1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
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}}{}
37 \@ifpackageloaded{babel}{
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41 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
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
153 \font_typewriter default
155 \font_default_family default
156 \use_non_tex_fonts false
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 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
10607 \begin_inset Note Note
10610 \begin_layout Plain Layout
10617 is only used as spacer.
10629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10632 \begin_layout Plain Layout
10636 \begin_inset space \textvisiblespace{}
10644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10647 \begin_layout Plain Layout
10648 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10658 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10661 \begin_layout Plain Layout
10665 \begin_inset space \textvisiblespace{}
10673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10676 \begin_layout Plain Layout
10677 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10690 \begin_layout Plain Layout
10694 \begin_inset space \textvisiblespace{}
10702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10705 \begin_layout Plain Layout
10706 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10716 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10719 \begin_layout Plain Layout
10722 underleftrightarrow
10723 \begin_inset space \textvisiblespace{}
10731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10734 \begin_layout Plain Layout
10735 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10749 \begin_inset space \hfill{}
10753 \begin_inset Tabular
10754 <lyxtabular version="3" rows="5" columns="2">
10755 <features tabularvalignment="middle">
10756 <column alignment="center" valignment="top" width="0pt">
10757 <column alignment="center" valignment="top" width="0pt">
10759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10762 \begin_layout Plain Layout
10768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10771 \begin_layout Plain Layout
10779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10782 \begin_layout Plain Layout
10786 \begin_inset space \textvisiblespace{}
10794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10797 \begin_layout Plain Layout
10798 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10811 \begin_layout Plain Layout
10815 \begin_inset space \textvisiblespace{}
10823 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10826 \begin_layout Plain Layout
10827 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10840 \begin_layout Plain Layout
10844 \begin_inset space \textvisiblespace{}
10852 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10855 \begin_layout Plain Layout
10856 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10869 \begin_layout Plain Layout
10873 \begin_inset space \textvisiblespace{}
10881 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10884 \begin_layout Plain Layout
10885 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10899 \begin_inset space \hfill{}
10905 \begin_layout Standard
10906 \begin_inset VSpace medskip
10909 With these commands as many characters as you like can be accented.
10922 will only be set in the output with a length of three characters, as shown
10923 in the following example:
10924 \begin_inset Formula
10926 \widetilde{A+B=C-D}
10934 \begin_layout Standard
10942 \begin_inset Index idx
10945 \begin_layout Plain Layout
10960 \begin_inset Index idx
10963 \begin_layout Plain Layout
10971 described in the previous subsection it is also possible to accent several
10978 \begin_inset space \textvisiblespace{}
10982 \begin_inset Formula $\downarrow$
10988 \begin_inset Formula
10990 \underset{***}{A=B}
10998 \begin_layout Section
11000 \begin_inset CommandInset label
11002 name "subsec:Space"
11007 \begin_inset Index idx
11010 \begin_layout Plain Layout
11019 \begin_layout Subsection
11021 \begin_inset CommandInset label
11023 name "subsec:Predefined-Space"
11028 \begin_inset Index idx
11031 \begin_layout Plain Layout
11032 Space ! horizontal ! predefined
11040 \begin_layout Standard
11041 Sometimes it is necessary to insert horizontal space into a formula.
11042 This is done by inserting a protected space (shortcut
11045 arg "command-alternatives space-insert protected ; math-space"
11050 \begin_inset Quotes eld
11056 \begin_inset space \textvisiblespace{}
11062 \begin_inset Quotes erd
11065 appears and by pressing
11069 several times one can select one of eight different space sizes.
11070 The spaces can also be inserted using the math toolbar button
11073 arg "math-insert \\space"
11076 or special commands.
11077 Independent from the inserted command, one can select the size again by
11083 \begin_inset Separator parbreak
11089 \begin_layout Standard
11092 \begin_inset Tabular
11093 <lyxtabular version="3" rows="6" columns="3">
11094 <features tabularvalignment="middle">
11095 <column alignment="center" valignment="top">
11096 <column alignment="center" valignment="top" width="15col%">
11097 <column alignment="center" valignment="top">
11099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11102 \begin_layout Plain Layout
11108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11111 \begin_layout Plain Layout
11121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11124 \begin_layout Plain Layout
11132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11135 \begin_layout Plain Layout
11143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11146 \begin_layout Plain Layout
11152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11155 \begin_layout Plain Layout
11156 \begin_inset Formula $A\,B$
11166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11169 \begin_layout Plain Layout
11177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11180 \begin_layout Plain Layout
11186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11189 \begin_layout Plain Layout
11190 \begin_inset Formula $A\:B$
11200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11203 \begin_layout Plain Layout
11211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11214 \begin_layout Plain Layout
11220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11223 \begin_layout Plain Layout
11224 \begin_inset Formula $A\;B$
11234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11237 \begin_layout Plain Layout
11245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11248 \begin_layout Plain Layout
11254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11257 \begin_layout Plain Layout
11258 \begin_inset Formula $A\quad B$
11268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11271 \begin_layout Plain Layout
11279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11282 \begin_layout Plain Layout
11288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11291 \begin_layout Plain Layout
11292 \begin_inset Formula $A\qquad B$
11306 \begin_inset space \hfill{}
11310 \begin_inset Tabular
11311 <lyxtabular version="3" rows="6" columns="3">
11312 <features tabularvalignment="middle">
11313 <column alignment="center" valignment="top">
11314 <column alignment="center" valignment="top" width="15col%">
11315 <column alignment="center" valignment="top">
11317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11320 \begin_layout Plain Layout
11326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11329 \begin_layout Plain Layout
11339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11342 \begin_layout Plain Layout
11350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11353 \begin_layout Plain Layout
11361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11364 \begin_layout Plain Layout
11370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11373 \begin_layout Plain Layout
11374 \begin_inset Formula $A\hfill B$
11384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11387 \begin_layout Plain Layout
11395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11398 \begin_layout Plain Layout
11404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11407 \begin_layout Plain Layout
11408 \begin_inset Formula $A\hspace*{1em}B$
11418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11421 \begin_layout Plain Layout
11429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11432 \begin_layout Plain Layout
11438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11441 \begin_layout Plain Layout
11442 \begin_inset Formula $A\hspace{1em}B$
11452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11455 \begin_layout Plain Layout
11459 \begin_inset space \textvisiblespace{}
11467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11470 \begin_layout Plain Layout
11476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11479 \begin_layout Plain Layout
11480 \begin_inset Formula $A\ B$
11490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11493 \begin_layout Plain Layout
11501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11504 \begin_layout Plain Layout
11510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11513 \begin_layout Plain Layout
11514 \begin_inset Formula $A\!B$
11530 \begin_layout Standard
11532 \begin_inset space ~
11536 \begin_inset space \thinspace{}
11540 \begin_inset space \thinspace{}
11543 7 are variable spaces which are explained in
11544 \begin_inset CommandInset ref
11546 reference "subsec:Variable-Space"
11552 \begin_inset space ~
11555 9 seems to produce no space.
11556 It is displayed red in \SpecialChar LyX
11557 contrary to the other sizes, because it is a negative
11559 There are two more negative spaces:
11560 \begin_inset Separator parbreak
11566 \begin_layout Standard
11568 \begin_inset Tabular
11569 <lyxtabular version="3" rows="3" columns="3">
11570 <features tabularvalignment="middle">
11571 <column alignment="center" valignment="middle" width="6.8cm">
11572 <column alignment="center" valignment="top" width="0pt">
11573 <column alignment="center" valignment="top" width="0pt">
11575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11578 \begin_layout Plain Layout
11584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11587 \begin_layout Plain Layout
11595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11598 \begin_layout Plain Layout
11608 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11611 \begin_layout Plain Layout
11616 keystrokes after inserting the protected space
11621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11624 \begin_layout Plain Layout
11630 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11633 \begin_layout Plain Layout
11641 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11644 \begin_layout Plain Layout
11650 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11653 \begin_layout Plain Layout
11654 \begin_inset Formula $A\negmedspace B$
11662 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11665 \begin_layout Plain Layout
11666 \begin_inset Formula $A\negthickspace B$
11682 \begin_layout Standard
11683 Negative spaces can lead to characters overlapping each other.
11684 Thus they can be used to enforce ligatures, which are e.
11685 \begin_inset space \thinspace{}
11689 \begin_inset space \space{}
11692 useful for summation operators:
11693 \begin_inset Separator parbreak
11699 \begin_layout Standard
11701 \begin_inset Tabular
11702 <lyxtabular version="3" rows="3" columns="2">
11703 <features tabularvalignment="middle">
11704 <column alignment="center" valignment="top">
11705 <column alignment="center" valignment="top">
11707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11710 \begin_layout Plain Layout
11716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11719 \begin_layout Plain Layout
11721 \begin_inset Note Note
11724 \begin_layout Plain Layout
11731 is only used as spacer.
11743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11746 \begin_layout Plain Layout
11752 \begin_inset space \textvisiblespace{}
11760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11763 \begin_layout Plain Layout
11764 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11777 \begin_layout Plain Layout
11785 \begin_inset space \textvisiblespace{}
11793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11796 \begin_layout Plain Layout
11797 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11813 \begin_layout Standard
11815 \begin_inset VSpace medskip
11821 \begin_layout Standard
11823 Relations like for example equal signs, are always surrounded by space.
11824 To suppress this, the equal sign is placed into a \SpecialChar TeX
11826 The following example demonstrates this:
11827 \begin_inset Separator parbreak
11833 \begin_layout Standard
11835 \begin_inset Tabular
11836 <lyxtabular version="3" rows="2" columns="2">
11837 <features tabularvalignment="middle">
11838 <column alignment="center" valignment="top" width="0pt">
11839 <column alignment="center" valignment="top" width="0pt">
11841 <cell alignment="center" valignment="top" usebox="none">
11844 \begin_layout Plain Layout
11850 <cell alignment="center" valignment="top" usebox="none">
11853 \begin_layout Plain Layout
11854 \begin_inset Formula $A=B$
11864 <cell alignment="center" valignment="top" usebox="none">
11867 \begin_layout Plain Layout
11868 \begin_inset Note Note
11871 \begin_layout Plain Layout
11878 is only used as spacer.
11884 \begin_inset Formula $\raisebox{5mm}{}$
11887 equation without space
11892 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11895 \begin_layout Plain Layout
11896 \begin_inset Formula $A{=}B$
11912 \begin_layout Standard
11914 The command for the last formula is:
11919 \begin_inset Formula $\to$
11925 \begin_layout Standard
11926 \begin_inset VSpace bigskip
11932 \begin_layout Standard
11933 Spaces are needed for physical units, because the space between the value
11934 and the unit is the smallest one and not a normal space.
11935 For units in text, the smallest space is inserted via the menu
11937 Insert\SpecialChar menuseparator
11938 Formatting\SpecialChar menuseparator
11940 \begin_inset space ~
11948 arg "space-insert thin"
11954 \begin_layout Standard
11955 An example to visualize the difference:
11958 \begin_layout Standard
11959 \begin_inset Tabular
11960 <lyxtabular version="3" rows="2" columns="2">
11961 <features tabularvalignment="middle">
11962 <column alignment="left" valignment="top">
11963 <column alignment="left" valignment="top">
11965 <cell alignment="center" valignment="top" usebox="none">
11968 \begin_layout Plain Layout
11970 \begin_inset Formula $\cdot$
11978 <cell alignment="center" valignment="top" usebox="none">
11981 \begin_layout Plain Layout
11982 space between value and unit
11989 <cell alignment="center" valignment="top" usebox="none">
11992 \begin_layout Plain Layout
11994 \begin_inset space \thinspace{}
11998 \begin_inset Formula $\cdot$
12006 <cell alignment="center" valignment="top" usebox="none">
12009 \begin_layout Plain Layout
12010 smallest space between value and unit
12023 \begin_layout Subsection
12028 \begin_layout Plain Layout
12041 \begin_layout Plain Layout
12042 for vertical space in formulas see
12043 \begin_inset CommandInset ref
12045 reference "subsec:Line-Separation"
12058 \begin_layout Plain Layout
12066 \begin_inset Note Note
12069 \begin_layout Plain Layout
12072 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12075 \begin_layout Plain Layout
12078 texorpdfstring is in section
12079 \begin_inset CommandInset ref
12081 reference "subsec:Formulas-in-Section"
12091 \begin_inset CommandInset label
12093 name "subsec:Variable-Space"
12098 \begin_inset Index idx
12101 \begin_layout Plain Layout
12102 Space ! horizontal ! variable
12110 \begin_layout Standard
12111 Space with a defined length can be inserted with the command
12118 \begin_inset Index idx
12121 \begin_layout Plain Layout
12131 \begin_inset Quotes eld
12137 \begin_inset space \textvisiblespace{}
12143 \begin_inset Quotes erd
12147 The length can be specified by left-clicking on the
12148 \begin_inset Quotes eld
12154 \begin_inset space \textvisiblespace{}
12160 \begin_inset Quotes erd
12164 The length may also be negative.
12165 When a space would be the first character in a line it would be omitted.
12166 To force its output use the command
12178 or left-click on the
12179 \begin_inset Quotes eld
12185 \begin_inset space \textvisiblespace{}
12191 \begin_inset Quotes erd
12194 and check the option
12199 \begin_inset Newline newline
12202 To insert as much space as is available, the command
12209 \begin_inset Index idx
12212 \begin_layout Plain Layout
12223 \begin_layout Standard
12224 \begin_inset VSpace -1mm
12230 \begin_layout Standard
12232 \begin_inset Tabular
12233 <lyxtabular version="3" rows="4" columns="2">
12234 <features tabularvalignment="middle">
12235 <column alignment="center" valignment="top">
12236 <column alignment="center" valignment="top">
12238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12241 \begin_layout Plain Layout
12249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12252 \begin_layout Plain Layout
12260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12263 \begin_layout Plain Layout
12267 \begin_inset space \textvisiblespace{}
12273 \begin_inset space \thinspace{}
12281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12284 \begin_layout Plain Layout
12285 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12298 \begin_layout Plain Layout
12302 \begin_inset space \textvisiblespace{}
12308 \begin_inset space \thinspace{}
12316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12319 \begin_layout Plain Layout
12320 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12333 \begin_layout Plain Layout
12337 \begin_inset space \textvisiblespace{}
12345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12348 \begin_layout Plain Layout
12349 \begin_inset Formula $A=A\hfill B=B$
12365 \begin_layout Standard
12366 In the last example the available space is given by the longest column entry
12368 In an inline formula the space depends on the length of the line in which
12376 Thus, when the line uses the full width, no space will be created.
12383 only has an effect on displayed formulas when the formula style
12388 (Formula styles are explained in
12389 \begin_inset CommandInset ref
12391 reference "sec:Formula-Styles"
12398 \begin_layout Standard
12405 , there are the commands
12417 that fill the space with a pattern, see
12418 \begin_inset CommandInset ref
12420 reference "subsec:Ellipses"
12427 \begin_layout Standard
12428 For text, variable space can be inserted via the menu
12430 Insert\SpecialChar menuseparator
12431 Formatting\SpecialChar menuseparator
12433 \begin_inset space ~
12441 \begin_layout Standard
12442 This is a line with
12443 \begin_inset space \hspace{}
12448 \begin_inset space \thinspace{}
12454 \begin_layout Standard
12455 This is a line with
12456 \begin_inset space \hfill{}
12462 \begin_layout Subsection
12463 Space besides inline Formulas
12464 \begin_inset Index idx
12467 \begin_layout Plain Layout
12468 Space ! besides inline formulas
12476 \begin_layout Standard
12477 The space that surrounds inline formulas can be adjusted with the length
12485 \begin_inset Index idx
12488 \begin_layout Plain Layout
12497 The value of a length is set with the command
12504 \begin_inset Index idx
12507 \begin_layout Plain Layout
12515 which has the following scheme:
12518 \begin_layout Standard
12523 setlength{length name}{value}
12526 \begin_layout Standard
12534 \begin_inset space \thinspace{}
12540 \begin_layout Standard
12550 \begin_layout Standard
12551 is inserted in \SpecialChar TeX
12554 \begin_inset space \thinspace{}
12557 mm space will now be set around all inline formulas:
12561 \begin_layout Plain Layout
12575 \begin_layout Standard
12576 This is a line with an inline formula
12577 \begin_inset Formula $A=B$
12581 \begin_inset space \thinspace{}
12584 mm surrounding space.
12588 \begin_layout Plain Layout
12602 \begin_layout Standard
12603 To return to the predefined value,
12609 is set to the value 0
12610 \begin_inset space \thinspace{}
12616 \begin_layout Section
12618 \begin_inset Index idx
12621 \begin_layout Plain Layout
12628 \begin_inset Index idx
12631 \begin_layout Plain Layout
12636 \begin_layout Plain Layout
12647 \begin_layout Plain Layout
12662 \begin_layout Standard
12663 Boxes for text are described in chapter
12670 \begin_inset space ~
12678 \begin_layout Subsection
12680 \begin_inset CommandInset label
12682 name "subsec:Boxes-with-Frame"
12687 \begin_inset Index idx
12690 \begin_layout Plain Layout
12699 \begin_layout Standard
12700 It is possible to frame a formula or part of one with the commands
12707 \begin_inset Index idx
12710 \begin_layout Plain Layout
12725 \begin_inset Index idx
12728 \begin_layout Plain Layout
12739 \begin_layout Standard
12740 When one of these commands is inserted in a formula, a blue box appears
12741 within a frame to enter formula parts.
12748 an additional formula has to be created by
12752 within this box, because the box content will otherwise be treated as mathemati
12760 is used, a new formula is automatically created inside the frame.
12763 \begin_layout Standard
12770 is not suitable to frame displayed formulas because the formula will always
12771 be set in the size of the text.
12778 is in contrary not suitable to frame inline formulas, because the formula
12779 will always be set in the size of a displayed formula.
12782 \begin_layout Standard
12796 \begin_inset Index idx
12799 \begin_layout Plain Layout
12807 where additionally the frame width and the alignment can be specified.
12814 is used in the following scheme:
12817 \begin_layout Standard
12822 framebox[frame width][position]{box content}
12825 \begin_layout Standard
12826 The position can either be
12843 right aligns the formula in the box.
12844 When no position is given, the formula will be centered.
12845 \begin_inset Newline newline
12848 If no width is given, also no position can be given.
12849 In this case the frame width is adjusted to the box content like for
12858 \begin_layout Standard
12865 is inserted, a box appears containing three blue boxes.
12866 The first two boxes are surrounded by brackets and denote the two optional
12868 The third box is for formula parts like for
12875 \begin_inset Separator parbreak
12881 \begin_layout Standard
12883 \begin_inset Tabular
12884 <lyxtabular version="3" rows="5" columns="2">
12885 <features tabularvalignment="middle">
12886 <column alignment="center" valignment="top">
12887 <column alignment="center" valignment="top">
12889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12892 \begin_layout Plain Layout
12898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12901 \begin_layout Plain Layout
12903 \begin_inset Note Note
12906 \begin_layout Plain Layout
12913 is only used as spacer.
12925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12928 \begin_layout Plain Layout
12932 \begin_inset space \textvisiblespace{}
12942 \begin_inset space \textvisiblespace{}
12950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12953 \begin_layout Plain Layout
12954 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12967 \begin_layout Plain Layout
12971 \begin_inset space \textvisiblespace{}
12977 \begin_inset space \textvisiblespace{}
12985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12988 \begin_layout Plain Layout
12989 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13002 \begin_layout Plain Layout
13006 \begin_inset space \textvisiblespace{}
13014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13017 \begin_layout Plain Layout
13018 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13031 \begin_layout Plain Layout
13035 \begin_inset space \textvisiblespace{}
13039 \begin_inset Formula $\to$
13043 \begin_inset Formula $\to$
13053 \begin_inset space \textvisiblespace{}
13057 \begin_inset Formula $\downarrow$
13065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13068 \begin_layout Plain Layout
13069 \begin_inset Formula $\raisebox{6mm}{}$
13073 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13077 \begin_inset Formula $\raisebox{-4mm}{}$
13093 \begin_layout Standard
13094 The frame thickness can also be adjusted.
13095 To do this the following commands have to be inserted in \SpecialChar TeX
13100 \begin_layout Standard
13110 \begin_inset Quotes eld
13114 \begin_inset Quotes erd
13128 \begin_inset Quotes eld
13132 \begin_inset Quotes erd
13138 \begin_layout Standard
13139 \begin_inset Quotes eld
13143 \begin_inset Quotes erd
13146 specifies the minimal distance between the frame and the first character
13148 An example for this is the following framed formula:
13152 \begin_layout Plain Layout
13164 \begin_inset Formula
13171 Before this formula the commands
13174 \begin_layout Standard
13196 \begin_layout Standard
13197 were inserted in \SpecialChar TeX
13199 The given values are used for all following boxes.
13202 \begin_layout Standard
13203 To return to the standard frame size, the command
13206 \begin_layout Standard
13231 \begin_layout Plain Layout
13245 \begin_layout Standard
13246 is inserted in \SpecialChar TeX
13247 mode before the next formula.
13250 \begin_layout Subsection
13251 Boxes without Frame
13252 \begin_inset CommandInset label
13254 name "subsec:Boxes-without-Frame"
13259 \begin_inset Index idx
13262 \begin_layout Plain Layout
13263 Boxes ! without frame
13271 \begin_layout Standard
13272 For boxes without a frame there are the following box commands:
13279 \begin_inset Index idx
13282 \begin_layout Plain Layout
13297 \begin_inset Index idx
13300 \begin_layout Plain Layout
13315 \begin_inset Index idx
13318 \begin_layout Plain Layout
13329 \begin_layout Standard
13336 a box can be super- or subscripted.
13337 But in contrary to normal super- and subscripting, the characters in the
13338 box keep their font size.
13345 is used in the following scheme:
13348 \begin_layout Standard
13353 raisebox{height}{box content}
13356 \begin_layout Standard
13357 When the box should contain a formula, an extra formula is needed like for
13368 \begin_inset Note Greyedout
13371 \begin_layout Plain Layout
13382 this extra formula is created by pressing
13386 twice instead of once because \SpecialChar LyX
13387 doesn't yet support
13401 \begin_inset Separator parbreak
13407 \begin_layout Standard
13409 \begin_inset Tabular
13410 <lyxtabular version="3" rows="4" columns="2">
13411 <features tabularvalignment="middle">
13412 <column alignment="center" valignment="top">
13413 <column alignment="center" valignment="top">
13415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13418 \begin_layout Plain Layout
13424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13427 \begin_layout Plain Layout
13435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13438 \begin_layout Plain Layout
13442 \begin_inset Formula $\to$
13448 \begin_inset Formula $\to$
13456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13459 \begin_layout Plain Layout
13460 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13473 \begin_layout Plain Layout
13477 \begin_inset Formula $\to$
13483 \begin_inset Formula $\to$
13491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13494 \begin_layout Plain Layout
13495 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13508 \begin_layout Plain Layout
13512 \begin_inset Formula $\to$
13528 \begin_inset space \textvisiblespace{}
13536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13539 \begin_layout Plain Layout
13540 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13556 \begin_layout Standard
13581 , with the difference that there is no frame.
13584 \begin_layout Subsection
13586 \begin_inset CommandInset label
13588 name "subsec:Colored-Boxes"
13593 \begin_inset Index idx
13596 \begin_layout Plain Layout
13605 \begin_layout Standard
13606 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13615 \begin_layout Plain Layout
13616 The \SpecialChar LaTeX
13621 is part of every \SpecialChar LaTeX
13622 standard installation.
13628 \begin_inset Index idx
13631 \begin_layout Plain Layout
13637 has to be loaded in the \SpecialChar LaTeX
13638 -preamble with the line
13642 \begin_layout Plain Layout
13643 When text is colored somewhere in the document with a predefined color,
13645 loads the \SpecialChar LaTeX
13651 Thus it is possible that the package is loaded twice, but this does not
13658 \begin_inset Note Note
13661 \begin_layout Plain Layout
13662 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13671 \begin_layout Standard
13679 \begin_layout Standard
13680 \begin_inset VSpace medskip
13683 To color boxes, the command
13690 \begin_inset Index idx
13693 \begin_layout Plain Layout
13701 is used in the following scheme:
13704 \begin_layout Standard
13709 colorbox{color}{box content}
13712 \begin_layout Standard
13713 The box content can also be a box and a
13719 can also be part of another box (see the 2nd and 3rd example).
13720 When the box should contain a formula, an extra formula has to be created,
13721 the same way as for
13731 \begin_layout Plain Layout
13732 This also applies for the command
13746 \begin_layout Standard
13747 One of the following predefined colors can be chosen:
13750 \begin_layout Standard
13784 \begin_inset Separator parbreak
13790 \begin_layout Standard
13792 \begin_inset Tabular
13793 <lyxtabular version="3" rows="4" columns="2">
13794 <features tabularvalignment="middle">
13795 <column alignment="center" valignment="top">
13796 <column alignment="center" valignment="top">
13798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13801 \begin_layout Plain Layout
13807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13810 \begin_layout Plain Layout
13812 \begin_inset Note Note
13815 \begin_layout Plain Layout
13822 is only used as spacer.
13834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13837 \begin_layout Plain Layout
13841 \begin_inset Formula $\to$
13851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13854 \begin_layout Plain Layout
13855 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13868 \begin_layout Plain Layout
13872 \begin_inset Formula $\to$
13880 \begin_inset space \textvisiblespace{}
13888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13891 \begin_layout Plain Layout
13892 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13905 \begin_layout Plain Layout
13909 \begin_inset space \textvisiblespace{}
13915 \begin_inset Formula $\to$
13931 \begin_inset space \textvisiblespace{}
13939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13942 \begin_layout Plain Layout
13943 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13959 \begin_layout Standard
13966 only colors the box but not the characters in the box.
13967 To color all characters, the whole formula is highlighted and the desired
13968 color is chosen in the
13971 \begin_inset space ~
13977 The dialog can be called with the toolbar button
13980 arg "dialog-show character"
13985 Edit\SpecialChar menuseparator
13987 \begin_inset space ~
13990 Style\SpecialChar menuseparator
13994 The formula number then has the same color as the formula.
13995 When the formula number should get another color than the formula characters,
13996 the color must be changed within the formula.
13999 \begin_layout Standard
14003 \begin_layout Standard
14006 \begin_inset Formula
14008 \int A=B\label{eq:red}
14016 \begin_inset Formula
14018 \textcolor{red}{\int A=B}\label{eq:redgreen}
14026 \begin_layout Standard
14028 \begin_inset CommandInset ref
14034 is completely colored red.
14035 \begin_inset Newline newline
14039 \begin_inset CommandInset ref
14041 reference "eq:redgreen"
14045 was first completely colored green to set the color for the formula number.
14046 Subsequently the formula characters were colored red.
14049 \begin_layout Standard
14050 \begin_inset VSpace bigskip
14053 To color the frame different than the rest of the box, the command
14060 \begin_inset Index idx
14063 \begin_layout Plain Layout
14071 is used in the following scheme:
14074 \begin_layout Standard
14079 fcolorbox{frame color}{color}{box content}
14082 \begin_layout Standard
14089 is an extension of the command
14096 The frame width is set, like for
14119 \begin_layout Plain Layout
14131 \begin_inset Formula
14133 \fcolorbox{cyan}{magenta}{A=B}
14142 \begin_layout Plain Layout
14156 \begin_layout Standard
14157 This formula was created with the command
14158 \begin_inset Newline newline
14166 \begin_inset Formula $\to$
14172 \begin_inset Formula $\to$
14182 \begin_layout Standard
14183 \begin_inset VSpace bigskip
14186 To use other colors than the predefined ones, they have to be defined first.
14189 \begin_layout Standard
14190 One can for example define the color
14191 \begin_inset Quotes eld
14199 \begin_inset Quotes erd
14202 with the \SpecialChar LaTeX
14206 \begin_layout Standard
14211 definecolor{darkgreen}{cmyk}{0.5,
14226 \begin_inset Index idx
14229 \begin_layout Plain Layout
14240 \begin_layout Standard
14245 is the color space that denotes the colors
14262 The four comma separated numbers are the portion factor for the corresponding
14263 colors of the color space.
14264 The factors can be in the range of 0
14265 \begin_inset space \thinspace{}
14269 \begin_inset space \thinspace{}
14277 also the color space
14281 can be used for definitions.
14298 , so that there are in this case three portion factors for the corresponding
14300 Furthermore there is the color space
14304 with one portion factor for the gray value.
14307 \begin_layout Standard
14308 As example a framed box with the new defined color
14312 where the characters have been colored
14317 \begin_inset Formula
14319 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14327 \begin_layout Standard
14328 Self-defined colors can also be used for text with the help of the command
14336 \begin_inset Index idx
14339 \begin_layout Plain Layout
14348 \begin_layout Standard
14352 \begin_layout Plain Layout
14356 textcolor{darkgreen}{
14362 \begin_inset Quotes eld
14366 \begin_inset Quotes erd
14373 \begin_layout Plain Layout
14383 \begin_layout Standard
14391 \begin_inset Index idx
14394 \begin_layout Plain Layout
14402 is used in the scheme
14406 textcolor{color}{characters to color}
14411 \begin_layout Subsection
14413 \begin_inset CommandInset label
14415 name "subsec:Paragraph-Boxes"
14420 \begin_inset Index idx
14423 \begin_layout Plain Layout
14424 Boxes ! as paragraph
14432 \begin_layout Standard
14433 A box that can contain several lines and paragraphs, a so-called paragraph
14434 box (parbox), can be created with the menu
14436 Insert\SpecialChar menuseparator
14439 or the toolbar button
14448 \begin_layout Standard
14449 The following example shows a framed parbox in a line:
14452 \begin_layout Standard
14453 \begin_inset VSpace medskip
14457 \begin_inset Box Boxed
14467 height_special "totalheight"
14472 backgroundcolor "none"
14475 \begin_layout Plain Layout
14476 This is a paragraph box.
14478 \begin_inset space \thinspace{}
14481 cm long and can also contain formulas:
14482 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14493 \begin_layout Standard
14494 \begin_inset VSpace medskip
14500 \begin_layout Standard
14501 Such a box is created by right-clicking on the gray box inset.
14502 A dialog pops up showing the box properties.
14516 \begin_inset space \thinspace{}
14521 Vertical Box Alignment
14526 \begin_layout Standard
14527 \begin_inset VSpace medskip
14530 In \SpecialChar LaTeX
14531 a parbox is created with the command
14538 \begin_inset Index idx
14541 \begin_layout Plain Layout
14549 which has the following scheme:
14552 \begin_layout Standard
14557 parbox[position]{width}{box content}
14560 \begin_layout Standard
14575 \begin_inset Quotes eld
14579 \begin_inset Quotes erd
14582 means that the box is aligned within the surrounding text with its last
14589 \begin_inset Quotes eld
14593 \begin_inset Quotes erd
14596 this is done with the first line.
14597 When no position is given, the box will be vertically centered, see section
14605 \begin_inset space ~
14610 manual for examples.
14613 \begin_layout Standard
14614 \begin_inset VSpace bigskip
14617 To frame formulas completely, including the formula number, the formula
14618 must be set into a parbox.
14619 To do this, the command
14633 is inserted in \SpecialChar TeX
14634 mode before the formula.
14642 \begin_inset Index idx
14645 \begin_layout Plain Layout
14653 is hereby the line width set for the document.
14654 Because the frame is outside the parbox, 2
14655 \begin_inset space \thinspace{}
14658 times the frame separation and the frame thickness must be subtracted from
14660 As this is not automatically done by \SpecialChar LyX
14665 \begin_layout Plain Layout
14666 \begin_inset CommandInset href
14668 name "LyX-bug #4483"
14669 target "http://www.lyx.org/trac/ticket/4483"
14679 mode has to be used.
14680 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14689 \begin_layout Plain Layout
14694 is part of every \SpecialChar LaTeX
14695 standard installation.
14701 \begin_inset Index idx
14704 \begin_layout Plain Layout
14710 must be loaded in the \SpecialChar LaTeX
14711 -preamble with the line
14714 \begin_layout Standard
14722 \begin_layout Standard
14723 Behind the formula both boxes are closed by entering
14727 in \SpecialChar TeX
14729 Here is an example:
14733 \begin_layout Plain Layout
14747 \begin_layout Standard
14751 \begin_layout Plain Layout
14769 \begin_inset Formula
14771 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14780 \begin_layout Plain Layout
14791 \begin_layout Plain Layout
14805 \begin_layout Standard
14806 \begin_inset VSpace medskip
14809 As a parbox is used as the argument of
14815 , there is in this case no difference between
14830 \begin_layout Standard
14831 \begin_inset VSpace bigskip
14834 Paragraph boxes are very useful to comment formulas directly.
14841 is used in combination with the command
14855 \begin_inset CommandInset ref
14857 reference "subsec:User-defined-Numbering"
14864 \begin_layout Standard
14865 An example of a formula commented with
14874 \begin_layout Standard
14878 \begin_layout Plain Layout
14891 This is a description.
14892 It is distinctly separated from the formula and multiline.
14896 \begin_layout Plain Layout
14908 \begin_layout Standard
14909 Such a formula must be inserted completely in \SpecialChar TeX
14910 mode because \SpecialChar LyX
14912 support the command
14919 The formula is created with the following command sequence:
14922 \begin_layout Standard
14935 is inserted in \SpecialChar TeX
14940 \begin_layout Plain Layout
14941 When the formula style
14953 can also be replaced by
14960 (formula styles see
14961 \begin_inset CommandInset ref
14963 reference "sec:Formula-Styles"
14972 Then the description follows as normal text and finally
14978 is inserted in \SpecialChar TeX
14992 hereby create a displayed formula.
14995 \begin_layout Standard
15002 can be seen in this example that was
15003 \begin_inset Quotes eld
15007 \begin_inset Quotes erd
15010 using the mathematical textmode:
15011 \begin_inset Formula
15013 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15021 \begin_layout Section
15023 \begin_inset Index idx
15026 \begin_layout Plain Layout
15035 \begin_layout Subsection
15037 \begin_inset CommandInset label
15039 name "subsec:Big-Operators"
15044 \begin_inset Index idx
15047 \begin_layout Plain Layout
15054 \begin_inset Index idx
15057 \begin_layout Plain Layout
15064 \begin_inset Index idx
15067 \begin_layout Plain Layout
15076 \begin_layout Standard
15077 To be able to use all integral operators listed here, the option
15079 Use esint package automatically
15081 must be set in the document settings under
15084 \begin_inset space ~
15092 \begin_layout Standard
15093 \begin_inset space \hfill{}
15097 \begin_inset Tabular
15098 <lyxtabular version="3" rows="11" columns="2">
15099 <features tabularvalignment="middle">
15100 <column alignment="center" valignment="top" width="0pt">
15101 <column alignment="center" valignment="top" width="0pt">
15103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15106 \begin_layout Plain Layout
15112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15115 \begin_layout Plain Layout
15123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15126 \begin_layout Plain Layout
15130 \begin_inset Index idx
15133 \begin_layout Plain Layout
15146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15149 \begin_layout Plain Layout
15150 \begin_inset Formula $\int$
15160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15163 \begin_layout Plain Layout
15171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15174 \begin_layout Plain Layout
15175 \begin_inset Formula $\oint$
15185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15188 \begin_layout Plain Layout
15196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15199 \begin_layout Plain Layout
15200 \begin_inset Formula $\ointctrclockwise$
15210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15213 \begin_layout Plain Layout
15221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15224 \begin_layout Plain Layout
15225 \begin_inset Formula $\ointclockwise$
15235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15238 \begin_layout Plain Layout
15246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15249 \begin_layout Plain Layout
15250 \begin_inset Formula $\sqint$
15260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15263 \begin_layout Plain Layout
15271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15274 \begin_layout Plain Layout
15276 \begin_inset Formula $\fint$
15286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15289 \begin_layout Plain Layout
15297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15300 \begin_layout Plain Layout
15302 \begin_inset Formula $\landupint$
15312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15315 \begin_layout Plain Layout
15323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15326 \begin_layout Plain Layout
15328 \begin_inset Formula $\landdownint$
15338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15341 \begin_layout Plain Layout
15349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15352 \begin_layout Plain Layout
15353 \begin_inset Formula $\bigcap$
15363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15366 \begin_layout Plain Layout
15374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15377 \begin_layout Plain Layout
15378 \begin_inset Formula $\bigcup$
15392 \begin_inset space \hfill{}
15396 \begin_inset Tabular
15397 <lyxtabular version="3" rows="11" columns="2">
15398 <features tabularvalignment="middle">
15399 <column alignment="center" valignment="top" width="0pt">
15400 <column alignment="center" valignment="top" width="0pt">
15402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15405 \begin_layout Plain Layout
15411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15414 \begin_layout Plain Layout
15422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15425 \begin_layout Plain Layout
15429 \begin_inset Index idx
15432 \begin_layout Plain Layout
15445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15448 \begin_layout Plain Layout
15449 \begin_inset Formula $\sum$
15459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15462 \begin_layout Plain Layout
15466 \begin_inset Index idx
15469 \begin_layout Plain Layout
15476 \begin_layout Plain Layout
15495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15498 \begin_layout Plain Layout
15499 \begin_inset Formula $\prod$
15509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15512 \begin_layout Plain Layout
15520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15523 \begin_layout Plain Layout
15524 \begin_inset Formula $\coprod$
15534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15537 \begin_layout Plain Layout
15545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15548 \begin_layout Plain Layout
15549 \begin_inset Formula $\bigodot$
15559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15562 \begin_layout Plain Layout
15570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15573 \begin_layout Plain Layout
15574 \begin_inset Formula $\bigotimes$
15584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15587 \begin_layout Plain Layout
15595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15598 \begin_layout Plain Layout
15599 \begin_inset Formula $\bigoplus$
15609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15612 \begin_layout Plain Layout
15620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15623 \begin_layout Plain Layout
15624 \begin_inset Formula $\bigwedge$
15634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15637 \begin_layout Plain Layout
15645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15648 \begin_layout Plain Layout
15649 \begin_inset Formula $\bigvee$
15659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15662 \begin_layout Plain Layout
15670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15673 \begin_layout Plain Layout
15674 \begin_inset Formula $\bigsqcup$
15684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15687 \begin_layout Plain Layout
15695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15698 \begin_layout Plain Layout
15699 \begin_inset Formula $\biguplus$
15713 \begin_inset space \hfill{}
15719 \begin_layout Standard
15720 All big operators can also be inserted via the math toolbar button
15723 arg "math-insert \\intop"
15729 \begin_layout Standard
15730 The operators are called big because they are bigger than the sometimes
15731 equal looking binary operators.
15732 All big operators can have limits as described in the next subsection.
15735 \begin_layout Standard
15736 For all integral operators there is a second version available, ending in
15754 These operators are different from
15761 \begin_inset space \space{}
15764 in the style the operator limits are displayed, see
15765 \begin_inset CommandInset ref
15767 reference "subsec:Operator-Limits"
15775 \begin_layout Subsubsection*
15776 Advice for Integrals
15779 \begin_layout Standard
15784 in an integral is an operator, that therefore has to be set upright.
15785 This is done by highlighting the
15789 and using the keyboard shortcut
15799 \begin_layout Plain Layout
15805 \begin_inset CommandInset ref
15807 reference "subsec:Font-Styles"
15817 Finally the smallest space is inserted before the
15821 , as this is usual for operators.
15825 \begin_layout Standard
15827 \begin_inset Formula $\int A(x)dx$
15831 \begin_inset Newline newline
15835 \begin_inset Phantom HPhantom
15838 \begin_layout Plain Layout
15845 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15851 \begin_layout Standard
15852 For multiple integrals there are the following commands:
15853 \begin_inset VSpace medskip
15859 \begin_layout Standard
15860 \begin_inset space \hfill{}
15864 \begin_inset Tabular
15865 <lyxtabular version="3" rows="4" columns="2">
15866 <features tabularvalignment="middle">
15867 <column alignment="center" valignment="top">
15868 <column alignment="center" valignment="top">
15870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15873 \begin_layout Plain Layout
15879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15882 \begin_layout Plain Layout
15884 \begin_inset Note Note
15887 \begin_layout Plain Layout
15894 is only used as spacer.
15906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15909 \begin_layout Plain Layout
15917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15920 \begin_layout Plain Layout
15921 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15934 \begin_layout Plain Layout
15942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15945 \begin_layout Plain Layout
15946 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15959 \begin_layout Plain Layout
15967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15970 \begin_layout Plain Layout
15971 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15985 \begin_inset space \hfill{}
15989 \begin_inset Tabular
15990 <lyxtabular version="3" rows="4" columns="2">
15991 <features tabularvalignment="middle">
15992 <column alignment="center" valignment="top">
15993 <column alignment="center" valignment="top">
15995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15998 \begin_layout Plain Layout
16004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16007 \begin_layout Plain Layout
16015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16018 \begin_layout Plain Layout
16026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16029 \begin_layout Plain Layout
16030 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16043 \begin_layout Plain Layout
16051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16054 \begin_layout Plain Layout
16055 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16068 \begin_layout Plain Layout
16076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16079 \begin_layout Plain Layout
16080 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16094 \begin_inset space \hfill{}
16100 \begin_layout Subsection
16102 \begin_inset CommandInset label
16104 name "subsec:Operator-Limits"
16109 \begin_inset Index idx
16112 \begin_layout Plain Layout
16121 \begin_layout Standard
16122 Limits are created by super- and subscripts:
16123 \begin_inset Separator parbreak
16129 \begin_layout Standard
16131 \begin_inset Tabular
16132 <lyxtabular version="3" rows="2" columns="2">
16133 <features tabularvalignment="middle">
16134 <column alignment="center" valignment="top" width="0pt">
16135 <column alignment="center" valignment="top" width="0pt">
16137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16140 \begin_layout Plain Layout
16146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16149 \begin_layout Plain Layout
16151 \begin_inset Note Note
16154 \begin_layout Plain Layout
16161 is only used as spacer.
16173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16176 \begin_layout Plain Layout
16182 \begin_inset space \textvisiblespace{}
16186 \begin_inset Formula $\to$
16190 \begin_inset Formula $\to$
16198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16201 \begin_layout Plain Layout
16202 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16218 \begin_layout Standard
16219 Limits of inline formulas are set right beside the operator.
16220 Limits in displayed formulas are set above or below the operator, except
16221 for integral limits.
16224 \begin_layout Standard
16225 To force that the limits are set beside the operator, the cursor is set
16226 directly behind the operator and the limits type is changed with the menu
16229 Edit\SpecialChar menuseparator
16230 Math\SpecialChar menuseparator
16249 \begin_layout Standard
16250 The default limits type is this:
16251 \begin_inset Formula
16253 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16258 This is how it looks when the limits type was changed to
16265 \begin_inset Formula
16267 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16272 For integrals, except those ending with
16288 etc., the limits are by default set beside the operator.
16289 But for multiple integrals the limits are often set below the operator.
16290 In the following example the limits type was therefore set to
16294 and so set below the integrals:
16295 \begin_inset Formula
16297 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16305 \begin_layout Standard
16306 \begin_inset VSpace medskip
16309 To specify conditions for limits, the commands
16316 \begin_inset Index idx
16319 \begin_layout Plain Layout
16334 \begin_inset Index idx
16337 \begin_layout Plain Layout
16346 To create for example this expression
16347 \begin_inset Formula
16349 \sum_{\begin{subarray}{c}
16353 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16361 \begin_layout Standard
16362 the following has to be done:
16363 \begin_inset Newline newline
16375 \begin_inset space \textvisiblespace{}
16381 One is now in a blue box under the summation operator and insert there
16387 \begin_inset space \textvisiblespace{}
16393 The blue box is now within a purple box and now several lines can be written
16395 A new line is created by inserting a line break (
16398 arg "newline-insert newline"
16403 \begin_inset Newline newline
16408 0<k<1000 Ctrl+Return
16409 \begin_inset Newline newline
16414 is typed in, a new box appears below for the new line.
16417 \begin_layout Standard
16418 The alignment of the lines can be changed to left aligned with the
16428 Edit\SpecialChar menuseparator
16432 To get right alignment,
16437 \begin_inset space \textvisiblespace{}
16442 is inserted at the beginning of the line.
16445 \begin_layout Standard
16458 with the difference that the lines are always centered.
16461 \begin_layout Standard
16462 \begin_inset VSpace bigskip
16466 \begin_inset CommandInset ref
16468 reference "eq:substack"
16472 there can be too much space beside an operator, because the characters
16473 following the operator are set beside the limits.
16474 To avoid this the command
16481 \begin_inset Index idx
16484 \begin_layout Plain Layout
16493 To activate it, set in the document settings under
16496 \begin_inset space ~
16506 \begin_inset Index idx
16509 \begin_layout Plain Layout
16510 Packages ! mathtools
16518 \begin_inset space ~
16530 sets the space besides the operator to 0
16531 \begin_inset space \thinspace{}
16535 \begin_inset Newline newline
16539 \begin_inset CommandInset ref
16541 reference "eq:substack"
16545 , one uses the command
16548 \begin_layout Standard
16556 \begin_layout Standard
16557 and inserts the operator with its limits into the braces.
16558 Behind the brace one continues the formula:
16559 \begin_inset Formula
16561 \smashoperator{\sum_{\begin{subarray}{c}
16565 \end{subarray}}^{n}}k^{-2}
16573 \begin_layout Standard
16574 It is possible to set the space of only one side of the operator to 0
16575 \begin_inset space \thinspace{}
16579 To do this write either
16598 stands for the left and
16602 for the right side of the operator.
16603 Here is an example of the possible
16612 \begin_layout Standard
16613 \begin_inset Formula
16615 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}
16623 \begin_layout Standard
16624 \begin_inset VSpace bigskip
16630 \begin_layout Standard
16631 When several consecutive operators have limits the typesetting of the limits
16632 looks often imperfect in the output, see this example:
16633 \begin_inset Formula
16635 \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}
16640 To improve the typesetting set in the document settings under
16643 \begin_inset space ~
16653 \begin_inset Index idx
16656 \begin_layout Plain Layout
16657 Packages ! mathtools
16665 \begin_inset space ~
16671 Then insert into your formula the command
16678 \begin_inset Index idx
16681 \begin_layout Plain Layout
16689 directly before the first operator.
16690 The example will then look like this:
16691 \begin_inset Formula
16693 \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}
16701 \begin_layout Standard
16702 \begin_inset VSpace bigskip
16705 How to use one limit for several operators is described in
16706 \begin_inset CommandInset ref
16708 reference "subsec:Self-defined-Operators"
16715 \begin_layout Subsection
16716 Decoration for Operators
16717 \begin_inset Index idx
16720 \begin_layout Plain Layout
16721 Operators ! Decoration
16729 \begin_layout Standard
16737 \begin_inset Index idx
16740 \begin_layout Plain Layout
16755 \begin_inset Index idx
16758 \begin_layout Plain Layout
16766 characters can be placed above or below an operator, respectively.
16774 \begin_inset Index idx
16777 \begin_layout Plain Layout
16785 characters can be set before and behind a big operator.
16788 \begin_layout Standard
16790 \begin_inset space ~
16802 \begin_layout Itemize
16809 is used to set characters at the corners of the operator
16812 \begin_layout Itemize
16819 is used to set characters before and/or behind the operator (this variant
16820 represents \SpecialChar LaTeX
16830 \begin_layout Itemize
16837 is used to set characters at the left corners and/or behind the operator
16840 \begin_layout Itemize
16847 is used to set characters at the right corners and/or before the operator
16850 \begin_layout Standard
16851 For example the command
16856 \begin_inset space \textvisiblespace{}
16862 \begin_inset space \textvisiblespace{}
16866 \begin_inset Formula $\to$
16870 \begin_inset Formula $\to$
16874 \begin_inset space \textvisiblespace{}
16884 \begin_inset Formula
16886 \sideset{}{'}\sum_{k=1}^{n}
16894 \begin_layout Standard
16895 \begin_inset Note Greyedout
16898 \begin_layout Plain Layout
16905 can only be used to decorate big operators, binary operators are not allowed.
16913 \begin_layout Standard
16926 can also be used to decorate symbols and characters.
16927 For example, the command
16932 \begin_inset space \textvisiblespace{}
16938 \begin_inset space \textvisiblespace{}
16944 \begin_inset Formula $\uparrow$
16952 \begin_inset Formula
16954 \overset{a}{\maltese}
16962 \begin_layout Subsection
16964 \begin_inset CommandInset label
16966 name "subsec:Binary-Operators"
16971 \begin_inset Index idx
16974 \begin_layout Plain Layout
16983 \begin_layout Standard
16984 Binary operators are surrounded by space when there is a character before
16986 \begin_inset VSpace medskip
16992 \begin_layout Standard
16993 \begin_inset Tabular
16994 <lyxtabular version="3" rows="13" columns="2">
16995 <features booktabs="true" tabularvalignment="middle">
16996 <column alignment="center" valignment="top" width="0pt">
16997 <column alignment="center" valignment="top" width="0pt">
16999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17002 \begin_layout Plain Layout
17004 \begin_inset Note Note
17007 \begin_layout Plain Layout
17014 is only used as spacer.
17024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17027 \begin_layout Plain Layout
17035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17038 \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 $+$
17058 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17061 \begin_layout Plain Layout
17067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17070 \begin_layout Plain Layout
17071 \begin_inset Formula $-$
17081 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17084 \begin_layout Plain Layout
17092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17095 \begin_layout Plain Layout
17096 \begin_inset Formula $\pm$
17106 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17109 \begin_layout Plain Layout
17117 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17120 \begin_layout Plain Layout
17121 \begin_inset Formula $\mp$
17131 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17134 \begin_layout Plain Layout
17142 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17145 \begin_layout Plain Layout
17146 \begin_inset Formula $\cdot$
17156 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17159 \begin_layout Plain Layout
17167 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17170 \begin_layout Plain Layout
17171 \begin_inset Formula $\times$
17181 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17184 \begin_layout Plain Layout
17192 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17195 \begin_layout Plain Layout
17196 \begin_inset Formula $\div$
17206 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17209 \begin_layout Plain Layout
17213 \begin_layout Plain Layout
17226 \begin_layout Plain Layout
17238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17241 \begin_layout Plain Layout
17242 \begin_inset Formula $*$
17252 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17255 \begin_layout Plain Layout
17263 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17266 \begin_layout Plain Layout
17267 \begin_inset Formula $\star$
17277 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17280 \begin_layout Plain Layout
17288 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17291 \begin_layout Plain Layout
17292 \begin_inset Formula $\circ$
17302 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17305 \begin_layout Plain Layout
17313 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17316 \begin_layout Plain Layout
17317 \begin_inset Formula $\diamond$
17327 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17330 \begin_layout Plain Layout
17338 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17341 \begin_layout Plain Layout
17342 \begin_inset Formula $\bullet$
17356 \begin_inset space \hfill{}
17360 \begin_inset Tabular
17361 <lyxtabular version="3" rows="13" columns="2">
17362 <features booktabs="true" tabularvalignment="middle">
17363 <column alignment="center" valignment="top" width="0pt">
17364 <column alignment="center" valignment="top" width="0pt">
17366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17369 \begin_layout Plain Layout
17375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17378 \begin_layout Plain Layout
17386 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17389 \begin_layout Plain Layout
17397 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17400 \begin_layout Plain Layout
17401 \begin_inset Formula $\nabla$
17411 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17414 \begin_layout Plain Layout
17422 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17425 \begin_layout Plain Layout
17426 \begin_inset Formula $\bigtriangledown$
17436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17439 \begin_layout Plain Layout
17447 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17450 \begin_layout Plain Layout
17451 \begin_inset Formula $\bigtriangleup$
17461 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17464 \begin_layout Plain Layout
17472 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17475 \begin_layout Plain Layout
17476 \begin_inset Formula $\Box$
17486 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17489 \begin_layout Plain Layout
17497 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17500 \begin_layout Plain Layout
17501 \begin_inset Formula $\cap$
17511 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17514 \begin_layout Plain Layout
17522 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17525 \begin_layout Plain Layout
17526 \begin_inset Formula $\cup$
17536 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17539 \begin_layout Plain Layout
17547 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17550 \begin_layout Plain Layout
17551 \begin_inset Formula $\dagger$
17561 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17564 \begin_layout Plain Layout
17572 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17575 \begin_layout Plain Layout
17576 \begin_inset Formula $\ddagger$
17586 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17589 \begin_layout Plain Layout
17597 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17600 \begin_layout Plain Layout
17601 \begin_inset Formula $\wr$
17611 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17614 \begin_layout Plain Layout
17622 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17625 \begin_layout Plain Layout
17626 \begin_inset Formula $\bigcirc$
17636 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17639 \begin_layout Plain Layout
17647 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17650 \begin_layout Plain Layout
17651 \begin_inset Formula $\wedge$
17661 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17664 \begin_layout Plain Layout
17672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17675 \begin_layout Plain Layout
17676 \begin_inset Formula $\vee$
17690 \begin_inset space \hfill{}
17694 \begin_inset Tabular
17695 <lyxtabular version="3" rows="13" columns="2">
17696 <features booktabs="true" tabularvalignment="middle">
17697 <column alignment="center" valignment="top" width="0pt">
17698 <column alignment="center" valignment="top" width="0pt">
17700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17703 \begin_layout Plain Layout
17709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17712 \begin_layout Plain Layout
17720 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17723 \begin_layout Plain Layout
17731 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17734 \begin_layout Plain Layout
17735 \begin_inset Formula $\oplus$
17745 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17748 \begin_layout Plain Layout
17756 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17759 \begin_layout Plain Layout
17760 \begin_inset Formula $\ominus$
17770 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17773 \begin_layout Plain Layout
17781 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17784 \begin_layout Plain Layout
17785 \begin_inset Formula $\otimes$
17795 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17798 \begin_layout Plain Layout
17806 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17809 \begin_layout Plain Layout
17810 \begin_inset Formula $\oslash$
17820 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17823 \begin_layout Plain Layout
17831 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17834 \begin_layout Plain Layout
17835 \begin_inset Formula $\odot$
17845 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17848 \begin_layout Plain Layout
17856 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17859 \begin_layout Plain Layout
17860 \begin_inset Formula $\amalg$
17870 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17873 \begin_layout Plain Layout
17881 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17884 \begin_layout Plain Layout
17885 \begin_inset Formula $\uplus$
17895 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17898 \begin_layout Plain Layout
17906 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17909 \begin_layout Plain Layout
17910 \begin_inset Formula $\setminus$
17920 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17923 \begin_layout Plain Layout
17931 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17934 \begin_layout Plain Layout
17935 \begin_inset Formula $\sqcap$
17945 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17948 \begin_layout Plain Layout
17956 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17959 \begin_layout Plain Layout
17960 \begin_inset Formula $\sqcup$
17970 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17973 \begin_layout Plain Layout
17981 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17984 \begin_layout Plain Layout
17985 \begin_inset Formula $\triangleleft$
17995 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17998 \begin_layout Plain Layout
18006 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18009 \begin_layout Plain Layout
18010 \begin_inset Formula $\triangleright$
18026 \begin_layout Standard
18027 All binary operators can also be inserted via the math toolbar button
18030 arg "math-insert \\pm"
18036 \begin_layout Standard
18037 To typeset the Laplace operator also
18054 \begin_inset Formula $\nabla^{2}$
18057 ) can be used instead of
18066 \begin_layout Standard
18073 Insert\SpecialChar menuseparator
18085 \begin_layout Subsection
18086 Self-defined Operators
18087 \begin_inset CommandInset label
18089 name "subsec:Self-defined-Operators"
18094 \begin_inset Index idx
18097 \begin_layout Plain Layout
18098 Operators ! self-defined
18106 \begin_layout Standard
18107 With the help of the command
18111 DeclareMathOperator
18114 \begin_inset Index idx
18117 \begin_layout Plain Layout
18122 DeclareMathOperator
18127 custom operators can be defined in the \SpecialChar LaTeX
18129 Its command scheme is:
18132 \begin_layout Standard
18137 DeclareMathOperator{new command}{display}
18140 \begin_layout Standard
18141 Display can be characters or symbols that define how the operator looks
18143 To define a big operator a * is set behind the command.
18144 All self-defined big operators can have limits as described in
18145 \begin_inset CommandInset ref
18147 reference "subsec:Operator-Limits"
18154 \begin_layout Standard
18155 For example the \SpecialChar LaTeX
18159 \begin_layout Standard
18164 DeclareMathOperator*{
18171 \begin_layout Standard
18172 defines the command
18178 , that inserts a big operator consisting of the lozenge symbol from
18179 \begin_inset CommandInset ref
18181 reference "subsec:Miscellaneous-Symbols"
18186 \begin_inset Formula
18188 \Lozenge_{n=1}^{\infty}
18193 The command for this formula is:
18204 \begin_inset Formula $\to$
18210 \begin_layout Standard
18211 \begin_inset VSpace bigskip
18214 When self-defined operators are not used several times in the document,
18215 they can also be defined with the commands
18222 \begin_inset Index idx
18225 \begin_layout Plain Layout
18240 \begin_inset Index idx
18243 \begin_layout Plain Layout
18251 , which have the following scheme:
18254 \begin_layout Standard
18268 \begin_layout Standard
18275 defines big operators,
18284 \begin_layout Standard
18292 \begin_inset space \thinspace{}
18296 \begin_inset space \space{}
18299 be used to use one limit for several operators:
18302 \begin_layout Standard
18303 \begin_inset Formula
18305 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18313 \begin_layout Standard
18314 The command for the formula above is:
18315 \begin_inset Newline newline
18331 \begin_inset space \textvisiblespace{}
18337 \begin_inset Formula $\to$
18343 \begin_inset space \textvisiblespace{}
18351 \begin_layout Section
18353 \begin_inset Index idx
18356 \begin_layout Plain Layout
18365 \begin_layout Subsection
18367 \begin_inset CommandInset label
18369 name "subsec:Font-Styles"
18374 \begin_inset Index idx
18377 \begin_layout Plain Layout
18386 \begin_layout Standard
18387 Latin letters in formulas can be set in one of the following font styles:
18390 \begin_layout Standard
18392 \begin_inset space \hfill{}
18396 \begin_inset Tabular
18397 <lyxtabular version="3" rows="6" columns="2">
18398 <features booktabs="true" tabularvalignment="middle">
18399 <column alignment="center" valignment="top" width="0pt">
18400 <column alignment="center" valignment="top">
18402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18405 \begin_layout Plain Layout
18411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18414 \begin_layout Plain Layout
18422 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18425 \begin_layout Plain Layout
18431 \begin_inset space \textvisiblespace{}
18441 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18444 \begin_layout Plain Layout
18445 \begin_inset Formula $\mathbb{ABC}$
18455 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18458 \begin_layout Plain Layout
18464 \begin_inset space \textvisiblespace{}
18474 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18477 \begin_layout Plain Layout
18478 \begin_inset Formula $\mathbf{AbC}$
18488 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18491 \begin_layout Plain Layout
18497 \begin_inset space \textvisiblespace{}
18507 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18510 \begin_layout Plain Layout
18511 \begin_inset Formula $\boldsymbol{AbC}$
18521 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18524 \begin_layout Plain Layout
18530 \begin_inset space \textvisiblespace{}
18540 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18543 \begin_layout Plain Layout
18544 \begin_inset Formula $\mathcal{ABC}$
18554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18557 \begin_layout Plain Layout
18563 \begin_inset space \textvisiblespace{}
18573 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18576 \begin_layout Plain Layout
18577 \begin_inset Formula $\mathfrak{AbC}$
18591 \begin_inset space \hfill{}
18595 \begin_inset Tabular
18596 <lyxtabular version="3" rows="6" columns="2">
18597 <features booktabs="true" tabularvalignment="middle">
18598 <column alignment="center" valignment="top" width="0pt">
18599 <column alignment="center" valignment="top">
18601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18604 \begin_layout Plain Layout
18610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18613 \begin_layout Plain Layout
18621 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18624 \begin_layout Plain Layout
18630 \begin_inset space \textvisiblespace{}
18640 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18643 \begin_layout Plain Layout
18644 \begin_inset Formula $\mathit{AbC}$
18654 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18657 \begin_layout Plain Layout
18663 \begin_inset space \textvisiblespace{}
18673 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18676 \begin_layout Plain Layout
18677 \begin_inset Formula $\mathrm{AbC}$
18687 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18690 \begin_layout Plain Layout
18696 \begin_inset space \textvisiblespace{}
18706 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18709 \begin_layout Plain Layout
18710 \begin_inset Formula $\mathsf{AbC}$
18720 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18723 \begin_layout Plain Layout
18729 \begin_inset space \textvisiblespace{}
18739 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18742 \begin_layout Plain Layout
18743 \begin_inset Formula $\mathtt{AbC}$
18753 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18756 \begin_layout Plain Layout
18762 \begin_inset space \textvisiblespace{}
18772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18775 \begin_layout Plain Layout
18776 \begin_inset Formula $\mathscr{ABC}$
18790 \begin_inset space \hfill{}
18796 \begin_layout Standard
18797 \begin_inset Note Greyedout
18800 \begin_layout Plain Layout
18823 can only be used for big letters.
18831 \begin_layout Standard
18832 Predefined is the style
18841 \begin_layout Standard
18842 The style commands work also for letters in mathematical constructs:
18843 \begin_inset Formula
18845 \mathfrak{A=\frac{b}{C}}
18853 \begin_layout Standard
18854 Characters in mathematical text don't appear in a math font style but in
18855 the text font style
18862 That their style can't be set correctly via the text style dialog is a
18863 bug in \SpecialChar LyX
18868 \begin_layout Plain Layout
18869 \begin_inset CommandInset href
18871 name "LyX-bug #4629"
18872 target "http://www.lyx.org/trac/ticket/4629"
18884 \begin_layout Standard
18885 Instead of the style commands the dialog
18887 Edit\SpecialChar menuseparator
18888 Math\SpecialChar menuseparator
18891 or the toolbar button
18894 arg "math-insert \\font"
18900 \begin_layout Subsection
18902 \begin_inset CommandInset label
18904 name "subsec:Bold-Formulas"
18909 \begin_inset Index idx
18912 \begin_layout Plain Layout
18921 \begin_layout Standard
18922 To make a complete formula bold, the command
18928 from the previous subsection cannot be used, because it doesn't work for
18929 small Greek letters.
18930 Furthermore it prints Latin letters always upright, like in the following
18934 \begin_layout Standard
18935 \begin_inset Formula
18937 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18945 \begin_layout Standard
18946 To display the formula correctly, the command
18953 \begin_inset Formula
18955 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18960 It is also possible to set the formula in a
18962 boldmath environment
18965 This environment is created by inserting the command
18972 \begin_inset Index idx
18975 \begin_layout Plain Layout
18983 in \SpecialChar TeX
18985 To end the environment, the command
18992 \begin_inset Index idx
18995 \begin_layout Plain Layout
19003 is inserted in \SpecialChar TeX
19008 \begin_layout Plain Layout
19018 \begin_inset Formula
19020 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19029 \begin_layout Plain Layout
19041 \begin_layout Subsection
19043 \begin_inset Index idx
19046 \begin_layout Plain Layout
19055 \begin_layout Standard
19056 Formulas can be colored like normal text: Highlight a formula or a formula
19062 Here is a formula in magenta:
19063 \begin_inset Formula
19065 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19073 \begin_layout Standard
19074 You can also define your own colors as described in
19075 \begin_inset CommandInset ref
19077 reference "subsec:Colored-Boxes"
19082 They can be used with the \SpecialChar TeX
19090 \begin_inset Index idx
19093 \begin_layout Plain Layout
19104 \begin_layout Standard
19109 textcolor{color}{characters or formula}
19112 \begin_layout Standard
19113 The following example was colored completely dark green and partly red:
19116 \begin_layout Standard
19120 \begin_layout Plain Layout
19124 textcolor{darkgreen}{
19130 \begin_inset Formula
19132 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19141 \begin_layout Plain Layout
19151 \begin_layout Standard
19152 Due to a bug in \SpecialChar LyX
19153 only complete formulas can be colored with self-defined
19158 \begin_layout Plain Layout
19159 \begin_inset CommandInset href
19161 name "LyX-bug #5269"
19162 target "http://www.lyx.org/trac/ticket/5269"
19174 \begin_layout Subsection
19176 \begin_inset CommandInset label
19178 name "subsec:Font-Sizes"
19183 \begin_inset Index idx
19186 \begin_layout Plain Layout
19195 \begin_layout Standard
19196 For characters in formulas there are, analog to characters in text, the
19197 following size commands:
19200 \begin_layout Standard
19244 \begin_inset Newline newline
19266 \begin_layout Standard
19267 The size produced by the commands depends on the document font size, which
19268 corresponds to the command
19275 The other commands produce smaller or larger sizes than
19282 The font size can however not exceed a certain value.
19283 Is for example the document font size 12
19284 \begin_inset space \thinspace{}
19293 switches to the same size as
19303 \begin_layout Standard
19304 A size command is inserted in \SpecialChar TeX
19305 mode before the formula and sets the size
19306 for all following formula and text characters.
19307 To switch back to the initial size, the command
19313 is inserted behind the formula in \SpecialChar TeX
19317 \begin_layout Standard
19318 Within a formula the size can be changed using the following size commands
19319 or the toolbar button
19322 arg "math-insert \\style"
19326 \begin_inset Separator parbreak
19332 \begin_layout Standard
19335 \begin_inset Tabular
19336 <lyxtabular version="3" rows="5" columns="2">
19337 <features booktabs="true" tabularvalignment="middle">
19338 <column alignment="center" valignment="top" width="0pt">
19339 <column alignment="center" valignment="top">
19341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19344 \begin_layout Plain Layout
19350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19353 \begin_layout Plain Layout
19361 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19364 \begin_layout Plain Layout
19368 \begin_inset Index idx
19371 \begin_layout Plain Layout
19384 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19387 \begin_layout Plain Layout
19388 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19397 <row topspace="1mm">
19398 <cell alignment="center" valignment="top" usebox="none">
19401 \begin_layout Plain Layout
19409 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19412 \begin_layout Plain Layout
19413 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19423 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19426 \begin_layout Plain Layout
19434 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19437 \begin_layout Plain Layout
19438 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19448 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19451 \begin_layout Plain Layout
19459 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19462 \begin_layout Plain Layout
19463 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19479 \begin_layout Standard
19480 After entering these commands, a blue box appears in which the formula parts
19484 \begin_layout Standard
19485 There is a further method to change the font size, that though only works
19486 for symbols or letters in mathematical text.
19487 To use it, one of the above text size commands is inserted in mathematical
19489 All following characters until the end of the mathematical text or until
19490 another size command will have the selected size.
19492 \begin_inset VSpace -2mm
19498 \begin_layout Standard
19502 \begin_layout Plain Layout
19512 \begin_inset Formula
19514 A=\frac{B}{c}\cdot\maltese
19520 \begin_inset Formula
19522 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19531 \begin_layout Plain Layout
19543 \begin_layout Standard
19544 \begin_inset VSpace medskip
19547 Before both formulas the command
19554 The command for the second formula is:
19555 \begin_inset Newline newline
19563 \begin_inset space \textvisiblespace{}
19569 \begin_inset space \textvisiblespace{}
19575 \begin_inset space \textvisiblespace{}
19581 \begin_inset space \textvisiblespace{}
19585 \begin_inset Formula $\to$
19589 \begin_inset Formula $\to$
19593 \begin_inset Newline newline
19597 \begin_inset space \hspace*{}
19608 \begin_inset space \textvisiblespace{}
19614 \begin_inset space \textvisiblespace{}
19620 \begin_inset space \textvisiblespace{}
19626 \begin_layout Standard
19627 If a symbol cannot be displayed in different sizes, it will always be displayed
19628 in the default size.
19631 \begin_layout Section
19633 \begin_inset Index idx
19636 \begin_layout Plain Layout
19645 \begin_layout Standard
19646 Greek letters can also be inserted via the toolbar button
19649 arg "math-insert \\alpha"
19653 All international typesetting norms purport that Greek letters in math
19654 have to be typeset italic/slanted.
19655 In some languages, like French or Russian, they are nevertheless sometimes
19659 \begin_layout Subsection
19661 \begin_inset Index idx
19664 \begin_layout Plain Layout
19665 Greek letters ! small
19673 \begin_layout Standard
19674 \begin_inset space \hfill{}
19678 \begin_inset Tabular
19679 <lyxtabular version="3" rows="11" columns="2">
19680 <features booktabs="true" tabularvalignment="middle">
19681 <column alignment="center" valignment="top" width="0pt">
19682 <column alignment="center" valignment="top" width="0pt">
19684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19687 \begin_layout Plain Layout
19693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19696 \begin_layout Plain Layout
19704 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19707 \begin_layout Plain Layout
19715 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19718 \begin_layout Plain Layout
19719 \begin_inset Formula $\alpha$
19729 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19732 \begin_layout Plain Layout
19740 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19743 \begin_layout Plain Layout
19744 \begin_inset Formula $\beta$
19754 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19757 \begin_layout Plain Layout
19765 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19768 \begin_layout Plain Layout
19769 \begin_inset Formula $\gamma$
19779 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19782 \begin_layout Plain Layout
19790 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19793 \begin_layout Plain Layout
19794 \begin_inset Formula $\delta$
19804 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19807 \begin_layout Plain Layout
19815 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19818 \begin_layout Plain Layout
19819 \begin_inset Formula $\epsilon$
19829 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19832 \begin_layout Plain Layout
19840 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19843 \begin_layout Plain Layout
19844 \begin_inset Formula $\varepsilon$
19854 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19857 \begin_layout Plain Layout
19865 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19868 \begin_layout Plain Layout
19869 \begin_inset Formula $\zeta$
19879 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19882 \begin_layout Plain Layout
19890 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19893 \begin_layout Plain Layout
19894 \begin_inset Formula $\eta$
19904 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19907 \begin_layout Plain Layout
19915 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19918 \begin_layout Plain Layout
19919 \begin_inset Formula $\theta$
19929 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19932 \begin_layout Plain Layout
19940 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19943 \begin_layout Plain Layout
19944 \begin_inset Formula $\vartheta$
19958 \begin_inset space \hfill{}
19962 \begin_inset Tabular
19963 <lyxtabular version="3" rows="12" columns="2">
19964 <features booktabs="true" tabularvalignment="middle">
19965 <column alignment="center" valignment="top" width="0pt">
19966 <column alignment="center" valignment="top" width="0pt">
19968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19971 \begin_layout Plain Layout
19977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19980 \begin_layout Plain Layout
19988 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19991 \begin_layout Plain Layout
19999 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20002 \begin_layout Plain Layout
20003 \begin_inset Formula $\iota$
20013 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20016 \begin_layout Plain Layout
20024 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20027 \begin_layout Plain Layout
20028 \begin_inset Formula $\kappa$
20038 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20041 \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 $\varkappa$
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 $\lambda$
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 $\mu$
20113 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20116 \begin_layout Plain Layout
20124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20127 \begin_layout Plain Layout
20128 \begin_inset Formula $\nu$
20138 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20141 \begin_layout Plain Layout
20149 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20152 \begin_layout Plain Layout
20153 \begin_inset Formula $\xi$
20163 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20166 \begin_layout Plain Layout
20172 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20175 \begin_layout Plain Layout
20176 \begin_inset Formula $o$
20186 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20189 \begin_layout Plain Layout
20197 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20200 \begin_layout Plain Layout
20201 \begin_inset Formula $\pi$
20211 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20214 \begin_layout Plain Layout
20222 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20225 \begin_layout Plain Layout
20226 \begin_inset Formula $\varpi$
20236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20239 \begin_layout Plain Layout
20247 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20250 \begin_layout Plain Layout
20251 \begin_inset Formula $\rho$
20265 \begin_inset space \hfill{}
20269 \begin_inset Tabular
20270 <lyxtabular version="3" rows="11" columns="2">
20271 <features booktabs="true" tabularvalignment="middle">
20272 <column alignment="center" valignment="top" width="0pt">
20273 <column alignment="center" valignment="top" width="0pt">
20275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20278 \begin_layout Plain Layout
20284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20287 \begin_layout Plain Layout
20295 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20298 \begin_layout Plain Layout
20306 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20309 \begin_layout Plain Layout
20310 \begin_inset Formula $\varrho$
20320 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20323 \begin_layout Plain Layout
20331 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20334 \begin_layout Plain Layout
20335 \begin_inset Formula $\sigma$
20345 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20348 \begin_layout Plain Layout
20356 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20359 \begin_layout Plain Layout
20360 \begin_inset Formula $\varsigma$
20370 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20373 \begin_layout Plain Layout
20381 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20384 \begin_layout Plain Layout
20385 \begin_inset Formula $\tau$
20395 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20398 \begin_layout Plain Layout
20406 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20409 \begin_layout Plain Layout
20410 \begin_inset Formula $\upsilon$
20420 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20423 \begin_layout Plain Layout
20431 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20434 \begin_layout Plain Layout
20435 \begin_inset Formula $\phi$
20445 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20448 \begin_layout Plain Layout
20456 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20459 \begin_layout Plain Layout
20460 \begin_inset Formula $\varphi$
20470 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20473 \begin_layout Plain Layout
20481 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20484 \begin_layout Plain Layout
20485 \begin_inset Formula $\chi$
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 $\psi$
20520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20523 \begin_layout Plain Layout
20531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20534 \begin_layout Plain Layout
20535 \begin_inset Formula $\omega$
20549 \begin_inset space \hfill{}
20555 \begin_layout Standard
20556 \begin_inset VSpace medskip
20562 \begin_layout Standard
20563 How to create special upright Greek letters is explained in
20564 \begin_inset CommandInset ref
20566 reference "subsec:Upright-small-Greek"
20573 \begin_layout Subsection
20575 \begin_inset Index idx
20578 \begin_layout Plain Layout
20579 Greek letters ! big
20587 \begin_layout Standard
20588 \begin_inset space \hfill{}
20592 \begin_inset Tabular
20593 <lyxtabular version="3" rows="7" columns="2">
20594 <features booktabs="true" tabularvalignment="middle">
20595 <column alignment="center" valignment="top" width="0pt">
20596 <column alignment="center" valignment="top" width="0pt">
20598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20601 \begin_layout Plain Layout
20607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20610 \begin_layout Plain Layout
20618 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20621 \begin_layout Plain Layout
20629 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20632 \begin_layout Plain Layout
20633 \begin_inset Formula $\Gamma$
20643 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20646 \begin_layout Plain Layout
20654 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20657 \begin_layout Plain Layout
20658 \begin_inset Formula $\Delta$
20668 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20671 \begin_layout Plain Layout
20679 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20682 \begin_layout Plain Layout
20683 \begin_inset Formula $\Theta$
20693 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20696 \begin_layout Plain Layout
20704 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20707 \begin_layout Plain Layout
20708 \begin_inset Formula $\Lambda$
20718 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20721 \begin_layout Plain Layout
20729 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20732 \begin_layout Plain Layout
20733 \begin_inset Formula $\Xi$
20743 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20746 \begin_layout Plain Layout
20754 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20757 \begin_layout Plain Layout
20758 \begin_inset Formula $\Pi$
20772 \begin_inset space \hfill{}
20776 \begin_inset Tabular
20777 <lyxtabular version="3" rows="6" columns="2">
20778 <features booktabs="true" tabularvalignment="middle">
20779 <column alignment="center" valignment="top" width="0pt">
20780 <column alignment="center" valignment="top" width="0pt">
20782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20785 \begin_layout Plain Layout
20791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20794 \begin_layout Plain Layout
20802 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20805 \begin_layout Plain Layout
20813 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20816 \begin_layout Plain Layout
20817 \begin_inset Formula $\Sigma$
20827 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20830 \begin_layout Plain Layout
20838 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20841 \begin_layout Plain Layout
20842 \begin_inset Formula $\Upsilon$
20852 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20855 \begin_layout Plain Layout
20863 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20866 \begin_layout Plain Layout
20867 \begin_inset Formula $\Phi$
20877 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20880 \begin_layout Plain Layout
20888 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20891 \begin_layout Plain Layout
20892 \begin_inset Formula $\Psi$
20902 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20905 \begin_layout Plain Layout
20913 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20916 \begin_layout Plain Layout
20917 \begin_inset Formula $\Omega$
20931 \begin_inset space \hfill{}
20937 \begin_layout Standard
20938 \begin_inset VSpace medskip
20941 That the big Greek letters appear upright is caused by a design bug when
20944 To get correct italic big letters, begin every command with
20949 For example the command
20956 \begin_inset Formula $\varGamma$
20960 Another way is to load the package
20968 \begin_layout Plain Layout
20973 is part of the \SpecialChar LaTeX
20979 \begin_inset Index idx
20982 \begin_layout Plain Layout
20987 \begin_layout Plain Layout
21007 \begin_inset Index idx
21010 \begin_layout Plain Layout
21016 with the \SpecialChar LaTeX
21020 \begin_layout Standard
21025 usepackage{fixmath}
21028 \begin_layout Standard
21029 Then all big Greek letters in a document will automatically be typeset italic.
21032 \begin_layout Subsection
21034 \begin_inset Index idx
21037 \begin_layout Plain Layout
21038 Greek letters ! bold
21046 \begin_layout Standard
21047 Greek letters cannot be set with different font styles like Latin letters.
21048 They can only be made bold with the command
21055 \begin_inset Index idx
21058 \begin_layout Plain Layout
21067 \begin_inset Separator parbreak
21073 \begin_layout Standard
21075 \begin_inset Tabular
21076 <lyxtabular version="3" rows="3" columns="2">
21077 <features booktabs="true" tabularvalignment="middle">
21078 <column alignment="center" valignment="top" width="0pt">
21079 <column alignment="center" valignment="top">
21081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21084 \begin_layout Plain Layout
21090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21093 \begin_layout Plain Layout
21101 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21104 \begin_layout Plain Layout
21116 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21119 \begin_layout Plain Layout
21120 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21130 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21133 \begin_layout Plain Layout
21145 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21148 \begin_layout Plain Layout
21149 \begin_inset Formula $\theta\boldsymbol{\theta}$
21165 \begin_layout Section
21170 \begin_layout Plain Layout
21183 \begin_layout Plain Layout
21184 A list with all symbols of most of the \SpecialChar LaTeX
21185 -packages can be found in
21186 \begin_inset CommandInset citation
21201 \begin_layout Plain Layout
21209 \begin_inset Note Note
21212 \begin_layout Plain Layout
21215 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21218 \begin_layout Plain Layout
21221 texorpdfstring is in section
21222 \begin_inset CommandInset ref
21224 reference "subsec:Formulas-in-Section"
21234 \begin_inset Index idx
21237 \begin_layout Plain Layout
21246 \begin_layout Standard
21247 Many of the symbols listed in this section can also be inserted via the
21251 arg "math-insert \\nabla"
21257 arg "math-insert \\digamma"
21263 \begin_layout Subsection
21264 Mathematical Symbols
21265 \begin_inset CommandInset label
21267 name "subsec:Mathematical-Symbols"
21272 \begin_inset Index idx
21275 \begin_layout Plain Layout
21276 Symbols ! mathematical
21284 \begin_layout Standard
21285 \begin_inset Tabular
21286 <lyxtabular version="3" rows="10" columns="2">
21287 <features booktabs="true" tabularvalignment="middle">
21288 <column alignment="center" valignment="top" width="0pt">
21289 <column alignment="center" valignment="top" width="0pt">
21291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21294 \begin_layout Plain Layout
21300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21303 \begin_layout Plain Layout
21311 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21314 \begin_layout Plain Layout
21322 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21325 \begin_layout Plain Layout
21326 \begin_inset Formula $\neg$
21336 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21339 \begin_layout Plain Layout
21347 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21350 \begin_layout Plain Layout
21351 \begin_inset Formula $\Im$
21361 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21364 \begin_layout Plain Layout
21372 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21375 \begin_layout Plain Layout
21376 \begin_inset Formula $\Re$
21386 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21389 \begin_layout Plain Layout
21397 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21400 \begin_layout Plain Layout
21401 \begin_inset Formula $\aleph$
21411 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21414 \begin_layout Plain Layout
21422 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21425 \begin_layout Plain Layout
21426 \begin_inset Formula $\partial$
21436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21439 \begin_layout Plain Layout
21447 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21450 \begin_layout Plain Layout
21451 \begin_inset Formula $\infty$
21461 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21464 \begin_layout Plain Layout
21472 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21475 \begin_layout Plain Layout
21476 \begin_inset Formula $\wp$
21486 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21489 \begin_layout Plain Layout
21497 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21500 \begin_layout Plain Layout
21501 \begin_inset Formula $\imath$
21511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21514 \begin_layout Plain Layout
21522 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21525 \begin_layout Plain Layout
21526 \begin_inset Formula $\jmath$
21540 \begin_inset space \hfill{}
21544 \begin_inset Tabular
21545 <lyxtabular version="3" rows="10" columns="2">
21546 <features booktabs="true" tabularvalignment="middle">
21547 <column alignment="center" valignment="top" width="0pt">
21548 <column alignment="center" valignment="top" width="0pt">
21550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21553 \begin_layout Plain Layout
21559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21562 \begin_layout Plain Layout
21564 \begin_inset Note Note
21567 \begin_layout Plain Layout
21574 is only used as spacer.
21586 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21589 \begin_layout Plain Layout
21597 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21600 \begin_layout Plain Layout
21601 \begin_inset Formula $\forall$
21611 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21614 \begin_layout Plain Layout
21622 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21625 \begin_layout Plain Layout
21626 \begin_inset Formula $\exists$
21636 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21639 \begin_layout Plain Layout
21647 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21650 \begin_layout Plain Layout
21651 \begin_inset Formula $\nexists$
21661 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21664 \begin_layout Plain Layout
21672 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21675 \begin_layout Plain Layout
21676 \begin_inset Formula $\emptyset$
21686 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21689 \begin_layout Plain Layout
21697 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21700 \begin_layout Plain Layout
21701 \begin_inset Formula $\varnothing$
21711 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21714 \begin_layout Plain Layout
21722 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21725 \begin_layout Plain Layout
21726 \begin_inset Formula $\dag$
21736 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21739 \begin_layout Plain Layout
21747 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21750 \begin_layout Plain Layout
21751 \begin_inset Formula $\ddag$
21761 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21764 \begin_layout Plain Layout
21772 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21775 \begin_layout Plain Layout
21779 \begin_layout Plain Layout
21789 \begin_inset Formula $\complement$
21796 \begin_layout Plain Layout
21810 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21813 \begin_layout Plain Layout
21821 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21824 \begin_layout Plain Layout
21825 \begin_inset Formula $\Bbbk$
21839 \begin_inset space \hfill{}
21843 \begin_inset Tabular
21844 <lyxtabular version="3" rows="10" columns="2">
21845 <features booktabs="true" tabularvalignment="middle">
21846 <column alignment="center" valignment="top" width="0pt">
21847 <column alignment="center" valignment="top" width="0pt">
21849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21852 \begin_layout Plain Layout
21858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21861 \begin_layout Plain Layout
21869 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21872 \begin_layout Plain Layout
21880 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21883 \begin_layout Plain Layout
21884 \begin_inset Formula $\prime$
21894 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21897 \begin_layout Plain Layout
21905 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21908 \begin_layout Plain Layout
21909 \begin_inset Formula $\backprime$
21919 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21922 \begin_layout Plain Layout
21930 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21933 \begin_layout Plain Layout
21934 \begin_inset Formula $\mho$
21944 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21947 \begin_layout Plain Layout
21955 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21958 \begin_layout Plain Layout
21959 \begin_inset Formula $\triangle$
21969 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21972 \begin_layout Plain Layout
21980 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21983 \begin_layout Plain Layout
21984 \begin_inset Formula $\angle$
21994 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21997 \begin_layout Plain Layout
22005 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22008 \begin_layout Plain Layout
22009 \begin_inset Formula $\measuredangle$
22019 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22022 \begin_layout Plain Layout
22030 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22033 \begin_layout Plain Layout
22034 \begin_inset Formula $\sphericalangle$
22044 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22047 \begin_layout Plain Layout
22055 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22058 \begin_layout Plain Layout
22059 \begin_inset Formula $\top$
22069 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22072 \begin_layout Plain Layout
22080 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22083 \begin_layout Plain Layout
22084 \begin_inset Formula $\bot$
22100 \begin_layout Standard
22101 \begin_inset Newpage newpage
22107 \begin_layout Subsection
22108 Miscellaneous Symbols
22109 \begin_inset CommandInset label
22111 name "subsec:Miscellaneous-Symbols"
22116 \begin_inset Index idx
22119 \begin_layout Plain Layout
22120 Symbols ! miscellaneous
22128 \begin_layout Standard
22131 \begin_inset Tabular
22132 <lyxtabular version="3" rows="10" columns="2">
22133 <features booktabs="true" tabularvalignment="middle">
22134 <column alignment="center" valignment="top" width="0pt">
22135 <column alignment="center" valignment="top" width="0pt">
22137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22140 \begin_layout Plain Layout
22146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22149 \begin_layout Plain Layout
22157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22160 \begin_layout Plain Layout
22168 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22171 \begin_layout Plain Layout
22172 \begin_inset Formula $\flat$
22182 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22185 \begin_layout Plain Layout
22193 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22196 \begin_layout Plain Layout
22197 \begin_inset Formula $\natural$
22207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22210 \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 $\sharp$
22232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22235 \begin_layout Plain Layout
22243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22246 \begin_layout Plain Layout
22247 \begin_inset Formula $\surd$
22257 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22260 \begin_layout Plain Layout
22268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22271 \begin_layout Plain Layout
22272 \begin_inset Formula $\checkmark$
22282 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22285 \begin_layout Plain Layout
22293 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22296 \begin_layout Plain Layout
22297 \begin_inset Formula $\yen$
22307 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22310 \begin_layout Plain Layout
22318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22321 \begin_layout Plain Layout
22322 \begin_inset Formula $\pounds$
22332 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22335 \begin_layout Plain Layout
22341 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22344 \begin_layout Plain Layout
22345 \begin_inset Formula $\$$
22355 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22358 \begin_layout Plain Layout
22364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22367 \begin_layout Plain Layout
22368 \begin_inset Formula $§$
22382 \begin_inset space \hfill{}
22386 \begin_inset Tabular
22387 <lyxtabular version="3" rows="10" columns="2">
22388 <features booktabs="true" tabularvalignment="middle">
22389 <column alignment="center" valignment="top" width="0pt">
22390 <column alignment="center" valignment="top">
22392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22395 \begin_layout Plain Layout
22401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22404 \begin_layout Plain Layout
22412 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22415 \begin_layout Plain Layout
22423 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22426 \begin_layout Plain Layout
22427 \begin_inset Formula $\hbar$
22437 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22440 \begin_layout Plain Layout
22448 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22451 \begin_layout Plain Layout
22452 \begin_inset Formula $\hslash$
22462 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22465 \begin_layout Plain Layout
22473 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22476 \begin_layout Plain Layout
22477 \begin_inset Formula $\clubsuit$
22487 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22490 \begin_layout Plain Layout
22498 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22501 \begin_layout Plain Layout
22502 \begin_inset Formula $\spadesuit$
22512 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22515 \begin_layout Plain Layout
22523 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22526 \begin_layout Plain Layout
22527 \begin_inset Formula $\bigstar$
22537 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22540 \begin_layout Plain Layout
22548 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22551 \begin_layout Plain Layout
22552 \begin_inset Formula $\blacklozenge$
22562 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22565 \begin_layout Plain Layout
22573 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22576 \begin_layout Plain Layout
22577 \begin_inset Formula $\blacktriangle$
22587 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22590 \begin_layout Plain Layout
22598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22601 \begin_layout Plain Layout
22602 \begin_inset Formula $\blacktriangledown$
22612 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22615 \begin_layout Plain Layout
22623 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22626 \begin_layout Plain Layout
22627 \begin_inset Formula $\bullet$
22641 \begin_inset space \hfill{}
22645 \begin_inset Tabular
22646 <lyxtabular version="3" rows="10" columns="2">
22647 <features booktabs="true" tabularvalignment="middle">
22648 <column alignment="center" valignment="top" width="0pt">
22649 <column alignment="center" valignment="top" width="0pt">
22651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22654 \begin_layout Plain Layout
22660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22663 \begin_layout Plain Layout
22671 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22674 \begin_layout Plain Layout
22682 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22685 \begin_layout Plain Layout
22686 \begin_inset Formula $\diamondsuit$
22696 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22699 \begin_layout Plain Layout
22707 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22710 \begin_layout Plain Layout
22711 \begin_inset Formula $\Diamond$
22721 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22724 \begin_layout Plain Layout
22732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22735 \begin_layout Plain Layout
22736 \begin_inset Formula $\heartsuit$
22746 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22749 \begin_layout Plain Layout
22757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22760 \begin_layout Plain Layout
22761 \begin_inset Formula $\P$
22771 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22774 \begin_layout Plain Layout
22782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22785 \begin_layout Plain Layout
22786 \begin_inset Formula $\copyright$
22796 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22799 \begin_layout Plain Layout
22807 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22810 \begin_layout Plain Layout
22811 \begin_inset Formula $\circledR$
22821 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22824 \begin_layout Plain Layout
22832 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22835 \begin_layout Plain Layout
22836 \begin_inset Formula $\maltese$
22846 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22849 \begin_layout Plain Layout
22857 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22860 \begin_layout Plain Layout
22861 \begin_inset Formula $\diagup$
22871 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22874 \begin_layout Plain Layout
22882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22885 \begin_layout Plain Layout
22886 \begin_inset Formula $\diagdown$
22902 \begin_layout Standard
22903 \begin_inset VSpace medskip
22909 \begin_layout Standard
22910 Some symbols can be displayed in different sizes, see
22911 \begin_inset CommandInset ref
22913 reference "subsec:Font-Sizes"
22920 \begin_layout Subsection
22922 \begin_inset Index idx
22925 \begin_layout Plain Layout
22926 Symbols ! Euro-symbol
22932 \begin_inset Index idx
22935 \begin_layout Plain Layout
22942 \begin_layout Plain Layout
22959 \begin_layout Standard
22960 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22966 \begin_inset Index idx
22969 \begin_layout Plain Layout
22975 must be installed and loaded with the \SpecialChar LaTeX
22979 \begin_layout Standard
22984 usepackage[gennarrow]{eurosym}
22987 \begin_layout Standard
22988 The Euro symbol can now be inserted with the command
22995 \begin_inset Index idx
22998 \begin_layout Plain Layout
23009 \begin_layout Standard
23010 The Euro symbol can directly be inserted with the € key in mathematical
23011 text, without having
23026 can also be inserted in \SpecialChar TeX
23028 The official currency symbol can then be inserted with the command
23035 \begin_inset Index idx
23038 \begin_layout Plain Layout
23046 , that is only available in \SpecialChar TeX
23050 \begin_layout Standard
23054 \begin_layout Plain Layout
23064 \begin_inset Note Note
23067 \begin_layout Plain Layout
23068 The following table will only be displayed when the \SpecialChar LaTeX
23081 \begin_layout Standard
23082 An overview about the different Euro symbols:
23083 \begin_inset Separator parbreak
23089 \begin_layout Standard
23091 \begin_inset Tabular
23092 <lyxtabular version="3" rows="4" columns="3">
23093 <features booktabs="true" tabularvalignment="middle">
23094 <column alignment="center" valignment="top" width="0pt">
23095 <column alignment="center" valignment="top" width="0pt">
23096 <column alignment="center" valignment="top" width="0pt">
23098 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
23101 \begin_layout Plain Layout
23105 \begin_layout Plain Layout
23109 cmidrule[0.08em]{2-3}
23119 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23122 \begin_layout Plain Layout
23128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23131 \begin_layout Plain Layout
23139 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23142 \begin_layout Plain Layout
23148 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23151 \begin_layout Plain Layout
23159 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23162 \begin_layout Plain Layout
23163 \begin_inset Formula $\euro$
23173 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23176 \begin_layout Plain Layout
23182 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23185 \begin_layout Plain Layout
23191 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23194 \begin_layout Plain Layout
23195 \begin_inset Formula $\mbox{€}$
23205 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23208 \begin_layout Plain Layout
23215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23218 \begin_layout Plain Layout
23226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23229 \begin_layout Plain Layout
23233 \begin_layout Plain Layout
23253 \begin_inset Note Note
23256 \begin_layout Plain Layout
23263 is used here only for table borders.
23273 manual for details.
23281 \begin_layout Standard
23285 \begin_layout Plain Layout
23295 \begin_inset Note Note
23298 \begin_layout Plain Layout
23299 The following will be displayed when the \SpecialChar LaTeX
23312 \begin_layout Standard
23313 You need to install the \SpecialChar LaTeX
23318 to see the rest of this subsection in the output.
23321 \begin_layout Standard
23325 \begin_layout Plain Layout
23337 \begin_layout Standard
23338 \begin_inset Newpage newpage
23344 \begin_layout Section
23346 \begin_inset CommandInset label
23348 name "sec:Relations"
23353 \begin_inset Index idx
23356 \begin_layout Plain Layout
23363 \begin_inset Index idx
23366 \begin_layout Plain Layout
23371 \begin_layout Plain Layout
23382 \begin_layout Plain Layout
23397 \begin_layout Standard
23398 All following relations can also be inserted via the toolbar button
23401 arg "math-insert \\leq"
23407 \begin_layout Standard
23408 \begin_inset Tabular
23409 <lyxtabular version="3" rows="17" columns="2">
23410 <features booktabs="true" tabularvalignment="middle">
23411 <column alignment="center" valignment="top" width="0pt">
23412 <column alignment="center" valignment="top" width="0pt">
23414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23417 \begin_layout Plain Layout
23423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23426 \begin_layout Plain Layout
23434 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23437 \begin_layout Plain Layout
23443 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23446 \begin_layout Plain Layout
23447 \begin_inset Formula $<$
23457 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23460 \begin_layout Plain Layout
23468 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23471 \begin_layout Plain Layout
23472 \begin_inset Formula $\le$
23482 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23485 \begin_layout Plain Layout
23493 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23496 \begin_layout Plain Layout
23497 \begin_inset Formula $\ll$
23507 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23510 \begin_layout Plain Layout
23518 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23521 \begin_layout Plain Layout
23522 \begin_inset Formula $\prec$
23532 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23535 \begin_layout Plain Layout
23543 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23546 \begin_layout Plain Layout
23547 \begin_inset Formula $\preceq$
23557 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23560 \begin_layout Plain Layout
23568 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23571 \begin_layout Plain Layout
23572 \begin_inset Formula $\subset$
23582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23585 \begin_layout Plain Layout
23593 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23596 \begin_layout Plain Layout
23597 \begin_inset Formula $\subseteq$
23607 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23610 \begin_layout Plain Layout
23618 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23621 \begin_layout Plain Layout
23622 \begin_inset Formula $\sqsubseteq$
23632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23635 \begin_layout Plain Layout
23643 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23646 \begin_layout Plain Layout
23647 \begin_inset Formula $\in$
23657 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23660 \begin_layout Plain Layout
23668 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23671 \begin_layout Plain Layout
23672 \begin_inset Formula $\vdash$
23682 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23685 \begin_layout Plain Layout
23693 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23696 \begin_layout Plain Layout
23697 \begin_inset Formula $\smile$
23707 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23710 \begin_layout Plain Layout
23718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23721 \begin_layout Plain Layout
23722 \begin_inset Formula $\lhd$
23732 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23735 \begin_layout Plain Layout
23743 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23746 \begin_layout Plain Layout
23747 \begin_inset Formula $\unlhd$
23757 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23760 \begin_layout Plain Layout
23768 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23771 \begin_layout Plain Layout
23772 \begin_inset Formula $\gtrless$
23782 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23785 \begin_layout Plain Layout
23793 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23796 \begin_layout Plain Layout
23797 \begin_inset Formula $\mid$
23807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23810 \begin_layout Plain Layout
23818 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23821 \begin_layout Plain Layout
23822 \begin_inset Formula $\nmid$
23836 \begin_inset space \hfill{}
23840 \begin_inset Tabular
23841 <lyxtabular version="3" rows="17" columns="2">
23842 <features booktabs="true" tabularvalignment="middle">
23843 <column alignment="center" valignment="top" width="0pt">
23844 <column alignment="center" valignment="top" width="0pt">
23846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23849 \begin_layout Plain Layout
23855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23858 \begin_layout Plain Layout
23866 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23869 \begin_layout Plain Layout
23875 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23878 \begin_layout Plain Layout
23879 \begin_inset Formula $=$
23889 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23892 \begin_layout Plain Layout
23900 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23903 \begin_layout Plain Layout
23904 \begin_inset Formula $\not=$
23914 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23917 \begin_layout Plain Layout
23925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23928 \begin_layout Plain Layout
23929 \begin_inset Formula $\equiv$
23939 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23942 \begin_layout Plain Layout
23950 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23953 \begin_layout Plain Layout
23954 \begin_inset Formula $\sim$
23964 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23967 \begin_layout Plain Layout
23975 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23978 \begin_layout Plain Layout
23979 \begin_inset Formula $\simeq$
23989 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23992 \begin_layout Plain Layout
24000 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24003 \begin_layout Plain Layout
24004 \begin_inset Formula $\approx$
24014 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24017 \begin_layout Plain Layout
24025 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24028 \begin_layout Plain Layout
24029 \begin_inset Formula $\cong$
24039 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24042 \begin_layout Plain Layout
24050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24053 \begin_layout Plain Layout
24054 \begin_inset Formula $\bowtie$
24064 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24067 \begin_layout Plain Layout
24075 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24078 \begin_layout Plain Layout
24079 \begin_inset Formula $\notin$
24089 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24092 \begin_layout Plain Layout
24100 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24103 \begin_layout Plain Layout
24104 \begin_inset Formula $\perp$
24114 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24117 \begin_layout Plain Layout
24125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24128 \begin_layout Plain Layout
24129 \begin_inset Formula $\propto$
24139 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24142 \begin_layout Plain Layout
24150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24153 \begin_layout Plain Layout
24154 \begin_inset Formula $\asymp$
24164 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24167 \begin_layout Plain Layout
24175 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24178 \begin_layout Plain Layout
24179 \begin_inset Formula $\doteq$
24189 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24192 \begin_layout Plain Layout
24200 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24203 \begin_layout Plain Layout
24204 \begin_inset Formula $\circeq$
24214 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24217 \begin_layout Plain Layout
24225 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24228 \begin_layout Plain Layout
24229 \begin_inset Formula $\models$
24239 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24242 \begin_layout Plain Layout
24250 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24253 \begin_layout Plain Layout
24254 \begin_inset Formula $\widehat{=}$
24268 \begin_inset space \hfill{}
24272 \begin_inset Tabular
24273 <lyxtabular version="3" rows="17" columns="2">
24274 <features booktabs="true" tabularvalignment="middle">
24275 <column alignment="center" valignment="top" width="0pt">
24276 <column alignment="center" valignment="top" width="0pt">
24278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24281 \begin_layout Plain Layout
24287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24290 \begin_layout Plain Layout
24298 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24301 \begin_layout Plain Layout
24307 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24310 \begin_layout Plain Layout
24311 \begin_inset Formula $>$
24321 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24324 \begin_layout Plain Layout
24332 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24335 \begin_layout Plain Layout
24336 \begin_inset Formula $\ge$
24346 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24349 \begin_layout Plain Layout
24357 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24360 \begin_layout Plain Layout
24361 \begin_inset Formula $\gg$
24371 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24374 \begin_layout Plain Layout
24382 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24385 \begin_layout Plain Layout
24386 \begin_inset Formula $\succ$
24396 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24399 \begin_layout Plain Layout
24407 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24410 \begin_layout Plain Layout
24411 \begin_inset Formula $\succeq$
24421 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24424 \begin_layout Plain Layout
24432 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24435 \begin_layout Plain Layout
24436 \begin_inset Formula $\supset$
24446 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24449 \begin_layout Plain Layout
24457 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24460 \begin_layout Plain Layout
24461 \begin_inset Formula $\supseteq$
24471 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24474 \begin_layout Plain Layout
24482 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24485 \begin_layout Plain Layout
24486 \begin_inset Formula $\sqsupseteq$
24496 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24499 \begin_layout Plain Layout
24507 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24510 \begin_layout Plain Layout
24511 \begin_inset Formula $\ni$
24521 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24524 \begin_layout Plain Layout
24532 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24535 \begin_layout Plain Layout
24536 \begin_inset Formula $\dashv$
24546 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24549 \begin_layout Plain Layout
24557 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24560 \begin_layout Plain Layout
24561 \begin_inset Formula $\frown$
24571 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24574 \begin_layout Plain Layout
24582 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24585 \begin_layout Plain Layout
24586 \begin_inset Formula $\rhd$
24596 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24599 \begin_layout Plain Layout
24607 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24610 \begin_layout Plain Layout
24611 \begin_inset Formula $\unrhd$
24621 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24624 \begin_layout Plain Layout
24632 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24635 \begin_layout Plain Layout
24636 \begin_inset Formula $\lessgtr$
24646 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24649 \begin_layout Plain Layout
24657 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24660 \begin_layout Plain Layout
24661 \begin_inset Formula $\parallel$
24671 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24674 \begin_layout Plain Layout
24682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24685 \begin_layout Plain Layout
24686 \begin_inset Formula $\nparallel$
24702 \begin_layout Standard
24703 \begin_inset VSpace medskip
24718 are bigger than the equal looking operators
24733 \begin_layout Standard
24735 supports also many special relations.
24736 Use the toolbar button
24739 arg "math-insert \\leqq"
24742 to see a list of these relations.
24745 \begin_layout Standard
24746 Relations are, in contrary to symbols, always surrounded by space.
24749 \begin_layout Standard
24750 Relations with labels can be created with the command
24757 \begin_inset Index idx
24760 \begin_layout Plain Layout
24769 \begin_inset Separator parbreak
24775 \begin_layout Standard
24777 \begin_inset Tabular
24778 <lyxtabular version="3" rows="2" columns="2">
24779 <features booktabs="true" tabularvalignment="middle">
24780 <column alignment="center" valignment="top" width="0pt">
24781 <column alignment="center" valignment="top">
24783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24786 \begin_layout Plain Layout
24792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24795 \begin_layout Plain Layout
24802 <row topspace="1.5mm">
24803 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24806 \begin_layout Plain Layout
24810 \begin_inset space \textvisiblespace{}
24818 \begin_inset space \textvisiblespace{}
24822 \begin_inset Formula $\downarrow$
24828 \begin_inset space \textvisiblespace{}
24832 \begin_inset space \textvisiblespace{}
24840 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24843 \begin_layout Plain Layout
24844 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24860 \begin_layout Section
24864 \begin_layout Subsection
24865 Predefined Functions
24866 \begin_inset CommandInset label
24868 name "subsec:Predefined-Functions"
24873 \begin_inset Index idx
24876 \begin_layout Plain Layout
24877 Functions ! predefined
24885 \begin_layout Standard
24886 In general, variables are set
24890 in mathematical expressions, but not function names, because
24891 \begin_inset Formula $sin$
24894 could be misunderstood as
24895 \begin_inset Formula $s\cdot i\cdot n$
24899 Therefore there are predefined functionswhich are additionally a bit separated
24901 They are inserted as commands starting with a backslash before their name.
24902 \begin_inset Separator parbreak
24908 \begin_layout Standard
24910 \begin_inset Tabular
24911 <lyxtabular version="3" rows="2" columns="2">
24912 <features booktabs="true" tabularvalignment="middle">
24913 <column alignment="center" valignment="top" width="0pt">
24914 <column alignment="center" valignment="top" width="0pt">
24916 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24919 \begin_layout Plain Layout
24925 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24928 \begin_layout Plain Layout
24936 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24939 \begin_layout Plain Layout
24945 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24948 \begin_layout Plain Layout
24949 \begin_inset Formula $Asin(x)+B$
24963 \begin_inset space \quad{}
24967 \begin_inset Tabular
24968 <lyxtabular version="3" rows="2" columns="2">
24969 <features booktabs="true" tabularvalignment="middle">
24970 <column alignment="center" valignment="top" width="0pt">
24971 <column alignment="center" valignment="top" width="0pt">
24973 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24976 \begin_layout Plain Layout
24982 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24985 \begin_layout Plain Layout
24993 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24996 \begin_layout Plain Layout
25004 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25007 \begin_layout Plain Layout
25008 \begin_inset Formula $A\sin(x)+B$
25024 \begin_layout Standard
25025 The following functions are predefined:
25028 \begin_layout Standard
25029 \begin_inset VSpace -2mm
25035 \begin_layout Standard
25037 \begin_inset Tabular
25038 <lyxtabular version="3" rows="9" columns="4">
25039 <features booktabs="true" tabularvalignment="middle">
25040 <column alignment="center" valignment="top" width="0pt">
25041 <column alignment="center" valignment="top" width="0pt">
25042 <column alignment="center" valignment="top" width="0pt">
25043 <column alignment="center" valignment="top" width="0pt">
25045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25048 \begin_layout Plain Layout
25054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25057 \begin_layout Plain Layout
25063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25066 \begin_layout Plain Layout
25072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25075 \begin_layout Plain Layout
25083 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25086 \begin_layout Plain Layout
25094 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25097 \begin_layout Plain Layout
25105 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25108 \begin_layout Plain Layout
25116 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25119 \begin_layout Plain Layout
25129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25132 \begin_layout Plain Layout
25140 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25143 \begin_layout Plain Layout
25151 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25154 \begin_layout Plain Layout
25162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25165 \begin_layout Plain Layout
25175 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25178 \begin_layout Plain Layout
25186 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25189 \begin_layout Plain Layout
25197 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25200 \begin_layout Plain Layout
25208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25211 \begin_layout Plain Layout
25221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25224 \begin_layout Plain Layout
25232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25235 \begin_layout Plain Layout
25243 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25246 \begin_layout Plain Layout
25254 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25257 \begin_layout Plain Layout
25267 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25270 \begin_layout Plain Layout
25278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25281 \begin_layout Plain Layout
25289 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25292 \begin_layout Plain Layout
25300 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25303 \begin_layout Plain Layout
25313 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25316 \begin_layout Plain Layout
25324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25327 \begin_layout Plain Layout
25335 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25338 \begin_layout Plain Layout
25346 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25349 \begin_layout Plain Layout
25359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25362 \begin_layout Plain Layout
25370 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25373 \begin_layout Plain Layout
25381 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25384 \begin_layout Plain Layout
25392 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25395 \begin_layout Plain Layout
25405 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25408 \begin_layout Plain Layout
25416 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25419 \begin_layout Plain Layout
25427 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25430 \begin_layout Plain Layout
25438 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25441 \begin_layout Plain Layout
25457 \begin_layout Standard
25458 They can also be inserted with the math toolbar button
25461 arg "math-insert \\functions"
25467 \begin_layout Subsection
25468 Self-defined Functions
25469 \begin_inset Index idx
25472 \begin_layout Plain Layout
25473 Functions ! self-defined
25481 \begin_layout Standard
25482 To use a function that is not predefined, like for example the sign function
25483 sgn(x), there are two possibilities:
25486 \begin_layout Itemize
25487 Define the function by inserting the following line to the \SpecialChar LaTeX
25492 \begin_layout Plain Layout
25497 DeclareMathOperator
25500 \begin_inset CommandInset ref
25502 reference "subsec:Self-defined-Operators"
25512 \begin_inset Newline newline
25516 \begin_inset VSpace -3mm
25520 \begin_inset Newline newline
25527 DeclareMathOperator{
25532 \begin_inset Index idx
25535 \begin_layout Plain Layout
25540 DeclareMathOperator
25546 \begin_inset Newline newline
25550 \begin_inset VSpace -2mm
25554 \begin_inset Newline newline
25557 Now the new defined function can be called with the command
25566 \begin_layout Itemize
25567 Write the formula as usual, mark the formula name, in our example the letters
25572 , and change it to mathematical text.
25573 Finally, a space is inserted between prefactor and function.
25576 \begin_layout Standard
25577 The result is the same with both methods as with a predefined function
25581 \begin_layout Plain Layout
25582 In \SpecialChar LyX
25583 self-defined functions are displayed red, predefined ones black.
25589 \begin_inset Separator parbreak
25595 \begin_layout Standard
25597 \begin_inset Tabular
25598 <lyxtabular version="3" rows="3" columns="2">
25599 <features booktabs="true" tabularvalignment="middle">
25600 <column alignment="center" valignment="top" width="0pt">
25601 <column alignment="center" valignment="top" width="0pt">
25603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25606 \begin_layout Plain Layout
25612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25615 \begin_layout Plain Layout
25623 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25626 \begin_layout Plain Layout
25634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25637 \begin_layout Plain Layout
25638 \begin_inset Formula $A\sgn(x)+B$
25648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25651 \begin_layout Plain Layout
25655 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25666 \begin_layout Plain Layout
25667 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25683 \begin_layout Standard
25684 The first method is more suitable when the self-defined function should
25685 be used several times.
25688 \begin_layout Subsection
25690 \begin_inset Index idx
25693 \begin_layout Plain Layout
25702 \begin_layout Standard
25703 For limits, in addition to the commands
25710 \begin_inset Index idx
25713 \begin_layout Plain Layout
25733 the following functions are defined:
25734 \begin_inset Separator parbreak
25740 \begin_layout Standard
25742 \begin_inset Tabular
25743 <lyxtabular version="3" rows="5" columns="2">
25744 <features booktabs="true" tabularvalignment="middle">
25745 <column alignment="center" valignment="top" width="0pt">
25746 <column alignment="center" valignment="top" width="0pt">
25748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25751 \begin_layout Plain Layout
25757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25760 \begin_layout Plain Layout
25768 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25771 \begin_layout Plain Layout
25779 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25782 \begin_layout Plain Layout
25783 \begin_inset Formula $\varliminf$
25792 <row topspace="1.5mm">
25793 <cell alignment="center" valignment="top" usebox="none">
25796 \begin_layout Plain Layout
25804 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25807 \begin_layout Plain Layout
25808 \begin_inset Formula $\varlimsup$
25817 <row topspace="1.5mm">
25818 <cell alignment="center" valignment="top" usebox="none">
25821 \begin_layout Plain Layout
25829 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25832 \begin_layout Plain Layout
25833 \begin_inset Formula $\varprojlim$
25842 <row topspace="1.5mm" bottomspace="1mm">
25843 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25846 \begin_layout Plain Layout
25854 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25857 \begin_layout Plain Layout
25858 \begin_inset Formula $\varinjlim$
25874 \begin_layout Standard
25875 \begin_inset VSpace medskip
25878 The limit is created by inserting a subscript.
25879 It is set right beside the function in an inline formula:
25882 \begin_layout Standard
25884 \begin_inset Tabular
25885 <lyxtabular version="3" rows="2" columns="2">
25886 <features booktabs="true" tabularvalignment="middle">
25887 <column alignment="center" valignment="top" width="0pt">
25888 <column alignment="center" valignment="top" width="0pt">
25890 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25893 \begin_layout Plain Layout
25899 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25902 \begin_layout Plain Layout
25910 <cell alignment="center" valignment="top" usebox="none">
25913 \begin_layout Plain Layout
25919 \begin_inset space \textvisiblespace{}
25923 \begin_inset space \textvisiblespace{}
25931 <cell alignment="center" valignment="top" usebox="none">
25934 \begin_layout Plain Layout
25935 \begin_inset Formula $\lim_{x\to A}x=B$
25951 \begin_layout Standard
25952 In a displayed formula the limit is set below the formula, as usual:
25953 \begin_inset Formula
25963 \begin_layout Standard
25964 \begin_inset VSpace medskip
25970 \begin_layout Standard
25971 How to adjust the typesetting of the limits see
25972 \begin_inset CommandInset ref
25974 reference "subsec:Operator-Limits"
25981 \begin_layout Subsection
25983 \begin_inset Index idx
25986 \begin_layout Plain Layout
25987 Functions ! modulo-
25995 \begin_layout Standard
25996 The modulo-function is special, because it exists in four variants.
25997 The variants in a displayed formula are:
25998 \begin_inset Formula
26000 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26001 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
26002 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
26003 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
26004 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
26012 \begin_layout Standard
26013 In an inline formula less space is set before the function names for all
26015 By default the modulo-functions take only the first following character
26017 To use more than one character, one has to put them into \SpecialChar TeX
26019 \begin_inset Formula
26021 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26022 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
26023 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26031 \begin_layout Section
26033 \begin_inset Index idx
26036 \begin_layout Plain Layout
26045 \begin_layout Standard
26046 The characters ^ and _ would normally create a superscript and subscript,
26048 To get these characters you have to insert them with a leading
26051 \begin_inset Separator parbreak
26057 \begin_layout Standard
26060 \begin_inset Tabular
26061 <lyxtabular version="3" rows="3" columns="2">
26062 <features booktabs="true" tabularvalignment="middle">
26063 <column alignment="left" valignment="top" width="0pt">
26064 <column alignment="block" valignment="top">
26066 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26069 \begin_layout Plain Layout
26075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26078 \begin_layout Plain Layout
26086 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26089 \begin_layout Plain Layout
26093 \begin_inset space \textvisiblespace{}
26101 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26104 \begin_layout Plain Layout
26105 \begin_inset Formula $\mathcircumflex$
26115 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26118 \begin_layout Plain Layout
26126 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26129 \begin_layout Plain Layout
26130 \begin_inset Formula $\_$
26146 \begin_layout Subsection
26147 Special Characters in Mathematical Text
26150 \begin_layout Standard
26151 The following commands can only be used in mathematical text or in \SpecialChar TeX
26155 \begin_layout Standard
26156 \begin_inset space \hfill{}
26160 \begin_inset Tabular
26161 <lyxtabular version="3" rows="8" columns="2">
26162 <features booktabs="true" tabularvalignment="middle">
26163 <column alignment="left" valignment="top" width="0pt">
26164 <column alignment="block" valignment="top">
26166 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26169 \begin_layout Plain Layout
26175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26178 \begin_layout Plain Layout
26186 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26189 \begin_layout Plain Layout
26197 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26200 \begin_layout Plain Layout
26201 \begin_inset Formula $\textrm{œ}$
26211 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26214 \begin_layout Plain Layout
26222 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26225 \begin_layout Plain Layout
26226 \begin_inset Formula $\textrm{Œ}$
26236 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26239 \begin_layout Plain Layout
26247 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26250 \begin_layout Plain Layout
26251 \begin_inset Formula $\textrm{æ}$
26261 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26264 \begin_layout Plain Layout
26272 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26275 \begin_layout Plain Layout
26276 \begin_inset Formula $\textrm{Æ}$
26286 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26289 \begin_layout Plain Layout
26297 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26300 \begin_layout Plain Layout
26301 \begin_inset Formula $\textrm{\aa}$
26311 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26314 \begin_layout Plain Layout
26318 \begin_inset Index idx
26321 \begin_layout Plain Layout
26328 \begin_layout Plain Layout
26349 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26352 \begin_layout Plain Layout
26353 \begin_inset Formula $\textrm{Å}$
26363 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26366 \begin_layout Plain Layout
26374 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26377 \begin_layout Plain Layout
26378 \begin_inset Formula $\textrm{ı}$
26392 \begin_inset space \hfill{}
26396 \begin_inset Tabular
26397 <lyxtabular version="3" rows="8" columns="2">
26398 <features booktabs="true" tabularvalignment="middle">
26399 <column alignment="left" valignment="top" width="0pt">
26400 <column alignment="center" valignment="top">
26402 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26405 \begin_layout Plain Layout
26407 \begin_inset Note Note
26410 \begin_layout Plain Layout
26412 \begin_inset space \thinspace{}
26415 mm is used for separation, because otherwise the output will be ¡ and ¿
26426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26429 \begin_layout Plain Layout
26437 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26440 \begin_layout Plain Layout
26448 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26451 \begin_layout Plain Layout
26452 \begin_inset Formula $\textrm{ø}$
26462 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26465 \begin_layout Plain Layout
26473 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26476 \begin_layout Plain Layout
26477 \begin_inset Formula $\textrm{Ø}$
26487 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26490 \begin_layout Plain Layout
26498 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26501 \begin_layout Plain Layout
26502 \begin_inset Formula $\textrm{ł}$
26512 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26515 \begin_layout Plain Layout
26523 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26526 \begin_layout Plain Layout
26527 \begin_inset Formula $\textrm{Ł}$
26537 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26540 \begin_layout Plain Layout
26542 \begin_inset space \hspace{}
26547 \begin_inset space \textvisiblespace{}
26555 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26558 \begin_layout Plain Layout
26559 \begin_inset Formula $\textrm{!`}$
26569 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26572 \begin_layout Plain Layout
26574 \begin_inset space \hspace{}
26579 \begin_inset space \textvisiblespace{}
26587 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26590 \begin_layout Plain Layout
26591 \begin_inset Formula $\textrm{?`}$
26601 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26604 \begin_layout Plain Layout
26612 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26615 \begin_layout Plain Layout
26616 \begin_inset Formula $\textrm{ȷ}$
26630 \begin_inset space \hfill{}
26636 \begin_layout Standard
26638 \begin_inset Formula $\textrm{\textrm{Å}}$
26642 \begin_inset Formula $\textrm{\textrm{Ø}}$
26645 can also be inserted via the math toolbar button
26648 arg "math-insert \\digamma"
26654 \begin_layout Standard
26655 An exception are the commands
26658 \begin_inset space \hspace{}
26667 \begin_inset space \hspace{}
26673 , because they can be inserted in \SpecialChar LyX
26677 \begin_layout Subsection
26679 \begin_inset CommandInset label
26681 name "subsec:Accents-in-Text"
26686 \begin_inset Index idx
26689 \begin_layout Plain Layout
26698 \begin_layout Standard
26699 With the following commands all letters can be accented.
26700 The commands must be inserted in \SpecialChar TeX
26704 \begin_layout Standard
26705 \begin_inset space \hfill{}
26709 \begin_inset Tabular
26710 <lyxtabular version="3" rows="8" columns="2">
26711 <features booktabs="true" tabularvalignment="middle">
26712 <column alignment="left" valignment="top" width="0pt">
26713 <column alignment="block" valignment="top">
26715 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26718 \begin_layout Plain Layout
26724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26727 \begin_layout Plain Layout
26735 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26738 \begin_layout Plain Layout
26742 \begin_inset Quotes grd
26750 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26753 \begin_layout Plain Layout
26757 \begin_layout Plain Layout
26773 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26776 \begin_layout Plain Layout
26784 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26787 \begin_layout Plain Layout
26791 \begin_layout Plain Layout
26807 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26810 \begin_layout Plain Layout
26814 \begin_inset space \textvisiblespace{}
26822 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26825 \begin_layout Plain Layout
26829 \begin_layout Plain Layout
26845 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26848 \begin_layout Plain Layout
26856 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26859 \begin_layout Plain Layout
26863 \begin_layout Plain Layout
26879 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26882 \begin_layout Plain Layout
26886 \begin_inset space \textvisiblespace{}
26894 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26897 \begin_layout Plain Layout
26901 \begin_layout Plain Layout
26917 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26920 \begin_layout Plain Layout
26924 \begin_inset space \textvisiblespace{}
26932 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26935 \begin_layout Plain Layout
26939 \begin_layout Plain Layout
26955 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26958 \begin_layout Plain Layout
26962 \begin_inset space \textvisiblespace{}
26970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26973 \begin_layout Plain Layout
26977 \begin_layout Plain Layout
26997 \begin_inset space \hfill{}
27001 \begin_inset Tabular
27002 <lyxtabular version="3" rows="8" columns="2">
27003 <features booktabs="true" tabularvalignment="middle">
27004 <column alignment="left" valignment="top" width="0pt">
27005 <column alignment="center" valignment="top">
27007 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27010 \begin_layout Plain Layout
27016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27019 \begin_layout Plain Layout
27027 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27030 \begin_layout Plain Layout
27034 \begin_inset space \textvisiblespace{}
27042 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27045 \begin_layout Plain Layout
27049 \begin_layout Plain Layout
27065 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27068 \begin_layout Plain Layout
27076 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27079 \begin_layout Plain Layout
27083 \begin_layout Plain Layout
27099 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27102 \begin_layout Plain Layout
27106 \begin_inset Index idx
27109 \begin_layout Plain Layout
27120 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27123 \begin_layout Plain Layout
27127 \begin_layout Plain Layout
27143 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27146 \begin_layout Plain Layout
27154 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27157 \begin_layout Plain Layout
27161 \begin_layout Plain Layout
27177 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27180 \begin_layout Plain Layout
27184 \begin_inset space \textvisiblespace{}
27192 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27195 \begin_layout Plain Layout
27199 \begin_layout Plain Layout
27215 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27218 \begin_layout Plain Layout
27222 \begin_inset space \textvisiblespace{}
27230 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27233 \begin_layout Plain Layout
27237 \begin_layout Plain Layout
27253 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27256 \begin_layout Plain Layout
27260 \begin_inset space \textvisiblespace{}
27268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27271 \begin_layout Plain Layout
27275 \begin_layout Plain Layout
27295 \begin_inset space \hfill{}
27301 \begin_layout Standard
27302 \begin_inset VSpace medskip
27311 also two different characters can be accented.
27317 \begin_inset space \textvisiblespace{}
27326 \begin_layout Plain Layout
27338 \begin_layout Standard
27351 can in combination with vowels directly be inserted with the keyboard without
27352 using \SpecialChar TeX
27354 The same applies for the tilde
27358 \begin_layout Plain Layout
27359 This only applies for keyboards where the tilde is defined as accent.
27368 in combination with
27383 \begin_layout Standard
27426 and accents that are inserted directly with the keyboard are also available
27427 in mathematical text.
27428 For the other accents there are special math commands to be used in formulas,
27430 \begin_inset CommandInset ref
27432 reference "subsec:Accents-for-one"
27439 \begin_layout Standard
27440 \begin_inset VSpace bigskip
27443 Furthermore, with the command
27450 \begin_inset Index idx
27453 \begin_layout Plain Layout
27461 all numbers and letters can be set into a circle, quasi accented with a
27462 circle, similar to the copyright symbol.
27465 \begin_layout Standard
27467 \begin_inset Tabular
27468 <lyxtabular version="3" rows="3" columns="2">
27469 <features booktabs="true" tabularvalignment="middle">
27470 <column alignment="center" valignment="top" width="0pt">
27471 <column alignment="center" valignment="top">
27473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27476 \begin_layout Plain Layout
27482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27485 \begin_layout Plain Layout
27493 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27496 \begin_layout Plain Layout
27504 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27507 \begin_layout Plain Layout
27511 \begin_layout Plain Layout
27526 <row topspace="1mm">
27527 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27530 \begin_layout Plain Layout
27541 raisebox{-1.5pt}{W}}
27546 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27549 \begin_layout Plain Layout
27553 \begin_layout Plain Layout
27583 \begin_layout Standard
27584 One has to take care that the character fits in the circle.
27595 \begin_layout Plain Layout
27597 \begin_inset CommandInset ref
27599 reference "subsec:Font-Sizes"
27608 specifies thereby the size of the circle.
27619 \begin_layout Plain Layout
27621 \begin_inset CommandInset ref
27623 reference "subsec:Boxes-without-Frame"
27632 the character can be centered.
27635 \begin_layout Subsection
27637 \begin_inset Index idx
27640 \begin_layout Plain Layout
27649 \begin_layout Standard
27650 Old-style figures (also known as old-style numerals) are created with the
27658 \begin_inset Index idx
27661 \begin_layout Plain Layout
27670 The command can be used in formulas and in \SpecialChar TeX
27672 The command scheme is:
27675 \begin_layout Standard
27680 oldstylenums{number}
27683 \begin_layout Standard
27688 oldstylenums{0123456789
27691 \begin_inset Formula $\oldstylenums{0123456789}$
27697 \begin_layout Section
27699 \begin_inset CommandInset label
27701 name "sec:Formula-Styles"
27706 \begin_inset Index idx
27709 \begin_layout Plain Layout
27718 \begin_layout Itemize
27719 There are two different alignment styles:
27720 \begin_inset Separator parbreak
27727 \begin_layout Description
27728 Centered is the predefined standard
27731 \begin_layout Description
27732 Indented for this the option
27736 must be inserted in the menu
27738 Document\SpecialChar menuseparator
27744 \begin_inset space ~
27750 \begin_layout Standard
27755 is used, the indentation can be adjusted with the length
27762 \begin_inset Index idx
27765 \begin_layout Plain Layout
27774 Should the distance be 15
27775 \begin_inset space \thinspace{}
27778 mm, the following command line is inserted in the \SpecialChar LaTeX
27782 \begin_layout Standard
27792 \begin_layout Standard
27793 When no length is specified, the predefined value of 30
27794 \begin_inset space \thinspace{}
27801 \begin_layout Itemize
27802 And two different numbering styles:
27803 \begin_inset Separator parbreak
27810 \begin_layout Description
27811 Right is the predefined standard
27814 \begin_layout Description
27815 Left for this the option
27819 must be inserted in the menu
27821 Document\SpecialChar menuseparator
27827 \begin_inset space ~
27834 \begin_layout Standard
27843 can also be used together.
27844 In this case both options are inserted, separated by a comma.
27847 \begin_layout Standard
27848 The chosen styles are used for all displayed formulas of the document.
27849 When both, centered and indented formulas should be created in a document,
27855 The indented formulas are then set in a flalign environment, see
27856 \begin_inset CommandInset ref
27858 reference "subsec:Flalign-Environment"
27865 \begin_layout Section
27867 \begin_inset CommandInset label
27869 name "sec:Multiline-Formulas"
27874 \begin_inset Index idx
27877 \begin_layout Plain Layout
27878 Formula ! multiline
27886 \begin_layout Subsection
27890 \begin_layout Standard
27891 In \SpecialChar LyX
27892 multiline formulas are created by pressing
27895 arg "newline-insert newline"
27899 This creates either an
27901 eqnarray environment
27903 that is described in
27904 \begin_inset CommandInset ref
27906 reference "subsec:Eqnarray-Environment"
27910 or, when the option
27912 Use AMS math package
27914 in the document settings is selected, an
27918 that is described in
27919 \begin_inset CommandInset ref
27921 reference "subsec:Standard-align-Environment"
27926 The align environment is recommended because it provides in any case a
27927 typographically correct output.
27930 \begin_layout Standard
27931 There are other multiline formula environments that can be created via the
27934 Insert\SpecialChar menuseparator
27938 These environments are described in the following sections.
27941 \begin_layout Standard
27942 In all multiline formula environments a new line is created by pressing
27946 arg "newline-insert newline"
27950 To add or delete lines, the math toolbar buttons
27953 arg "inset-modify tabular append-row"
27959 arg "inset-modify tabular delete-row"
27962 , respectively, or the menu
27964 Edit\SpecialChar menuseparator
27970 \begin_layout Subsubsection
27972 \begin_inset CommandInset label
27974 name "subsec:Line-Separation"
27979 \begin_inset Index idx
27982 \begin_layout Plain Layout
27983 Formula ! multiline ! Line separation
27991 \begin_layout Standard
27992 There is sometimes not enough space in multiline formulas between the lines:
27993 \begin_inset Formula
27995 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}\\
27996 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
28004 \begin_layout Standard
28005 In \SpecialChar LaTeX
28006 additional line space is specified as optional argument of the new line
28008 This is not yet possible in \SpecialChar LyX
28013 \begin_layout Plain Layout
28015 \begin_inset CommandInset href
28017 name "LyX-bug #1505"
28018 target "http://www.lyx.org/trac/ticket/1505"
28027 , therefore the whole formula must be inserted in \SpecialChar TeX
28029 To add in our example space, the command
28037 is inserted at the end of the first line.
28042 \begin_layout Plain Layout
28049 \begin_layout Plain Layout
28051 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28054 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28061 \begin_layout Plain Layout
28065 left(B^{2}+x_{0}^{2}
28073 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28078 \begin_layout Plain Layout
28090 \begin_layout Standard
28091 \begin_inset VSpace bigskip
28094 To set the line separation for all lines in a formula, the length
28101 \begin_inset Index idx
28104 \begin_layout Plain Layout
28114 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28125 \begin_inset space \thinspace{}
28130 \begin_inset space \thinspace{}
28133 mm additional line separation as in the previous example, the command
28136 \begin_layout Standard
28146 \begin_layout Standard
28147 is inserted in \SpecialChar TeX
28148 mode before the formula.
28149 This requires that the \SpecialChar LaTeX
28158 \begin_layout Plain Layout
28163 is part of every \SpecialChar LaTeX
28164 standard installation.
28170 \begin_inset Index idx
28173 \begin_layout Plain Layout
28179 was loaded in \SpecialChar LaTeX
28180 -preamble with the line
28183 \begin_layout Standard
28191 \begin_layout Standard
28196 \begin_layout Plain Layout
28208 \begin_inset Formula
28210 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}\\
28211 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
28219 \begin_layout Standard
28223 \begin_layout Plain Layout
28234 To get back to the predefined distance,
28240 is set to the value 3
28241 \begin_inset space \thinspace{}
28247 \begin_layout Subsubsection
28249 \begin_inset CommandInset label
28251 name "subsec:Column-Separation"
28256 \begin_inset Index idx
28259 \begin_layout Plain Layout
28260 Formula ! multiline ! Column separation
28268 \begin_layout Standard
28269 Multiline formulas form a matrix.
28270 A formula in the eqnarray environment is for example a matrix with three
28272 By changing the column separation in this environment, the space beside
28273 the relation sign can be changed.
28276 \begin_layout Standard
28277 The column separation is specified with the length
28284 \begin_inset Index idx
28287 \begin_layout Plain Layout
28296 \begin_inset Newline newline
28299 column separation = 2
28300 \begin_inset space \thinspace{}
28310 \begin_inset Newline newline
28316 \begin_layout Standard
28326 \begin_layout Standard
28327 inserted in \SpecialChar TeX
28328 mode, sets for all following formulas a column separation of
28330 \begin_inset space \thinspace{}
28334 To get back to the predefined distance,
28341 \begin_inset space \thinspace{}
28347 \begin_layout Standard
28349 \begin_inset space \thinspace{}
28352 cm column separation:
28356 \begin_layout Plain Layout
28368 \begin_inset Formula
28376 A formula with the predefined column separation for matrices of 10
28377 \begin_inset space \thinspace{}
28384 \begin_layout Plain Layout
28396 \begin_inset Formula
28407 \begin_layout Subsubsection
28409 \begin_inset Index idx
28412 \begin_layout Plain Layout
28421 \begin_layout Standard
28422 Long formulas can be typeset using these methods:
28425 \begin_layout Itemize
28426 When one side of the equation is much shorter than the line width, this
28427 one is chosen for the left side and the right side is typeset over two
28429 \begin_inset Formula
28431 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 \\
28432 & & -\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}
28437 The minus sign at the beginning of the second line does normally not appear
28438 as an operator because it is the first character of the line.
28439 Thus it would not be surrounded by space and could not be distinguished
28440 from the fraction bar.
28442 \begin_inset space \thinspace{}
28445 pt space was inserted behind the minus sign with the command
28455 \begin_layout Plain Layout
28463 \begin_inset CommandInset ref
28465 reference "subsec:Variable-Space"
28475 \begin_inset Index idx
28478 \begin_layout Plain Layout
28489 \begin_layout Itemize
28490 When both sides of the equation are too long, the command
28497 \begin_inset Index idx
28500 \begin_layout Plain Layout
28509 It is inserted in the first column of the first line and causes all further
28510 insertions to overwrite the following columns:
28511 \begin_inset Formula
28513 \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 \\
28514 & & -\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 \\
28515 & & =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}
28520 After the insertion of
28526 , the cursor is in a purple box that is a bit shifted to the left from the
28528 In this the formula is inserted.
28529 \begin_inset Newline newline
28532 The content of the further lines is inserted to the second or another formula
28534 The greater the column number where it was inserted, the larger the indentation.
28535 \begin_inset VSpace medskip
28539 \begin_inset Newline newline
28543 \begin_inset Note Greyedout
28546 \begin_layout Plain Layout
28547 Note the following when using
28556 \begin_layout Itemize
28557 The formula doesn't use the full page width.
28559 \begin_inset space \thinspace{}
28563 \begin_inset space \space{}
28567 \begin_inset Formula $-B^{2}$
28570 is added to the first line in the above example, it would have been outside
28572 To better use the width, negative space can be inserted at the beginning
28576 \begin_layout Itemize
28577 Due to a bug in \SpecialChar LyX
28578 the cursor cannot be set with the mouse into the first
28583 \begin_layout Plain Layout
28584 \begin_inset CommandInset href
28586 name "LyX-bug #1429"
28587 target "http://www.lyx.org/trac/ticket/1429"
28596 One can only set the cursor at the beginning of the line and move it with
28605 \begin_layout Itemize
28606 Other methods to set long formulas are offered by the environments described
28608 \begin_inset CommandInset ref
28610 reference "subsec:Multline-Environment"
28615 \begin_inset CommandInset ref
28617 reference "subsec:Multiline-Formula-Parts"
28624 \begin_layout Subsubsection
28625 Multiline Fractions
28626 \begin_inset CommandInset label
28628 name "subsec:Multiline-Fractions"
28633 \begin_inset Index idx
28636 \begin_layout Plain Layout
28637 Fractions ! multiline
28645 \begin_layout Standard
28646 There are cases where the denominator and/or the numerator of a fraction
28647 is so long that the fraction does not fit into one line.
28648 It is then necessary to add a line break within the fraction.
28649 This can be done using the command
28656 \begin_inset Index idx
28659 \begin_layout Plain Layout
28668 To activate it, set in the document settings under
28671 \begin_inset space ~
28681 \begin_inset Index idx
28684 \begin_layout Plain Layout
28685 Packages ! mathtools
28693 \begin_inset space ~
28708 \begin_layout Standard
28713 splitfrac{first line}{second line}
28716 \begin_layout Standard
28717 and is used as denominator and/or numerator:
28720 \begin_layout Standard
28721 \begin_inset Formula
28723 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}
28728 The command for the first numerator above is:
28731 \begin_layout Standard
28736 splitfrac{xy+xy+xy+xy+xy
28737 \begin_inset space \textvisiblespace{}
28745 \begin_layout Subsubsection
28747 \begin_inset CommandInset label
28749 name "subsec:Multiline-Brackets"
28754 \begin_inset Index idx
28757 \begin_layout Plain Layout
28758 Brackets ! for multiline expressions
28766 \begin_layout Standard
28767 For brackets spanning multiple lines the following problem occurs:
28768 \begin_inset Formula
28770 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28771 & & \left.\cdots+B-D\right]
28779 \begin_layout Standard
28780 The closing bracket is smaller than the opening bracket because brackets
28781 with variable size may not span multiple lines.
28784 \begin_layout Standard
28785 To set the bracket size for the second line correctly, the first line is
28793 \begin_inset Index idx
28796 \begin_layout Plain Layout
28804 and the second line with
28812 \begin_layout Plain Layout
28826 \begin_inset CommandInset ref
28828 reference "subsec:Automatic-Bracket-Size"
28840 \begin_inset Index idx
28843 \begin_layout Plain Layout
28866 \begin_inset space \textvisiblespace{}
28876 \begin_inset space \textvisiblespace{}
28886 \begin_inset space \textvisiblespace{}
28892 \begin_inset Formula $\downarrow$
28898 \begin_inset Index idx
28901 \begin_layout Plain Layout
28909 is inserted, because the multiplication operator with its limits is the
28910 largest symbol in the first line and this should be the size for the bracket
28911 in the second line.
28914 \begin_layout Standard
28915 The result is this:
28916 \begin_inset Formula
28918 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28919 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28927 \begin_layout Subsection
28931 \begin_layout Standard
28932 Align environments can be used for every kind of multiline formulas.
28933 They are especially useful to set several formulas side by side.
28936 \begin_layout Standard
28937 Align environments consist of columns.
28938 The odd columns are right aligned, the even ones left aligned.
28939 Every line in an Align environment can be numbered.
28942 \begin_layout Standard
28943 Align environments are created via the menu
28945 Insert\SpecialChar menuseparator
28951 Edit\SpecialChar menuseparator
28952 Math\SpecialChar menuseparator
28953 Change Formula Type
28955 already existing formulas can be converted to Align environments.
28958 \begin_layout Standard
28959 To add or delete columns, the math toolbar buttons
28962 arg "inset-modify tabular append-column"
28968 arg "inset-modify tabular delete-column"
28971 , respectively, or the menu
28973 Edit\SpecialChar menuseparator
28979 \begin_layout Subsubsection
28980 Standard align Environment
28981 \begin_inset CommandInset label
28983 name "subsec:Standard-align-Environment"
28988 \begin_inset Index idx
28991 \begin_layout Plain Layout
28992 Formula ! multiline ! align environment
29000 \begin_layout Standard
29001 This Align environment is created by pressing
29004 arg "newline-insert newline"
29007 in a formula or by the menu
29009 Insert\SpecialChar menuseparator
29010 Math\SpecialChar menuseparator
29011 AMS align Environment
29016 \begin_layout Standard
29017 An example for two formulas set side by side, that are created with a four
29018 column align environment:
29019 \begin_inset Formula
29021 A & =\sin(B) & C & =D\\
29022 C & \ne A & B & \ne D
29027 As it can be seen, the formulas in this environment are placed so as if
29036 \begin_layout Plain Layout
29044 \begin_inset CommandInset ref
29046 reference "subsec:Variable-Space"
29057 before the first and after every even column.
29058 When the formula style
29064 \begin_layout Plain Layout
29066 \begin_inset CommandInset ref
29068 reference "sec:Formula-Styles"
29079 is used, the formula is set without the
29085 before the first column.
29088 \begin_layout Subsubsection
29089 Alignat Environment
29090 \begin_inset Index idx
29093 \begin_layout Plain Layout
29094 Formula ! multiline ! alignat environment
29102 \begin_layout Standard
29103 The alignat environment has no predefined column separation.
29104 It can be inserted manually with the spaces that are described
29105 \begin_inset CommandInset ref
29107 reference "subsec:Space"
29114 \begin_layout Standard
29115 The above example in the alignat environment where 1
29116 \begin_inset space \thinspace{}
29119 cm space was inserted at the beginning of the second formula:
29120 \begin_inset Formula
29121 \begin{alignat*}{2}
29122 A & =\sin(B) & \hspace{1cm}C & =D\\
29123 C & \ne A & B & \ne D
29128 Because the column separation can be set separately for every column, this
29129 environment is especially suitable to set three and more formulas side
29133 \begin_layout Subsubsection
29134 Flalign Environment
29135 \begin_inset CommandInset label
29137 name "subsec:Flalign-Environment"
29142 \begin_inset Index idx
29145 \begin_layout Plain Layout
29146 Formula ! multiline ! flalign environment
29154 \begin_layout Standard
29155 In this environment the first two columns are always set as much as possible
29156 to the left and the last two ones to the right.
29158 \begin_inset Formula
29160 A & =1 & B & =2 & C & =3\\
29161 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29169 \begin_layout Standard
29170 By creating a flalign environment with an odd number of columns where an
29171 empty \SpecialChar TeX
29172 brace is inserted to the last column, several formulas in a document
29173 can be set to the left, although the formula style
29178 As example the indented formula
29179 \begin_inset CommandInset ref
29181 reference "eq:VolInt"
29186 \begin_inset Formula
29188 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29193 The first two columns contain the formula.
29194 To indent it as with the formula style
29199 \begin_inset space \thinspace{}
29202 pt space was inserted at the beginning of the first column.
29205 \begin_layout Subsection
29206 Eqnarray Environment
29207 \begin_inset CommandInset label
29209 name "subsec:Eqnarray-Environment"
29214 \begin_inset Index idx
29217 \begin_layout Plain Layout
29218 Formula ! multiline ! eqnarray environment
29226 \begin_layout Standard
29227 When this environment has been created, three blue boxes appear.
29228 The content of the first box is right aligned, the content of the last
29230 The content of the middle box appears centered and a bit smaller, because
29231 it is designed to insert there only relation characters.
29232 \begin_inset Formula
29234 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29244 \begin_layout Subsection
29246 \begin_inset Index idx
29249 \begin_layout Plain Layout
29250 Formula ! multiline ! gather environment
29258 \begin_layout Standard
29259 This environment consists of only one centered column.
29260 Every line can be numbered.
29261 \begin_inset Formula
29272 \begin_layout Subsection
29273 Multline Environment
29274 \begin_inset CommandInset label
29276 name "subsec:Multline-Environment"
29281 \begin_inset Index idx
29284 \begin_layout Plain Layout
29285 Formula ! multiline ! multline environment
29293 \begin_layout Standard
29294 The multline environment consists, like the gather environment, of only
29296 But the first line is left aligned, the last one right aligned.
29297 All other lines are centered.
29298 Therefore this environment is suitable for long formulas.
29300 \begin_inset CommandInset ref
29302 reference "eq:lefteqn"
29306 in the multline environment:
29307 \begin_inset Formula
29309 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}\\
29310 -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}\\
29311 =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}}
29319 \begin_layout Standard
29320 In the output only the last (first) line of a multline environment appears
29321 numbered when the document numbering is right (left).
29325 \begin_layout Plain Layout
29326 numbering styles see
29327 \begin_inset CommandInset ref
29329 reference "sec:Formula-Styles"
29341 \begin_layout Standard
29349 \begin_inset Index idx
29352 \begin_layout Plain Layout
29367 \begin_inset Index idx
29370 \begin_layout Plain Layout
29378 a centered line can be right or left aligned, respectively.
29379 The commands are used as follows:
29382 \begin_layout Standard
29387 shoveright{line content}
29393 shoveleft{line content}
29396 \begin_layout Standard
29397 \begin_inset VSpace medskip
29407 \begin_inset Index idx
29410 \begin_layout Plain Layout
29418 specifies the distance of the first line from the left page margin.
29419 Predefined is the length 0
29420 \begin_inset space \thinspace{}
29426 \begin_layout Standard
29427 As example the above formula where the command
29430 \begin_layout Standard
29440 \begin_layout Standard
29441 was inserted in \SpecialChar TeX
29446 \begin_layout Plain Layout
29458 \begin_inset Formula
29460 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}\\
29461 \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}}\\
29462 =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}}
29471 \begin_layout Plain Layout
29482 The second line was left aligned using
29491 \begin_layout Subsection
29492 Multiline Formula Parts
29493 \begin_inset CommandInset label
29495 name "subsec:Multiline-Formula-Parts"
29500 \begin_inset Index idx
29503 \begin_layout Plain Layout
29504 Formula ! multiline ! formula parts
29512 \begin_layout Standard
29513 To display only parts of a formula with multiple lines, one of the following
29514 environments is used:
29531 They can be inserted via the menu
29533 Insert\SpecialChar menuseparator
29536 or by using the commands described in this section.
29539 \begin_layout Standard
29540 The first three have the same properties as the corresponding multiline
29541 formula environments, but it is possible to set further formula parts beside
29544 \begin_inset Formula
29546 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29547 \Delta E\Delta t & \ge\frac{\hbar}{2}
29549 \right\} \textrm{Uncertainty relations}
29557 \begin_layout Standard
29558 To get this formula, a displayed formula is created where the command
29565 \begin_inset Index idx
29568 \begin_layout Plain Layout
29577 A purple box appears around the blue formula box where now columns and
29578 lines can be added.
29579 Outside the multiline environment other formula parts can be set, like
29583 \begin_layout Standard
29584 The aligned environment is also suitable for long formulas whose lines are
29585 horizontally aligned.
29586 Using aligned in a displayed formula has the advantage that the formula
29587 number is vertically centered behind the lines.
29589 \begin_inset CommandInset ref
29591 reference "eq:shortlong"
29595 in the aligned environment:
29596 \begin_inset Formula
29598 \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}|}\\
29599 & -\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}|}
29608 \begin_layout Standard
29609 To use the environments
29628 \begin_inset Index idx
29631 \begin_layout Plain Layout
29646 \begin_inset Index idx
29649 \begin_layout Plain Layout
29664 \begin_inset Index idx
29667 \begin_layout Plain Layout
29675 are inserted, respectively.
29676 The split environment has the same properties as the aligned environment
29677 but it can only have two columns.
29680 \begin_layout Subsection
29681 Text in multiline Formulas
29682 \begin_inset CommandInset label
29684 name "subsec:Text-in-multiline"
29689 \begin_inset Index idx
29692 \begin_layout Plain Layout
29699 \begin_inset Index idx
29702 \begin_layout Plain Layout
29703 Formula ! multiline ! text
29711 \begin_layout Standard
29712 In the Align environments, and the multline and gather environment, text
29713 can be inserted that will appear in a separate line and doesn't affect
29714 the column alignment.
29715 To do this, the command
29722 \begin_inset Index idx
29725 \begin_layout Plain Layout
29733 is used in the following scheme:
29736 \begin_layout Standard
29744 \begin_layout Standard
29745 The text should not be longer than a line because it cannot be hyphenated.
29746 As \SpecialChar LyX
29747 doesn't yet support
29753 directly, the text is written as mathematical text.
29760 must hereby be at the beginning of a line and appears in the output above
29762 An example where the text was inserted at the beginning of the second line:
29763 \begin_inset Formula
29765 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29766 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29774 \begin_layout Standard
29781 always creates some vertical space between the text and the formula lines.
29782 To avoid this space, set in the document settings under
29785 \begin_inset space ~
29795 \begin_inset Index idx
29798 \begin_layout Plain Layout
29799 Packages ! mathtools
29807 \begin_inset space ~
29813 Then you can use the command
29820 \begin_inset Index idx
29823 \begin_layout Plain Layout
29840 \begin_layout Standard
29841 \begin_inset Formula
29843 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29844 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29852 \begin_layout Section
29854 \begin_inset Index idx
29857 \begin_layout Plain Layout
29864 \begin_inset Index idx
29867 \begin_layout Plain Layout
29868 Formula ! numbering|see
29872 \begin_layout Plain Layout
29883 \begin_layout Plain Layout
29898 \begin_layout Subsection
29902 \begin_layout Standard
29903 Numbered formulas can be created with the menu
29905 Insert\SpecialChar menuseparator
29906 Math\SpecialChar menuseparator
29908 \begin_inset space ~
29916 \begin_inset space ~
29922 Existing formulas can be numbered with the menu
29924 Edit\SpecialChar menuseparator
29925 Math\SpecialChar menuseparator
29927 \begin_inset space ~
29935 arg "math-number-toggle"
29939 The formula number is displayed in \SpecialChar LyX
29940 behind the formula as a number sign
29942 The number sign is replaced in the output by the formula number.
29945 \begin_layout Standard
29946 When numbering is turned on in multiline formulas, all lines will be numbered.
29947 But the numbering can be controlled with the menu
29949 Edit\SpecialChar menuseparator
29950 Math\SpecialChar menuseparator
29952 \begin_inset space ~
29956 \begin_inset space ~
29960 \begin_inset space ~
29968 arg "math-number-line-toggle"
29974 \begin_layout Standard
29975 Except for inline formulas, all formulas can be numbered with two different
29977 \begin_inset CommandInset ref
29979 reference "sec:Formula-Styles"
29986 \begin_layout Subsection
29988 \begin_inset Index idx
29991 \begin_layout Plain Layout
29992 Cross-references ! to formulas
30000 \begin_layout Standard
30001 All labeled formulas can be cross-referenced.
30002 A label is added by the menu
30004 Insert\SpecialChar menuseparator
30007 or the toolbar button
30014 The cursor must hereby be inside a displayed formula.
30015 Alternatively you can right-click on the formula and choose
30020 A dialog pops up displaying the prefix
30025 The label is inserted there behind the prefix.
30026 The predefined prefix means
30027 \begin_inset Quotes eld
30031 \begin_inset Quotes erd
30034 and makes it easier to find labels in large documents because it marks
30035 it as formula label to divide it from e.
30036 \begin_inset space \thinspace{}
30040 \begin_inset space \space{}
30044 To change a label, the menu
30046 Insert\SpecialChar menuseparator
30049 is used again or you right-click on a formula and then on
30056 \begin_layout Standard
30057 The name of the label is displayed in \SpecialChar LyX
30058 within two parentheses behind formula.
30059 A formula with a label is always numbered.
30062 \begin_layout Standard
30063 Cross-references are inserted via the menu
30065 Insert\SpecialChar menuseparator
30068 or with the toolbar button
30071 arg "dialog-show-new-inset ref"
30075 A formula cross-reference appears in the output as formula number.
30076 When in the cross-reference dialog window the format
30080 is chosen, the cross-reference appears in the output as formula number
30082 \begin_inset Newline newline
30085 By right-clicking on a cross-reference in \SpecialChar LyX
30086 , one jumps to the formula that
30090 \begin_layout Standard
30091 Here are as examples cross-references to formulas of the following subsections:
30092 \begin_inset Note Note
30095 \begin_layout Plain Layout
30096 Note the different cross-reference types.
30104 \begin_layout Standard
30106 \begin_inset CommandInset ref
30113 \begin_inset CommandInset ref
30121 \begin_inset CommandInset ref
30127 ) big Latin letters are used for the numbering in contrary to (
30128 \begin_inset CommandInset ref
30137 \begin_layout Standard
30138 \begin_inset VSpace medskip
30141 When the argument of
30149 \begin_layout Plain Layout
30157 \begin_inset CommandInset ref
30159 reference "subsec:User-defined-Numbering"
30170 contains a box like in
30171 \begin_inset CommandInset ref
30173 reference "subsec:Paragraph-Boxes"
30177 , the formula cannot be referenced.
30180 \begin_layout Subsection
30182 \begin_inset Index idx
30185 \begin_layout Plain Layout
30186 Formula numbering ! subnumbering
30194 \begin_layout Standard
30195 With the help of the commands
30199 begin{subequations}
30207 formulas can be subnumbered.
30208 Both commands are inserted in \SpecialChar TeX
30212 \begin_layout Standard
30214 \begin_inset Formula
30225 \begin_layout Plain Layout
30229 addtocounter{equation}{-1}
30238 \begin_layout Plain Layout
30242 begin{subequations}
30248 \begin_inset VSpace -5mm
30252 \begin_inset Formula
30260 \begin_inset Formula
30270 \begin_layout Standard
30274 \begin_layout Plain Layout
30286 \begin_layout Standard
30287 To create the example, the following is done:
30290 \begin_layout Enumerate
30291 first formula is inserted
30294 \begin_layout Enumerate
30299 addtocounter{equation}{-1}
30301 begin{subequations}
30302 \begin_inset Index idx
30305 \begin_layout Plain Layout
30314 \begin_inset Newline newline
30319 is inserted after the first formula
30322 \begin_layout Enumerate
30323 second formula is inserted
30326 \begin_layout Enumerate
30327 third formula is inserted
30330 \begin_layout Enumerate
30337 is inserted after the third formula
30340 \begin_layout Standard
30341 Every formula between the commands
30353 is subnumbered as a, b,
30354 \begin_inset Newline linebreak
30357 c, \SpecialChar ldots
30358 For multiline formulas every line will be subnumbered.
30359 All subnumbered formulas are treated as
30364 But as every numbered formula increases the counter
30368 by one, the command
30374 is needed to decrease it.
30375 Otherwise the formulas
30376 \begin_inset CommandInset ref
30383 \begin_inset CommandInset ref
30390 \begin_inset CommandInset ref
30396 would be numbered as
30397 \begin_inset CommandInset ref
30404 \begin_inset CommandInset ref
30411 \begin_inset CommandInset ref
30420 \begin_layout Standard
30421 By inserting the commands in \SpecialChar TeX
30422 mode, a space is created between the first
30425 \begin_inset space \thinspace{}
30428 mm vertical space is inserted after the command
30432 begin{subequations}
30435 When the formula style
30441 \begin_layout Plain Layout
30443 \begin_inset CommandInset ref
30445 reference "sec:Formula-Styles"
30457 \begin_inset space \thinspace{}
30460 mm space is inserted instead.
30463 \begin_layout Standard
30464 Here is an example for a multiline formula where the numbering was turned
30465 off for the second line:
30469 \begin_layout Plain Layout
30473 begin{subequations}
30479 \begin_inset Formula
30481 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30482 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30483 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30492 \begin_layout Plain Layout
30504 \begin_layout Subsection
30505 User-defined Numbering
30506 \begin_inset CommandInset label
30508 name "subsec:User-defined-Numbering"
30513 \begin_inset Index idx
30516 \begin_layout Plain Layout
30517 Formula numbering ! user-defined
30525 \begin_layout Standard
30526 \begin_inset Index idx
30529 \begin_layout Plain Layout
30530 Formula numbering ! self-defined delimiters
30535 With the standard numbering parentheses are set around the formula number.
30536 To replace the parentheses for example by vertical bars, the following
30537 line is added to the \SpecialChar LaTeX
30541 \begin_layout Standard
30553 \begin_inset Note Note
30556 \begin_layout Plain Layout
30557 This macro is already declared in the \SpecialChar LaTeX
30558 -preamble for testing.
30559 To activate it, remove the percent sign at the beginning.
30567 \begin_layout Standard
30568 To use other characters, the vertical bars besides the
30572 are replaced by one ore more characters.
30573 To get only the formula number the vertical bars are omitted.
30576 \begin_layout Standard
30577 \begin_inset VSpace bigskip
30580 When there should be an expression of your choice instead of the consecutive
30581 formula number in parentheses behind the formula, the command
30588 \begin_inset Index idx
30591 \begin_layout Plain Layout
30600 \begin_inset Formula
30602 A+B=C\tag{something}\label{eq:tag}
30607 In this example the command
30612 \begin_inset space \textvisiblespace{}
30617 was inserted in the formula.
30620 \begin_layout Standard
30626 \begin_inset space \textvisiblespace{}
30631 is inserted instead, the star prevents the parentheses around the expression:
30632 \begin_inset Formula
30634 A+B=C\tag*{something}
30642 \begin_layout Standard
30643 \begin_inset VSpace bigskip
30646 To restart the formula numbering with new document parts or sections, the
30647 following command is used:
30650 \begin_layout Standard
30655 @addtoreset{equation}{part}
30658 \begin_inset Index idx
30661 \begin_layout Plain Layout
30666 \begin_layout Plain Layout
30677 \begin_layout Plain Layout
30690 \begin_layout Plain Layout
30701 \begin_layout Plain Layout
30714 \begin_inset Newline newline
30718 \begin_inset Newline newline
30725 @addtoreset{equation}{section}
30728 \begin_layout Standard
30729 To be able to use these commands in \SpecialChar TeX
30731 \begin_inset Quotes eld
30735 \begin_inset Quotes erd
30738 character has to be made
30739 \begin_inset Quotes eld
30743 \begin_inset Quotes erd
30746 for \SpecialChar LaTeX
30761 So the command sequence in \SpecialChar TeX
30765 \begin_layout Standard
30771 \begin_inset Newline newline
30776 @addtoreset{equation}{section}
30777 \begin_inset Newline newline
30785 \begin_layout Standard
30786 In the \SpecialChar LaTeX
30799 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30803 \begin_layout Standard
30818 \begin_layout Plain Layout
30823 is part of the \SpecialChar LaTeX
30829 \begin_inset Index idx
30832 \begin_layout Plain Layout
30833 Packages ! carlisle
30838 that is part of every \SpecialChar LaTeX
30839 standard installation.
30845 \begin_inset Index idx
30848 \begin_layout Plain Layout
30849 Packages ! remreset
30854 has to be loaded in the \SpecialChar LaTeX
30855 -preamble with the line
30858 \begin_layout Standard
30863 usepackage{remreset}
30866 \begin_layout Standard
30874 \begin_inset Index idx
30877 \begin_layout Plain Layout
30882 \begin_layout Plain Layout
30893 \begin_layout Plain Layout
30906 \begin_layout Plain Layout
30917 \begin_layout Plain Layout
30929 can be used with the same scheme as
30938 \begin_layout Standard
30939 \begin_inset VSpace bigskip
30942 Sometimes formulas should be numbered in the following form:
30945 \begin_layout Standard
30948 (section number.formula number)
30951 \begin_layout Standard
30952 The formula number should start with every section with
30953 \begin_inset Quotes eld
30957 \begin_inset Quotes erd
30963 \begin_layout Standard
30964 For this case there is the command
30971 \begin_inset Index idx
30974 \begin_layout Plain Layout
30982 , which is used with the following scheme:
30985 \begin_layout Standard
30990 numberwithin{counter}{sectioning}
30993 \begin_layout Standard
30994 Counter denotes what kind of numbering is affected, sectioning denotes what
30995 number is before the dot.
30998 \begin_layout Standard
30999 Thus in our case the following \SpecialChar LaTeX
31000 preamble or \SpecialChar TeX
31004 \begin_layout Standard
31009 numberwithin{equation}{section}
31012 \begin_layout Standard
31013 This is the result:
31017 \begin_layout Plain Layout
31021 numberwithin{equation}{section}
31027 \begin_inset Formula
31037 \begin_layout Standard
31039 \begin_inset space \thinspace{}
31043 \begin_inset space \space{}
31046 tables so that the number of the part is the sectioning,
31047 \begin_inset Newline newline
31054 numberwithin{table}{part}
31059 \begin_layout Standard
31060 To go back to the standard numbering or to prevent this kind of numbering
31061 when it is defined by the document class, the following command is inserted
31062 as \SpecialChar TeX
31063 code or to the \SpecialChar LaTeX
31067 \begin_layout Standard
31077 \begin_inset Index idx
31080 \begin_layout Plain Layout
31094 \begin_layout Plain Layout
31110 \begin_inset Newline newline
31118 \begin_inset Newline newline
31130 \begin_layout Standard
31137 uses internally the command
31143 , described above, that also needs to be reverted.
31147 \begin_layout Plain Layout
31154 \begin_layout Plain Layout
31158 @removefromreset{equation}{section}
31161 \begin_layout Plain Layout
31173 \begin_layout Subsection
31174 Numbering with Roman Numbers and Letters
31175 \begin_inset Index idx
31178 \begin_layout Plain Layout
31179 Formula numbering ! with letters
31185 \begin_inset Index idx
31188 \begin_layout Plain Layout
31189 Formula numbering ! with Roman numbers
31197 \begin_layout Standard
31198 Formulas can also be numbered with Roman numbers and Latin letters.
31199 To number for example with small Roman numbers, the command
31202 \begin_layout Standard
31214 \begin_layout Standard
31215 is inserted before the formula in \SpecialChar TeX
31224 \begin_inset Index idx
31227 \begin_layout Plain Layout
31235 redefines the predefined command
31251 \begin_layout Plain Layout
31258 has the same scheme like the command
31264 that is described in
31265 \begin_inset CommandInset ref
31267 reference "subsec:The-Command-newcommand"
31280 is the formula counter.
31287 is used as prefix for a counter, the value of the counter is output as
31289 When a formula is numbered, \SpecialChar LaTeX
31290 sets internally the command
31296 behind the formula.
31302 \begin_inset Index idx
31305 \begin_layout Plain Layout
31315 outputs the counter as small Roman number.
31318 \begin_layout Standard
31319 All formulas behind the command
31329 are now numbered Roman.
31330 To switch to numbering with big Roman numbers, the command is inserted
31344 \begin_inset Index idx
31347 \begin_layout Plain Layout
31359 \begin_inset Quotes eld
31363 \begin_inset Quotes erd
31366 with small Latin letters there is the command
31373 \begin_inset Index idx
31376 \begin_layout Plain Layout
31384 , for big ones there is the command
31391 \begin_inset Index idx
31394 \begin_layout Plain Layout
31407 \begin_layout Standard
31408 \begin_inset Note Greyedout
31411 \begin_layout Plain Layout
31418 \begin_inset space ~
31421 formulas can be numbered with Latin letters in one document.
31429 \begin_layout Standard
31433 \begin_layout Plain Layout
31449 \begin_layout Standard
31450 \begin_inset Formula
31452 A=\textrm{small roman}
31461 \begin_layout Plain Layout
31475 \begin_inset Formula
31477 B=\textrm{big Roman}\label{eq:Rom}
31486 \begin_layout Plain Layout
31500 \begin_inset Formula
31502 C=\textrm{small Latin}
31511 \begin_layout Plain Layout
31525 \begin_inset Formula
31527 D=\textrm{big Latin}\label{eq:Lat}
31535 \begin_layout Standard
31536 To switch back to the default numbering, insert the command:
31539 \begin_layout Standard
31549 \begin_inset Index idx
31552 \begin_layout Plain Layout
31563 \begin_layout Standard
31567 \begin_layout Plain Layout
31581 \begin_inset Formula
31591 \begin_layout Standard
31592 \begin_inset VSpace medskip
31595 As you see, formulas are numbered serially independent from the numbering
31597 When then numbering should start with
31598 \begin_inset Quotes eld
31602 \begin_inset Quotes erd
31605 when the style is changed, new equation counters have to be defined.
31606 A description about this can be found in the file
31607 \begin_inset CommandInset href
31609 name "Formula-numbering.lyx"
31610 target "run:Formula-numbering.lyx"
31617 \begin_layout Section
31618 Chemical Symbols and Equations
31619 \begin_inset CommandInset label
31621 name "subsec:Chemical-Symbols-and"
31626 \begin_inset Index idx
31629 \begin_layout Plain Layout
31630 Chemical characters ! Symbols
31636 \begin_inset Index idx
31639 \begin_layout Plain Layout
31646 \begin_inset Index idx
31649 \begin_layout Plain Layout
31658 \begin_layout Standard
31659 An example text from chemistry:
31662 \begin_layout Quote
31664 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31667 -ion reacts with two
31668 \begin_inset Formula $\mathrm{Na^{+}}$
31671 -ions to sodium sulfate
31672 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31676 The chemical equation for this is:
31677 \begin_inset Formula
31679 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31687 \begin_layout Standard
31688 This chemical equation can directly be created as formula.
31689 To avoid that the symbols appear italic, everything is highlighted and
31690 changed by the shortcut
31696 to the upright font style.
31700 \begin_layout Plain Layout
31706 \begin_inset CommandInset ref
31708 reference "subsec:Font-Styles"
31720 \begin_layout Standard
31721 A more convenient way to typeset chemical formulas is to use the command
31729 \begin_inset Index idx
31732 \begin_layout Plain Layout
31740 that is available when the \SpecialChar LaTeX
31746 \begin_inset Index idx
31749 \begin_layout Plain Layout
31762 to a formula a new blue box appears where chemical formulas can be inserted
31763 in an intuitive way.
31764 \begin_inset Separator parbreak
31770 \begin_layout Standard
31772 \begin_inset Tabular
31773 <lyxtabular version="3" rows="10" columns="2">
31774 <features booktabs="true" tabularvalignment="middle">
31775 <column alignment="center" valignment="top" width="0pt">
31776 <column alignment="center" valignment="top">
31778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31781 \begin_layout Plain Layout
31787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31790 \begin_layout Plain Layout
31798 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31801 \begin_layout Plain Layout
31805 \begin_inset space \textvisiblespace{}
31813 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31816 \begin_layout Plain Layout
31817 \begin_inset Formula $\ce{H2CO3}$
31826 <row topspace="1.5mm">
31827 <cell alignment="center" valignment="top" usebox="none">
31830 \begin_layout Plain Layout
31834 \begin_inset space \textvisiblespace{}
31842 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31845 \begin_layout Plain Layout
31846 \begin_inset Formula $\ce{SO4^{2-}}$
31855 <row topspace="1.5mm">
31856 <cell alignment="center" valignment="top" usebox="none">
31859 \begin_layout Plain Layout
31863 \begin_inset space \textvisiblespace{}
31871 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31874 \begin_layout Plain Layout
31875 \begin_inset Formula $\ce{(NH4)2S}$
31884 <row topspace="1.5mm">
31885 <cell alignment="center" valignment="top" usebox="none">
31888 \begin_layout Plain Layout
31892 \begin_inset space \textvisiblespace{}
31900 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31903 \begin_layout Plain Layout
31904 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31913 <row topspace="1.5mm">
31914 <cell alignment="center" valignment="top" usebox="none">
31917 \begin_layout Plain Layout
31921 \begin_inset space \textvisiblespace{}
31927 \begin_inset space \textvisiblespace{}
31933 \begin_inset space \textvisiblespace{}
31941 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31944 \begin_layout Plain Layout
31945 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31954 <row topspace="1.5mm">
31955 <cell alignment="center" valignment="top" usebox="none">
31958 \begin_layout Plain Layout
31962 \begin_inset space \textvisiblespace{}
31966 \begin_inset Formula $\downarrow$
31970 \begin_inset Formula $\to$
31978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31981 \begin_layout Plain Layout
31982 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31992 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31995 \begin_layout Plain Layout
31999 \begin_inset space \textvisiblespace{}
32005 \begin_inset space \textvisiblespace{}
32011 \begin_inset space \textvisiblespace{}
32019 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32022 \begin_layout Plain Layout
32023 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
32033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32036 \begin_layout Plain Layout
32040 \begin_inset space \textvisiblespace{}
32044 \begin_inset space \textvisiblespace{}
32048 \begin_inset space \textvisiblespace{}
32052 \begin_inset space \textvisiblespace{}
32056 \begin_inset space \textvisiblespace{}
32064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32067 \begin_layout Plain Layout
32068 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
32077 <row topspace="1.5mm">
32078 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
32081 \begin_layout Plain Layout
32085 \begin_inset space \textvisiblespace{}
32089 \begin_inset space \textvisiblespace{}
32093 \begin_inset space \textvisiblespace{}
32097 \begin_inset space \textvisiblespace{}
32105 \begin_inset space \textvisiblespace{}
32113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
32116 \begin_layout Plain Layout
32117 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
32133 \begin_layout Standard
32134 \begin_inset Note Greyedout
32137 \begin_layout Plain Layout
32143 It is not possible in \SpecialChar LyX
32144 to use the character ^ to get an up-arrow as described
32150 One instead uses a negative thin space followed by the command
32157 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32168 \begin_layout Standard
32175 the command for equation
32176 \begin_inset space ~
32180 \begin_inset CommandInset ref
32182 reference "eq:chem-reaction"
32187 \begin_inset Newline newline
32195 \begin_inset space \textvisiblespace{}
32199 \begin_inset space \textvisiblespace{}
32203 \begin_inset space \textvisiblespace{}
32207 \begin_inset space \textvisiblespace{}
32211 \begin_inset space \textvisiblespace{}
32215 \begin_inset space \textvisiblespace{}
32221 \begin_layout Standard
32222 To create multiline chemical equations first a multiline formula is created
32224 \begin_inset CommandInset ref
32226 reference "sec:Multiline-Formulas"
32231 Afterwards the command
32237 is used in every small blue box of the formula.
32239 \begin_inset CommandInset ref
32241 reference "eq:TEOS-reaction-1"
32246 \begin_inset CommandInset ref
32248 reference "eq:TEOS-reaction-2"
32252 are an example of a multi-stage chemical reaction where every equation
32253 has its own number.
32254 \begin_inset Formula
32256 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32257 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32265 \begin_layout Standard
32276 package provides the command
32283 \begin_inset Index idx
32286 \begin_layout Plain Layout
32294 that has to be used for special cases.
32295 For more information about
32301 and more examples have a look at the documentation of
32306 \begin_inset CommandInset citation
32315 \begin_layout Section
32319 \begin_layout Standard
32321 supports two types of commutative diagrams:
32329 that are explained in the following.
32332 \begin_layout Subsection
32334 \begin_inset Index idx
32337 \begin_layout Plain Layout
32346 \begin_layout Standard
32347 Diagrams of this type visualize relations by vertical and horizontal lines
32349 \begin_inset Formula
32351 \begin{CD}A@>>>B@>>>C\\
32362 \begin_layout Standard
32363 To get them, the command
32368 \begin_inset Index idx
32371 \begin_layout Plain Layout
32381 is inserted to a formula.
32382 A blue box appears with two dashed lines where further commands can be
32387 arg "newline-insert newline"
32390 a new line is created.
32391 Horizontal relations are inserted in odd, vertical in even formula lines.
32394 \begin_layout Standard
32395 To create the relations there are the following commands:
32398 \begin_layout Itemize
32403 creates a left arrow,
32414 \begin_layout Itemize
32419 creates an up arrow,
32427 a vertical equal sign
32430 \begin_layout Itemize
32436 is a placeholder for non-existent relations
32439 \begin_layout Standard
32440 All arrows can be labeled as follows:
32443 \begin_layout Itemize
32444 If text inserted between the first and second < or >, resp., it is placed
32446 When it is inserted between the second and third one, it appears under
32450 \begin_layout Itemize
32451 When text for vertical arrows is inserted between the first and second A
32452 or V, resp., it is placed left beside the arrow.
32453 When it is inserted between the second and third one, it appears right
32455 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32459 \begin_layout Standard
32460 As example a diagram with all possible relations:
32463 \begin_layout Standard
32464 \begin_inset Formula
32466 \begin{CD}A@>j>>B@>>k>C@=F\\
32477 \begin_layout Standard
32478 The command for this is:
32479 \begin_inset Newline newline
32487 \begin_inset space \textvisiblespace{}
32490 A@>j>>B@>>k>C@=F Ctrl+Return
32491 \begin_inset Newline newline
32495 \begin_inset Phantom HPhantom
32498 \begin_layout Plain Layout
32504 \begin_inset space \textvisiblespace{}
32517 \begin_inset Formula $\to$
32523 \begin_inset Newline newline
32527 \begin_inset Phantom HPhantom
32530 \begin_layout Plain Layout
32536 \begin_inset space \textvisiblespace{}
32547 \begin_layout Subsection
32549 \begin_inset Index idx
32552 \begin_layout Plain Layout
32553 Diagrams ! xymatrix
32561 \begin_layout Standard
32562 To be able to use xymatrices, the \SpecialChar LaTeX
32568 A xymatrix is created by inserting the command
32575 Then you are able to add new matrix columns and rows like for normal matrices,
32577 \begin_inset CommandInset ref
32579 reference "sec:Matrices"
32586 \begin_layout Standard
32587 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32589 All possibilities to create commutative diagrams and decorations are explained
32594 that you find in the menu
32596 Help\SpecialChar menuseparator
32598 \begin_inset space ~
32606 \begin_layout Subsection
32612 \begin_inset Index idx
32615 \begin_layout Plain Layout
32624 \begin_layout Standard
32629 -diagrams, the \SpecialChar LaTeX
32639 -diagram is created by inserting the command
32646 Then you are able to add new matrix columns and rows like for normal matrices,
32648 \begin_inset CommandInset ref
32650 reference "sec:Matrices"
32657 \begin_layout Standard
32658 Examples how to create
32662 diagrams in \SpecialChar LyX
32665 Feynman-diagram manual
32667 that you find in the menu
32669 Help\SpecialChar menuseparator
32671 \begin_inset space ~
32679 \begin_layout Standard
32680 \begin_inset Newpage newpage
32686 \begin_layout Section
32687 User-defined Commands
32688 \begin_inset Index idx
32691 \begin_layout Plain Layout
32692 User-defined commands
32700 \begin_layout Standard
32701 \begin_inset Note Greyedout
32704 \begin_layout Plain Layout
32709 The names of user-defined commands and macros may only consist of Latin
32718 \begin_layout Subsection
32722 \begin_inset CommandInset label
32724 name "subsec:The-Command-newcommand"
32729 \begin_inset Index idx
32732 \begin_layout Plain Layout
32733 User-defined commands !
32741 \begin_inset Index idx
32744 \begin_layout Plain Layout
32755 \begin_layout Standard
32756 Many \SpecialChar LaTeX
32757 -commands are too long to be used frequently.
32758 But it is possible to define with the command
32764 new shorter commands.
32767 \begin_layout Standard
32768 The command scheme of
32777 \begin_layout Standard
32782 newcommand{new command name}[number of arguments][optional
32787 \begin_inset Newline newline
32791 \begin_inset Phantom HPhantom
32794 \begin_layout Plain Layout
32804 {command definition}
32807 \begin_layout Standard
32808 \begin_inset Note Greyedout
32811 \begin_layout Plain Layout
32816 Assure that the name of the new command is not already used in your document
32817 or by \SpecialChar LaTeX
32818 -packages that you use.
32819 When you for example define the command
32831 , you get an error message because
32837 is already defined as command for
32838 \begin_inset Quotes eld
32842 \begin_inset Formula $\le$
32846 \begin_inset Quotes erd
32857 \begin_layout Standard
32858 The number of arguments is an integer in the range 0
32859 \begin_inset space \thinspace{}
32863 \begin_inset space \thinspace{}
32866 9 and specifies how many arguments the new command should have.
32867 With the optional value a value for an optional argument can be predefined.
32868 When this is done, the
32876 rgument of the new command is automatically an optional one.
32879 \begin_layout Standard
32880 Here are some examples:
32883 \begin_layout Itemize
32884 To define the command
32896 , the \SpecialChar LaTeX
32898 \begin_inset VSpace medskip
32902 \begin_inset Newline newline
32916 \begin_layout Itemize
32917 To define the command
32929 , the argument (that should be underlined) must be taken into account.
32930 For this the preamble line is:
32931 \begin_inset VSpace medskip
32935 \begin_inset Newline newline
32949 \begin_inset VSpace medskip
32953 \begin_inset Newline newline
32960 acts as argument placeholder, the
32964 behind it denotes that it is the placeholder for the first argument.
32967 \begin_layout Itemize
32975 \begin_inset space \thinspace{}
32979 \begin_inset space \space{}
32989 \begin_inset VSpace medskip
32993 \begin_inset Newline newline
33004 framebox#1#2{$#3$}}
33007 \begin_inset VSpace medskip
33011 \begin_inset Newline newline
33014 The two Dollar signs creates the extra formula needed for
33021 \begin_inset CommandInset ref
33023 reference "subsec:Boxes-with-Frame"
33030 \begin_layout Itemize
33031 To create a new command for
33037 where the color for the box need not be specified, the argument for the
33038 color is defined optional:
33039 \begin_inset VSpace medskip
33043 \begin_inset Newline newline
33054 fcolorbox{#2}{#1}{$#3$}}
33057 \begin_inset VSpace medskip
33061 \begin_inset Newline newline
33064 When the color is not specified when using
33070 , the predefined color
33077 \begin_layout Standard
33078 A test of the new defined commands:
33079 \begin_inset Separator parbreak
33085 \begin_layout Standard
33087 \begin_inset Tabular
33088 <lyxtabular version="3" rows="6" columns="2">
33089 <features booktabs="true" tabularvalignment="middle">
33090 <column alignment="center" valignment="top" width="0pt">
33091 <column alignment="center" valignment="top">
33093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33096 \begin_layout Plain Layout
33102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33105 \begin_layout Plain Layout
33113 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33116 \begin_layout Plain Layout
33120 \begin_inset space \textvisiblespace{}
33128 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33131 \begin_layout Plain Layout
33132 \begin_inset Formula $A\gr B$
33142 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33145 \begin_layout Plain Layout
33153 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33156 \begin_layout Plain Layout
33157 \begin_inset Formula $\us{ABcd}$
33166 <row topspace="1mm">
33167 <cell alignment="center" valignment="top" usebox="none">
33170 \begin_layout Plain Layout
33174 \begin_inset Formula $\to$
33180 \begin_inset Formula $\to$
33188 \begin_inset space \textvisiblespace{}
33196 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33199 \begin_layout Plain Layout
33200 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33209 <row topspace="1.5mm">
33210 <cell alignment="center" valignment="top" usebox="none">
33213 \begin_layout Plain Layout
33217 \begin_inset Formula $\to$
33225 \begin_inset space \textvisiblespace{}
33233 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33236 \begin_layout Plain Layout
33237 \begin_inset Formula $\cb{red}{\int A=B}$
33246 <row topspace="1.5mm" bottomspace="1mm">
33247 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33250 \begin_layout Plain Layout
33256 \begin_inset Formula $\to$
33264 \begin_inset space \textvisiblespace{}
33272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33275 \begin_layout Plain Layout
33276 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33292 \begin_layout Subsection
33294 \begin_inset Index idx
33297 \begin_layout Plain Layout
33298 User-defined commands! Math macros
33304 \begin_inset Index idx
33307 \begin_layout Plain Layout
33316 \begin_layout Standard
33317 User-defined commands are especially convenient for complex expressions.
33318 When you are for example dealing with a document that has quadratic equations,
33319 the same solution type occurs several times.
33320 The general form of a quadratic equation is
33321 \begin_inset Formula
33323 0=\lambda^{2}+p\lambda+q
33328 The general form of the solution is
33329 \begin_inset Formula
33331 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33339 \begin_layout Standard
33340 To define a command for the solution formula where only the three parameters
33342 \begin_inset Formula $\lambda$
33346 \begin_inset Formula $p$
33350 \begin_inset Formula $q$
33353 need to be specified and the index of
33354 \begin_inset Formula $\lambda$
33357 can be given optionally, the \SpecialChar LaTeX
33359 \begin_inset Newline newline
33375 \begin_inset Newline newline
33379 \begin_inset Phantom HPhantom
33382 \begin_layout Plain Layout
33396 frac{#3^{2}}{4}-#4}}
33399 \begin_layout Standard
33400 To create with this the solution formula, the command
33401 \begin_inset Newline newline
33411 \begin_inset Formula $\to$
33417 \begin_inset Formula $\to$
33424 is inserted to a formula
33429 \begin_layout Standard
33430 The definition of the new command is unintuitive because one has to know
33431 the schemes of all used \SpecialChar LaTeX
33433 \begin_inset space \thinspace{}
33437 \begin_inset space \space{}
33440 that a fraction is inserted in \SpecialChar LaTeX
33445 frac{numerator}{denominator}
33448 Furthermore one can easily forget a brace in the definition and cannot
33449 see in \SpecialChar LyX
33450 what the new command is doing.
33451 To avoid these problems \SpecialChar LyX
33452 offers the possibility to use math macros instead
33462 \begin_layout Standard
33463 A math macro is created by using the menu
33465 Insert\SpecialChar menuseparator
33466 Math\SpecialChar menuseparator
33469 or the toolbar button
33472 arg "math-macro newmacroname_newcommand"
33476 The math macro toolbar appears together with the following box where the
33478 \begin_inset Newline newline
33482 \begin_inset space \hspace*{\fill}
33486 \begin_inset Graphics
33487 filename clipart/macrobox.png
33493 \begin_inset space \hspace*{\fill}
33497 \begin_inset Newline newline
33501 \begin_inset FormulaMacro
33502 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33507 newmacroname is the default name of the macro that should be changed to
33508 something sensible.
33509 The wanted formula is inserted in the first blue box.
33510 An argument placeholder is inserted with the command
33517 \begin_inset space \thinspace{}
33521 \begin_inset space \space{}
33530 or by using the macro toolbar button
33533 arg "math-macro-add-param"
33537 Argument placeholders are displayed red.
33539 \begin_inset space ~
33542 arguments are possible.
33543 Optional arguments are created with the toolbar button
33546 arg "math-macro-add-optional-param"
33550 The first non-optional argument can be transformed to an optional one with
33554 arg "math-macro-make-optional"
33558 In the second blue box the appearance of the macro in \SpecialChar LyX
33560 Normally you want to see it as it is defined, so the box is kept empty.
33561 But when you have created a macro that needs lot of space on the screen,
33562 you can insert in the box for example
33563 \begin_inset Newline newline
33593 \begin_inset Newline newline
33598 For the macro only the arguments with the macro name in front of them will
33599 then be displayed in \SpecialChar LyX
33600 , leading to a better overview.
33601 The formula appears in the output as defined in the first box.
33602 \begin_inset Newline newline
33605 The appearance of macros in formulas can furthermore be changed for single
33606 macros by setting the cursor in the macro and using the menu
33608 View\SpecialChar menuseparator
33610 \begin_inset space ~
33614 \begin_inset space ~
33622 \begin_layout Standard
33623 To use a macro, the macro name is inserted as command to a formula, in our
33631 Our macro looks in \SpecialChar LyX
33633 \begin_inset Newline newline
33637 \begin_inset space \hspace*{\fill}
33641 \begin_inset Graphics
33642 filename clipart/macrouse.png
33648 \begin_inset space \hspace*{\fill}
33652 \begin_inset Newline newline
33655 Here is our macro example with the arguments
33656 \begin_inset Formula $x$
33660 \begin_inset Formula $\ln(x)$
33664 \begin_inset Formula $B$
33670 \begin_layout Standard
33671 \begin_inset Formula
33681 \begin_layout Standard
33685 Tools\SpecialChar menuseparator
33686 Preferences\SpecialChar menuseparator
33687 Editing\SpecialChar menuseparator
33690 different styles to edit macros.
33691 To find the style that suits you the most, choose a style and set the cursor
33692 in a macro formula to see the difference.
33695 \begin_layout Standard
33696 A math macro is transformed internally to a
33702 command when exporting the document.
33709 command is not placed in the \SpecialChar LaTeX
33710 -preamble, therefore macros can only be used
33711 in formulas that are in the document below the macro definition box.
33714 \begin_layout Standard
33715 Math macros can also be directly created from a
33722 When writing for example the command
33725 \begin_inset Newline newline
33734 xleftarrow[#2]{#1}}
33735 \begin_inset Newline newline
33740 in \SpecialChar LyX
33741 as normal text, highlighting it completely and using then the shortcut
33746 , the command will be transformed to a math macro.
33747 Using this method you need to be careful that the
33753 command is typed correctly, otherwise you get a faulty macro leading to
33758 \begin_layout Standard
33759 Math macros currently have the problem that further formulas in macro definition
33760 s are handled wrongly.
33761 Therefore the example
33768 \begin_inset CommandInset ref
33770 reference "subsec:The-Command-newcommand"
33774 cannot be created as macro.
33777 \begin_layout Standard
33778 When the cursor is in a macro definition box, you will see the macro toolbar
33779 in \SpecialChar LyX
33783 \begin_layout Standard
33784 \begin_inset VSpace defskip
33790 \begin_layout Standard
33791 \begin_inset Graphics
33792 filename clipart/MacroToolbar.png
33797 \begin_inset Index idx
33800 \begin_layout Plain Layout
33809 \begin_layout Standard
33810 \begin_inset VSpace defskip
33816 \begin_layout Standard
33817 The macro toolbar contains from left to right the following buttons:
33820 \begin_layout Standard
33821 \begin_inset VSpace defskip
33827 \begin_layout Standard
33828 \begin_inset Tabular
33829 <lyxtabular version="3" rows="9" columns="2">
33830 <features islongtable="true" longtabularalignment="center">
33831 <column alignment="left" valignment="top">
33832 <column alignment="left" valignment="top" width="85col%">
33833 <row interlinespace="2.5mm">
33834 <cell alignment="center" valignment="top" usebox="none">
33837 \begin_layout Plain Layout
33840 arg "math-macro-remove-param"
33848 <cell alignment="center" valignment="top" usebox="none">
33851 \begin_layout Plain Layout
33854 Edit\SpecialChar menuseparator
33855 Math\SpecialChar menuseparator
33857 \begin_inset space ~
33860 Definition\SpecialChar menuseparator
33861 Remove Last Argument
33867 <row interlinespace="2.5mm">
33868 <cell alignment="center" valignment="top" usebox="none">
33871 \begin_layout Plain Layout
33874 arg "math-macro-add-param"
33882 <cell alignment="center" valignment="top" usebox="none">
33885 \begin_layout Plain Layout
33888 Edit\SpecialChar menuseparator
33889 Math\SpecialChar menuseparator
33891 \begin_inset space ~
33894 Definition\SpecialChar menuseparator
33901 <row interlinespace="2.5mm">
33902 <cell alignment="center" valignment="top" usebox="none">
33905 \begin_layout Plain Layout
33908 arg "math-macro-make-optional"
33916 <cell alignment="center" valignment="top" usebox="none">
33919 \begin_layout Plain Layout
33922 Edit\SpecialChar menuseparator
33923 Math\SpecialChar menuseparator
33925 \begin_inset space ~
33928 Definition\SpecialChar menuseparator
33929 Transform First Non-Optional to
33930 \begin_inset Newline newline
33934 \begin_inset Phantom HPhantom
33937 \begin_layout Plain Layout
33940 Edit\SpecialChar menuseparator
33941 Math\SpecialChar menuseparator
33943 \begin_inset space ~
33946 Definition\SpecialChar menuseparator
33958 <row interlinespace="2.5mm">
33959 <cell alignment="center" valignment="top" usebox="none">
33962 \begin_layout Plain Layout
33965 arg "math-macro-make-nonoptional"
33973 <cell alignment="center" valignment="top" usebox="none">
33976 \begin_layout Plain Layout
33979 Edit\SpecialChar menuseparator
33980 Math\SpecialChar menuseparator
33982 \begin_inset space ~
33985 Definition\SpecialChar menuseparator
33986 Transform Last Optional to
33987 \begin_inset Newline newline
33991 \begin_inset Phantom HPhantom
33994 \begin_layout Plain Layout
33997 Edit\SpecialChar menuseparator
33998 Math\SpecialChar menuseparator
34000 \begin_inset space ~
34003 Definition\SpecialChar menuseparator
34009 Non-Optional Argument
34015 <row interlinespace="2.5mm">
34016 <cell alignment="center" valignment="top" usebox="none">
34019 \begin_layout Plain Layout
34022 arg "math-macro-remove-optional-param"
34030 <cell alignment="center" valignment="top" usebox="none">
34033 \begin_layout Plain Layout
34036 Edit\SpecialChar menuseparator
34037 Math\SpecialChar menuseparator
34039 \begin_inset space ~
34042 Definition\SpecialChar menuseparator
34043 Remove Optional Argument
34049 <row interlinespace="2.5mm">
34050 <cell alignment="center" valignment="top" usebox="none">
34053 \begin_layout Plain Layout
34056 arg "math-macro-add-optional-param"
34064 <cell alignment="center" valignment="top" usebox="none">
34067 \begin_layout Plain Layout
34070 Edit\SpecialChar menuseparator
34071 Math\SpecialChar menuseparator
34073 \begin_inset space ~
34076 Definition\SpecialChar menuseparator
34077 Insert Optional Argument
34083 <row interlinespace="2.5mm">
34084 <cell alignment="center" valignment="top" usebox="none">
34087 \begin_layout Plain Layout
34090 arg "math-macro-remove-greedy-param"
34098 <cell alignment="center" valignment="top" usebox="none">
34101 \begin_layout Plain Layout
34104 Edit\SpecialChar menuseparator
34105 Math\SpecialChar menuseparator
34107 \begin_inset space ~
34110 Definition\SpecialChar menuseparator
34111 Remove Last Argument
34112 \begin_inset Newline newline
34116 \begin_inset Phantom HPhantom
34119 \begin_layout Plain Layout
34122 Edit\SpecialChar menuseparator
34123 Math\SpecialChar menuseparator
34125 \begin_inset space ~
34128 Definition\SpecialChar menuseparator
34134 Spitting Out To The Right
34140 <row interlinespace="2.5mm">
34141 <cell alignment="center" valignment="top" usebox="none">
34144 \begin_layout Plain Layout
34147 arg "math-macro-append-greedy-param"
34155 <cell alignment="center" valignment="top" usebox="none">
34158 \begin_layout Plain Layout
34161 Edit\SpecialChar menuseparator
34162 Math\SpecialChar menuseparator
34164 \begin_inset space ~
34167 Definition\SpecialChar menuseparator
34169 \begin_inset Newline newline
34173 \begin_inset Phantom HPhantom
34176 \begin_layout Plain Layout
34179 Edit\SpecialChar menuseparator
34180 Math\SpecialChar menuseparator
34182 \begin_inset space ~
34185 Definition\SpecialChar menuseparator
34191 Eating From The Right
34197 <row interlinespace="2.5mm">
34198 <cell alignment="center" valignment="top" usebox="none">
34201 \begin_layout Plain Layout
34204 arg "math-macro-add-greedy-optional-param"
34212 <cell alignment="center" valignment="top" usebox="none">
34215 \begin_layout Plain Layout
34218 Edit\SpecialChar menuseparator
34219 Math\SpecialChar menuseparator
34221 \begin_inset space ~
34224 Definition\SpecialChar menuseparator
34225 Append Optional Argument
34226 \begin_inset Newline newline
34230 \begin_inset Phantom HPhantom
34233 \begin_layout Plain Layout
34236 Edit\SpecialChar menuseparator
34237 Math\SpecialChar menuseparator
34239 \begin_inset space ~
34242 Definition\SpecialChar menuseparator
34248 Eating From The Right
34261 \begin_layout Section
34262 Computer Algebra Systems
34265 \begin_layout Standard
34267 offers the exchange between mathematical expressions written in \SpecialChar LyX
34269 editor and external applications or user defined scripts.
34270 Currently supported applications are
34287 Note that the set of supported mathematical constructs is limited only
34288 to very simple cases.
34291 \begin_layout Subsection
34295 \begin_layout Standard
34296 Write some expression in a formula, go to the
34298 Edit\SpecialChar menuseparator
34299 Math\SpecialChar menuseparator
34300 Use Computer Algebra System
34302 menu and choose the application you have installed on the computer.
34303 After that the result of computation should show on the right side of the
34304 expression together with the
34305 \begin_inset Quotes eld
34309 \begin_inset Quotes erd
34315 \begin_layout Standard
34316 Here are few simple examples (with results from
34320 ) to show what kind of computations can be performed:
34323 \begin_layout Itemize
34324 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34330 \begin_layout Itemize
34331 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34337 \begin_layout Itemize
34338 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34344 \begin_layout Itemize
34345 \begin_inset Formula $\det\left[\begin{array}{ccc}
34349 \end{array}\right]=-56$
34355 \begin_layout Itemize
34356 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34362 \begin_layout Subsection
34366 \begin_layout Standard
34367 Currently there is no keyboard shortcut for calling the algebra applications.
34368 One can easily bind a shortcut to the
34382 \begin_inset space \thinspace{}
34386 \begin_inset space \space{}
34393 key inside the math editor.
34398 one would use this shortcut definition command:
34401 \begin_layout Standard
34404 command-alternatives paragraph-break;math-extern maxima
34407 \begin_layout Section
34409 \begin_inset Index idx
34412 \begin_layout Plain Layout
34421 \begin_layout Subsection
34423 \begin_inset Index idx
34426 \begin_layout Plain Layout
34435 \begin_layout Standard
34436 Negative numbers often look ugly in formulas because the minus sign before
34437 the number is set with the same length as the minus operator sign.
34438 When writing the negative number in normal text, the minus sign appears
34442 \begin_layout Standard
34443 Thus, the problem disappears when converting the minus sign to mathematical
34447 \begin_layout Standard
34448 An example to visualize the problem:
34449 \begin_inset Separator parbreak
34455 \begin_layout Standard
34457 \begin_inset Tabular
34458 <lyxtabular version="3" rows="3" columns="2">
34459 <features booktabs="true" tabularvalignment="middle">
34460 <column alignment="right" valignment="top" width="0pt">
34461 <column alignment="left" valignment="top">
34463 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34466 \begin_layout Plain Layout
34472 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34475 \begin_layout Plain Layout
34483 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34486 \begin_layout Plain Layout
34492 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34495 \begin_layout Plain Layout
34496 \begin_inset Formula $x=-2$
34506 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34509 \begin_layout Plain Layout
34515 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34518 \begin_layout Plain Layout
34519 \begin_inset Formula $x=\textrm{-}2$
34535 \begin_layout Subsection
34536 Comma as decimal Separator
34537 \begin_inset Index idx
34540 \begin_layout Plain Layout
34549 \begin_layout Standard
34550 In \SpecialChar LaTeX
34551 a comma inside a formula is used, according to the English convention,
34552 as number group separator.
34553 So there will be space added behind all commas in formulas.
34556 \begin_layout Standard
34557 To avoid this, the comma is highlighted and changed to mathematical text
34567 \begin_layout Standard
34568 To use all formula commas in the document as decimal separator, the file
34577 \begin_layout Plain Layout
34582 is part of the \SpecialChar LaTeX
34588 \begin_inset Index idx
34591 \begin_layout Plain Layout
34596 \begin_layout Plain Layout
34616 \begin_inset Index idx
34619 \begin_layout Plain Layout
34625 is loaded with the \SpecialChar LaTeX
34629 \begin_layout Standard
34637 \begin_layout Subsection
34639 \begin_inset CommandInset label
34641 name "subsec:Physical-Vectors"
34646 \begin_inset Index idx
34649 \begin_layout Plain Layout
34658 \begin_layout Standard
34659 Predefined vectors are offered by the \SpecialChar LaTeX
34665 \begin_inset Index idx
34668 \begin_layout Plain Layout
34674 that is loaded with the \SpecialChar LaTeX
34678 \begin_layout Standard
34686 \begin_layout Standard
34690 \begin_layout Plain Layout
34700 \begin_inset Note Note
34703 \begin_layout Plain Layout
34704 The following table will only be displayed when the \SpecialChar LaTeX
34717 \begin_layout Standard
34718 The following commands are defined:
34719 \begin_inset Separator parbreak
34725 \begin_layout Standard
34727 \begin_inset Tabular
34728 <lyxtabular version="3" rows="4" columns="2">
34729 <features booktabs="true" tabularvalignment="middle">
34730 <column alignment="center" valignment="top" width="0pt">
34731 <column alignment="center" valignment="top">
34733 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34736 \begin_layout Plain Layout
34742 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34745 \begin_layout Plain Layout
34753 <cell alignment="center" valignment="top" usebox="none">
34756 \begin_layout Plain Layout
34766 <cell alignment="center" valignment="top" usebox="none">
34769 \begin_layout Plain Layout
34770 \begin_inset Formula $\Bra{\psi}$
34780 <cell alignment="center" valignment="top" usebox="none">
34783 \begin_layout Plain Layout
34793 <cell alignment="center" valignment="top" usebox="none">
34796 \begin_layout Plain Layout
34797 \begin_inset Formula $\Ket{\psi}$
34807 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34810 \begin_layout Plain Layout
34822 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34825 \begin_layout Plain Layout
34826 \begin_inset Formula $\Braket{\psi|\phi}$
34842 \begin_layout Standard
34849 assures that all vertical bars are set in the size of the surrounding brackets:
34850 \begin_inset Formula
34852 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34861 \begin_layout Plain Layout
34871 \begin_inset Note Note
34874 \begin_layout Plain Layout
34875 The following will be displayed when the \SpecialChar LaTeX
34888 \begin_layout Standard
34889 You need to install the \SpecialChar LaTeX
34894 to see the rest of this subsection in the output.
34897 \begin_layout Standard
34901 \begin_layout Plain Layout
34913 \begin_layout Standard
34920 can also be achieved using the command
34926 , that is described in
34927 \begin_inset CommandInset ref
34929 reference "subsec:Automatic-Bracket-Size"
34936 \begin_layout Subsection
34937 Self-defined Fractions
34938 \begin_inset CommandInset label
34940 name "subsec:Self-defined-Fractions"
34945 \begin_inset Index idx
34948 \begin_layout Plain Layout
34949 Fractions ! self-defined
34957 \begin_layout Standard
34958 To define custom commands for fractions, the command
34965 \begin_inset Index idx
34968 \begin_layout Plain Layout
34975 \begin_layout Plain Layout
34989 is used in the following scheme:
34992 \begin_layout Standard
35005 bracket}{fraction bar thickness}{style}
35006 \begin_inset Newline newline
35010 \begin_inset Phantom HPhantom
35013 \begin_layout Plain Layout
35023 {numerator}{denominator}
35026 \begin_layout Standard
35027 The style is a number in the range of 0
35028 \begin_inset space \thinspace{}
35032 \begin_inset space \thinspace{}
35036 \begin_inset Separator parbreak
35042 \begin_layout Standard
35044 \begin_inset Tabular
35045 <lyxtabular version="3" rows="5" columns="2">
35046 <features booktabs="true" tabularvalignment="middle">
35047 <column alignment="center" valignment="top" width="0pt">
35048 <column alignment="center" valignment="top">
35050 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35053 \begin_layout Plain Layout
35059 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35062 \begin_layout Plain Layout
35070 <cell alignment="center" valignment="top" usebox="none">
35073 \begin_layout Plain Layout
35079 <cell alignment="center" valignment="top" usebox="none">
35082 \begin_layout Plain Layout
35083 display style formula
35090 <cell alignment="center" valignment="top" usebox="none">
35093 \begin_layout Plain Layout
35099 <cell alignment="center" valignment="top" usebox="none">
35102 \begin_layout Plain Layout
35110 <cell alignment="center" valignment="top" usebox="none">
35113 \begin_layout Plain Layout
35119 <cell alignment="center" valignment="top" usebox="none">
35122 \begin_layout Plain Layout
35130 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35133 \begin_layout Plain Layout
35139 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35142 \begin_layout Plain Layout
35156 \begin_layout Standard
35157 When no style is given, the size is adjusted to the surrounding environment
35158 like for the command
35167 \begin_layout Standard
35168 When no fraction bar thickness is given, the predefined value of 0.4
35169 \begin_inset space \thinspace{}
35175 \begin_layout Standard
35176 \begin_inset VSpace medskip
35179 For example, the commands
35192 \begin_inset CommandInset ref
35194 reference "subsec:Fractions"
35198 are defined with the commands
35201 \begin_layout Standard
35210 genfrac{}{}{}{0}{#1}{#2}}
35213 \begin_layout Standard
35217 \begin_layout Standard
35226 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35229 \begin_layout Standard
35230 \begin_inset VSpace medskip
35233 To define a fraction where the fraction bar thickness can be given as optional
35234 argument, the following line is inserted to the \SpecialChar LaTeX
35238 \begin_layout Standard
35247 genfrac{}{}{#1}{}{#2}{#3}}
35250 \begin_layout Standard
35252 \begin_inset Formula
35254 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35255 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35260 As one can see, the distance of the numerator and the denominator to the
35261 fraction bar is round about three times the bar thickness.
35264 \begin_layout Subsection
35266 \begin_inset Index idx
35269 \begin_layout Plain Layout
35278 \begin_layout Standard
35279 There are four ways to cancel formulas or parts of formulas:
35282 \begin_layout Standard
35286 \begin_layout Plain Layout
35296 \begin_inset Note Note
35299 \begin_layout Plain Layout
35300 The following table will only be displayed when the \SpecialChar LaTeX
35311 \begin_inset Separator parbreak
35317 \begin_layout Standard
35319 \begin_inset Tabular
35320 <lyxtabular version="3" rows="5" columns="2">
35321 <features booktabs="true" tabularvalignment="middle">
35322 <column alignment="center" valignment="top" width="0pt">
35323 <column alignment="center" valignment="top">
35325 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35328 \begin_layout Plain Layout
35334 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35337 \begin_layout Plain Layout
35345 <cell alignment="center" valignment="top" usebox="none">
35348 \begin_layout Plain Layout
35352 \begin_inset space \textvisiblespace{}
35358 \begin_inset space \textvisiblespace{}
35366 <cell alignment="center" valignment="top" usebox="none">
35369 \begin_layout Plain Layout
35370 \begin_inset Formula $\cancel{\int A=B}$
35379 <row topspace="1.5mm">
35380 <cell alignment="center" valignment="top" usebox="none">
35383 \begin_layout Plain Layout
35387 \begin_inset space \textvisiblespace{}
35393 \begin_inset space \textvisiblespace{}
35401 <cell alignment="center" valignment="top" usebox="none">
35404 \begin_layout Plain Layout
35405 \begin_inset Formula $\bcancel{\int A=B}$
35414 <row topspace="1.5mm">
35415 <cell alignment="center" valignment="top" usebox="none">
35418 \begin_layout Plain Layout
35422 \begin_inset space \textvisiblespace{}
35428 \begin_inset space \textvisiblespace{}
35436 <cell alignment="center" valignment="top" usebox="none">
35439 \begin_layout Plain Layout
35440 \begin_inset Formula $\xcancel{\int A=B}$
35450 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35453 \begin_layout Plain Layout
35457 \begin_inset space \textvisiblespace{}
35463 \begin_inset space \textvisiblespace{}
35467 \begin_inset Formula $\to$
35475 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35478 \begin_layout Plain Layout
35479 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35495 \begin_layout Standard
35502 is especially suitable to visualize the reduction of fractions within formulas:
35503 \begin_inset Formula
35505 \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}}}
35513 \begin_layout Standard
35514 To change the size of
35521 \begin_inset Quotes eld
35525 \begin_inset Quotes erd
35528 value one can add the \SpecialChar LaTeX
35532 \begin_layout Standard
35537 PassOptionsToPackage{option}{cancel}
35540 \begin_layout Standard
35549 which leads to the same size as for the canceled value, or
35553 which makes is it a bit smaller than normal.
35556 \begin_layout Standard
35557 To color the cancellation bar one adds this command as \SpecialChar TeX
35561 \begin_layout Standard
35573 \begin_layout Standard
35578 can be replaced by a color of your choice.
35581 \begin_layout Standard
35585 \begin_layout Plain Layout
35601 \begin_layout Standard
35602 \begin_inset Formula
35604 \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}}}
35612 \begin_layout Standard
35616 \begin_layout Plain Layout
35630 \begin_inset Note Note
35633 \begin_layout Plain Layout
35642 \begin_layout Standard
35643 For further customizations, see the documentation of the package
35648 \begin_inset CommandInset citation
35655 \begin_inset Index idx
35658 \begin_layout Plain Layout
35667 \begin_layout Standard
35671 \begin_layout Plain Layout
35681 \begin_inset Note Note
35684 \begin_layout Plain Layout
35685 The following will be displayed when the \SpecialChar LaTeX
35698 \begin_layout Standard
35699 You need to install the \SpecialChar LaTeX
35704 to see the rest of this subsection in the output.
35707 \begin_layout Standard
35711 \begin_layout Plain Layout
35723 \begin_layout Subsection
35724 Formulas in Section Headings
35725 \begin_inset CommandInset label
35727 name "subsec:Formulas-in-Section"
35732 \begin_inset Index idx
35735 \begin_layout Plain Layout
35736 Formula ! in section headings
35744 \begin_layout Standard
35745 When formulas are used in section headings, the following has to be taken
35749 \begin_layout Standard
35750 \begin_inset Note Greyedout
35753 \begin_layout Plain Layout
35759 \begin_inset Index idx
35762 \begin_layout Plain Layout
35763 Packages ! hyperref
35768 support is enabled in the document settings dialog under
35771 \begin_inset space ~
35776 , PDF-bookmarks are created for every section heading in the table of contents.
35777 If a section heading contains formulas, they are incorrectly displayed
35778 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35787 \begin_layout Standard
35788 Both problems can be solved by inserting at the end of the section heading
35789 a short title with the menu
35791 Insert\SpecialChar menuseparator
35793 \begin_inset space ~
35799 Short titles are used as alternative for multiline section headings to
35800 keep the table of contents clearly arranged.
35801 Only the short title appears in the table of contents and therefore also
35802 in the PDF-bookmark.
35805 \begin_layout Standard
35806 When formulas should be used in the table of contents but
35810 is used, one can use the following command in \SpecialChar TeX
35814 \begin_layout Standard
35819 texorpdfstring{part}{alternative}
35820 \begin_inset Index idx
35823 \begin_layout Plain Layout
35834 \begin_layout Standard
35835 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35836 This can be characters, formulas, footnotes, but also cross-references.
35837 The alternative is used instead of the part for the bookmark.
35840 \begin_layout Standard
35841 Here are two example headings:
35842 \begin_inset VSpace -3mm
35849 \begin_layout Plain Layout
35861 \begin_layout Subsubsection
35862 Heading without formula in table of contents
35863 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35867 \begin_inset Argument 1
35870 \begin_layout Plain Layout
35871 Heading without formula in table of contents
35879 \begin_layout Subsubsection
35880 Heading with formula in table of contents
35884 \begin_layout Plain Layout
35894 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35901 \begin_layout Plain Layout
35911 \begin_layout Standard
35915 \begin_layout Plain Layout
35924 In the first heading a short title was used, in the second one
35933 \begin_layout Standard
35934 To get the same formatting as for the other headings, the complete heading
35943 \begin_layout Plain Layout
35945 \begin_inset CommandInset ref
35947 reference "subsec:Bold-Formulas"
35959 \begin_layout Subsection
35960 Formulas in multi-column Text
35961 \begin_inset Index idx
35964 \begin_layout Plain Layout
35965 Formula ! in multi-column text
35973 \begin_layout Standard
35974 Formulas in multi-column text are often too wide to fit into a column and
35975 thus need to be set over the whole page width.
35976 This is done by using the \SpecialChar LaTeX
35985 \begin_layout Plain Layout
35990 is part of every \SpecialChar LaTeX
35991 standard installation.
35997 \begin_inset Index idx
36000 \begin_layout Plain Layout
36001 Packages ! multicol
36006 , that is loaded with the \SpecialChar LaTeX
36010 \begin_layout Standard
36015 usepackage{multicol}
36018 \begin_layout Standard
36019 \begin_inset Note Greyedout
36022 \begin_layout Plain Layout
36023 Note that in this case the setting
36026 \begin_inset space ~
36033 Document\SpecialChar menuseparator
36039 \begin_inset space ~
36059 \begin_layout Standard
36060 Before the multi-column text the command
36063 \begin_layout Standard
36068 begin{multicols}{column number}
36071 \begin_layout Standard
36072 is written in \SpecialChar TeX
36074 The column number is a number in the range of 2
36075 \begin_inset space \thinspace{}
36079 \begin_inset space \thinspace{}
36083 Before the formula the multi-column text is ended by inserting the command
36086 \begin_layout Standard
36094 \begin_layout Standard
36095 in \SpecialChar TeX
36099 \begin_layout Standard
36100 Due to the command some space is automatically added before the formula.
36102 \begin_inset space \thinspace{}
36105 mm vertical space is inserted before the formula.
36106 When the formula style
36112 \begin_layout Plain Layout
36114 \begin_inset CommandInset ref
36116 reference "sec:Formula-Styles"
36128 \begin_inset space \thinspace{}
36131 mm space is inserted instead.
36134 \begin_layout Standard
36135 As example a multi-column text with a displayed formula:
36138 \begin_layout Standard
36144 \begin_layout Plain Layout
36148 begin{multicols}{2}
36153 Das Spektrum wird fouriertransformiert.
36154 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36155 , Lösungsmittel) zu trennen.
36156 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36157 nun das Aussehen des Ausgangssignals.
36158 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36159 über alle Phasen integrieren muss.
36161 \begin_inset Formula $S$
36164 unser normiertes Ausgangssignal und
36165 \begin_inset Formula $P$
36168 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36172 \begin_layout Plain Layout
36182 \begin_inset VSpace -6mm
36186 \begin_inset Formula
36188 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36197 \begin_layout Plain Layout
36201 begin{multicols}{2}
36207 \begin_inset Formula $S_{0}$
36210 das Signal ohne Gradient ist und die Normierungsbedingung
36211 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36215 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36217 \begin_inset Formula $\nicefrac{\pi}{2}$
36221 \begin_inset space \thinspace{}
36224 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36225 das Signal zusätzlich abschwächt.
36226 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36228 \begin_inset Formula $T_{2}$
36234 \begin_layout Standard
36240 \begin_layout Plain Layout
36252 \begin_layout Subsection
36253 Formulas with Description of Variables
36254 \begin_inset Index idx
36257 \begin_layout Plain Layout
36258 Formula ! with description of variables
36266 \begin_layout Standard
36267 To describe variables within a formula, like in formula
36268 \begin_inset CommandInset ref
36270 reference "eq:within"
36279 \begin_inset Formula $n$
36283 \begin_inset space ~
36286 matrix is used with left aligned columns for the
36287 \begin_inset Formula $n$
36294 \begin_layout Plain Layout
36296 \begin_inset CommandInset ref
36298 reference "sec:Matrices"
36307 To set the description in a smaller size, before the matrix e.
36308 \begin_inset space \thinspace{}
36312 \begin_inset space \space{}
36325 \begin_layout Plain Layout
36327 \begin_inset CommandInset ref
36329 reference "subsec:Font-Sizes"
36341 \begin_layout Standard
36342 When the formula style
36348 \begin_layout Plain Layout
36350 \begin_inset CommandInset ref
36352 reference "sec:Formula-Styles"
36373 \begin_layout Plain Layout
36380 only works in formulas with the style
36385 \begin_inset CommandInset ref
36387 reference "subsec:Variable-Space"
36396 is inserted before and after the matrix to have the same separation of
36397 the matrix from the equation and the side margin.
36400 \begin_layout Standard
36401 When the formula style
36405 is used, the method described in
36406 \begin_inset CommandInset ref
36408 reference "subsec:Flalign-Environment"
36412 is used to indent formulas.
36414 \begin_inset CommandInset ref
36416 reference "eq:within"
36420 consists of five columns where in the first two columns contain the equation,
36421 the third the matrix and the last one an empty \SpecialChar TeX
36423 \begin_inset Formula
36425 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36426 \rho & \textrm{density}\\
36427 V & \textrm{volume}\\
36428 g & \textrm{gravitational acceleration}
36429 \end{array} & & {}\label{eq:within}
36437 \begin_layout Subsection
36438 Upright small Greek Letters
36439 \begin_inset CommandInset label
36441 name "subsec:Upright-small-Greek"
36446 \begin_inset Index idx
36449 \begin_layout Plain Layout
36450 Greek letters ! upright
36458 \begin_layout Standard
36459 Most of the math fonts only provide italic small Greek letters.
36460 But for symbols of elementary particles like pions and neutrinos, upright
36461 Greek letters are needed.
36470 \begin_layout Plain Layout
36475 is part of the \SpecialChar LaTeX
36481 \begin_inset Index idx
36484 \begin_layout Plain Layout
36489 \begin_layout Plain Layout
36509 \begin_inset Index idx
36512 \begin_layout Plain Layout
36518 that is loaded with the \SpecialChar LaTeX
36522 \begin_layout Standard
36527 usepackage{upgreek}
36530 \begin_layout Standard
36536 \begin_layout Plain Layout
36546 \begin_inset Note Note
36549 \begin_layout Plain Layout
36550 The following table will only be displayed when the \SpecialChar LaTeX
36560 They are created when the command for a small Greek letter is started with
36566 For example the command
36573 \begin_inset Formula $\uptau$
36579 \begin_layout Standard
36580 With these commands reactions of elementary particles can be typeset:
36581 \begin_inset Formula
36583 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36591 \begin_layout Standard
36592 The upright letters are more bold and wider than the italic ones.
36593 They should therefore not be used for units like
36594 \begin_inset Quotes eld
36598 \begin_inset Quotes erd
36604 \begin_layout Standard
36608 \begin_layout Plain Layout
36618 \begin_inset Note Note
36621 \begin_layout Plain Layout
36622 The following will be displayed when the \SpecialChar LaTeX
36635 \begin_layout Standard
36636 You need to install the \SpecialChar LaTeX
36641 to see the rest of this subsection in the output.
36644 \begin_layout Standard
36648 \begin_layout Plain Layout
36660 \begin_layout Subsection
36661 Text Characters in Formulas
36662 \begin_inset Index idx
36665 \begin_layout Plain Layout
36674 \begin_layout Standard
36675 In some cases you might want to insert text characters directly into formulas.
36676 When for example the centered dot · is often used in formulas like
36677 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36680 , one would have to insert the command
36690 \begin_layout Plain Layout
36692 \begin_inset CommandInset ref
36694 reference "subsec:Binary-Operators"
36703 all the time, because this character is defined in all encodings as text
36705 But the encoding can be changed by this \SpecialChar LaTeX
36709 \begin_layout Standard
36714 Declare Inputtext{183}{
36724 f\SpecialChar ligaturebreak
36728 \begin_layout Standard
36729 The character encoding (menu
36731 Document\SpecialChar menuseparator
36732 Settings\SpecialChar menuseparator
36735 ) specifies what character appears when a keyboard key is pressed.
36736 When the key for the character '·' is pressed, internally the command
36743 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36745 With the changed encoding the right command is chosen automatically, depending
36746 on if the character was inserted into a formula or not.
36749 \begin_layout Standard
36750 The encoding of several characters is saved in definition files.
36751 For example the encoding
36755 is defined in the file
36759 which is in the installation folder of \SpecialChar LaTeX
36761 Encodings should only be changed via the \SpecialChar LaTeX
36762 -preamble and not in the definition
36764 Otherwise documents could not be edited by other \SpecialChar LyX
36765 users working on other
36769 \begin_layout Standard
36770 \begin_inset VSpace medskip
36773 Besides the centered dot, in this document the degree sign ° is defined
36774 with the following \SpecialChar LaTeX
36775 -preamble line so that it can be directly inserted into
36779 \begin_layout Standard
36784 DeclareInputtext{176}{
36794 f\SpecialChar ligaturebreak
36798 \begin_layout Subsection
36800 -comments in formulas
36801 \begin_inset Index idx
36804 \begin_layout Plain Layout
36814 \begin_layout Standard
36815 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36817 code of your file with the menu
36819 Insert\SpecialChar menuseparator
36820 Note\SpecialChar menuseparator
36824 This is not possible in a formula but you can insert \SpecialChar LaTeX
36829 \begin_layout Standard
36837 \begin_layout Standard
36838 This creates a box in which you can write your comment.
36839 Due to a bug in \SpecialChar LyX
36844 \begin_layout Plain Layout
36845 \begin_inset CommandInset href
36847 name "LyX-bug #9002"
36848 target "http://www.lyx.org/trac/ticket/9002"
36857 you cannot write normal text inside the comment, even when you use mathematical
36858 text, you will see its \SpecialChar LaTeX
36859 -commands in the \SpecialChar LaTeX
36861 \begin_inset Newline newline
36864 This a formula with a \SpecialChar LaTeX
36866 \begin_inset Formula
36868 A=B%\text{This is the comment}
36876 \begin_layout Standard
36877 \begin_inset Newpage newpage
36883 \begin_layout Section
36886 \begin_inset Index idx
36889 \begin_layout Plain Layout
36898 \begin_layout Standard
36899 This section is a summary of the most important typographic rules, listed
36904 \begin_layout Plain Layout
36905 This collection was partly taken from the German semi-official dictionary
36907 \begin_inset Quotes eld
36911 \begin_inset Quotes erd
36915 \begin_inset CommandInset citation
36921 that lists some of the ISO rules.
36922 More rules are listed in
36923 \begin_inset CommandInset citation
36937 \begin_layout Itemize
36946 \begin_layout Plain Layout
36947 done with font styles, see
36948 \begin_inset CommandInset ref
36950 reference "subsec:Font-Styles"
36959 , no matter if they appear in italic text: 30
36960 \begin_inset space \thinspace{}
36964 \begin_inset Newline newline
36967 Between the value and the unit is the smallest space, see
36968 \begin_inset CommandInset ref
36970 reference "subsec:Predefined-Space"
36975 \begin_inset Newline newline
36978 This convention is automatically fulfilled when the command
36985 When it is entered to a formula, two boxes appear.
36986 In the first one the value is inserted, in the second one the unit, and
36988 \begin_inset Formula $\unit[30]{km/h}$
36992 \begin_inset space \thinspace{}
37002 is not a real \SpecialChar LaTeX
37003 command but the command
37009 , therefore you cannot use it in \SpecialChar TeX
37013 \begin_layout Itemize
37014 Percent and perthousand signs are set like physical units:
37015 \begin_inset Newline newline
37019 \begin_inset space \thinspace{}
37025 \begin_layout Itemize
37026 The degree sign follows directly on the value: 15°, but not when it is used
37028 \begin_inset space \thinspace{}
37034 \begin_layout Itemize
37035 In numbers with more than four digits the smallest space is inserted before
37036 every third digit to group them:
37046 \begin_inset space \thinspace{}
37050 \begin_inset space \thinspace{}
37056 \begin_layout Itemize
37057 For dimensions like 120×90×40
37058 \begin_inset space \thinspace{}
37061 cm the multiplication sign
37062 \begin_inset Quotes eld
37066 \begin_inset Quotes erd
37070 It is available either via the command
37078 Insert\SpecialChar menuseparator
37079 Special Character\SpecialChar menuseparator
37085 \begin_layout Itemize
37086 Functions with names consisting of several letters are set upright to avoid
37088 \begin_inset CommandInset ref
37090 reference "subsec:Predefined-Functions"
37097 \begin_layout Itemize
37098 Indices consisting of several letters, are set upright:
37099 \begin_inset Formula $E_{\mathrm{kin}}$
37103 \begin_inset Newline newline
37106 Components of matrices are set italic:
37107 \begin_inset Formula $\hat{H}_{kl}$
37113 \begin_layout Itemize
37114 The differentiation/integration operator 'd', the Euler's number 'e' and
37115 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37119 \begin_layout Itemize
37120 The character that denotes a
37124 transformation is inserted either by the command
37129 \begin_inset space \textvisiblespace{}
37136 Insert\SpecialChar menuseparator
37137 Special Character\SpecialChar menuseparator
37138 Symbols\SpecialChar menuseparator
37140 \begin_inset space ~
37146 \begin_inset Formula $\mathscr{F}$
37152 \begin_layout Standard
37153 \begin_inset Newpage newpage
37159 \begin_layout Section
37161 \begin_inset Index idx
37164 \begin_layout Plain Layout
37173 \begin_layout Standard
37174 Some characters and symbols can be created with several commands.
37175 Here is a list of the synonym commands:
37178 \begin_layout Standard
37179 \begin_inset VSpace bigskip
37183 \begin_inset space \hfill{}
37187 \begin_inset Tabular
37188 <lyxtabular version="3" rows="12" columns="2">
37189 <features booktabs="true" tabularvalignment="middle">
37190 <column alignment="center" valignment="top" width="0pt">
37191 <column alignment="center" valignment="top" width="0pt">
37193 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37196 \begin_layout Plain Layout
37202 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37205 \begin_layout Plain Layout
37213 <cell alignment="center" valignment="top" usebox="none">
37216 \begin_layout Plain Layout
37224 <cell alignment="center" valignment="top" usebox="none">
37227 \begin_layout Plain Layout
37235 <cell alignment="center" valignment="top" usebox="none">
37238 \begin_layout Plain Layout
37246 <cell alignment="center" valignment="top" usebox="none">
37249 \begin_layout Plain Layout
37259 <cell alignment="center" valignment="top" usebox="none">
37262 \begin_layout Plain Layout
37270 <cell alignment="center" valignment="top" usebox="none">
37273 \begin_layout Plain Layout
37283 <cell alignment="center" valignment="top" usebox="none">
37286 \begin_layout Plain Layout
37294 <cell alignment="center" valignment="top" usebox="none">
37297 \begin_layout Plain Layout
37305 <cell alignment="center" valignment="top" usebox="none">
37308 \begin_layout Plain Layout
37316 <cell alignment="center" valignment="top" usebox="none">
37319 \begin_layout Plain Layout
37327 <cell alignment="center" valignment="top" usebox="none">
37330 \begin_layout Plain Layout
37338 <cell alignment="center" valignment="top" usebox="none">
37341 \begin_layout Plain Layout
37351 <cell alignment="center" valignment="top" usebox="none">
37354 \begin_layout Plain Layout
37362 <cell alignment="center" valignment="top" usebox="none">
37365 \begin_layout Plain Layout
37375 <cell alignment="center" valignment="top" usebox="none">
37378 \begin_layout Plain Layout
37386 <cell alignment="center" valignment="top" usebox="none">
37389 \begin_layout Plain Layout
37399 <cell alignment="center" valignment="top" usebox="none">
37402 \begin_layout Plain Layout
37410 <cell alignment="center" valignment="top" usebox="none">
37413 \begin_layout Plain Layout
37423 <cell alignment="center" valignment="top" usebox="none">
37426 \begin_layout Plain Layout
37434 <cell alignment="center" valignment="top" usebox="none">
37437 \begin_layout Plain Layout
37445 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37448 \begin_layout Plain Layout
37456 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37459 \begin_layout Plain Layout
37471 \begin_inset space \hfill{}
37475 \begin_inset Tabular
37476 <lyxtabular version="3" rows="12" columns="2">
37477 <features booktabs="true" tabularvalignment="middle">
37478 <column alignment="center" valignment="top" width="0pt">
37479 <column alignment="center" valignment="top" width="0pt">
37481 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37484 \begin_layout Plain Layout
37490 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37493 \begin_layout Plain Layout
37501 <cell alignment="center" valignment="top" usebox="none">
37504 \begin_layout Plain Layout
37512 <cell alignment="center" valignment="top" usebox="none">
37515 \begin_layout Plain Layout
37527 <cell alignment="center" valignment="top" usebox="none">
37530 \begin_layout Plain Layout
37538 <cell alignment="center" valignment="top" usebox="none">
37541 \begin_layout Plain Layout
37551 <cell alignment="center" valignment="top" usebox="none">
37554 \begin_layout Plain Layout
37562 <cell alignment="center" valignment="top" usebox="none">
37565 \begin_layout Plain Layout
37575 <cell alignment="center" valignment="top" usebox="none">
37578 \begin_layout Plain Layout
37586 <cell alignment="center" valignment="top" usebox="none">
37589 \begin_layout Plain Layout
37597 <cell alignment="center" valignment="top" usebox="none">
37600 \begin_layout Plain Layout
37608 <cell alignment="center" valignment="top" usebox="none">
37611 \begin_layout Plain Layout
37619 <cell alignment="center" valignment="top" usebox="none">
37622 \begin_layout Plain Layout
37630 <cell alignment="center" valignment="top" usebox="none">
37633 \begin_layout Plain Layout
37643 <cell alignment="center" valignment="top" usebox="none">
37646 \begin_layout Plain Layout
37654 <cell alignment="center" valignment="top" usebox="none">
37657 \begin_layout Plain Layout
37667 <cell alignment="center" valignment="top" usebox="none">
37670 \begin_layout Plain Layout
37678 <cell alignment="center" valignment="top" usebox="none">
37681 \begin_layout Plain Layout
37691 <cell alignment="center" valignment="top" usebox="none">
37694 \begin_layout Plain Layout
37702 <cell alignment="center" valignment="top" usebox="none">
37705 \begin_layout Plain Layout
37715 <cell alignment="center" valignment="top" usebox="none">
37718 \begin_layout Plain Layout
37726 <cell alignment="center" valignment="top" usebox="none">
37729 \begin_layout Plain Layout
37739 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37742 \begin_layout Plain Layout
37750 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37753 \begin_layout Plain Layout
37767 \begin_inset space \hfill{}
37773 \begin_layout Standard
37774 \begin_inset Newpage newpage
37780 \begin_layout Bibliography
37781 \begin_inset CommandInset bibitem
37782 LatexCommand bibitem
37794 The \SpecialChar LaTeX
37798 Addison Wesley, 2004
37801 \begin_layout Bibliography
37802 \begin_inset CommandInset bibitem
37803 LatexCommand bibitem
37809 \begin_inset CommandInset href
37812 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37816 of \SpecialChar LaTeX
37820 \begin_layout Bibliography
37821 \begin_inset CommandInset bibitem
37822 LatexCommand bibitem
37828 \begin_inset CommandInset href
37831 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37839 \begin_layout Plain Layout
37848 -\SpecialChar LaTeX
37852 \begin_layout Bibliography
37853 \begin_inset CommandInset bibitem
37854 LatexCommand bibitem
37860 \begin_inset CommandInset href
37863 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37867 of all symbols available with \SpecialChar LaTeX
37871 \begin_layout Bibliography
37872 \begin_inset CommandInset bibitem
37873 LatexCommand bibitem
37879 \begin_inset CommandInset href
37881 name "Documentation"
37882 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37886 of the \SpecialChar LaTeX
37892 \begin_inset Index idx
37895 \begin_layout Plain Layout
37904 \begin_layout Bibliography
37905 \begin_inset CommandInset bibitem
37906 LatexCommand bibitem
37912 \begin_inset CommandInset href
37914 name "Documentation"
37915 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37919 of the \SpecialChar LaTeX
37925 \begin_inset Index idx
37928 \begin_layout Plain Layout
37929 Packages ! hyperref
37937 \begin_layout Bibliography
37938 \begin_inset CommandInset bibitem
37939 LatexCommand bibitem
37945 \begin_inset CommandInset href
37947 name "Documentation"
37948 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37952 of the \SpecialChar LaTeX
37958 \begin_inset Index idx
37961 \begin_layout Plain Layout
37970 \begin_layout Bibliography
37971 \begin_inset CommandInset bibitem
37972 LatexCommand bibitem
37983 Auflage, Duden 2001
37986 \begin_layout Bibliography
37987 \begin_inset CommandInset bibitem
37988 LatexCommand bibitem
37994 \begin_inset CommandInset href
37997 target "http://physics.nist.gov/Document/checklist.pdf"
38001 for reviewing manuscripts
38004 \begin_layout Standard
38005 \begin_inset CommandInset index_print
38006 LatexCommand printindex