 \begin_layout Plain Layout
7360 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7376 \begin_layout Standard
7377 \begin_inset VSpace bigskip
7380 When brackets should overlap each other, multiline formulas, as described
7382 \begin_inset CommandInset ref
7384 reference "sec:Multiline-Formulas"
7389 \begin_inset Formula
7391 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7392 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7397 In the first row the formula is inserted together with the first brace.
7398 It is hereby important that the space command
7402 \begin_layout Plain Layout
7403 Space commands are explained in
7404 \begin_inset CommandInset ref
7406 reference "subsec:Predefined-Space"
7421 is inserted before the first
7422 \begin_inset Formula $d$
7425 , because the brace that ends behind the
7426 \begin_inset Formula $q$
7429 prevents that the following
7430 \begin_inset Quotes eld
7434 \begin_inset Quotes erd
7437 is surrounded by space.
7441 \begin_layout Plain Layout
7442 because a bracket is not handled as a character, see
7443 \begin_inset CommandInset ref
7445 reference "subsec:Binary-Operators"
7454 In the second row the second brace is inserted.
7455 As it should begin before the
7456 \begin_inset Formula $b$
7471 \begin_layout Plain Layout
7479 \begin_inset CommandInset ref
7481 reference "subsec:Placeholders"
7490 This space is needed because the
7491 \begin_inset Quotes eld
7495 \begin_inset Quotes erd
7498 is also surrounded by space in the formula.
7499 The brace is placed under the command
7508 \begin_layout Standard
7509 It gets more complicated when brackets overlap each other above and under
7510 the formula, like in the following example:
7514 \begin_layout Plain Layout
7526 \begin_inset Formula
7528 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7529 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7538 \begin_layout Plain Layout
7549 The first formula row is the same as the second row of the previous example,
7550 with the difference that the brace is above.
7551 The second row contains the formula together with the second brace.
7552 To avoid that there is space between the upper brace in the first row and
7553 the formula, the row spacing needs to be reduced.
7554 This is not easily possible due to a bug in \SpecialChar LyX
7559 \begin_layout Plain Layout
7560 \begin_inset CommandInset href
7562 name "LyX-bug #1505"
7563 target "http://www.lyx.org/trac/ticket/1505"
7572 As a solution for the problem, the global formula row separation
7579 \begin_inset Index idx
7582 \begin_layout Plain Layout
7590 must be changed to -6
7591 \begin_inset space \thinspace{}
7594 pt before the formula with the command
7610 is set back after the formula to the standard value of 3
7611 \begin_inset space \thinspace{}
7614 pt using the same command.
7615 More about the row separation in formulas is explained in
7616 \begin_inset CommandInset ref
7618 reference "subsec:Line-Separation"
7625 \begin_layout Section
7627 \begin_inset Index idx
7630 \begin_layout Plain Layout
7639 \begin_layout Standard
7640 Arrows can be inserted via the math toolbar button
7643 arg "math-insert \\leftarrow"
7646 or the commands listed in the following subsections.
7649 \begin_layout Subsection
7651 \begin_inset Index idx
7654 \begin_layout Plain Layout
7663 \begin_layout Standard
7664 \begin_inset space \hfill{}
7668 \begin_inset Tabular
7669 <lyxtabular version="3" rows="8" columns="2">
7670 <features booktabs="true" tabularvalignment="middle">
7671 <column alignment="center" valignment="top" width="0pt">
7672 <column alignment="center" valignment="top" width="0pt">
7674 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7677 \begin_layout Plain Layout
7683 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7686 \begin_layout Plain Layout
7694 <cell alignment="center" valignment="top" usebox="none">
7697 \begin_layout Plain Layout
7705 <cell alignment="center" valignment="top" usebox="none">
7708 \begin_layout Plain Layout
7709 \begin_inset Formula $\gets$
7719 <cell alignment="center" valignment="top" usebox="none">
7722 \begin_layout Plain Layout
7730 <cell alignment="center" valignment="top" usebox="none">
7733 \begin_layout Plain Layout
7734 \begin_inset Formula $\Leftarrow$
7744 <cell alignment="center" valignment="top" usebox="none">
7747 \begin_layout Plain Layout
7755 <cell alignment="center" valignment="top" usebox="none">
7758 \begin_layout Plain Layout
7759 \begin_inset Formula $\longleftarrow$
7769 <cell alignment="center" valignment="top" usebox="none">
7772 \begin_layout Plain Layout
7780 <cell alignment="center" valignment="top" usebox="none">
7783 \begin_layout Plain Layout
7784 \begin_inset Formula $\Longleftarrow$
7794 <cell alignment="center" valignment="top" usebox="none">
7797 \begin_layout Plain Layout
7805 <cell alignment="center" valignment="top" usebox="none">
7808 \begin_layout Plain Layout
7809 \begin_inset Formula $\leftharpoonup$
7819 <cell alignment="center" valignment="top" usebox="none">
7822 \begin_layout Plain Layout
7830 <cell alignment="center" valignment="top" usebox="none">
7833 \begin_layout Plain Layout
7834 \begin_inset Formula $\leftharpoondown$
7844 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7847 \begin_layout Plain Layout
7855 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7858 \begin_layout Plain Layout
7859 \begin_inset Formula $\hookleftarrow$
7873 \begin_inset space \hfill{}
7877 \begin_inset Tabular
7878 <lyxtabular version="3" rows="8" columns="2">
7879 <features booktabs="true" tabularvalignment="middle">
7880 <column alignment="center" valignment="top" width="0pt">
7881 <column alignment="center" valignment="top" width="0pt">
7883 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7886 \begin_layout Plain Layout
7892 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7895 \begin_layout Plain Layout
7903 <cell alignment="center" valignment="top" usebox="none">
7906 \begin_layout Plain Layout
7914 <cell alignment="center" valignment="top" usebox="none">
7917 \begin_layout Plain Layout
7918 \begin_inset Formula $\to$
7928 <cell alignment="center" valignment="top" usebox="none">
7931 \begin_layout Plain Layout
7939 <cell alignment="center" valignment="top" usebox="none">
7942 \begin_layout Plain Layout
7943 \begin_inset Formula $\Rightarrow$
7953 <cell alignment="center" valignment="top" usebox="none">
7956 \begin_layout Plain Layout
7964 <cell alignment="center" valignment="top" usebox="none">
7967 \begin_layout Plain Layout
7968 \begin_inset Formula $\longrightarrow$
7978 <cell alignment="center" valignment="top" usebox="none">
7981 \begin_layout Plain Layout
7989 <cell alignment="center" valignment="top" usebox="none">
7992 \begin_layout Plain Layout
7993 \begin_inset Formula $\Longrightarrow$
8003 <cell alignment="center" valignment="top" usebox="none">
8006 \begin_layout Plain Layout
8014 <cell alignment="center" valignment="top" usebox="none">
8017 \begin_layout Plain Layout
8018 \begin_inset Formula $\rightharpoonup$
8028 <cell alignment="center" valignment="top" usebox="none">
8031 \begin_layout Plain Layout
8039 <cell alignment="center" valignment="top" usebox="none">
8042 \begin_layout Plain Layout
8043 \begin_inset Formula $\rightharpoondown$
8053 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8056 \begin_layout Plain Layout
8064 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8067 \begin_layout Plain Layout
8068 \begin_inset Formula $\hookrightarrow$
8082 \begin_inset space \hfill{}
8088 \begin_layout Standard
8089 \begin_inset space \hfill{}
8093 \begin_inset Tabular
8094 <lyxtabular version="3" rows="6" columns="2">
8095 <features booktabs="true" tabularvalignment="middle">
8096 <column alignment="center" valignment="top" width="0pt">
8097 <column alignment="center" valignment="top" width="0pt">
8099 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8102 \begin_layout Plain Layout
8108 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8111 \begin_layout Plain Layout
8119 <cell alignment="center" valignment="top" usebox="none">
8122 \begin_layout Plain Layout
8130 <cell alignment="center" valignment="top" usebox="none">
8133 \begin_layout Plain Layout
8134 \begin_inset Formula $\leftrightarrow$
8144 <cell alignment="center" valignment="top" usebox="none">
8147 \begin_layout Plain Layout
8155 <cell alignment="center" valignment="top" usebox="none">
8158 \begin_layout Plain Layout
8159 \begin_inset Formula $\Leftrightarrow$
8169 <cell alignment="center" valignment="top" usebox="none">
8172 \begin_layout Plain Layout
8180 <cell alignment="center" valignment="top" usebox="none">
8183 \begin_layout Plain Layout
8184 \begin_inset Formula $\longleftrightarrow$
8194 <cell alignment="center" valignment="top" usebox="none">
8197 \begin_layout Plain Layout
8205 <cell alignment="center" valignment="top" usebox="none">
8208 \begin_layout Plain Layout
8209 \begin_inset Formula $\Longleftrightarrow$
8219 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8222 \begin_layout Plain Layout
8230 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8233 \begin_layout Plain Layout
8234 \begin_inset Formula $\rightleftharpoons$
8248 \begin_inset space \hspace{}
8253 \begin_inset space \hfill{}
8257 \begin_inset Tabular
8258 <lyxtabular version="3" rows="5" columns="2">
8259 <features booktabs="true" tabularvalignment="middle">
8260 <column alignment="center" valignment="top" width="0pt">
8261 <column alignment="center" valignment="top" width="0pt">
8263 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8266 \begin_layout Plain Layout
8272 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8275 \begin_layout Plain Layout
8283 <cell alignment="center" valignment="top" usebox="none">
8286 \begin_layout Plain Layout
8294 <cell alignment="center" valignment="top" usebox="none">
8297 \begin_layout Plain Layout
8298 \begin_inset Formula $\mapsto$
8308 <cell alignment="center" valignment="top" usebox="none">
8311 \begin_layout Plain Layout
8319 <cell alignment="center" valignment="top" usebox="none">
8322 \begin_layout Plain Layout
8323 \begin_inset Formula $\longmapsto$
8333 <cell alignment="center" valignment="top" usebox="none">
8336 \begin_layout Plain Layout
8344 <cell alignment="center" valignment="top" usebox="none">
8347 \begin_layout Plain Layout
8348 \begin_inset Formula $\leadsto$
8358 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8361 \begin_layout Plain Layout
8369 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8372 \begin_layout Plain Layout
8373 \begin_inset Formula $\dasharrow$
8387 \begin_inset space \hfill{}
8393 \begin_layout Standard
8394 \begin_inset VSpace medskip
8397 Arrows used as accents like e.
8398 \begin_inset space \thinspace{}
8402 \begin_inset space \space{}
8405 vector arrows are listed in
8406 \begin_inset CommandInset ref
8408 reference "sec:Accents"
8415 \begin_layout Standard
8416 \begin_inset VSpace bigskip
8419 Furthermore there are the labeled arrows
8420 \begin_inset Index idx
8423 \begin_layout Plain Layout
8436 \begin_inset Index idx
8439 \begin_layout Plain Layout
8454 \begin_inset Index idx
8457 \begin_layout Plain Layout
8464 \begin_layout Plain Layout
8479 When inserting one of these commands in a formula, an arrow with two blue
8480 boxes appear where the label can be inserted.
8481 The length of the arrow adapts to the label width.
8484 \begin_layout Standard
8486 \begin_inset Tabular
8487 <lyxtabular version="3" rows="3" columns="2">
8488 <features booktabs="true" tabularvalignment="middle">
8489 <column alignment="center" valignment="top" width="0pt">
8490 <column alignment="center" valignment="top" width="0pt">
8492 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8495 \begin_layout Plain Layout
8501 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8504 \begin_layout Plain Layout
8512 <cell alignment="center" valignment="top" usebox="none">
8515 \begin_layout Plain Layout
8519 \begin_inset space \textvisiblespace{}
8523 \begin_inset Formula $\downarrow$
8527 \begin_inset Formula $\to$
8535 <cell alignment="center" valignment="top" usebox="none">
8538 \begin_layout Plain Layout
8539 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8548 <row topspace="2mm">
8549 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8552 \begin_layout Plain Layout
8556 \begin_inset space \textvisiblespace{}
8560 \begin_inset Formula $\downarrow$
8564 \begin_inset Formula $\to$
8572 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8575 \begin_layout Plain Layout
8576 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8592 \begin_layout Standard
8593 \begin_inset VSpace medskip
8599 \begin_layout Standard
8600 If you set in the document settings under
8603 \begin_inset space ~
8613 \begin_inset Index idx
8616 \begin_layout Plain Layout
8617 Packages ! mathtools
8625 \begin_inset space ~
8630 , you have access to the following labeled arrows:
8633 \begin_layout Standard
8634 \begin_inset Newpage newpage
8638 \begin_inset Separator parbreak
8644 \begin_layout Standard
8646 \begin_inset space \hspace*{\fill}
8650 \begin_inset Tabular
8651 <lyxtabular version="3" rows="7" columns="2">
8652 <features booktabs="true" tabularvalignment="middle">
8653 <column alignment="center" valignment="top" width="0pt">
8654 <column alignment="center" valignment="top" width="0pt">
8656 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8659 \begin_layout Plain Layout
8665 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8668 \begin_layout Plain Layout
8676 <cell alignment="center" valignment="top" usebox="none">
8679 \begin_layout Plain Layout
8699 <cell alignment="center" valignment="top" usebox="none">
8702 \begin_layout Plain Layout
8703 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8712 <row topspace="2mm">
8713 <cell alignment="center" valignment="top" usebox="none">
8716 \begin_layout Plain Layout
8736 <cell alignment="center" valignment="top" usebox="none">
8739 \begin_layout Plain Layout
8740 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8749 <row topspace="2mm">
8750 <cell alignment="center" valignment="top" usebox="none">
8753 \begin_layout Plain Layout
8773 <cell alignment="center" valignment="top" usebox="none">
8776 \begin_layout Plain Layout
8777 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8786 <row topspace="2mm">
8787 <cell alignment="center" valignment="top" usebox="none">
8790 \begin_layout Plain Layout
8810 <cell alignment="center" valignment="top" usebox="none">
8813 \begin_layout Plain Layout
8814 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8823 <row topspace="2mm">
8824 <cell alignment="center" valignment="top" usebox="none">
8827 \begin_layout Plain Layout
8847 <cell alignment="center" valignment="top" usebox="none">
8850 \begin_layout Plain Layout
8851 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8860 <row topspace="2mm">
8861 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8864 \begin_layout Plain Layout
8884 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8887 \begin_layout Plain Layout
8888 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8902 \begin_inset space \hspace*{\fill}
8906 \begin_inset Tabular
8907 <lyxtabular version="3" rows="7" columns="2">
8908 <features booktabs="true" tabularvalignment="middle">
8909 <column alignment="center" valignment="top" width="0pt">
8910 <column alignment="center" valignment="top" width="0pt">
8912 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8915 \begin_layout Plain Layout
8921 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8924 \begin_layout Plain Layout
8932 <cell alignment="center" valignment="top" usebox="none">
8935 \begin_layout Plain Layout
8955 <cell alignment="center" valignment="top" usebox="none">
8958 \begin_layout Plain Layout
8959 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8968 <row topspace="2mm">
8969 <cell alignment="center" valignment="top" usebox="none">
8972 \begin_layout Plain Layout
8992 <cell alignment="center" valignment="top" usebox="none">
8995 \begin_layout Plain Layout
8996 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
9005 <row topspace="2mm">
9006 <cell alignment="center" valignment="top" usebox="none">
9009 \begin_layout Plain Layout
9029 <cell alignment="center" valignment="top" usebox="none">
9032 \begin_layout Plain Layout
9033 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9042 <row topspace="2mm">
9043 <cell alignment="center" valignment="top" usebox="none">
9046 \begin_layout Plain Layout
9066 <cell alignment="center" valignment="top" usebox="none">
9069 \begin_layout Plain Layout
9070 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9079 <row topspace="2mm">
9080 <cell alignment="center" valignment="top" usebox="none">
9083 \begin_layout Plain Layout
9103 <cell alignment="center" valignment="top" usebox="none">
9106 \begin_layout Plain Layout
9107 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9116 <row topspace="2mm">
9117 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9120 \begin_layout Plain Layout
9140 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9143 \begin_layout Plain Layout
9144 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9158 \begin_inset space \hspace*{\fill}
9164 \begin_layout Standard
9165 The command scheme is for all these arrows:
9166 \begin_inset Separator parbreak
9172 \begin_layout Standard
9174 \begin_inset Tabular
9175 <lyxtabular version="3" rows="2" columns="2">
9176 <features booktabs="true" tabularvalignment="middle">
9177 <column alignment="center" valignment="top" width="0pt">
9178 <column alignment="center" valignment="top" width="0pt">
9180 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9183 \begin_layout Plain Layout
9189 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9192 \begin_layout Plain Layout
9199 <row bottomspace="0.5mm">
9200 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9203 \begin_layout Plain Layout
9206 xleftrightarrow[x=a]
9209 \begin_inset Formula $\to$
9217 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9220 \begin_layout Plain Layout
9221 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9237 \begin_layout Subsection
9238 Vertical and diagonal Arrows
9239 \begin_inset Index idx
9242 \begin_layout Plain Layout
9249 \begin_inset Index idx
9252 \begin_layout Plain Layout
9261 \begin_layout Standard
9262 \begin_inset space \hfill{}
9266 \begin_inset Tabular
9267 <lyxtabular version="3" rows="7" columns="2">
9268 <features booktabs="true" tabularvalignment="middle">
9269 <column alignment="center" valignment="top" width="0pt">
9270 <column alignment="center" valignment="top" width="0pt">
9272 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9275 \begin_layout Plain Layout
9281 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9284 \begin_layout Plain Layout
9292 <cell alignment="center" valignment="top" usebox="none">
9295 \begin_layout Plain Layout
9303 <cell alignment="center" valignment="top" usebox="none">
9306 \begin_layout Plain Layout
9307 \begin_inset Formula $\uparrow$
9317 <cell alignment="center" valignment="top" usebox="none">
9320 \begin_layout Plain Layout
9328 <cell alignment="center" valignment="top" usebox="none">
9331 \begin_layout Plain Layout
9332 \begin_inset Formula $\Uparrow$
9342 <cell alignment="center" valignment="top" usebox="none">
9345 \begin_layout Plain Layout
9353 <cell alignment="center" valignment="top" usebox="none">
9356 \begin_layout Plain Layout
9357 \begin_inset Formula $\updownarrow$
9367 <cell alignment="center" valignment="top" usebox="none">
9370 \begin_layout Plain Layout
9378 <cell alignment="center" valignment="top" usebox="none">
9381 \begin_layout Plain Layout
9382 \begin_inset Formula $\Updownarrow$
9392 <cell alignment="center" valignment="top" usebox="none">
9395 \begin_layout Plain Layout
9403 <cell alignment="center" valignment="top" usebox="none">
9406 \begin_layout Plain Layout
9407 \begin_inset Formula $\Downarrow$
9417 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9420 \begin_layout Plain Layout
9428 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9431 \begin_layout Plain Layout
9432 \begin_inset Formula $\downarrow$
9446 \begin_inset space \hfill{}
9450 \begin_inset Tabular
9451 <lyxtabular version="3" rows="5" columns="2">
9452 <features booktabs="true" tabularvalignment="middle">
9453 <column alignment="center" valignment="top" width="0pt">
9454 <column alignment="center" valignment="top" width="0pt">
9456 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9459 \begin_layout Plain Layout
9465 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9468 \begin_layout Plain Layout
9476 <cell alignment="center" valignment="top" usebox="none">
9479 \begin_layout Plain Layout
9487 <cell alignment="center" valignment="top" usebox="none">
9490 \begin_layout Plain Layout
9491 \begin_inset Formula $\nearrow$
9501 <cell alignment="center" valignment="top" usebox="none">
9504 \begin_layout Plain Layout
9512 <cell alignment="center" valignment="top" usebox="none">
9515 \begin_layout Plain Layout
9516 \begin_inset Formula $\searrow$
9526 <cell alignment="center" valignment="top" usebox="none">
9529 \begin_layout Plain Layout
9537 <cell alignment="center" valignment="top" usebox="none">
9540 \begin_layout Plain Layout
9541 \begin_inset Formula $\swarrow$
9551 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9554 \begin_layout Plain Layout
9562 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9565 \begin_layout Plain Layout
9566 \begin_inset Formula $\nwarrow$
9580 \begin_inset space \hfill{}
9586 \begin_layout Standard
9587 \begin_inset VSpace medskip
9590 Vertical arrows can be used also as delimiters together with the commands
9592 \begin_inset CommandInset ref
9594 reference "subsec:Manual-Bracket-Size"
9599 \begin_inset CommandInset ref
9601 reference "subsec:Automatic-Bracket-Size"
9608 \begin_layout Section
9610 \begin_inset CommandInset label
9617 \begin_inset Index idx
9620 \begin_layout Plain Layout
9629 \begin_layout Standard
9630 Accents can be inserted via the math toolbar button
9633 arg "math-insert \\hat"
9636 or the commands listed in the following subsections.
9639 \begin_layout Subsection
9640 Accents for one Character
9644 \begin_layout Plain Layout
9657 \begin_layout Plain Layout
9659 \begin_inset CommandInset ref
9661 reference "subsec:Accents-in-Text"
9674 \begin_layout Plain Layout
9682 \begin_inset Note Note
9685 \begin_layout Plain Layout
9692 is used to avoid that the footnote appears in the PDF-bookmark.
9695 \begin_layout Plain Layout
9703 \begin_inset CommandInset ref
9705 reference "subsec:Formulas-in-Section"
9715 \begin_inset CommandInset label
9717 name "subsec:Accents-for-one"
9722 \begin_inset Index idx
9725 \begin_layout Plain Layout
9726 Accents ! for one character
9734 \begin_layout Standard
9735 \begin_inset space \hfill{}
9739 \begin_inset Tabular
9740 <lyxtabular version="3" rows="8" columns="2">
9741 <features booktabs="true" tabularvalignment="middle">
9742 <column alignment="center" valignment="top" width="0pt">
9743 <column alignment="center" valignment="top" width="0pt">
9745 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9748 \begin_layout Plain Layout
9754 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9757 \begin_layout Plain Layout
9764 <row topspace="1.5mm">
9765 <cell alignment="center" valignment="top" usebox="none">
9768 \begin_layout Plain Layout
9772 \begin_inset space \textvisiblespace{}
9780 <cell alignment="center" valignment="top" usebox="none">
9783 \begin_layout Plain Layout
9784 \begin_inset Formula $\dot{A}$
9793 <row topspace="1.5mm">
9794 <cell alignment="center" valignment="top" usebox="none">
9797 \begin_layout Plain Layout
9801 \begin_inset space \textvisiblespace{}
9809 <cell alignment="center" valignment="top" usebox="none">
9812 \begin_layout Plain Layout
9813 \begin_inset Formula $\ddot{A}$
9822 <row topspace="1.5mm">
9823 <cell alignment="center" valignment="top" usebox="none">
9826 \begin_layout Plain Layout
9830 \begin_inset space \textvisiblespace{}
9838 <cell alignment="center" valignment="top" usebox="none">
9841 \begin_layout Plain Layout
9842 \begin_inset Formula $\dddot{A}$
9851 <row topspace="1.5mm">
9852 <cell alignment="center" valignment="top" usebox="none">
9855 \begin_layout Plain Layout
9859 \begin_inset space \textvisiblespace{}
9867 <cell alignment="center" valignment="top" usebox="none">
9870 \begin_layout Plain Layout
9871 \begin_inset Formula $\ddddot{A}$
9880 <row topspace="1.5mm">
9881 <cell alignment="center" valignment="top" usebox="none">
9884 \begin_layout Plain Layout
9888 \begin_inset space \textvisiblespace{}
9892 \begin_inset Index idx
9895 \begin_layout Plain Layout
9906 <cell alignment="center" valignment="top" usebox="none">
9909 \begin_layout Plain Layout
9910 \begin_inset Formula $\vec{A}$
9919 <row topspace="1.5mm">
9920 <cell alignment="center" valignment="top" usebox="none">
9923 \begin_layout Plain Layout
9927 \begin_inset space \textvisiblespace{}
9935 <cell alignment="center" valignment="top" usebox="none">
9938 \begin_layout Plain Layout
9939 \begin_inset Formula $\bar{A}$
9948 <row topspace="1.5mm">
9949 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9952 \begin_layout Plain Layout
9956 \begin_inset space \textvisiblespace{}
9964 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9967 \begin_layout Plain Layout
9968 \begin_inset Formula $\mathring{A}$
9982 \begin_inset space \hfill{}
9986 \begin_inset Tabular
9987 <lyxtabular version="3" rows="7" columns="2">
9988 <features booktabs="true" tabularvalignment="middle">
9989 <column alignment="center" valignment="top" width="0pt">
9990 <column alignment="center" valignment="top" width="0pt">
9992 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9995 \begin_layout Plain Layout
10001 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10004 \begin_layout Plain Layout
10011 <row topspace="1.5mm">
10012 <cell alignment="center" valignment="top" usebox="none">
10015 \begin_layout Plain Layout
10019 \begin_inset space \textvisiblespace{}
10027 <cell alignment="center" valignment="top" usebox="none">
10030 \begin_layout Plain Layout
10031 \begin_inset Formula $\tilde{A}$
10040 <row topspace="1.5mm">
10041 <cell alignment="center" valignment="top" usebox="none">
10044 \begin_layout Plain Layout
10048 \begin_inset space \textvisiblespace{}
10056 <cell alignment="center" valignment="top" usebox="none">
10059 \begin_layout Plain Layout
10060 \begin_inset Formula $\hat{A}$
10069 <row topspace="1.5mm">
10070 <cell alignment="center" valignment="top" usebox="none">
10073 \begin_layout Plain Layout
10077 \begin_inset space \textvisiblespace{}
10085 <cell alignment="center" valignment="top" usebox="none">
10088 \begin_layout Plain Layout
10089 \begin_inset Formula $\check{A}$
10098 <row topspace="1.5mm">
10099 <cell alignment="center" valignment="top" usebox="none">
10102 \begin_layout Plain Layout
10106 \begin_inset space \textvisiblespace{}
10114 <cell alignment="center" valignment="top" usebox="none">
10117 \begin_layout Plain Layout
10118 \begin_inset Formula $\acute{A}$
10127 <row topspace="1.5mm">
10128 <cell alignment="center" valignment="top" usebox="none">
10131 \begin_layout Plain Layout
10135 \begin_inset space \textvisiblespace{}
10143 <cell alignment="center" valignment="top" usebox="none">
10146 \begin_layout Plain Layout
10147 \begin_inset Formula $\grave{A}$
10156 <row topspace="1.5mm">
10157 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10160 \begin_layout Plain Layout
10164 \begin_inset space \textvisiblespace{}
10172 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10175 \begin_layout Plain Layout
10176 \begin_inset Formula $\breve{A}$
10190 \begin_inset space \hfill{}
10196 \begin_layout Standard
10197 \begin_inset VSpace bigskip
10203 \begin_layout Standard
10204 You can directly insert accents like é to formulas.
10206 will transform them to the corresponding accent command.
10208 \begin_inset Index idx
10211 \begin_layout Plain Layout
10217 it is better to insert a quotation mark before the vowel.
10218 These two characters are then treated by \SpecialChar LaTeX
10223 character when the formula part with the umlaut is marked as German.
10231 \begin_inset Quotes eld
10235 \begin_inset Quotes erd
10238 umlauts are created as demonstrated in the following example:
10241 \begin_layout Standard
10242 \begin_inset VSpace -2mm
10248 \begin_layout Standard
10250 \begin_inset Tabular
10251 <lyxtabular version="3" rows="3" columns="2">
10252 <features booktabs="true" tabularvalignment="middle">
10253 <column alignment="center" valignment="top" width="0pt">
10254 <column alignment="center" valignment="top">
10256 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10259 \begin_layout Plain Layout
10265 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10268 \begin_layout Plain Layout
10276 <cell alignment="center" valignment="top" usebox="none">
10279 \begin_layout Plain Layout
10280 \begin_inset Quotes grd
10288 <cell alignment="center" valignment="top" usebox="none">
10291 \begin_layout Plain Layout
10292 \begin_inset space \hspace{}
10299 \begin_inset Formula $"i$
10308 <row topspace="1.5mm">
10309 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10312 \begin_layout Plain Layout
10316 \begin_inset space \textvisiblespace{}
10324 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10327 \begin_layout Plain Layout
10328 \begin_inset Formula $\ddot{i}$
10344 \begin_layout Standard
10345 Another advantage to
10351 is that umlauts can directly be converted to mathematical text because
10352 the accent commands above are
10358 in mathematical text
10361 To convert an accented character to mathematical text, only the character
10362 under the accent may be converted.
10363 This applies also for all other conversions, e.
10364 \begin_inset space \thinspace{}
10368 \begin_inset space \space{}
10374 \begin_layout Standard
10375 In mathematical text, umlauts and other accented characters can directly
10379 \begin_layout Standard
10380 \begin_inset VSpace bigskip
10386 \begin_layout Standard
10388 also supports a tilde under the character if the \SpecialChar LaTeX
10394 \begin_inset Index idx
10397 \begin_layout Plain Layout
10398 Packages ! undertilde
10403 is installed on your system:
10406 \begin_layout Standard
10410 \begin_layout Plain Layout
10420 \begin_inset Note Note
10423 \begin_layout Plain Layout
10424 The following table will only be displayed when the \SpecialChar LaTeX
10435 \begin_inset Separator parbreak
10441 \begin_layout Standard
10444 \begin_inset Tabular
10445 <lyxtabular version="3" rows="2" columns="2">
10446 <features booktabs="true" tabularvalignment="middle">
10447 <column alignment="center" valignment="top" width="0pt">
10448 <column alignment="center" valignment="top" width="0pt">
10450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10453 \begin_layout Plain Layout
10459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10462 \begin_layout Plain Layout
10470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10473 \begin_layout Plain Layout
10477 \begin_inset space \textvisiblespace{}
10485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10488 \begin_layout Plain Layout
10489 \begin_inset Formula $\utilde{A}$
10505 \begin_layout Standard
10509 \begin_layout Plain Layout
10519 \begin_inset Note Note
10522 \begin_layout Plain Layout
10523 The following will be displayed when the \SpecialChar LaTeX
10536 \begin_layout Standard
10537 You need to install the \SpecialChar LaTeX
10542 to see the rest of this subsection in the output.
10545 \begin_layout Standard
10549 \begin_layout Plain Layout
10561 \begin_layout Standard
10562 \begin_inset Newpage newpage
10568 \begin_layout Subsection
10569 Accents for several Characters
10570 \begin_inset Index idx
10573 \begin_layout Plain Layout
10574 Accents ! for several characters
10582 \begin_layout Standard
10583 \begin_inset space \hfill{}
10587 \begin_inset Tabular
10588 <lyxtabular version="3" rows="5" columns="2">
10589 <features booktabs="true" tabularvalignment="middle">
10590 <column alignment="center" valignment="top" width="0pt">
10591 <column alignment="center" valignment="top" width="0pt">
10593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10596 \begin_layout Plain Layout
10602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10605 \begin_layout Plain Layout
10612 <row topspace="1.5mm">
10613 <cell alignment="center" valignment="top" usebox="none">
10616 \begin_layout Plain Layout
10620 \begin_inset space \textvisiblespace{}
10628 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10631 \begin_layout Plain Layout
10632 \begin_inset Formula $\overleftarrow{A=B}$
10641 <row topspace="1.5mm">
10642 <cell alignment="center" valignment="top" usebox="none">
10645 \begin_layout Plain Layout
10649 \begin_inset space \textvisiblespace{}
10657 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10660 \begin_layout Plain Layout
10661 \begin_inset Formula $\underleftarrow{A=B}$
10670 <row topspace="1.5mm">
10671 <cell alignment="center" valignment="top" usebox="none">
10674 \begin_layout Plain Layout
10678 \begin_inset space \textvisiblespace{}
10686 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10689 \begin_layout Plain Layout
10690 \begin_inset Formula $\overleftrightarrow{A=B}$
10699 <row topspace="1.5mm" bottomspace="1mm">
10700 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10703 \begin_layout Plain Layout
10706 underleftrightarrow
10707 \begin_inset space \textvisiblespace{}
10715 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10718 \begin_layout Plain Layout
10719 \begin_inset Formula $\underleftrightarrow{A=B}$
10733 \begin_inset space \hfill{}
10737 \begin_inset Tabular
10738 <lyxtabular version="3" rows="5" columns="2">
10739 <features booktabs="true" tabularvalignment="middle">
10740 <column alignment="center" valignment="top" width="0pt">
10741 <column alignment="center" valignment="top" width="0pt">
10743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10746 \begin_layout Plain Layout
10752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10755 \begin_layout Plain Layout
10762 <row topspace="1.5mm">
10763 <cell alignment="center" valignment="top" usebox="none">
10766 \begin_layout Plain Layout
10770 \begin_inset space \textvisiblespace{}
10778 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10781 \begin_layout Plain Layout
10782 \begin_inset Formula $\overrightarrow{A=B}$
10791 <row topspace="1.5mm">
10792 <cell alignment="center" valignment="top" usebox="none">
10795 \begin_layout Plain Layout
10799 \begin_inset space \textvisiblespace{}
10807 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10810 \begin_layout Plain Layout
10811 \begin_inset Formula $\underrightarrow{A=B}$
10820 <row topspace="1.5mm">
10821 <cell alignment="center" valignment="top" usebox="none">
10824 \begin_layout Plain Layout
10828 \begin_inset space \textvisiblespace{}
10836 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10839 \begin_layout Plain Layout
10840 \begin_inset Formula $\widetilde{A=B}$
10849 <row topspace="1.5mm" bottomspace="1mm">
10850 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10853 \begin_layout Plain Layout
10857 \begin_inset space \textvisiblespace{}
10865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10868 \begin_layout Plain Layout
10869 \begin_inset Formula $\widehat{A=B}$
10883 \begin_inset space \hfill{}
10889 \begin_layout Standard
10890 \begin_inset VSpace medskip
10893 With these commands as many characters as you like can be accented.
10906 will only be set in the output with a length of three characters, as shown
10907 in the following example:
10908 \begin_inset Formula
10910 \widetilde{A+B=C-D}
10918 \begin_layout Standard
10926 \begin_inset Index idx
10929 \begin_layout Plain Layout
10944 \begin_inset Index idx
10947 \begin_layout Plain Layout
10955 described in the previous subsection it is also possible to accent several
10962 \begin_inset space \textvisiblespace{}
10966 \begin_inset Formula $\downarrow$
10972 \begin_inset Formula
10974 \underset{***}{A=B}
10982 \begin_layout Section
10984 \begin_inset CommandInset label
10986 name "subsec:Space"
10991 \begin_inset Index idx
10994 \begin_layout Plain Layout
11003 \begin_layout Subsection
11005 \begin_inset CommandInset label
11007 name "subsec:Predefined-Space"
11012 \begin_inset Index idx
11015 \begin_layout Plain Layout
11016 Space ! horizontal ! predefined
11024 \begin_layout Standard
11025 Sometimes it is necessary to insert horizontal space into a formula.
11026 This is done by inserting a protected space (shortcut
11029 arg "command-alternatives space-insert protected ; math-space"
11034 \begin_inset Quotes eld
11040 \begin_inset space \textvisiblespace{}
11046 \begin_inset Quotes erd
11049 appears and by pressing
11053 several times one can select one of eight different space sizes.
11054 The spaces can also be inserted using the math toolbar button
11057 arg "math-insert \\space"
11060 or special commands.
11061 Independent from the inserted command, one can select the size again by
11067 \begin_inset Separator parbreak
11073 \begin_layout Standard
11076 \begin_inset Tabular
11077 <lyxtabular version="3" rows="6" columns="3">
11078 <features booktabs="true" tabularvalignment="middle">
11079 <column alignment="center" valignment="top">
11080 <column alignment="center" valignment="top" width="15col%">
11081 <column alignment="center" valignment="top">
11083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11086 \begin_layout Plain Layout
11092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11095 \begin_layout Plain Layout
11105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11108 \begin_layout Plain Layout
11116 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11119 \begin_layout Plain Layout
11127 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11130 \begin_layout Plain Layout
11136 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11139 \begin_layout Plain Layout
11140 \begin_inset Formula $A\,B$
11150 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11153 \begin_layout Plain Layout
11161 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11164 \begin_layout Plain Layout
11170 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11173 \begin_layout Plain Layout
11174 \begin_inset Formula $A\:B$
11184 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11187 \begin_layout Plain Layout
11195 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11198 \begin_layout Plain Layout
11204 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11207 \begin_layout Plain Layout
11208 \begin_inset Formula $A\;B$
11218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11221 \begin_layout Plain Layout
11229 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11232 \begin_layout Plain Layout
11238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11241 \begin_layout Plain Layout
11242 \begin_inset Formula $A\quad B$
11252 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11255 \begin_layout Plain Layout
11263 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11266 \begin_layout Plain Layout
11272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11275 \begin_layout Plain Layout
11276 \begin_inset Formula $A\qquad B$
11290 \begin_inset space \hfill{}
11294 \begin_inset Tabular
11295 <lyxtabular version="3" rows="6" columns="3">
11296 <features booktabs="true" tabularvalignment="middle">
11297 <column alignment="center" valignment="top">
11298 <column alignment="center" valignment="top" width="15col%">
11299 <column alignment="center" valignment="top">
11301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11304 \begin_layout Plain Layout
11310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11313 \begin_layout Plain Layout
11323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11326 \begin_layout Plain Layout
11334 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11337 \begin_layout Plain Layout
11345 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11348 \begin_layout Plain Layout
11354 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11357 \begin_layout Plain Layout
11358 \begin_inset Formula $A\hfill B$
11368 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11371 \begin_layout Plain Layout
11379 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11382 \begin_layout Plain Layout
11388 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11391 \begin_layout Plain Layout
11392 \begin_inset Formula $A\hspace*{1em}B$
11402 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11405 \begin_layout Plain Layout
11413 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11416 \begin_layout Plain Layout
11422 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11425 \begin_layout Plain Layout
11426 \begin_inset Formula $A\hspace{1em}B$
11436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11439 \begin_layout Plain Layout
11443 \begin_inset space \textvisiblespace{}
11451 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11454 \begin_layout Plain Layout
11460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11463 \begin_layout Plain Layout
11464 \begin_inset Formula $A\ B$
11474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11477 \begin_layout Plain Layout
11485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11488 \begin_layout Plain Layout
11494 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11497 \begin_layout Plain Layout
11498 \begin_inset Formula $A\!B$
11514 \begin_layout Standard
11516 \begin_inset space ~
11520 \begin_inset space \thinspace{}
11524 \begin_inset space \thinspace{}
11527 7 are variable spaces which are explained in
11528 \begin_inset CommandInset ref
11530 reference "subsec:Variable-Space"
11536 \begin_inset space ~
11539 9 seems to produce no space.
11540 It is displayed red in \SpecialChar LyX
11541 contrary to the other sizes, because it is a negative
11543 There are two more negative spaces:
11544 \begin_inset Separator parbreak
11550 \begin_layout Standard
11552 \begin_inset Tabular
11553 <lyxtabular version="3" rows="3" columns="3">
11554 <features booktabs="true" tabularvalignment="middle">
11555 <column alignment="center" valignment="middle" width="6.8cm">
11556 <column alignment="center" valignment="top" width="0pt">
11557 <column alignment="center" valignment="top" width="0pt">
11559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11562 \begin_layout Plain Layout
11568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11571 \begin_layout Plain Layout
11579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11582 \begin_layout Plain Layout
11592 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11595 \begin_layout Plain Layout
11600 keystrokes after inserting the protected space
11605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11608 \begin_layout Plain Layout
11614 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11617 \begin_layout Plain Layout
11625 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11628 \begin_layout Plain Layout
11634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11637 \begin_layout Plain Layout
11638 \begin_inset Formula $A\negmedspace B$
11646 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11649 \begin_layout Plain Layout
11650 \begin_inset Formula $A\negthickspace B$
11666 \begin_layout Standard
11667 Negative spaces can lead to characters overlapping each other.
11668 Thus they can be used to enforce ligatures, which are e.
11669 \begin_inset space \thinspace{}
11673 \begin_inset space \space{}
11676 useful for summation operators:
11677 \begin_inset Separator parbreak
11683 \begin_layout Standard
11685 \begin_inset Tabular
11686 <lyxtabular version="3" rows="3" columns="2">
11687 <features booktabs="true" tabularvalignment="middle">
11688 <column alignment="center" valignment="top" width="0pt">
11689 <column alignment="center" valignment="top">
11691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11694 \begin_layout Plain Layout
11700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11703 \begin_layout Plain Layout
11711 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11714 \begin_layout Plain Layout
11720 \begin_inset space \textvisiblespace{}
11728 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11731 \begin_layout Plain Layout
11732 \begin_inset Formula $\sum\sum f_{kl}$
11742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11745 \begin_layout Plain Layout
11753 \begin_inset space \textvisiblespace{}
11761 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11764 \begin_layout Plain Layout
11765 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11781 \begin_layout Standard
11783 \begin_inset VSpace medskip
11789 \begin_layout Standard
11791 Relations like for example equal signs, are always surrounded by space.
11792 To suppress this, the equal sign is placed into a \SpecialChar TeX
11794 The following example demonstrates this:
11795 \begin_inset Separator parbreak
11801 \begin_layout Standard
11803 \begin_inset Tabular
11804 <lyxtabular version="3" rows="2" columns="2">
11805 <features tabularvalignment="middle">
11806 <column alignment="center" valignment="top" width="0pt">
11807 <column alignment="center" valignment="top" width="0pt">
11809 <cell alignment="center" valignment="top" usebox="none">
11812 \begin_layout Plain Layout
11818 <cell alignment="center" valignment="top" usebox="none">
11821 \begin_layout Plain Layout
11822 \begin_inset Formula $A=B$
11832 <cell alignment="center" valignment="top" usebox="none">
11835 \begin_layout Plain Layout
11836 equation without space
11841 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11844 \begin_layout Plain Layout
11845 \begin_inset Formula $A{=}B$
11861 \begin_layout Standard
11863 The command for the last formula is:
11868 \begin_inset Formula $\to$
11874 \begin_layout Standard
11875 \begin_inset VSpace bigskip
11881 \begin_layout Standard
11882 Spaces are needed for physical units, because the space between the value
11883 and the unit is the smallest one and not a normal space.
11884 For units in text, the smallest space is inserted via the menu
11886 Insert\SpecialChar menuseparator
11887 Formatting\SpecialChar menuseparator
11889 \begin_inset space ~
11897 arg "space-insert thin"
11903 \begin_layout Standard
11904 An example to visualize the difference:
11907 \begin_layout Standard
11908 \begin_inset Tabular
11909 <lyxtabular version="3" rows="2" columns="2">
11910 <features tabularvalignment="middle">
11911 <column alignment="left" valignment="top">
11912 <column alignment="left" valignment="top">
11914 <cell alignment="center" valignment="top" usebox="none">
11917 \begin_layout Plain Layout
11919 \begin_inset Formula $\cdot$
11927 <cell alignment="center" valignment="top" usebox="none">
11930 \begin_layout Plain Layout
11931 space between value and unit
11938 <cell alignment="center" valignment="top" usebox="none">
11941 \begin_layout Plain Layout
11943 \begin_inset space \thinspace{}
11947 \begin_inset Formula $\cdot$
11955 <cell alignment="center" valignment="top" usebox="none">
11958 \begin_layout Plain Layout
11959 smallest space between value and unit
11972 \begin_layout Subsection
11977 \begin_layout Plain Layout
11990 \begin_layout Plain Layout
11991 for vertical space in formulas see
11992 \begin_inset CommandInset ref
11994 reference "subsec:Line-Separation"
12007 \begin_layout Plain Layout
12015 \begin_inset Note Note
12018 \begin_layout Plain Layout
12021 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12024 \begin_layout Plain Layout
12027 texorpdfstring is in section
12028 \begin_inset CommandInset ref
12030 reference "subsec:Formulas-in-Section"
12040 \begin_inset CommandInset label
12042 name "subsec:Variable-Space"
12047 \begin_inset Index idx
12050 \begin_layout Plain Layout
12051 Space ! horizontal ! variable
12059 \begin_layout Standard
12060 Space with a defined length can be inserted with the command
12067 \begin_inset Index idx
12070 \begin_layout Plain Layout
12080 \begin_inset Quotes eld
12086 \begin_inset space \textvisiblespace{}
12092 \begin_inset Quotes erd
12096 The length can be specified by left-clicking on the
12097 \begin_inset Quotes eld
12103 \begin_inset space \textvisiblespace{}
12109 \begin_inset Quotes erd
12113 The length may also be negative.
12114 When a space would be the first character in a line it would be omitted.
12115 To force its output use the command
12127 or left-click on the
12128 \begin_inset Quotes eld
12134 \begin_inset space \textvisiblespace{}
12140 \begin_inset Quotes erd
12143 and check the option
12148 \begin_inset Newline newline
12151 To insert as much space as is available, the command
12158 \begin_inset Index idx
12161 \begin_layout Plain Layout
12172 \begin_layout Standard
12174 \begin_inset Tabular
12175 <lyxtabular version="3" rows="4" columns="2">
12176 <features booktabs="true" tabularvalignment="middle">
12177 <column alignment="center" valignment="top" width="0pt">
12178 <column alignment="center" valignment="top">
12180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12183 \begin_layout Plain Layout
12191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12194 \begin_layout Plain Layout
12202 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12205 \begin_layout Plain Layout
12209 \begin_inset space \textvisiblespace{}
12215 \begin_inset space \thinspace{}
12223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12226 \begin_layout Plain Layout
12227 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12237 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12240 \begin_layout Plain Layout
12244 \begin_inset space \textvisiblespace{}
12250 \begin_inset space \thinspace{}
12258 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12261 \begin_layout Plain Layout
12262 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12275 \begin_layout Plain Layout
12279 \begin_inset space \textvisiblespace{}
12287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12290 \begin_layout Plain Layout
12291 \begin_inset Formula $A=A\hfill B=B$
12307 \begin_layout Standard
12308 In the last example the available space is given by the longest column entry
12310 In an inline formula the space depends on the length of the line in which
12318 Thus, when the line uses the full width, no space will be created.
12325 only has an effect on displayed formulas when the formula style
12330 (Formula styles are explained in
12331 \begin_inset CommandInset ref
12333 reference "sec:Formula-Styles"
12340 \begin_layout Standard
12347 , there are the commands
12359 that fill the space with a pattern, see
12360 \begin_inset CommandInset ref
12362 reference "subsec:Ellipses"
12369 \begin_layout Standard
12370 For text, variable space can be inserted via the menu
12372 Insert\SpecialChar menuseparator
12373 Formatting\SpecialChar menuseparator
12375 \begin_inset space ~
12383 \begin_layout Standard
12384 This is a line with
12385 \begin_inset space \hspace{}
12390 \begin_inset space \thinspace{}
12396 \begin_layout Standard
12397 This is a line with
12398 \begin_inset space \hfill{}
12404 \begin_layout Subsection
12405 Space besides inline Formulas
12406 \begin_inset Index idx
12409 \begin_layout Plain Layout
12410 Space ! besides inline formulas
12418 \begin_layout Standard
12419 The space that surrounds inline formulas can be adjusted with the length
12427 \begin_inset Index idx
12430 \begin_layout Plain Layout
12439 The value of a length is set with the command
12446 \begin_inset Index idx
12449 \begin_layout Plain Layout
12457 which has the following scheme:
12460 \begin_layout Standard
12465 setlength{length name}{value}
12468 \begin_layout Standard
12476 \begin_inset space \thinspace{}
12482 \begin_layout Standard
12492 \begin_layout Standard
12493 is inserted in \SpecialChar TeX
12496 \begin_inset space \thinspace{}
12499 mm space will now be set around all inline formulas:
12503 \begin_layout Plain Layout
12517 \begin_layout Standard
12518 This is a line with an inline formula
12519 \begin_inset Formula $A=B$
12523 \begin_inset space \thinspace{}
12526 mm surrounding space.
12530 \begin_layout Plain Layout
12544 \begin_layout Standard
12545 To return to the predefined value,
12551 is set to the value 0
12552 \begin_inset space \thinspace{}
12558 \begin_layout Standard
12559 \begin_inset Newpage newpage
12565 \begin_layout Section
12567 \begin_inset Index idx
12570 \begin_layout Plain Layout
12577 \begin_inset Index idx
12580 \begin_layout Plain Layout
12585 \begin_layout Plain Layout
12596 \begin_layout Plain Layout
12611 \begin_layout Standard
12612 Boxes for text are described in chapter
12619 \begin_inset space ~
12627 \begin_layout Subsection
12629 \begin_inset CommandInset label
12631 name "subsec:Boxes-with-Frame"
12636 \begin_inset Index idx
12639 \begin_layout Plain Layout
12648 \begin_layout Standard
12649 It is possible to frame a formula or part of one with the commands
12656 \begin_inset Index idx
12659 \begin_layout Plain Layout
12674 \begin_inset Index idx
12677 \begin_layout Plain Layout
12688 \begin_layout Standard
12689 When one of these commands is inserted in a formula, a blue box appears
12690 within a frame to enter formula parts.
12697 an additional formula has to be created by
12701 within this box, because the box content will otherwise be treated as mathemati
12709 is used, a new formula is automatically created inside the frame.
12712 \begin_layout Standard
12719 is not suitable to frame displayed formulas because the formula will always
12720 be set in the size of the text.
12727 is in contrary not suitable to frame inline formulas, because the formula
12728 will always be set in the size of a displayed formula.
12731 \begin_layout Standard
12745 \begin_inset Index idx
12748 \begin_layout Plain Layout
12756 where additionally the frame width and the alignment can be specified.
12763 is used in the following scheme:
12766 \begin_layout Standard
12771 framebox[frame width][position]{box content}
12774 \begin_layout Standard
12775 The position can either be
12792 right aligns the formula in the box.
12793 When no position is given, the formula will be centered.
12794 \begin_inset Newline newline
12797 If no width is given, also no position can be given.
12798 In this case the frame width is adjusted to the box content like for
12807 \begin_layout Standard
12814 is inserted, a box appears containing three blue boxes.
12815 The first two boxes are surrounded by brackets and denote the two optional
12817 The third box is for formula parts like for
12824 \begin_inset Separator parbreak
12830 \begin_layout Standard
12832 \begin_inset Tabular
12833 <lyxtabular version="3" rows="5" columns="2">
12834 <features booktabs="true" tabularvalignment="middle">
12835 <column alignment="center" valignment="top" width="0pt">
12836 <column alignment="center" valignment="top">
12838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12841 \begin_layout Plain Layout
12847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12850 \begin_layout Plain Layout
12857 <row topspace="1.5mm">
12858 <cell alignment="center" valignment="top" usebox="none">
12861 \begin_layout Plain Layout
12865 \begin_inset space \textvisiblespace{}
12875 \begin_inset space \textvisiblespace{}
12883 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12886 \begin_layout Plain Layout
12887 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12896 <row topspace="1.5mm">
12897 <cell alignment="center" valignment="top" usebox="none">
12900 \begin_layout Plain Layout
12904 \begin_inset space \textvisiblespace{}
12910 \begin_inset space \textvisiblespace{}
12918 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12921 \begin_layout Plain Layout
12922 \begin_inset Formula $\boxed{\int A=B}$
12931 <row topspace="1.5mm">
12932 <cell alignment="center" valignment="top" usebox="none">
12935 \begin_layout Plain Layout
12939 \begin_inset space \textvisiblespace{}
12947 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12950 \begin_layout Plain Layout
12951 \begin_inset Formula $A+\fbox{B}$
12960 <row topspace="1.5mm" bottomspace="1mm">
12961 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12964 \begin_layout Plain Layout
12968 \begin_inset space \textvisiblespace{}
12972 \begin_inset Formula $\to$
12976 \begin_inset Formula $\to$
12986 \begin_inset space \textvisiblespace{}
12990 \begin_inset Formula $\downarrow$
12998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13001 \begin_layout Plain Layout
13002 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13018 \begin_layout Standard
13019 The frame thickness can also be adjusted.
13020 To do this the following commands have to be inserted in \SpecialChar TeX
13025 \begin_layout Standard
13035 \begin_inset Quotes eld
13039 \begin_inset Quotes erd
13053 \begin_inset Quotes eld
13057 \begin_inset Quotes erd
13063 \begin_layout Standard
13064 \begin_inset Quotes eld
13068 \begin_inset Quotes erd
13071 specifies the minimal distance between the frame and the first character
13073 An example for this is the following framed formula:
13077 \begin_layout Plain Layout
13089 \begin_inset Formula
13096 Before this formula the commands
13099 \begin_layout Standard
13121 \begin_layout Standard
13122 were inserted in \SpecialChar TeX
13124 The given values are used for all following boxes.
13127 \begin_layout Standard
13128 To return to the standard frame size, the command
13131 \begin_layout Standard
13156 \begin_layout Plain Layout
13170 \begin_layout Standard
13171 is inserted in \SpecialChar TeX
13172 mode before the next formula.
13175 \begin_layout Subsection
13176 Boxes without Frame
13177 \begin_inset CommandInset label
13179 name "subsec:Boxes-without-Frame"
13184 \begin_inset Index idx
13187 \begin_layout Plain Layout
13188 Boxes ! without frame
13196 \begin_layout Standard
13197 For boxes without a frame there are the following box commands:
13204 \begin_inset Index idx
13207 \begin_layout Plain Layout
13222 \begin_inset Index idx
13225 \begin_layout Plain Layout
13240 \begin_inset Index idx
13243 \begin_layout Plain Layout
13254 \begin_layout Standard
13261 a box can be super- or subscripted.
13262 But in contrary to normal super- and subscripting, the characters in the
13263 box keep their font size.
13270 is used in the following scheme:
13273 \begin_layout Standard
13278 raisebox{height}{box content}
13281 \begin_layout Standard
13282 When the box should contain a formula, an extra formula is needed like for
13293 \begin_inset Note Greyedout
13296 \begin_layout Plain Layout
13307 this extra formula is created by pressing
13311 twice instead of once because \SpecialChar LyX
13312 doesn't yet support
13326 \begin_inset Separator parbreak
13332 \begin_layout Standard
13334 \begin_inset Tabular
13335 <lyxtabular version="3" rows="4" columns="2">
13336 <features booktabs="true" tabularvalignment="middle">
13337 <column alignment="center" valignment="top" width="0pt">
13338 <column alignment="center" valignment="top">
13340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13343 \begin_layout Plain Layout
13349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13352 \begin_layout Plain Layout
13360 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13363 \begin_layout Plain Layout
13367 \begin_inset Formula $\to$
13373 \begin_inset Formula $\to$
13381 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13384 \begin_layout Plain Layout
13385 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13395 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13398 \begin_layout Plain Layout
13402 \begin_inset Formula $\to$
13408 \begin_inset Formula $\to$
13416 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13419 \begin_layout Plain Layout
13420 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13433 \begin_layout Plain Layout
13437 \begin_inset Formula $\to$
13453 \begin_inset space \textvisiblespace{}
13461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13464 \begin_layout Plain Layout
13465 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13481 \begin_layout Standard
13506 , with the difference that there is no frame.
13509 \begin_layout Subsection
13511 \begin_inset CommandInset label
13513 name "subsec:Colored-Boxes"
13518 \begin_inset Index idx
13521 \begin_layout Plain Layout
13530 \begin_layout Standard
13531 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13540 \begin_layout Plain Layout
13541 The \SpecialChar LaTeX
13546 is part of every \SpecialChar LaTeX
13547 standard installation.
13553 \begin_inset Index idx
13556 \begin_layout Plain Layout
13562 has to be loaded in the \SpecialChar LaTeX
13563 -preamble with the line
13567 \begin_layout Plain Layout
13568 When text is colored somewhere in the document with a predefined color,
13570 loads the \SpecialChar LaTeX
13576 Thus it is possible that the package is loaded twice, but this does not
13583 \begin_inset Note Note
13586 \begin_layout Plain Layout
13587 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13596 \begin_layout Standard
13604 \begin_layout Standard
13605 \begin_inset VSpace medskip
13608 To color boxes, the command
13615 \begin_inset Index idx
13618 \begin_layout Plain Layout
13626 is used in the following scheme:
13629 \begin_layout Standard
13634 colorbox{color}{box content}
13637 \begin_layout Standard
13638 The box content can also be a box and a
13644 can also be part of another box (see the 2nd and 3rd example).
13645 When the box should contain a formula, an extra formula has to be created,
13646 the same way as for
13656 \begin_layout Plain Layout
13657 This also applies for the command
13671 \begin_layout Standard
13672 One of the following predefined colors can be chosen:
13675 \begin_layout Standard
13709 \begin_inset Separator parbreak
13715 \begin_layout Standard
13717 \begin_inset Tabular
13718 <lyxtabular version="3" rows="4" columns="2">
13719 <features booktabs="true" tabularvalignment="middle">
13720 <column alignment="center" valignment="top" width="0pt">
13721 <column alignment="center" valignment="top">
13723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13726 \begin_layout Plain Layout
13732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13735 \begin_layout Plain Layout
13743 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13746 \begin_layout Plain Layout
13750 \begin_inset Formula $\to$
13760 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13763 \begin_layout Plain Layout
13764 \begin_inset Formula $\colorbox{yellow}{A=B}$
13773 <row topspace="1.5mm">
13774 <cell alignment="center" valignment="top" usebox="none">
13777 \begin_layout Plain Layout
13781 \begin_inset Formula $\to$
13789 \begin_inset space \textvisiblespace{}
13797 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13800 \begin_layout Plain Layout
13801 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13810 <row topspace="1.5mm" bottomspace="1mm">
13811 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13814 \begin_layout Plain Layout
13818 \begin_inset space \textvisiblespace{}
13824 \begin_inset Formula $\to$
13840 \begin_inset space \textvisiblespace{}
13848 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13851 \begin_layout Plain Layout
13852 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13868 \begin_layout Standard
13875 only colors the box but not the characters in the box.
13876 To color all characters, the whole formula is highlighted and the desired
13877 color is chosen in the
13880 \begin_inset space ~
13886 The dialog can be called with the toolbar button
13889 arg "dialog-show character"
13894 Edit\SpecialChar menuseparator
13896 \begin_inset space ~
13899 Style\SpecialChar menuseparator
13903 The formula number then has the same color as the formula.
13904 When the formula number should get another color than the formula characters,
13905 the color must be changed within the formula.
13908 \begin_layout Standard
13912 \begin_layout Standard
13915 \begin_inset Formula
13917 \int A=B\label{eq:red}
13925 \begin_inset Formula
13927 \textcolor{red}{\int A=B}\label{eq:redgreen}
13935 \begin_layout Standard
13937 \begin_inset CommandInset ref
13943 is completely colored red.
13944 \begin_inset Newline newline
13948 \begin_inset CommandInset ref
13950 reference "eq:redgreen"
13954 was first completely colored green to set the color for the formula number.
13955 Subsequently the formula characters were colored red.
13958 \begin_layout Standard
13959 \begin_inset VSpace bigskip
13962 To color the frame different than the rest of the box, the command
13969 \begin_inset Index idx
13972 \begin_layout Plain Layout
13980 is used in the following scheme:
13983 \begin_layout Standard
13988 fcolorbox{frame color}{color}{box content}
13991 \begin_layout Standard
13998 is an extension of the command
14005 The frame width is set, like for
14028 \begin_layout Plain Layout
14040 \begin_inset Formula
14042 \fcolorbox{cyan}{magenta}{A=B}
14051 \begin_layout Plain Layout
14065 \begin_layout Standard
14066 This formula was created with the command
14067 \begin_inset Newline newline
14075 \begin_inset Formula $\to$
14081 \begin_inset Formula $\to$
14091 \begin_layout Standard
14092 \begin_inset VSpace bigskip
14095 To use other colors than the predefined ones, they have to be defined first.
14098 \begin_layout Standard
14099 One can for example define the color
14100 \begin_inset Quotes eld
14108 \begin_inset Quotes erd
14111 with the \SpecialChar LaTeX
14115 \begin_layout Standard
14120 definecolor{darkgreen}{cmyk}{0.5,
14135 \begin_inset Index idx
14138 \begin_layout Plain Layout
14149 \begin_layout Standard
14154 is the color space that denotes the colors
14171 The four comma separated numbers are the portion factor for the corresponding
14172 colors of the color space.
14173 The factors can be in the range of 0
14174 \begin_inset space \thinspace{}
14178 \begin_inset space \thinspace{}
14186 also the color space
14190 can be used for definitions.
14207 , so that there are in this case three portion factors for the corresponding
14209 Furthermore there is the color space
14213 with one portion factor for the gray value.
14216 \begin_layout Standard
14217 As example a framed box with the new defined color
14221 where the characters have been colored
14226 \begin_inset Formula
14228 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14236 \begin_layout Standard
14237 Self-defined colors can also be used for text with the help of the command
14245 \begin_inset Index idx
14248 \begin_layout Plain Layout
14257 \begin_layout Standard
14261 \begin_layout Plain Layout
14265 textcolor{darkgreen}{
14271 \begin_inset Quotes eld
14275 \begin_inset Quotes erd
14282 \begin_layout Plain Layout
14292 \begin_layout Standard
14300 \begin_inset Index idx
14303 \begin_layout Plain Layout
14311 is used in the scheme
14315 textcolor{color}{characters to color}
14320 \begin_layout Subsection
14322 \begin_inset CommandInset label
14324 name "subsec:Paragraph-Boxes"
14329 \begin_inset Index idx
14332 \begin_layout Plain Layout
14333 Boxes ! as paragraph
14341 \begin_layout Standard
14342 A box that can contain several lines and paragraphs, a so-called paragraph
14343 box (parbox), can be created with the menu
14345 Insert\SpecialChar menuseparator
14348 or the toolbar button
14357 \begin_layout Standard
14358 The following example shows a framed parbox in a line:
14361 \begin_layout Standard
14362 \begin_inset VSpace medskip
14366 \begin_inset Box Boxed
14376 height_special "totalheight"
14381 backgroundcolor "none"
14384 \begin_layout Plain Layout
14385 This is a paragraph box.
14387 \begin_inset space \thinspace{}
14390 cm long and can also contain formulas:
14391 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14402 \begin_layout Standard
14403 \begin_inset VSpace medskip
14409 \begin_layout Standard
14410 Such a box is created by right-clicking on the gray box inset.
14411 A dialog pops up showing the box properties.
14425 \begin_inset space \thinspace{}
14430 Vertical Box Alignment
14435 \begin_layout Standard
14436 \begin_inset VSpace medskip
14439 In \SpecialChar LaTeX
14440 a parbox is created with the command
14447 \begin_inset Index idx
14450 \begin_layout Plain Layout
14458 which has the following scheme:
14461 \begin_layout Standard
14466 parbox[position]{width}{box content}
14469 \begin_layout Standard
14484 \begin_inset Quotes eld
14488 \begin_inset Quotes erd
14491 means that the box is aligned within the surrounding text with its last
14498 \begin_inset Quotes eld
14502 \begin_inset Quotes erd
14505 this is done with the first line.
14506 When no position is given, the box will be vertically centered, see section
14514 \begin_inset space ~
14519 manual for examples.
14522 \begin_layout Standard
14523 \begin_inset VSpace bigskip
14526 To frame formulas completely, including the formula number, the formula
14527 must be set into a parbox.
14528 To do this, the command
14542 is inserted in \SpecialChar TeX
14543 mode before the formula.
14551 \begin_inset Index idx
14554 \begin_layout Plain Layout
14562 is hereby the line width set for the document.
14563 Because the frame is outside the parbox, 2
14564 \begin_inset space \thinspace{}
14567 times the frame separation and the frame thickness must be subtracted from
14569 As this is not automatically done by \SpecialChar LyX
14574 \begin_layout Plain Layout
14575 \begin_inset CommandInset href
14577 name "LyX-bug #4483"
14578 target "http://www.lyx.org/trac/ticket/4483"
14588 mode has to be used.
14589 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14598 \begin_layout Plain Layout
14603 is part of every \SpecialChar LaTeX
14604 standard installation.
14610 \begin_inset Index idx
14613 \begin_layout Plain Layout
14619 must be loaded in the \SpecialChar LaTeX
14620 -preamble with the line
14623 \begin_layout Standard
14631 \begin_layout Standard
14632 Behind the formula both boxes are closed by entering
14636 in \SpecialChar TeX
14638 Here is an example:
14642 \begin_layout Plain Layout
14656 \begin_layout Standard
14660 \begin_layout Plain Layout
14678 \begin_inset Formula
14680 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14689 \begin_layout Plain Layout
14700 \begin_layout Plain Layout
14714 \begin_layout Standard
14715 \begin_inset VSpace medskip
14718 As a parbox is used as the argument of
14724 , there is in this case no difference between
14739 \begin_layout Standard
14740 \begin_inset VSpace bigskip
14743 Paragraph boxes are very useful to comment formulas directly.
14750 is used in combination with the command
14764 \begin_inset CommandInset ref
14766 reference "subsec:User-defined-Numbering"
14773 \begin_layout Standard
14774 An example of a formula commented with
14783 \begin_layout Standard
14787 \begin_layout Plain Layout
14800 This is a description.
14801 It is distinctly separated from the formula and multiline.
14805 \begin_layout Plain Layout
14817 \begin_layout Standard
14818 Such a formula must be inserted completely in \SpecialChar TeX
14819 mode because \SpecialChar LyX
14821 support the command
14828 The formula is created with the following command sequence:
14831 \begin_layout Standard
14844 is inserted in \SpecialChar TeX
14849 \begin_layout Plain Layout
14850 When the formula style
14862 can also be replaced by
14869 (formula styles see
14870 \begin_inset CommandInset ref
14872 reference "sec:Formula-Styles"
14881 Then the description follows as normal text and finally
14887 is inserted in \SpecialChar TeX
14901 hereby create a displayed formula.
14904 \begin_layout Standard
14911 can be seen in this example that was
14912 \begin_inset Quotes eld
14916 \begin_inset Quotes erd
14919 using the mathematical textmode:
14920 \begin_inset Formula
14922 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14930 \begin_layout Section
14932 \begin_inset Index idx
14935 \begin_layout Plain Layout
14944 \begin_layout Subsection
14946 \begin_inset CommandInset label
14948 name "subsec:Big-Operators"
14953 \begin_inset Index idx
14956 \begin_layout Plain Layout
14963 \begin_inset Index idx
14966 \begin_layout Plain Layout
14973 \begin_inset Index idx
14976 \begin_layout Plain Layout
14985 \begin_layout Standard
14986 To be able to use all integral operators listed here, the option
14988 Use esint package automatically
14990 must be set in the document settings under
14993 \begin_inset space ~
15001 \begin_layout Standard
15002 \begin_inset space \hfill{}
15006 \begin_inset Tabular
15007 <lyxtabular version="3" rows="11" columns="2">
15008 <features booktabs="true" tabularvalignment="middle">
15009 <column alignment="center" valignment="top" width="0pt">
15010 <column alignment="center" valignment="top" width="0pt">
15012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15015 \begin_layout Plain Layout
15021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15024 \begin_layout Plain Layout
15032 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15035 \begin_layout Plain Layout
15039 \begin_inset Index idx
15042 \begin_layout Plain Layout
15055 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15058 \begin_layout Plain Layout
15059 \begin_inset Formula $\int$
15069 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15072 \begin_layout Plain Layout
15080 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15083 \begin_layout Plain Layout
15084 \begin_inset Formula $\oint$
15094 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15097 \begin_layout Plain Layout
15105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15108 \begin_layout Plain Layout
15109 \begin_inset Formula $\ointctrclockwise$
15119 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15122 \begin_layout Plain Layout
15130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15133 \begin_layout Plain Layout
15134 \begin_inset Formula $\ointclockwise$
15144 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15147 \begin_layout Plain Layout
15155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15158 \begin_layout Plain Layout
15159 \begin_inset Formula $\sqint$
15169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15172 \begin_layout Plain Layout
15180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15183 \begin_layout Plain Layout
15185 \begin_inset Formula $\fint$
15195 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15198 \begin_layout Plain Layout
15206 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15209 \begin_layout Plain Layout
15211 \begin_inset Formula $\landupint$
15221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15224 \begin_layout Plain Layout
15232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15235 \begin_layout Plain Layout
15237 \begin_inset Formula $\landdownint$
15247 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15250 \begin_layout Plain Layout
15258 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15261 \begin_layout Plain Layout
15262 \begin_inset Formula $\bigcap$
15272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15275 \begin_layout Plain Layout
15283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15286 \begin_layout Plain Layout
15287 \begin_inset Formula $\bigcup$
15301 \begin_inset space \hfill{}
15305 \begin_inset Tabular
15306 <lyxtabular version="3" rows="11" columns="2">
15307 <features booktabs="true" tabularvalignment="middle">
15308 <column alignment="center" valignment="top" width="0pt">
15309 <column alignment="center" valignment="top" width="0pt">
15311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15314 \begin_layout Plain Layout
15320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15323 \begin_layout Plain Layout
15331 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15334 \begin_layout Plain Layout
15338 \begin_inset Index idx
15341 \begin_layout Plain Layout
15354 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15357 \begin_layout Plain Layout
15358 \begin_inset Formula $\sum$
15368 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15371 \begin_layout Plain Layout
15375 \begin_inset Index idx
15378 \begin_layout Plain Layout
15385 \begin_layout Plain Layout
15404 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15407 \begin_layout Plain Layout
15408 \begin_inset Formula $\prod$
15418 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15421 \begin_layout Plain Layout
15429 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15432 \begin_layout Plain Layout
15433 \begin_inset Formula $\coprod$
15443 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15446 \begin_layout Plain Layout
15454 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15457 \begin_layout Plain Layout
15458 \begin_inset Formula $\bigodot$
15468 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15471 \begin_layout Plain Layout
15479 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15482 \begin_layout Plain Layout
15483 \begin_inset Formula $\bigotimes$
15493 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15496 \begin_layout Plain Layout
15504 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15507 \begin_layout Plain Layout
15508 \begin_inset Formula $\bigoplus$
15518 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15521 \begin_layout Plain Layout
15529 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15532 \begin_layout Plain Layout
15533 \begin_inset Formula $\bigwedge$
15543 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15546 \begin_layout Plain Layout
15554 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15557 \begin_layout Plain Layout
15558 \begin_inset Formula $\bigvee$
15568 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15571 \begin_layout Plain Layout
15579 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15582 \begin_layout Plain Layout
15583 \begin_inset Formula $\bigsqcup$
15593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15596 \begin_layout Plain Layout
15604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15607 \begin_layout Plain Layout
15608 \begin_inset Formula $\biguplus$
15622 \begin_inset space \hfill{}
15628 \begin_layout Standard
15629 All big operators can also be inserted via the math toolbar button
15632 arg "math-insert \\intop"
15638 \begin_layout Standard
15639 The operators are called big because they are bigger than the sometimes
15640 equal looking binary operators.
15641 All big operators can have limits as described in the next subsection.
15644 \begin_layout Standard
15645 For all integral operators there is a second version available, ending in
15663 These operators are different from
15670 \begin_inset space \space{}
15673 in the style the operator limits are displayed, see
15674 \begin_inset CommandInset ref
15676 reference "subsec:Operator-Limits"
15684 \begin_layout Subsubsection*
15685 Advice for Integrals
15688 \begin_layout Standard
15693 in an integral is an operator, that therefore has to be set upright.
15694 This is done by highlighting the
15698 and using the keyboard shortcut
15708 \begin_layout Plain Layout
15714 \begin_inset CommandInset ref
15716 reference "subsec:Font-Styles"
15726 Finally the smallest space is inserted before the
15730 , as this is usual for operators.
15734 \begin_layout Standard
15736 \begin_inset Formula $\int A(x)dx$
15740 \begin_inset Newline newline
15744 \begin_inset Phantom HPhantom
15747 \begin_layout Plain Layout
15754 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15760 \begin_layout Standard
15761 For multiple integrals there are the following commands:
15762 \begin_inset VSpace medskip
15768 \begin_layout Standard
15769 \begin_inset space \hfill{}
15773 \begin_inset Tabular
15774 <lyxtabular version="3" rows="4" columns="2">
15775 <features booktabs="true" tabularvalignment="middle">
15776 <column alignment="center" valignment="top" width="0pt">
15777 <column alignment="center" valignment="top" width="0pt">
15779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15782 \begin_layout Plain Layout
15788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15791 \begin_layout Plain Layout
15798 <row bottomspace="1mm">
15799 <cell alignment="center" valignment="top" usebox="none">
15802 \begin_layout Plain Layout
15810 <cell alignment="center" valignment="top" usebox="none">
15813 \begin_layout Plain Layout
15814 \begin_inset Formula $\iint$
15823 <row bottomspace="1mm">
15824 <cell alignment="center" valignment="top" usebox="none">
15827 \begin_layout Plain Layout
15835 <cell alignment="center" valignment="top" usebox="none">
15838 \begin_layout Plain Layout
15839 \begin_inset Formula $\oiint$
15848 <row bottomspace="1mm">
15849 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15852 \begin_layout Plain Layout
15860 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15863 \begin_layout Plain Layout
15864 \begin_inset Formula $\sqiint$
15878 \begin_inset space \hfill{}
15882 \begin_inset Tabular
15883 <lyxtabular version="3" rows="4" columns="2">
15884 <features booktabs="true" tabularvalignment="middle">
15885 <column alignment="center" valignment="top" width="0pt">
15886 <column alignment="center" valignment="top" width="0pt">
15888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15891 \begin_layout Plain Layout
15897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15900 \begin_layout Plain Layout
15907 <row bottomspace="1mm">
15908 <cell alignment="center" valignment="top" usebox="none">
15911 \begin_layout Plain Layout
15919 <cell alignment="center" valignment="top" usebox="none">
15922 \begin_layout Plain Layout
15923 \begin_inset Formula $\iiint$
15932 <row bottomspace="1mm">
15933 <cell alignment="center" valignment="top" usebox="none">
15936 \begin_layout Plain Layout
15944 <cell alignment="center" valignment="top" usebox="none">
15947 \begin_layout Plain Layout
15948 \begin_inset Formula $\iiiint$
15957 <row bottomspace="1mm">
15958 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15961 \begin_layout Plain Layout
15969 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15972 \begin_layout Plain Layout
15973 \begin_inset Formula $\dotsint$
15987 \begin_inset space \hfill{}
15993 \begin_layout Subsection
15995 \begin_inset CommandInset label
15997 name "subsec:Operator-Limits"
16002 \begin_inset Index idx
16005 \begin_layout Plain Layout
16014 \begin_layout Standard
16015 Limits are created by super- and subscripts:
16016 \begin_inset Separator parbreak
16022 \begin_layout Standard
16024 \begin_inset Tabular
16025 <lyxtabular version="3" rows="2" columns="2">
16026 <features booktabs="true" tabularvalignment="middle">
16027 <column alignment="center" valignment="top" width="0pt">
16028 <column alignment="center" valignment="top" width="0pt">
16030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16033 \begin_layout Plain Layout
16039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16042 \begin_layout Plain Layout
16050 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16053 \begin_layout Plain Layout
16059 \begin_inset space \textvisiblespace{}
16063 \begin_inset Formula $\to$
16067 \begin_inset Formula $\to$
16075 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16078 \begin_layout Plain Layout
16079 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16095 \begin_layout Standard
16096 Limits of inline formulas are set right beside the operator.
16097 Limits in displayed formulas are set above or below the operator, except
16098 for integral limits.
16101 \begin_layout Standard
16102 To force that the limits are set beside the operator, the cursor is set
16103 directly behind the operator and the limits type is changed with the menu
16106 Edit\SpecialChar menuseparator
16107 Math\SpecialChar menuseparator
16126 \begin_layout Standard
16127 The default limits type is this:
16128 \begin_inset Formula
16130 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16135 This is how it looks when the limits type was changed to
16142 \begin_inset Formula
16144 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16149 For integrals, except those ending with
16165 etc., the limits are by default set beside the operator.
16166 But for multiple integrals the limits are often set below the operator.
16167 In the following example the limits type was therefore set to
16171 and so set below the integrals:
16172 \begin_inset Formula
16174 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16182 \begin_layout Standard
16183 \begin_inset VSpace medskip
16186 To specify conditions for limits, the commands
16193 \begin_inset Index idx
16196 \begin_layout Plain Layout
16211 \begin_inset Index idx
16214 \begin_layout Plain Layout
16223 To create for example this expression
16224 \begin_inset Formula
16226 \sum_{\begin{subarray}{c}
16230 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16238 \begin_layout Standard
16239 the following has to be done:
16240 \begin_inset Newline newline
16252 \begin_inset space \textvisiblespace{}
16258 One is now in a blue box under the summation operator and insert there
16264 \begin_inset space \textvisiblespace{}
16270 The blue box is now within a purple box and now several lines can be written
16272 A new line is created by inserting a line break (
16275 arg "newline-insert newline"
16280 \begin_inset Newline newline
16285 0<k<1000 Ctrl+Return
16286 \begin_inset Newline newline
16291 is typed in, a new box appears below for the new line.
16294 \begin_layout Standard
16295 The alignment of the lines can be changed to left aligned with the
16305 Edit\SpecialChar menuseparator
16309 To get right alignment,
16314 \begin_inset space \textvisiblespace{}
16319 is inserted at the beginning of the line.
16322 \begin_layout Standard
16335 with the difference that the lines are always centered.
16338 \begin_layout Standard
16339 \begin_inset VSpace bigskip
16343 \begin_inset CommandInset ref
16345 reference "eq:substack"
16349 there can be too much space beside an operator, because the characters
16350 following the operator are set beside the limits.
16351 To avoid this the command
16358 \begin_inset Index idx
16361 \begin_layout Plain Layout
16370 To activate it, set in the document settings under
16373 \begin_inset space ~
16383 \begin_inset Index idx
16386 \begin_layout Plain Layout
16387 Packages ! mathtools
16395 \begin_inset space ~
16407 sets the space besides the operator to 0
16408 \begin_inset space \thinspace{}
16412 \begin_inset Newline newline
16416 \begin_inset CommandInset ref
16418 reference "eq:substack"
16422 , one uses the command
16425 \begin_layout Standard
16433 \begin_layout Standard
16434 and inserts the operator with its limits into the braces.
16435 Behind the brace one continues the formula:
16436 \begin_inset Formula
16438 \smashoperator{\sum_{\begin{subarray}{c}
16442 \end{subarray}}^{n}}k^{-2}
16450 \begin_layout Standard
16451 It is possible to set the space of only one side of the operator to 0
16452 \begin_inset space \thinspace{}
16456 To do this write either
16475 stands for the left and
16479 for the right side of the operator.
16480 Here is an example of the possible
16489 \begin_layout Standard
16490 \begin_inset Formula
16492 Y\smashoperator{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[l]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[r]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}
16500 \begin_layout Standard
16501 \begin_inset VSpace bigskip
16507 \begin_layout Standard
16508 When several consecutive operators have limits the typesetting of the limits
16509 looks often imperfect in the output, see this example:
16510 \begin_inset Formula
16512 \text{a)}\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\limsup_{n\to\infty}\max_{p\ge n}
16517 To improve the typesetting set in the document settings under
16520 \begin_inset space ~
16530 \begin_inset Index idx
16533 \begin_layout Plain Layout
16534 Packages ! mathtools
16542 \begin_inset space ~
16548 Then insert into your formula the command
16555 \begin_inset Index idx
16558 \begin_layout Plain Layout
16566 directly before the first operator.
16567 The example will then look like this:
16568 \begin_inset Formula
16570 \text{a)}\adjustlimits\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\adjustlimits\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\adjustlimits\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\adjustlimits\limsup_{n\to\infty}\max_{p\ge n}
16578 \begin_layout Standard
16579 \begin_inset VSpace bigskip
16582 How to use one limit for several operators is described in
16583 \begin_inset CommandInset ref
16585 reference "subsec:Self-defined-Operators"
16592 \begin_layout Subsection
16593 Decoration for Operators
16594 \begin_inset Index idx
16597 \begin_layout Plain Layout
16598 Operators ! Decoration
16606 \begin_layout Standard
16614 \begin_inset Index idx
16617 \begin_layout Plain Layout
16632 \begin_inset Index idx
16635 \begin_layout Plain Layout
16643 characters can be placed above or below an operator, respectively.
16651 \begin_inset Index idx
16654 \begin_layout Plain Layout
16662 characters can be set before and behind a big operator.
16665 \begin_layout Standard
16667 \begin_inset space ~
16679 \begin_layout Itemize
16686 is used to set characters at the corners of the operator
16689 \begin_layout Itemize
16696 is used to set characters before and/or behind the operator (this variant
16697 represents \SpecialChar LaTeX
16707 \begin_layout Itemize
16714 is used to set characters at the left corners and/or behind the operator
16717 \begin_layout Itemize
16724 is used to set characters at the right corners and/or before the operator
16727 \begin_layout Standard
16728 For example the command
16733 \begin_inset space \textvisiblespace{}
16739 \begin_inset space \textvisiblespace{}
16743 \begin_inset Formula $\to$
16747 \begin_inset Formula $\to$
16751 \begin_inset space \textvisiblespace{}
16761 \begin_inset Formula
16763 \sideset{}{'}\sum_{k=1}^{n}
16771 \begin_layout Standard
16772 \begin_inset Note Greyedout
16775 \begin_layout Plain Layout
16782 can only be used to decorate big operators, binary operators are not allowed.
16790 \begin_layout Standard
16803 can also be used to decorate symbols and characters.
16804 For example, the command
16809 \begin_inset space \textvisiblespace{}
16815 \begin_inset space \textvisiblespace{}
16821 \begin_inset Formula $\uparrow$
16829 \begin_inset Formula
16831 \overset{a}{\maltese}
16839 \begin_layout Subsection
16841 \begin_inset CommandInset label
16843 name "subsec:Binary-Operators"
16848 \begin_inset Index idx
16851 \begin_layout Plain Layout
16860 \begin_layout Standard
16861 Binary operators are surrounded by space when there is a character before
16863 \begin_inset VSpace medskip
16869 \begin_layout Standard
16870 \begin_inset Tabular
16871 <lyxtabular version="3" rows="13" columns="2">
16872 <features booktabs="true" tabularvalignment="middle">
16873 <column alignment="center" valignment="top" width="0pt">
16874 <column alignment="center" valignment="top" width="0pt">
16876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16879 \begin_layout Plain Layout
16881 \begin_inset Note Note
16884 \begin_layout Plain Layout
16891 is only used as spacer.
16901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16904 \begin_layout Plain Layout
16912 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16915 \begin_layout Plain Layout
16921 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16924 \begin_layout Plain Layout
16925 \begin_inset Formula $+$
16935 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16938 \begin_layout Plain Layout
16944 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16947 \begin_layout Plain Layout
16948 \begin_inset Formula $-$
16958 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16961 \begin_layout Plain Layout
16969 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16972 \begin_layout Plain Layout
16973 \begin_inset Formula $\pm$
16983 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16986 \begin_layout Plain Layout
16994 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16997 \begin_layout Plain Layout
16998 \begin_inset Formula $\mp$
17008 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17011 \begin_layout Plain Layout
17019 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17022 \begin_layout Plain Layout
17023 \begin_inset Formula $\cdot$
17033 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17036 \begin_layout Plain Layout
17044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17047 \begin_layout Plain Layout
17048 \begin_inset Formula $\times$
17058 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17061 \begin_layout Plain Layout
17069 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17072 \begin_layout Plain Layout
17073 \begin_inset Formula $\div$
17083 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17086 \begin_layout Plain Layout
17090 \begin_layout Plain Layout
17103 \begin_layout Plain Layout
17115 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17118 \begin_layout Plain Layout
17119 \begin_inset Formula $*$
17129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17132 \begin_layout Plain Layout
17140 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17143 \begin_layout Plain Layout
17144 \begin_inset Formula $\star$
17154 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17157 \begin_layout Plain Layout
17165 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17168 \begin_layout Plain Layout
17169 \begin_inset Formula $\circ$
17179 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17182 \begin_layout Plain Layout
17190 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17193 \begin_layout Plain Layout
17194 \begin_inset Formula $\diamond$
17204 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17207 \begin_layout Plain Layout
17215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17218 \begin_layout Plain Layout
17219 \begin_inset Formula $\bullet$
17233 \begin_inset space \hfill{}
17237 \begin_inset Tabular
17238 <lyxtabular version="3" rows="13" columns="2">
17239 <features booktabs="true" tabularvalignment="middle">
17240 <column alignment="center" valignment="top" width="0pt">
17241 <column alignment="center" valignment="top" width="0pt">
17243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17246 \begin_layout Plain Layout
17252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17255 \begin_layout Plain Layout
17263 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17266 \begin_layout Plain Layout
17274 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17277 \begin_layout Plain Layout
17278 \begin_inset Formula $\nabla$
17288 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17291 \begin_layout Plain Layout
17299 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17302 \begin_layout Plain Layout
17303 \begin_inset Formula $\bigtriangledown$
17313 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17316 \begin_layout Plain Layout
17324 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17327 \begin_layout Plain Layout
17328 \begin_inset Formula $\bigtriangleup$
17338 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17341 \begin_layout Plain Layout
17349 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17352 \begin_layout Plain Layout
17353 \begin_inset Formula $\Box$
17363 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17366 \begin_layout Plain Layout
17374 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17377 \begin_layout Plain Layout
17378 \begin_inset Formula $\cap$
17388 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17391 \begin_layout Plain Layout
17399 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17402 \begin_layout Plain Layout
17403 \begin_inset Formula $\cup$
17413 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17416 \begin_layout Plain Layout
17424 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17427 \begin_layout Plain Layout
17428 \begin_inset Formula $\dagger$
17438 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17441 \begin_layout Plain Layout
17449 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17452 \begin_layout Plain Layout
17453 \begin_inset Formula $\ddagger$
17463 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17466 \begin_layout Plain Layout
17474 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17477 \begin_layout Plain Layout
17478 \begin_inset Formula $\wr$
17488 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17491 \begin_layout Plain Layout
17499 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17502 \begin_layout Plain Layout
17503 \begin_inset Formula $\bigcirc$
17513 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17516 \begin_layout Plain Layout
17524 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17527 \begin_layout Plain Layout
17528 \begin_inset Formula $\wedge$
17538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17541 \begin_layout Plain Layout
17549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17552 \begin_layout Plain Layout
17553 \begin_inset Formula $\vee$
17567 \begin_inset space \hfill{}
17571 \begin_inset Tabular
17572 <lyxtabular version="3" rows="13" columns="2">
17573 <features booktabs="true" tabularvalignment="middle">
17574 <column alignment="center" valignment="top" width="0pt">
17575 <column alignment="center" valignment="top" width="0pt">
17577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17580 \begin_layout Plain Layout
17586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17589 \begin_layout Plain Layout
17597 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17600 \begin_layout Plain Layout
17608 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17611 \begin_layout Plain Layout
17612 \begin_inset Formula $\oplus$
17622 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17625 \begin_layout Plain Layout
17633 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17636 \begin_layout Plain Layout
17637 \begin_inset Formula $\ominus$
17647 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17650 \begin_layout Plain Layout
17658 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17661 \begin_layout Plain Layout
17662 \begin_inset Formula $\otimes$
17672 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17675 \begin_layout Plain Layout
17683 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17686 \begin_layout Plain Layout
17687 \begin_inset Formula $\oslash$
17697 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17700 \begin_layout Plain Layout
17708 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17711 \begin_layout Plain Layout
17712 \begin_inset Formula $\odot$
17722 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17725 \begin_layout Plain Layout
17733 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17736 \begin_layout Plain Layout
17737 \begin_inset Formula $\amalg$
17747 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17750 \begin_layout Plain Layout
17758 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17761 \begin_layout Plain Layout
17762 \begin_inset Formula $\uplus$
17772 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17775 \begin_layout Plain Layout
17783 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17786 \begin_layout Plain Layout
17787 \begin_inset Formula $\setminus$
17797 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17800 \begin_layout Plain Layout
17808 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17811 \begin_layout Plain Layout
17812 \begin_inset Formula $\sqcap$
17822 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17825 \begin_layout Plain Layout
17833 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17836 \begin_layout Plain Layout
17837 \begin_inset Formula $\sqcup$
17847 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17850 \begin_layout Plain Layout
17858 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17861 \begin_layout Plain Layout
17862 \begin_inset Formula $\triangleleft$
17872 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17875 \begin_layout Plain Layout
17883 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17886 \begin_layout Plain Layout
17887 \begin_inset Formula $\triangleright$
17903 \begin_layout Standard
17904 All binary operators can also be inserted via the math toolbar button
17907 arg "math-insert \\pm"
17913 \begin_layout Standard
17914 To typeset the Laplace operator also
17931 \begin_inset Formula $\nabla^{2}$
17934 ) can be used instead of
17943 \begin_layout Standard
17950 Insert\SpecialChar menuseparator
17962 \begin_layout Subsection
17963 Self-defined Operators
17964 \begin_inset CommandInset label
17966 name "subsec:Self-defined-Operators"
17971 \begin_inset Index idx
17974 \begin_layout Plain Layout
17975 Operators ! self-defined
17983 \begin_layout Standard
17984 With the help of the command
17988 DeclareMathOperator
17991 \begin_inset Index idx
17994 \begin_layout Plain Layout
17999 DeclareMathOperator
18004 custom operators can be defined in the \SpecialChar LaTeX
18006 Its command scheme is:
18009 \begin_layout Standard
18014 DeclareMathOperator{new command}{display}
18017 \begin_layout Standard
18018 Display can be characters or symbols that define how the operator looks
18020 To define a big operator a * is set behind the command.
18021 All self-defined big operators can have limits as described in
18022 \begin_inset CommandInset ref
18024 reference "subsec:Operator-Limits"
18031 \begin_layout Standard
18032 For example the \SpecialChar LaTeX
18036 \begin_layout Standard
18041 DeclareMathOperator*{
18048 \begin_layout Standard
18049 defines the command
18055 , that inserts a big operator consisting of the lozenge symbol from
18056 \begin_inset CommandInset ref
18058 reference "subsec:Miscellaneous-Symbols"
18063 \begin_inset Formula
18065 \Lozenge_{n=1}^{\infty}
18070 The command for this formula is:
18081 \begin_inset Formula $\to$
18087 \begin_layout Standard
18088 \begin_inset VSpace bigskip
18091 When self-defined operators are not used several times in the document,
18092 they can also be defined with the commands
18099 \begin_inset Index idx
18102 \begin_layout Plain Layout
18117 \begin_inset Index idx
18120 \begin_layout Plain Layout
18128 , which have the following scheme:
18131 \begin_layout Standard
18145 \begin_layout Standard
18152 defines big operators,
18161 \begin_layout Standard
18169 \begin_inset space \thinspace{}
18173 \begin_inset space \space{}
18176 be used to use one limit for several operators:
18179 \begin_layout Standard
18180 \begin_inset Formula
18182 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18190 \begin_layout Standard
18191 The command for the formula above is:
18192 \begin_inset Newline newline
18208 \begin_inset space \textvisiblespace{}
18214 \begin_inset Formula $\to$
18220 \begin_inset space \textvisiblespace{}
18228 \begin_layout Section
18230 \begin_inset Index idx
18233 \begin_layout Plain Layout
18242 \begin_layout Subsection
18244 \begin_inset CommandInset label
18246 name "subsec:Font-Styles"
18251 \begin_inset Index idx
18254 \begin_layout Plain Layout
18263 \begin_layout Standard
18264 Latin letters in formulas can be set in one of the following font styles:
18267 \begin_layout Standard
18269 \begin_inset space \hfill{}
18273 \begin_inset Tabular
18274 <lyxtabular version="3" rows="6" columns="2">
18275 <features booktabs="true" tabularvalignment="middle">
18276 <column alignment="center" valignment="top" width="0pt">
18277 <column alignment="center" valignment="top">
18279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18282 \begin_layout Plain Layout
18288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18291 \begin_layout Plain Layout
18299 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18302 \begin_layout Plain Layout
18308 \begin_inset space \textvisiblespace{}
18318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18321 \begin_layout Plain Layout
18322 \begin_inset Formula $\mathbb{ABC}$
18332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18335 \begin_layout Plain Layout
18341 \begin_inset space \textvisiblespace{}
18351 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18354 \begin_layout Plain Layout
18355 \begin_inset Formula $\mathbf{AbC}$
18365 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18368 \begin_layout Plain Layout
18374 \begin_inset space \textvisiblespace{}
18384 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18387 \begin_layout Plain Layout
18388 \begin_inset Formula $\boldsymbol{AbC}$
18398 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18401 \begin_layout Plain Layout
18407 \begin_inset space \textvisiblespace{}
18417 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18420 \begin_layout Plain Layout
18421 \begin_inset Formula $\mathcal{ABC}$
18431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18434 \begin_layout Plain Layout
18440 \begin_inset space \textvisiblespace{}
18450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18453 \begin_layout Plain Layout
18454 \begin_inset Formula $\mathfrak{AbC}$
18468 \begin_inset space \hfill{}
18472 \begin_inset Tabular
18473 <lyxtabular version="3" rows="6" columns="2">
18474 <features booktabs="true" tabularvalignment="middle">
18475 <column alignment="center" valignment="top" width="0pt">
18476 <column alignment="center" valignment="top">
18478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18481 \begin_layout Plain Layout
18487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18490 \begin_layout Plain Layout
18498 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18501 \begin_layout Plain Layout
18507 \begin_inset space \textvisiblespace{}
18517 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18520 \begin_layout Plain Layout
18521 \begin_inset Formula $\mathit{AbC}$
18531 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18534 \begin_layout Plain Layout
18540 \begin_inset space \textvisiblespace{}
18550 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18553 \begin_layout Plain Layout
18554 \begin_inset Formula $\mathrm{AbC}$
18564 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18567 \begin_layout Plain Layout
18573 \begin_inset space \textvisiblespace{}
18583 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18586 \begin_layout Plain Layout
18587 \begin_inset Formula $\mathsf{AbC}$
18597 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18600 \begin_layout Plain Layout
18606 \begin_inset space \textvisiblespace{}
18616 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18619 \begin_layout Plain Layout
18620 \begin_inset Formula $\mathtt{AbC}$
18630 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18633 \begin_layout Plain Layout
18639 \begin_inset space \textvisiblespace{}
18649 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18652 \begin_layout Plain Layout
18653 \begin_inset Formula $\mathscr{ABC}$
18667 \begin_inset space \hfill{}
18673 \begin_layout Standard
18674 \begin_inset Note Greyedout
18677 \begin_layout Plain Layout
18700 can only be used for big letters.
18708 \begin_layout Standard
18709 Predefined is the style
18718 \begin_layout Standard
18719 The style commands work also for letters in mathematical constructs:
18720 \begin_inset Formula
18722 \mathfrak{A=\frac{b}{C}}
18730 \begin_layout Standard
18731 Characters in mathematical text don't appear in a math font style but in
18732 the text font style
18739 That their style can't be set correctly via the text style dialog is a
18740 bug in \SpecialChar LyX
18745 \begin_layout Plain Layout
18746 \begin_inset CommandInset href
18748 name "LyX-bug #4629"
18749 target "http://www.lyx.org/trac/ticket/4629"
18761 \begin_layout Standard
18762 Instead of the style commands the dialog
18764 Edit\SpecialChar menuseparator
18765 Math\SpecialChar menuseparator
18768 or the toolbar button
18771 arg "math-insert \\font"
18777 \begin_layout Subsection
18779 \begin_inset CommandInset label
18781 name "subsec:Bold-Formulas"
18786 \begin_inset Index idx
18789 \begin_layout Plain Layout
18798 \begin_layout Standard
18799 To make a complete formula bold, the command
18805 from the previous subsection cannot be used, because it doesn't work for
18806 small Greek letters.
18807 Furthermore it prints Latin letters always upright, like in the following
18811 \begin_layout Standard
18812 \begin_inset Formula
18814 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18822 \begin_layout Standard
18823 To display the formula correctly, the command
18830 \begin_inset Formula
18832 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18837 It is also possible to set the formula in a
18839 boldmath environment
18842 This environment is created by inserting the command
18849 \begin_inset Index idx
18852 \begin_layout Plain Layout
18860 in \SpecialChar TeX
18862 To end the environment, the command
18869 \begin_inset Index idx
18872 \begin_layout Plain Layout
18880 is inserted in \SpecialChar TeX
18885 \begin_layout Plain Layout
18895 \begin_inset Formula
18897 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18906 \begin_layout Plain Layout
18918 \begin_layout Subsection
18920 \begin_inset Index idx
18923 \begin_layout Plain Layout
18932 \begin_layout Standard
18933 Formulas can be colored like normal text: Highlight a formula or a formula
18939 Here is a formula in magenta:
18940 \begin_inset Formula
18942 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18950 \begin_layout Standard
18951 You can also define your own colors as described in
18952 \begin_inset CommandInset ref
18954 reference "subsec:Colored-Boxes"
18959 They can be used with the \SpecialChar TeX
18967 \begin_inset Index idx
18970 \begin_layout Plain Layout
18981 \begin_layout Standard
18986 textcolor{color}{characters or formula}
18989 \begin_layout Standard
18990 The following example was colored completely dark green and partly red:
18993 \begin_layout Standard
18997 \begin_layout Plain Layout
19001 textcolor{darkgreen}{
19007 \begin_inset Formula
19009 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19018 \begin_layout Plain Layout
19028 \begin_layout Standard
19029 Due to a bug in \SpecialChar LyX
19030 only complete formulas can be colored with self-defined
19035 \begin_layout Plain Layout
19036 \begin_inset CommandInset href
19038 name "LyX-bug #5269"
19039 target "http://www.lyx.org/trac/ticket/5269"
19051 \begin_layout Subsection
19053 \begin_inset CommandInset label
19055 name "subsec:Font-Sizes"
19060 \begin_inset Index idx
19063 \begin_layout Plain Layout
19072 \begin_layout Standard
19073 For characters in formulas there are, analog to characters in text, the
19074 following size commands:
19077 \begin_layout Standard
19121 \begin_inset Newline newline
19143 \begin_layout Standard
19144 The size produced by the commands depends on the document font size, which
19145 corresponds to the command
19152 The other commands produce smaller or larger sizes than
19159 The font size can however not exceed a certain value.
19160 Is for example the document font size 12
19161 \begin_inset space \thinspace{}
19170 switches to the same size as
19180 \begin_layout Standard
19181 A size command is inserted in \SpecialChar TeX
19182 mode before the formula and sets the size
19183 for all following formula and text characters.
19184 To switch back to the initial size, the command
19190 is inserted behind the formula in \SpecialChar TeX
19194 \begin_layout Standard
19195 Within a formula the size can be changed using the following size commands
19196 or the toolbar button
19199 arg "math-insert \\style"
19203 \begin_inset Separator parbreak
19209 \begin_layout Standard
19212 \begin_inset Tabular
19213 <lyxtabular version="3" rows="5" columns="2">
19214 <features booktabs="true" tabularvalignment="middle">
19215 <column alignment="center" valignment="top" width="0pt">
19216 <column alignment="center" valignment="top">
19218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19221 \begin_layout Plain Layout
19227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19230 \begin_layout Plain Layout
19238 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19241 \begin_layout Plain Layout
19245 \begin_inset Index idx
19248 \begin_layout Plain Layout
19261 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19264 \begin_layout Plain Layout
19265 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19274 <row topspace="1mm">
19275 <cell alignment="center" valignment="top" usebox="none">
19278 \begin_layout Plain Layout
19286 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19289 \begin_layout Plain Layout
19290 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19300 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19303 \begin_layout Plain Layout
19311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19314 \begin_layout Plain Layout
19315 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19328 \begin_layout Plain Layout
19336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19339 \begin_layout Plain Layout
19340 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19356 \begin_layout Standard
19357 After entering these commands, a blue box appears in which the formula parts
19361 \begin_layout Standard
19362 There is a further method to change the font size, that though only works
19363 for symbols or letters in mathematical text.
19364 To use it, one of the above text size commands is inserted in mathematical
19366 All following characters until the end of the mathematical text or until
19367 another size command will have the selected size.
19369 \begin_inset VSpace -2mm
19375 \begin_layout Standard
19379 \begin_layout Plain Layout
19389 \begin_inset Formula
19391 A=\frac{B}{c}\cdot\maltese
19397 \begin_inset Formula
19399 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19408 \begin_layout Plain Layout
19420 \begin_layout Standard
19421 \begin_inset VSpace medskip
19424 Before both formulas the command
19431 The command for the second formula is:
19432 \begin_inset Newline newline
19440 \begin_inset space \textvisiblespace{}
19446 \begin_inset space \textvisiblespace{}
19452 \begin_inset space \textvisiblespace{}
19458 \begin_inset space \textvisiblespace{}
19462 \begin_inset Formula $\to$
19466 \begin_inset Formula $\to$
19470 \begin_inset Newline newline
19474 \begin_inset space \hspace*{}
19485 \begin_inset space \textvisiblespace{}
19491 \begin_inset space \textvisiblespace{}
19497 \begin_inset space \textvisiblespace{}
19503 \begin_layout Standard
19504 If a symbol cannot be displayed in different sizes, it will always be displayed
19505 in the default size.
19508 \begin_layout Section
19510 \begin_inset Index idx
19513 \begin_layout Plain Layout
19522 \begin_layout Standard
19523 Greek letters can also be inserted via the toolbar button
19526 arg "math-insert \\alpha"
19530 All international typesetting norms purport that Greek letters in math
19531 have to be typeset italic/slanted.
19532 In some languages, like French or Russian, they are nevertheless sometimes
19536 \begin_layout Subsection
19538 \begin_inset Index idx
19541 \begin_layout Plain Layout
19542 Greek letters ! small
19550 \begin_layout Standard
19551 \begin_inset space \hfill{}
19555 \begin_inset Tabular
19556 <lyxtabular version="3" rows="11" columns="2">
19557 <features booktabs="true" tabularvalignment="middle">
19558 <column alignment="center" valignment="top" width="0pt">
19559 <column alignment="center" valignment="top" width="0pt">
19561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19564 \begin_layout Plain Layout
19570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19573 \begin_layout Plain Layout
19581 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19584 \begin_layout Plain Layout
19592 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19595 \begin_layout Plain Layout
19596 \begin_inset Formula $\alpha$
19606 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19609 \begin_layout Plain Layout
19617 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19620 \begin_layout Plain Layout
19621 \begin_inset Formula $\beta$
19631 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19634 \begin_layout Plain Layout
19642 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19645 \begin_layout Plain Layout
19646 \begin_inset Formula $\gamma$
19656 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19659 \begin_layout Plain Layout
19667 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19670 \begin_layout Plain Layout
19671 \begin_inset Formula $\delta$
19681 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19684 \begin_layout Plain Layout
19692 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19695 \begin_layout Plain Layout
19696 \begin_inset Formula $\epsilon$
19706 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19709 \begin_layout Plain Layout
19717 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19720 \begin_layout Plain Layout
19721 \begin_inset Formula $\varepsilon$
19731 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19734 \begin_layout Plain Layout
19742 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19745 \begin_layout Plain Layout
19746 \begin_inset Formula $\zeta$
19756 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19759 \begin_layout Plain Layout
19767 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19770 \begin_layout Plain Layout
19771 \begin_inset Formula $\eta$
19781 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19784 \begin_layout Plain Layout
19792 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19795 \begin_layout Plain Layout
19796 \begin_inset Formula $\theta$
19806 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19809 \begin_layout Plain Layout
19817 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19820 \begin_layout Plain Layout
19821 \begin_inset Formula $\vartheta$
19835 \begin_inset space \hfill{}
19839 \begin_inset Tabular
19840 <lyxtabular version="3" rows="12" columns="2">
19841 <features booktabs="true" tabularvalignment="middle">
19842 <column alignment="center" valignment="top" width="0pt">
19843 <column alignment="center" valignment="top" width="0pt">
19845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19848 \begin_layout Plain Layout
19854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19857 \begin_layout Plain Layout
19865 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19868 \begin_layout Plain Layout
19876 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19879 \begin_layout Plain Layout
19880 \begin_inset Formula $\iota$
19890 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19893 \begin_layout Plain Layout
19901 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19904 \begin_layout Plain Layout
19905 \begin_inset Formula $\kappa$
19915 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19918 \begin_layout Plain Layout
19926 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19929 \begin_layout Plain Layout
19930 \begin_inset Formula $\varkappa$
19940 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19943 \begin_layout Plain Layout
19951 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19954 \begin_layout Plain Layout
19955 \begin_inset Formula $\lambda$
19965 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19968 \begin_layout Plain Layout
19976 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19979 \begin_layout Plain Layout
19980 \begin_inset Formula $\mu$
19990 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19993 \begin_layout Plain Layout
20001 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20004 \begin_layout Plain Layout
20005 \begin_inset Formula $\nu$
20015 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20018 \begin_layout Plain Layout
20026 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20029 \begin_layout Plain Layout
20030 \begin_inset Formula $\xi$
20040 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20043 \begin_layout Plain Layout
20049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20052 \begin_layout Plain Layout
20053 \begin_inset Formula $o$
20063 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20066 \begin_layout Plain Layout
20074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20077 \begin_layout Plain Layout
20078 \begin_inset Formula $\pi$
20088 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20091 \begin_layout Plain Layout
20099 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20102 \begin_layout Plain Layout
20103 \begin_inset Formula $\varpi$
20113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20116 \begin_layout Plain Layout
20124 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20127 \begin_layout Plain Layout
20128 \begin_inset Formula $\rho$
20142 \begin_inset space \hfill{}
20146 \begin_inset Tabular
20147 <lyxtabular version="3" rows="11" columns="2">
20148 <features booktabs="true" tabularvalignment="middle">
20149 <column alignment="center" valignment="top" width="0pt">
20150 <column alignment="center" valignment="top" width="0pt">
20152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20155 \begin_layout Plain Layout
20161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20164 \begin_layout Plain Layout
20172 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20175 \begin_layout Plain Layout
20183 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20186 \begin_layout Plain Layout
20187 \begin_inset Formula $\varrho$
20197 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20200 \begin_layout Plain Layout
20208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20211 \begin_layout Plain Layout
20212 \begin_inset Formula $\sigma$
20222 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20225 \begin_layout Plain Layout
20233 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20236 \begin_layout Plain Layout
20237 \begin_inset Formula $\varsigma$
20247 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20250 \begin_layout Plain Layout
20258 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20261 \begin_layout Plain Layout
20262 \begin_inset Formula $\tau$
20272 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20275 \begin_layout Plain Layout
20283 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20286 \begin_layout Plain Layout
20287 \begin_inset Formula $\upsilon$
20297 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20300 \begin_layout Plain Layout
20308 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20311 \begin_layout Plain Layout
20312 \begin_inset Formula $\phi$
20322 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20325 \begin_layout Plain Layout
20333 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20336 \begin_layout Plain Layout
20337 \begin_inset Formula $\varphi$
20347 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20350 \begin_layout Plain Layout
20358 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20361 \begin_layout Plain Layout
20362 \begin_inset Formula $\chi$
20372 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20375 \begin_layout Plain Layout
20383 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20386 \begin_layout Plain Layout
20387 \begin_inset Formula $\psi$
20397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20400 \begin_layout Plain Layout
20408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20411 \begin_layout Plain Layout
20412 \begin_inset Formula $\omega$
20426 \begin_inset space \hfill{}
20432 \begin_layout Standard
20433 \begin_inset VSpace medskip
20439 \begin_layout Standard
20440 How to create special upright Greek letters is explained in
20441 \begin_inset CommandInset ref
20443 reference "subsec:Upright-small-Greek"
20450 \begin_layout Subsection
20452 \begin_inset Index idx
20455 \begin_layout Plain Layout
20456 Greek letters ! big
20464 \begin_layout Standard
20465 \begin_inset space \hfill{}
20469 \begin_inset Tabular
20470 <lyxtabular version="3" rows="7" columns="2">
20471 <features booktabs="true" tabularvalignment="middle">
20472 <column alignment="center" valignment="top" width="0pt">
20473 <column alignment="center" valignment="top" width="0pt">
20475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20478 \begin_layout Plain Layout
20484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20487 \begin_layout Plain Layout
20495 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20498 \begin_layout Plain Layout
20506 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20509 \begin_layout Plain Layout
20510 \begin_inset Formula $\Gamma$
20520 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20523 \begin_layout Plain Layout
20531 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20534 \begin_layout Plain Layout
20535 \begin_inset Formula $\Delta$
20545 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20548 \begin_layout Plain Layout
20556 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20559 \begin_layout Plain Layout
20560 \begin_inset Formula $\Theta$
20570 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20573 \begin_layout Plain Layout
20581 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20584 \begin_layout Plain Layout
20585 \begin_inset Formula $\Lambda$
20595 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20598 \begin_layout Plain Layout
20606 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20609 \begin_layout Plain Layout
20610 \begin_inset Formula $\Xi$
20620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20623 \begin_layout Plain Layout
20631 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20634 \begin_layout Plain Layout
20635 \begin_inset Formula $\Pi$
20649 \begin_inset space \hfill{}
20653 \begin_inset Tabular
20654 <lyxtabular version="3" rows="6" columns="2">
20655 <features booktabs="true" tabularvalignment="middle">
20656 <column alignment="center" valignment="top" width="0pt">
20657 <column alignment="center" valignment="top" width="0pt">
20659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20662 \begin_layout Plain Layout
20668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20671 \begin_layout Plain Layout
20679 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20682 \begin_layout Plain Layout
20690 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20693 \begin_layout Plain Layout
20694 \begin_inset Formula $\Sigma$
20704 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20707 \begin_layout Plain Layout
20715 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20718 \begin_layout Plain Layout
20719 \begin_inset Formula $\Upsilon$
20729 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20732 \begin_layout Plain Layout
20740 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20743 \begin_layout Plain Layout
20744 \begin_inset Formula $\Phi$
20754 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20757 \begin_layout Plain Layout
20765 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20768 \begin_layout Plain Layout
20769 \begin_inset Formula $\Psi$
20779 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20782 \begin_layout Plain Layout
20790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20793 \begin_layout Plain Layout
20794 \begin_inset Formula $\Omega$
20808 \begin_inset space \hfill{}
20814 \begin_layout Standard
20815 \begin_inset VSpace medskip
20818 That the big Greek letters appear upright is caused by a design bug when
20821 To get correct italic big letters, begin every command with
20826 For example the command
20833 \begin_inset Formula $\varGamma$
20837 Another way is to load the package
20845 \begin_layout Plain Layout
20850 is part of the \SpecialChar LaTeX
20856 \begin_inset Index idx
20859 \begin_layout Plain Layout
20864 \begin_layout Plain Layout
20884 \begin_inset Index idx
20887 \begin_layout Plain Layout
20893 with the \SpecialChar LaTeX
20897 \begin_layout Standard
20902 usepackage{fixmath}
20905 \begin_layout Standard
20906 Then all big Greek letters in a document will automatically be typeset italic.
20909 \begin_layout Subsection
20911 \begin_inset Index idx
20914 \begin_layout Plain Layout
20915 Greek letters ! bold
20923 \begin_layout Standard
20924 Greek letters cannot be set with different font styles like Latin letters.
20925 They can only be made bold with the command
20932 \begin_inset Index idx
20935 \begin_layout Plain Layout
20944 \begin_inset Separator parbreak
20950 \begin_layout Standard
20952 \begin_inset Tabular
20953 <lyxtabular version="3" rows="3" columns="2">
20954 <features booktabs="true" tabularvalignment="middle">
20955 <column alignment="center" valignment="top" width="0pt">
20956 <column alignment="center" valignment="top">
20958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20961 \begin_layout Plain Layout
20967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20970 \begin_layout Plain Layout
20978 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20981 \begin_layout Plain Layout
20993 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20996 \begin_layout Plain Layout
20997 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21007 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21010 \begin_layout Plain Layout
21022 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21025 \begin_layout Plain Layout
21026 \begin_inset Formula $\theta\boldsymbol{\theta}$
21042 \begin_layout Section
21047 \begin_layout Plain Layout
21060 \begin_layout Plain Layout
21061 A list with all symbols of most of the \SpecialChar LaTeX
21062 -packages can be found in
21063 \begin_inset CommandInset citation
21078 \begin_layout Plain Layout
21086 \begin_inset Note Note
21089 \begin_layout Plain Layout
21092 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21095 \begin_layout Plain Layout
21098 texorpdfstring is in section
21099 \begin_inset CommandInset ref
21101 reference "subsec:Formulas-in-Section"
21111 \begin_inset Index idx
21114 \begin_layout Plain Layout
21123 \begin_layout Standard
21124 Many of the symbols listed in this section can also be inserted via the
21128 arg "math-insert \\nabla"
21134 arg "math-insert \\digamma"
21140 \begin_layout Subsection
21141 Mathematical Symbols
21142 \begin_inset CommandInset label
21144 name "subsec:Mathematical-Symbols"
21149 \begin_inset Index idx
21152 \begin_layout Plain Layout
21153 Symbols ! mathematical
21161 \begin_layout Standard
21162 \begin_inset Tabular
21163 <lyxtabular version="3" rows="10" columns="2">
21164 <features booktabs="true" tabularvalignment="middle">
21165 <column alignment="center" valignment="top" width="0pt">
21166 <column alignment="center" valignment="top" width="0pt">
21168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21171 \begin_layout Plain Layout
21177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21180 \begin_layout Plain Layout
21188 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21191 \begin_layout Plain Layout
21199 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21202 \begin_layout Plain Layout
21203 \begin_inset Formula $\neg$
21213 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21216 \begin_layout Plain Layout
21224 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21227 \begin_layout Plain Layout
21228 \begin_inset Formula $\Im$
21238 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21241 \begin_layout Plain Layout
21249 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21252 \begin_layout Plain Layout
21253 \begin_inset Formula $\Re$
21263 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21266 \begin_layout Plain Layout
21274 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21277 \begin_layout Plain Layout
21278 \begin_inset Formula $\aleph$
21288 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21291 \begin_layout Plain Layout
21299 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21302 \begin_layout Plain Layout
21303 \begin_inset Formula $\partial$
21313 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21316 \begin_layout Plain Layout
21324 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21327 \begin_layout Plain Layout
21328 \begin_inset Formula $\infty$
21338 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21341 \begin_layout Plain Layout
21349 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21352 \begin_layout Plain Layout
21353 \begin_inset Formula $\wp$
21363 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21366 \begin_layout Plain Layout
21374 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21377 \begin_layout Plain Layout
21378 \begin_inset Formula $\imath$
21388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21391 \begin_layout Plain Layout
21399 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21402 \begin_layout Plain Layout
21403 \begin_inset Formula $\jmath$
21417 \begin_inset space \hfill{}
21421 \begin_inset Tabular
21422 <lyxtabular version="3" rows="10" columns="2">
21423 <features booktabs="true" tabularvalignment="middle">
21424 <column alignment="center" valignment="top" width="0pt">
21425 <column alignment="center" valignment="top" width="0pt">
21427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21430 \begin_layout Plain Layout
21436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21439 \begin_layout Plain Layout
21441 \begin_inset Note Note
21444 \begin_layout Plain Layout
21451 is only used as spacer.
21463 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21466 \begin_layout Plain Layout
21474 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21477 \begin_layout Plain Layout
21478 \begin_inset Formula $\forall$
21488 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21491 \begin_layout Plain Layout
21499 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21502 \begin_layout Plain Layout
21503 \begin_inset Formula $\exists$
21513 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21516 \begin_layout Plain Layout
21524 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21527 \begin_layout Plain Layout
21528 \begin_inset Formula $\nexists$
21538 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21541 \begin_layout Plain Layout
21549 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21552 \begin_layout Plain Layout
21553 \begin_inset Formula $\emptyset$
21563 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21566 \begin_layout Plain Layout
21574 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21577 \begin_layout Plain Layout
21578 \begin_inset Formula $\varnothing$
21588 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21591 \begin_layout Plain Layout
21599 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21602 \begin_layout Plain Layout
21603 \begin_inset Formula $\dag$
21613 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21616 \begin_layout Plain Layout
21624 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21627 \begin_layout Plain Layout
21628 \begin_inset Formula $\ddag$
21638 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21641 \begin_layout Plain Layout
21649 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21652 \begin_layout Plain Layout
21656 \begin_layout Plain Layout
21666 \begin_inset Formula $\complement$
21673 \begin_layout Plain Layout
21687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21690 \begin_layout Plain Layout
21698 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21701 \begin_layout Plain Layout
21702 \begin_inset Formula $\Bbbk$
21716 \begin_inset space \hfill{}
21720 \begin_inset Tabular
21721 <lyxtabular version="3" rows="10" columns="2">
21722 <features booktabs="true" tabularvalignment="middle">
21723 <column alignment="center" valignment="top" width="0pt">
21724 <column alignment="center" valignment="top" width="0pt">
21726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21729 \begin_layout Plain Layout
21735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21738 \begin_layout Plain Layout
21746 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21749 \begin_layout Plain Layout
21757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21760 \begin_layout Plain Layout
21761 \begin_inset Formula $\prime$
21771 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21774 \begin_layout Plain Layout
21782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21785 \begin_layout Plain Layout
21786 \begin_inset Formula $\backprime$
21796 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21799 \begin_layout Plain Layout
21807 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21810 \begin_layout Plain Layout
21811 \begin_inset Formula $\mho$
21821 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21824 \begin_layout Plain Layout
21832 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21835 \begin_layout Plain Layout
21836 \begin_inset Formula $\triangle$
21846 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21849 \begin_layout Plain Layout
21857 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21860 \begin_layout Plain Layout
21861 \begin_inset Formula $\angle$
21871 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21874 \begin_layout Plain Layout
21882 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21885 \begin_layout Plain Layout
21886 \begin_inset Formula $\measuredangle$
21896 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21899 \begin_layout Plain Layout
21907 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21910 \begin_layout Plain Layout
21911 \begin_inset Formula $\sphericalangle$
21921 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21924 \begin_layout Plain Layout
21932 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21935 \begin_layout Plain Layout
21936 \begin_inset Formula $\top$
21946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21949 \begin_layout Plain Layout
21957 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21960 \begin_layout Plain Layout
21961 \begin_inset Formula $\bot$
21977 \begin_layout Standard
21978 \begin_inset Newpage newpage
21984 \begin_layout Subsection
21985 Miscellaneous Symbols
21986 \begin_inset CommandInset label
21988 name "subsec:Miscellaneous-Symbols"
21993 \begin_inset Index idx
21996 \begin_layout Plain Layout
21997 Symbols ! miscellaneous
22005 \begin_layout Standard
22008 \begin_inset Tabular
22009 <lyxtabular version="3" rows="10" columns="2">
22010 <features booktabs="true" tabularvalignment="middle">
22011 <column alignment="center" valignment="top" width="0pt">
22012 <column alignment="center" valignment="top" width="0pt">
22014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22017 \begin_layout Plain Layout
22023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22026 \begin_layout Plain Layout
22034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22037 \begin_layout Plain Layout
22045 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22048 \begin_layout Plain Layout
22049 \begin_inset Formula $\flat$
22059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22062 \begin_layout Plain Layout
22070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22073 \begin_layout Plain Layout
22074 \begin_inset Formula $\natural$
22084 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22087 \begin_layout Plain Layout
22095 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22098 \begin_layout Plain Layout
22099 \begin_inset Formula $\sharp$
22109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22112 \begin_layout Plain Layout
22120 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22123 \begin_layout Plain Layout
22124 \begin_inset Formula $\surd$
22134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22137 \begin_layout Plain Layout
22145 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22148 \begin_layout Plain Layout
22149 \begin_inset Formula $\checkmark$
22159 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22162 \begin_layout Plain Layout
22170 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22173 \begin_layout Plain Layout
22174 \begin_inset Formula $\yen$
22184 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22187 \begin_layout Plain Layout
22195 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22198 \begin_layout Plain Layout
22199 \begin_inset Formula $\pounds$
22209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22212 \begin_layout Plain Layout
22218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22221 \begin_layout Plain Layout
22222 \begin_inset Formula $\$$
22232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22235 \begin_layout Plain Layout
22241 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22244 \begin_layout Plain Layout
22245 \begin_inset Formula $§$
22259 \begin_inset space \hfill{}
22263 \begin_inset Tabular
22264 <lyxtabular version="3" rows="10" columns="2">
22265 <features booktabs="true" tabularvalignment="middle">
22266 <column alignment="center" valignment="top" width="0pt">
22267 <column alignment="center" valignment="top">
22269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22272 \begin_layout Plain Layout
22278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22281 \begin_layout Plain Layout
22289 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22292 \begin_layout Plain Layout
22300 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22303 \begin_layout Plain Layout
22304 \begin_inset Formula $\hbar$
22314 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22317 \begin_layout Plain Layout
22325 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22328 \begin_layout Plain Layout
22329 \begin_inset Formula $\hslash$
22339 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22342 \begin_layout Plain Layout
22350 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22353 \begin_layout Plain Layout
22354 \begin_inset Formula $\clubsuit$
22364 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22367 \begin_layout Plain Layout
22375 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22378 \begin_layout Plain Layout
22379 \begin_inset Formula $\spadesuit$
22389 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22392 \begin_layout Plain Layout
22400 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22403 \begin_layout Plain Layout
22404 \begin_inset Formula $\bigstar$
22414 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22417 \begin_layout Plain Layout
22425 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22428 \begin_layout Plain Layout
22429 \begin_inset Formula $\blacklozenge$
22439 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22442 \begin_layout Plain Layout
22450 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22453 \begin_layout Plain Layout
22454 \begin_inset Formula $\blacktriangle$
22464 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22467 \begin_layout Plain Layout
22475 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22478 \begin_layout Plain Layout
22479 \begin_inset Formula $\blacktriangledown$
22489 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22492 \begin_layout Plain Layout
22500 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22503 \begin_layout Plain Layout
22504 \begin_inset Formula $\bullet$
22518 \begin_inset space \hfill{}
22522 \begin_inset Tabular
22523 <lyxtabular version="3" rows="10" columns="2">
22524 <features booktabs="true" tabularvalignment="middle">
22525 <column alignment="center" valignment="top" width="0pt">
22526 <column alignment="center" valignment="top" width="0pt">
22528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22531 \begin_layout Plain Layout
22537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22540 \begin_layout Plain Layout
22548 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22551 \begin_layout Plain Layout
22559 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22562 \begin_layout Plain Layout
22563 \begin_inset Formula $\diamondsuit$
22573 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22576 \begin_layout Plain Layout
22584 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22587 \begin_layout Plain Layout
22588 \begin_inset Formula $\Diamond$
22598 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22601 \begin_layout Plain Layout
22609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22612 \begin_layout Plain Layout
22613 \begin_inset Formula $\heartsuit$
22623 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22626 \begin_layout Plain Layout
22634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22637 \begin_layout Plain Layout
22638 \begin_inset Formula $\P$
22648 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22651 \begin_layout Plain Layout
22659 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22662 \begin_layout Plain Layout
22663 \begin_inset Formula $\copyright$
22673 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22676 \begin_layout Plain Layout
22684 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22687 \begin_layout Plain Layout
22688 \begin_inset Formula $\circledR$
22698 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22701 \begin_layout Plain Layout
22709 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22712 \begin_layout Plain Layout
22713 \begin_inset Formula $\maltese$
22723 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22726 \begin_layout Plain Layout
22734 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22737 \begin_layout Plain Layout
22738 \begin_inset Formula $\diagup$
22748 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22751 \begin_layout Plain Layout
22759 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22762 \begin_layout Plain Layout
22763 \begin_inset Formula $\diagdown$
22779 \begin_layout Standard
22780 \begin_inset VSpace medskip
22786 \begin_layout Standard
22787 Some symbols can be displayed in different sizes, see
22788 \begin_inset CommandInset ref
22790 reference "subsec:Font-Sizes"
22797 \begin_layout Subsection
22799 \begin_inset Index idx
22802 \begin_layout Plain Layout
22803 Symbols ! Euro-symbol
22809 \begin_inset Index idx
22812 \begin_layout Plain Layout
22819 \begin_layout Plain Layout
22836 \begin_layout Standard
22837 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22843 \begin_inset Index idx
22846 \begin_layout Plain Layout
22852 must be installed and loaded with the \SpecialChar LaTeX
22856 \begin_layout Standard
22861 usepackage[gennarrow]{eurosym}
22864 \begin_layout Standard
22865 The Euro symbol can now be inserted with the command
22872 \begin_inset Index idx
22875 \begin_layout Plain Layout
22886 \begin_layout Standard
22887 The Euro symbol can directly be inserted with the € key in mathematical
22888 text, without having
22903 can also be inserted in \SpecialChar TeX
22905 The official currency symbol can then be inserted with the command
22912 \begin_inset Index idx
22915 \begin_layout Plain Layout
22923 , that is only available in \SpecialChar TeX
22927 \begin_layout Standard
22931 \begin_layout Plain Layout
22941 \begin_inset Note Note
22944 \begin_layout Plain Layout
22945 The following table will only be displayed when the \SpecialChar LaTeX
22958 \begin_layout Standard
22959 An overview about the different Euro symbols:
22960 \begin_inset Separator parbreak
22966 \begin_layout Standard
22968 \begin_inset Tabular
22969 <lyxtabular version="3" rows="4" columns="3">
22970 <features booktabs="true" tabularvalignment="middle">
22971 <column alignment="center" valignment="top" width="0pt">
22972 <column alignment="center" valignment="top" width="0pt">
22973 <column alignment="center" valignment="top" width="0pt">
22975 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22978 \begin_layout Plain Layout
22982 \begin_layout Plain Layout
22986 cmidrule[0.08em]{2-3}
22996 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22999 \begin_layout Plain Layout
23005 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23008 \begin_layout Plain Layout
23016 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23019 \begin_layout Plain Layout
23025 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23028 \begin_layout Plain Layout
23036 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23039 \begin_layout Plain Layout
23040 \begin_inset Formula $\euro$
23050 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23053 \begin_layout Plain Layout
23059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23062 \begin_layout Plain Layout
23068 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23071 \begin_layout Plain Layout
23072 \begin_inset Formula $\mbox{€}$
23082 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23085 \begin_layout Plain Layout
23092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23095 \begin_layout Plain Layout
23103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23106 \begin_layout Plain Layout
23110 \begin_layout Plain Layout
23130 \begin_inset Note Note
23133 \begin_layout Plain Layout
23140 is used here only for table borders.
23150 manual for details.
23158 \begin_layout Standard
23162 \begin_layout Plain Layout
23172 \begin_inset Note Note
23175 \begin_layout Plain Layout
23176 The following will be displayed when the \SpecialChar LaTeX
23189 \begin_layout Standard
23190 You need to install the \SpecialChar LaTeX
23195 to see the rest of this subsection in the output.
23198 \begin_layout Standard
23202 \begin_layout Plain Layout
23214 \begin_layout Standard
23215 \begin_inset Newpage newpage
23221 \begin_layout Section
23223 \begin_inset CommandInset label
23225 name "sec:Relations"
23230 \begin_inset Index idx
23233 \begin_layout Plain Layout
23240 \begin_inset Index idx
23243 \begin_layout Plain Layout
23248 \begin_layout Plain Layout
23259 \begin_layout Plain Layout
23274 \begin_layout Standard
23275 All following relations can also be inserted via the toolbar button
23278 arg "math-insert \\leq"
23284 \begin_layout Standard
23285 \begin_inset Tabular
23286 <lyxtabular version="3" rows="17" columns="2">
23287 <features booktabs="true" tabularvalignment="middle">
23288 <column alignment="center" valignment="top" width="0pt">
23289 <column alignment="center" valignment="top" width="0pt">
23291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23294 \begin_layout Plain Layout
23300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23303 \begin_layout Plain Layout
23311 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23314 \begin_layout Plain Layout
23320 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23323 \begin_layout Plain Layout
23324 \begin_inset Formula $<$
23334 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23337 \begin_layout Plain Layout
23345 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23348 \begin_layout Plain Layout
23349 \begin_inset Formula $\le$
23359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23362 \begin_layout Plain Layout
23370 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23373 \begin_layout Plain Layout
23374 \begin_inset Formula $\ll$
23384 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23387 \begin_layout Plain Layout
23395 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23398 \begin_layout Plain Layout
23399 \begin_inset Formula $\prec$
23409 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23412 \begin_layout Plain Layout
23420 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23423 \begin_layout Plain Layout
23424 \begin_inset Formula $\preceq$
23434 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23437 \begin_layout Plain Layout
23445 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23448 \begin_layout Plain Layout
23449 \begin_inset Formula $\subset$
23459 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23462 \begin_layout Plain Layout
23470 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23473 \begin_layout Plain Layout
23474 \begin_inset Formula $\subseteq$
23484 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23487 \begin_layout Plain Layout
23495 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23498 \begin_layout Plain Layout
23499 \begin_inset Formula $\sqsubseteq$
23509 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23512 \begin_layout Plain Layout
23520 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23523 \begin_layout Plain Layout
23524 \begin_inset Formula $\in$
23534 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23537 \begin_layout Plain Layout
23545 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23548 \begin_layout Plain Layout
23549 \begin_inset Formula $\vdash$
23559 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23562 \begin_layout Plain Layout
23570 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23573 \begin_layout Plain Layout
23574 \begin_inset Formula $\smile$
23584 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23587 \begin_layout Plain Layout
23595 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23598 \begin_layout Plain Layout
23599 \begin_inset Formula $\lhd$
23609 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23612 \begin_layout Plain Layout
23620 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23623 \begin_layout Plain Layout
23624 \begin_inset Formula $\unlhd$
23634 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23637 \begin_layout Plain Layout
23645 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23648 \begin_layout Plain Layout
23649 \begin_inset Formula $\gtrless$
23659 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23662 \begin_layout Plain Layout
23670 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23673 \begin_layout Plain Layout
23674 \begin_inset Formula $\mid$
23684 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23687 \begin_layout Plain Layout
23695 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23698 \begin_layout Plain Layout
23699 \begin_inset Formula $\nmid$
23713 \begin_inset space \hfill{}
23717 \begin_inset Tabular
23718 <lyxtabular version="3" rows="17" columns="2">
23719 <features booktabs="true" tabularvalignment="middle">
23720 <column alignment="center" valignment="top" width="0pt">
23721 <column alignment="center" valignment="top" width="0pt">
23723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23726 \begin_layout Plain Layout
23732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23735 \begin_layout Plain Layout
23743 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23746 \begin_layout Plain Layout
23752 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23755 \begin_layout Plain Layout
23756 \begin_inset Formula $=$
23766 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23769 \begin_layout Plain Layout
23777 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23780 \begin_layout Plain Layout
23781 \begin_inset Formula $\not=$
23791 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23794 \begin_layout Plain Layout
23802 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23805 \begin_layout Plain Layout
23806 \begin_inset Formula $\equiv$
23816 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23819 \begin_layout Plain Layout
23827 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23830 \begin_layout Plain Layout
23831 \begin_inset Formula $\sim$
23841 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23844 \begin_layout Plain Layout
23852 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23855 \begin_layout Plain Layout
23856 \begin_inset Formula $\simeq$
23866 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23869 \begin_layout Plain Layout
23877 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23880 \begin_layout Plain Layout
23881 \begin_inset Formula $\approx$
23891 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23894 \begin_layout Plain Layout
23902 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23905 \begin_layout Plain Layout
23906 \begin_inset Formula $\cong$
23916 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23919 \begin_layout Plain Layout
23927 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23930 \begin_layout Plain Layout
23931 \begin_inset Formula $\bowtie$
23941 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23944 \begin_layout Plain Layout
23952 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23955 \begin_layout Plain Layout
23956 \begin_inset Formula $\notin$
23966 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23969 \begin_layout Plain Layout
23977 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23980 \begin_layout Plain Layout
23981 \begin_inset Formula $\perp$
23991 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23994 \begin_layout Plain Layout
24002 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24005 \begin_layout Plain Layout
24006 \begin_inset Formula $\propto$
24016 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24019 \begin_layout Plain Layout
24027 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24030 \begin_layout Plain Layout
24031 \begin_inset Formula $\asymp$
24041 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24044 \begin_layout Plain Layout
24052 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24055 \begin_layout Plain Layout
24056 \begin_inset Formula $\doteq$
24066 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24069 \begin_layout Plain Layout
24077 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24080 \begin_layout Plain Layout
24081 \begin_inset Formula $\circeq$
24091 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24094 \begin_layout Plain Layout
24102 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24105 \begin_layout Plain Layout
24106 \begin_inset Formula $\models$
24116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24119 \begin_layout Plain Layout
24127 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24130 \begin_layout Plain Layout
24131 \begin_inset Formula $\widehat{=}$
24145 \begin_inset space \hfill{}
24149 \begin_inset Tabular
24150 <lyxtabular version="3" rows="17" columns="2">
24151 <features booktabs="true" tabularvalignment="middle">
24152 <column alignment="center" valignment="top" width="0pt">
24153 <column alignment="center" valignment="top" width="0pt">
24155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24158 \begin_layout Plain Layout
24164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24167 \begin_layout Plain Layout
24175 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24178 \begin_layout Plain Layout
24184 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24187 \begin_layout Plain Layout
24188 \begin_inset Formula $>$
24198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24201 \begin_layout Plain Layout
24209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24212 \begin_layout Plain Layout
24213 \begin_inset Formula $\ge$
24223 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24226 \begin_layout Plain Layout
24234 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24237 \begin_layout Plain Layout
24238 \begin_inset Formula $\gg$
24248 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24251 \begin_layout Plain Layout
24259 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24262 \begin_layout Plain Layout
24263 \begin_inset Formula $\succ$
24273 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24276 \begin_layout Plain Layout
24284 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24287 \begin_layout Plain Layout
24288 \begin_inset Formula $\succeq$
24298 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24301 \begin_layout Plain Layout
24309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24312 \begin_layout Plain Layout
24313 \begin_inset Formula $\supset$
24323 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24326 \begin_layout Plain Layout
24334 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24337 \begin_layout Plain Layout
24338 \begin_inset Formula $\supseteq$
24348 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24351 \begin_layout Plain Layout
24359 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24362 \begin_layout Plain Layout
24363 \begin_inset Formula $\sqsupseteq$
24373 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24376 \begin_layout Plain Layout
24384 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24387 \begin_layout Plain Layout
24388 \begin_inset Formula $\ni$
24398 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24401 \begin_layout Plain Layout
24409 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24412 \begin_layout Plain Layout
24413 \begin_inset Formula $\dashv$
24423 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24426 \begin_layout Plain Layout
24434 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24437 \begin_layout Plain Layout
24438 \begin_inset Formula $\frown$
24448 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24451 \begin_layout Plain Layout
24459 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24462 \begin_layout Plain Layout
24463 \begin_inset Formula $\rhd$
24473 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24476 \begin_layout Plain Layout
24484 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24487 \begin_layout Plain Layout
24488 \begin_inset Formula $\unrhd$
24498 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24501 \begin_layout Plain Layout
24509 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24512 \begin_layout Plain Layout
24513 \begin_inset Formula $\lessgtr$
24523 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24526 \begin_layout Plain Layout
24534 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24537 \begin_layout Plain Layout
24538 \begin_inset Formula $\parallel$
24548 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24551 \begin_layout Plain Layout
24559 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24562 \begin_layout Plain Layout
24563 \begin_inset Formula $\nparallel$
24579 \begin_layout Standard
24580 \begin_inset VSpace medskip
24595 are bigger than the equal looking operators
24610 \begin_layout Standard
24612 supports also many special relations.
24613 Use the toolbar button
24616 arg "math-insert \\leqq"
24619 to see a list of these relations.
24622 \begin_layout Standard
24623 Relations are, in contrary to symbols, always surrounded by space.
24626 \begin_layout Standard
24627 Relations with labels can be created with the command
24634 \begin_inset Index idx
24637 \begin_layout Plain Layout
24646 \begin_inset Separator parbreak
24652 \begin_layout Standard
24654 \begin_inset Tabular
24655 <lyxtabular version="3" rows="2" columns="2">
24656 <features booktabs="true" tabularvalignment="middle">
24657 <column alignment="center" valignment="top" width="0pt">
24658 <column alignment="center" valignment="top">
24660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24663 \begin_layout Plain Layout
24669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24672 \begin_layout Plain Layout
24679 <row topspace="1.5mm">
24680 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24683 \begin_layout Plain Layout
24687 \begin_inset space \textvisiblespace{}
24695 \begin_inset space \textvisiblespace{}
24699 \begin_inset Formula $\downarrow$
24705 \begin_inset space \textvisiblespace{}
24709 \begin_inset space \textvisiblespace{}
24717 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24720 \begin_layout Plain Layout
24721 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24737 \begin_layout Section
24741 \begin_layout Subsection
24742 Predefined Functions
24743 \begin_inset CommandInset label
24745 name "subsec:Predefined-Functions"
24750 \begin_inset Index idx
24753 \begin_layout Plain Layout
24754 Functions ! predefined
24762 \begin_layout Standard
24763 In general, variables are set
24767 in mathematical expressions, but not function names, because
24768 \begin_inset Formula $sin$
24771 could be misunderstood as
24772 \begin_inset Formula $s\cdot i\cdot n$
24776 Therefore there are predefined functionswhich are additionally a bit separated
24778 They are inserted as commands starting with a backslash before their name.
24779 \begin_inset Separator parbreak
24785 \begin_layout Standard
24787 \begin_inset Tabular
24788 <lyxtabular version="3" rows="2" columns="2">
24789 <features booktabs="true" tabularvalignment="middle">
24790 <column alignment="center" valignment="top" width="0pt">
24791 <column alignment="center" valignment="top" width="0pt">
24793 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24796 \begin_layout Plain Layout
24802 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24805 \begin_layout Plain Layout
24813 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24816 \begin_layout Plain Layout
24822 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24825 \begin_layout Plain Layout
24826 \begin_inset Formula $Asin(x)+B$
24840 \begin_inset space \quad{}
24844 \begin_inset Tabular
24845 <lyxtabular version="3" rows="2" columns="2">
24846 <features booktabs="true" tabularvalignment="middle">
24847 <column alignment="center" valignment="top" width="0pt">
24848 <column alignment="center" valignment="top" width="0pt">
24850 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24853 \begin_layout Plain Layout
24859 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24862 \begin_layout Plain Layout
24870 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24873 \begin_layout Plain Layout
24881 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24884 \begin_layout Plain Layout
24885 \begin_inset Formula $A\sin(x)+B$
24901 \begin_layout Standard
24902 The following functions are predefined:
24905 \begin_layout Standard
24906 \begin_inset VSpace -2mm
24912 \begin_layout Standard
24914 \begin_inset Tabular
24915 <lyxtabular version="3" rows="9" columns="4">
24916 <features booktabs="true" tabularvalignment="middle">
24917 <column alignment="center" valignment="top" width="0pt">
24918 <column alignment="center" valignment="top" width="0pt">
24919 <column alignment="center" valignment="top" width="0pt">
24920 <column alignment="center" valignment="top" width="0pt">
24922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24925 \begin_layout Plain Layout
24931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24934 \begin_layout Plain Layout
24940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24943 \begin_layout Plain Layout
24949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24952 \begin_layout Plain Layout
24960 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24963 \begin_layout Plain Layout
24971 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24974 \begin_layout Plain Layout
24982 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24985 \begin_layout Plain Layout
24993 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24996 \begin_layout Plain Layout
25006 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25009 \begin_layout Plain Layout
25017 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25020 \begin_layout Plain Layout
25028 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25031 \begin_layout Plain Layout
25039 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25042 \begin_layout Plain Layout
25052 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25055 \begin_layout Plain Layout
25063 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25066 \begin_layout Plain Layout
25074 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25077 \begin_layout Plain Layout
25085 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25088 \begin_layout Plain Layout
25098 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25101 \begin_layout Plain Layout
25109 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25112 \begin_layout Plain Layout
25120 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25123 \begin_layout Plain Layout
25131 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25134 \begin_layout Plain Layout
25144 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25147 \begin_layout Plain Layout
25155 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25158 \begin_layout Plain Layout
25166 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25169 \begin_layout Plain Layout
25177 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25180 \begin_layout Plain Layout
25190 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25193 \begin_layout Plain Layout
25201 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25204 \begin_layout Plain Layout
25212 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25215 \begin_layout Plain Layout
25223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25226 \begin_layout Plain Layout
25236 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25239 \begin_layout Plain Layout
25247 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25250 \begin_layout Plain Layout
25258 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25261 \begin_layout Plain Layout
25269 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25272 \begin_layout Plain Layout
25282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25285 \begin_layout Plain Layout
25293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25296 \begin_layout Plain Layout
25304 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25307 \begin_layout Plain Layout
25315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25318 \begin_layout Plain Layout
25334 \begin_layout Standard
25335 They can also be inserted with the math toolbar button
25338 arg "math-insert \\functions"
25344 \begin_layout Subsection
25345 Self-defined Functions
25346 \begin_inset Index idx
25349 \begin_layout Plain Layout
25350 Functions ! self-defined
25358 \begin_layout Standard
25359 To use a function that is not predefined, like for example the sign function
25360 sgn(x), there are two possibilities:
25363 \begin_layout Itemize
25364 Define the function by inserting the following line to the \SpecialChar LaTeX
25369 \begin_layout Plain Layout
25374 DeclareMathOperator
25377 \begin_inset CommandInset ref
25379 reference "subsec:Self-defined-Operators"
25389 \begin_inset Newline newline
25393 \begin_inset VSpace -3mm
25397 \begin_inset Newline newline
25404 DeclareMathOperator{
25409 \begin_inset Index idx
25412 \begin_layout Plain Layout
25417 DeclareMathOperator
25423 \begin_inset Newline newline
25427 \begin_inset VSpace -2mm
25431 \begin_inset Newline newline
25434 Now the new defined function can be called with the command
25443 \begin_layout Itemize
25444 Write the formula as usual, mark the formula name, in our example the letters
25449 , and change it to mathematical text.
25450 Finally, a space is inserted between prefactor and function.
25453 \begin_layout Standard
25454 The result is the same with both methods as with a predefined function
25458 \begin_layout Plain Layout
25459 In \SpecialChar LyX
25460 self-defined functions are displayed red, predefined ones black.
25466 \begin_inset Separator parbreak
25472 \begin_layout Standard
25474 \begin_inset Tabular
25475 <lyxtabular version="3" rows="3" columns="2">
25476 <features booktabs="true" tabularvalignment="middle">
25477 <column alignment="center" valignment="top" width="0pt">
25478 <column alignment="center" valignment="top" width="0pt">
25480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25483 \begin_layout Plain Layout
25489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25492 \begin_layout Plain Layout
25500 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25503 \begin_layout Plain Layout
25511 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25514 \begin_layout Plain Layout
25515 \begin_inset Formula $A\sgn(x)+B$
25525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25528 \begin_layout Plain Layout
25532 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25543 \begin_layout Plain Layout
25544 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25560 \begin_layout Standard
25561 The first method is more suitable when the self-defined function should
25562 be used several times.
25565 \begin_layout Subsection
25567 \begin_inset Index idx
25570 \begin_layout Plain Layout
25579 \begin_layout Standard
25580 For limits, in addition to the commands
25587 \begin_inset Index idx
25590 \begin_layout Plain Layout
25610 the following functions are defined:
25611 \begin_inset Separator parbreak
25617 \begin_layout Standard
25619 \begin_inset Tabular
25620 <lyxtabular version="3" rows="5" columns="2">
25621 <features booktabs="true" tabularvalignment="middle">
25622 <column alignment="center" valignment="top" width="0pt">
25623 <column alignment="center" valignment="top" width="0pt">
25625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25628 \begin_layout Plain Layout
25634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25637 \begin_layout Plain Layout
25645 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25648 \begin_layout Plain Layout
25656 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25659 \begin_layout Plain Layout
25660 \begin_inset Formula $\varliminf$
25669 <row topspace="1.5mm">
25670 <cell alignment="center" valignment="top" usebox="none">
25673 \begin_layout Plain Layout
25681 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25684 \begin_layout Plain Layout
25685 \begin_inset Formula $\varlimsup$
25694 <row topspace="1.5mm">
25695 <cell alignment="center" valignment="top" usebox="none">
25698 \begin_layout Plain Layout
25706 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25709 \begin_layout Plain Layout
25710 \begin_inset Formula $\varprojlim$
25719 <row topspace="1.5mm" bottomspace="1mm">
25720 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25723 \begin_layout Plain Layout
25731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25734 \begin_layout Plain Layout
25735 \begin_inset Formula $\varinjlim$
25751 \begin_layout Standard
25752 \begin_inset VSpace medskip
25755 The limit is created by inserting a subscript.
25756 It is set right beside the function in an inline formula:
25759 \begin_layout Standard
25761 \begin_inset Tabular
25762 <lyxtabular version="3" rows="2" columns="2">
25763 <features booktabs="true" tabularvalignment="middle">
25764 <column alignment="center" valignment="top" width="0pt">
25765 <column alignment="center" valignment="top" width="0pt">
25767 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25770 \begin_layout Plain Layout
25776 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25779 \begin_layout Plain Layout
25787 <cell alignment="center" valignment="top" usebox="none">
25790 \begin_layout Plain Layout
25796 \begin_inset space \textvisiblespace{}
25800 \begin_inset space \textvisiblespace{}
25808 <cell alignment="center" valignment="top" usebox="none">
25811 \begin_layout Plain Layout
25812 \begin_inset Formula $\lim_{x\to A}x=B$
25828 \begin_layout Standard
25829 In a displayed formula the limit is set below the formula, as usual:
25830 \begin_inset Formula
25840 \begin_layout Standard
25841 \begin_inset VSpace medskip
25847 \begin_layout Standard
25848 How to adjust the typesetting of the limits see
25849 \begin_inset CommandInset ref
25851 reference "subsec:Operator-Limits"
25858 \begin_layout Subsection
25860 \begin_inset Index idx
25863 \begin_layout Plain Layout
25864 Functions ! modulo-
25872 \begin_layout Standard
25873 The modulo-function is special, because it exists in four variants.
25874 The variants in a displayed formula are:
25875 \begin_inset Formula
25877 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25878 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25879 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25880 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25881 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25889 \begin_layout Standard
25890 In an inline formula less space is set before the function names for all
25892 By default the modulo-functions take only the first following character
25894 To use more than one character, one has to put them into \SpecialChar TeX
25896 \begin_inset Formula
25898 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25899 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25900 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25908 \begin_layout Section
25910 \begin_inset Index idx
25913 \begin_layout Plain Layout
25922 \begin_layout Standard
25923 The characters ^ and _ would normally create a superscript and subscript,
25925 To get these characters you have to insert them with a leading
25928 \begin_inset Separator parbreak
25934 \begin_layout Standard
25937 \begin_inset Tabular
25938 <lyxtabular version="3" rows="3" columns="2">
25939 <features booktabs="true" tabularvalignment="middle">
25940 <column alignment="left" valignment="top" width="0pt">
25941 <column alignment="block" valignment="top">
25943 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25946 \begin_layout Plain Layout
25952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25955 \begin_layout Plain Layout
25963 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25966 \begin_layout Plain Layout
25970 \begin_inset space \textvisiblespace{}
25978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25981 \begin_layout Plain Layout
25982 \begin_inset Formula $\mathcircumflex$
25992 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25995 \begin_layout Plain Layout
26003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26006 \begin_layout Plain Layout
26007 \begin_inset Formula $\_$
26023 \begin_layout Subsection
26024 Special Characters in Mathematical Text
26027 \begin_layout Standard
26028 The following commands can only be used in mathematical text or in \SpecialChar TeX
26032 \begin_layout Standard
26033 \begin_inset space \hfill{}
26037 \begin_inset Tabular
26038 <lyxtabular version="3" rows="8" columns="2">
26039 <features booktabs="true" tabularvalignment="middle">
26040 <column alignment="left" valignment="top" width="0pt">
26041 <column alignment="block" valignment="top">
26043 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26046 \begin_layout Plain Layout
26052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26055 \begin_layout Plain Layout
26063 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26066 \begin_layout Plain Layout
26074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26077 \begin_layout Plain Layout
26078 \begin_inset Formula $\textrm{œ}$
26088 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26091 \begin_layout Plain Layout
26099 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26102 \begin_layout Plain Layout
26103 \begin_inset Formula $\textrm{Œ}$
26113 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26116 \begin_layout Plain Layout
26124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26127 \begin_layout Plain Layout
26128 \begin_inset Formula $\textrm{æ}$
26138 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26141 \begin_layout Plain Layout
26149 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26152 \begin_layout Plain Layout
26153 \begin_inset Formula $\textrm{Æ}$
26163 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26166 \begin_layout Plain Layout
26174 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26177 \begin_layout Plain Layout
26178 \begin_inset Formula $\textrm{\aa}$
26188 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26191 \begin_layout Plain Layout
26195 \begin_inset Index idx
26198 \begin_layout Plain Layout
26205 \begin_layout Plain Layout
26226 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26229 \begin_layout Plain Layout
26230 \begin_inset Formula $\textrm{Å}$
26240 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26243 \begin_layout Plain Layout
26251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26254 \begin_layout Plain Layout
26255 \begin_inset Formula $\textrm{ı}$
26269 \begin_inset space \hfill{}
26273 \begin_inset Tabular
26274 <lyxtabular version="3" rows="8" columns="2">
26275 <features booktabs="true" tabularvalignment="middle">
26276 <column alignment="left" valignment="top" width="0pt">
26277 <column alignment="center" valignment="top">
26279 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26282 \begin_layout Plain Layout
26284 \begin_inset Note Note
26287 \begin_layout Plain Layout
26289 \begin_inset space \thinspace{}
26292 mm is used for separation, because otherwise the output will be ¡ and ¿
26303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26306 \begin_layout Plain Layout
26314 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26317 \begin_layout Plain Layout
26325 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26328 \begin_layout Plain Layout
26329 \begin_inset Formula $\textrm{ø}$
26339 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26342 \begin_layout Plain Layout
26350 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26353 \begin_layout Plain Layout
26354 \begin_inset Formula $\textrm{Ø}$
26364 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26367 \begin_layout Plain Layout
26375 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26378 \begin_layout Plain Layout
26379 \begin_inset Formula $\textrm{ł}$
26389 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26392 \begin_layout Plain Layout
26400 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26403 \begin_layout Plain Layout
26404 \begin_inset Formula $\textrm{Ł}$
26414 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26417 \begin_layout Plain Layout
26419 \begin_inset space \hspace{}
26424 \begin_inset space \textvisiblespace{}
26432 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26435 \begin_layout Plain Layout
26436 \begin_inset Formula $\textrm{!`}$
26446 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26449 \begin_layout Plain Layout
26451 \begin_inset space \hspace{}
26456 \begin_inset space \textvisiblespace{}
26464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26467 \begin_layout Plain Layout
26468 \begin_inset Formula $\textrm{?`}$
26478 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26481 \begin_layout Plain Layout
26489 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26492 \begin_layout Plain Layout
26493 \begin_inset Formula $\textrm{ȷ}$
26507 \begin_inset space \hfill{}
26513 \begin_layout Standard
26515 \begin_inset Formula $\textrm{\textrm{Å}}$
26519 \begin_inset Formula $\textrm{\textrm{Ø}}$
26522 can also be inserted via the math toolbar button
26525 arg "math-insert \\digamma"
26531 \begin_layout Standard
26532 An exception are the commands
26535 \begin_inset space \hspace{}
26544 \begin_inset space \hspace{}
26550 , because they can be inserted in \SpecialChar LyX
26554 \begin_layout Subsection
26556 \begin_inset CommandInset label
26558 name "subsec:Accents-in-Text"
26563 \begin_inset Index idx
26566 \begin_layout Plain Layout
26575 \begin_layout Standard
26576 With the following commands all letters can be accented.
26577 The commands must be inserted in \SpecialChar TeX
26581 \begin_layout Standard
26582 \begin_inset space \hfill{}
26586 \begin_inset Tabular
26587 <lyxtabular version="3" rows="8" columns="2">
26588 <features booktabs="true" tabularvalignment="middle">
26589 <column alignment="left" valignment="top" width="0pt">
26590 <column alignment="block" valignment="top">
26592 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26595 \begin_layout Plain Layout
26601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26604 \begin_layout Plain Layout
26612 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26615 \begin_layout Plain Layout
26619 \begin_inset Quotes grd
26627 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26630 \begin_layout Plain Layout
26634 \begin_layout Plain Layout
26650 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26653 \begin_layout Plain Layout
26661 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26664 \begin_layout Plain Layout
26668 \begin_layout Plain Layout
26684 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26687 \begin_layout Plain Layout
26691 \begin_inset space \textvisiblespace{}
26699 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26702 \begin_layout Plain Layout
26706 \begin_layout Plain Layout
26722 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26725 \begin_layout Plain Layout
26733 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26736 \begin_layout Plain Layout
26740 \begin_layout Plain Layout
26756 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26759 \begin_layout Plain Layout
26763 \begin_inset space \textvisiblespace{}
26771 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26774 \begin_layout Plain Layout
26778 \begin_layout Plain Layout
26794 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26797 \begin_layout Plain Layout
26801 \begin_inset space \textvisiblespace{}
26809 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26812 \begin_layout Plain Layout
26816 \begin_layout Plain Layout
26832 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26835 \begin_layout Plain Layout
26839 \begin_inset space \textvisiblespace{}
26847 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26850 \begin_layout Plain Layout
26854 \begin_layout Plain Layout
26874 \begin_inset space \hfill{}
26878 \begin_inset Tabular
26879 <lyxtabular version="3" rows="8" columns="2">
26880 <features booktabs="true" tabularvalignment="middle">
26881 <column alignment="left" valignment="top" width="0pt">
26882 <column alignment="center" valignment="top">
26884 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26887 \begin_layout Plain Layout
26893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26896 \begin_layout Plain Layout
26904 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26907 \begin_layout Plain Layout
26911 \begin_inset space \textvisiblespace{}
26919 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26922 \begin_layout Plain Layout
26926 \begin_layout Plain Layout
26942 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26945 \begin_layout Plain Layout
26953 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26956 \begin_layout Plain Layout
26960 \begin_layout Plain Layout
26976 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26979 \begin_layout Plain Layout
26983 \begin_inset Index idx
26986 \begin_layout Plain Layout
26997 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27000 \begin_layout Plain Layout
27004 \begin_layout Plain Layout
27020 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27023 \begin_layout Plain Layout
27031 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27034 \begin_layout Plain Layout
27038 \begin_layout Plain Layout
27054 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27057 \begin_layout Plain Layout
27061 \begin_inset space \textvisiblespace{}
27069 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27072 \begin_layout Plain Layout
27076 \begin_layout Plain Layout
27092 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27095 \begin_layout Plain Layout
27099 \begin_inset space \textvisiblespace{}
27107 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27110 \begin_layout Plain Layout
27114 \begin_layout Plain Layout
27130 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27133 \begin_layout Plain Layout
27137 \begin_inset space \textvisiblespace{}
27145 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27148 \begin_layout Plain Layout
27152 \begin_layout Plain Layout
27172 \begin_inset space \hfill{}
27178 \begin_layout Standard
27179 \begin_inset VSpace medskip
27188 also two different characters can be accented.
27194 \begin_inset space \textvisiblespace{}
27203 \begin_layout Plain Layout
27215 \begin_layout Standard
27228 can in combination with vowels directly be inserted with the keyboard without
27229 using \SpecialChar TeX
27231 The same applies for the tilde
27235 \begin_layout Plain Layout
27236 This only applies for keyboards where the tilde is defined as accent.
27245 in combination with
27260 \begin_layout Standard
27303 and accents that are inserted directly with the keyboard are also available
27304 in mathematical text.
27305 For the other accents there are special math commands to be used in formulas,
27307 \begin_inset CommandInset ref
27309 reference "subsec:Accents-for-one"
27316 \begin_layout Standard
27317 \begin_inset VSpace bigskip
27320 Furthermore, with the command
27327 \begin_inset Index idx
27330 \begin_layout Plain Layout
27338 all numbers and letters can be set into a circle, quasi accented with a
27339 circle, similar to the copyright symbol.
27342 \begin_layout Standard
27344 \begin_inset Tabular
27345 <lyxtabular version="3" rows="3" columns="2">
27346 <features booktabs="true" tabularvalignment="middle">
27347 <column alignment="center" valignment="top" width="0pt">
27348 <column alignment="center" valignment="top">
27350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27353 \begin_layout Plain Layout
27359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27362 \begin_layout Plain Layout
27370 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27373 \begin_layout Plain Layout
27381 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27384 \begin_layout Plain Layout
27388 \begin_layout Plain Layout
27403 <row topspace="1mm">
27404 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27407 \begin_layout Plain Layout
27418 raisebox{-1.5pt}{W}}
27423 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27426 \begin_layout Plain Layout
27430 \begin_layout Plain Layout
27460 \begin_layout Standard
27461 One has to take care that the character fits in the circle.
27472 \begin_layout Plain Layout
27474 \begin_inset CommandInset ref
27476 reference "subsec:Font-Sizes"
27485 specifies thereby the size of the circle.
27496 \begin_layout Plain Layout
27498 \begin_inset CommandInset ref
27500 reference "subsec:Boxes-without-Frame"
27509 the character can be centered.
27512 \begin_layout Subsection
27514 \begin_inset Index idx
27517 \begin_layout Plain Layout
27526 \begin_layout Standard
27527 Old-style figures (also known as old-style numerals) are created with the
27535 \begin_inset Index idx
27538 \begin_layout Plain Layout
27547 The command can be used in formulas and in \SpecialChar TeX
27549 The command scheme is:
27552 \begin_layout Standard
27557 oldstylenums{number}
27560 \begin_layout Standard
27565 oldstylenums{0123456789
27568 \begin_inset Formula $\oldstylenums{0123456789}$
27574 \begin_layout Section
27576 \begin_inset CommandInset label
27578 name "sec:Formula-Styles"
27583 \begin_inset Index idx
27586 \begin_layout Plain Layout
27595 \begin_layout Itemize
27596 There are two different alignment styles:
27597 \begin_inset Separator parbreak
27604 \begin_layout Description
27605 Centered is the predefined standard
27608 \begin_layout Description
27609 Indented for this the option
27613 must be inserted in the menu
27615 Document\SpecialChar menuseparator
27621 \begin_inset space ~
27627 \begin_layout Standard
27632 is used, the indentation can be adjusted with the length
27639 \begin_inset Index idx
27642 \begin_layout Plain Layout
27651 Should the distance be 15
27652 \begin_inset space \thinspace{}
27655 mm, the following command line is inserted in the \SpecialChar LaTeX
27659 \begin_layout Standard
27669 \begin_layout Standard
27670 When no length is specified, the predefined value of 30
27671 \begin_inset space \thinspace{}
27678 \begin_layout Itemize
27679 And two different numbering styles:
27680 \begin_inset Separator parbreak
27687 \begin_layout Description
27688 Right is the predefined standard
27691 \begin_layout Description
27692 Left for this the option
27696 must be inserted in the menu
27698 Document\SpecialChar menuseparator
27704 \begin_inset space ~
27711 \begin_layout Standard
27720 can also be used together.
27721 In this case both options are inserted, separated by a comma.
27724 \begin_layout Standard
27725 The chosen styles are used for all displayed formulas of the document.
27726 When both, centered and indented formulas should be created in a document,
27732 The indented formulas are then set in a flalign environment, see
27733 \begin_inset CommandInset ref
27735 reference "subsec:Flalign-Environment"
27742 \begin_layout Section
27744 \begin_inset CommandInset label
27746 name "sec:Multiline-Formulas"
27751 \begin_inset Index idx
27754 \begin_layout Plain Layout
27755 Formula ! multiline
27763 \begin_layout Subsection
27767 \begin_layout Standard
27768 In \SpecialChar LyX
27769 multiline formulas are created by pressing
27772 arg "newline-insert newline"
27776 This creates either an
27778 eqnarray environment
27780 that is described in
27781 \begin_inset CommandInset ref
27783 reference "subsec:Eqnarray-Environment"
27787 or, when the option
27789 Use AMS math package
27791 in the document settings is selected, an
27795 that is described in
27796 \begin_inset CommandInset ref
27798 reference "subsec:Standard-align-Environment"
27803 The align environment is recommended because it provides in any case a
27804 typographically correct output.
27807 \begin_layout Standard
27808 There are other multiline formula environments that can be created via the
27811 Insert\SpecialChar menuseparator
27815 These environments are described in the following sections.
27818 \begin_layout Standard
27819 In all multiline formula environments a new line is created by pressing
27823 arg "newline-insert newline"
27827 To add or delete lines, the math toolbar buttons
27830 arg "inset-modify tabular append-row"
27836 arg "inset-modify tabular delete-row"
27839 , respectively, or the menu
27841 Edit\SpecialChar menuseparator
27847 \begin_layout Subsubsection
27849 \begin_inset CommandInset label
27851 name "subsec:Line-Separation"
27856 \begin_inset Index idx
27859 \begin_layout Plain Layout
27860 Formula ! multiline ! Line separation
27868 \begin_layout Standard
27869 There is sometimes not enough space in multiline formulas between the lines:
27870 \begin_inset Formula
27872 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}\\
27873 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
27881 \begin_layout Standard
27882 In \SpecialChar LaTeX
27883 additional line space is specified as optional argument of the new line
27885 This is not yet possible in \SpecialChar LyX
27890 \begin_layout Plain Layout
27892 \begin_inset CommandInset href
27894 name "LyX-bug #1505"
27895 target "http://www.lyx.org/trac/ticket/1505"
27904 , therefore the whole formula must be inserted in \SpecialChar TeX
27906 To add in our example space, the command
27914 is inserted at the end of the first line.
27919 \begin_layout Plain Layout
27926 \begin_layout Plain Layout
27928 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27931 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27938 \begin_layout Plain Layout
27942 left(B^{2}+x_{0}^{2}
27950 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27955 \begin_layout Plain Layout
27967 \begin_layout Standard
27968 \begin_inset VSpace bigskip
27971 To set the line separation for all lines in a formula, the length
27978 \begin_inset Index idx
27981 \begin_layout Plain Layout
27991 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28002 \begin_inset space \thinspace{}
28007 \begin_inset space \thinspace{}
28010 mm additional line separation as in the previous example, the command
28013 \begin_layout Standard
28023 \begin_layout Standard
28024 is inserted in \SpecialChar TeX
28025 mode before the formula.
28026 This requires that the \SpecialChar LaTeX
28035 \begin_layout Plain Layout
28040 is part of every \SpecialChar LaTeX
28041 standard installation.
28047 \begin_inset Index idx
28050 \begin_layout Plain Layout
28056 was loaded in \SpecialChar LaTeX
28057 -preamble with the line
28060 \begin_layout Standard
28068 \begin_layout Standard
28073 \begin_layout Plain Layout
28085 \begin_inset Formula
28087 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}\\
28088 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
28096 \begin_layout Standard
28100 \begin_layout Plain Layout
28111 To get back to the predefined distance,
28117 is set to the value 3
28118 \begin_inset space \thinspace{}
28124 \begin_layout Subsubsection
28126 \begin_inset CommandInset label
28128 name "subsec:Column-Separation"
28133 \begin_inset Index idx
28136 \begin_layout Plain Layout
28137 Formula ! multiline ! Column separation
28145 \begin_layout Standard
28146 Multiline formulas form a matrix.
28147 A formula in the eqnarray environment is for example a matrix with three
28149 By changing the column separation in this environment, the space beside
28150 the relation sign can be changed.
28153 \begin_layout Standard
28154 The column separation is specified with the length
28161 \begin_inset Index idx
28164 \begin_layout Plain Layout
28173 \begin_inset Newline newline
28176 column separation = 2
28177 \begin_inset space \thinspace{}
28187 \begin_inset Newline newline
28193 \begin_layout Standard
28203 \begin_layout Standard
28204 inserted in \SpecialChar TeX
28205 mode, sets for all following formulas a column separation of
28207 \begin_inset space \thinspace{}
28211 To get back to the predefined distance,
28218 \begin_inset space \thinspace{}
28224 \begin_layout Standard
28226 \begin_inset space \thinspace{}
28229 cm column separation:
28233 \begin_layout Plain Layout
28245 \begin_inset Formula
28253 A formula with the predefined column separation for matrices of 10
28254 \begin_inset space \thinspace{}
28261 \begin_layout Plain Layout
28273 \begin_inset Formula
28284 \begin_layout Subsubsection
28286 \begin_inset Index idx
28289 \begin_layout Plain Layout
28298 \begin_layout Standard
28299 Long formulas can be typeset using these methods:
28302 \begin_layout Itemize
28303 When one side of the equation is much shorter than the line width, this
28304 one is chosen for the left side and the right side is typeset over two
28306 \begin_inset Formula
28308 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 \\
28309 & & -\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}
28314 The minus sign at the beginning of the second line does normally not appear
28315 as an operator because it is the first character of the line.
28316 Thus it would not be surrounded by space and could not be distinguished
28317 from the fraction bar.
28319 \begin_inset space \thinspace{}
28322 pt space was inserted behind the minus sign with the command
28332 \begin_layout Plain Layout
28340 \begin_inset CommandInset ref
28342 reference "subsec:Variable-Space"
28352 \begin_inset Index idx
28355 \begin_layout Plain Layout
28366 \begin_layout Itemize
28367 When both sides of the equation are too long, the command
28374 \begin_inset Index idx
28377 \begin_layout Plain Layout
28386 It is inserted in the first column of the first line and causes all further
28387 insertions to overwrite the following columns:
28388 \begin_inset Formula
28390 \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 \\
28391 & & -\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 \\
28392 & & =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}
28397 After the insertion of
28403 , the cursor is in a purple box that is a bit shifted to the left from the
28405 In this the formula is inserted.
28406 \begin_inset Newline newline
28409 The content of the further lines is inserted to the second or another formula
28411 The greater the column number where it was inserted, the larger the indentation.
28412 \begin_inset VSpace medskip
28416 \begin_inset Newline newline
28420 \begin_inset Note Greyedout
28423 \begin_layout Plain Layout
28424 Note the following when using
28433 \begin_layout Itemize
28434 The formula doesn't use the full page width.
28436 \begin_inset space \thinspace{}
28440 \begin_inset space \space{}
28444 \begin_inset Formula $-B^{2}$
28447 is added to the first line in the above example, it would have been outside
28449 To better use the width, negative space can be inserted at the beginning
28453 \begin_layout Itemize
28454 Due to a bug in \SpecialChar LyX
28455 the cursor cannot be set with the mouse into the first
28460 \begin_layout Plain Layout
28461 \begin_inset CommandInset href
28463 name "LyX-bug #1429"
28464 target "http://www.lyx.org/trac/ticket/1429"
28473 One can only set the cursor at the beginning of the line and move it with
28482 \begin_layout Itemize
28483 Other methods to set long formulas are offered by the environments described
28485 \begin_inset CommandInset ref
28487 reference "subsec:Multline-Environment"
28492 \begin_inset CommandInset ref
28494 reference "subsec:Multiline-Formula-Parts"
28501 \begin_layout Subsubsection
28502 Multiline Fractions
28503 \begin_inset CommandInset label
28505 name "subsec:Multiline-Fractions"
28510 \begin_inset Index idx
28513 \begin_layout Plain Layout
28514 Fractions ! multiline
28522 \begin_layout Standard
28523 There are cases where the denominator and/or the numerator of a fraction
28524 is so long that the fraction does not fit into one line.
28525 It is then necessary to add a line break within the fraction.
28526 This can be done using the command
28533 \begin_inset Index idx
28536 \begin_layout Plain Layout
28545 To activate it, set in the document settings under
28548 \begin_inset space ~
28558 \begin_inset Index idx
28561 \begin_layout Plain Layout
28562 Packages ! mathtools
28570 \begin_inset space ~
28585 \begin_layout Standard
28590 splitfrac{first line}{second line}
28593 \begin_layout Standard
28594 and is used as denominator and/or numerator:
28597 \begin_layout Standard
28598 \begin_inset Formula
28600 a=\frac{\splitfrac{xy+xy+xy+xy+xy}{+wy+wy+wy+wy}}{z}\ne\frac{\splitdfrac{xy+\frac{xy}{z}+xy+xy+xy}{+xy+xy+xy+xy}}{z}
28605 The command for the first numerator above is:
28608 \begin_layout Standard
28613 splitfrac{xy+xy+xy+xy+xy
28614 \begin_inset space \textvisiblespace{}
28622 \begin_layout Subsubsection
28624 \begin_inset CommandInset label
28626 name "subsec:Multiline-Brackets"
28631 \begin_inset Index idx
28634 \begin_layout Plain Layout
28635 Brackets ! for multiline expressions
28643 \begin_layout Standard
28644 For brackets spanning multiple lines the following problem occurs:
28645 \begin_inset Formula
28647 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28648 & & \left.\cdots+B-D\right]
28656 \begin_layout Standard
28657 The closing bracket is smaller than the opening bracket because brackets
28658 with variable size may not span multiple lines.
28661 \begin_layout Standard
28662 To set the bracket size for the second line correctly, the first line is
28670 \begin_inset Index idx
28673 \begin_layout Plain Layout
28681 and the second line with
28689 \begin_layout Plain Layout
28703 \begin_inset CommandInset ref
28705 reference "subsec:Automatic-Bracket-Size"
28717 \begin_inset Index idx
28720 \begin_layout Plain Layout
28743 \begin_inset space \textvisiblespace{}
28753 \begin_inset space \textvisiblespace{}
28763 \begin_inset space \textvisiblespace{}
28769 \begin_inset Formula $\downarrow$
28775 \begin_inset Index idx
28778 \begin_layout Plain Layout
28786 is inserted, because the multiplication operator with its limits is the
28787 largest symbol in the first line and this should be the size for the bracket
28788 in the second line.
28791 \begin_layout Standard
28792 The result is this:
28793 \begin_inset Formula
28795 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28796 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28804 \begin_layout Subsection
28808 \begin_layout Standard
28809 Align environments can be used for every kind of multiline formulas.
28810 They are especially useful to set several formulas side by side.
28813 \begin_layout Standard
28814 Align environments consist of columns.
28815 The odd columns are right aligned, the even ones left aligned.
28816 Every line in an Align environment can be numbered.
28819 \begin_layout Standard
28820 Align environments are created via the menu
28822 Insert\SpecialChar menuseparator
28828 Edit\SpecialChar menuseparator
28829 Math\SpecialChar menuseparator
28830 Change Formula Type
28832 already existing formulas can be converted to Align environments.
28835 \begin_layout Standard
28836 To add or delete columns, the math toolbar buttons
28839 arg "inset-modify tabular append-column"
28845 arg "inset-modify tabular delete-column"
28848 , respectively, or the menu
28850 Edit\SpecialChar menuseparator
28856 \begin_layout Subsubsection
28857 Standard align Environment
28858 \begin_inset CommandInset label
28860 name "subsec:Standard-align-Environment"
28865 \begin_inset Index idx
28868 \begin_layout Plain Layout
28869 Formula ! multiline ! align environment
28877 \begin_layout Standard
28878 This Align environment is created by pressing
28881 arg "newline-insert newline"
28884 in a formula or by the menu
28886 Insert\SpecialChar menuseparator
28887 Math\SpecialChar menuseparator
28888 AMS align Environment
28893 \begin_layout Standard
28894 An example for two formulas set side by side, that are created with a four
28895 column align environment:
28896 \begin_inset Formula
28898 A & =\sin(B) & C & =D\\
28899 C & \ne A & B & \ne D
28904 As it can be seen, the formulas in this environment are placed so as if
28913 \begin_layout Plain Layout
28921 \begin_inset CommandInset ref
28923 reference "subsec:Variable-Space"
28934 before the first and after every even column.
28935 When the formula style
28941 \begin_layout Plain Layout
28943 \begin_inset CommandInset ref
28945 reference "sec:Formula-Styles"
28956 is used, the formula is set without the
28962 before the first column.
28965 \begin_layout Subsubsection
28966 Alignat Environment
28967 \begin_inset Index idx
28970 \begin_layout Plain Layout
28971 Formula ! multiline ! alignat environment
28979 \begin_layout Standard
28980 The alignat environment has no predefined column separation.
28981 It can be inserted manually with the spaces that are described
28982 \begin_inset CommandInset ref
28984 reference "subsec:Space"
28991 \begin_layout Standard
28992 The above example in the alignat environment where 1
28993 \begin_inset space \thinspace{}
28996 cm space was inserted at the beginning of the second formula:
28997 \begin_inset Formula
28998 \begin{alignat*}{2}
28999 A & =\sin(B) & \hspace{1cm}C & =D\\
29000 C & \ne A & B & \ne D
29005 Because the column separation can be set separately for every column, this
29006 environment is especially suitable to set three and more formulas side
29010 \begin_layout Subsubsection
29011 Flalign Environment
29012 \begin_inset CommandInset label
29014 name "subsec:Flalign-Environment"
29019 \begin_inset Index idx
29022 \begin_layout Plain Layout
29023 Formula ! multiline ! flalign environment
29031 \begin_layout Standard
29032 In this environment the first two columns are always set as much as possible
29033 to the left and the last two ones to the right.
29035 \begin_inset Formula
29037 A & =1 & B & =2 & C & =3\\
29038 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29046 \begin_layout Standard
29047 By creating a flalign environment with an odd number of columns where an
29048 empty \SpecialChar TeX
29049 brace is inserted to the last column, several formulas in a document
29050 can be set to the left, although the formula style
29055 As example the indented formula
29056 \begin_inset CommandInset ref
29058 reference "eq:VolInt"
29063 \begin_inset Formula
29065 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29070 The first two columns contain the formula.
29071 To indent it as with the formula style
29076 \begin_inset space \thinspace{}
29079 pt space was inserted at the beginning of the first column.
29082 \begin_layout Subsection
29083 Eqnarray Environment
29084 \begin_inset CommandInset label
29086 name "subsec:Eqnarray-Environment"
29091 \begin_inset Index idx
29094 \begin_layout Plain Layout
29095 Formula ! multiline ! eqnarray environment
29103 \begin_layout Standard
29104 When this environment has been created, three blue boxes appear.
29105 The content of the first box is right aligned, the content of the last
29107 The content of the middle box appears centered and a bit smaller, because
29108 it is designed to insert there only relation characters.
29109 \begin_inset Formula
29111 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29121 \begin_layout Subsection
29123 \begin_inset Index idx
29126 \begin_layout Plain Layout
29127 Formula ! multiline ! gather environment
29135 \begin_layout Standard
29136 This environment consists of only one centered column.
29137 Every line can be numbered.
29138 \begin_inset Formula
29149 \begin_layout Subsection
29150 Multline Environment
29151 \begin_inset CommandInset label
29153 name "subsec:Multline-Environment"
29158 \begin_inset Index idx
29161 \begin_layout Plain Layout
29162 Formula ! multiline ! multline environment
29170 \begin_layout Standard
29171 The multline environment consists, like the gather environment, of only
29173 But the first line is left aligned, the last one right aligned.
29174 All other lines are centered.
29175 Therefore this environment is suitable for long formulas.
29177 \begin_inset CommandInset ref
29179 reference "eq:lefteqn"
29183 in the multline environment:
29184 \begin_inset Formula
29186 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}\\
29187 -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}\\
29188 =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}}
29196 \begin_layout Standard
29197 In the output only the last (first) line of a multline environment appears
29198 numbered when the document numbering is right (left).
29202 \begin_layout Plain Layout
29203 numbering styles see
29204 \begin_inset CommandInset ref
29206 reference "sec:Formula-Styles"
29218 \begin_layout Standard
29226 \begin_inset Index idx
29229 \begin_layout Plain Layout
29244 \begin_inset Index idx
29247 \begin_layout Plain Layout
29255 a centered line can be right or left aligned, respectively.
29256 The commands are used as follows:
29259 \begin_layout Standard
29264 shoveright{line content}
29270 shoveleft{line content}
29273 \begin_layout Standard
29274 \begin_inset VSpace medskip
29284 \begin_inset Index idx
29287 \begin_layout Plain Layout
29295 specifies the distance of the first line from the left page margin.
29296 Predefined is the length 0
29297 \begin_inset space \thinspace{}
29303 \begin_layout Standard
29304 As example the above formula where the command
29307 \begin_layout Standard
29317 \begin_layout Standard
29318 was inserted in \SpecialChar TeX
29323 \begin_layout Plain Layout
29335 \begin_inset Formula
29337 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}\\
29338 \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}}\\
29339 =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}}
29348 \begin_layout Plain Layout
29359 The second line was left aligned using
29368 \begin_layout Subsection
29369 Multiline Formula Parts
29370 \begin_inset CommandInset label
29372 name "subsec:Multiline-Formula-Parts"
29377 \begin_inset Index idx
29380 \begin_layout Plain Layout
29381 Formula ! multiline ! formula parts
29389 \begin_layout Standard
29390 To display only parts of a formula with multiple lines, one of the following
29391 environments is used:
29408 They can be inserted via the menu
29410 Insert\SpecialChar menuseparator
29413 or by using the commands described in this section.
29416 \begin_layout Standard
29417 The first three have the same properties as the corresponding multiline
29418 formula environments, but it is possible to set further formula parts beside
29421 \begin_inset Formula
29423 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29424 \Delta E\Delta t & \ge\frac{\hbar}{2}
29426 \right\} \textrm{Uncertainty relations}
29434 \begin_layout Standard
29435 To get this formula, a displayed formula is created where the command
29442 \begin_inset Index idx
29445 \begin_layout Plain Layout
29454 A purple box appears around the blue formula box where now columns and
29455 lines can be added.
29456 Outside the multiline environment other formula parts can be set, like
29460 \begin_layout Standard
29461 The aligned environment is also suitable for long formulas whose lines are
29462 horizontally aligned.
29463 Using aligned in a displayed formula has the advantage that the formula
29464 number is vertically centered behind the lines.
29466 \begin_inset CommandInset ref
29468 reference "eq:shortlong"
29472 in the aligned environment:
29473 \begin_inset Formula
29475 \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}|}\\
29476 & -\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}|}
29485 \begin_layout Standard
29486 To use the environments
29505 \begin_inset Index idx
29508 \begin_layout Plain Layout
29523 \begin_inset Index idx
29526 \begin_layout Plain Layout
29541 \begin_inset Index idx
29544 \begin_layout Plain Layout
29552 are inserted, respectively.
29553 The split environment has the same properties as the aligned environment
29554 but it can only have two columns.
29557 \begin_layout Subsection
29558 Text in multiline Formulas
29559 \begin_inset CommandInset label
29561 name "subsec:Text-in-multiline"
29566 \begin_inset Index idx
29569 \begin_layout Plain Layout
29576 \begin_inset Index idx
29579 \begin_layout Plain Layout
29580 Formula ! multiline ! text
29588 \begin_layout Standard
29589 In the Align environments, and the multline and gather environment, text
29590 can be inserted that will appear in a separate line and doesn't affect
29591 the column alignment.
29592 To do this, the command
29599 \begin_inset Index idx
29602 \begin_layout Plain Layout
29610 is used in the following scheme:
29613 \begin_layout Standard
29621 \begin_layout Standard
29622 The text should not be longer than a line because it cannot be hyphenated.
29623 As \SpecialChar LyX
29624 doesn't yet support
29630 directly, the text is written as mathematical text.
29637 must hereby be at the beginning of a line and appears in the output above
29639 An example where the text was inserted at the beginning of the second line:
29640 \begin_inset Formula
29642 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29643 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29651 \begin_layout Standard
29658 always creates some vertical space between the text and the formula lines.
29659 To avoid this space, set in the document settings under
29662 \begin_inset space ~
29672 \begin_inset Index idx
29675 \begin_layout Plain Layout
29676 Packages ! mathtools
29684 \begin_inset space ~
29690 Then you can use the command
29697 \begin_inset Index idx
29700 \begin_layout Plain Layout
29717 \begin_layout Standard
29718 \begin_inset Formula
29720 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29721 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29729 \begin_layout Section
29731 \begin_inset Index idx
29734 \begin_layout Plain Layout
29741 \begin_inset Index idx
29744 \begin_layout Plain Layout
29745 Formula ! numbering|see
29749 \begin_layout Plain Layout
29760 \begin_layout Plain Layout
29775 \begin_layout Subsection
29779 \begin_layout Standard
29780 Numbered formulas can be created with the menu
29782 Insert\SpecialChar menuseparator
29783 Math\SpecialChar menuseparator
29785 \begin_inset space ~
29793 \begin_inset space ~
29799 Existing formulas can be numbered with the menu
29801 Edit\SpecialChar menuseparator
29802 Math\SpecialChar menuseparator
29804 \begin_inset space ~
29812 arg "math-number-toggle"
29816 The formula number is displayed in \SpecialChar LyX
29817 behind the formula as a number sign
29819 The number sign is replaced in the output by the formula number.
29822 \begin_layout Standard
29823 When numbering is turned on in multiline formulas, all lines will be numbered.
29824 But the numbering can be controlled with the menu
29826 Edit\SpecialChar menuseparator
29827 Math\SpecialChar menuseparator
29829 \begin_inset space ~
29833 \begin_inset space ~
29837 \begin_inset space ~
29845 arg "math-number-line-toggle"
29851 \begin_layout Standard
29852 Except for inline formulas, all formulas can be numbered with two different
29854 \begin_inset CommandInset ref
29856 reference "sec:Formula-Styles"
29863 \begin_layout Subsection
29865 \begin_inset Index idx
29868 \begin_layout Plain Layout
29869 Cross-references ! to formulas
29877 \begin_layout Standard
29878 All labeled formulas can be cross-referenced.
29879 A label is added by the menu
29881 Insert\SpecialChar menuseparator
29884 or the toolbar button
29891 The cursor must hereby be inside a displayed formula.
29892 Alternatively you can right-click on the formula and choose
29897 A dialog pops up displaying the prefix
29902 The label is inserted there behind the prefix.
29903 The predefined prefix means
29904 \begin_inset Quotes eld
29908 \begin_inset Quotes erd
29911 and makes it easier to find labels in large documents because it marks
29912 it as formula label to divide it from e.
29913 \begin_inset space \thinspace{}
29917 \begin_inset space \space{}
29921 To change a label, the menu
29923 Insert\SpecialChar menuseparator
29926 is used again or you right-click on a formula and then on
29933 \begin_layout Standard
29934 The name of the label is displayed in \SpecialChar LyX
29935 within two parentheses behind formula.
29936 A formula with a label is always numbered.
29939 \begin_layout Standard
29940 Cross-references are inserted via the menu
29942 Insert\SpecialChar menuseparator
29945 or with the toolbar button
29948 arg "dialog-show-new-inset ref"
29952 A formula cross-reference appears in the output as formula number.
29953 When in the cross-reference dialog window the format
29957 is chosen, the cross-reference appears in the output as formula number
29959 \begin_inset Newline newline
29962 By right-clicking on a cross-reference in \SpecialChar LyX
29963 , one jumps to the formula that
29967 \begin_layout Standard
29968 Here are as examples cross-references to formulas of the following subsections:
29969 \begin_inset Note Note
29972 \begin_layout Plain Layout
29973 Note the different cross-reference types.
29981 \begin_layout Standard
29983 \begin_inset CommandInset ref
29990 \begin_inset CommandInset ref
29998 \begin_inset CommandInset ref
30004 ) big Latin letters are used for the numbering in contrary to (
30005 \begin_inset CommandInset ref
30014 \begin_layout Standard
30015 \begin_inset VSpace medskip
30018 When the argument of
30026 \begin_layout Plain Layout
30034 \begin_inset CommandInset ref
30036 reference "subsec:User-defined-Numbering"
30047 contains a box like in
30048 \begin_inset CommandInset ref
30050 reference "subsec:Paragraph-Boxes"
30054 , the formula cannot be referenced.
30057 \begin_layout Subsection
30059 \begin_inset Index idx
30062 \begin_layout Plain Layout
30063 Formula numbering ! subnumbering
30071 \begin_layout Standard
30072 With the help of the commands
30076 begin{subequations}
30084 formulas can be subnumbered.
30085 Both commands are inserted in \SpecialChar TeX
30089 \begin_layout Standard
30091 \begin_inset Formula
30102 \begin_layout Plain Layout
30106 addtocounter{equation}{-1}
30115 \begin_layout Plain Layout
30119 begin{subequations}
30125 \begin_inset VSpace -5mm
30129 \begin_inset Formula
30137 \begin_inset Formula
30147 \begin_layout Standard
30151 \begin_layout Plain Layout
30163 \begin_layout Standard
30164 To create the example, the following is done:
30167 \begin_layout Enumerate
30168 first formula is inserted
30171 \begin_layout Enumerate
30176 addtocounter{equation}{-1}
30178 begin{subequations}
30179 \begin_inset Index idx
30182 \begin_layout Plain Layout
30191 \begin_inset Newline newline
30196 is inserted after the first formula
30199 \begin_layout Enumerate
30200 second formula is inserted
30203 \begin_layout Enumerate
30204 third formula is inserted
30207 \begin_layout Enumerate
30214 is inserted after the third formula
30217 \begin_layout Standard
30218 Every formula between the commands
30230 is subnumbered as a, b,
30231 \begin_inset Newline linebreak
30234 c, \SpecialChar ldots
30235 For multiline formulas every line will be subnumbered.
30236 All subnumbered formulas are treated as
30241 But as every numbered formula increases the counter
30245 by one, the command
30251 is needed to decrease it.
30252 Otherwise the formulas
30253 \begin_inset CommandInset ref
30260 \begin_inset CommandInset ref
30267 \begin_inset CommandInset ref
30273 would be numbered as
30274 \begin_inset CommandInset ref
30281 \begin_inset CommandInset ref
30288 \begin_inset CommandInset ref
30297 \begin_layout Standard
30298 By inserting the commands in \SpecialChar TeX
30299 mode, a space is created between the first
30302 \begin_inset space \thinspace{}
30305 mm vertical space is inserted after the command
30309 begin{subequations}
30312 When the formula style
30318 \begin_layout Plain Layout
30320 \begin_inset CommandInset ref
30322 reference "sec:Formula-Styles"
30334 \begin_inset space \thinspace{}
30337 mm space is inserted instead.
30340 \begin_layout Standard
30341 Here is an example for a multiline formula where the numbering was turned
30342 off for the second line:
30346 \begin_layout Plain Layout
30350 begin{subequations}
30356 \begin_inset Formula
30358 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30359 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30360 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30369 \begin_layout Plain Layout
30381 \begin_layout Subsection
30382 User-defined Numbering
30383 \begin_inset CommandInset label
30385 name "subsec:User-defined-Numbering"
30390 \begin_inset Index idx
30393 \begin_layout Plain Layout
30394 Formula numbering ! user-defined
30402 \begin_layout Standard
30403 \begin_inset Index idx
30406 \begin_layout Plain Layout
30407 Formula numbering ! self-defined delimiters
30412 With the standard numbering parentheses are set around the formula number.
30413 To replace the parentheses for example by vertical bars, the following
30414 line is added to the \SpecialChar LaTeX
30418 \begin_layout Standard
30430 \begin_inset Note Note
30433 \begin_layout Plain Layout
30434 This macro is already declared in the \SpecialChar LaTeX
30435 -preamble for testing.
30436 To activate it, remove the percent sign at the beginning.
30444 \begin_layout Standard
30445 To use other characters, the vertical bars besides the
30449 are replaced by one ore more characters.
30450 To get only the formula number the vertical bars are omitted.
30453 \begin_layout Standard
30454 \begin_inset VSpace bigskip
30457 When there should be an expression of your choice instead of the consecutive
30458 formula number in parentheses behind the formula, the command
30465 \begin_inset Index idx
30468 \begin_layout Plain Layout
30477 \begin_inset Formula
30479 A+B=C\tag{something}\label{eq:tag}
30484 In this example the command
30489 \begin_inset space \textvisiblespace{}
30494 was inserted in the formula.
30497 \begin_layout Standard
30503 \begin_inset space \textvisiblespace{}
30508 is inserted instead, the star prevents the parentheses around the expression:
30509 \begin_inset Formula
30511 A+B=C\tag*{something}
30519 \begin_layout Standard
30520 \begin_inset VSpace bigskip
30523 To restart the formula numbering with new document parts or sections, the
30524 following command is used:
30527 \begin_layout Standard
30532 @addtoreset{equation}{part}
30535 \begin_inset Index idx
30538 \begin_layout Plain Layout
30543 \begin_layout Plain Layout
30554 \begin_layout Plain Layout
30567 \begin_layout Plain Layout
30578 \begin_layout Plain Layout
30591 \begin_inset Newline newline
30595 \begin_inset Newline newline
30602 @addtoreset{equation}{section}
30605 \begin_layout Standard
30606 To be able to use these commands in \SpecialChar TeX
30608 \begin_inset Quotes eld
30612 \begin_inset Quotes erd
30615 character has to be made
30616 \begin_inset Quotes eld
30620 \begin_inset Quotes erd
30623 for \SpecialChar LaTeX
30638 So the command sequence in \SpecialChar TeX
30642 \begin_layout Standard
30648 \begin_inset Newline newline
30653 @addtoreset{equation}{section}
30654 \begin_inset Newline newline
30662 \begin_layout Standard
30663 In the \SpecialChar LaTeX
30676 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30680 \begin_layout Standard
30695 \begin_layout Plain Layout
30700 is part of the \SpecialChar LaTeX
30706 \begin_inset Index idx
30709 \begin_layout Plain Layout
30710 Packages ! carlisle
30715 that is part of every \SpecialChar LaTeX
30716 standard installation.
30722 \begin_inset Index idx
30725 \begin_layout Plain Layout
30726 Packages ! remreset
30731 has to be loaded in the \SpecialChar LaTeX
30732 -preamble with the line
30735 \begin_layout Standard
30740 usepackage{remreset}
30743 \begin_layout Standard
30751 \begin_inset Index idx
30754 \begin_layout Plain Layout
30759 \begin_layout Plain Layout
30770 \begin_layout Plain Layout
30783 \begin_layout Plain Layout
30794 \begin_layout Plain Layout
30806 can be used with the same scheme as
30815 \begin_layout Standard
30816 \begin_inset VSpace bigskip
30819 Sometimes formulas should be numbered in the following form:
30822 \begin_layout Standard
30825 (section number.formula number)
30828 \begin_layout Standard
30829 The formula number should start with every section with
30830 \begin_inset Quotes eld
30834 \begin_inset Quotes erd
30840 \begin_layout Standard
30841 For this case there is the command
30848 \begin_inset Index idx
30851 \begin_layout Plain Layout
30859 , which is used with the following scheme:
30862 \begin_layout Standard
30867 numberwithin{counter}{sectioning}
30870 \begin_layout Standard
30871 Counter denotes what kind of numbering is affected, sectioning denotes what
30872 number is before the dot.
30875 \begin_layout Standard
30876 Thus in our case the following \SpecialChar LaTeX
30877 preamble or \SpecialChar TeX
30881 \begin_layout Standard
30886 numberwithin{equation}{section}
30889 \begin_layout Standard
30890 This is the result:
30894 \begin_layout Plain Layout
30898 numberwithin{equation}{section}
30904 \begin_inset Formula
30914 \begin_layout Standard
30916 \begin_inset space \thinspace{}
30920 \begin_inset space \space{}
30923 tables so that the number of the part is the sectioning,
30924 \begin_inset Newline newline
30931 numberwithin{table}{part}
30936 \begin_layout Standard
30937 To go back to the standard numbering or to prevent this kind of numbering
30938 when it is defined by the document class, the following command is inserted
30939 as \SpecialChar TeX
30940 code or to the \SpecialChar LaTeX
30944 \begin_layout Standard
30954 \begin_inset Index idx
30957 \begin_layout Plain Layout
30971 \begin_layout Plain Layout
30987 \begin_inset Newline newline
30995 \begin_inset Newline newline
31007 \begin_layout Standard
31014 uses internally the command
31020 , described above, that also needs to be reverted.
31024 \begin_layout Plain Layout
31031 \begin_layout Plain Layout
31035 @removefromreset{equation}{section}
31038 \begin_layout Plain Layout
31050 \begin_layout Subsection
31051 Numbering with Roman Numbers and Letters
31052 \begin_inset Index idx
31055 \begin_layout Plain Layout
31056 Formula numbering ! with letters
31062 \begin_inset Index idx
31065 \begin_layout Plain Layout
31066 Formula numbering ! with Roman numbers
31074 \begin_layout Standard
31075 Formulas can also be numbered with Roman numbers and Latin letters.
31076 To number for example with small Roman numbers, the command
31079 \begin_layout Standard
31091 \begin_layout Standard
31092 is inserted before the formula in \SpecialChar TeX
31101 \begin_inset Index idx
31104 \begin_layout Plain Layout
31112 redefines the predefined command
31128 \begin_layout Plain Layout
31135 has the same scheme like the command
31141 that is described in
31142 \begin_inset CommandInset ref
31144 reference "subsec:The-Command-newcommand"
31157 is the formula counter.
31164 is used as prefix for a counter, the value of the counter is output as
31166 When a formula is numbered, \SpecialChar LaTeX
31167 sets internally the command
31173 behind the formula.
31179 \begin_inset Index idx
31182 \begin_layout Plain Layout
31192 outputs the counter as small Roman number.
31195 \begin_layout Standard
31196 All formulas behind the command
31206 are now numbered Roman.
31207 To switch to numbering with big Roman numbers, the command is inserted
31221 \begin_inset Index idx
31224 \begin_layout Plain Layout
31236 \begin_inset Quotes eld
31240 \begin_inset Quotes erd
31243 with small Latin letters there is the command
31250 \begin_inset Index idx
31253 \begin_layout Plain Layout
31261 , for big ones there is the command
31268 \begin_inset Index idx
31271 \begin_layout Plain Layout
31284 \begin_layout Standard
31285 \begin_inset Note Greyedout
31288 \begin_layout Plain Layout
31295 \begin_inset space ~
31298 formulas can be numbered with Latin letters in one document.
31306 \begin_layout Standard
31310 \begin_layout Plain Layout
31326 \begin_layout Standard
31327 \begin_inset Formula
31329 A=\textrm{small roman}
31338 \begin_layout Plain Layout
31352 \begin_inset Formula
31354 B=\textrm{big Roman}\label{eq:Rom}
31363 \begin_layout Plain Layout
31377 \begin_inset Formula
31379 C=\textrm{small Latin}
31388 \begin_layout Plain Layout
31402 \begin_inset Formula
31404 D=\textrm{big Latin}\label{eq:Lat}
31412 \begin_layout Standard
31413 To switch back to the default numbering, insert the command:
31416 \begin_layout Standard
31426 \begin_inset Index idx
31429 \begin_layout Plain Layout
31440 \begin_layout Standard
31444 \begin_layout Plain Layout
31458 \begin_inset Formula
31468 \begin_layout Standard
31469 \begin_inset VSpace medskip
31472 As you see, formulas are numbered serially independent from the numbering
31474 When then numbering should start with
31475 \begin_inset Quotes eld
31479 \begin_inset Quotes erd
31482 when the style is changed, new equation counters have to be defined.
31483 A description about this can be found in the file
31484 \begin_inset CommandInset href
31486 name "Formula-numbering.lyx"
31487 target "run:Formula-numbering.lyx"
31494 \begin_layout Section
31495 Chemical Symbols and Equations
31496 \begin_inset CommandInset label
31498 name "subsec:Chemical-Symbols-and"
31503 \begin_inset Index idx
31506 \begin_layout Plain Layout
31507 Chemical characters ! Symbols
31513 \begin_inset Index idx
31516 \begin_layout Plain Layout
31523 \begin_inset Index idx
31526 \begin_layout Plain Layout
31535 \begin_layout Standard
31536 An example text from chemistry:
31539 \begin_layout Quote
31541 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31544 -ion reacts with two
31545 \begin_inset Formula $\mathrm{Na^{+}}$
31548 -ions to sodium sulfate
31549 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31553 The chemical equation for this is:
31554 \begin_inset Formula
31556 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31564 \begin_layout Standard
31565 This chemical equation can directly be created as formula.
31566 To avoid that the symbols appear italic, everything is highlighted and
31567 changed by the shortcut
31573 to the upright font style.
31577 \begin_layout Plain Layout
31583 \begin_inset CommandInset ref
31585 reference "subsec:Font-Styles"
31597 \begin_layout Standard
31598 A more convenient way to typeset chemical formulas is to use the command
31606 \begin_inset Index idx
31609 \begin_layout Plain Layout
31617 that is available when the \SpecialChar LaTeX
31623 \begin_inset Index idx
31626 \begin_layout Plain Layout
31639 to a formula a new blue box appears where chemical formulas can be inserted
31640 in an intuitive way.
31641 \begin_inset Separator parbreak
31647 \begin_layout Standard
31649 \begin_inset Tabular
31650 <lyxtabular version="3" rows="10" columns="2">
31651 <features booktabs="true" tabularvalignment="middle">
31652 <column alignment="center" valignment="top" width="0pt">
31653 <column alignment="center" valignment="top">
31655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31658 \begin_layout Plain Layout
31664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31667 \begin_layout Plain Layout
31675 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31678 \begin_layout Plain Layout
31682 \begin_inset space \textvisiblespace{}
31690 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31693 \begin_layout Plain Layout
31694 \begin_inset Formula $\ce{H2CO3}$
31703 <row topspace="1.5mm">
31704 <cell alignment="center" valignment="top" usebox="none">
31707 \begin_layout Plain Layout
31711 \begin_inset space \textvisiblespace{}
31719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31722 \begin_layout Plain Layout
31723 \begin_inset Formula $\ce{SO4^{2-}}$
31732 <row topspace="1.5mm">
31733 <cell alignment="center" valignment="top" usebox="none">
31736 \begin_layout Plain Layout
31740 \begin_inset space \textvisiblespace{}
31748 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31751 \begin_layout Plain Layout
31752 \begin_inset Formula $\ce{(NH4)2S}$
31761 <row topspace="1.5mm">
31762 <cell alignment="center" valignment="top" usebox="none">
31765 \begin_layout Plain Layout
31769 \begin_inset space \textvisiblespace{}
31777 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31780 \begin_layout Plain Layout
31781 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31790 <row topspace="1.5mm">
31791 <cell alignment="center" valignment="top" usebox="none">
31794 \begin_layout Plain Layout
31798 \begin_inset space \textvisiblespace{}
31804 \begin_inset space \textvisiblespace{}
31810 \begin_inset space \textvisiblespace{}
31818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31821 \begin_layout Plain Layout
31822 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31831 <row topspace="1.5mm">
31832 <cell alignment="center" valignment="top" usebox="none">
31835 \begin_layout Plain Layout
31839 \begin_inset space \textvisiblespace{}
31843 \begin_inset Formula $\downarrow$
31847 \begin_inset Formula $\to$
31855 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31858 \begin_layout Plain Layout
31859 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31869 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31872 \begin_layout Plain Layout
31876 \begin_inset space \textvisiblespace{}
31882 \begin_inset space \textvisiblespace{}
31888 \begin_inset space \textvisiblespace{}
31896 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31899 \begin_layout Plain Layout
31900 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31913 \begin_layout Plain Layout
31917 \begin_inset space \textvisiblespace{}
31921 \begin_inset space \textvisiblespace{}
31925 \begin_inset space \textvisiblespace{}
31929 \begin_inset space \textvisiblespace{}
31933 \begin_inset space \textvisiblespace{}
31941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31944 \begin_layout Plain Layout
31945 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31954 <row topspace="1.5mm">
31955 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31958 \begin_layout Plain Layout
31962 \begin_inset space \textvisiblespace{}
31966 \begin_inset space \textvisiblespace{}
31970 \begin_inset space \textvisiblespace{}
31974 \begin_inset space \textvisiblespace{}
31982 \begin_inset space \textvisiblespace{}
31990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31993 \begin_layout Plain Layout
31994 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
32010 \begin_layout Standard
32011 \begin_inset Note Greyedout
32014 \begin_layout Plain Layout
32020 It is not possible in \SpecialChar LyX
32021 to use the character ^ to get an up-arrow as described
32027 One instead uses a negative thin space followed by the command
32034 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32045 \begin_layout Standard
32052 the command for equation
32053 \begin_inset space ~
32057 \begin_inset CommandInset ref
32059 reference "eq:chem-reaction"
32064 \begin_inset Newline newline
32072 \begin_inset space \textvisiblespace{}
32076 \begin_inset space \textvisiblespace{}
32080 \begin_inset space \textvisiblespace{}
32084 \begin_inset space \textvisiblespace{}
32088 \begin_inset space \textvisiblespace{}
32092 \begin_inset space \textvisiblespace{}
32098 \begin_layout Standard
32099 To create multiline chemical equations first a multiline formula is created
32101 \begin_inset CommandInset ref
32103 reference "sec:Multiline-Formulas"
32108 Afterwards the command
32114 is used in every small blue box of the formula.
32116 \begin_inset CommandInset ref
32118 reference "eq:TEOS-reaction-1"
32123 \begin_inset CommandInset ref
32125 reference "eq:TEOS-reaction-2"
32129 are an example of a multi-stage chemical reaction where every equation
32130 has its own number.
32131 \begin_inset Formula
32133 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32134 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32142 \begin_layout Standard
32153 package provides the command
32160 \begin_inset Index idx
32163 \begin_layout Plain Layout
32171 that has to be used for special cases.
32172 For more information about
32178 and more examples have a look at the documentation of
32183 \begin_inset CommandInset citation
32192 \begin_layout Section
32196 \begin_layout Standard
32198 supports two types of commutative diagrams:
32206 that are explained in the following.
32209 \begin_layout Subsection
32211 \begin_inset Index idx
32214 \begin_layout Plain Layout
32223 \begin_layout Standard
32224 Diagrams of this type visualize relations by vertical and horizontal lines
32226 \begin_inset Formula
32228 \begin{CD}A@>>>B@>>>C\\
32239 \begin_layout Standard
32240 To get them, the command
32245 \begin_inset Index idx
32248 \begin_layout Plain Layout
32258 is inserted to a formula.
32259 A blue box appears with two dashed lines where further commands can be
32264 arg "newline-insert newline"
32267 a new line is created.
32268 Horizontal relations are inserted in odd, vertical in even formula lines.
32271 \begin_layout Standard
32272 To create the relations there are the following commands:
32275 \begin_layout Itemize
32280 creates a left arrow,
32291 \begin_layout Itemize
32296 creates an up arrow,
32304 a vertical equal sign
32307 \begin_layout Itemize
32313 is a placeholder for non-existent relations
32316 \begin_layout Standard
32317 All arrows can be labeled as follows:
32320 \begin_layout Itemize
32321 If text inserted between the first and second < or >, resp., it is placed
32323 When it is inserted between the second and third one, it appears under
32327 \begin_layout Itemize
32328 When text for vertical arrows is inserted between the first and second A
32329 or V, resp., it is placed left beside the arrow.
32330 When it is inserted between the second and third one, it appears right
32332 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32336 \begin_layout Standard
32337 As example a diagram with all possible relations:
32340 \begin_layout Standard
32341 \begin_inset Formula
32343 \begin{CD}A@>j>>B@>>k>C@=F\\
32354 \begin_layout Standard
32355 The command for this is:
32356 \begin_inset Newline newline
32364 \begin_inset space \textvisiblespace{}
32367 A@>j>>B@>>k>C@=F Ctrl+Return
32368 \begin_inset Newline newline
32372 \begin_inset Phantom HPhantom
32375 \begin_layout Plain Layout
32381 \begin_inset space \textvisiblespace{}
32394 \begin_inset Formula $\to$
32400 \begin_inset Newline newline
32404 \begin_inset Phantom HPhantom
32407 \begin_layout Plain Layout
32413 \begin_inset space \textvisiblespace{}
32424 \begin_layout Subsection
32426 \begin_inset Index idx
32429 \begin_layout Plain Layout
32430 Diagrams ! xymatrix
32438 \begin_layout Standard
32439 To be able to use xymatrices, the \SpecialChar LaTeX
32445 A xymatrix is created by inserting the command
32452 Then you are able to add new matrix columns and rows like for normal matrices,
32454 \begin_inset CommandInset ref
32456 reference "sec:Matrices"
32463 \begin_layout Standard
32464 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32466 All possibilities to create commutative diagrams and decorations are explained
32471 that you find in the menu
32473 Help\SpecialChar menuseparator
32475 \begin_inset space ~
32483 \begin_layout Subsection
32489 \begin_inset Index idx
32492 \begin_layout Plain Layout
32501 \begin_layout Standard
32506 -diagrams, the \SpecialChar LaTeX
32516 -diagram is created by inserting the command
32523 Then you are able to add new matrix columns and rows like for normal matrices,
32525 \begin_inset CommandInset ref
32527 reference "sec:Matrices"
32534 \begin_layout Standard
32535 Examples how to create
32539 diagrams in \SpecialChar LyX
32542 Feynman-diagram manual
32544 that you find in the menu
32546 Help\SpecialChar menuseparator
32548 \begin_inset space ~
32556 \begin_layout Standard
32557 \begin_inset Newpage newpage
32563 \begin_layout Section
32564 User-defined Commands
32565 \begin_inset Index idx
32568 \begin_layout Plain Layout
32569 User-defined commands
32577 \begin_layout Standard
32578 \begin_inset Note Greyedout
32581 \begin_layout Plain Layout
32586 The names of user-defined commands and macros may only consist of Latin
32595 \begin_layout Subsection
32599 \begin_inset CommandInset label
32601 name "subsec:The-Command-newcommand"
32606 \begin_inset Index idx
32609 \begin_layout Plain Layout
32610 User-defined commands !
32618 \begin_inset Index idx
32621 \begin_layout Plain Layout
32632 \begin_layout Standard
32633 Many \SpecialChar LaTeX
32634 -commands are too long to be used frequently.
32635 But it is possible to define with the command
32641 new shorter commands.
32644 \begin_layout Standard
32645 The command scheme of
32654 \begin_layout Standard
32659 newcommand{new command name}[number of arguments][optional
32664 \begin_inset Newline newline
32668 \begin_inset Phantom HPhantom
32671 \begin_layout Plain Layout
32681 {command definition}
32684 \begin_layout Standard
32685 \begin_inset Note Greyedout
32688 \begin_layout Plain Layout
32693 Assure that the name of the new command is not already used in your document
32694 or by \SpecialChar LaTeX
32695 -packages that you use.
32696 When you for example define the command
32708 , you get an error message because
32714 is already defined as command for
32715 \begin_inset Quotes eld
32719 \begin_inset Formula $\le$
32723 \begin_inset Quotes erd
32734 \begin_layout Standard
32735 The number of arguments is an integer in the range 0
32736 \begin_inset space \thinspace{}
32740 \begin_inset space \thinspace{}
32743 9 and specifies how many arguments the new command should have.
32744 With the optional value a value for an optional argument can be predefined.
32745 When this is done, the
32753 rgument of the new command is automatically an optional one.
32756 \begin_layout Standard
32757 Here are some examples:
32760 \begin_layout Itemize
32761 To define the command
32773 , the \SpecialChar LaTeX
32775 \begin_inset VSpace medskip
32779 \begin_inset Newline newline
32793 \begin_layout Itemize
32794 To define the command
32806 , the argument (that should be underlined) must be taken into account.
32807 For this the preamble line is:
32808 \begin_inset VSpace medskip
32812 \begin_inset Newline newline
32826 \begin_inset VSpace medskip
32830 \begin_inset Newline newline
32837 acts as argument placeholder, the
32841 behind it denotes that it is the placeholder for the first argument.
32844 \begin_layout Itemize
32852 \begin_inset space \thinspace{}
32856 \begin_inset space \space{}
32866 \begin_inset VSpace medskip
32870 \begin_inset Newline newline
32881 framebox#1#2{$#3$}}
32884 \begin_inset VSpace medskip
32888 \begin_inset Newline newline
32891 The two Dollar signs creates the extra formula needed for
32898 \begin_inset CommandInset ref
32900 reference "subsec:Boxes-with-Frame"
32907 \begin_layout Itemize
32908 To create a new command for
32914 where the color for the box need not be specified, the argument for the
32915 color is defined optional:
32916 \begin_inset VSpace medskip
32920 \begin_inset Newline newline
32931 fcolorbox{#2}{#1}{$#3$}}
32934 \begin_inset VSpace medskip
32938 \begin_inset Newline newline
32941 When the color is not specified when using
32947 , the predefined color
32954 \begin_layout Standard
32955 A test of the new defined commands:
32956 \begin_inset Separator parbreak
32962 \begin_layout Standard
32964 \begin_inset Tabular
32965 <lyxtabular version="3" rows="6" columns="2">
32966 <features booktabs="true" tabularvalignment="middle">
32967 <column alignment="center" valignment="top" width="0pt">
32968 <column alignment="center" valignment="top">
32970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32973 \begin_layout Plain Layout
32979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32982 \begin_layout Plain Layout
32990 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32993 \begin_layout Plain Layout
32997 \begin_inset space \textvisiblespace{}
33005 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33008 \begin_layout Plain Layout
33009 \begin_inset Formula $A\gr B$
33019 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33022 \begin_layout Plain Layout
33030 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33033 \begin_layout Plain Layout
33034 \begin_inset Formula $\us{ABcd}$
33043 <row topspace="1mm">
33044 <cell alignment="center" valignment="top" usebox="none">
33047 \begin_layout Plain Layout
33051 \begin_inset Formula $\to$
33057 \begin_inset Formula $\to$
33065 \begin_inset space \textvisiblespace{}
33073 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33076 \begin_layout Plain Layout
33077 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33086 <row topspace="1.5mm">
33087 <cell alignment="center" valignment="top" usebox="none">
33090 \begin_layout Plain Layout
33094 \begin_inset Formula $\to$
33102 \begin_inset space \textvisiblespace{}
33110 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33113 \begin_layout Plain Layout
33114 \begin_inset Formula $\cb{red}{\int A=B}$
33123 <row topspace="1.5mm" bottomspace="1mm">
33124 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33127 \begin_layout Plain Layout
33133 \begin_inset Formula $\to$
33141 \begin_inset space \textvisiblespace{}
33149 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33152 \begin_layout Plain Layout
33153 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33169 \begin_layout Subsection
33171 \begin_inset Index idx
33174 \begin_layout Plain Layout
33175 User-defined commands! Math macros
33181 \begin_inset Index idx
33184 \begin_layout Plain Layout
33193 \begin_layout Standard
33194 User-defined commands are especially convenient for complex expressions.
33195 When you are for example dealing with a document that has quadratic equations,
33196 the same solution type occurs several times.
33197 The general form of a quadratic equation is
33198 \begin_inset Formula
33200 0=\lambda^{2}+p\lambda+q
33205 The general form of the solution is
33206 \begin_inset Formula
33208 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33216 \begin_layout Standard
33217 To define a command for the solution formula where only the three parameters
33219 \begin_inset Formula $\lambda$
33223 \begin_inset Formula $p$
33227 \begin_inset Formula $q$
33230 need to be specified and the index of
33231 \begin_inset Formula $\lambda$
33234 can be given optionally, the \SpecialChar LaTeX
33236 \begin_inset Newline newline
33252 \begin_inset Newline newline
33256 \begin_inset Phantom HPhantom
33259 \begin_layout Plain Layout
33273 frac{#3^{2}}{4}-#4}}
33276 \begin_layout Standard
33277 To create with this the solution formula, the command
33278 \begin_inset Newline newline
33288 \begin_inset Formula $\to$
33294 \begin_inset Formula $\to$
33301 is inserted to a formula
33306 \begin_layout Standard
33307 The definition of the new command is unintuitive because one has to know
33308 the schemes of all used \SpecialChar LaTeX
33310 \begin_inset space \thinspace{}
33314 \begin_inset space \space{}
33317 that a fraction is inserted in \SpecialChar LaTeX
33322 frac{numerator}{denominator}
33325 Furthermore one can easily forget a brace in the definition and cannot
33326 see in \SpecialChar LyX
33327 what the new command is doing.
33328 To avoid these problems \SpecialChar LyX
33329 offers the possibility to use math macros instead
33339 \begin_layout Standard
33340 A math macro is created by using the menu
33342 Insert\SpecialChar menuseparator
33343 Math\SpecialChar menuseparator
33346 or the toolbar button
33349 arg "math-macro newmacroname_newcommand"
33353 The math macro toolbar appears together with the following box where the
33355 \begin_inset Newline newline
33359 \begin_inset space \hspace*{\fill}
33363 \begin_inset Graphics
33364 filename clipart/macrobox.png
33370 \begin_inset space \hspace*{\fill}
33374 \begin_inset Newline newline
33378 \begin_inset FormulaMacro
33379 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33384 newmacroname is the default name of the macro that should be changed to
33385 something sensible.
33386 The wanted formula is inserted in the first blue box.
33387 An argument placeholder is inserted with the command
33394 \begin_inset space \thinspace{}
33398 \begin_inset space \space{}
33407 or by using the macro toolbar button
33410 arg "math-macro-add-param"
33414 Argument placeholders are displayed red.
33416 \begin_inset space ~
33419 arguments are possible.
33420 Optional arguments are created with the toolbar button
33423 arg "math-macro-add-optional-param"
33427 The first non-optional argument can be transformed to an optional one with
33431 arg "math-macro-make-optional"
33435 In the second blue box the appearance of the macro in \SpecialChar LyX
33437 Normally you want to see it as it is defined, so the box is kept empty.
33438 But when you have created a macro that needs lot of space on the screen,
33439 you can insert in the box for example
33440 \begin_inset Newline newline
33470 \begin_inset Newline newline
33475 For the macro only the arguments with the macro name in front of them will
33476 then be displayed in \SpecialChar LyX
33477 , leading to a better overview.
33478 The formula appears in the output as defined in the first box.
33479 \begin_inset Newline newline
33482 The appearance of macros in formulas can furthermore be changed for single
33483 macros by setting the cursor in the macro and using the menu
33485 View\SpecialChar menuseparator
33487 \begin_inset space ~
33491 \begin_inset space ~
33499 \begin_layout Standard
33500 To use a macro, the macro name is inserted as command to a formula, in our
33508 Our macro looks in \SpecialChar LyX
33510 \begin_inset Newline newline
33514 \begin_inset space \hspace*{\fill}
33518 \begin_inset Graphics
33519 filename clipart/macrouse.png
33525 \begin_inset space \hspace*{\fill}
33529 \begin_inset Newline newline
33532 Here is our macro example with the arguments
33533 \begin_inset Formula $x$
33537 \begin_inset Formula $\ln(x)$
33541 \begin_inset Formula $B$
33547 \begin_layout Standard
33548 \begin_inset Formula
33558 \begin_layout Standard
33562 Tools\SpecialChar menuseparator
33563 Preferences\SpecialChar menuseparator
33564 Editing\SpecialChar menuseparator
33567 different styles to edit macros.
33568 To find the style that suits you the most, choose a style and set the cursor
33569 in a macro formula to see the difference.
33572 \begin_layout Standard
33573 A math macro is transformed internally to a
33579 command when exporting the document.
33586 command is not placed in the \SpecialChar LaTeX
33587 -preamble, therefore macros can only be used
33588 in formulas that are in the document below the macro definition box.
33591 \begin_layout Standard
33592 Math macros can also be directly created from a
33599 When writing for example the command
33602 \begin_inset Newline newline
33611 xleftarrow[#2]{#1}}
33612 \begin_inset Newline newline
33617 in \SpecialChar LyX
33618 as normal text, highlighting it completely and using then the shortcut
33623 , the command will be transformed to a math macro.
33624 Using this method you need to be careful that the
33630 command is typed correctly, otherwise you get a faulty macro leading to
33635 \begin_layout Standard
33636 Math macros currently have the problem that further formulas in macro definition
33637 s are handled wrongly.
33638 Therefore the example
33645 \begin_inset CommandInset ref
33647 reference "subsec:The-Command-newcommand"
33651 cannot be created as macro.
33654 \begin_layout Standard
33655 When the cursor is in a macro definition box, you will see the macro toolbar
33656 in \SpecialChar LyX
33660 \begin_layout Standard
33661 \begin_inset VSpace defskip
33667 \begin_layout Standard
33668 \begin_inset Graphics
33669 filename clipart/MacroToolbar.png
33674 \begin_inset Index idx
33677 \begin_layout Plain Layout
33686 \begin_layout Standard
33687 \begin_inset VSpace defskip
33693 \begin_layout Standard
33694 The macro toolbar contains from left to right the following buttons:
33697 \begin_layout Standard
33698 \begin_inset VSpace defskip
33704 \begin_layout Standard
33705 \begin_inset Tabular
33706 <lyxtabular version="3" rows="9" columns="2">
33707 <features islongtable="true" longtabularalignment="center">
33708 <column alignment="left" valignment="top">
33709 <column alignment="left" valignment="top" width="85col%">
33710 <row interlinespace="2.5mm">
33711 <cell alignment="center" valignment="top" usebox="none">
33714 \begin_layout Plain Layout
33717 arg "math-macro-remove-param"
33725 <cell alignment="center" valignment="top" usebox="none">
33728 \begin_layout Plain Layout
33731 Edit\SpecialChar menuseparator
33732 Math\SpecialChar menuseparator
33734 \begin_inset space ~
33737 Definition\SpecialChar menuseparator
33738 Remove Last Argument
33744 <row interlinespace="2.5mm">
33745 <cell alignment="center" valignment="top" usebox="none">
33748 \begin_layout Plain Layout
33751 arg "math-macro-add-param"
33759 <cell alignment="center" valignment="top" usebox="none">
33762 \begin_layout Plain Layout
33765 Edit\SpecialChar menuseparator
33766 Math\SpecialChar menuseparator
33768 \begin_inset space ~
33771 Definition\SpecialChar menuseparator
33778 <row interlinespace="2.5mm">
33779 <cell alignment="center" valignment="top" usebox="none">
33782 \begin_layout Plain Layout
33785 arg "math-macro-make-optional"
33793 <cell alignment="center" valignment="top" usebox="none">
33796 \begin_layout Plain Layout
33799 Edit\SpecialChar menuseparator
33800 Math\SpecialChar menuseparator
33802 \begin_inset space ~
33805 Definition\SpecialChar menuseparator
33806 Transform First Non-Optional to
33807 \begin_inset Newline newline
33811 \begin_inset Phantom HPhantom
33814 \begin_layout Plain Layout
33817 Edit\SpecialChar menuseparator
33818 Math\SpecialChar menuseparator
33820 \begin_inset space ~
33823 Definition\SpecialChar menuseparator
33835 <row interlinespace="2.5mm">
33836 <cell alignment="center" valignment="top" usebox="none">
33839 \begin_layout Plain Layout
33842 arg "math-macro-make-nonoptional"
33850 <cell alignment="center" valignment="top" usebox="none">
33853 \begin_layout Plain Layout
33856 Edit\SpecialChar menuseparator
33857 Math\SpecialChar menuseparator
33859 \begin_inset space ~
33862 Definition\SpecialChar menuseparator
33863 Transform Last Optional to
33864 \begin_inset Newline newline
33868 \begin_inset Phantom HPhantom
33871 \begin_layout Plain Layout
33874 Edit\SpecialChar menuseparator
33875 Math\SpecialChar menuseparator
33877 \begin_inset space ~
33880 Definition\SpecialChar menuseparator
33886 Non-Optional Argument
33892 <row interlinespace="2.5mm">
33893 <cell alignment="center" valignment="top" usebox="none">
33896 \begin_layout Plain Layout
33899 arg "math-macro-remove-optional-param"
33907 <cell alignment="center" valignment="top" usebox="none">
33910 \begin_layout Plain Layout
33913 Edit\SpecialChar menuseparator
33914 Math\SpecialChar menuseparator
33916 \begin_inset space ~
33919 Definition\SpecialChar menuseparator
33920 Remove Optional Argument
33926 <row interlinespace="2.5mm">
33927 <cell alignment="center" valignment="top" usebox="none">
33930 \begin_layout Plain Layout
33933 arg "math-macro-add-optional-param"
33941 <cell alignment="center" valignment="top" usebox="none">
33944 \begin_layout Plain Layout
33947 Edit\SpecialChar menuseparator
33948 Math\SpecialChar menuseparator
33950 \begin_inset space ~
33953 Definition\SpecialChar menuseparator
33954 Insert Optional Argument
33960 <row interlinespace="2.5mm">
33961 <cell alignment="center" valignment="top" usebox="none">
33964 \begin_layout Plain Layout
33967 arg "math-macro-remove-greedy-param"
33975 <cell alignment="center" valignment="top" usebox="none">
33978 \begin_layout Plain Layout
33981 Edit\SpecialChar menuseparator
33982 Math\SpecialChar menuseparator
33984 \begin_inset space ~
33987 Definition\SpecialChar menuseparator
33988 Remove Last Argument
33989 \begin_inset Newline newline
33993 \begin_inset Phantom HPhantom
33996 \begin_layout Plain Layout
33999 Edit\SpecialChar menuseparator
34000 Math\SpecialChar menuseparator
34002 \begin_inset space ~
34005 Definition\SpecialChar menuseparator
34011 Spitting Out To The Right
34017 <row interlinespace="2.5mm">
34018 <cell alignment="center" valignment="top" usebox="none">
34021 \begin_layout Plain Layout
34024 arg "math-macro-append-greedy-param"
34032 <cell alignment="center" valignment="top" usebox="none">
34035 \begin_layout Plain Layout
34038 Edit\SpecialChar menuseparator
34039 Math\SpecialChar menuseparator
34041 \begin_inset space ~
34044 Definition\SpecialChar menuseparator
34046 \begin_inset Newline newline
34050 \begin_inset Phantom HPhantom
34053 \begin_layout Plain Layout
34056 Edit\SpecialChar menuseparator
34057 Math\SpecialChar menuseparator
34059 \begin_inset space ~
34062 Definition\SpecialChar menuseparator
34068 Eating From The Right
34074 <row interlinespace="2.5mm">
34075 <cell alignment="center" valignment="top" usebox="none">
34078 \begin_layout Plain Layout
34081 arg "math-macro-add-greedy-optional-param"
34089 <cell alignment="center" valignment="top" usebox="none">
34092 \begin_layout Plain Layout
34095 Edit\SpecialChar menuseparator
34096 Math\SpecialChar menuseparator
34098 \begin_inset space ~
34101 Definition\SpecialChar menuseparator
34102 Append Optional Argument
34103 \begin_inset Newline newline
34107 \begin_inset Phantom HPhantom
34110 \begin_layout Plain Layout
34113 Edit\SpecialChar menuseparator
34114 Math\SpecialChar menuseparator
34116 \begin_inset space ~
34119 Definition\SpecialChar menuseparator
34125 Eating From The Right
34138 \begin_layout Section
34139 Computer Algebra Systems
34142 \begin_layout Standard
34144 offers the exchange between mathematical expressions written in \SpecialChar LyX
34146 editor and external applications or user defined scripts.
34147 Currently supported applications are
34164 Note that the set of supported mathematical constructs is limited only
34165 to very simple cases.
34168 \begin_layout Subsection
34172 \begin_layout Standard
34173 Write some expression in a formula, go to the
34175 Edit\SpecialChar menuseparator
34176 Math\SpecialChar menuseparator
34177 Use Computer Algebra System
34179 menu and choose the application you have installed on the computer.
34180 After that the result of computation should show on the right side of the
34181 expression together with the
34182 \begin_inset Quotes eld
34186 \begin_inset Quotes erd
34192 \begin_layout Standard
34193 Here are few simple examples (with results from
34197 ) to show what kind of computations can be performed:
34200 \begin_layout Itemize
34201 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34207 \begin_layout Itemize
34208 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34214 \begin_layout Itemize
34215 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34221 \begin_layout Itemize
34222 \begin_inset Formula $\det\left[\begin{array}{ccc}
34226 \end{array}\right]=-56$
34232 \begin_layout Itemize
34233 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34239 \begin_layout Subsection
34243 \begin_layout Standard
34244 Currently there is no keyboard shortcut for calling the algebra applications.
34245 One can easily bind a shortcut to the
34259 \begin_inset space \thinspace{}
34263 \begin_inset space \space{}
34270 key inside the math editor.
34275 one would use this shortcut definition command:
34278 \begin_layout Standard
34281 command-alternatives paragraph-break;math-extern maxima
34284 \begin_layout Section
34286 \begin_inset Index idx
34289 \begin_layout Plain Layout
34298 \begin_layout Subsection
34300 \begin_inset Index idx
34303 \begin_layout Plain Layout
34312 \begin_layout Standard
34313 Negative numbers often look ugly in formulas because the minus sign before
34314 the number is set with the same length as the minus operator sign.
34315 When writing the negative number in normal text, the minus sign appears
34319 \begin_layout Standard
34320 Thus, the problem disappears when converting the minus sign to mathematical
34324 \begin_layout Standard
34325 An example to visualize the problem:
34326 \begin_inset Separator parbreak
34332 \begin_layout Standard
34334 \begin_inset Tabular
34335 <lyxtabular version="3" rows="3" columns="2">
34336 <features booktabs="true" tabularvalignment="middle">
34337 <column alignment="right" valignment="top" width="0pt">
34338 <column alignment="left" valignment="top">
34340 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34343 \begin_layout Plain Layout
34349 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34352 \begin_layout Plain Layout
34360 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34363 \begin_layout Plain Layout
34369 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34372 \begin_layout Plain Layout
34373 \begin_inset Formula $x=-2$
34383 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34386 \begin_layout Plain Layout
34392 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34395 \begin_layout Plain Layout
34396 \begin_inset Formula $x=\textrm{-}2$
34412 \begin_layout Subsection
34413 Comma as decimal Separator
34414 \begin_inset Index idx
34417 \begin_layout Plain Layout
34426 \begin_layout Standard
34427 In \SpecialChar LaTeX
34428 a comma inside a formula is used, according to the English convention,
34429 as number group separator.
34430 So there will be space added behind all commas in formulas.
34433 \begin_layout Standard
34434 To avoid this, the comma is highlighted and changed to mathematical text
34444 \begin_layout Standard
34445 To use all formula commas in the document as decimal separator, the file
34454 \begin_layout Plain Layout
34459 is part of the \SpecialChar LaTeX
34465 \begin_inset Index idx
34468 \begin_layout Plain Layout
34473 \begin_layout Plain Layout
34493 \begin_inset Index idx
34496 \begin_layout Plain Layout
34502 is loaded with the \SpecialChar LaTeX
34506 \begin_layout Standard
34514 \begin_layout Subsection
34516 \begin_inset CommandInset label
34518 name "subsec:Physical-Vectors"
34523 \begin_inset Index idx
34526 \begin_layout Plain Layout
34535 \begin_layout Standard
34536 Predefined vectors are offered by the \SpecialChar LaTeX
34542 \begin_inset Index idx
34545 \begin_layout Plain Layout
34551 that is loaded with the \SpecialChar LaTeX
34555 \begin_layout Standard
34563 \begin_layout Standard
34567 \begin_layout Plain Layout
34577 \begin_inset Note Note
34580 \begin_layout Plain Layout
34581 The following table will only be displayed when the \SpecialChar LaTeX
34594 \begin_layout Standard
34595 The following commands are defined:
34596 \begin_inset Separator parbreak
34602 \begin_layout Standard
34604 \begin_inset Tabular
34605 <lyxtabular version="3" rows="4" columns="2">
34606 <features booktabs="true" tabularvalignment="middle">
34607 <column alignment="center" valignment="top" width="0pt">
34608 <column alignment="center" valignment="top">
34610 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34613 \begin_layout Plain Layout
34619 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34622 \begin_layout Plain Layout
34630 <cell alignment="center" valignment="top" usebox="none">
34633 \begin_layout Plain Layout
34643 <cell alignment="center" valignment="top" usebox="none">
34646 \begin_layout Plain Layout
34647 \begin_inset Formula $\Bra{\psi}$
34657 <cell alignment="center" valignment="top" usebox="none">
34660 \begin_layout Plain Layout
34670 <cell alignment="center" valignment="top" usebox="none">
34673 \begin_layout Plain Layout
34674 \begin_inset Formula $\Ket{\psi}$
34684 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34687 \begin_layout Plain Layout
34699 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34702 \begin_layout Plain Layout
34703 \begin_inset Formula $\Braket{\psi|\phi}$
34719 \begin_layout Standard
34726 assures that all vertical bars are set in the size of the surrounding brackets:
34727 \begin_inset Formula
34729 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34738 \begin_layout Plain Layout
34748 \begin_inset Note Note
34751 \begin_layout Plain Layout
34752 The following will be displayed when the \SpecialChar LaTeX
34765 \begin_layout Standard
34766 You need to install the \SpecialChar LaTeX
34771 to see the rest of this subsection in the output.
34774 \begin_layout Standard
34778 \begin_layout Plain Layout
34790 \begin_layout Standard
34797 can also be achieved using the command
34803 , that is described in
34804 \begin_inset CommandInset ref
34806 reference "subsec:Automatic-Bracket-Size"
34813 \begin_layout Subsection
34814 Self-defined Fractions
34815 \begin_inset CommandInset label
34817 name "subsec:Self-defined-Fractions"
34822 \begin_inset Index idx
34825 \begin_layout Plain Layout
34826 Fractions ! self-defined
34834 \begin_layout Standard
34835 To define custom commands for fractions, the command
34842 \begin_inset Index idx
34845 \begin_layout Plain Layout
34852 \begin_layout Plain Layout
34866 is used in the following scheme:
34869 \begin_layout Standard
34882 bracket}{fraction bar thickness}{style}
34883 \begin_inset Newline newline
34887 \begin_inset Phantom HPhantom
34890 \begin_layout Plain Layout
34900 {numerator}{denominator}
34903 \begin_layout Standard
34904 The style is a number in the range of 0
34905 \begin_inset space \thinspace{}
34909 \begin_inset space \thinspace{}
34913 \begin_inset Separator parbreak
34919 \begin_layout Standard
34921 \begin_inset Tabular
34922 <lyxtabular version="3" rows="5" columns="2">
34923 <features booktabs="true" tabularvalignment="middle">
34924 <column alignment="center" valignment="top" width="0pt">
34925 <column alignment="center" valignment="top">
34927 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34930 \begin_layout Plain Layout
34936 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34939 \begin_layout Plain Layout
34947 <cell alignment="center" valignment="top" usebox="none">
34950 \begin_layout Plain Layout
34956 <cell alignment="center" valignment="top" usebox="none">
34959 \begin_layout Plain Layout
34960 display style formula
34967 <cell alignment="center" valignment="top" usebox="none">
34970 \begin_layout Plain Layout
34976 <cell alignment="center" valignment="top" usebox="none">
34979 \begin_layout Plain Layout
34987 <cell alignment="center" valignment="top" usebox="none">
34990 \begin_layout Plain Layout
34996 <cell alignment="center" valignment="top" usebox="none">
34999 \begin_layout Plain Layout
35007 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35010 \begin_layout Plain Layout
35016 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35019 \begin_layout Plain Layout
35033 \begin_layout Standard
35034 When no style is given, the size is adjusted to the surrounding environment
35035 like for the command
35044 \begin_layout Standard
35045 When no fraction bar thickness is given, the predefined value of 0.4
35046 \begin_inset space \thinspace{}
35052 \begin_layout Standard
35053 \begin_inset VSpace medskip
35056 For example, the commands
35069 \begin_inset CommandInset ref
35071 reference "subsec:Fractions"
35075 are defined with the commands
35078 \begin_layout Standard
35087 genfrac{}{}{}{0}{#1}{#2}}
35090 \begin_layout Standard
35094 \begin_layout Standard
35103 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35106 \begin_layout Standard
35107 \begin_inset VSpace medskip
35110 To define a fraction where the fraction bar thickness can be given as optional
35111 argument, the following line is inserted to the \SpecialChar LaTeX
35115 \begin_layout Standard
35124 genfrac{}{}{#1}{}{#2}{#3}}
35127 \begin_layout Standard
35129 \begin_inset Formula
35131 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35132 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35137 As one can see, the distance of the numerator and the denominator to the
35138 fraction bar is round about three times the bar thickness.
35141 \begin_layout Subsection
35143 \begin_inset Index idx
35146 \begin_layout Plain Layout
35155 \begin_layout Standard
35156 There are four ways to cancel formulas or parts of formulas:
35159 \begin_layout Standard
35163 \begin_layout Plain Layout
35173 \begin_inset Note Note
35176 \begin_layout Plain Layout
35177 The following table will only be displayed when the \SpecialChar LaTeX
35188 \begin_inset Separator parbreak
35194 \begin_layout Standard
35196 \begin_inset Tabular
35197 <lyxtabular version="3" rows="5" columns="2">
35198 <features booktabs="true" tabularvalignment="middle">
35199 <column alignment="center" valignment="top" width="0pt">
35200 <column alignment="center" valignment="top">
35202 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35205 \begin_layout Plain Layout
35211 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35214 \begin_layout Plain Layout
35222 <cell alignment="center" valignment="top" usebox="none">
35225 \begin_layout Plain Layout
35229 \begin_inset space \textvisiblespace{}
35235 \begin_inset space \textvisiblespace{}
35243 <cell alignment="center" valignment="top" usebox="none">
35246 \begin_layout Plain Layout
35247 \begin_inset Formula $\cancel{\int A=B}$
35256 <row topspace="1.5mm">
35257 <cell alignment="center" valignment="top" usebox="none">
35260 \begin_layout Plain Layout
35264 \begin_inset space \textvisiblespace{}
35270 \begin_inset space \textvisiblespace{}
35278 <cell alignment="center" valignment="top" usebox="none">
35281 \begin_layout Plain Layout
35282 \begin_inset Formula $\bcancel{\int A=B}$
35291 <row topspace="1.5mm">
35292 <cell alignment="center" valignment="top" usebox="none">
35295 \begin_layout Plain Layout
35299 \begin_inset space \textvisiblespace{}
35305 \begin_inset space \textvisiblespace{}
35313 <cell alignment="center" valignment="top" usebox="none">
35316 \begin_layout Plain Layout
35317 \begin_inset Formula $\xcancel{\int A=B}$
35327 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35330 \begin_layout Plain Layout
35334 \begin_inset space \textvisiblespace{}
35340 \begin_inset space \textvisiblespace{}
35344 \begin_inset Formula $\to$
35352 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35355 \begin_layout Plain Layout
35356 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35372 \begin_layout Standard
35379 is especially suitable to visualize the reduction of fractions within formulas:
35380 \begin_inset Formula
35382 \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}}}
35390 \begin_layout Standard
35391 To change the size of
35398 \begin_inset Quotes eld
35402 \begin_inset Quotes erd
35405 value one can add the \SpecialChar LaTeX
35409 \begin_layout Standard
35414 PassOptionsToPackage{option}{cancel}
35417 \begin_layout Standard
35426 which leads to the same size as for the canceled value, or
35430 which makes is it a bit smaller than normal.
35433 \begin_layout Standard
35434 To color the cancellation bar one adds this command as \SpecialChar TeX
35438 \begin_layout Standard
35450 \begin_layout Standard
35455 can be replaced by a color of your choice.
35458 \begin_layout Standard
35462 \begin_layout Plain Layout
35478 \begin_layout Standard
35479 \begin_inset Formula
35481 \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}}}
35489 \begin_layout Standard
35493 \begin_layout Plain Layout
35507 \begin_inset Note Note
35510 \begin_layout Plain Layout
35519 \begin_layout Standard
35520 For further customizations, see the documentation of the package
35525 \begin_inset CommandInset citation
35532 \begin_inset Index idx
35535 \begin_layout Plain Layout
35544 \begin_layout Standard
35548 \begin_layout Plain Layout
35558 \begin_inset Note Note
35561 \begin_layout Plain Layout
35562 The following will be displayed when the \SpecialChar LaTeX
35575 \begin_layout Standard
35576 You need to install the \SpecialChar LaTeX
35581 to see the rest of this subsection in the output.
35584 \begin_layout Standard
35588 \begin_layout Plain Layout
35600 \begin_layout Subsection
35601 Formulas in Section Headings
35602 \begin_inset CommandInset label
35604 name "subsec:Formulas-in-Section"
35609 \begin_inset Index idx
35612 \begin_layout Plain Layout
35613 Formula ! in section headings
35621 \begin_layout Standard
35622 When formulas are used in section headings, the following has to be taken
35626 \begin_layout Standard
35627 \begin_inset Note Greyedout
35630 \begin_layout Plain Layout
35636 \begin_inset Index idx
35639 \begin_layout Plain Layout
35640 Packages ! hyperref
35645 support is enabled in the document settings dialog under
35648 \begin_inset space ~
35653 , PDF-bookmarks are created for every section heading in the table of contents.
35654 If a section heading contains formulas, they are incorrectly displayed
35655 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35664 \begin_layout Standard
35665 Both problems can be solved by inserting at the end of the section heading
35666 a short title with the menu
35668 Insert\SpecialChar menuseparator
35670 \begin_inset space ~
35676 Short titles are used as alternative for multiline section headings to
35677 keep the table of contents clearly arranged.
35678 Only the short title appears in the table of contents and therefore also
35679 in the PDF-bookmark.
35682 \begin_layout Standard
35683 When formulas should be used in the table of contents but
35687 is used, one can use the following command in \SpecialChar TeX
35691 \begin_layout Standard
35696 texorpdfstring{part}{alternative}
35697 \begin_inset Index idx
35700 \begin_layout Plain Layout
35711 \begin_layout Standard
35712 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35713 This can be characters, formulas, footnotes, but also cross-references.
35714 The alternative is used instead of the part for the bookmark.
35717 \begin_layout Standard
35718 Here are two example headings:
35719 \begin_inset VSpace -3mm
35726 \begin_layout Plain Layout
35738 \begin_layout Subsubsection
35739 Heading without formula in table of contents
35740 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35744 \begin_inset Argument 1
35747 \begin_layout Plain Layout
35748 Heading without formula in table of contents
35756 \begin_layout Subsubsection
35757 Heading with formula in table of contents
35761 \begin_layout Plain Layout
35771 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35778 \begin_layout Plain Layout
35788 \begin_layout Standard
35792 \begin_layout Plain Layout
35801 In the first heading a short title was used, in the second one
35810 \begin_layout Standard
35811 To get the same formatting as for the other headings, the complete heading
35820 \begin_layout Plain Layout
35822 \begin_inset CommandInset ref
35824 reference "subsec:Bold-Formulas"
35836 \begin_layout Subsection
35837 Formulas in multi-column Text
35838 \begin_inset Index idx
35841 \begin_layout Plain Layout
35842 Formula ! in multi-column text
35850 \begin_layout Standard
35851 Formulas in multi-column text are often too wide to fit into a column and
35852 thus need to be set over the whole page width.
35853 This is done by using the \SpecialChar LaTeX
35862 \begin_layout Plain Layout
35867 is part of every \SpecialChar LaTeX
35868 standard installation.
35874 \begin_inset Index idx
35877 \begin_layout Plain Layout
35878 Packages ! multicol
35883 , that is loaded with the \SpecialChar LaTeX
35887 \begin_layout Standard
35892 usepackage{multicol}
35895 \begin_layout Standard
35896 \begin_inset Note Greyedout
35899 \begin_layout Plain Layout
35900 Note that in this case the setting
35903 \begin_inset space ~
35910 Document\SpecialChar menuseparator
35916 \begin_inset space ~
35936 \begin_layout Standard
35937 Before the multi-column text the command
35940 \begin_layout Standard
35945 begin{multicols}{column number}
35948 \begin_layout Standard
35949 is written in \SpecialChar TeX
35951 The column number is a number in the range of 2
35952 \begin_inset space \thinspace{}
35956 \begin_inset space \thinspace{}
35960 Before the formula the multi-column text is ended by inserting the command
35963 \begin_layout Standard
35971 \begin_layout Standard
35972 in \SpecialChar TeX
35976 \begin_layout Standard
35977 Due to the command some space is automatically added before the formula.
35979 \begin_inset space \thinspace{}
35982 mm vertical space is inserted before the formula.
35983 When the formula style
35989 \begin_layout Plain Layout
35991 \begin_inset CommandInset ref
35993 reference "sec:Formula-Styles"
36005 \begin_inset space \thinspace{}
36008 mm space is inserted instead.
36011 \begin_layout Standard
36012 As example a multi-column text with a displayed formula:
36015 \begin_layout Standard
36021 \begin_layout Plain Layout
36025 begin{multicols}{2}
36030 Das Spektrum wird fouriertransformiert.
36031 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36032 , Lösungsmittel) zu trennen.
36033 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36034 nun das Aussehen des Ausgangssignals.
36035 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36036 über alle Phasen integrieren muss.
36038 \begin_inset Formula $S$
36041 unser normiertes Ausgangssignal und
36042 \begin_inset Formula $P$
36045 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36049 \begin_layout Plain Layout
36059 \begin_inset VSpace -6mm
36063 \begin_inset Formula
36065 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36074 \begin_layout Plain Layout
36078 begin{multicols}{2}
36084 \begin_inset Formula $S_{0}$
36087 das Signal ohne Gradient ist und die Normierungsbedingung
36088 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36092 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36094 \begin_inset Formula $\nicefrac{\pi}{2}$
36098 \begin_inset space \thinspace{}
36101 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36102 das Signal zusätzlich abschwächt.
36103 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36105 \begin_inset Formula $T_{2}$
36111 \begin_layout Standard
36117 \begin_layout Plain Layout
36129 \begin_layout Subsection
36130 Formulas with Description of Variables
36131 \begin_inset Index idx
36134 \begin_layout Plain Layout
36135 Formula ! with description of variables
36143 \begin_layout Standard
36144 To describe variables within a formula, like in formula
36145 \begin_inset CommandInset ref
36147 reference "eq:within"
36156 \begin_inset Formula $n$
36160 \begin_inset space ~
36163 matrix is used with left aligned columns for the
36164 \begin_inset Formula $n$
36171 \begin_layout Plain Layout
36173 \begin_inset CommandInset ref
36175 reference "sec:Matrices"
36184 To set the description in a smaller size, before the matrix e.
36185 \begin_inset space \thinspace{}
36189 \begin_inset space \space{}
36202 \begin_layout Plain Layout
36204 \begin_inset CommandInset ref
36206 reference "subsec:Font-Sizes"
36218 \begin_layout Standard
36219 When the formula style
36225 \begin_layout Plain Layout
36227 \begin_inset CommandInset ref
36229 reference "sec:Formula-Styles"
36250 \begin_layout Plain Layout
36257 only works in formulas with the style
36262 \begin_inset CommandInset ref
36264 reference "subsec:Variable-Space"
36273 is inserted before and after the matrix to have the same separation of
36274 the matrix from the equation and the side margin.
36277 \begin_layout Standard
36278 When the formula style
36282 is used, the method described in
36283 \begin_inset CommandInset ref
36285 reference "subsec:Flalign-Environment"
36289 is used to indent formulas.
36291 \begin_inset CommandInset ref
36293 reference "eq:within"
36297 consists of five columns where in the first two columns contain the equation,
36298 the third the matrix and the last one an empty \SpecialChar TeX
36300 \begin_inset Formula
36302 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36303 \rho & \textrm{density}\\
36304 V & \textrm{volume}\\
36305 g & \textrm{gravitational acceleration}
36306 \end{array} & & {}\label{eq:within}
36314 \begin_layout Subsection
36315 Upright small Greek Letters
36316 \begin_inset CommandInset label
36318 name "subsec:Upright-small-Greek"
36323 \begin_inset Index idx
36326 \begin_layout Plain Layout
36327 Greek letters ! upright
36335 \begin_layout Standard
36336 Most of the math fonts only provide italic small Greek letters.
36337 But for symbols of elementary particles like pions and neutrinos, upright
36338 Greek letters are needed.
36347 \begin_layout Plain Layout
36352 is part of the \SpecialChar LaTeX
36358 \begin_inset Index idx
36361 \begin_layout Plain Layout
36366 \begin_layout Plain Layout
36386 \begin_inset Index idx
36389 \begin_layout Plain Layout
36395 that is loaded with the \SpecialChar LaTeX
36399 \begin_layout Standard
36404 usepackage{upgreek}
36407 \begin_layout Standard
36413 \begin_layout Plain Layout
36423 \begin_inset Note Note
36426 \begin_layout Plain Layout
36427 The following table will only be displayed when the \SpecialChar LaTeX
36437 They are created when the command for a small Greek letter is started with
36443 For example the command
36450 \begin_inset Formula $\uptau$
36456 \begin_layout Standard
36457 With these commands reactions of elementary particles can be typeset:
36458 \begin_inset Formula
36460 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36468 \begin_layout Standard
36469 The upright letters are more bold and wider than the italic ones.
36470 They should therefore not be used for units like
36471 \begin_inset Quotes eld
36475 \begin_inset Quotes erd
36481 \begin_layout Standard
36485 \begin_layout Plain Layout
36495 \begin_inset Note Note
36498 \begin_layout Plain Layout
36499 The following will be displayed when the \SpecialChar LaTeX
36512 \begin_layout Standard
36513 You need to install the \SpecialChar LaTeX
36518 to see the rest of this subsection in the output.
36521 \begin_layout Standard
36525 \begin_layout Plain Layout
36537 \begin_layout Subsection
36538 Text Characters in Formulas
36539 \begin_inset Index idx
36542 \begin_layout Plain Layout
36551 \begin_layout Standard
36552 In some cases you might want to insert text characters directly into formulas.
36553 When for example the centered dot · is often used in formulas like
36554 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36557 , one would have to insert the command
36567 \begin_layout Plain Layout
36569 \begin_inset CommandInset ref
36571 reference "subsec:Binary-Operators"
36580 all the time, because this character is defined in all encodings as text
36582 But the encoding can be changed by this \SpecialChar LaTeX
36586 \begin_layout Standard
36591 Declare Inputtext{183}{
36601 f\SpecialChar ligaturebreak
36605 \begin_layout Standard
36606 The character encoding (menu
36608 Document\SpecialChar menuseparator
36609 Settings\SpecialChar menuseparator
36612 ) specifies what character appears when a keyboard key is pressed.
36613 When the key for the character '·' is pressed, internally the command
36620 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36622 With the changed encoding the right command is chosen automatically, depending
36623 on if the character was inserted into a formula or not.
36626 \begin_layout Standard
36627 The encoding of several characters is saved in definition files.
36628 For example the encoding
36632 is defined in the file
36636 which is in the installation folder of \SpecialChar LaTeX
36638 Encodings should only be changed via the \SpecialChar LaTeX
36639 -preamble and not in the definition
36641 Otherwise documents could not be edited by other \SpecialChar LyX
36642 users working on other
36646 \begin_layout Standard
36647 \begin_inset VSpace medskip
36650 Besides the centered dot, in this document the degree sign ° is defined
36651 with the following \SpecialChar LaTeX
36652 -preamble line so that it can be directly inserted into
36656 \begin_layout Standard
36661 DeclareInputtext{176}{
36671 f\SpecialChar ligaturebreak
36675 \begin_layout Subsection
36677 -comments in formulas
36678 \begin_inset Index idx
36681 \begin_layout Plain Layout
36691 \begin_layout Standard
36692 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36694 code of your file with the menu
36696 Insert\SpecialChar menuseparator
36697 Note\SpecialChar menuseparator
36701 This is not possible in a formula but you can insert \SpecialChar LaTeX
36706 \begin_layout Standard
36714 \begin_layout Standard
36715 This creates a box in which you can write your comment.
36716 Due to a bug in \SpecialChar LyX
36721 \begin_layout Plain Layout
36722 \begin_inset CommandInset href
36724 name "LyX-bug #9002"
36725 target "http://www.lyx.org/trac/ticket/9002"
36734 you cannot write normal text inside the comment, even when you use mathematical
36735 text, you will see its \SpecialChar LaTeX
36736 -commands in the \SpecialChar LaTeX
36738 \begin_inset Newline newline
36741 This a formula with a \SpecialChar LaTeX
36743 \begin_inset Formula
36745 A=B%\text{This is the comment}
36753 \begin_layout Standard
36754 \begin_inset Newpage newpage
36760 \begin_layout Section
36763 \begin_inset Index idx
36766 \begin_layout Plain Layout
36775 \begin_layout Standard
36776 This section is a summary of the most important typographic rules, listed
36781 \begin_layout Plain Layout
36782 This collection was partly taken from the German semi-official dictionary
36784 \begin_inset Quotes eld
36788 \begin_inset Quotes erd
36792 \begin_inset CommandInset citation
36798 that lists some of the ISO rules.
36799 More rules are listed in
36800 \begin_inset CommandInset citation
36814 \begin_layout Itemize
36823 \begin_layout Plain Layout
36824 done with font styles, see
36825 \begin_inset CommandInset ref
36827 reference "subsec:Font-Styles"
36836 , no matter if they appear in italic text: 30
36837 \begin_inset space \thinspace{}
36841 \begin_inset Newline newline
36844 Between the value and the unit is the smallest space, see
36845 \begin_inset CommandInset ref
36847 reference "subsec:Predefined-Space"
36852 \begin_inset Newline newline
36855 This convention is automatically fulfilled when the command
36862 When it is entered to a formula, two boxes appear.
36863 In the first one the value is inserted, in the second one the unit, and
36865 \begin_inset Formula $\unit[30]{km/h}$
36869 \begin_inset space \thinspace{}
36879 is not a real \SpecialChar LaTeX
36880 command but the command
36886 , therefore you cannot use it in \SpecialChar TeX
36890 \begin_layout Itemize
36891 Percent and perthousand signs are set like physical units:
36892 \begin_inset Newline newline
36896 \begin_inset space \thinspace{}
36902 \begin_layout Itemize
36903 The degree sign follows directly on the value: 15°, but not when it is used
36905 \begin_inset space \thinspace{}
36911 \begin_layout Itemize
36912 In numbers with more than four digits the smallest space is inserted before
36913 every third digit to group them:
36923 \begin_inset space \thinspace{}
36927 \begin_inset space \thinspace{}
36933 \begin_layout Itemize
36934 For dimensions like 120×90×40
36935 \begin_inset space \thinspace{}
36938 cm the multiplication sign
36939 \begin_inset Quotes eld
36943 \begin_inset Quotes erd
36947 It is available either via the command
36955 Insert\SpecialChar menuseparator
36956 Special Character\SpecialChar menuseparator
36962 \begin_layout Itemize
36963 Functions with names consisting of several letters are set upright to avoid
36965 \begin_inset CommandInset ref
36967 reference "subsec:Predefined-Functions"
36974 \begin_layout Itemize
36975 Indices consisting of several letters, are set upright:
36976 \begin_inset Formula $E_{\mathrm{kin}}$
36980 \begin_inset Newline newline
36983 Components of matrices are set italic:
36984 \begin_inset Formula $\hat{H}_{kl}$
36990 \begin_layout Itemize
36991 The differentiation/integration operator 'd', the Euler's number 'e' and
36992 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36996 \begin_layout Itemize
36997 The character that denotes a
37001 transformation is inserted either by the command
37006 \begin_inset space \textvisiblespace{}
37013 Insert\SpecialChar menuseparator
37014 Special Character\SpecialChar menuseparator
37015 Symbols\SpecialChar menuseparator
37017 \begin_inset space ~
37023 \begin_inset Formula $\mathscr{F}$
37029 \begin_layout Standard
37030 \begin_inset Newpage newpage
37036 \begin_layout Section
37038 \begin_inset Index idx
37041 \begin_layout Plain Layout
37050 \begin_layout Standard
37051 Some characters and symbols can be created with several commands.
37052 Here is a list of the synonym commands:
37055 \begin_layout Standard
37056 \begin_inset VSpace bigskip
37060 \begin_inset space \hfill{}
37064 \begin_inset Tabular
37065 <lyxtabular version="3" rows="12" columns="2">
37066 <features booktabs="true" tabularvalignment="middle">
37067 <column alignment="center" valignment="top" width="0pt">
37068 <column alignment="center" valignment="top" width="0pt">
37070 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37073 \begin_layout Plain Layout
37079 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37082 \begin_layout Plain Layout
37090 <cell alignment="center" valignment="top" usebox="none">
37093 \begin_layout Plain Layout
37101 <cell alignment="center" valignment="top" usebox="none">
37104 \begin_layout Plain Layout
37112 <cell alignment="center" valignment="top" usebox="none">
37115 \begin_layout Plain Layout
37123 <cell alignment="center" valignment="top" usebox="none">
37126 \begin_layout Plain Layout
37136 <cell alignment="center" valignment="top" usebox="none">
37139 \begin_layout Plain Layout
37147 <cell alignment="center" valignment="top" usebox="none">
37150 \begin_layout Plain Layout
37160 <cell alignment="center" valignment="top" usebox="none">
37163 \begin_layout Plain Layout
37171 <cell alignment="center" valignment="top" usebox="none">
37174 \begin_layout Plain Layout
37182 <cell alignment="center" valignment="top" usebox="none">
37185 \begin_layout Plain Layout
37193 <cell alignment="center" valignment="top" usebox="none">
37196 \begin_layout Plain Layout
37204 <cell alignment="center" valignment="top" usebox="none">
37207 \begin_layout Plain Layout
37215 <cell alignment="center" valignment="top" usebox="none">
37218 \begin_layout Plain Layout
37228 <cell alignment="center" valignment="top" usebox="none">
37231 \begin_layout Plain Layout
37239 <cell alignment="center" valignment="top" usebox="none">
37242 \begin_layout Plain Layout
37252 <cell alignment="center" valignment="top" usebox="none">
37255 \begin_layout Plain Layout
37263 <cell alignment="center" valignment="top" usebox="none">
37266 \begin_layout Plain Layout
37276 <cell alignment="center" valignment="top" usebox="none">
37279 \begin_layout Plain Layout
37287 <cell alignment="center" valignment="top" usebox="none">
37290 \begin_layout Plain Layout
37300 <cell alignment="center" valignment="top" usebox="none">
37303 \begin_layout Plain Layout
37311 <cell alignment="center" valignment="top" usebox="none">
37314 \begin_layout Plain Layout
37322 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37325 \begin_layout Plain Layout
37333 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37336 \begin_layout Plain Layout
37348 \begin_inset space \hfill{}
37352 \begin_inset Tabular
37353 <lyxtabular version="3" rows="12" columns="2">
37354 <features booktabs="true" tabularvalignment="middle">
37355 <column alignment="center" valignment="top" width="0pt">
37356 <column alignment="center" valignment="top" width="0pt">
37358 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37361 \begin_layout Plain Layout
37367 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37370 \begin_layout Plain Layout
37378 <cell alignment="center" valignment="top" usebox="none">
37381 \begin_layout Plain Layout
37389 <cell alignment="center" valignment="top" usebox="none">
37392 \begin_layout Plain Layout
37404 <cell alignment="center" valignment="top" usebox="none">
37407 \begin_layout Plain Layout
37415 <cell alignment="center" valignment="top" usebox="none">
37418 \begin_layout Plain Layout
37428 <cell alignment="center" valignment="top" usebox="none">
37431 \begin_layout Plain Layout
37439 <cell alignment="center" valignment="top" usebox="none">
37442 \begin_layout Plain Layout
37452 <cell alignment="center" valignment="top" usebox="none">
37455 \begin_layout Plain Layout
37463 <cell alignment="center" valignment="top" usebox="none">
37466 \begin_layout Plain Layout
37474 <cell alignment="center" valignment="top" usebox="none">
37477 \begin_layout Plain Layout
37485 <cell alignment="center" valignment="top" usebox="none">
37488 \begin_layout Plain Layout
37496 <cell alignment="center" valignment="top" usebox="none">
37499 \begin_layout Plain Layout
37507 <cell alignment="center" valignment="top" usebox="none">
37510 \begin_layout Plain Layout
37520 <cell alignment="center" valignment="top" usebox="none">
37523 \begin_layout Plain Layout
37531 <cell alignment="center" valignment="top" usebox="none">
37534 \begin_layout Plain Layout
37544 <cell alignment="center" valignment="top" usebox="none">
37547 \begin_layout Plain Layout
37555 <cell alignment="center" valignment="top" usebox="none">
37558 \begin_layout Plain Layout
37568 <cell alignment="center" valignment="top" usebox="none">
37571 \begin_layout Plain Layout
37579 <cell alignment="center" valignment="top" usebox="none">
37582 \begin_layout Plain Layout
37592 <cell alignment="center" valignment="top" usebox="none">
37595 \begin_layout Plain Layout
37603 <cell alignment="center" valignment="top" usebox="none">
37606 \begin_layout Plain Layout
37616 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37619 \begin_layout Plain Layout
37627 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37630 \begin_layout Plain Layout
37644 \begin_inset space \hfill{}
37650 \begin_layout Standard
37651 \begin_inset Newpage newpage
37657 \begin_layout Bibliography
37658 \begin_inset CommandInset bibitem
37659 LatexCommand bibitem
37671 The \SpecialChar LaTeX
37675 Addison Wesley, 2004
37678 \begin_layout Bibliography
37679 \begin_inset CommandInset bibitem
37680 LatexCommand bibitem
37686 \begin_inset CommandInset href
37689 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37693 of \SpecialChar LaTeX
37697 \begin_layout Bibliography
37698 \begin_inset CommandInset bibitem
37699 LatexCommand bibitem
37705 \begin_inset CommandInset href
37708 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37716 \begin_layout Plain Layout
37725 -\SpecialChar LaTeX
37729 \begin_layout Bibliography
37730 \begin_inset CommandInset bibitem
37731 LatexCommand bibitem
37737 \begin_inset CommandInset href
37740 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37744 of all symbols available with \SpecialChar LaTeX
37748 \begin_layout Bibliography
37749 \begin_inset CommandInset bibitem
37750 LatexCommand bibitem
37756 \begin_inset CommandInset href
37758 name "Documentation"
37759 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37763 of the \SpecialChar LaTeX
37769 \begin_inset Index idx
37772 \begin_layout Plain Layout
37781 \begin_layout Bibliography
37782 \begin_inset CommandInset bibitem
37783 LatexCommand bibitem
37789 \begin_inset CommandInset href
37791 name "Documentation"
37792 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37796 of the \SpecialChar LaTeX
37802 \begin_inset Index idx
37805 \begin_layout Plain Layout
37806 Packages ! hyperref
37814 \begin_layout Bibliography
37815 \begin_inset CommandInset bibitem
37816 LatexCommand bibitem
37822 \begin_inset CommandInset href
37824 name "Documentation"
37825 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37829 of the \SpecialChar LaTeX
37835 \begin_inset Index idx
37838 \begin_layout Plain Layout
37847 \begin_layout Bibliography
37848 \begin_inset CommandInset bibitem
37849 LatexCommand bibitem
37860 Auflage, Duden 2001
37863 \begin_layout Bibliography
37864 \begin_inset CommandInset bibitem
37865 LatexCommand bibitem
37871 \begin_inset CommandInset href
37874 target "http://physics.nist.gov/Document/checklist.pdf"
37878 for reviewing manuscripts
37881 \begin_layout Standard
37882 \begin_inset CommandInset index_print
37883 LatexCommand printindex