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 space \hfill{}
16997 \begin_inset Tabular
16998 <lyxtabular version="3" rows="13" columns="2">
16999 <features tabularvalignment="middle">
17000 <column alignment="center" valignment="top" width="0pt">
17001 <column alignment="center" valignment="top" width="0pt">
17003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17006 \begin_layout Plain Layout
17008 \begin_inset Note Note
17011 \begin_layout Plain Layout
17018 is only used as spacer.
17028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17031 \begin_layout Plain Layout
17039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17042 \begin_layout Plain Layout
17048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17051 \begin_layout Plain Layout
17052 \begin_inset Formula $+$
17062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17065 \begin_layout Plain Layout
17071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17074 \begin_layout Plain Layout
17075 \begin_inset Formula $-$
17085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17088 \begin_layout Plain Layout
17096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17099 \begin_layout Plain Layout
17100 \begin_inset Formula $\pm$
17110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17113 \begin_layout Plain Layout
17121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17124 \begin_layout Plain Layout
17125 \begin_inset Formula $\mp$
17135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17138 \begin_layout Plain Layout
17146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17149 \begin_layout Plain Layout
17150 \begin_inset Formula $\cdot$
17160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17163 \begin_layout Plain Layout
17171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17174 \begin_layout Plain Layout
17175 \begin_inset Formula $\times$
17185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17188 \begin_layout Plain Layout
17196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17199 \begin_layout Plain Layout
17200 \begin_inset Formula $\div$
17210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17213 \begin_layout Plain Layout
17217 \begin_layout Plain Layout
17230 \begin_layout Plain Layout
17242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17245 \begin_layout Plain Layout
17246 \begin_inset Formula $*$
17256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17259 \begin_layout Plain Layout
17267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17270 \begin_layout Plain Layout
17271 \begin_inset Formula $\star$
17281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17284 \begin_layout Plain Layout
17292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17295 \begin_layout Plain Layout
17296 \begin_inset Formula $\circ$
17306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17309 \begin_layout Plain Layout
17317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17320 \begin_layout Plain Layout
17321 \begin_inset Formula $\diamond$
17331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17334 \begin_layout Plain Layout
17342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17345 \begin_layout Plain Layout
17346 \begin_inset Formula $\bullet$
17360 \begin_inset space \hfill{}
17364 \begin_inset Tabular
17365 <lyxtabular version="3" rows="13" columns="2">
17366 <features tabularvalignment="middle">
17367 <column alignment="center" valignment="top" width="0pt">
17368 <column alignment="center" valignment="top" width="0pt">
17370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17373 \begin_layout Plain Layout
17379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17382 \begin_layout Plain Layout
17390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17393 \begin_layout Plain Layout
17401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17404 \begin_layout Plain Layout
17405 \begin_inset Formula $\nabla$
17415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17418 \begin_layout Plain Layout
17426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17429 \begin_layout Plain Layout
17430 \begin_inset Formula $\bigtriangledown$
17440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17443 \begin_layout Plain Layout
17451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17454 \begin_layout Plain Layout
17455 \begin_inset Formula $\bigtriangleup$
17465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17468 \begin_layout Plain Layout
17476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17479 \begin_layout Plain Layout
17480 \begin_inset Formula $\Box$
17490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17493 \begin_layout Plain Layout
17501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17504 \begin_layout Plain Layout
17505 \begin_inset Formula $\cap$
17515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17518 \begin_layout Plain Layout
17526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17529 \begin_layout Plain Layout
17530 \begin_inset Formula $\cup$
17540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17543 \begin_layout Plain Layout
17551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17554 \begin_layout Plain Layout
17555 \begin_inset Formula $\dagger$
17565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17568 \begin_layout Plain Layout
17576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17579 \begin_layout Plain Layout
17580 \begin_inset Formula $\ddagger$
17590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17593 \begin_layout Plain Layout
17601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17604 \begin_layout Plain Layout
17605 \begin_inset Formula $\wr$
17615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17618 \begin_layout Plain Layout
17626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17629 \begin_layout Plain Layout
17630 \begin_inset Formula $\bigcirc$
17640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17643 \begin_layout Plain Layout
17651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17654 \begin_layout Plain Layout
17655 \begin_inset Formula $\wedge$
17665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17668 \begin_layout Plain Layout
17676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17679 \begin_layout Plain Layout
17680 \begin_inset Formula $\vee$
17694 \begin_inset space \hfill{}
17698 \begin_inset Tabular
17699 <lyxtabular version="3" rows="13" columns="2">
17700 <features tabularvalignment="middle">
17701 <column alignment="center" valignment="top" width="0pt">
17702 <column alignment="center" valignment="top" width="0pt">
17704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17707 \begin_layout Plain Layout
17713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17716 \begin_layout Plain Layout
17724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17727 \begin_layout Plain Layout
17735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17738 \begin_layout Plain Layout
17739 \begin_inset Formula $\oplus$
17749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17752 \begin_layout Plain Layout
17760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17763 \begin_layout Plain Layout
17764 \begin_inset Formula $\ominus$
17774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17777 \begin_layout Plain Layout
17785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17788 \begin_layout Plain Layout
17789 \begin_inset Formula $\otimes$
17799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17802 \begin_layout Plain Layout
17810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17813 \begin_layout Plain Layout
17814 \begin_inset Formula $\oslash$
17824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17827 \begin_layout Plain Layout
17835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17838 \begin_layout Plain Layout
17839 \begin_inset Formula $\odot$
17849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17852 \begin_layout Plain Layout
17860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17863 \begin_layout Plain Layout
17864 \begin_inset Formula $\amalg$
17874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17877 \begin_layout Plain Layout
17885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17888 \begin_layout Plain Layout
17889 \begin_inset Formula $\uplus$
17899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17902 \begin_layout Plain Layout
17910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17913 \begin_layout Plain Layout
17914 \begin_inset Formula $\setminus$
17924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17927 \begin_layout Plain Layout
17935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17938 \begin_layout Plain Layout
17939 \begin_inset Formula $\sqcap$
17949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17952 \begin_layout Plain Layout
17960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17963 \begin_layout Plain Layout
17964 \begin_inset Formula $\sqcup$
17974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17977 \begin_layout Plain Layout
17985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17988 \begin_layout Plain Layout
17989 \begin_inset Formula $\triangleleft$
17999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18002 \begin_layout Plain Layout
18010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18013 \begin_layout Plain Layout
18014 \begin_inset Formula $\triangleright$
18028 \begin_inset space \hfill{}
18034 \begin_layout Standard
18035 All binary operators can also be inserted via the math toolbar button
18038 arg "math-insert \\pm"
18044 \begin_layout Standard
18045 To typeset the Laplace operator also
18062 \begin_inset Formula $\nabla^{2}$
18065 ) can be used instead of
18074 \begin_layout Standard
18081 Insert\SpecialChar menuseparator
18093 \begin_layout Subsection
18094 Self-defined Operators
18095 \begin_inset CommandInset label
18097 name "subsec:Self-defined-Operators"
18102 \begin_inset Index idx
18105 \begin_layout Plain Layout
18106 Operators ! self-defined
18114 \begin_layout Standard
18115 With the help of the command
18119 DeclareMathOperator
18122 \begin_inset Index idx
18125 \begin_layout Plain Layout
18130 DeclareMathOperator
18135 custom operators can be defined in the \SpecialChar LaTeX
18137 Its command scheme is:
18140 \begin_layout Standard
18145 DeclareMathOperator{new command}{display}
18148 \begin_layout Standard
18149 Display can be characters or symbols that define how the operator looks
18151 To define a big operator a * is set behind the command.
18152 All self-defined big operators can have limits as described in
18153 \begin_inset CommandInset ref
18155 reference "subsec:Operator-Limits"
18162 \begin_layout Standard
18163 For example the \SpecialChar LaTeX
18167 \begin_layout Standard
18172 DeclareMathOperator*{
18179 \begin_layout Standard
18180 defines the command
18186 , that inserts a big operator consisting of the lozenge symbol from
18187 \begin_inset CommandInset ref
18189 reference "subsec:Miscellaneous-Symbols"
18194 \begin_inset Formula
18196 \Lozenge_{n=1}^{\infty}
18201 The command for this formula is:
18212 \begin_inset Formula $\to$
18218 \begin_layout Standard
18219 \begin_inset VSpace bigskip
18222 When self-defined operators are not used several times in the document,
18223 they can also be defined with the commands
18230 \begin_inset Index idx
18233 \begin_layout Plain Layout
18248 \begin_inset Index idx
18251 \begin_layout Plain Layout
18259 , which have the following scheme:
18262 \begin_layout Standard
18276 \begin_layout Standard
18283 defines big operators,
18292 \begin_layout Standard
18300 \begin_inset space \thinspace{}
18304 \begin_inset space \space{}
18307 be used to use one limit for several operators:
18310 \begin_layout Standard
18311 \begin_inset Formula
18313 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18321 \begin_layout Standard
18322 The command for the formula above is:
18323 \begin_inset Newline newline
18339 \begin_inset space \textvisiblespace{}
18345 \begin_inset Formula $\to$
18351 \begin_inset space \textvisiblespace{}
18359 \begin_layout Section
18361 \begin_inset Index idx
18364 \begin_layout Plain Layout
18373 \begin_layout Subsection
18375 \begin_inset CommandInset label
18377 name "subsec:Font-Styles"
18382 \begin_inset Index idx
18385 \begin_layout Plain Layout
18394 \begin_layout Standard
18395 Latin letters in formulas can be set in one of the following font styles:
18398 \begin_layout Standard
18400 \begin_inset space \hfill{}
18404 \begin_inset Tabular
18405 <lyxtabular version="3" rows="6" columns="2">
18406 <features tabularvalignment="middle">
18407 <column alignment="center" valignment="top">
18408 <column alignment="center" valignment="top">
18410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18413 \begin_layout Plain Layout
18419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18422 \begin_layout Plain Layout
18430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18433 \begin_layout Plain Layout
18439 \begin_inset space \textvisiblespace{}
18449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18452 \begin_layout Plain Layout
18453 \begin_inset Formula $\mathbb{ABC}$
18463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18466 \begin_layout Plain Layout
18472 \begin_inset space \textvisiblespace{}
18482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18485 \begin_layout Plain Layout
18486 \begin_inset Formula $\mathbf{AbC}$
18496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18499 \begin_layout Plain Layout
18505 \begin_inset space \textvisiblespace{}
18515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18518 \begin_layout Plain Layout
18519 \begin_inset Formula $\boldsymbol{AbC}$
18529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18532 \begin_layout Plain Layout
18538 \begin_inset space \textvisiblespace{}
18548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18551 \begin_layout Plain Layout
18552 \begin_inset Formula $\mathcal{ABC}$
18562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18565 \begin_layout Plain Layout
18571 \begin_inset space \textvisiblespace{}
18581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18584 \begin_layout Plain Layout
18585 \begin_inset Formula $\mathfrak{AbC}$
18599 \begin_inset space \hfill{}
18603 \begin_inset Tabular
18604 <lyxtabular version="3" rows="6" columns="2">
18605 <features tabularvalignment="middle">
18606 <column alignment="center" valignment="top">
18607 <column alignment="center" valignment="top">
18609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18612 \begin_layout Plain Layout
18618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18621 \begin_layout Plain Layout
18629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18632 \begin_layout Plain Layout
18638 \begin_inset space \textvisiblespace{}
18648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18651 \begin_layout Plain Layout
18652 \begin_inset Formula $\mathit{AbC}$
18662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18665 \begin_layout Plain Layout
18671 \begin_inset space \textvisiblespace{}
18681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18684 \begin_layout Plain Layout
18685 \begin_inset Formula $\mathrm{AbC}$
18695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18698 \begin_layout Plain Layout
18704 \begin_inset space \textvisiblespace{}
18714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18717 \begin_layout Plain Layout
18718 \begin_inset Formula $\mathsf{AbC}$
18728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18731 \begin_layout Plain Layout
18737 \begin_inset space \textvisiblespace{}
18747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18750 \begin_layout Plain Layout
18751 \begin_inset Formula $\mathtt{AbC}$
18761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18764 \begin_layout Plain Layout
18770 \begin_inset space \textvisiblespace{}
18780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18783 \begin_layout Plain Layout
18784 \begin_inset Formula $\mathscr{ABC}$
18798 \begin_inset space \hfill{}
18804 \begin_layout Standard
18805 \begin_inset Note Greyedout
18808 \begin_layout Plain Layout
18831 can only be used for big letters.
18839 \begin_layout Standard
18840 Predefined is the style
18849 \begin_layout Standard
18850 The style commands work also for letters in mathematical constructs:
18851 \begin_inset Formula
18853 \mathfrak{A=\frac{b}{C}}
18861 \begin_layout Standard
18862 Characters in mathematical text don't appear in a math font style but in
18863 the text font style
18870 That their style can't be set correctly via the text style dialog is a
18871 bug in \SpecialChar LyX
18876 \begin_layout Plain Layout
18877 \begin_inset CommandInset href
18879 name "LyX-bug #4629"
18880 target "http://www.lyx.org/trac/ticket/4629"
18892 \begin_layout Standard
18893 Instead of the style commands the dialog
18895 Edit\SpecialChar menuseparator
18896 Math\SpecialChar menuseparator
18899 or the toolbar button
18902 arg "math-insert \\font"
18908 \begin_layout Subsection
18910 \begin_inset CommandInset label
18912 name "subsec:Bold-Formulas"
18917 \begin_inset Index idx
18920 \begin_layout Plain Layout
18929 \begin_layout Standard
18930 To make a complete formula bold, the command
18936 from the previous subsection cannot be used, because it doesn't work for
18937 small Greek letters.
18938 Furthermore it prints Latin letters always upright, like in the following
18942 \begin_layout Standard
18943 \begin_inset Formula
18945 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18953 \begin_layout Standard
18954 To display the formula correctly, the command
18961 \begin_inset Formula
18963 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18968 It is also possible to set the formula in a
18970 boldmath environment
18973 This environment is created by inserting the command
18980 \begin_inset Index idx
18983 \begin_layout Plain Layout
18991 in \SpecialChar TeX
18993 To end the environment, the command
19000 \begin_inset Index idx
19003 \begin_layout Plain Layout
19011 is inserted in \SpecialChar TeX
19016 \begin_layout Plain Layout
19026 \begin_inset Formula
19028 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19037 \begin_layout Plain Layout
19049 \begin_layout Subsection
19051 \begin_inset Index idx
19054 \begin_layout Plain Layout
19063 \begin_layout Standard
19064 Formulas can be colored like normal text: Highlight a formula or a formula
19070 Here is a formula in magenta:
19071 \begin_inset Formula
19073 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19081 \begin_layout Standard
19082 You can also define your own colors as described in
19083 \begin_inset CommandInset ref
19085 reference "subsec:Colored-Boxes"
19090 They can be used with the \SpecialChar TeX
19098 \begin_inset Index idx
19101 \begin_layout Plain Layout
19112 \begin_layout Standard
19117 textcolor{color}{characters or formula}
19120 \begin_layout Standard
19121 The following example was colored completely dark green and partly red:
19124 \begin_layout Standard
19128 \begin_layout Plain Layout
19132 textcolor{darkgreen}{
19138 \begin_inset Formula
19140 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19149 \begin_layout Plain Layout
19159 \begin_layout Standard
19160 Due to a bug in \SpecialChar LyX
19161 only complete formulas can be colored with self-defined
19166 \begin_layout Plain Layout
19167 \begin_inset CommandInset href
19169 name "LyX-bug #5269"
19170 target "http://www.lyx.org/trac/ticket/5269"
19182 \begin_layout Subsection
19184 \begin_inset CommandInset label
19186 name "subsec:Font-Sizes"
19191 \begin_inset Index idx
19194 \begin_layout Plain Layout
19203 \begin_layout Standard
19204 For characters in formulas there are, analog to characters in text, the
19205 following size commands:
19208 \begin_layout Standard
19252 \begin_inset Newline newline
19274 \begin_layout Standard
19275 The size produced by the commands depends on the document font size, which
19276 corresponds to the command
19283 The other commands produce smaller or larger sizes than
19290 The font size can however not exceed a certain value.
19291 Is for example the document font size 12
19292 \begin_inset space \thinspace{}
19301 switches to the same size as
19311 \begin_layout Standard
19312 A size command is inserted in \SpecialChar TeX
19313 mode before the formula and sets the size
19314 for all following formula and text characters.
19315 To switch back to the initial size, the command
19321 is inserted behind the formula in \SpecialChar TeX
19325 \begin_layout Standard
19326 Within a formula the size can be changed using the following size commands
19327 or the toolbar button
19330 arg "math-insert \\style"
19334 \begin_inset Separator parbreak
19340 \begin_layout Standard
19343 \begin_inset Tabular
19344 <lyxtabular version="3" rows="5" columns="2">
19345 <features tabularvalignment="middle">
19346 <column alignment="center" valignment="top">
19347 <column alignment="center" valignment="top">
19349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19352 \begin_layout Plain Layout
19358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19361 \begin_layout Plain Layout
19363 \begin_inset Note Note
19366 \begin_layout Plain Layout
19373 is only used as spacer.
19385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19388 \begin_layout Plain Layout
19392 \begin_inset Index idx
19395 \begin_layout Plain Layout
19408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19411 \begin_layout Plain Layout
19412 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19425 \begin_layout Plain Layout
19433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19436 \begin_layout Plain Layout
19437 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19450 \begin_layout Plain Layout
19458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19461 \begin_layout Plain Layout
19462 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19475 \begin_layout Plain Layout
19483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19486 \begin_layout Plain Layout
19487 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19503 \begin_layout Standard
19504 After entering these commands, a blue box appears in which the formula parts
19508 \begin_layout Standard
19509 There is a further method to change the font size, that though only works
19510 for symbols or letters in mathematical text.
19511 To use it, one of the above text size commands is inserted in mathematical
19513 All following characters until the end of the mathematical text or until
19514 another size command will have the selected size.
19516 \begin_inset VSpace -2mm
19522 \begin_layout Standard
19526 \begin_layout Plain Layout
19536 \begin_inset Formula
19538 A=\frac{B}{c}\cdot\maltese
19544 \begin_inset Formula
19546 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19555 \begin_layout Plain Layout
19567 \begin_layout Standard
19568 \begin_inset VSpace medskip
19571 Before both formulas the command
19578 The command for the second formula is:
19579 \begin_inset Newline newline
19587 \begin_inset space \textvisiblespace{}
19593 \begin_inset space \textvisiblespace{}
19599 \begin_inset space \textvisiblespace{}
19605 \begin_inset space \textvisiblespace{}
19609 \begin_inset Formula $\to$
19613 \begin_inset Formula $\to$
19617 \begin_inset Newline newline
19621 \begin_inset space \hspace*{}
19632 \begin_inset space \textvisiblespace{}
19638 \begin_inset space \textvisiblespace{}
19644 \begin_inset space \textvisiblespace{}
19650 \begin_layout Standard
19651 If a symbol cannot be displayed in different sizes, it will always be displayed
19652 in the default size.
19655 \begin_layout Section
19657 \begin_inset Index idx
19660 \begin_layout Plain Layout
19669 \begin_layout Standard
19670 Greek letters can also be inserted via the toolbar button
19673 arg "math-insert \\alpha"
19677 All international typesetting norms purport that Greek letters in math
19678 have to be typeset italic/slanted.
19679 In some languages, like French or Russian, they are nevertheless sometimes
19683 \begin_layout Subsection
19685 \begin_inset Index idx
19688 \begin_layout Plain Layout
19689 Greek letters ! small
19697 \begin_layout Standard
19698 \begin_inset space \hfill{}
19702 \begin_inset Tabular
19703 <lyxtabular version="3" rows="11" columns="2">
19704 <features tabularvalignment="middle">
19705 <column alignment="center" valignment="top" width="0pt">
19706 <column alignment="center" valignment="top" width="0pt">
19708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19711 \begin_layout Plain Layout
19717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19720 \begin_layout Plain Layout
19728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19731 \begin_layout Plain Layout
19739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19742 \begin_layout Plain Layout
19743 \begin_inset Formula $\alpha$
19753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19756 \begin_layout Plain Layout
19764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19767 \begin_layout Plain Layout
19768 \begin_inset Formula $\beta$
19778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19781 \begin_layout Plain Layout
19789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19792 \begin_layout Plain Layout
19793 \begin_inset Formula $\gamma$
19803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19806 \begin_layout Plain Layout
19814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19817 \begin_layout Plain Layout
19818 \begin_inset Formula $\delta$
19828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19831 \begin_layout Plain Layout
19839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19842 \begin_layout Plain Layout
19843 \begin_inset Formula $\epsilon$
19853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19856 \begin_layout Plain Layout
19864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19867 \begin_layout Plain Layout
19868 \begin_inset Formula $\varepsilon$
19878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19881 \begin_layout Plain Layout
19889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19892 \begin_layout Plain Layout
19893 \begin_inset Formula $\zeta$
19903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19906 \begin_layout Plain Layout
19914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19917 \begin_layout Plain Layout
19918 \begin_inset Formula $\eta$
19928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19931 \begin_layout Plain Layout
19939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19942 \begin_layout Plain Layout
19943 \begin_inset Formula $\theta$
19953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19956 \begin_layout Plain Layout
19964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19967 \begin_layout Plain Layout
19968 \begin_inset Formula $\vartheta$
19982 \begin_inset space \hfill{}
19986 \begin_inset Tabular
19987 <lyxtabular version="3" rows="12" columns="2">
19988 <features tabularvalignment="middle">
19989 <column alignment="center" valignment="top" width="0pt">
19990 <column alignment="center" valignment="top" width="0pt">
19992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19995 \begin_layout Plain Layout
20001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20004 \begin_layout Plain Layout
20012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20015 \begin_layout Plain Layout
20023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20026 \begin_layout Plain Layout
20027 \begin_inset Formula $\iota$
20037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20040 \begin_layout Plain Layout
20048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20051 \begin_layout Plain Layout
20052 \begin_inset Formula $\kappa$
20062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20065 \begin_layout Plain Layout
20073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20076 \begin_layout Plain Layout
20077 \begin_inset Formula $\varkappa$
20087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20090 \begin_layout Plain Layout
20098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20101 \begin_layout Plain Layout
20102 \begin_inset Formula $\lambda$
20112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20115 \begin_layout Plain Layout
20123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20126 \begin_layout Plain Layout
20127 \begin_inset Formula $\mu$
20137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20140 \begin_layout Plain Layout
20148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20151 \begin_layout Plain Layout
20152 \begin_inset Formula $\nu$
20162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20165 \begin_layout Plain Layout
20173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20176 \begin_layout Plain Layout
20177 \begin_inset Formula $\xi$
20187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20190 \begin_layout Plain Layout
20196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20199 \begin_layout Plain Layout
20200 \begin_inset Formula $o$
20210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20213 \begin_layout Plain Layout
20221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20224 \begin_layout Plain Layout
20225 \begin_inset Formula $\pi$
20235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20238 \begin_layout Plain Layout
20246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20249 \begin_layout Plain Layout
20250 \begin_inset Formula $\varpi$
20260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20263 \begin_layout Plain Layout
20271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20274 \begin_layout Plain Layout
20275 \begin_inset Formula $\rho$
20289 \begin_inset space \hfill{}
20293 \begin_inset Tabular
20294 <lyxtabular version="3" rows="11" columns="2">
20295 <features tabularvalignment="middle">
20296 <column alignment="center" valignment="top" width="0pt">
20297 <column alignment="center" valignment="top" width="0pt">
20299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20302 \begin_layout Plain Layout
20308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20311 \begin_layout Plain Layout
20319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20322 \begin_layout Plain Layout
20330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20333 \begin_layout Plain Layout
20334 \begin_inset Formula $\varrho$
20344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20347 \begin_layout Plain Layout
20355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20358 \begin_layout Plain Layout
20359 \begin_inset Formula $\sigma$
20369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20372 \begin_layout Plain Layout
20380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20383 \begin_layout Plain Layout
20384 \begin_inset Formula $\varsigma$
20394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20397 \begin_layout Plain Layout
20405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20408 \begin_layout Plain Layout
20409 \begin_inset Formula $\tau$
20419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20422 \begin_layout Plain Layout
20430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20433 \begin_layout Plain Layout
20434 \begin_inset Formula $\upsilon$
20444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20447 \begin_layout Plain Layout
20455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20458 \begin_layout Plain Layout
20459 \begin_inset Formula $\phi$
20469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20472 \begin_layout Plain Layout
20480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20483 \begin_layout Plain Layout
20484 \begin_inset Formula $\varphi$
20494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20497 \begin_layout Plain Layout
20505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20508 \begin_layout Plain Layout
20509 \begin_inset Formula $\chi$
20519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20522 \begin_layout Plain Layout
20530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20533 \begin_layout Plain Layout
20534 \begin_inset Formula $\psi$
20544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20547 \begin_layout Plain Layout
20555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20558 \begin_layout Plain Layout
20559 \begin_inset Formula $\omega$
20573 \begin_inset space \hfill{}
20579 \begin_layout Standard
20580 \begin_inset VSpace medskip
20586 \begin_layout Standard
20587 How to create special upright Greek letters is explained in
20588 \begin_inset CommandInset ref
20590 reference "subsec:Upright-small-Greek"
20597 \begin_layout Subsection
20599 \begin_inset Index idx
20602 \begin_layout Plain Layout
20603 Greek letters ! big
20611 \begin_layout Standard
20612 \begin_inset space \hfill{}
20616 \begin_inset Tabular
20617 <lyxtabular version="3" rows="7" columns="2">
20618 <features tabularvalignment="middle">
20619 <column alignment="center" valignment="top" width="0pt">
20620 <column alignment="center" valignment="top" width="0pt">
20622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20625 \begin_layout Plain Layout
20631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20634 \begin_layout Plain Layout
20642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20645 \begin_layout Plain Layout
20653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20656 \begin_layout Plain Layout
20657 \begin_inset Formula $\Gamma$
20667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20670 \begin_layout Plain Layout
20678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20681 \begin_layout Plain Layout
20682 \begin_inset Formula $\Delta$
20692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20695 \begin_layout Plain Layout
20703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20706 \begin_layout Plain Layout
20707 \begin_inset Formula $\Theta$
20717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20720 \begin_layout Plain Layout
20728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20731 \begin_layout Plain Layout
20732 \begin_inset Formula $\Lambda$
20742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20745 \begin_layout Plain Layout
20753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20756 \begin_layout Plain Layout
20757 \begin_inset Formula $\Xi$
20767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20770 \begin_layout Plain Layout
20778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20781 \begin_layout Plain Layout
20782 \begin_inset Formula $\Pi$
20796 \begin_inset space \hfill{}
20800 \begin_inset Tabular
20801 <lyxtabular version="3" rows="6" columns="2">
20802 <features tabularvalignment="middle">
20803 <column alignment="center" valignment="top" width="0pt">
20804 <column alignment="center" valignment="top" width="0pt">
20806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20809 \begin_layout Plain Layout
20815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20818 \begin_layout Plain Layout
20826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20829 \begin_layout Plain Layout
20837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20840 \begin_layout Plain Layout
20841 \begin_inset Formula $\Sigma$
20851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20854 \begin_layout Plain Layout
20862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20865 \begin_layout Plain Layout
20866 \begin_inset Formula $\Upsilon$
20876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20879 \begin_layout Plain Layout
20887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20890 \begin_layout Plain Layout
20891 \begin_inset Formula $\Phi$
20901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20904 \begin_layout Plain Layout
20912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20915 \begin_layout Plain Layout
20916 \begin_inset Formula $\Psi$
20926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20929 \begin_layout Plain Layout
20937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20940 \begin_layout Plain Layout
20941 \begin_inset Formula $\Omega$
20955 \begin_inset space \hfill{}
20961 \begin_layout Standard
20962 \begin_inset VSpace medskip
20965 That the big Greek letters appear upright is caused by a design bug when
20968 To get correct italic big letters, begin every command with
20973 For example the command
20980 \begin_inset Formula $\varGamma$
20984 Another way is to load the package
20992 \begin_layout Plain Layout
20997 is part of the \SpecialChar LaTeX
21003 \begin_inset Index idx
21006 \begin_layout Plain Layout
21011 \begin_layout Plain Layout
21031 \begin_inset Index idx
21034 \begin_layout Plain Layout
21040 with the \SpecialChar LaTeX
21044 \begin_layout Standard
21049 usepackage{fixmath}
21052 \begin_layout Standard
21053 Then all big Greek letters in a document will automatically be typeset italic.
21056 \begin_layout Subsection
21058 \begin_inset Index idx
21061 \begin_layout Plain Layout
21062 Greek letters ! bold
21070 \begin_layout Standard
21071 Greek letters cannot be set with different font styles like Latin letters.
21072 They can only be made bold with the command
21079 \begin_inset Index idx
21082 \begin_layout Plain Layout
21091 \begin_inset Separator parbreak
21097 \begin_layout Standard
21099 \begin_inset Tabular
21100 <lyxtabular version="3" rows="3" columns="2">
21101 <features tabularvalignment="middle">
21102 <column alignment="center" valignment="top">
21103 <column alignment="center" valignment="top">
21105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21108 \begin_layout Plain Layout
21114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21117 \begin_layout Plain Layout
21125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21128 \begin_layout Plain Layout
21140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21143 \begin_layout Plain Layout
21144 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21157 \begin_layout Plain Layout
21169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21172 \begin_layout Plain Layout
21173 \begin_inset Formula $\theta\boldsymbol{\theta}$
21189 \begin_layout Section
21194 \begin_layout Plain Layout
21207 \begin_layout Plain Layout
21208 A list with all symbols of most of the \SpecialChar LaTeX
21209 -packages can be found in
21210 \begin_inset CommandInset citation
21225 \begin_layout Plain Layout
21233 \begin_inset Note Note
21236 \begin_layout Plain Layout
21239 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21242 \begin_layout Plain Layout
21245 texorpdfstring is in section
21246 \begin_inset CommandInset ref
21248 reference "subsec:Formulas-in-Section"
21258 \begin_inset Index idx
21261 \begin_layout Plain Layout
21270 \begin_layout Standard
21271 Many of the symbols listed in this section can also be inserted via the
21275 arg "math-insert \\nabla"
21281 arg "math-insert \\digamma"
21287 \begin_layout Subsection
21288 Mathematical Symbols
21289 \begin_inset CommandInset label
21291 name "subsec:Mathematical-Symbols"
21296 \begin_inset Index idx
21299 \begin_layout Plain Layout
21300 Symbols ! mathematical
21308 \begin_layout Standard
21309 \begin_inset space \hfill{}
21313 \begin_inset Tabular
21314 <lyxtabular version="3" rows="10" columns="2">
21315 <features tabularvalignment="middle">
21316 <column alignment="center" valignment="top" width="0pt">
21317 <column alignment="center" valignment="top" width="0pt">
21319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21322 \begin_layout Plain Layout
21328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21331 \begin_layout Plain Layout
21339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21342 \begin_layout Plain Layout
21350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21353 \begin_layout Plain Layout
21354 \begin_inset Formula $\neg$
21364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21367 \begin_layout Plain Layout
21375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21378 \begin_layout Plain Layout
21379 \begin_inset Formula $\Im$
21389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21392 \begin_layout Plain Layout
21400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21403 \begin_layout Plain Layout
21404 \begin_inset Formula $\Re$
21414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21417 \begin_layout Plain Layout
21425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21428 \begin_layout Plain Layout
21429 \begin_inset Formula $\aleph$
21439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21442 \begin_layout Plain Layout
21450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21453 \begin_layout Plain Layout
21454 \begin_inset Formula $\partial$
21464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21467 \begin_layout Plain Layout
21475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21478 \begin_layout Plain Layout
21479 \begin_inset Formula $\infty$
21489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21492 \begin_layout Plain Layout
21500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21503 \begin_layout Plain Layout
21504 \begin_inset Formula $\wp$
21514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21517 \begin_layout Plain Layout
21525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21528 \begin_layout Plain Layout
21529 \begin_inset Formula $\imath$
21539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21542 \begin_layout Plain Layout
21550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21553 \begin_layout Plain Layout
21554 \begin_inset Formula $\jmath$
21568 \begin_inset space \hfill{}
21572 \begin_inset Tabular
21573 <lyxtabular version="3" rows="10" columns="2">
21574 <features tabularvalignment="middle">
21575 <column alignment="center" valignment="top" width="0pt">
21576 <column alignment="center" valignment="top" width="0pt">
21578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21581 \begin_layout Plain Layout
21587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21590 \begin_layout Plain Layout
21592 \begin_inset Note Note
21595 \begin_layout Plain Layout
21602 is only used as spacer.
21614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21617 \begin_layout Plain Layout
21625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21628 \begin_layout Plain Layout
21629 \begin_inset Formula $\forall$
21639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21642 \begin_layout Plain Layout
21650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21653 \begin_layout Plain Layout
21654 \begin_inset Formula $\exists$
21664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21667 \begin_layout Plain Layout
21675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21678 \begin_layout Plain Layout
21679 \begin_inset Formula $\nexists$
21689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21692 \begin_layout Plain Layout
21700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21703 \begin_layout Plain Layout
21704 \begin_inset Formula $\emptyset$
21714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21717 \begin_layout Plain Layout
21725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21728 \begin_layout Plain Layout
21729 \begin_inset Formula $\varnothing$
21739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21742 \begin_layout Plain Layout
21750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21753 \begin_layout Plain Layout
21754 \begin_inset Formula $\dag$
21764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21767 \begin_layout Plain Layout
21775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21778 \begin_layout Plain Layout
21779 \begin_inset Formula $\ddag$
21789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21792 \begin_layout Plain Layout
21800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21803 \begin_layout Plain Layout
21807 \begin_layout Plain Layout
21817 \begin_inset Formula $\complement$
21824 \begin_layout Plain Layout
21838 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21841 \begin_layout Plain Layout
21849 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21852 \begin_layout Plain Layout
21853 \begin_inset Formula $\Bbbk$
21867 \begin_inset space \hfill{}
21871 \begin_inset Tabular
21872 <lyxtabular version="3" rows="10" columns="2">
21873 <features tabularvalignment="middle">
21874 <column alignment="center" valignment="top" width="0pt">
21875 <column alignment="center" valignment="top" width="0pt">
21877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21880 \begin_layout Plain Layout
21886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21889 \begin_layout Plain Layout
21897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21900 \begin_layout Plain Layout
21908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21911 \begin_layout Plain Layout
21912 \begin_inset Formula $\prime$
21922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21925 \begin_layout Plain Layout
21933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21936 \begin_layout Plain Layout
21937 \begin_inset Formula $\backprime$
21947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21950 \begin_layout Plain Layout
21958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21961 \begin_layout Plain Layout
21962 \begin_inset Formula $\mho$
21972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21975 \begin_layout Plain Layout
21983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21986 \begin_layout Plain Layout
21987 \begin_inset Formula $\triangle$
21997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22000 \begin_layout Plain Layout
22008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22011 \begin_layout Plain Layout
22012 \begin_inset Formula $\angle$
22022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22025 \begin_layout Plain Layout
22033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22036 \begin_layout Plain Layout
22037 \begin_inset Formula $\measuredangle$
22047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22050 \begin_layout Plain Layout
22058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22061 \begin_layout Plain Layout
22062 \begin_inset Formula $\sphericalangle$
22072 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22075 \begin_layout Plain Layout
22083 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22086 \begin_layout Plain Layout
22087 \begin_inset Formula $\top$
22097 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22100 \begin_layout Plain Layout
22108 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22111 \begin_layout Plain Layout
22112 \begin_inset Formula $\bot$
22126 \begin_inset space \hfill{}
22132 \begin_layout Standard
22133 \begin_inset Newpage newpage
22139 \begin_layout Subsection
22140 Miscellaneous Symbols
22141 \begin_inset CommandInset label
22143 name "subsec:Miscellaneous-Symbols"
22148 \begin_inset Index idx
22151 \begin_layout Plain Layout
22152 Symbols ! miscellaneous
22160 \begin_layout Standard
22163 \begin_inset Tabular
22164 <lyxtabular version="3" rows="10" columns="2">
22165 <features tabularvalignment="middle">
22166 <column alignment="center" valignment="top" width="0pt">
22167 <column alignment="center" valignment="top" width="0pt">
22169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22172 \begin_layout Plain Layout
22178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22181 \begin_layout Plain Layout
22189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22192 \begin_layout Plain Layout
22200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22203 \begin_layout Plain Layout
22204 \begin_inset Formula $\flat$
22214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22217 \begin_layout Plain Layout
22225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22228 \begin_layout Plain Layout
22229 \begin_inset Formula $\natural$
22239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22242 \begin_layout Plain Layout
22250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22253 \begin_layout Plain Layout
22254 \begin_inset Formula $\sharp$
22264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22267 \begin_layout Plain Layout
22275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22278 \begin_layout Plain Layout
22279 \begin_inset Formula $\surd$
22289 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22292 \begin_layout Plain Layout
22300 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22303 \begin_layout Plain Layout
22304 \begin_inset Formula $\checkmark$
22314 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22317 \begin_layout Plain Layout
22325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22328 \begin_layout Plain Layout
22329 \begin_inset Formula $\yen$
22339 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22342 \begin_layout Plain Layout
22350 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22353 \begin_layout Plain Layout
22354 \begin_inset Formula $\pounds$
22364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22367 \begin_layout Plain Layout
22373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22376 \begin_layout Plain Layout
22377 \begin_inset Formula $\$$
22387 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22390 \begin_layout Plain Layout
22396 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22399 \begin_layout Plain Layout
22400 \begin_inset Formula $§$
22414 \begin_inset Tabular
22415 <lyxtabular version="3" rows="10" columns="2">
22416 <features tabularvalignment="middle">
22417 <column alignment="center" valignment="top">
22418 <column alignment="center" valignment="top">
22420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22423 \begin_layout Plain Layout
22429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22432 \begin_layout Plain Layout
22440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22443 \begin_layout Plain Layout
22451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22454 \begin_layout Plain Layout
22455 \begin_inset Formula $\hbar$
22465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22468 \begin_layout Plain Layout
22476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22479 \begin_layout Plain Layout
22480 \begin_inset Formula $\hslash$
22490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22493 \begin_layout Plain Layout
22501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22504 \begin_layout Plain Layout
22505 \begin_inset Formula $\clubsuit$
22515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22518 \begin_layout Plain Layout
22526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22529 \begin_layout Plain Layout
22530 \begin_inset Formula $\spadesuit$
22540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22543 \begin_layout Plain Layout
22551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22554 \begin_layout Plain Layout
22555 \begin_inset Formula $\bigstar$
22565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22568 \begin_layout Plain Layout
22576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22579 \begin_layout Plain Layout
22580 \begin_inset Formula $\blacklozenge$
22590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22593 \begin_layout Plain Layout
22601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22604 \begin_layout Plain Layout
22605 \begin_inset Formula $\blacktriangle$
22615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22618 \begin_layout Plain Layout
22626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22629 \begin_layout Plain Layout
22630 \begin_inset Formula $\blacktriangledown$
22640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22643 \begin_layout Plain Layout
22651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22654 \begin_layout Plain Layout
22655 \begin_inset Formula $\bullet$
22669 \begin_inset Tabular
22670 <lyxtabular version="3" rows="10" columns="2">
22671 <features tabularvalignment="middle">
22672 <column alignment="center" valignment="top" width="0pt">
22673 <column alignment="center" valignment="top" width="0pt">
22675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22678 \begin_layout Plain Layout
22684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22687 \begin_layout Plain Layout
22695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22698 \begin_layout Plain Layout
22706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22709 \begin_layout Plain Layout
22710 \begin_inset Formula $\diamondsuit$
22720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22723 \begin_layout Plain Layout
22731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22734 \begin_layout Plain Layout
22735 \begin_inset Formula $\Diamond$
22745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22748 \begin_layout Plain Layout
22756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22759 \begin_layout Plain Layout
22760 \begin_inset Formula $\heartsuit$
22770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22773 \begin_layout Plain Layout
22781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22784 \begin_layout Plain Layout
22785 \begin_inset Formula $\P$
22795 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22798 \begin_layout Plain Layout
22806 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22809 \begin_layout Plain Layout
22810 \begin_inset Formula $\copyright$
22820 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22823 \begin_layout Plain Layout
22831 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22834 \begin_layout Plain Layout
22835 \begin_inset Formula $\circledR$
22845 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22848 \begin_layout Plain Layout
22856 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22859 \begin_layout Plain Layout
22860 \begin_inset Formula $\maltese$
22870 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22873 \begin_layout Plain Layout
22881 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22884 \begin_layout Plain Layout
22885 \begin_inset Formula $\diagup$
22895 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22898 \begin_layout Plain Layout
22906 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22909 \begin_layout Plain Layout
22910 \begin_inset Formula $\diagdown$
22926 \begin_layout Standard
22927 \begin_inset VSpace medskip
22933 \begin_layout Standard
22934 Some symbols can be displayed in different sizes, see
22935 \begin_inset CommandInset ref
22937 reference "subsec:Font-Sizes"
22944 \begin_layout Subsection
22946 \begin_inset Index idx
22949 \begin_layout Plain Layout
22950 Symbols ! Euro-symbol
22956 \begin_inset Index idx
22959 \begin_layout Plain Layout
22966 \begin_layout Plain Layout
22983 \begin_layout Standard
22984 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22990 \begin_inset Index idx
22993 \begin_layout Plain Layout
22999 must be installed and loaded with the \SpecialChar LaTeX
23003 \begin_layout Standard
23008 usepackage[gennarrow]{eurosym}
23011 \begin_layout Standard
23012 The Euro symbol can now be inserted with the command
23019 \begin_inset Index idx
23022 \begin_layout Plain Layout
23033 \begin_layout Standard
23034 The Euro symbol can directly be inserted with the € key in mathematical
23035 text, without having
23050 can also be inserted in \SpecialChar TeX
23052 The official currency symbol can then be inserted with the command
23059 \begin_inset Index idx
23062 \begin_layout Plain Layout
23070 , that is only available in \SpecialChar TeX
23074 \begin_layout Standard
23078 \begin_layout Plain Layout
23088 \begin_inset Note Note
23091 \begin_layout Plain Layout
23092 The following table will only be displayed when the \SpecialChar LaTeX
23105 \begin_layout Standard
23106 An overview about the different Euro symbols:
23107 \begin_inset Separator parbreak
23113 \begin_layout Standard
23115 \begin_inset Tabular
23116 <lyxtabular version="3" rows="4" columns="3">
23117 <features tabularvalignment="middle">
23118 <column alignment="center" valignment="top" width="0pt">
23119 <column alignment="center" valignment="top" width="0pt">
23120 <column alignment="center" valignment="top" width="0pt">
23122 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23125 \begin_layout Plain Layout
23131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23134 \begin_layout Plain Layout
23140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23143 \begin_layout Plain Layout
23151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23154 \begin_layout Plain Layout
23160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23163 \begin_layout Plain Layout
23171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23174 \begin_layout Plain Layout
23175 \begin_inset Formula $\euro$
23185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23188 \begin_layout Plain Layout
23194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23197 \begin_layout Plain Layout
23203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23206 \begin_layout Plain Layout
23207 \begin_inset Formula $\mbox{€}$
23217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23220 \begin_layout Plain Layout
23227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23230 \begin_layout Plain Layout
23238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23241 \begin_layout Plain Layout
23245 \begin_layout Plain Layout
23267 \begin_layout Standard
23271 \begin_layout Plain Layout
23281 \begin_inset Note Note
23284 \begin_layout Plain Layout
23285 The following will be displayed when the \SpecialChar LaTeX
23298 \begin_layout Standard
23299 You need to install the \SpecialChar LaTeX
23304 to see the rest of this subsection in the output.
23307 \begin_layout Standard
23311 \begin_layout Plain Layout
23323 \begin_layout Standard
23324 \begin_inset Newpage newpage
23330 \begin_layout Section
23332 \begin_inset CommandInset label
23334 name "sec:Relations"
23339 \begin_inset Index idx
23342 \begin_layout Plain Layout
23349 \begin_inset Index idx
23352 \begin_layout Plain Layout
23357 \begin_layout Plain Layout
23368 \begin_layout Plain Layout
23383 \begin_layout Standard
23384 All following relations can also be inserted via the toolbar button
23387 arg "math-insert \\leq"
23393 \begin_layout Standard
23394 \begin_inset space \hfill{}
23398 \begin_inset Tabular
23399 <lyxtabular version="3" rows="17" columns="2">
23400 <features tabularvalignment="middle">
23401 <column alignment="center" valignment="top" width="0pt">
23402 <column alignment="center" valignment="top" width="0pt">
23404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23407 \begin_layout Plain Layout
23413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23416 \begin_layout Plain Layout
23424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23427 \begin_layout Plain Layout
23433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23436 \begin_layout Plain Layout
23437 \begin_inset Formula $<$
23447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23450 \begin_layout Plain Layout
23458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23461 \begin_layout Plain Layout
23462 \begin_inset Formula $\le$
23472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23475 \begin_layout Plain Layout
23483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23486 \begin_layout Plain Layout
23487 \begin_inset Formula $\ll$
23497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23500 \begin_layout Plain Layout
23508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23511 \begin_layout Plain Layout
23512 \begin_inset Formula $\prec$
23522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23525 \begin_layout Plain Layout
23533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23536 \begin_layout Plain Layout
23537 \begin_inset Formula $\preceq$
23547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23550 \begin_layout Plain Layout
23558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23561 \begin_layout Plain Layout
23562 \begin_inset Formula $\subset$
23572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23575 \begin_layout Plain Layout
23583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23586 \begin_layout Plain Layout
23587 \begin_inset Formula $\subseteq$
23597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23600 \begin_layout Plain Layout
23608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23611 \begin_layout Plain Layout
23612 \begin_inset Formula $\sqsubseteq$
23622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23625 \begin_layout Plain Layout
23633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23636 \begin_layout Plain Layout
23637 \begin_inset Formula $\in$
23647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23650 \begin_layout Plain Layout
23658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23661 \begin_layout Plain Layout
23662 \begin_inset Formula $\vdash$
23672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23675 \begin_layout Plain Layout
23683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23686 \begin_layout Plain Layout
23687 \begin_inset Formula $\smile$
23697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23700 \begin_layout Plain Layout
23708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23711 \begin_layout Plain Layout
23712 \begin_inset Formula $\lhd$
23722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23725 \begin_layout Plain Layout
23733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23736 \begin_layout Plain Layout
23737 \begin_inset Formula $\unlhd$
23747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23750 \begin_layout Plain Layout
23758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23761 \begin_layout Plain Layout
23762 \begin_inset Formula $\gtrless$
23772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23775 \begin_layout Plain Layout
23783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23786 \begin_layout Plain Layout
23787 \begin_inset Formula $\mid$
23797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23800 \begin_layout Plain Layout
23808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23811 \begin_layout Plain Layout
23812 \begin_inset Formula $\nmid$
23826 \begin_inset space \hfill{}
23830 \begin_inset Tabular
23831 <lyxtabular version="3" rows="17" columns="2">
23832 <features tabularvalignment="middle">
23833 <column alignment="center" valignment="top" width="0pt">
23834 <column alignment="center" valignment="top" width="0pt">
23836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23839 \begin_layout Plain Layout
23845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23848 \begin_layout Plain Layout
23856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23859 \begin_layout Plain Layout
23865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23868 \begin_layout Plain Layout
23869 \begin_inset Formula $=$
23879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23882 \begin_layout Plain Layout
23890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23893 \begin_layout Plain Layout
23894 \begin_inset Formula $\not=$
23904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23907 \begin_layout Plain Layout
23915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23918 \begin_layout Plain Layout
23919 \begin_inset Formula $\equiv$
23929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23932 \begin_layout Plain Layout
23940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23943 \begin_layout Plain Layout
23944 \begin_inset Formula $\sim$
23954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23957 \begin_layout Plain Layout
23965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23968 \begin_layout Plain Layout
23969 \begin_inset Formula $\simeq$
23979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23982 \begin_layout Plain Layout
23990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23993 \begin_layout Plain Layout
23994 \begin_inset Formula $\approx$
24004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24007 \begin_layout Plain Layout
24015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24018 \begin_layout Plain Layout
24019 \begin_inset Formula $\cong$
24029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24032 \begin_layout Plain Layout
24040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24043 \begin_layout Plain Layout
24044 \begin_inset Formula $\bowtie$
24054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24057 \begin_layout Plain Layout
24065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24068 \begin_layout Plain Layout
24069 \begin_inset Formula $\notin$
24079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24082 \begin_layout Plain Layout
24090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24093 \begin_layout Plain Layout
24094 \begin_inset Formula $\perp$
24104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24107 \begin_layout Plain Layout
24115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24118 \begin_layout Plain Layout
24119 \begin_inset Formula $\propto$
24129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24132 \begin_layout Plain Layout
24140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24143 \begin_layout Plain Layout
24144 \begin_inset Formula $\asymp$
24154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24157 \begin_layout Plain Layout
24165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24168 \begin_layout Plain Layout
24169 \begin_inset Formula $\doteq$
24179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24182 \begin_layout Plain Layout
24190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24193 \begin_layout Plain Layout
24194 \begin_inset Formula $\circeq$
24204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24207 \begin_layout Plain Layout
24215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24218 \begin_layout Plain Layout
24219 \begin_inset Formula $\models$
24229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24232 \begin_layout Plain Layout
24240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24243 \begin_layout Plain Layout
24244 \begin_inset Formula $\widehat{=}$
24258 \begin_inset space \hfill{}
24262 \begin_inset Tabular
24263 <lyxtabular version="3" rows="17" columns="2">
24264 <features tabularvalignment="middle">
24265 <column alignment="center" valignment="top" width="0pt">
24266 <column alignment="center" valignment="top" width="0pt">
24268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24271 \begin_layout Plain Layout
24277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24280 \begin_layout Plain Layout
24288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24291 \begin_layout Plain Layout
24297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24300 \begin_layout Plain Layout
24301 \begin_inset Formula $>$
24311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24314 \begin_layout Plain Layout
24322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24325 \begin_layout Plain Layout
24326 \begin_inset Formula $\ge$
24336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24339 \begin_layout Plain Layout
24347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24350 \begin_layout Plain Layout
24351 \begin_inset Formula $\gg$
24361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24364 \begin_layout Plain Layout
24372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24375 \begin_layout Plain Layout
24376 \begin_inset Formula $\succ$
24386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24389 \begin_layout Plain Layout
24397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24400 \begin_layout Plain Layout
24401 \begin_inset Formula $\succeq$
24411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24414 \begin_layout Plain Layout
24422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24425 \begin_layout Plain Layout
24426 \begin_inset Formula $\supset$
24436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24439 \begin_layout Plain Layout
24447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24450 \begin_layout Plain Layout
24451 \begin_inset Formula $\supseteq$
24461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24464 \begin_layout Plain Layout
24472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24475 \begin_layout Plain Layout
24476 \begin_inset Formula $\sqsupseteq$
24486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24489 \begin_layout Plain Layout
24497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24500 \begin_layout Plain Layout
24501 \begin_inset Formula $\ni$
24511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24514 \begin_layout Plain Layout
24522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24525 \begin_layout Plain Layout
24526 \begin_inset Formula $\dashv$
24536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24539 \begin_layout Plain Layout
24547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24550 \begin_layout Plain Layout
24551 \begin_inset Formula $\frown$
24561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24564 \begin_layout Plain Layout
24572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24575 \begin_layout Plain Layout
24576 \begin_inset Formula $\rhd$
24586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24589 \begin_layout Plain Layout
24597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24600 \begin_layout Plain Layout
24601 \begin_inset Formula $\unrhd$
24611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24614 \begin_layout Plain Layout
24622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24625 \begin_layout Plain Layout
24626 \begin_inset Formula $\lessgtr$
24636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24639 \begin_layout Plain Layout
24647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24650 \begin_layout Plain Layout
24651 \begin_inset Formula $\parallel$
24661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24664 \begin_layout Plain Layout
24672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24675 \begin_layout Plain Layout
24676 \begin_inset Formula $\nparallel$
24690 \begin_inset space \hfill{}
24696 \begin_layout Standard
24697 \begin_inset VSpace medskip
24712 are bigger than the equal looking operators
24727 \begin_layout Standard
24729 supports also many special relations.
24730 Use the toolbar button
24733 arg "math-insert \\leqq"
24736 to see a list of these relations.
24739 \begin_layout Standard
24740 Relations are, in contrary to symbols, always surrounded by space.
24743 \begin_layout Standard
24744 Relations with labels can be created with the command
24751 \begin_inset Index idx
24754 \begin_layout Plain Layout
24763 \begin_inset Separator parbreak
24769 \begin_layout Standard
24771 \begin_inset Tabular
24772 <lyxtabular version="3" rows="2" columns="2">
24773 <features tabularvalignment="middle">
24774 <column alignment="center" valignment="top">
24775 <column alignment="center" valignment="top">
24777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24780 \begin_layout Plain Layout
24786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24789 \begin_layout Plain Layout
24791 \begin_inset Note Note
24794 \begin_layout Plain Layout
24801 is only used as spacer.
24813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24816 \begin_layout Plain Layout
24820 \begin_inset space \textvisiblespace{}
24828 \begin_inset space \textvisiblespace{}
24832 \begin_inset Formula $\downarrow$
24838 \begin_inset space \textvisiblespace{}
24842 \begin_inset space \textvisiblespace{}
24850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24853 \begin_layout Plain Layout
24854 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24870 \begin_layout Section
24874 \begin_layout Subsection
24875 Predefined Functions
24876 \begin_inset CommandInset label
24878 name "subsec:Predefined-Functions"
24883 \begin_inset Index idx
24886 \begin_layout Plain Layout
24887 Functions ! predefined
24895 \begin_layout Standard
24896 In general, variables are set
24900 in mathematical expressions, but not function names, because
24901 \begin_inset Formula $sin$
24904 could be misunderstood as
24905 \begin_inset Formula $s\cdot i\cdot n$
24909 Therefore there are predefined functionswhich are additionally a bit separated
24911 They are inserted as commands starting with a backslash before their name.
24912 \begin_inset Separator parbreak
24918 \begin_layout Standard
24920 \begin_inset Tabular
24921 <lyxtabular version="3" rows="2" columns="4">
24922 <features tabularvalignment="middle">
24923 <column alignment="center" valignment="top" width="0pt">
24924 <column alignment="center" valignment="top" width="0pt">
24925 <column alignment="center" valignment="top" width="0pt">
24926 <column alignment="center" valignment="top" width="0pt">
24928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24931 \begin_layout Plain Layout
24937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24940 \begin_layout Plain Layout
24946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24949 \begin_layout Plain Layout
24955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24958 \begin_layout Plain Layout
24966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24969 \begin_layout Plain Layout
24975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24978 \begin_layout Plain Layout
24979 \begin_inset Formula $Asin(x)+B$
24987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24990 \begin_layout Plain Layout
24998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25001 \begin_layout Plain Layout
25002 \begin_inset Formula $A\sin(x)+B$
25018 \begin_layout Standard
25019 The following functions are predefined:
25022 \begin_layout Standard
25023 \begin_inset VSpace -2mm
25029 \begin_layout Standard
25031 \begin_inset Tabular
25032 <lyxtabular version="3" rows="9" columns="4">
25033 <features tabularvalignment="middle">
25034 <column alignment="center" valignment="top" width="0pt">
25035 <column alignment="center" valignment="top" width="0pt">
25036 <column alignment="center" valignment="top" width="0pt">
25037 <column alignment="center" valignment="top" width="0pt">
25039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25042 \begin_layout Plain Layout
25048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25051 \begin_layout Plain Layout
25057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25060 \begin_layout Plain Layout
25066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25069 \begin_layout Plain Layout
25077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25080 \begin_layout Plain Layout
25088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25091 \begin_layout Plain Layout
25099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25102 \begin_layout Plain Layout
25110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25113 \begin_layout Plain Layout
25123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25126 \begin_layout Plain Layout
25134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25137 \begin_layout Plain Layout
25145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25148 \begin_layout Plain Layout
25156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25159 \begin_layout Plain Layout
25169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25172 \begin_layout Plain Layout
25180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25183 \begin_layout Plain Layout
25191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25194 \begin_layout Plain Layout
25202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25205 \begin_layout Plain Layout
25215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25218 \begin_layout Plain Layout
25226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25229 \begin_layout Plain Layout
25237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25240 \begin_layout Plain Layout
25248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25251 \begin_layout Plain Layout
25261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25264 \begin_layout Plain Layout
25272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25275 \begin_layout Plain Layout
25283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25286 \begin_layout Plain Layout
25294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25297 \begin_layout Plain Layout
25307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25310 \begin_layout Plain Layout
25318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25321 \begin_layout Plain Layout
25329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25332 \begin_layout Plain Layout
25340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25343 \begin_layout Plain Layout
25353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25356 \begin_layout Plain Layout
25364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25367 \begin_layout Plain Layout
25375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25378 \begin_layout Plain Layout
25386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25389 \begin_layout Plain Layout
25399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25402 \begin_layout Plain Layout
25410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25413 \begin_layout Plain Layout
25421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25424 \begin_layout Plain Layout
25432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25435 \begin_layout Plain Layout
25451 \begin_layout Standard
25452 They can also be inserted with the math toolbar button
25455 arg "math-insert \\functions"
25461 \begin_layout Subsection
25462 Self-defined Functions
25463 \begin_inset Index idx
25466 \begin_layout Plain Layout
25467 Functions ! self-defined
25475 \begin_layout Standard
25476 To use a function that is not predefined, like for example the sign function
25477 sgn(x), there are two possibilities:
25480 \begin_layout Itemize
25481 Define the function by inserting the following line to the \SpecialChar LaTeX
25486 \begin_layout Plain Layout
25491 DeclareMathOperator
25494 \begin_inset CommandInset ref
25496 reference "subsec:Self-defined-Operators"
25506 \begin_inset Newline newline
25510 \begin_inset VSpace -3mm
25514 \begin_inset Newline newline
25521 DeclareMathOperator{
25526 \begin_inset Index idx
25529 \begin_layout Plain Layout
25534 DeclareMathOperator
25540 \begin_inset Newline newline
25544 \begin_inset VSpace -2mm
25548 \begin_inset Newline newline
25551 Now the new defined function can be called with the command
25560 \begin_layout Itemize
25561 Write the formula as usual, mark the formula name, in our example the letters
25566 , and change it to mathematical text.
25567 Finally, a space is inserted between prefactor and function.
25570 \begin_layout Standard
25571 The result is the same with both methods as with a predefined function
25575 \begin_layout Plain Layout
25576 In \SpecialChar LyX
25577 self-defined functions are displayed red, predefined ones black.
25583 \begin_inset Separator parbreak
25589 \begin_layout Standard
25591 \begin_inset Tabular
25592 <lyxtabular version="3" rows="3" columns="2">
25593 <features tabularvalignment="middle">
25594 <column alignment="center" valignment="top" width="0pt">
25595 <column alignment="center" valignment="top" width="0pt">
25597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25600 \begin_layout Plain Layout
25606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25609 \begin_layout Plain Layout
25617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25620 \begin_layout Plain Layout
25628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25631 \begin_layout Plain Layout
25632 \begin_inset Formula $A\sgn(x)+B$
25642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25645 \begin_layout Plain Layout
25649 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25660 \begin_layout Plain Layout
25661 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25677 \begin_layout Standard
25678 The first method is more suitable when the self-defined function should
25679 be used several times.
25682 \begin_layout Subsection
25684 \begin_inset Index idx
25687 \begin_layout Plain Layout
25696 \begin_layout Standard
25697 For limits, in addition to the commands
25704 \begin_inset Index idx
25707 \begin_layout Plain Layout
25727 the following functions are defined:
25728 \begin_inset Separator parbreak
25734 \begin_layout Standard
25736 \begin_inset Tabular
25737 <lyxtabular version="3" rows="5" columns="2">
25738 <features tabularvalignment="middle">
25739 <column alignment="center" valignment="top">
25740 <column alignment="center" valignment="top">
25742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25745 \begin_layout Plain Layout
25751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25754 \begin_layout Plain Layout
25756 \begin_inset Note Note
25759 \begin_layout Plain Layout
25766 is only used as spacer.
25778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25781 \begin_layout Plain Layout
25789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25792 \begin_layout Plain Layout
25793 \begin_inset Formula $\varliminf$
25803 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25806 \begin_layout Plain Layout
25814 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25817 \begin_layout Plain Layout
25818 \begin_inset Formula $\varlimsup$
25828 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25831 \begin_layout Plain Layout
25839 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25842 \begin_layout Plain Layout
25843 \begin_inset Formula $\varprojlim$
25853 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25856 \begin_layout Plain Layout
25864 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25867 \begin_layout Plain Layout
25868 \begin_inset Formula $\varinjlim$
25872 \begin_inset Formula $\raisebox{-2.5mm}{}$
25888 \begin_layout Standard
25889 \begin_inset VSpace medskip
25892 The limit is created by inserting a subscript.
25893 It is set right beside the function in an inline formula:
25896 \begin_layout Standard
25898 \begin_inset Tabular
25899 <lyxtabular version="3" rows="2" columns="2">
25900 <features tabularvalignment="middle">
25901 <column alignment="center" valignment="top" width="0pt">
25902 <column alignment="center" valignment="top" width="0pt">
25904 <cell alignment="center" valignment="top" usebox="none">
25907 \begin_layout Plain Layout
25913 <cell alignment="center" valignment="top" usebox="none">
25916 \begin_layout Plain Layout
25917 \begin_inset space \hspace{}
25922 \begin_inset Note Note
25925 \begin_layout Plain Layout
25932 are used here as spacer.
25944 <cell alignment="center" valignment="top" usebox="none">
25947 \begin_layout Plain Layout
25953 \begin_inset space \textvisiblespace{}
25957 \begin_inset space \textvisiblespace{}
25965 <cell alignment="center" valignment="top" usebox="none">
25968 \begin_layout Plain Layout
25969 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25985 \begin_layout Standard
25986 In a displayed formula the limit is set below the formula, as usual:
25987 \begin_inset Formula
25997 \begin_layout Standard
25998 \begin_inset VSpace medskip
26004 \begin_layout Standard
26005 How to adjust the typesetting of the limits see
26006 \begin_inset CommandInset ref
26008 reference "subsec:Operator-Limits"
26015 \begin_layout Subsection
26017 \begin_inset Index idx
26020 \begin_layout Plain Layout
26021 Functions ! modulo-
26029 \begin_layout Standard
26030 The modulo-function is special, because it exists in four variants.
26031 The variants in a displayed formula are:
26032 \begin_inset Formula
26034 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26035 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
26036 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
26037 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
26038 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
26046 \begin_layout Standard
26047 In an inline formula less space is set before the function names for all
26049 By default the modulo-functions take only the first following character
26051 To use more than one character, one has to put them into \SpecialChar TeX
26053 \begin_inset Formula
26055 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26056 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
26057 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26065 \begin_layout Section
26067 \begin_inset Index idx
26070 \begin_layout Plain Layout
26079 \begin_layout Standard
26080 The characters ^ and _ would normally create a superscript and subscript,
26082 To get these characters you have to insert them with a leading
26085 \begin_inset Separator parbreak
26091 \begin_layout Standard
26094 \begin_inset Tabular
26095 <lyxtabular version="3" rows="3" columns="2">
26096 <features tabularvalignment="middle">
26097 <column alignment="block" valignment="top">
26098 <column alignment="block" valignment="top">
26100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26103 \begin_layout Plain Layout
26109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26112 \begin_layout Plain Layout
26120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26123 \begin_layout Plain Layout
26127 \begin_inset space \textvisiblespace{}
26135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26138 \begin_layout Plain Layout
26139 \begin_inset Formula $\mathcircumflex$
26149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26152 \begin_layout Plain Layout
26160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26163 \begin_layout Plain Layout
26164 \begin_inset Formula $\_$
26180 \begin_layout Subsection
26181 Special Characters in Mathematical Text
26184 \begin_layout Standard
26185 The following commands can only be used in mathematical text or in \SpecialChar TeX
26189 \begin_layout Standard
26190 \begin_inset space \hfill{}
26194 \begin_inset Tabular
26195 <lyxtabular version="3" rows="8" columns="2">
26196 <features tabularvalignment="middle">
26197 <column alignment="block" valignment="top">
26198 <column alignment="block" valignment="top">
26200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26203 \begin_layout Plain Layout
26209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26212 \begin_layout Plain Layout
26220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26223 \begin_layout Plain Layout
26231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26234 \begin_layout Plain Layout
26235 \begin_inset Formula $\textrm{œ}$
26245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26248 \begin_layout Plain Layout
26256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26259 \begin_layout Plain Layout
26260 \begin_inset Formula $\textrm{Œ}$
26270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26273 \begin_layout Plain Layout
26281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26284 \begin_layout Plain Layout
26285 \begin_inset Formula $\textrm{æ}$
26295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26298 \begin_layout Plain Layout
26306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26309 \begin_layout Plain Layout
26310 \begin_inset Formula $\textrm{Æ}$
26320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26323 \begin_layout Plain Layout
26331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26334 \begin_layout Plain Layout
26335 \begin_inset Formula $\textrm{\aa}$
26345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26348 \begin_layout Plain Layout
26352 \begin_inset Index idx
26355 \begin_layout Plain Layout
26362 \begin_layout Plain Layout
26383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26386 \begin_layout Plain Layout
26387 \begin_inset Formula $\textrm{Å}$
26397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26400 \begin_layout Plain Layout
26408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26411 \begin_layout Plain Layout
26412 \begin_inset Formula $\textrm{ı}$
26426 \begin_inset space \hfill{}
26430 \begin_inset Tabular
26431 <lyxtabular version="3" rows="8" columns="2">
26432 <features tabularvalignment="middle">
26433 <column alignment="block" valignment="top">
26434 <column alignment="center" valignment="top">
26436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26439 \begin_layout Plain Layout
26441 \begin_inset Note Note
26444 \begin_layout Plain Layout
26446 \begin_inset space \thinspace{}
26449 mm is used for separation, because otherwise the output will be ¡ and ¿
26460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26463 \begin_layout Plain Layout
26471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26474 \begin_layout Plain Layout
26482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26485 \begin_layout Plain Layout
26486 \begin_inset Formula $\textrm{ø}$
26496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26499 \begin_layout Plain Layout
26507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26510 \begin_layout Plain Layout
26511 \begin_inset Formula $\textrm{Ø}$
26521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26524 \begin_layout Plain Layout
26532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26535 \begin_layout Plain Layout
26536 \begin_inset Formula $\textrm{ł}$
26546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26549 \begin_layout Plain Layout
26557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26560 \begin_layout Plain Layout
26561 \begin_inset Formula $\textrm{Ł}$
26571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26574 \begin_layout Plain Layout
26576 \begin_inset space \hspace{}
26581 \begin_inset space \textvisiblespace{}
26589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26592 \begin_layout Plain Layout
26593 \begin_inset Formula $\textrm{!`}$
26603 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26606 \begin_layout Plain Layout
26608 \begin_inset space \hspace{}
26613 \begin_inset space \textvisiblespace{}
26621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26624 \begin_layout Plain Layout
26625 \begin_inset Formula $\textrm{?`}$
26635 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26638 \begin_layout Plain Layout
26646 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26649 \begin_layout Plain Layout
26650 \begin_inset Formula $\textrm{ȷ}$
26664 \begin_inset space \hfill{}
26670 \begin_layout Standard
26672 \begin_inset Formula $\textrm{\textrm{Å}}$
26676 \begin_inset Formula $\textrm{\textrm{Ø}}$
26679 can also be inserted via the math toolbar button
26682 arg "math-insert \\digamma"
26688 \begin_layout Standard
26689 An exception are the commands
26692 \begin_inset space \hspace{}
26701 \begin_inset space \hspace{}
26707 , because they can be inserted in \SpecialChar LyX
26711 \begin_layout Subsection
26713 \begin_inset CommandInset label
26715 name "subsec:Accents-in-Text"
26720 \begin_inset Index idx
26723 \begin_layout Plain Layout
26732 \begin_layout Standard
26733 With the following commands all letters can be accented.
26734 The commands must be inserted in \SpecialChar TeX
26738 \begin_layout Standard
26739 \begin_inset space \hfill{}
26743 \begin_inset Tabular
26744 <lyxtabular version="3" rows="8" columns="2">
26745 <features tabularvalignment="middle">
26746 <column alignment="block" valignment="top">
26747 <column alignment="block" valignment="top">
26749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26752 \begin_layout Plain Layout
26758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26761 \begin_layout Plain Layout
26769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26772 \begin_layout Plain Layout
26776 \begin_inset Quotes grd
26784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26787 \begin_layout Plain Layout
26791 \begin_layout Plain Layout
26807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26810 \begin_layout Plain Layout
26818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26821 \begin_layout Plain Layout
26825 \begin_layout Plain Layout
26841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26844 \begin_layout Plain Layout
26848 \begin_inset space \textvisiblespace{}
26856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26859 \begin_layout Plain Layout
26863 \begin_layout Plain Layout
26879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26882 \begin_layout Plain Layout
26890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26893 \begin_layout Plain Layout
26897 \begin_layout Plain Layout
26913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26916 \begin_layout Plain Layout
26920 \begin_inset space \textvisiblespace{}
26928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26931 \begin_layout Plain Layout
26935 \begin_layout Plain Layout
26951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26954 \begin_layout Plain Layout
26958 \begin_inset space \textvisiblespace{}
26966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26969 \begin_layout Plain Layout
26973 \begin_layout Plain Layout
26989 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26992 \begin_layout Plain Layout
26996 \begin_inset space \textvisiblespace{}
27004 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27007 \begin_layout Plain Layout
27011 \begin_layout Plain Layout
27031 \begin_inset space \hfill{}
27035 \begin_inset Tabular
27036 <lyxtabular version="3" rows="8" columns="2">
27037 <features tabularvalignment="middle">
27038 <column alignment="block" valignment="top">
27039 <column alignment="center" valignment="top">
27041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27044 \begin_layout Plain Layout
27050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27053 \begin_layout Plain Layout
27061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27064 \begin_layout Plain Layout
27068 \begin_inset space \textvisiblespace{}
27076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27079 \begin_layout Plain Layout
27083 \begin_layout Plain Layout
27099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27102 \begin_layout Plain Layout
27110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27113 \begin_layout Plain Layout
27117 \begin_layout Plain Layout
27133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27136 \begin_layout Plain Layout
27140 \begin_inset Index idx
27143 \begin_layout Plain Layout
27154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27157 \begin_layout Plain Layout
27161 \begin_layout Plain Layout
27177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27180 \begin_layout Plain Layout
27188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27191 \begin_layout Plain Layout
27195 \begin_layout Plain Layout
27211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27214 \begin_layout Plain Layout
27218 \begin_inset space \textvisiblespace{}
27226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27229 \begin_layout Plain Layout
27233 \begin_layout Plain Layout
27249 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27252 \begin_layout Plain Layout
27256 \begin_inset space \textvisiblespace{}
27264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27267 \begin_layout Plain Layout
27271 \begin_layout Plain Layout
27287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27290 \begin_layout Plain Layout
27294 \begin_inset space \textvisiblespace{}
27302 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27305 \begin_layout Plain Layout
27309 \begin_layout Plain Layout
27329 \begin_inset space \hfill{}
27335 \begin_layout Standard
27336 \begin_inset VSpace medskip
27345 also two different characters can be accented.
27351 \begin_inset space \textvisiblespace{}
27360 \begin_layout Plain Layout
27372 \begin_layout Standard
27385 can in combination with vowels directly be inserted with the keyboard without
27386 using \SpecialChar TeX
27388 The same applies for the tilde
27392 \begin_layout Plain Layout
27393 This only applies for keyboards where the tilde is defined as accent.
27402 in combination with
27417 \begin_layout Standard
27460 and accents that are inserted directly with the keyboard are also available
27461 in mathematical text.
27462 For the other accents there are special math commands to be used in formulas,
27464 \begin_inset CommandInset ref
27466 reference "subsec:Accents-for-one"
27473 \begin_layout Standard
27474 \begin_inset VSpace bigskip
27477 Furthermore, with the command
27484 \begin_inset Index idx
27487 \begin_layout Plain Layout
27495 all numbers and letters can be set into a circle, quasi accented with a
27496 circle, similar to the copyright symbol.
27499 \begin_layout Standard
27501 \begin_inset Tabular
27502 <lyxtabular version="3" rows="3" columns="2">
27503 <features tabularvalignment="middle">
27504 <column alignment="center" valignment="top">
27505 <column alignment="center" valignment="top">
27507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27510 \begin_layout Plain Layout
27516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27519 \begin_layout Plain Layout
27521 \begin_inset Note Note
27524 \begin_layout Plain Layout
27531 is only used as spacer.
27543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27546 \begin_layout Plain Layout
27554 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27557 \begin_layout Plain Layout
27561 \begin_layout Plain Layout
27577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27580 \begin_layout Plain Layout
27591 raisebox{-1.5pt}{W}}
27596 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27599 \begin_layout Plain Layout
27600 \begin_inset Formula $\raisebox{4.5mm}{}$
27607 \begin_layout Plain Layout
27625 \begin_inset Formula $\raisebox{-2mm}{}$
27641 \begin_layout Standard
27642 One has to take care that the character fits in the circle.
27653 \begin_layout Plain Layout
27655 \begin_inset CommandInset ref
27657 reference "subsec:Font-Sizes"
27666 specifies thereby the size of the circle.
27677 \begin_layout Plain Layout
27679 \begin_inset CommandInset ref
27681 reference "subsec:Boxes-without-Frame"
27690 the character can be centered.
27693 \begin_layout Subsection
27695 \begin_inset Index idx
27698 \begin_layout Plain Layout
27707 \begin_layout Standard
27708 Old-style figures (also known as old-style numerals) are created with the
27716 \begin_inset Index idx
27719 \begin_layout Plain Layout
27728 The command can be used in formulas and in \SpecialChar TeX
27730 The command scheme is:
27733 \begin_layout Standard
27738 oldstylenums{number}
27741 \begin_layout Standard
27746 oldstylenums{0123456789
27749 \begin_inset Formula $\oldstylenums{0123456789}$
27755 \begin_layout Section
27757 \begin_inset CommandInset label
27759 name "sec:Formula-Styles"
27764 \begin_inset Index idx
27767 \begin_layout Plain Layout
27776 \begin_layout Itemize
27777 There are two different alignment styles:
27778 \begin_inset Separator parbreak
27785 \begin_layout Description
27786 Centered is the predefined standard
27789 \begin_layout Description
27790 Indented for this the option
27794 must be inserted in the menu
27796 Document\SpecialChar menuseparator
27802 \begin_inset space ~
27808 \begin_layout Standard
27813 is used, the indentation can be adjusted with the length
27820 \begin_inset Index idx
27823 \begin_layout Plain Layout
27832 Should the distance be 15
27833 \begin_inset space \thinspace{}
27836 mm, the following command line is inserted in the \SpecialChar LaTeX
27840 \begin_layout Standard
27850 \begin_layout Standard
27851 When no length is specified, the predefined value of 30
27852 \begin_inset space \thinspace{}
27859 \begin_layout Itemize
27860 And two different numbering styles:
27861 \begin_inset Separator parbreak
27868 \begin_layout Description
27869 Right is the predefined standard
27872 \begin_layout Description
27873 Left for this the option
27877 must be inserted in the menu
27879 Document\SpecialChar menuseparator
27885 \begin_inset space ~
27892 \begin_layout Standard
27901 can also be used together.
27902 In this case both options are inserted, separated by a comma.
27905 \begin_layout Standard
27906 The chosen styles are used for all displayed formulas of the document.
27907 When both, centered and indented formulas should be created in a document,
27913 The indented formulas are then set in a flalign environment, see
27914 \begin_inset CommandInset ref
27916 reference "subsec:Flalign-Environment"
27923 \begin_layout Section
27925 \begin_inset CommandInset label
27927 name "sec:Multiline-Formulas"
27932 \begin_inset Index idx
27935 \begin_layout Plain Layout
27936 Formula ! multiline
27944 \begin_layout Subsection
27948 \begin_layout Standard
27949 In \SpecialChar LyX
27950 multiline formulas are created by pressing
27953 arg "newline-insert newline"
27957 This creates either an
27959 eqnarray environment
27961 that is described in
27962 \begin_inset CommandInset ref
27964 reference "subsec:Eqnarray-Environment"
27968 or, when the option
27970 Use AMS math package
27972 in the document settings is selected, an
27976 that is described in
27977 \begin_inset CommandInset ref
27979 reference "subsec:Standard-align-Environment"
27984 The align environment is recommended because it provides in any case a
27985 typographically correct output.
27988 \begin_layout Standard
27989 There are other multiline formula environments that can be created via the
27992 Insert\SpecialChar menuseparator
27996 These environments are described in the following sections.
27999 \begin_layout Standard
28000 In all multiline formula environments a new line is created by pressing
28004 arg "newline-insert newline"
28008 To add or delete lines, the math toolbar buttons
28011 arg "inset-modify tabular append-row"
28017 arg "inset-modify tabular delete-row"
28020 , respectively, or the menu
28022 Edit\SpecialChar menuseparator
28028 \begin_layout Subsubsection
28030 \begin_inset CommandInset label
28032 name "subsec:Line-Separation"
28037 \begin_inset Index idx
28040 \begin_layout Plain Layout
28041 Formula ! multiline ! Line separation
28049 \begin_layout Standard
28050 There is sometimes not enough space in multiline formulas between the lines:
28051 \begin_inset Formula
28053 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}\\
28054 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
28062 \begin_layout Standard
28063 In \SpecialChar LaTeX
28064 additional line space is specified as optional argument of the new line
28066 This is not yet possible in \SpecialChar LyX
28071 \begin_layout Plain Layout
28073 \begin_inset CommandInset href
28075 name "LyX-bug #1505"
28076 target "http://www.lyx.org/trac/ticket/1505"
28085 , therefore the whole formula must be inserted in \SpecialChar TeX
28087 To add in our example space, the command
28095 is inserted at the end of the first line.
28100 \begin_layout Plain Layout
28107 \begin_layout Plain Layout
28109 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28112 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28119 \begin_layout Plain Layout
28123 left(B^{2}+x_{0}^{2}
28131 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28136 \begin_layout Plain Layout
28148 \begin_layout Standard
28149 \begin_inset VSpace bigskip
28152 To set the line separation for all lines in a formula, the length
28159 \begin_inset Index idx
28162 \begin_layout Plain Layout
28172 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28183 \begin_inset space \thinspace{}
28188 \begin_inset space \thinspace{}
28191 mm additional line separation as in the previous example, the command
28194 \begin_layout Standard
28204 \begin_layout Standard
28205 is inserted in \SpecialChar TeX
28206 mode before the formula.
28207 This requires that the \SpecialChar LaTeX
28216 \begin_layout Plain Layout
28221 is part of every \SpecialChar LaTeX
28222 standard installation.
28228 \begin_inset Index idx
28231 \begin_layout Plain Layout
28237 was loaded in \SpecialChar LaTeX
28238 -preamble with the line
28241 \begin_layout Standard
28249 \begin_layout Standard
28254 \begin_layout Plain Layout
28266 \begin_inset Formula
28268 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}\\
28269 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
28277 \begin_layout Standard
28281 \begin_layout Plain Layout
28292 To get back to the predefined distance,
28298 is set to the value 3
28299 \begin_inset space \thinspace{}
28305 \begin_layout Subsubsection
28307 \begin_inset CommandInset label
28309 name "subsec:Column-Separation"
28314 \begin_inset Index idx
28317 \begin_layout Plain Layout
28318 Formula ! multiline ! Column separation
28326 \begin_layout Standard
28327 Multiline formulas form a matrix.
28328 A formula in the eqnarray environment is for example a matrix with three
28330 By changing the column separation in this environment, the space beside
28331 the relation sign can be changed.
28334 \begin_layout Standard
28335 The column separation is specified with the length
28342 \begin_inset Index idx
28345 \begin_layout Plain Layout
28354 \begin_inset Newline newline
28357 column separation = 2
28358 \begin_inset space \thinspace{}
28368 \begin_inset Newline newline
28374 \begin_layout Standard
28384 \begin_layout Standard
28385 inserted in \SpecialChar TeX
28386 mode, sets for all following formulas a column separation of
28388 \begin_inset space \thinspace{}
28392 To get back to the predefined distance,
28399 \begin_inset space \thinspace{}
28405 \begin_layout Standard
28407 \begin_inset space \thinspace{}
28410 cm column separation:
28414 \begin_layout Plain Layout
28426 \begin_inset Formula
28434 A formula with the predefined column separation for matrices of 10
28435 \begin_inset space \thinspace{}
28442 \begin_layout Plain Layout
28454 \begin_inset Formula
28465 \begin_layout Subsubsection
28467 \begin_inset Index idx
28470 \begin_layout Plain Layout
28479 \begin_layout Standard
28480 Long formulas can be typeset using these methods:
28483 \begin_layout Itemize
28484 When one side of the equation is much shorter than the line width, this
28485 one is chosen for the left side and the right side is typeset over two
28487 \begin_inset Formula
28489 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 \\
28490 & & -\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}
28495 The minus sign at the beginning of the second line does normally not appear
28496 as an operator because it is the first character of the line.
28497 Thus it would not be surrounded by space and could not be distinguished
28498 from the fraction bar.
28500 \begin_inset space \thinspace{}
28503 pt space was inserted behind the minus sign with the command
28513 \begin_layout Plain Layout
28521 \begin_inset CommandInset ref
28523 reference "subsec:Variable-Space"
28533 \begin_inset Index idx
28536 \begin_layout Plain Layout
28547 \begin_layout Itemize
28548 When both sides of the equation are too long, the command
28555 \begin_inset Index idx
28558 \begin_layout Plain Layout
28567 It is inserted in the first column of the first line and causes all further
28568 insertions to overwrite the following columns:
28569 \begin_inset Formula
28571 \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 \\
28572 & & -\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 \\
28573 & & =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}
28578 After the insertion of
28584 , the cursor is in a purple box that is a bit shifted to the left from the
28586 In this the formula is inserted.
28587 \begin_inset Newline newline
28590 The content of the further lines is inserted to the second or another formula
28592 The greater the column number where it was inserted, the larger the indentation.
28593 \begin_inset VSpace medskip
28597 \begin_inset Newline newline
28601 \begin_inset Note Greyedout
28604 \begin_layout Plain Layout
28605 Note the following when using
28614 \begin_layout Itemize
28615 The formula doesn't use the full page width.
28617 \begin_inset space \thinspace{}
28621 \begin_inset space \space{}
28625 \begin_inset Formula $-B^{2}$
28628 is added to the first line in the above example, it would have been outside
28630 To better use the width, negative space can be inserted at the beginning
28634 \begin_layout Itemize
28635 Due to a bug in \SpecialChar LyX
28636 the cursor cannot be set with the mouse into the first
28641 \begin_layout Plain Layout
28642 \begin_inset CommandInset href
28644 name "LyX-bug #1429"
28645 target "http://www.lyx.org/trac/ticket/1429"
28654 One can only set the cursor at the beginning of the line and move it with
28663 \begin_layout Itemize
28664 Other methods to set long formulas are offered by the environments described
28666 \begin_inset CommandInset ref
28668 reference "subsec:Multline-Environment"
28673 \begin_inset CommandInset ref
28675 reference "subsec:Multiline-Formula-Parts"
28682 \begin_layout Subsubsection
28683 Multiline Fractions
28684 \begin_inset CommandInset label
28686 name "subsec:Multiline-Fractions"
28691 \begin_inset Index idx
28694 \begin_layout Plain Layout
28695 Fractions ! multiline
28703 \begin_layout Standard
28704 There are cases where the denominator and/or the numerator of a fraction
28705 is so long that the fraction does not fit into one line.
28706 It is then necessary to add a line break within the fraction.
28707 This can be done using the command
28714 \begin_inset Index idx
28717 \begin_layout Plain Layout
28726 To activate it, set in the document settings under
28729 \begin_inset space ~
28739 \begin_inset Index idx
28742 \begin_layout Plain Layout
28743 Packages ! mathtools
28751 \begin_inset space ~
28766 \begin_layout Standard
28771 splitfrac{first line}{second line}
28774 \begin_layout Standard
28775 and is used as denominator and/or numerator:
28778 \begin_layout Standard
28779 \begin_inset Formula
28781 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}
28786 The command for the first numerator above is:
28789 \begin_layout Standard
28794 splitfrac{xy+xy+xy+xy+xy
28795 \begin_inset space \textvisiblespace{}
28803 \begin_layout Subsubsection
28805 \begin_inset CommandInset label
28807 name "subsec:Multiline-Brackets"
28812 \begin_inset Index idx
28815 \begin_layout Plain Layout
28816 Brackets ! for multiline expressions
28824 \begin_layout Standard
28825 For brackets spanning multiple lines the following problem occurs:
28826 \begin_inset Formula
28828 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28829 & & \left.\cdots+B-D\right]
28837 \begin_layout Standard
28838 The closing bracket is smaller than the opening bracket because brackets
28839 with variable size may not span multiple lines.
28842 \begin_layout Standard
28843 To set the bracket size for the second line correctly, the first line is
28851 \begin_inset Index idx
28854 \begin_layout Plain Layout
28862 and the second line with
28870 \begin_layout Plain Layout
28884 \begin_inset CommandInset ref
28886 reference "subsec:Automatic-Bracket-Size"
28898 \begin_inset Index idx
28901 \begin_layout Plain Layout
28924 \begin_inset space \textvisiblespace{}
28934 \begin_inset space \textvisiblespace{}
28944 \begin_inset space \textvisiblespace{}
28950 \begin_inset Formula $\downarrow$
28956 \begin_inset Index idx
28959 \begin_layout Plain Layout
28967 is inserted, because the multiplication operator with its limits is the
28968 largest symbol in the first line and this should be the size for the bracket
28969 in the second line.
28972 \begin_layout Standard
28973 The result is this:
28974 \begin_inset Formula
28976 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28977 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28985 \begin_layout Subsection
28989 \begin_layout Standard
28990 Align environments can be used for every kind of multiline formulas.
28991 They are especially useful to set several formulas side by side.
28994 \begin_layout Standard
28995 Align environments consist of columns.
28996 The odd columns are right aligned, the even ones left aligned.
28997 Every line in an Align environment can be numbered.
29000 \begin_layout Standard
29001 Align environments are created via the menu
29003 Insert\SpecialChar menuseparator
29009 Edit\SpecialChar menuseparator
29010 Math\SpecialChar menuseparator
29011 Change Formula Type
29013 already existing formulas can be converted to Align environments.
29016 \begin_layout Standard
29017 To add or delete columns, the math toolbar buttons
29020 arg "inset-modify tabular append-column"
29026 arg "inset-modify tabular delete-column"
29029 , respectively, or the menu
29031 Edit\SpecialChar menuseparator
29037 \begin_layout Subsubsection
29038 Standard align Environment
29039 \begin_inset CommandInset label
29041 name "subsec:Standard-align-Environment"
29046 \begin_inset Index idx
29049 \begin_layout Plain Layout
29050 Formula ! multiline ! align environment
29058 \begin_layout Standard
29059 This Align environment is created by pressing
29062 arg "newline-insert newline"
29065 in a formula or by the menu
29067 Insert\SpecialChar menuseparator
29068 Math\SpecialChar menuseparator
29069 AMS align Environment
29074 \begin_layout Standard
29075 An example for two formulas set side by side, that are created with a four
29076 column align environment:
29077 \begin_inset Formula
29079 A & =\sin(B) & C & =D\\
29080 C & \ne A & B & \ne D
29085 As it can be seen, the formulas in this environment are placed so as if
29094 \begin_layout Plain Layout
29102 \begin_inset CommandInset ref
29104 reference "subsec:Variable-Space"
29115 before the first and after every even column.
29116 When the formula style
29122 \begin_layout Plain Layout
29124 \begin_inset CommandInset ref
29126 reference "sec:Formula-Styles"
29137 is used, the formula is set without the
29143 before the first column.
29146 \begin_layout Subsubsection
29147 Alignat Environment
29148 \begin_inset Index idx
29151 \begin_layout Plain Layout
29152 Formula ! multiline ! alignat environment
29160 \begin_layout Standard
29161 The alignat environment has no predefined column separation.
29162 It can be inserted manually with the spaces that are described
29163 \begin_inset CommandInset ref
29165 reference "subsec:Space"
29172 \begin_layout Standard
29173 The above example in the alignat environment where 1
29174 \begin_inset space \thinspace{}
29177 cm space was inserted at the beginning of the second formula:
29178 \begin_inset Formula
29179 \begin{alignat*}{2}
29180 A & =\sin(B) & \hspace{1cm}C & =D\\
29181 C & \ne A & B & \ne D
29186 Because the column separation can be set separately for every column, this
29187 environment is especially suitable to set three and more formulas side
29191 \begin_layout Subsubsection
29192 Flalign Environment
29193 \begin_inset CommandInset label
29195 name "subsec:Flalign-Environment"
29200 \begin_inset Index idx
29203 \begin_layout Plain Layout
29204 Formula ! multiline ! flalign environment
29212 \begin_layout Standard
29213 In this environment the first two columns are always set as much as possible
29214 to the left and the last two ones to the right.
29216 \begin_inset Formula
29218 A & =1 & B & =2 & C & =3\\
29219 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29227 \begin_layout Standard
29228 By creating a flalign environment with an odd number of columns where an
29229 empty \SpecialChar TeX
29230 brace is inserted to the last column, several formulas in a document
29231 can be set to the left, although the formula style
29236 As example the indented formula
29237 \begin_inset CommandInset ref
29239 reference "eq:VolInt"
29244 \begin_inset Formula
29246 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29251 The first two columns contain the formula.
29252 To indent it as with the formula style
29257 \begin_inset space \thinspace{}
29260 pt space was inserted at the beginning of the first column.
29263 \begin_layout Subsection
29264 Eqnarray Environment
29265 \begin_inset CommandInset label
29267 name "subsec:Eqnarray-Environment"
29272 \begin_inset Index idx
29275 \begin_layout Plain Layout
29276 Formula ! multiline ! eqnarray environment
29284 \begin_layout Standard
29285 When this environment has been created, three blue boxes appear.
29286 The content of the first box is right aligned, the content of the last
29288 The content of the middle box appears centered and a bit smaller, because
29289 it is designed to insert there only relation characters.
29290 \begin_inset Formula
29292 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29302 \begin_layout Subsection
29304 \begin_inset Index idx
29307 \begin_layout Plain Layout
29308 Formula ! multiline ! gather environment
29316 \begin_layout Standard
29317 This environment consists of only one centered column.
29318 Every line can be numbered.
29319 \begin_inset Formula
29330 \begin_layout Subsection
29331 Multline Environment
29332 \begin_inset CommandInset label
29334 name "subsec:Multline-Environment"
29339 \begin_inset Index idx
29342 \begin_layout Plain Layout
29343 Formula ! multiline ! multline environment
29351 \begin_layout Standard
29352 The multline environment consists, like the gather environment, of only
29354 But the first line is left aligned, the last one right aligned.
29355 All other lines are centered.
29356 Therefore this environment is suitable for long formulas.
29358 \begin_inset CommandInset ref
29360 reference "eq:lefteqn"
29364 in the multline environment:
29365 \begin_inset Formula
29367 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}\\
29368 -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}\\
29369 =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}}
29377 \begin_layout Standard
29378 In the output only the last (first) line of a multline environment appears
29379 numbered when the document numbering is right (left).
29383 \begin_layout Plain Layout
29384 numbering styles see
29385 \begin_inset CommandInset ref
29387 reference "sec:Formula-Styles"
29399 \begin_layout Standard
29407 \begin_inset Index idx
29410 \begin_layout Plain Layout
29425 \begin_inset Index idx
29428 \begin_layout Plain Layout
29436 a centered line can be right or left aligned, respectively.
29437 The commands are used as follows:
29440 \begin_layout Standard
29445 shoveright{line content}
29451 shoveleft{line content}
29454 \begin_layout Standard
29455 \begin_inset VSpace medskip
29465 \begin_inset Index idx
29468 \begin_layout Plain Layout
29476 specifies the distance of the first line from the left page margin.
29477 Predefined is the length 0
29478 \begin_inset space \thinspace{}
29484 \begin_layout Standard
29485 As example the above formula where the command
29488 \begin_layout Standard
29498 \begin_layout Standard
29499 was inserted in \SpecialChar TeX
29504 \begin_layout Plain Layout
29516 \begin_inset Formula
29518 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}\\
29519 \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}}\\
29520 =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}}
29529 \begin_layout Plain Layout
29540 The second line was left aligned using
29549 \begin_layout Subsection
29550 Multiline Formula Parts
29551 \begin_inset CommandInset label
29553 name "subsec:Multiline-Formula-Parts"
29558 \begin_inset Index idx
29561 \begin_layout Plain Layout
29562 Formula ! multiline ! formula parts
29570 \begin_layout Standard
29571 To display only parts of a formula with multiple lines, one of the following
29572 environments is used:
29589 They can be inserted via the menu
29591 Insert\SpecialChar menuseparator
29594 or by using the commands described in this section.
29597 \begin_layout Standard
29598 The first three have the same properties as the corresponding multiline
29599 formula environments, but it is possible to set further formula parts beside
29602 \begin_inset Formula
29604 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29605 \Delta E\Delta t & \ge\frac{\hbar}{2}
29607 \right\} \textrm{Uncertainty relations}
29615 \begin_layout Standard
29616 To get this formula, a displayed formula is created where the command
29623 \begin_inset Index idx
29626 \begin_layout Plain Layout
29635 A purple box appears around the blue formula box where now columns and
29636 lines can be added.
29637 Outside the multiline environment other formula parts can be set, like
29641 \begin_layout Standard
29642 The aligned environment is also suitable for long formulas whose lines are
29643 horizontally aligned.
29644 Using aligned in a displayed formula has the advantage that the formula
29645 number is vertically centered behind the lines.
29647 \begin_inset CommandInset ref
29649 reference "eq:shortlong"
29653 in the aligned environment:
29654 \begin_inset Formula
29656 \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}|}\\
29657 & -\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}|}
29666 \begin_layout Standard
29667 To use the environments
29686 \begin_inset Index idx
29689 \begin_layout Plain Layout
29704 \begin_inset Index idx
29707 \begin_layout Plain Layout
29722 \begin_inset Index idx
29725 \begin_layout Plain Layout
29733 are inserted, respectively.
29734 The split environment has the same properties as the aligned environment
29735 but it can only have two columns.
29738 \begin_layout Subsection
29739 Text in multiline Formulas
29740 \begin_inset CommandInset label
29742 name "subsec:Text-in-multiline"
29747 \begin_inset Index idx
29750 \begin_layout Plain Layout
29757 \begin_inset Index idx
29760 \begin_layout Plain Layout
29761 Formula ! multiline ! text
29769 \begin_layout Standard
29770 In the Align environments, and the multline and gather environment, text
29771 can be inserted that will appear in a separate line and doesn't affect
29772 the column alignment.
29773 To do this, the command
29780 \begin_inset Index idx
29783 \begin_layout Plain Layout
29791 is used in the following scheme:
29794 \begin_layout Standard
29802 \begin_layout Standard
29803 The text should not be longer than a line because it cannot be hyphenated.
29804 As \SpecialChar LyX
29805 doesn't yet support
29811 directly, the text is written as mathematical text.
29818 must hereby be at the beginning of a line and appears in the output above
29820 An example where the text was inserted at the beginning of the second line:
29821 \begin_inset Formula
29823 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29824 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29832 \begin_layout Standard
29839 always creates some vertical space between the text and the formula lines.
29840 To avoid this space, set in the document settings under
29843 \begin_inset space ~
29853 \begin_inset Index idx
29856 \begin_layout Plain Layout
29857 Packages ! mathtools
29865 \begin_inset space ~
29871 Then you can use the command
29878 \begin_inset Index idx
29881 \begin_layout Plain Layout
29898 \begin_layout Standard
29899 \begin_inset Formula
29901 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29902 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29910 \begin_layout Section
29912 \begin_inset Index idx
29915 \begin_layout Plain Layout
29922 \begin_inset Index idx
29925 \begin_layout Plain Layout
29926 Formula ! numbering|see
29930 \begin_layout Plain Layout
29941 \begin_layout Plain Layout
29956 \begin_layout Subsection
29960 \begin_layout Standard
29961 Numbered formulas can be created with the menu
29963 Insert\SpecialChar menuseparator
29964 Math\SpecialChar menuseparator
29966 \begin_inset space ~
29974 \begin_inset space ~
29980 Existing formulas can be numbered with the menu
29982 Edit\SpecialChar menuseparator
29983 Math\SpecialChar menuseparator
29985 \begin_inset space ~
29993 arg "math-number-toggle"
29997 The formula number is displayed in \SpecialChar LyX
29998 behind the formula as a number sign
30000 The number sign is replaced in the output by the formula number.
30003 \begin_layout Standard
30004 When numbering is turned on in multiline formulas, all lines will be numbered.
30005 But the numbering can be controlled with the menu
30007 Edit\SpecialChar menuseparator
30008 Math\SpecialChar menuseparator
30010 \begin_inset space ~
30014 \begin_inset space ~
30018 \begin_inset space ~
30026 arg "math-number-line-toggle"
30032 \begin_layout Standard
30033 Except for inline formulas, all formulas can be numbered with two different
30035 \begin_inset CommandInset ref
30037 reference "sec:Formula-Styles"
30044 \begin_layout Subsection
30046 \begin_inset Index idx
30049 \begin_layout Plain Layout
30050 Cross-references ! to formulas
30058 \begin_layout Standard
30059 All labeled formulas can be cross-referenced.
30060 A label is added by the menu
30062 Insert\SpecialChar menuseparator
30065 or the toolbar button
30072 The cursor must hereby be inside a displayed formula.
30073 Alternatively you can right-click on the formula and choose
30078 A dialog pops up displaying the prefix
30083 The label is inserted there behind the prefix.
30084 The predefined prefix means
30085 \begin_inset Quotes eld
30089 \begin_inset Quotes erd
30092 and makes it easier to find labels in large documents because it marks
30093 it as formula label to divide it from e.
30094 \begin_inset space \thinspace{}
30098 \begin_inset space \space{}
30102 To change a label, the menu
30104 Insert\SpecialChar menuseparator
30107 is used again or you right-click on a formula and then on
30114 \begin_layout Standard
30115 The name of the label is displayed in \SpecialChar LyX
30116 within two parentheses behind formula.
30117 A formula with a label is always numbered.
30120 \begin_layout Standard
30121 Cross-references are inserted via the menu
30123 Insert\SpecialChar menuseparator
30126 or with the toolbar button
30129 arg "dialog-show-new-inset ref"
30133 A formula cross-reference appears in the output as formula number.
30134 When in the cross-reference dialog window the format
30138 is chosen, the cross-reference appears in the output as formula number
30140 \begin_inset Newline newline
30143 By right-clicking on a cross-reference in \SpecialChar LyX
30144 , one jumps to the formula that
30148 \begin_layout Standard
30149 Here are as examples cross-references to formulas of the following subsections:
30150 \begin_inset Note Note
30153 \begin_layout Plain Layout
30154 Note the different cross-reference types.
30162 \begin_layout Standard
30164 \begin_inset CommandInset ref
30171 \begin_inset CommandInset ref
30179 \begin_inset CommandInset ref
30185 ) big Latin letters are used for the numbering in contrary to (
30186 \begin_inset CommandInset ref
30195 \begin_layout Standard
30196 \begin_inset VSpace medskip
30199 When the argument of
30207 \begin_layout Plain Layout
30215 \begin_inset CommandInset ref
30217 reference "subsec:User-defined-Numbering"
30228 contains a box like in
30229 \begin_inset CommandInset ref
30231 reference "subsec:Paragraph-Boxes"
30235 , the formula cannot be referenced.
30238 \begin_layout Subsection
30240 \begin_inset Index idx
30243 \begin_layout Plain Layout
30244 Formula numbering ! subnumbering
30252 \begin_layout Standard
30253 With the help of the commands
30257 begin{subequations}
30265 formulas can be subnumbered.
30266 Both commands are inserted in \SpecialChar TeX
30270 \begin_layout Standard
30272 \begin_inset Formula
30283 \begin_layout Plain Layout
30287 addtocounter{equation}{-1}
30296 \begin_layout Plain Layout
30300 begin{subequations}
30306 \begin_inset VSpace -5mm
30310 \begin_inset Formula
30318 \begin_inset Formula
30328 \begin_layout Standard
30332 \begin_layout Plain Layout
30344 \begin_layout Standard
30345 To create the example, the following is done:
30348 \begin_layout Enumerate
30349 first formula is inserted
30352 \begin_layout Enumerate
30357 addtocounter{equation}{-1}
30359 begin{subequations}
30360 \begin_inset Index idx
30363 \begin_layout Plain Layout
30372 \begin_inset Newline newline
30377 is inserted after the first formula
30380 \begin_layout Enumerate
30381 second formula is inserted
30384 \begin_layout Enumerate
30385 third formula is inserted
30388 \begin_layout Enumerate
30395 is inserted after the third formula
30398 \begin_layout Standard
30399 Every formula between the commands
30411 is subnumbered as a, b,
30412 \begin_inset Newline linebreak
30415 c, \SpecialChar ldots
30416 For multiline formulas every line will be subnumbered.
30417 All subnumbered formulas are treated as
30422 But as every numbered formula increases the counter
30426 by one, the command
30432 is needed to decrease it.
30433 Otherwise the formulas
30434 \begin_inset CommandInset ref
30441 \begin_inset CommandInset ref
30448 \begin_inset CommandInset ref
30454 would be numbered as
30455 \begin_inset CommandInset ref
30462 \begin_inset CommandInset ref
30469 \begin_inset CommandInset ref
30478 \begin_layout Standard
30479 By inserting the commands in \SpecialChar TeX
30480 mode, a space is created between the first
30483 \begin_inset space \thinspace{}
30486 mm vertical space is inserted after the command
30490 begin{subequations}
30493 When the formula style
30499 \begin_layout Plain Layout
30501 \begin_inset CommandInset ref
30503 reference "sec:Formula-Styles"
30515 \begin_inset space \thinspace{}
30518 mm space is inserted instead.
30521 \begin_layout Standard
30522 Here is an example for a multiline formula where the numbering was turned
30523 off for the second line:
30527 \begin_layout Plain Layout
30531 begin{subequations}
30537 \begin_inset Formula
30539 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30540 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30541 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30550 \begin_layout Plain Layout
30562 \begin_layout Subsection
30563 User-defined Numbering
30564 \begin_inset CommandInset label
30566 name "subsec:User-defined-Numbering"
30571 \begin_inset Index idx
30574 \begin_layout Plain Layout
30575 Formula numbering ! user-defined
30583 \begin_layout Standard
30584 \begin_inset Index idx
30587 \begin_layout Plain Layout
30588 Formula numbering ! self-defined delimiters
30593 With the standard numbering parentheses are set around the formula number.
30594 To replace the parentheses for example by vertical bars, the following
30595 line is added to the \SpecialChar LaTeX
30599 \begin_layout Standard
30611 \begin_inset Note Note
30614 \begin_layout Plain Layout
30615 This macro is already declared in the \SpecialChar LaTeX
30616 -preamble for testing.
30617 To activate it, remove the percent sign at the beginning.
30625 \begin_layout Standard
30626 To use other characters, the vertical bars besides the
30630 are replaced by one ore more characters.
30631 To get only the formula number the vertical bars are omitted.
30634 \begin_layout Standard
30635 \begin_inset VSpace bigskip
30638 When there should be an expression of your choice instead of the consecutive
30639 formula number in parentheses behind the formula, the command
30646 \begin_inset Index idx
30649 \begin_layout Plain Layout
30658 \begin_inset Formula
30660 A+B=C\tag{something}\label{eq:tag}
30665 In this example the command
30670 \begin_inset space \textvisiblespace{}
30675 was inserted in the formula.
30678 \begin_layout Standard
30684 \begin_inset space \textvisiblespace{}
30689 is inserted instead, the star prevents the parentheses around the expression:
30690 \begin_inset Formula
30692 A+B=C\tag*{something}
30700 \begin_layout Standard
30701 \begin_inset VSpace bigskip
30704 To restart the formula numbering with new document parts or sections, the
30705 following command is used:
30708 \begin_layout Standard
30713 @addtoreset{equation}{part}
30716 \begin_inset Index idx
30719 \begin_layout Plain Layout
30724 \begin_layout Plain Layout
30735 \begin_layout Plain Layout
30748 \begin_layout Plain Layout
30759 \begin_layout Plain Layout
30772 \begin_inset Newline newline
30776 \begin_inset Newline newline
30783 @addtoreset{equation}{section}
30786 \begin_layout Standard
30787 To be able to use these commands in \SpecialChar TeX
30789 \begin_inset Quotes eld
30793 \begin_inset Quotes erd
30796 character has to be made
30797 \begin_inset Quotes eld
30801 \begin_inset Quotes erd
30804 for \SpecialChar LaTeX
30819 So the command sequence in \SpecialChar TeX
30823 \begin_layout Standard
30829 \begin_inset Newline newline
30834 @addtoreset{equation}{section}
30835 \begin_inset Newline newline
30843 \begin_layout Standard
30844 In the \SpecialChar LaTeX
30857 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30861 \begin_layout Standard
30876 \begin_layout Plain Layout
30881 is part of the \SpecialChar LaTeX
30887 \begin_inset Index idx
30890 \begin_layout Plain Layout
30891 Packages ! carlisle
30896 that is part of every \SpecialChar LaTeX
30897 standard installation.
30903 \begin_inset Index idx
30906 \begin_layout Plain Layout
30907 Packages ! remreset
30912 has to be loaded in the \SpecialChar LaTeX
30913 -preamble with the line
30916 \begin_layout Standard
30921 usepackage{remreset}
30924 \begin_layout Standard
30932 \begin_inset Index idx
30935 \begin_layout Plain Layout
30940 \begin_layout Plain Layout
30951 \begin_layout Plain Layout
30964 \begin_layout Plain Layout
30975 \begin_layout Plain Layout
30987 can be used with the same scheme as
30996 \begin_layout Standard
30997 \begin_inset VSpace bigskip
31000 Sometimes formulas should be numbered in the following form:
31003 \begin_layout Standard
31006 (section number.formula number)
31009 \begin_layout Standard
31010 The formula number should start with every section with
31011 \begin_inset Quotes eld
31015 \begin_inset Quotes erd
31021 \begin_layout Standard
31022 For this case there is the command
31029 \begin_inset Index idx
31032 \begin_layout Plain Layout
31040 , which is used with the following scheme:
31043 \begin_layout Standard
31048 numberwithin{counter}{sectioning}
31051 \begin_layout Standard
31052 Counter denotes what kind of numbering is affected, sectioning denotes what
31053 number is before the dot.
31056 \begin_layout Standard
31057 Thus in our case the following \SpecialChar LaTeX
31058 preamble or \SpecialChar TeX
31062 \begin_layout Standard
31067 numberwithin{equation}{section}
31070 \begin_layout Standard
31071 This is the result:
31075 \begin_layout Plain Layout
31079 numberwithin{equation}{section}
31085 \begin_inset Formula
31095 \begin_layout Standard
31097 \begin_inset space \thinspace{}
31101 \begin_inset space \space{}
31104 tables so that the number of the part is the sectioning,
31105 \begin_inset Newline newline
31112 numberwithin{table}{part}
31117 \begin_layout Standard
31118 To go back to the standard numbering or to prevent this kind of numbering
31119 when it is defined by the document class, the following command is inserted
31120 as \SpecialChar TeX
31121 code or to the \SpecialChar LaTeX
31125 \begin_layout Standard
31135 \begin_inset Index idx
31138 \begin_layout Plain Layout
31152 \begin_layout Plain Layout
31168 \begin_inset Newline newline
31176 \begin_inset Newline newline
31188 \begin_layout Standard
31195 uses internally the command
31201 , described above, that also needs to be reverted.
31205 \begin_layout Plain Layout
31212 \begin_layout Plain Layout
31216 @removefromreset{equation}{section}
31219 \begin_layout Plain Layout
31231 \begin_layout Subsection
31232 Numbering with Roman Numbers and Letters
31233 \begin_inset Index idx
31236 \begin_layout Plain Layout
31237 Formula numbering ! with letters
31243 \begin_inset Index idx
31246 \begin_layout Plain Layout
31247 Formula numbering ! with Roman numbers
31255 \begin_layout Standard
31256 Formulas can also be numbered with Roman numbers and Latin letters.
31257 To number for example with small Roman numbers, the command
31260 \begin_layout Standard
31272 \begin_layout Standard
31273 is inserted before the formula in \SpecialChar TeX
31282 \begin_inset Index idx
31285 \begin_layout Plain Layout
31293 redefines the predefined command
31309 \begin_layout Plain Layout
31316 has the same scheme like the command
31322 that is described in
31323 \begin_inset CommandInset ref
31325 reference "subsec:The-Command-newcommand"
31338 is the formula counter.
31345 is used as prefix for a counter, the value of the counter is output as
31347 When a formula is numbered, \SpecialChar LaTeX
31348 sets internally the command
31354 behind the formula.
31360 \begin_inset Index idx
31363 \begin_layout Plain Layout
31373 outputs the counter as small Roman number.
31376 \begin_layout Standard
31377 All formulas behind the command
31387 are now numbered Roman.
31388 To switch to numbering with big Roman numbers, the command is inserted
31402 \begin_inset Index idx
31405 \begin_layout Plain Layout
31417 \begin_inset Quotes eld
31421 \begin_inset Quotes erd
31424 with small Latin letters there is the command
31431 \begin_inset Index idx
31434 \begin_layout Plain Layout
31442 , for big ones there is the command
31449 \begin_inset Index idx
31452 \begin_layout Plain Layout
31465 \begin_layout Standard
31466 \begin_inset Note Greyedout
31469 \begin_layout Plain Layout
31476 \begin_inset space ~
31479 formulas can be numbered with Latin letters in one document.
31487 \begin_layout Standard
31491 \begin_layout Plain Layout
31507 \begin_layout Standard
31508 \begin_inset Formula
31510 A=\textrm{small roman}
31519 \begin_layout Plain Layout
31533 \begin_inset Formula
31535 B=\textrm{big Roman}\label{eq:Rom}
31544 \begin_layout Plain Layout
31558 \begin_inset Formula
31560 C=\textrm{small Latin}
31569 \begin_layout Plain Layout
31583 \begin_inset Formula
31585 D=\textrm{big Latin}\label{eq:Lat}
31593 \begin_layout Standard
31594 To switch back to the default numbering, insert the command:
31597 \begin_layout Standard
31607 \begin_inset Index idx
31610 \begin_layout Plain Layout
31621 \begin_layout Standard
31625 \begin_layout Plain Layout
31639 \begin_inset Formula
31649 \begin_layout Standard
31650 \begin_inset VSpace medskip
31653 As you see, formulas are numbered serially independent from the numbering
31655 When then numbering should start with
31656 \begin_inset Quotes eld
31660 \begin_inset Quotes erd
31663 when the style is changed, new equation counters have to be defined.
31664 A description about this can be found in the file
31665 \begin_inset CommandInset href
31667 name "Formula-numbering.lyx"
31668 target "run:Formula-numbering.lyx"
31675 \begin_layout Section
31676 Chemical Symbols and Equations
31677 \begin_inset CommandInset label
31679 name "subsec:Chemical-Symbols-and"
31684 \begin_inset Index idx
31687 \begin_layout Plain Layout
31688 Chemical characters ! Symbols
31694 \begin_inset Index idx
31697 \begin_layout Plain Layout
31704 \begin_inset Index idx
31707 \begin_layout Plain Layout
31716 \begin_layout Standard
31717 An example text from chemistry:
31720 \begin_layout Quote
31722 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31725 -ion reacts with two
31726 \begin_inset Formula $\mathrm{Na^{+}}$
31729 -ions to sodium sulfate
31730 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31734 The chemical equation for this is:
31735 \begin_inset Formula
31737 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31745 \begin_layout Standard
31746 This chemical equation can directly be created as formula.
31747 To avoid that the symbols appear italic, everything is highlighted and
31748 changed by the shortcut
31754 to the upright font style.
31758 \begin_layout Plain Layout
31764 \begin_inset CommandInset ref
31766 reference "subsec:Font-Styles"
31778 \begin_layout Standard
31779 A more convenient way to typeset chemical formulas is to use the command
31787 \begin_inset Index idx
31790 \begin_layout Plain Layout
31798 that is available when the \SpecialChar LaTeX
31804 \begin_inset Index idx
31807 \begin_layout Plain Layout
31820 to a formula a new blue box appears where chemical formulas can be inserted
31821 in an intuitive way.
31822 \begin_inset Separator parbreak
31828 \begin_layout Standard
31830 \begin_inset Tabular
31831 <lyxtabular version="3" rows="10" columns="2">
31832 <features booktabs="true" tabularvalignment="middle">
31833 <column alignment="center" valignment="top" width="0pt">
31834 <column alignment="center" valignment="top">
31836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31839 \begin_layout Plain Layout
31845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31848 \begin_layout Plain Layout
31856 <cell alignment="center" valignment="top" leftline="true" 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 $\ce{H2CO3}$
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 $\ce{SO4^{2-}}$
31913 <row topspace="1.5mm">
31914 <cell alignment="center" valignment="top" usebox="none">
31917 \begin_layout Plain Layout
31921 \begin_inset space \textvisiblespace{}
31929 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31932 \begin_layout Plain Layout
31933 \begin_inset Formula $\ce{(NH4)2S}$
31942 <row topspace="1.5mm">
31943 <cell alignment="center" valignment="top" usebox="none">
31946 \begin_layout Plain Layout
31950 \begin_inset space \textvisiblespace{}
31958 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31961 \begin_layout Plain Layout
31962 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31971 <row topspace="1.5mm">
31972 <cell alignment="center" valignment="top" usebox="none">
31975 \begin_layout Plain Layout
31979 \begin_inset space \textvisiblespace{}
31985 \begin_inset space \textvisiblespace{}
31991 \begin_inset space \textvisiblespace{}
31999 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32002 \begin_layout Plain Layout
32003 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
32012 <row topspace="1.5mm">
32013 <cell alignment="center" valignment="top" usebox="none">
32016 \begin_layout Plain Layout
32020 \begin_inset space \textvisiblespace{}
32024 \begin_inset Formula $\downarrow$
32028 \begin_inset Formula $\to$
32036 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32039 \begin_layout Plain Layout
32040 \begin_inset Formula $\ce{_{90}^{227}Th+}$
32050 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32053 \begin_layout Plain Layout
32057 \begin_inset space \textvisiblespace{}
32063 \begin_inset space \textvisiblespace{}
32069 \begin_inset space \textvisiblespace{}
32077 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32080 \begin_layout Plain Layout
32081 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
32091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32094 \begin_layout Plain Layout
32098 \begin_inset space \textvisiblespace{}
32102 \begin_inset space \textvisiblespace{}
32106 \begin_inset space \textvisiblespace{}
32110 \begin_inset space \textvisiblespace{}
32114 \begin_inset space \textvisiblespace{}
32122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32125 \begin_layout Plain Layout
32126 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
32135 <row topspace="1.5mm">
32136 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
32139 \begin_layout Plain Layout
32143 \begin_inset space \textvisiblespace{}
32147 \begin_inset space \textvisiblespace{}
32151 \begin_inset space \textvisiblespace{}
32155 \begin_inset space \textvisiblespace{}
32163 \begin_inset space \textvisiblespace{}
32171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
32174 \begin_layout Plain Layout
32175 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
32191 \begin_layout Standard
32192 \begin_inset Note Greyedout
32195 \begin_layout Plain Layout
32201 It is not possible in \SpecialChar LyX
32202 to use the character ^ to get an up-arrow as described
32208 One instead uses a negative thin space followed by the command
32215 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32226 \begin_layout Standard
32233 the command for equation
32234 \begin_inset space ~
32238 \begin_inset CommandInset ref
32240 reference "eq:chem-reaction"
32245 \begin_inset Newline newline
32253 \begin_inset space \textvisiblespace{}
32257 \begin_inset space \textvisiblespace{}
32261 \begin_inset space \textvisiblespace{}
32265 \begin_inset space \textvisiblespace{}
32269 \begin_inset space \textvisiblespace{}
32273 \begin_inset space \textvisiblespace{}
32279 \begin_layout Standard
32280 To create multiline chemical equations first a multiline formula is created
32282 \begin_inset CommandInset ref
32284 reference "sec:Multiline-Formulas"
32289 Afterwards the command
32295 is used in every small blue box of the formula.
32297 \begin_inset CommandInset ref
32299 reference "eq:TEOS-reaction-1"
32304 \begin_inset CommandInset ref
32306 reference "eq:TEOS-reaction-2"
32310 are an example of a multi-stage chemical reaction where every equation
32311 has its own number.
32312 \begin_inset Formula
32314 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32315 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32323 \begin_layout Standard
32334 package provides the command
32341 \begin_inset Index idx
32344 \begin_layout Plain Layout
32352 that has to be used for special cases.
32353 For more information about
32359 and more examples have a look at the documentation of
32364 \begin_inset CommandInset citation
32373 \begin_layout Section
32377 \begin_layout Standard
32379 supports two types of commutative diagrams:
32387 that are explained in the following.
32390 \begin_layout Subsection
32392 \begin_inset Index idx
32395 \begin_layout Plain Layout
32404 \begin_layout Standard
32405 Diagrams of this type visualize relations by vertical and horizontal lines
32407 \begin_inset Formula
32409 \begin{CD}A@>>>B@>>>C\\
32420 \begin_layout Standard
32421 To get them, the command
32426 \begin_inset Index idx
32429 \begin_layout Plain Layout
32439 is inserted to a formula.
32440 A blue box appears with two dashed lines where further commands can be
32445 arg "newline-insert newline"
32448 a new line is created.
32449 Horizontal relations are inserted in odd, vertical in even formula lines.
32452 \begin_layout Standard
32453 To create the relations there are the following commands:
32456 \begin_layout Itemize
32461 creates a left arrow,
32472 \begin_layout Itemize
32477 creates an up arrow,
32485 a vertical equal sign
32488 \begin_layout Itemize
32494 is a placeholder for non-existent relations
32497 \begin_layout Standard
32498 All arrows can be labeled as follows:
32501 \begin_layout Itemize
32502 If text inserted between the first and second < or >, resp., it is placed
32504 When it is inserted between the second and third one, it appears under
32508 \begin_layout Itemize
32509 When text for vertical arrows is inserted between the first and second A
32510 or V, resp., it is placed left beside the arrow.
32511 When it is inserted between the second and third one, it appears right
32513 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32517 \begin_layout Standard
32518 As example a diagram with all possible relations:
32521 \begin_layout Standard
32522 \begin_inset Formula
32524 \begin{CD}A@>j>>B@>>k>C@=F\\
32535 \begin_layout Standard
32536 The command for this is:
32537 \begin_inset Newline newline
32545 \begin_inset space \textvisiblespace{}
32548 A@>j>>B@>>k>C@=F Ctrl+Return
32549 \begin_inset Newline newline
32553 \begin_inset Phantom HPhantom
32556 \begin_layout Plain Layout
32562 \begin_inset space \textvisiblespace{}
32575 \begin_inset Formula $\to$
32581 \begin_inset Newline newline
32585 \begin_inset Phantom HPhantom
32588 \begin_layout Plain Layout
32594 \begin_inset space \textvisiblespace{}
32605 \begin_layout Subsection
32607 \begin_inset Index idx
32610 \begin_layout Plain Layout
32611 Diagrams ! xymatrix
32619 \begin_layout Standard
32620 To be able to use xymatrices, the \SpecialChar LaTeX
32626 A xymatrix is created by inserting the command
32633 Then you are able to add new matrix columns and rows like for normal matrices,
32635 \begin_inset CommandInset ref
32637 reference "sec:Matrices"
32644 \begin_layout Standard
32645 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32647 All possibilities to create commutative diagrams and decorations are explained
32652 that you find in the menu
32654 Help\SpecialChar menuseparator
32656 \begin_inset space ~
32664 \begin_layout Subsection
32670 \begin_inset Index idx
32673 \begin_layout Plain Layout
32682 \begin_layout Standard
32687 -diagrams, the \SpecialChar LaTeX
32697 -diagram is created by inserting the command
32704 Then you are able to add new matrix columns and rows like for normal matrices,
32706 \begin_inset CommandInset ref
32708 reference "sec:Matrices"
32715 \begin_layout Standard
32716 Examples how to create
32720 diagrams in \SpecialChar LyX
32723 Feynman-diagram manual
32725 that you find in the menu
32727 Help\SpecialChar menuseparator
32729 \begin_inset space ~
32737 \begin_layout Standard
32738 \begin_inset Newpage newpage
32744 \begin_layout Section
32745 User-defined Commands
32746 \begin_inset Index idx
32749 \begin_layout Plain Layout
32750 User-defined commands
32758 \begin_layout Standard
32759 \begin_inset Note Greyedout
32762 \begin_layout Plain Layout
32767 The names of user-defined commands and macros may only consist of Latin
32776 \begin_layout Subsection
32780 \begin_inset CommandInset label
32782 name "subsec:The-Command-newcommand"
32787 \begin_inset Index idx
32790 \begin_layout Plain Layout
32791 User-defined commands !
32799 \begin_inset Index idx
32802 \begin_layout Plain Layout
32813 \begin_layout Standard
32814 Many \SpecialChar LaTeX
32815 -commands are too long to be used frequently.
32816 But it is possible to define with the command
32822 new shorter commands.
32825 \begin_layout Standard
32826 The command scheme of
32835 \begin_layout Standard
32840 newcommand{new command name}[number of arguments][optional
32845 \begin_inset Newline newline
32849 \begin_inset Phantom HPhantom
32852 \begin_layout Plain Layout
32862 {command definition}
32865 \begin_layout Standard
32866 \begin_inset Note Greyedout
32869 \begin_layout Plain Layout
32874 Assure that the name of the new command is not already used in your document
32875 or by \SpecialChar LaTeX
32876 -packages that you use.
32877 When you for example define the command
32889 , you get an error message because
32895 is already defined as command for
32896 \begin_inset Quotes eld
32900 \begin_inset Formula $\le$
32904 \begin_inset Quotes erd
32915 \begin_layout Standard
32916 The number of arguments is an integer in the range 0
32917 \begin_inset space \thinspace{}
32921 \begin_inset space \thinspace{}
32924 9 and specifies how many arguments the new command should have.
32925 With the optional value a value for an optional argument can be predefined.
32926 When this is done, the
32934 rgument of the new command is automatically an optional one.
32937 \begin_layout Standard
32938 Here are some examples:
32941 \begin_layout Itemize
32942 To define the command
32954 , the \SpecialChar LaTeX
32956 \begin_inset VSpace medskip
32960 \begin_inset Newline newline
32974 \begin_layout Itemize
32975 To define the command
32987 , the argument (that should be underlined) must be taken into account.
32988 For this the preamble line is:
32989 \begin_inset VSpace medskip
32993 \begin_inset Newline newline
33007 \begin_inset VSpace medskip
33011 \begin_inset Newline newline
33018 acts as argument placeholder, the
33022 behind it denotes that it is the placeholder for the first argument.
33025 \begin_layout Itemize
33033 \begin_inset space \thinspace{}
33037 \begin_inset space \space{}
33047 \begin_inset VSpace medskip
33051 \begin_inset Newline newline
33062 framebox#1#2{$#3$}}
33065 \begin_inset VSpace medskip
33069 \begin_inset Newline newline
33072 The two Dollar signs creates the extra formula needed for
33079 \begin_inset CommandInset ref
33081 reference "subsec:Boxes-with-Frame"
33088 \begin_layout Itemize
33089 To create a new command for
33095 where the color for the box need not be specified, the argument for the
33096 color is defined optional:
33097 \begin_inset VSpace medskip
33101 \begin_inset Newline newline
33112 fcolorbox{#2}{#1}{$#3$}}
33115 \begin_inset VSpace medskip
33119 \begin_inset Newline newline
33122 When the color is not specified when using
33128 , the predefined color
33135 \begin_layout Standard
33136 A test of the new defined commands:
33137 \begin_inset Separator parbreak
33143 \begin_layout Standard
33145 \begin_inset Tabular
33146 <lyxtabular version="3" rows="6" columns="2">
33147 <features booktabs="true" tabularvalignment="middle">
33148 <column alignment="center" valignment="top" width="0pt">
33149 <column alignment="center" valignment="top">
33151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33154 \begin_layout Plain Layout
33160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33163 \begin_layout Plain Layout
33171 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33174 \begin_layout Plain Layout
33178 \begin_inset space \textvisiblespace{}
33186 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33189 \begin_layout Plain Layout
33190 \begin_inset Formula $A\gr B$
33200 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33203 \begin_layout Plain Layout
33211 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33214 \begin_layout Plain Layout
33215 \begin_inset Formula $\us{ABcd}$
33224 <row topspace="1mm">
33225 <cell alignment="center" valignment="top" usebox="none">
33228 \begin_layout Plain Layout
33232 \begin_inset Formula $\to$
33238 \begin_inset Formula $\to$
33246 \begin_inset space \textvisiblespace{}
33254 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33257 \begin_layout Plain Layout
33258 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33267 <row topspace="1.5mm">
33268 <cell alignment="center" valignment="top" usebox="none">
33271 \begin_layout Plain Layout
33275 \begin_inset Formula $\to$
33283 \begin_inset space \textvisiblespace{}
33291 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33294 \begin_layout Plain Layout
33295 \begin_inset Formula $\cb{red}{\int A=B}$
33304 <row topspace="1.5mm" bottomspace="1mm">
33305 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33308 \begin_layout Plain Layout
33314 \begin_inset Formula $\to$
33322 \begin_inset space \textvisiblespace{}
33330 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33333 \begin_layout Plain Layout
33334 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33350 \begin_layout Subsection
33352 \begin_inset Index idx
33355 \begin_layout Plain Layout
33356 User-defined commands! Math macros
33362 \begin_inset Index idx
33365 \begin_layout Plain Layout
33374 \begin_layout Standard
33375 User-defined commands are especially convenient for complex expressions.
33376 When you are for example dealing with a document that has quadratic equations,
33377 the same solution type occurs several times.
33378 The general form of a quadratic equation is
33379 \begin_inset Formula
33381 0=\lambda^{2}+p\lambda+q
33386 The general form of the solution is
33387 \begin_inset Formula
33389 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33397 \begin_layout Standard
33398 To define a command for the solution formula where only the three parameters
33400 \begin_inset Formula $\lambda$
33404 \begin_inset Formula $p$
33408 \begin_inset Formula $q$
33411 need to be specified and the index of
33412 \begin_inset Formula $\lambda$
33415 can be given optionally, the \SpecialChar LaTeX
33417 \begin_inset Newline newline
33433 \begin_inset Newline newline
33437 \begin_inset Phantom HPhantom
33440 \begin_layout Plain Layout
33454 frac{#3^{2}}{4}-#4}}
33457 \begin_layout Standard
33458 To create with this the solution formula, the command
33459 \begin_inset Newline newline
33469 \begin_inset Formula $\to$
33475 \begin_inset Formula $\to$
33482 is inserted to a formula
33487 \begin_layout Standard
33488 The definition of the new command is unintuitive because one has to know
33489 the schemes of all used \SpecialChar LaTeX
33491 \begin_inset space \thinspace{}
33495 \begin_inset space \space{}
33498 that a fraction is inserted in \SpecialChar LaTeX
33503 frac{numerator}{denominator}
33506 Furthermore one can easily forget a brace in the definition and cannot
33507 see in \SpecialChar LyX
33508 what the new command is doing.
33509 To avoid these problems \SpecialChar LyX
33510 offers the possibility to use math macros instead
33520 \begin_layout Standard
33521 A math macro is created by using the menu
33523 Insert\SpecialChar menuseparator
33524 Math\SpecialChar menuseparator
33527 or the toolbar button
33530 arg "math-macro newmacroname_newcommand"
33534 The math macro toolbar appears together with the following box where the
33536 \begin_inset Newline newline
33540 \begin_inset space \hspace*{\fill}
33544 \begin_inset Graphics
33545 filename clipart/macrobox.png
33551 \begin_inset space \hspace*{\fill}
33555 \begin_inset Newline newline
33559 \begin_inset FormulaMacro
33560 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33565 newmacroname is the default name of the macro that should be changed to
33566 something sensible.
33567 The wanted formula is inserted in the first blue box.
33568 An argument placeholder is inserted with the command
33575 \begin_inset space \thinspace{}
33579 \begin_inset space \space{}
33588 or by using the macro toolbar button
33591 arg "math-macro-add-param"
33595 Argument placeholders are displayed red.
33597 \begin_inset space ~
33600 arguments are possible.
33601 Optional arguments are created with the toolbar button
33604 arg "math-macro-add-optional-param"
33608 The first non-optional argument can be transformed to an optional one with
33612 arg "math-macro-make-optional"
33616 In the second blue box the appearance of the macro in \SpecialChar LyX
33618 Normally you want to see it as it is defined, so the box is kept empty.
33619 But when you have created a macro that needs lot of space on the screen,
33620 you can insert in the box for example
33621 \begin_inset Newline newline
33651 \begin_inset Newline newline
33656 For the macro only the arguments with the macro name in front of them will
33657 then be displayed in \SpecialChar LyX
33658 , leading to a better overview.
33659 The formula appears in the output as defined in the first box.
33660 \begin_inset Newline newline
33663 The appearance of macros in formulas can furthermore be changed for single
33664 macros by setting the cursor in the macro and using the menu
33666 View\SpecialChar menuseparator
33668 \begin_inset space ~
33672 \begin_inset space ~
33680 \begin_layout Standard
33681 To use a macro, the macro name is inserted as command to a formula, in our
33689 Our macro looks in \SpecialChar LyX
33691 \begin_inset Newline newline
33695 \begin_inset space \hspace*{\fill}
33699 \begin_inset Graphics
33700 filename clipart/macrouse.png
33706 \begin_inset space \hspace*{\fill}
33710 \begin_inset Newline newline
33713 Here is our macro example with the arguments
33714 \begin_inset Formula $x$
33718 \begin_inset Formula $\ln(x)$
33722 \begin_inset Formula $B$
33728 \begin_layout Standard
33729 \begin_inset Formula
33739 \begin_layout Standard
33743 Tools\SpecialChar menuseparator
33744 Preferences\SpecialChar menuseparator
33745 Editing\SpecialChar menuseparator
33748 different styles to edit macros.
33749 To find the style that suits you the most, choose a style and set the cursor
33750 in a macro formula to see the difference.
33753 \begin_layout Standard
33754 A math macro is transformed internally to a
33760 command when exporting the document.
33767 command is not placed in the \SpecialChar LaTeX
33768 -preamble, therefore macros can only be used
33769 in formulas that are in the document below the macro definition box.
33772 \begin_layout Standard
33773 Math macros can also be directly created from a
33780 When writing for example the command
33783 \begin_inset Newline newline
33792 xleftarrow[#2]{#1}}
33793 \begin_inset Newline newline
33798 in \SpecialChar LyX
33799 as normal text, highlighting it completely and using then the shortcut
33804 , the command will be transformed to a math macro.
33805 Using this method you need to be careful that the
33811 command is typed correctly, otherwise you get a faulty macro leading to
33816 \begin_layout Standard
33817 Math macros currently have the problem that further formulas in macro definition
33818 s are handled wrongly.
33819 Therefore the example
33826 \begin_inset CommandInset ref
33828 reference "subsec:The-Command-newcommand"
33832 cannot be created as macro.
33835 \begin_layout Standard
33836 When the cursor is in a macro definition box, you will see the macro toolbar
33837 in \SpecialChar LyX
33841 \begin_layout Standard
33842 \begin_inset VSpace defskip
33848 \begin_layout Standard
33849 \begin_inset Graphics
33850 filename clipart/MacroToolbar.png
33855 \begin_inset Index idx
33858 \begin_layout Plain Layout
33867 \begin_layout Standard
33868 \begin_inset VSpace defskip
33874 \begin_layout Standard
33875 The macro toolbar contains from left to right the following buttons:
33878 \begin_layout Standard
33879 \begin_inset VSpace defskip
33885 \begin_layout Standard
33886 \begin_inset Tabular
33887 <lyxtabular version="3" rows="9" columns="2">
33888 <features islongtable="true" longtabularalignment="center">
33889 <column alignment="left" valignment="top">
33890 <column alignment="left" valignment="top" width="85col%">
33891 <row interlinespace="2.5mm">
33892 <cell alignment="center" valignment="top" usebox="none">
33895 \begin_layout Plain Layout
33898 arg "math-macro-remove-param"
33906 <cell alignment="center" valignment="top" usebox="none">
33909 \begin_layout Plain Layout
33912 Edit\SpecialChar menuseparator
33913 Math\SpecialChar menuseparator
33915 \begin_inset space ~
33918 Definition\SpecialChar menuseparator
33919 Remove Last Argument
33925 <row interlinespace="2.5mm">
33926 <cell alignment="center" valignment="top" usebox="none">
33929 \begin_layout Plain Layout
33932 arg "math-macro-add-param"
33940 <cell alignment="center" valignment="top" usebox="none">
33943 \begin_layout Plain Layout
33946 Edit\SpecialChar menuseparator
33947 Math\SpecialChar menuseparator
33949 \begin_inset space ~
33952 Definition\SpecialChar menuseparator
33959 <row interlinespace="2.5mm">
33960 <cell alignment="center" valignment="top" usebox="none">
33963 \begin_layout Plain Layout
33966 arg "math-macro-make-optional"
33974 <cell alignment="center" valignment="top" usebox="none">
33977 \begin_layout Plain Layout
33980 Edit\SpecialChar menuseparator
33981 Math\SpecialChar menuseparator
33983 \begin_inset space ~
33986 Definition\SpecialChar menuseparator
33987 Transform First Non-Optional to
33988 \begin_inset Newline newline
33992 \begin_inset Phantom HPhantom
33995 \begin_layout Plain Layout
33998 Edit\SpecialChar menuseparator
33999 Math\SpecialChar menuseparator
34001 \begin_inset space ~
34004 Definition\SpecialChar menuseparator
34016 <row interlinespace="2.5mm">
34017 <cell alignment="center" valignment="top" usebox="none">
34020 \begin_layout Plain Layout
34023 arg "math-macro-make-nonoptional"
34031 <cell alignment="center" valignment="top" usebox="none">
34034 \begin_layout Plain Layout
34037 Edit\SpecialChar menuseparator
34038 Math\SpecialChar menuseparator
34040 \begin_inset space ~
34043 Definition\SpecialChar menuseparator
34044 Transform Last Optional to
34045 \begin_inset Newline newline
34049 \begin_inset Phantom HPhantom
34052 \begin_layout Plain Layout
34055 Edit\SpecialChar menuseparator
34056 Math\SpecialChar menuseparator
34058 \begin_inset space ~
34061 Definition\SpecialChar menuseparator
34067 Non-Optional Argument
34073 <row interlinespace="2.5mm">
34074 <cell alignment="center" valignment="top" usebox="none">
34077 \begin_layout Plain Layout
34080 arg "math-macro-remove-optional-param"
34088 <cell alignment="center" valignment="top" usebox="none">
34091 \begin_layout Plain Layout
34094 Edit\SpecialChar menuseparator
34095 Math\SpecialChar menuseparator
34097 \begin_inset space ~
34100 Definition\SpecialChar menuseparator
34101 Remove Optional Argument
34107 <row interlinespace="2.5mm">
34108 <cell alignment="center" valignment="top" usebox="none">
34111 \begin_layout Plain Layout
34114 arg "math-macro-add-optional-param"
34122 <cell alignment="center" valignment="top" usebox="none">
34125 \begin_layout Plain Layout
34128 Edit\SpecialChar menuseparator
34129 Math\SpecialChar menuseparator
34131 \begin_inset space ~
34134 Definition\SpecialChar menuseparator
34135 Insert Optional Argument
34141 <row interlinespace="2.5mm">
34142 <cell alignment="center" valignment="top" usebox="none">
34145 \begin_layout Plain Layout
34148 arg "math-macro-remove-greedy-param"
34156 <cell alignment="center" valignment="top" usebox="none">
34159 \begin_layout Plain Layout
34162 Edit\SpecialChar menuseparator
34163 Math\SpecialChar menuseparator
34165 \begin_inset space ~
34168 Definition\SpecialChar menuseparator
34169 Remove Last Argument
34170 \begin_inset Newline newline
34174 \begin_inset Phantom HPhantom
34177 \begin_layout Plain Layout
34180 Edit\SpecialChar menuseparator
34181 Math\SpecialChar menuseparator
34183 \begin_inset space ~
34186 Definition\SpecialChar menuseparator
34192 Spitting Out To The Right
34198 <row interlinespace="2.5mm">
34199 <cell alignment="center" valignment="top" usebox="none">
34202 \begin_layout Plain Layout
34205 arg "math-macro-append-greedy-param"
34213 <cell alignment="center" valignment="top" usebox="none">
34216 \begin_layout Plain Layout
34219 Edit\SpecialChar menuseparator
34220 Math\SpecialChar menuseparator
34222 \begin_inset space ~
34225 Definition\SpecialChar menuseparator
34227 \begin_inset Newline newline
34231 \begin_inset Phantom HPhantom
34234 \begin_layout Plain Layout
34237 Edit\SpecialChar menuseparator
34238 Math\SpecialChar menuseparator
34240 \begin_inset space ~
34243 Definition\SpecialChar menuseparator
34249 Eating From The Right
34255 <row interlinespace="2.5mm">
34256 <cell alignment="center" valignment="top" usebox="none">
34259 \begin_layout Plain Layout
34262 arg "math-macro-add-greedy-optional-param"
34270 <cell alignment="center" valignment="top" usebox="none">
34273 \begin_layout Plain Layout
34276 Edit\SpecialChar menuseparator
34277 Math\SpecialChar menuseparator
34279 \begin_inset space ~
34282 Definition\SpecialChar menuseparator
34283 Append Optional Argument
34284 \begin_inset Newline newline
34288 \begin_inset Phantom HPhantom
34291 \begin_layout Plain Layout
34294 Edit\SpecialChar menuseparator
34295 Math\SpecialChar menuseparator
34297 \begin_inset space ~
34300 Definition\SpecialChar menuseparator
34306 Eating From The Right
34319 \begin_layout Section
34320 Computer Algebra Systems
34323 \begin_layout Standard
34325 offers the exchange between mathematical expressions written in \SpecialChar LyX
34327 editor and external applications or user defined scripts.
34328 Currently supported applications are
34345 Note that the set of supported mathematical constructs is limited only
34346 to very simple cases.
34349 \begin_layout Subsection
34353 \begin_layout Standard
34354 Write some expression in a formula, go to the
34356 Edit\SpecialChar menuseparator
34357 Math\SpecialChar menuseparator
34358 Use Computer Algebra System
34360 menu and choose the application you have installed on the computer.
34361 After that the result of computation should show on the right side of the
34362 expression together with the
34363 \begin_inset Quotes eld
34367 \begin_inset Quotes erd
34373 \begin_layout Standard
34374 Here are few simple examples (with results from
34378 ) to show what kind of computations can be performed:
34381 \begin_layout Itemize
34382 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34388 \begin_layout Itemize
34389 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34395 \begin_layout Itemize
34396 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34402 \begin_layout Itemize
34403 \begin_inset Formula $\det\left[\begin{array}{ccc}
34407 \end{array}\right]=-56$
34413 \begin_layout Itemize
34414 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34420 \begin_layout Subsection
34424 \begin_layout Standard
34425 Currently there is no keyboard shortcut for calling the algebra applications.
34426 One can easily bind a shortcut to the
34440 \begin_inset space \thinspace{}
34444 \begin_inset space \space{}
34451 key inside the math editor.
34456 one would use this shortcut definition command:
34459 \begin_layout Standard
34462 command-alternatives paragraph-break;math-extern maxima
34465 \begin_layout Section
34467 \begin_inset Index idx
34470 \begin_layout Plain Layout
34479 \begin_layout Subsection
34481 \begin_inset Index idx
34484 \begin_layout Plain Layout
34493 \begin_layout Standard
34494 Negative numbers often look ugly in formulas because the minus sign before
34495 the number is set with the same length as the minus operator sign.
34496 When writing the negative number in normal text, the minus sign appears
34500 \begin_layout Standard
34501 Thus, the problem disappears when converting the minus sign to mathematical
34505 \begin_layout Standard
34506 An example to visualize the problem:
34507 \begin_inset Separator parbreak
34513 \begin_layout Standard
34515 \begin_inset Tabular
34516 <lyxtabular version="3" rows="3" columns="2">
34517 <features booktabs="true" tabularvalignment="middle">
34518 <column alignment="right" valignment="top" width="0pt">
34519 <column alignment="left" valignment="top">
34521 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34524 \begin_layout Plain Layout
34530 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34533 \begin_layout Plain Layout
34541 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34544 \begin_layout Plain Layout
34550 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34553 \begin_layout Plain Layout
34554 \begin_inset Formula $x=-2$
34564 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34567 \begin_layout Plain Layout
34573 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34576 \begin_layout Plain Layout
34577 \begin_inset Formula $x=\textrm{-}2$
34593 \begin_layout Subsection
34594 Comma as decimal Separator
34595 \begin_inset Index idx
34598 \begin_layout Plain Layout
34607 \begin_layout Standard
34608 In \SpecialChar LaTeX
34609 a comma inside a formula is used, according to the English convention,
34610 as number group separator.
34611 So there will be space added behind all commas in formulas.
34614 \begin_layout Standard
34615 To avoid this, the comma is highlighted and changed to mathematical text
34625 \begin_layout Standard
34626 To use all formula commas in the document as decimal separator, the file
34635 \begin_layout Plain Layout
34640 is part of the \SpecialChar LaTeX
34646 \begin_inset Index idx
34649 \begin_layout Plain Layout
34654 \begin_layout Plain Layout
34674 \begin_inset Index idx
34677 \begin_layout Plain Layout
34683 is loaded with the \SpecialChar LaTeX
34687 \begin_layout Standard
34695 \begin_layout Subsection
34697 \begin_inset CommandInset label
34699 name "subsec:Physical-Vectors"
34704 \begin_inset Index idx
34707 \begin_layout Plain Layout
34716 \begin_layout Standard
34717 Predefined vectors are offered by the \SpecialChar LaTeX
34723 \begin_inset Index idx
34726 \begin_layout Plain Layout
34732 that is loaded with the \SpecialChar LaTeX
34736 \begin_layout Standard
34744 \begin_layout Standard
34748 \begin_layout Plain Layout
34758 \begin_inset Note Note
34761 \begin_layout Plain Layout
34762 The following table will only be displayed when the \SpecialChar LaTeX
34775 \begin_layout Standard
34776 The following commands are defined:
34777 \begin_inset Separator parbreak
34783 \begin_layout Standard
34785 \begin_inset Tabular
34786 <lyxtabular version="3" rows="4" columns="2">
34787 <features booktabs="true" tabularvalignment="middle">
34788 <column alignment="center" valignment="top" width="0pt">
34789 <column alignment="center" valignment="top">
34791 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34794 \begin_layout Plain Layout
34800 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34803 \begin_layout Plain Layout
34811 <cell alignment="center" valignment="top" usebox="none">
34814 \begin_layout Plain Layout
34824 <cell alignment="center" valignment="top" usebox="none">
34827 \begin_layout Plain Layout
34828 \begin_inset Formula $\Bra{\psi}$
34838 <cell alignment="center" valignment="top" usebox="none">
34841 \begin_layout Plain Layout
34851 <cell alignment="center" valignment="top" usebox="none">
34854 \begin_layout Plain Layout
34855 \begin_inset Formula $\Ket{\psi}$
34865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34868 \begin_layout Plain Layout
34880 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34883 \begin_layout Plain Layout
34884 \begin_inset Formula $\Braket{\psi|\phi}$
34900 \begin_layout Standard
34907 assures that all vertical bars are set in the size of the surrounding brackets:
34908 \begin_inset Formula
34910 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34919 \begin_layout Plain Layout
34929 \begin_inset Note Note
34932 \begin_layout Plain Layout
34933 The following will be displayed when the \SpecialChar LaTeX
34946 \begin_layout Standard
34947 You need to install the \SpecialChar LaTeX
34952 to see the rest of this subsection in the output.
34955 \begin_layout Standard
34959 \begin_layout Plain Layout
34971 \begin_layout Standard
34978 can also be achieved using the command
34984 , that is described in
34985 \begin_inset CommandInset ref
34987 reference "subsec:Automatic-Bracket-Size"
34994 \begin_layout Subsection
34995 Self-defined Fractions
34996 \begin_inset CommandInset label
34998 name "subsec:Self-defined-Fractions"
35003 \begin_inset Index idx
35006 \begin_layout Plain Layout
35007 Fractions ! self-defined
35015 \begin_layout Standard
35016 To define custom commands for fractions, the command
35023 \begin_inset Index idx
35026 \begin_layout Plain Layout
35033 \begin_layout Plain Layout
35047 is used in the following scheme:
35050 \begin_layout Standard
35063 bracket}{fraction bar thickness}{style}
35064 \begin_inset Newline newline
35068 \begin_inset Phantom HPhantom
35071 \begin_layout Plain Layout
35081 {numerator}{denominator}
35084 \begin_layout Standard
35085 The style is a number in the range of 0
35086 \begin_inset space \thinspace{}
35090 \begin_inset space \thinspace{}
35094 \begin_inset Separator parbreak
35100 \begin_layout Standard
35102 \begin_inset Tabular
35103 <lyxtabular version="3" rows="5" columns="2">
35104 <features booktabs="true" tabularvalignment="middle">
35105 <column alignment="center" valignment="top" width="0pt">
35106 <column alignment="center" valignment="top">
35108 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35111 \begin_layout Plain Layout
35117 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35120 \begin_layout Plain Layout
35128 <cell alignment="center" valignment="top" usebox="none">
35131 \begin_layout Plain Layout
35137 <cell alignment="center" valignment="top" usebox="none">
35140 \begin_layout Plain Layout
35141 display style formula
35148 <cell alignment="center" valignment="top" usebox="none">
35151 \begin_layout Plain Layout
35157 <cell alignment="center" valignment="top" usebox="none">
35160 \begin_layout Plain Layout
35168 <cell alignment="center" valignment="top" usebox="none">
35171 \begin_layout Plain Layout
35177 <cell alignment="center" valignment="top" usebox="none">
35180 \begin_layout Plain Layout
35188 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35191 \begin_layout Plain Layout
35197 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35200 \begin_layout Plain Layout
35214 \begin_layout Standard
35215 When no style is given, the size is adjusted to the surrounding environment
35216 like for the command
35225 \begin_layout Standard
35226 When no fraction bar thickness is given, the predefined value of 0.4
35227 \begin_inset space \thinspace{}
35233 \begin_layout Standard
35234 \begin_inset VSpace medskip
35237 For example, the commands
35250 \begin_inset CommandInset ref
35252 reference "subsec:Fractions"
35256 are defined with the commands
35259 \begin_layout Standard
35268 genfrac{}{}{}{0}{#1}{#2}}
35271 \begin_layout Standard
35275 \begin_layout Standard
35284 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35287 \begin_layout Standard
35288 \begin_inset VSpace medskip
35291 To define a fraction where the fraction bar thickness can be given as optional
35292 argument, the following line is inserted to the \SpecialChar LaTeX
35296 \begin_layout Standard
35305 genfrac{}{}{#1}{}{#2}{#3}}
35308 \begin_layout Standard
35310 \begin_inset Formula
35312 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35313 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35318 As one can see, the distance of the numerator and the denominator to the
35319 fraction bar is round about three times the bar thickness.
35322 \begin_layout Subsection
35324 \begin_inset Index idx
35327 \begin_layout Plain Layout
35336 \begin_layout Standard
35337 There are four ways to cancel formulas or parts of formulas:
35340 \begin_layout Standard
35344 \begin_layout Plain Layout
35354 \begin_inset Note Note
35357 \begin_layout Plain Layout
35358 The following table will only be displayed when the \SpecialChar LaTeX
35369 \begin_inset Separator parbreak
35375 \begin_layout Standard
35377 \begin_inset Tabular
35378 <lyxtabular version="3" rows="5" columns="2">
35379 <features booktabs="true" tabularvalignment="middle">
35380 <column alignment="center" valignment="top" width="0pt">
35381 <column alignment="center" valignment="top">
35383 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35386 \begin_layout Plain Layout
35392 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35395 \begin_layout Plain Layout
35403 <cell alignment="center" valignment="top" usebox="none">
35406 \begin_layout Plain Layout
35410 \begin_inset space \textvisiblespace{}
35416 \begin_inset space \textvisiblespace{}
35424 <cell alignment="center" valignment="top" usebox="none">
35427 \begin_layout Plain Layout
35428 \begin_inset Formula $\cancel{\int A=B}$
35437 <row topspace="1.5mm">
35438 <cell alignment="center" valignment="top" usebox="none">
35441 \begin_layout Plain Layout
35445 \begin_inset space \textvisiblespace{}
35451 \begin_inset space \textvisiblespace{}
35459 <cell alignment="center" valignment="top" usebox="none">
35462 \begin_layout Plain Layout
35463 \begin_inset Formula $\bcancel{\int A=B}$
35472 <row topspace="1.5mm">
35473 <cell alignment="center" valignment="top" usebox="none">
35476 \begin_layout Plain Layout
35480 \begin_inset space \textvisiblespace{}
35486 \begin_inset space \textvisiblespace{}
35494 <cell alignment="center" valignment="top" usebox="none">
35497 \begin_layout Plain Layout
35498 \begin_inset Formula $\xcancel{\int A=B}$
35508 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35511 \begin_layout Plain Layout
35515 \begin_inset space \textvisiblespace{}
35521 \begin_inset space \textvisiblespace{}
35525 \begin_inset Formula $\to$
35533 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35536 \begin_layout Plain Layout
35537 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35553 \begin_layout Standard
35560 is especially suitable to visualize the reduction of fractions within formulas:
35561 \begin_inset Formula
35563 \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}}}
35571 \begin_layout Standard
35572 To change the size of
35579 \begin_inset Quotes eld
35583 \begin_inset Quotes erd
35586 value one can add the \SpecialChar LaTeX
35590 \begin_layout Standard
35595 PassOptionsToPackage{option}{cancel}
35598 \begin_layout Standard
35607 which leads to the same size as for the canceled value, or
35611 which makes is it a bit smaller than normal.
35614 \begin_layout Standard
35615 To color the cancellation bar one adds this command as \SpecialChar TeX
35619 \begin_layout Standard
35631 \begin_layout Standard
35636 can be replaced by a color of your choice.
35639 \begin_layout Standard
35643 \begin_layout Plain Layout
35659 \begin_layout Standard
35660 \begin_inset Formula
35662 \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}}}
35670 \begin_layout Standard
35674 \begin_layout Plain Layout
35688 \begin_inset Note Note
35691 \begin_layout Plain Layout
35700 \begin_layout Standard
35701 For further customizations, see the documentation of the package
35706 \begin_inset CommandInset citation
35713 \begin_inset Index idx
35716 \begin_layout Plain Layout
35725 \begin_layout Standard
35729 \begin_layout Plain Layout
35739 \begin_inset Note Note
35742 \begin_layout Plain Layout
35743 The following will be displayed when the \SpecialChar LaTeX
35756 \begin_layout Standard
35757 You need to install the \SpecialChar LaTeX
35762 to see the rest of this subsection in the output.
35765 \begin_layout Standard
35769 \begin_layout Plain Layout
35781 \begin_layout Subsection
35782 Formulas in Section Headings
35783 \begin_inset CommandInset label
35785 name "subsec:Formulas-in-Section"
35790 \begin_inset Index idx
35793 \begin_layout Plain Layout
35794 Formula ! in section headings
35802 \begin_layout Standard
35803 When formulas are used in section headings, the following has to be taken
35807 \begin_layout Standard
35808 \begin_inset Note Greyedout
35811 \begin_layout Plain Layout
35817 \begin_inset Index idx
35820 \begin_layout Plain Layout
35821 Packages ! hyperref
35826 support is enabled in the document settings dialog under
35829 \begin_inset space ~
35834 , PDF-bookmarks are created for every section heading in the table of contents.
35835 If a section heading contains formulas, they are incorrectly displayed
35836 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35845 \begin_layout Standard
35846 Both problems can be solved by inserting at the end of the section heading
35847 a short title with the menu
35849 Insert\SpecialChar menuseparator
35851 \begin_inset space ~
35857 Short titles are used as alternative for multiline section headings to
35858 keep the table of contents clearly arranged.
35859 Only the short title appears in the table of contents and therefore also
35860 in the PDF-bookmark.
35863 \begin_layout Standard
35864 When formulas should be used in the table of contents but
35868 is used, one can use the following command in \SpecialChar TeX
35872 \begin_layout Standard
35877 texorpdfstring{part}{alternative}
35878 \begin_inset Index idx
35881 \begin_layout Plain Layout
35892 \begin_layout Standard
35893 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35894 This can be characters, formulas, footnotes, but also cross-references.
35895 The alternative is used instead of the part for the bookmark.
35898 \begin_layout Standard
35899 Here are two example headings:
35900 \begin_inset VSpace -3mm
35907 \begin_layout Plain Layout
35919 \begin_layout Subsubsection
35920 Heading without formula in table of contents
35921 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35925 \begin_inset Argument 1
35928 \begin_layout Plain Layout
35929 Heading without formula in table of contents
35937 \begin_layout Subsubsection
35938 Heading with formula in table of contents
35942 \begin_layout Plain Layout
35952 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35959 \begin_layout Plain Layout
35969 \begin_layout Standard
35973 \begin_layout Plain Layout
35982 In the first heading a short title was used, in the second one
35991 \begin_layout Standard
35992 To get the same formatting as for the other headings, the complete heading
36001 \begin_layout Plain Layout
36003 \begin_inset CommandInset ref
36005 reference "subsec:Bold-Formulas"
36017 \begin_layout Subsection
36018 Formulas in multi-column Text
36019 \begin_inset Index idx
36022 \begin_layout Plain Layout
36023 Formula ! in multi-column text
36031 \begin_layout Standard
36032 Formulas in multi-column text are often too wide to fit into a column and
36033 thus need to be set over the whole page width.
36034 This is done by using the \SpecialChar LaTeX
36043 \begin_layout Plain Layout
36048 is part of every \SpecialChar LaTeX
36049 standard installation.
36055 \begin_inset Index idx
36058 \begin_layout Plain Layout
36059 Packages ! multicol
36064 , that is loaded with the \SpecialChar LaTeX
36068 \begin_layout Standard
36073 usepackage{multicol}
36076 \begin_layout Standard
36077 \begin_inset Note Greyedout
36080 \begin_layout Plain Layout
36081 Note that in this case the setting
36084 \begin_inset space ~
36091 Document\SpecialChar menuseparator
36097 \begin_inset space ~
36117 \begin_layout Standard
36118 Before the multi-column text the command
36121 \begin_layout Standard
36126 begin{multicols}{column number}
36129 \begin_layout Standard
36130 is written in \SpecialChar TeX
36132 The column number is a number in the range of 2
36133 \begin_inset space \thinspace{}
36137 \begin_inset space \thinspace{}
36141 Before the formula the multi-column text is ended by inserting the command
36144 \begin_layout Standard
36152 \begin_layout Standard
36153 in \SpecialChar TeX
36157 \begin_layout Standard
36158 Due to the command some space is automatically added before the formula.
36160 \begin_inset space \thinspace{}
36163 mm vertical space is inserted before the formula.
36164 When the formula style
36170 \begin_layout Plain Layout
36172 \begin_inset CommandInset ref
36174 reference "sec:Formula-Styles"
36186 \begin_inset space \thinspace{}
36189 mm space is inserted instead.
36192 \begin_layout Standard
36193 As example a multi-column text with a displayed formula:
36196 \begin_layout Standard
36202 \begin_layout Plain Layout
36206 begin{multicols}{2}
36211 Das Spektrum wird fouriertransformiert.
36212 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36213 , Lösungsmittel) zu trennen.
36214 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36215 nun das Aussehen des Ausgangssignals.
36216 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36217 über alle Phasen integrieren muss.
36219 \begin_inset Formula $S$
36222 unser normiertes Ausgangssignal und
36223 \begin_inset Formula $P$
36226 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36230 \begin_layout Plain Layout
36240 \begin_inset VSpace -6mm
36244 \begin_inset Formula
36246 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36255 \begin_layout Plain Layout
36259 begin{multicols}{2}
36265 \begin_inset Formula $S_{0}$
36268 das Signal ohne Gradient ist und die Normierungsbedingung
36269 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36273 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36275 \begin_inset Formula $\nicefrac{\pi}{2}$
36279 \begin_inset space \thinspace{}
36282 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36283 das Signal zusätzlich abschwächt.
36284 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36286 \begin_inset Formula $T_{2}$
36292 \begin_layout Standard
36298 \begin_layout Plain Layout
36310 \begin_layout Subsection
36311 Formulas with Description of Variables
36312 \begin_inset Index idx
36315 \begin_layout Plain Layout
36316 Formula ! with description of variables
36324 \begin_layout Standard
36325 To describe variables within a formula, like in formula
36326 \begin_inset CommandInset ref
36328 reference "eq:within"
36337 \begin_inset Formula $n$
36341 \begin_inset space ~
36344 matrix is used with left aligned columns for the
36345 \begin_inset Formula $n$
36352 \begin_layout Plain Layout
36354 \begin_inset CommandInset ref
36356 reference "sec:Matrices"
36365 To set the description in a smaller size, before the matrix e.
36366 \begin_inset space \thinspace{}
36370 \begin_inset space \space{}
36383 \begin_layout Plain Layout
36385 \begin_inset CommandInset ref
36387 reference "subsec:Font-Sizes"
36399 \begin_layout Standard
36400 When the formula style
36406 \begin_layout Plain Layout
36408 \begin_inset CommandInset ref
36410 reference "sec:Formula-Styles"
36431 \begin_layout Plain Layout
36438 only works in formulas with the style
36443 \begin_inset CommandInset ref
36445 reference "subsec:Variable-Space"
36454 is inserted before and after the matrix to have the same separation of
36455 the matrix from the equation and the side margin.
36458 \begin_layout Standard
36459 When the formula style
36463 is used, the method described in
36464 \begin_inset CommandInset ref
36466 reference "subsec:Flalign-Environment"
36470 is used to indent formulas.
36472 \begin_inset CommandInset ref
36474 reference "eq:within"
36478 consists of five columns where in the first two columns contain the equation,
36479 the third the matrix and the last one an empty \SpecialChar TeX
36481 \begin_inset Formula
36483 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36484 \rho & \textrm{density}\\
36485 V & \textrm{volume}\\
36486 g & \textrm{gravitational acceleration}
36487 \end{array} & & {}\label{eq:within}
36495 \begin_layout Subsection
36496 Upright small Greek Letters
36497 \begin_inset CommandInset label
36499 name "subsec:Upright-small-Greek"
36504 \begin_inset Index idx
36507 \begin_layout Plain Layout
36508 Greek letters ! upright
36516 \begin_layout Standard
36517 Most of the math fonts only provide italic small Greek letters.
36518 But for symbols of elementary particles like pions and neutrinos, upright
36519 Greek letters are needed.
36528 \begin_layout Plain Layout
36533 is part of the \SpecialChar LaTeX
36539 \begin_inset Index idx
36542 \begin_layout Plain Layout
36547 \begin_layout Plain Layout
36567 \begin_inset Index idx
36570 \begin_layout Plain Layout
36576 that is loaded with the \SpecialChar LaTeX
36580 \begin_layout Standard
36585 usepackage{upgreek}
36588 \begin_layout Standard
36594 \begin_layout Plain Layout
36604 \begin_inset Note Note
36607 \begin_layout Plain Layout
36608 The following table will only be displayed when the \SpecialChar LaTeX
36618 They are created when the command for a small Greek letter is started with
36624 For example the command
36631 \begin_inset Formula $\uptau$
36637 \begin_layout Standard
36638 With these commands reactions of elementary particles can be typeset:
36639 \begin_inset Formula
36641 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36649 \begin_layout Standard
36650 The upright letters are more bold and wider than the italic ones.
36651 They should therefore not be used for units like
36652 \begin_inset Quotes eld
36656 \begin_inset Quotes erd
36662 \begin_layout Standard
36666 \begin_layout Plain Layout
36676 \begin_inset Note Note
36679 \begin_layout Plain Layout
36680 The following will be displayed when the \SpecialChar LaTeX
36693 \begin_layout Standard
36694 You need to install the \SpecialChar LaTeX
36699 to see the rest of this subsection in the output.
36702 \begin_layout Standard
36706 \begin_layout Plain Layout
36718 \begin_layout Subsection
36719 Text Characters in Formulas
36720 \begin_inset Index idx
36723 \begin_layout Plain Layout
36732 \begin_layout Standard
36733 In some cases you might want to insert text characters directly into formulas.
36734 When for example the centered dot · is often used in formulas like
36735 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36738 , one would have to insert the command
36748 \begin_layout Plain Layout
36750 \begin_inset CommandInset ref
36752 reference "subsec:Binary-Operators"
36761 all the time, because this character is defined in all encodings as text
36763 But the encoding can be changed by this \SpecialChar LaTeX
36767 \begin_layout Standard
36772 Declare Inputtext{183}{
36782 f\SpecialChar ligaturebreak
36786 \begin_layout Standard
36787 The character encoding (menu
36789 Document\SpecialChar menuseparator
36790 Settings\SpecialChar menuseparator
36793 ) specifies what character appears when a keyboard key is pressed.
36794 When the key for the character '·' is pressed, internally the command
36801 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36803 With the changed encoding the right command is chosen automatically, depending
36804 on if the character was inserted into a formula or not.
36807 \begin_layout Standard
36808 The encoding of several characters is saved in definition files.
36809 For example the encoding
36813 is defined in the file
36817 which is in the installation folder of \SpecialChar LaTeX
36819 Encodings should only be changed via the \SpecialChar LaTeX
36820 -preamble and not in the definition
36822 Otherwise documents could not be edited by other \SpecialChar LyX
36823 users working on other
36827 \begin_layout Standard
36828 \begin_inset VSpace medskip
36831 Besides the centered dot, in this document the degree sign ° is defined
36832 with the following \SpecialChar LaTeX
36833 -preamble line so that it can be directly inserted into
36837 \begin_layout Standard
36842 DeclareInputtext{176}{
36852 f\SpecialChar ligaturebreak
36856 \begin_layout Subsection
36858 -comments in formulas
36859 \begin_inset Index idx
36862 \begin_layout Plain Layout
36872 \begin_layout Standard
36873 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36875 code of your file with the menu
36877 Insert\SpecialChar menuseparator
36878 Note\SpecialChar menuseparator
36882 This is not possible in a formula but you can insert \SpecialChar LaTeX
36887 \begin_layout Standard
36895 \begin_layout Standard
36896 This creates a box in which you can write your comment.
36897 Due to a bug in \SpecialChar LyX
36902 \begin_layout Plain Layout
36903 \begin_inset CommandInset href
36905 name "LyX-bug #9002"
36906 target "http://www.lyx.org/trac/ticket/9002"
36915 you cannot write normal text inside the comment, even when you use mathematical
36916 text, you will see its \SpecialChar LaTeX
36917 -commands in the \SpecialChar LaTeX
36919 \begin_inset Newline newline
36922 This a formula with a \SpecialChar LaTeX
36924 \begin_inset Formula
36926 A=B%\text{This is the comment}
36934 \begin_layout Standard
36935 \begin_inset Newpage newpage
36941 \begin_layout Section
36944 \begin_inset Index idx
36947 \begin_layout Plain Layout
36956 \begin_layout Standard
36957 This section is a summary of the most important typographic rules, listed
36962 \begin_layout Plain Layout
36963 This collection was partly taken from the German semi-official dictionary
36965 \begin_inset Quotes eld
36969 \begin_inset Quotes erd
36973 \begin_inset CommandInset citation
36979 that lists some of the ISO rules.
36980 More rules are listed in
36981 \begin_inset CommandInset citation
36995 \begin_layout Itemize
37004 \begin_layout Plain Layout
37005 done with font styles, see
37006 \begin_inset CommandInset ref
37008 reference "subsec:Font-Styles"
37017 , no matter if they appear in italic text: 30
37018 \begin_inset space \thinspace{}
37022 \begin_inset Newline newline
37025 Between the value and the unit is the smallest space, see
37026 \begin_inset CommandInset ref
37028 reference "subsec:Predefined-Space"
37033 \begin_inset Newline newline
37036 This convention is automatically fulfilled when the command
37043 When it is entered to a formula, two boxes appear.
37044 In the first one the value is inserted, in the second one the unit, and
37046 \begin_inset Formula $\unit[30]{km/h}$
37050 \begin_inset space \thinspace{}
37060 is not a real \SpecialChar LaTeX
37061 command but the command
37067 , therefore you cannot use it in \SpecialChar TeX
37071 \begin_layout Itemize
37072 Percent and perthousand signs are set like physical units:
37073 \begin_inset Newline newline
37077 \begin_inset space \thinspace{}
37083 \begin_layout Itemize
37084 The degree sign follows directly on the value: 15°, but not when it is used
37086 \begin_inset space \thinspace{}
37092 \begin_layout Itemize
37093 In numbers with more than four digits the smallest space is inserted before
37094 every third digit to group them:
37104 \begin_inset space \thinspace{}
37108 \begin_inset space \thinspace{}
37114 \begin_layout Itemize
37115 For dimensions like 120×90×40
37116 \begin_inset space \thinspace{}
37119 cm the multiplication sign
37120 \begin_inset Quotes eld
37124 \begin_inset Quotes erd
37128 It is available either via the command
37136 Insert\SpecialChar menuseparator
37137 Special Character\SpecialChar menuseparator
37143 \begin_layout Itemize
37144 Functions with names consisting of several letters are set upright to avoid
37146 \begin_inset CommandInset ref
37148 reference "subsec:Predefined-Functions"
37155 \begin_layout Itemize
37156 Indices consisting of several letters, are set upright:
37157 \begin_inset Formula $E_{\mathrm{kin}}$
37161 \begin_inset Newline newline
37164 Components of matrices are set italic:
37165 \begin_inset Formula $\hat{H}_{kl}$
37171 \begin_layout Itemize
37172 The differentiation/integration operator 'd', the Euler's number 'e' and
37173 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37177 \begin_layout Itemize
37178 The character that denotes a
37182 transformation is inserted either by the command
37187 \begin_inset space \textvisiblespace{}
37194 Insert\SpecialChar menuseparator
37195 Special Character\SpecialChar menuseparator
37196 Symbols\SpecialChar menuseparator
37198 \begin_inset space ~
37204 \begin_inset Formula $\mathscr{F}$
37210 \begin_layout Standard
37211 \begin_inset Newpage newpage
37217 \begin_layout Section
37219 \begin_inset Index idx
37222 \begin_layout Plain Layout
37231 \begin_layout Standard
37232 Some characters and symbols can be created with several commands.
37233 Here is a list of the synonym commands:
37236 \begin_layout Standard
37237 \begin_inset VSpace bigskip
37241 \begin_inset space \hfill{}
37245 \begin_inset Tabular
37246 <lyxtabular version="3" rows="12" columns="2">
37247 <features booktabs="true" tabularvalignment="middle">
37248 <column alignment="center" valignment="top" width="0pt">
37249 <column alignment="center" valignment="top" width="0pt">
37251 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37254 \begin_layout Plain Layout
37260 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37263 \begin_layout Plain Layout
37271 <cell alignment="center" valignment="top" usebox="none">
37274 \begin_layout Plain Layout
37282 <cell alignment="center" valignment="top" usebox="none">
37285 \begin_layout Plain Layout
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