1 #LyX 2.3 created this file. For more info see http://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/doc/
9 % DO NOT ALTER THIS PREAMBLE!!!
11 % This preamble is designed to ensure that the file prints
12 % out as advertised. If you mess with this preamble,
13 % parts of this document may not print out as expected. If you
14 % have problems LaTeXing this file, please contact
15 % the documentation team
16 % email: lyx-docs@lists.lyx.org
18 % solves the following problem:
19 % If the dection number consits of too many numerals the section heading
20 % will be printed in the TOC without a space between it and the section number.
21 % As solution more space between the number and the heading is inserted:
22 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
23 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
25 % increase link area for cross-references and autoname them,
26 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
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28 \@ifpackageloaded{babel}{
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32 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
33 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
53 \@ifundefined{extrarowheight} {\usepackage{array}}{}
54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
90 %\def\tagform@#1{\maketag@@@{|#1|}}
93 % ------------------------------------
94 % used to check for needed LaTeX packages
97 % check for package undertilde
98 % used for the command \utilde
99 \newboolean{undertilde}
100 \IfFileExists{undertilde.sty}
101 {\usepackage{undertilde}
102 \setboolean{undertilde}{true}}
103 {\setboolean{undertilde}{false}}
105 % check for package eurosym
106 % used for the Euro symbol
108 \IfFileExists{eurosym.sty}
109 {\usepackage[gennarrow]{eurosym}
110 \setboolean{eurosym}{true}}
111 {\setboolean{eurosym}{false}}
113 % check for package braket
114 % used for physical vectors
116 \IfFileExists{braket.sty}
118 \setboolean{braket}{true}}
119 {\setboolean{braket}{false}}
121 % check for package cancel
123 \IfFileExists{cancel.sty}
125 \setboolean{cancel}{true}}
126 {\setboolean{cancel}{false}}
128 % check for package upgreek
130 \IfFileExists{upgreek.sty}
131 {\usepackage{upgreek}
132 \setboolean{upgreek}{true}}
133 {\setboolean{upgreek}{false}}
135 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
136 \use_default_options false
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139 \language_package default
142 \font_roman "lmodern" "default"
143 \font_sans "lmss" "default"
144 \font_typewriter "lmtt" "default"
145 \font_math "auto" "auto"
146 \font_default_family default
147 \use_non_tex_fonts false
150 \font_sf_scale 100 100
151 \font_tt_scale 100 100
153 \use_dash_ligatures false
155 \default_output_format pdf2
157 \bibtex_command default
158 \index_command default
162 \pdf_title "LyX's Math Manual"
163 \pdf_author "LyX Team, Uwe Stöhr"
164 \pdf_subject "LyX-documentation about math"
165 \pdf_keywords "LyX, Mathed"
167 \pdf_bookmarksnumbered true
168 \pdf_bookmarksopen true
169 \pdf_bookmarksopenlevel 1
170 \pdf_breaklinks false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
178 \use_package amsmath 2
179 \use_package amssymb 2
180 \use_package cancel 0
182 \use_package mathdots 1
183 \use_package mathtools 2
184 \use_package mhchem 1
185 \use_package stackrel 0
186 \use_package stmaryrd 0
187 \use_package undertilde 0
189 \cite_engine_type default
193 \paperorientation portrait
197 \notefontcolor #0000ff
204 \paragraph_separation skip
207 \quotes_style english
210 \paperpagestyle plain
214 \tracking_changes false
215 \output_changes false
218 \html_be_strict false
225 's detailed Math manual
229 by the \SpecialChar LyX
234 \begin_layout Plain Layout
236 If you have comments or error corrections, please send them to the \SpecialChar LyX
241 \begin_inset CommandInset href
243 name "lyx-docs@lists.lyx.org"
244 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
256 \begin_inset Note Note
259 \begin_layout Plain Layout
266 \begin_inset Newline newline
270 \begin_inset Newline newline
278 \begin_layout Standard
279 \begin_inset CommandInset toc
280 LatexCommand tableofcontents
287 \begin_layout Standard
288 \begin_inset Note Note
291 \begin_layout Plain Layout
292 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
295 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
302 If they are not installed the document can be exported anyway but the sections
303 where the packages are required will not appear in the output.
308 ; if it is not installed, this file cannot be exported.
311 \begin_layout Plain Layout
312 The latest PDF-version of this document can be found here:
313 \begin_inset Newline newline
318 http://wiki.lyx.org/LyX/Manuals#Math
326 \begin_layout Standard
327 \begin_inset Newpage newpage
333 \begin_layout Section
337 \begin_layout Standard
338 This document explains \SpecialChar LyX
339 's math features and is furthermore a collection
340 of \SpecialChar LaTeX
341 -commands used for mathematical characters and constructs.
342 The explanations are designed for the usage of commands.
343 It is therefore required that you have read the section
354 \begin_layout Standard
355 Most of the characters and many constructs explained in this manual are
356 also accessible via the menu
360 \SpecialChar menuseparator
376 But everybody who has to write lots of formulas will notice that it is
377 much faster to use commands instead of the math toolbar.
378 Therefore this manual is focused on commands but also mentions the correspondin
379 g toolbar buttons when available.
382 \begin_layout Standard
383 If not specially mentioned the commands are only available within formulas.
384 To be able to use all commands explained in this document, the option
388 must be checked in the document settings (menu
390 Document\SpecialChar menuseparator
391 Settings\SpecialChar menuseparator
402 \begin_layout Plain Layout
405 Use AMS math package automatically
411 \begin_layout Plain Layout
420 -math when math constructs are found that are supported by \SpecialChar LyX
429 \begin_layout Standard
430 This document doesn't list all
434 \begin_layout Plain Layout
447 \begin_layout Plain Layout
452 \begin_layout Plain Layout
461 -math commands is in the file
464 \begin_inset CommandInset href
467 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
474 , which is part of every \SpecialChar LaTeX
475 standard installation.
480 for lucidity reasons.
483 \begin_layout Section
487 \begin_layout Standard
488 To create an inline formula
489 \begin_inset Index idx
492 \begin_layout Plain Layout
498 that is embedded into a text line, use one of the shortcuts
504 or the toolbar button
511 \begin_inset Newline newline
514 To create a display style formula
515 \begin_inset Index idx
518 \begin_layout Plain Layout
519 Formula ! display style
524 which will appear bigger, has a different format, and will be in a separate
525 paragraph, use one of these shortcuts:
534 \begin_layout Standard
535 To change a display style formula to an inline formula, set the cursor into
536 the formula and use one of the shortcuts
544 Edit\SpecialChar menuseparator
545 Math\SpecialChar menuseparator
549 The same way is used to change an inline formula to a display style formula.
552 \begin_layout Standard
553 To display parts of an inline formula in the size of a display style formula,
561 \begin_inset Index idx
564 \begin_layout Plain Layout
573 Then a new blue box appears in which the desired formula part is inserted.
576 \begin_layout Standard
577 Only inline formulas are allowed inside tables.
580 \begin_layout Standard
585 can be turned on in the menu
587 View\SpecialChar menuseparator
591 When you click there on
592 \begin_inset Quotes eld
596 \begin_inset Quotes erd
599 the toolbar will be shown permanently at the bottom; this state is visualized
604 menu with a checkmark.
605 When you click in this state again on
606 \begin_inset Quotes eld
610 \begin_inset Quotes erd
621 is only shown when the cursor is within a formula; this state is visualized
622 by the renaming of the menu entry from
623 \begin_inset Quotes eld
627 \begin_inset Quotes erd
631 \begin_inset Quotes eld
639 \begin_inset Quotes erd
645 \begin_layout Standard
648 \begin_inset Index idx
651 \begin_layout Plain Layout
658 is invoked by pressing the toolbar button
666 Insert\SpecialChar menuseparator
678 \begin_layout Standard
679 To change the \SpecialChar LaTeX
681 \begin_inset Index idx
684 \begin_layout Plain Layout
693 Document\SpecialChar menuseparator
694 Settings\SpecialChar menuseparator
704 \begin_layout Standard
705 To edit matrices, case differentiations and multiline formulas subsequently,
708 Edit\SpecialChar menuseparator
713 Edit\SpecialChar menuseparator
715 \begin_inset space \thinspace{}
719 \begin_inset space \thinspace{}
729 When lines and columns are swapped via the menu, the column or line where
730 the cursor is in is exchanged with the column to the right or the line
732 Is the cursor in the last column or row, the exchange is done with the
733 column to the left or the line above.
736 \begin_layout Standard
737 To write text in formulas
741 \begin_layout Plain Layout
742 For multiline formulas the command
749 \begin_inset CommandInset ref
751 reference "subsec:Text-in-multiline"
765 \begin_inset Index idx
768 \begin_layout Plain Layout
775 \begin_inset Index idx
778 \begin_layout Plain Layout
785 This mode is invoked with the shortcut
791 or by the insertion of the command
798 \begin_inset Index idx
801 \begin_layout Plain Layout
810 The text appears black in \SpecialChar LyX
811 and can therefore be distinguished from the
812 other formula parts which appear blue.
813 In the output mathematical text is set upright, in contrary to other formula
817 \begin_layout Subsection*
821 \begin_layout Standard
822 Most of the \SpecialChar LaTeX
823 -commands for math constructs have the following scheme:
826 \begin_layout Standard
842 \begin_layout Standard
843 A command always starts with a backslash
844 \begin_inset Quotes gld
854 \begin_inset Quotes grd
858 To omit optional arguments, also omit the associated brackets.
859 The braces around the required arguments are named in this document as
862 \begin_inset Index idx
865 \begin_layout Plain Layout
873 If you add in a formula a left brace to a command name, \SpecialChar LyX
875 creates a \SpecialChar TeX
877 In all other cases \SpecialChar TeX
878 braces are created in formulas with the command
886 braces appear red in \SpecialChar LyX
887 , in contrary to normal braces which appear blue.
889 mode no command is needed to get \SpecialChar TeX
892 braces don't appear in the output.
895 \begin_layout Standard
896 When commands without arguments, like commands for symbols are entered in
898 mode, a space character must
902 be behind the command to end it.
903 This space doesn't appear in the output.
904 When the space should appear in the output, the space must be followed
905 by a protected space in normal text.
908 \begin_layout Standard
909 A protected space is inserted with
912 arg "command-alternatives space-insert protected ; math-space"
918 \begin_layout Subsection*
919 \begin_inset Newpage newpage
925 \begin_layout Itemize
927 \begin_inset space \textvisiblespace{}
930 denotes a space character to be input.
933 \begin_layout Itemize
935 \begin_inset Formula $\to$
938 denotes the usage of the corresponding arrow key on the keyboard.
943 key can often be used instead of
944 \begin_inset Formula $\to$
948 \begin_inset Formula $\downarrow$
956 \begin_inset Formula $\leftarrow$
960 \begin_inset Formula $\uparrow$
966 \begin_layout Subsection*
970 \begin_layout Standard
972 \begin_inset Float table
978 \begin_layout Plain Layout
980 \begin_inset Caption Standard
982 \begin_layout Plain Layout
983 \begin_inset CommandInset label
985 name "tab:Available-units"
997 \begin_layout Plain Layout
1000 <lyxtabular version="3" rows="13" columns="2">
1001 <features booktabs="true" tabularvalignment="middle">
1002 <column alignment="center" valignment="top">
1003 <column alignment="center" valignment="top" width="0pt">
1005 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1008 \begin_layout Plain Layout
1014 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1017 \begin_layout Plain Layout
1025 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1028 \begin_layout Plain Layout
1034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1037 \begin_layout Plain Layout
1045 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1048 \begin_layout Plain Layout
1054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1057 \begin_layout Plain Layout
1065 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1068 \begin_layout Plain Layout
1074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1077 \begin_layout Plain Layout
1079 \begin_inset space \thinspace{}
1083 \begin_inset space \thinspace{}
1093 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1096 \begin_layout Plain Layout
1102 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1105 \begin_layout Plain Layout
1107 \begin_inset space \thinspace{}
1111 \begin_inset space \thinspace{}
1121 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1124 \begin_layout Plain Layout
1130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1133 \begin_layout Plain Layout
1135 \begin_inset space \thinspace{}
1139 \begin_inset space \thinspace{}
1149 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1152 \begin_layout Plain Layout
1158 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1161 \begin_layout Plain Layout
1163 \begin_inset space \thinspace{}
1167 \begin_inset space \thinspace{}
1177 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1180 \begin_layout Plain Layout
1186 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1189 \begin_layout Plain Layout
1191 \begin_inset space \thinspace{}
1195 \begin_inset space \thinspace{}
1205 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1208 \begin_layout Plain Layout
1214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1217 \begin_layout Plain Layout
1219 \begin_inset space \thinspace{}
1223 \begin_inset Formula $\approx$
1227 \begin_inset space \thinspace{}
1237 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1240 \begin_layout Plain Layout
1246 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1249 \begin_layout Plain Layout
1251 \begin_inset space \thinspace{}
1255 \begin_inset space \thinspace{}
1265 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1268 \begin_layout Plain Layout
1274 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1277 \begin_layout Plain Layout
1281 \begin_inset Quotes eld
1287 \begin_inset Quotes erd
1297 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1300 \begin_layout Plain Layout
1306 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1309 \begin_layout Plain Layout
1311 \begin_inset Quotes eld
1319 \begin_inset Quotes erd
1329 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1332 \begin_layout Plain Layout
1338 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1341 \begin_layout Plain Layout
1343 \begin_inset space \thinspace{}
1347 \begin_inset Formula $\nicefrac{1}{18}$
1351 \begin_inset space \thinspace{}
1372 \begin_layout Standard
1373 \begin_inset Newpage newpage
1379 \begin_layout Section
1383 \begin_layout Subsection
1385 \begin_inset Index idx
1388 \begin_layout Plain Layout
1395 \begin_inset Index idx
1398 \begin_layout Plain Layout
1405 \begin_inset Index idx
1408 \begin_layout Plain Layout
1413 \begin_layout Plain Layout
1424 \begin_layout Plain Layout
1437 \begin_inset Index idx
1440 \begin_layout Plain Layout
1445 \begin_layout Plain Layout
1456 \begin_layout Plain Layout
1471 \begin_layout Standard
1472 Indices are created with an underscore
1473 \begin_inset Quotes eld
1477 \begin_inset Quotes erd
1480 or via the math toolbar button
1483 arg "math-subscript"
1486 , exponents with a caret
1487 \begin_inset Quotes eld
1491 \begin_inset Quotes erd
1494 or via the math toolbar button
1497 arg "math-superscript"
1503 \begin_layout Standard
1505 \begin_inset Tabular
1506 <lyxtabular version="3" rows="4" columns="2">
1507 <features booktabs="true" tabularvalignment="middle">
1508 <column alignment="center" valignment="top" width="0pt">
1509 <column alignment="center" valignment="top" width="0pt">
1511 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1514 \begin_layout Plain Layout
1520 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1523 \begin_layout Plain Layout
1531 <cell alignment="center" valignment="top" usebox="none">
1534 \begin_layout Plain Layout
1540 <cell alignment="center" valignment="top" usebox="none">
1543 \begin_layout Plain Layout
1544 \begin_inset Formula $B_{V}$
1553 <row topspace="1.5mm">
1554 <cell alignment="center" valignment="top" usebox="none">
1557 \begin_layout Plain Layout
1563 <cell alignment="center" valignment="top" usebox="none">
1566 \begin_layout Plain Layout
1567 \begin_inset Formula $B^{V}$
1576 <row topspace="1.5mm">
1577 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1580 \begin_layout Plain Layout
1582 \begin_inset space \textvisiblespace{}
1590 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1593 \begin_layout Plain Layout
1594 \begin_inset Formula $B^{A}$
1610 \begin_layout Standard
1611 As the caret is in some languages an accent, vowels will be accentuated
1612 in this case and not set as exponents
1616 \begin_layout Plain Layout
1617 Depending on the used keyboard settings this can also happen for characters
1624 To get exponents in this case, press
1628 after the caret as in the last example.
1631 \begin_layout Subsection
1633 \begin_inset CommandInset label
1635 name "subsec:Fractions"
1640 \begin_inset Index idx
1643 \begin_layout Plain Layout
1652 \begin_layout Standard
1653 Fractions are generated with the command
1660 \begin_inset Index idx
1663 \begin_layout Plain Layout
1671 or via the math toolbar button
1674 arg "math-insert \\frac"
1678 The font size is adjusted automatically, depending on whether the fraction
1679 is in an inline or display style formula.
1680 With the math toolbar button
1683 arg "math-insert \\frac-square"
1686 you can select different fraction types.
1689 \begin_layout Standard
1697 \begin_inset Index idx
1700 \begin_layout Plain Layout
1708 a fraction can be created that always has the size of a display style formula.
1716 \begin_inset Index idx
1719 \begin_layout Plain Layout
1727 the fraction appears always with the size of an inline formula.
1731 \begin_layout Standard
1732 A line with the fraction
1733 \begin_inset Formula $\frac{1}{2}$
1736 that was created with the command
1745 \begin_layout Standard
1746 A line with the fraction
1747 \begin_inset Formula $\dfrac{1}{2}$
1750 that was created with the command
1759 \begin_layout Standard
1761 \begin_inset Tabular
1762 <lyxtabular version="3" rows="4" columns="2">
1763 <features booktabs="true" tabularvalignment="middle">
1764 <column alignment="center" valignment="top" width="0pt">
1765 <column alignment="center" valignment="top" width="0pt">
1767 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1770 \begin_layout Plain Layout
1776 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1779 \begin_layout Plain Layout
1786 <row topspace="1.5mm">
1787 <cell alignment="center" valignment="top" usebox="none">
1790 \begin_layout Plain Layout
1794 \begin_inset space \textvisiblespace{}
1798 \begin_inset Formula $\downarrow$
1806 <cell alignment="center" valignment="top" usebox="none">
1809 \begin_layout Plain Layout
1810 \begin_inset Formula $\frac{A}{B}$
1819 <row topspace="2mm">
1820 <cell alignment="center" valignment="top" usebox="none">
1823 \begin_layout Plain Layout
1827 \begin_inset space \textvisiblespace{}
1831 \begin_inset Formula $\downarrow$
1839 <cell alignment="center" valignment="top" usebox="none">
1842 \begin_layout Plain Layout
1843 \begin_inset Formula $\dfrac{A}{B}$
1852 <row topspace="2mm" bottomspace="1mm">
1853 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1856 \begin_layout Plain Layout
1860 \begin_inset space \textvisiblespace{}
1866 \begin_inset space \textvisiblespace{}
1870 \begin_inset Formula $\downarrow$
1874 \begin_inset Formula $\downarrow\downarrow$
1882 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1885 \begin_layout Plain Layout
1886 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1902 \begin_layout Standard
1903 \begin_inset VSpace bigskip
1907 \begin_inset Newpage newpage
1910 For nested fractions the command
1917 \begin_inset Index idx
1920 \begin_layout Plain Layout
1930 \begin_inset VSpace -3mm
1936 \begin_layout Standard
1937 \begin_inset Formula
1939 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1940 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1948 \begin_layout Standard
1949 The command for the example above is:
1952 \begin_layout Standard
1958 \begin_inset space \textvisiblespace{}
1962 \begin_inset Formula $\downarrow$
1968 \begin_inset space \textvisiblespace{}
1974 \begin_inset space \textvisiblespace{}
1978 \begin_inset Formula $\downarrow$
1982 \begin_inset Formula $\downarrow$
1988 \begin_layout Standard
1989 \begin_inset VSpace medskip
1995 \begin_layout Standard
2002 sets the fraction always in the size of a displayed formula, also when
2003 it is part of another fraction.
2006 \begin_layout Standard
2007 It is possible to specify the alignment of the numerator.
2014 is used to left align it, the command
2027 centers the numerator.
2028 These fractions demonstrate the different alignments:
2031 \begin_layout Standard
2034 \begin_inset Formula
2036 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2044 \begin_layout Standard
2045 \begin_inset Note Greyedout
2048 \begin_layout Plain Layout
2065 are no real \SpecialChar LaTeX
2066 commands but represent the command
2070 cfrac[alignment]{numerator}{denominator}
2073 Therefore you cannot use them in \SpecialChar TeX
2082 \begin_layout Standard
2083 \begin_inset VSpace medskip
2086 It is often advantageous to combine
2099 \begin_inset Formula
2101 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2109 \begin_layout Standard
2110 For inline fractions with a sloped fraction stroke you can use the command
2118 \begin_inset Index idx
2121 \begin_layout Plain Layout
2130 \begin_inset Formula $\nicefrac{5}{31}$
2140 \begin_inset Index idx
2143 \begin_layout Plain Layout
2152 \begin_inset Formula $\unitfrac{5}{31}$
2155 There is furthermore the command
2161 that offers to write a fraction in combination with a number:
2162 \begin_inset Formula $\unitfrac[2]{1}{3}$
2168 \begin_layout Standard
2169 \begin_inset Note Greyedout
2172 \begin_layout Plain Layout
2183 is not a real \SpecialChar LaTeX
2184 command but the command
2185 \begin_inset Newline newline
2192 unitfrac[number]{numerator}{denominator}
2195 Therefore you cannot use it in \SpecialChar TeX
2204 \begin_layout Standard
2205 How to define own fractions where the fraction stroke can be changed, is
2207 \begin_inset CommandInset ref
2209 reference "subsec:Self-defined-Fractions"
2216 \begin_layout Standard
2217 Multiline fractions are explained in
2218 \begin_inset CommandInset ref
2220 reference "subsec:Multiline-Fractions"
2227 \begin_layout Subsection
2229 \begin_inset Index idx
2232 \begin_layout Plain Layout
2241 \begin_layout Standard
2242 Square roots are created with
2249 \begin_inset Index idx
2252 \begin_layout Plain Layout
2260 or the math toolbar button
2263 arg "math-insert \\sqrt"
2266 , all other roots with the command
2273 \begin_inset Index idx
2276 \begin_layout Plain Layout
2284 or with the math toolbar button
2287 arg "math-insert \\root"
2293 \begin_layout Standard
2295 \begin_inset Tabular
2296 <lyxtabular version="3" rows="3" columns="2">
2297 <features booktabs="true" tabularvalignment="middle">
2298 <column alignment="center" valignment="top" width="0pt">
2299 <column alignment="center" valignment="top" width="0pt">
2301 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2304 \begin_layout Plain Layout
2310 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2313 \begin_layout Plain Layout
2320 <row topspace="1mm">
2321 <cell alignment="center" valignment="top" usebox="none">
2324 \begin_layout Plain Layout
2328 \begin_inset space \textvisiblespace{}
2336 <cell alignment="center" valignment="top" usebox="none">
2339 \begin_layout Plain Layout
2340 \begin_inset Formula $\sqrt{A-B}$
2349 <row topspace="1mm">
2350 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2353 \begin_layout Plain Layout
2357 \begin_inset space \textvisiblespace{}
2361 \begin_inset Formula $\downarrow$
2369 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2372 \begin_layout Plain Layout
2373 \begin_inset Formula $\sqrt[3]{A-B}$
2389 \begin_layout Standard
2390 A square root can also be created with
2396 when the root index field is left empty.
2399 \begin_layout Standard
2400 With certain indices the distance to the root is too small, like in this
2402 \begin_inset Formula $\sqrt[\beta]{B}$
2406 \begin_inset Newline newline
2410 \begin_inset Formula $\beta$
2414 To avoid this, the commands
2421 \begin_inset Index idx
2424 \begin_layout Plain Layout
2439 \begin_inset Index idx
2442 \begin_layout Plain Layout
2450 are used with the following scheme:
2453 \begin_layout Standard
2467 \begin_layout Standard
2468 Distance is the number of Big Points (unit bp;
2469 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2472 ), that the index should be moved to the left or top, resp..
2473 The commands are written to the index.
2474 This way the command
2475 \begin_inset Newline newline
2485 \begin_inset Formula $\to$
2491 \begin_inset Formula $\to$
2497 \begin_inset space \textvisiblespace{}
2501 \begin_inset Formula $\to$
2505 \begin_inset Newline newline
2510 produces a correct typeset formula:
2511 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2517 \begin_layout Subsection
2518 Binomial Coefficients
2519 \begin_inset Index idx
2522 \begin_layout Plain Layout
2523 Binomial coefficients
2531 \begin_layout Standard
2532 Binomial coefficients are inserted with the command
2539 \begin_inset Index idx
2542 \begin_layout Plain Layout
2550 or with the submenu of the math toolbar button
2553 arg "math-insert \\frac-square"
2569 there are the commands
2576 \begin_inset Index idx
2579 \begin_layout Plain Layout
2594 \begin_inset Index idx
2597 \begin_layout Plain Layout
2606 For other brackets around binomial coeficients there are the commands
2613 \begin_inset Index idx
2616 \begin_layout Plain Layout
2631 \begin_inset Index idx
2634 \begin_layout Plain Layout
2645 \begin_layout Standard
2647 \begin_inset Tabular
2648 <lyxtabular version="3" rows="6" columns="2">
2649 <features booktabs="true" tabularvalignment="middle">
2650 <column alignment="center" valignment="top" width="0pt">
2651 <column alignment="center" valignment="top" width="0pt">
2653 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2656 \begin_layout Plain Layout
2662 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2665 \begin_layout Plain Layout
2672 <row topspace="1mm">
2673 <cell alignment="center" valignment="top" usebox="none">
2676 \begin_layout Plain Layout
2680 \begin_inset space \textvisiblespace{}
2684 \begin_inset Formula $\downarrow$
2692 <cell alignment="center" valignment="top" usebox="none">
2695 \begin_layout Plain Layout
2696 \begin_inset Formula $\binom{A}{B}$
2705 <row topspace="2mm">
2706 <cell alignment="center" valignment="top" usebox="none">
2709 \begin_layout Plain Layout
2713 \begin_inset space \textvisiblespace{}
2717 \begin_inset Formula $\downarrow$
2725 <cell alignment="center" valignment="top" usebox="none">
2728 \begin_layout Plain Layout
2729 \begin_inset Formula $\dbinom{A}{B}$
2738 <row topspace="2mm" bottomspace="0.5mm">
2739 <cell alignment="center" valignment="top" usebox="none">
2742 \begin_layout Plain Layout
2746 \begin_inset space \textvisiblespace{}
2750 \begin_inset Formula $\downarrow$
2758 <cell alignment="center" valignment="top" usebox="none">
2761 \begin_layout Plain Layout
2762 \begin_inset Formula $\tbinom{A}{B}$
2771 <row topspace="1mm">
2772 <cell alignment="center" valignment="top" topline="true" usebox="none">
2775 \begin_layout Plain Layout
2779 \begin_inset space \textvisiblespace{}
2783 \begin_inset Formula $\downarrow$
2791 <cell alignment="center" valignment="top" topline="true" usebox="none">
2794 \begin_layout Plain Layout
2795 \begin_inset Formula ${A \brack B}$
2804 <row topspace="2mm" bottomspace="0.5mm">
2805 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2808 \begin_layout Plain Layout
2812 \begin_inset space \textvisiblespace{}
2816 \begin_inset Formula $\downarrow$
2824 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2827 \begin_layout Plain Layout
2828 \begin_inset Formula ${A \brace B}$
2844 \begin_layout Subsection
2845 Case Differentiations
2846 \begin_inset Index idx
2849 \begin_layout Plain Layout
2850 Case differentiations
2858 \begin_layout Standard
2860 \begin_inset Tabular
2861 <lyxtabular version="3" rows="3" columns="2">
2862 <features booktabs="true" tabularvalignment="middle">
2863 <column alignment="center" valignment="top" width="0pt">
2864 <column alignment="center" valignment="top" width="0pt">
2866 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2869 \begin_layout Plain Layout
2875 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2878 \begin_layout Plain Layout
2886 <cell alignment="center" valignment="top" usebox="none">
2889 \begin_layout Plain Layout
2893 \begin_inset space \textvisiblespace{}
2897 \begin_inset Formula $\to$
2901 \begin_inset Index idx
2904 \begin_layout Plain Layout
2917 <cell alignment="center" valignment="top" usebox="none">
2920 \begin_layout Plain Layout
2921 \begin_inset Formula $\begin{cases}
2931 <row topspace="1.5mm">
2932 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2935 \begin_layout Plain Layout
2939 \begin_inset space \textvisiblespace{}
2945 arg "newline-insert newline"
2953 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2956 \begin_layout Plain Layout
2957 \begin_inset Formula $\begin{cases}
2958 A & \textrm{for }x>0\\
2959 B & \textrm{for }x=0
2976 \begin_layout Standard
2983 or pressing the math toolbar button
2986 arg "math-insert \\cases"
2989 you can create new lines with the shortcut
2992 arg "newline-insert newline"
2995 or the table toolbar button
2998 arg "tabular-feature append-row"
3004 \begin_layout Standard
3011 is also available via the menu
3013 Insert\SpecialChar menuseparator
3014 Math\SpecialChar menuseparator
3020 \begin_layout Subsection
3022 \begin_inset Index idx
3025 \begin_layout Plain Layout
3034 \begin_layout Standard
3042 \begin_inset Index idx
3045 \begin_layout Plain Layout
3053 every character can be displayed canceled.
3054 The characters are quasi accentuated by a slash.
3057 \begin_layout Standard
3059 \begin_inset Tabular
3060 <lyxtabular version="3" rows="4" columns="2">
3061 <features booktabs="true" tabularvalignment="middle">
3062 <column alignment="center" valignment="top" width="0pt">
3063 <column alignment="center" valignment="top" width="0pt">
3065 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3068 \begin_layout Plain Layout
3074 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3077 \begin_layout Plain Layout
3085 <cell alignment="center" valignment="top" usebox="none">
3088 \begin_layout Plain Layout
3096 <cell alignment="center" valignment="top" usebox="none">
3099 \begin_layout Plain Layout
3100 \begin_inset Formula $\not=$
3110 <cell alignment="center" valignment="top" usebox="none">
3113 \begin_layout Plain Layout
3123 <cell alignment="center" valignment="top" usebox="none">
3126 \begin_layout Plain Layout
3127 \begin_inset Formula $\not\le$
3137 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3140 \begin_layout Plain Layout
3150 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3153 \begin_layout Plain Layout
3154 \begin_inset Formula $\not\parallel$
3170 \begin_layout Standard
3171 The last example shows that not all negations look good.
3172 Therefore there are special commands for some negations (see
3173 \begin_inset CommandInset ref
3175 reference "subsec:Mathematical-Symbols"
3180 \begin_inset CommandInset ref
3182 reference "sec:Relations"
3189 \begin_layout Subsection
3191 \begin_inset CommandInset label
3193 name "subsec:Placeholders"
3198 \begin_inset Index idx
3201 \begin_layout Plain Layout
3208 \begin_inset Index idx
3211 \begin_layout Plain Layout
3212 Chemical characters ! Isotopes
3218 \begin_inset Index idx
3221 \begin_layout Plain Layout
3226 \begin_layout Plain Layout
3237 \begin_layout Plain Layout
3252 \begin_layout Standard
3254 \begin_inset space \thinspace{}
3258 \begin_inset space \space{}
3265 \begin_layout Plain Layout
3266 Typesetting isotopes and chemical symbols is described in
3267 \begin_inset CommandInset ref
3269 reference "subsec:Chemical-Symbols-and"
3278 the following problem occurs:
3281 \begin_layout Standard
3283 \begin_inset Tabular
3284 <lyxtabular version="3" rows="2" columns="2">
3285 <features booktabs="true" tabularvalignment="middle">
3286 <column alignment="center" valignment="top" width="0pt">
3287 <column alignment="center" valignment="top" width="0pt">
3289 <cell alignment="center" valignment="top" usebox="none">
3292 \begin_layout Plain Layout
3293 Indices created with sub- and superscripts:
3298 <cell alignment="center" valignment="top" usebox="none">
3301 \begin_layout Plain Layout
3302 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3311 <row topspace="1.5mm">
3312 <cell alignment="center" valignment="top" usebox="none">
3315 \begin_layout Plain Layout
3321 <cell alignment="center" valignment="top" usebox="none">
3324 \begin_layout Plain Layout
3325 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3341 \begin_layout Standard
3342 The shorter index is by default placed below or above the first character
3343 of the longer index.
3344 To avoid this there is the command
3351 \begin_inset Index idx
3354 \begin_layout Plain Layout
3362 or the math toolbar button
3363 \begin_inset space \thinspace{}
3370 \begin_layout Plain Layout
3371 can be found in the submenu of the toolbar button
3374 arg "math-insert \\space"
3388 that creates one or more phantom characters.
3395 a small blue box appears that is superposed with two red arrows.
3396 The arrows indicate that the complete width and height of the box content
3397 will be created as placeholder.
3398 Phantom characters are accordingly placeholders with the size of the characters.
3401 \begin_layout Standard
3403 \begin_inset Tabular
3404 <lyxtabular version="3" rows="4" columns="2">
3405 <features booktabs="true" tabularvalignment="middle">
3406 <column alignment="center" valignment="top" width="0pt">
3407 <column alignment="center" valignment="top" width="0pt">
3409 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3412 \begin_layout Plain Layout
3418 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3421 \begin_layout Plain Layout
3428 <row topspace="1.5mm">
3429 <cell alignment="center" valignment="top" usebox="none">
3432 \begin_layout Plain Layout
3434 \begin_inset space \textvisiblespace{}
3440 \begin_inset space \textvisiblespace{}
3444 \begin_inset Formula $\to$
3448 \begin_inset space \textvisiblespace{}
3456 <cell alignment="center" valignment="top" usebox="none">
3459 \begin_layout Plain Layout
3460 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3469 <row topspace="1.5mm" bottomspace="0.5mm">
3470 <cell alignment="center" valignment="top" usebox="none">
3473 \begin_layout Plain Layout
3475 \begin_inset space \textvisiblespace{}
3481 \begin_inset space \textvisiblespace{}
3485 \begin_inset Formula $\to$
3489 \begin_inset space \textvisiblespace{}
3497 <cell alignment="center" valignment="top" usebox="none">
3500 \begin_layout Plain Layout
3501 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3510 <row topspace="1.5mm" bottomspace="0.5mm">
3511 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3514 \begin_layout Plain Layout
3518 \begin_inset space \textvisiblespace{}
3524 \begin_inset space \textvisiblespace{}
3528 \begin_inset Formula $\to$
3532 \begin_inset space \textvisiblespace{}
3540 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3543 \begin_layout Plain Layout
3544 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3560 \begin_layout Standard
3561 Furthermore there are the commands
3568 \begin_inset Index idx
3571 \begin_layout Plain Layout
3592 \begin_inset Index idx
3595 \begin_layout Plain Layout
3616 creates only space for the maximal height of the characters in the box
3617 but not for its width.
3624 creates only space for the width of the box content.
3625 Therefore the boxes of both commands have only one red arrow.
3628 \begin_layout Standard
3629 For example the command
3634 \begin_inset space \textvisiblespace{}
3641 creates space for the height of the integral sign,
3645 \begin_layout Plain Layout
3652 creates an integral sign, see
3653 \begin_inset CommandInset ref
3655 reference "subsec:Big-Operators"
3664 because this is the larger character.
3665 An example application is in
3666 \begin_inset CommandInset ref
3668 reference "subsec:Multiline-Brackets"
3675 \begin_layout Standard
3676 Placeholders can also be used for text when they are inserted via the menu
3679 Insert\SpecialChar menuseparator
3680 Formatting\SpecialChar menuseparator
3686 \begin_layout Standard
3688 \begin_inset Newline newline
3692 \begin_inset Phantom Phantom
3695 \begin_layout Plain Layout
3704 \begin_layout Subsection
3706 \begin_inset Index idx
3709 \begin_layout Plain Layout
3716 \begin_inset Index idx
3719 \begin_layout Plain Layout
3720 Formula ! underlined
3728 \begin_layout Standard
3730 \begin_inset Tabular
3731 <lyxtabular version="3" rows="4" columns="2">
3732 <features booktabs="true" tabularvalignment="middle">
3733 <column alignment="center" valignment="top" width="0pt">
3734 <column alignment="center" valignment="top" width="0pt">
3736 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3739 \begin_layout Plain Layout
3745 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3748 \begin_layout Plain Layout
3755 <row topspace="2mm">
3756 <cell alignment="center" valignment="top" usebox="none">
3759 \begin_layout Plain Layout
3763 \begin_inset space \textvisiblespace{}
3767 \begin_inset Index idx
3770 \begin_layout Plain Layout
3783 <cell alignment="center" valignment="top" usebox="none">
3786 \begin_layout Plain Layout
3787 \begin_inset Formula $\overline{A+B}$
3796 <row bottomspace="1mm">
3797 <cell alignment="center" valignment="top" usebox="none">
3800 \begin_layout Plain Layout
3804 \begin_inset space \textvisiblespace{}
3808 \begin_inset Index idx
3811 \begin_layout Plain Layout
3824 <cell alignment="center" valignment="top" usebox="none">
3827 \begin_layout Plain Layout
3828 \begin_inset Formula $\underline{A+B}$
3837 <row topspace="2mm" bottomspace="1mm">
3838 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3841 \begin_layout Plain Layout
3845 \begin_inset space \textvisiblespace{}
3851 \begin_inset space \textvisiblespace{}
3859 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3862 \begin_layout Plain Layout
3863 \begin_inset Formula $\overline{\underline{A+B}}$
3879 \begin_layout Standard
3880 In the last example it doesn't matter if first
3895 \begin_layout Standard
3896 To double underline use
3905 \begin_layout Standard
3906 It is possible to place up to 6 lines above or below characters.
3909 \begin_layout Standard
3910 \begin_inset VSpace bigskip
3913 Custom lines can be created using the command
3920 \begin_inset Index idx
3923 \begin_layout Plain Layout
3931 which has the following scheme:
3934 \begin_layout Standard
3939 rule[vertical offset]{length}{thickness}
3942 \begin_layout Standard
3943 The optional vertical offset shifts the line upwards (or downwards, when
3944 the value is negative).
3946 \begin_inset CommandInset ref
3948 reference "tab:Available-units"
3952 can be used for the values.
3953 Here are two example lines created with the commands
3954 \begin_inset Newline newline
3961 rule[-2ex]{3cm}{2pt}
3972 \begin_layout Standard
3974 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
3980 \begin_layout Standard
3987 can also be used for text when a line is inserted via the menu
3989 Insert\SpecialChar menuseparator
3990 Formatting\SpecialChar menuseparator
3992 \begin_inset space ~
4000 \begin_layout Standard
4002 \begin_inset CommandInset line
4013 \begin_layout Subsection
4015 \begin_inset CommandInset label
4017 name "subsec:Ellipses"
4022 \begin_inset Index idx
4025 \begin_layout Plain Layout
4034 \begin_layout Standard
4035 There are different types of ellipses available.
4039 \begin_layout Plain Layout
4040 In the math toolbar in the submenu of the button
4043 arg "math-insert \\ldots"
4051 For listings dots at the baseline are used (
4058 \begin_inset Index idx
4061 \begin_layout Plain Layout
4069 ), while for operations dots are needed that are on the same height as the
4077 \begin_inset Index idx
4080 \begin_layout Plain Layout
4089 When using the command
4096 \begin_inset Index idx
4099 \begin_layout Plain Layout
4107 , \SpecialChar LaTeX
4108 decides on the basis of the next character what type is used.
4111 \begin_layout Standard
4113 \begin_inset Tabular
4114 <lyxtabular version="3" rows="9" columns="2">
4115 <features booktabs="true" tabularvalignment="middle">
4116 <column alignment="center" valignment="top" width="0pt">
4117 <column alignment="center" valignment="top" width="0pt">
4119 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4122 \begin_layout Plain Layout
4128 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4131 \begin_layout Plain Layout
4139 <cell alignment="center" valignment="top" usebox="none">
4142 \begin_layout Plain Layout
4144 \begin_inset space \textvisiblespace{}
4150 \begin_inset space \textvisiblespace{}
4158 <cell alignment="center" valignment="top" usebox="none">
4161 \begin_layout Plain Layout
4162 \begin_inset Formula $A_{1},\dots,A_{n}$
4172 <cell alignment="center" valignment="top" usebox="none">
4175 \begin_layout Plain Layout
4177 \begin_inset space \textvisiblespace{}
4183 \begin_inset space \textvisiblespace{}
4191 <cell alignment="center" valignment="top" usebox="none">
4194 \begin_layout Plain Layout
4195 \begin_inset Formula $A_{1}+\dots+A_{n}$
4205 <cell alignment="center" valignment="top" usebox="none">
4208 \begin_layout Plain Layout
4210 \begin_inset space \textvisiblespace{}
4216 \begin_inset space \textvisiblespace{}
4224 <cell alignment="center" valignment="top" usebox="none">
4227 \begin_layout Plain Layout
4228 \begin_inset Formula $A_{1},\ldots,A_{n}$
4238 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4241 \begin_layout Plain Layout
4243 \begin_inset space \textvisiblespace{}
4249 \begin_inset space \textvisiblespace{}
4257 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4260 \begin_layout Plain Layout
4261 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4271 <cell alignment="center" valignment="top" usebox="none">
4274 \begin_layout Plain Layout
4282 <cell alignment="center" valignment="top" usebox="none">
4285 \begin_layout Plain Layout
4286 \begin_inset Formula $\vdots$
4296 <cell alignment="center" valignment="top" usebox="none">
4299 \begin_layout Plain Layout
4307 <cell alignment="center" valignment="top" usebox="none">
4310 \begin_layout Plain Layout
4311 \begin_inset Formula $\ddots$
4321 <cell alignment="center" valignment="top" usebox="none">
4324 \begin_layout Plain Layout
4332 <cell alignment="center" valignment="top" usebox="none">
4335 \begin_layout Plain Layout
4336 \begin_inset Formula $\iddots$
4346 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4349 \begin_layout Plain Layout
4351 \begin_inset space \thinspace{}
4354 matrix with the different dots
4359 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4362 \begin_layout Plain Layout
4363 \begin_inset Formula $\begin{array}{ccc}
4364 A_{11} & \cdots & A_{1m}\\
4365 \vdots & \ddots & \vdots\\
4366 A_{n1} & \cdots & A_{nm}
4383 \begin_layout Standard
4384 The ellipses available in menu
4386 Insert\SpecialChar menuseparator
4388 \begin_inset space ~
4402 \begin_layout Standard
4403 \begin_inset VSpace medskip
4412 , one of the options
4414 Use mathdots package (automatically)
4416 must be set in the document settings under
4419 \begin_inset space ~
4425 \begin_inset Newline newline
4430 Use mathdots package
4432 will improve the appearance of all dots in the documents if their font
4433 style or size is not the default.
4436 \begin_layout Standard
4437 \begin_inset VSpace medskip
4440 Specially for matrices there are ellipses that span over several columns.
4441 They are created with the command
4448 \begin_inset Index idx
4451 \begin_layout Plain Layout
4459 , that has the following scheme:
4462 \begin_layout Standard
4467 hdotsfor[distance]{number of columns}
4470 \begin_layout Standard
4471 The number of columns specifies how many columns should be spanned.
4472 Distance is a factor for the distance between the dots.
4475 \begin_layout Standard
4476 In the following matrix the command
4482 was inserted in the first box of the second line, to get an ellipsis with
4483 a dot distance twice as long as with the command
4490 \begin_inset Formula
4492 \left(\begin{array}{cccc}
4501 Note that the matrix fields that should be spanned must be empty, otherwise
4502 you get \SpecialChar LaTeX
4506 \begin_layout Standard
4507 \begin_inset VSpace bigskip
4510 Furthermore you can fill with the command
4517 \begin_inset Index idx
4520 \begin_layout Plain Layout
4528 the rest of a line with dots.
4529 The effect of these commands is the same as with
4536 \begin_inset CommandInset ref
4538 reference "subsec:Variable-Space"
4545 \begin_layout Standard
4546 For example the command
4551 \begin_inset space \textvisiblespace{}
4559 \begin_layout Standard
4560 \begin_inset Formula $A\dotfill B$
4566 \begin_layout Standard
4573 there is for a line the command
4580 \begin_inset Index idx
4583 \begin_layout Plain Layout
4594 \begin_layout Standard
4595 \begin_inset Formula $A\hrulefill B$
4601 \begin_layout Standard
4602 To use the commands for text, they have to be inserted in \SpecialChar TeX
4606 \begin_layout Section
4608 \begin_inset CommandInset label
4615 \begin_inset Index idx
4618 \begin_layout Plain Layout
4627 \begin_layout Standard
4628 Matrices can be inserted via the math toolbar button
4631 arg "dialog-show mathmatrix"
4636 Insert\SpecialChar menuseparator
4637 Math\SpecialChar menuseparator
4641 In the matrix dialog you can specify the number of columns and rows, the
4642 alignment and the decoration.
4643 The vertical alignment is only of importance for matrices in inline formulas:
4646 \begin_layout Standard
4647 The first matrix is top
4648 \begin_inset Formula $\begin{array}[t]{cccc}
4656 \begin_inset Formula $\begin{array}{cccc}
4663 and the third bottom
4664 \begin_inset Formula $\begin{array}[b]{cccc}
4674 \begin_layout Standard
4675 The horizontal alignment specifies how the column entries should be aligned.
4676 It is set by entering a letter for every column.
4681 denotes left aligned,
4690 To create for example a 4
4695 \begin_inset space ~
4698 matrix where the first column is left aligned, the second and third are
4699 centered and the last one is right aligned, one enters for the horizontal
4705 Normally in a matrix all columns are centered, therefore the default for
4713 \begin_layout Standard
4714 Horizontal alignment:
4717 \begin_layout Standard
4723 \begin_inset Formula $\begin{array}{lll}
4735 \begin_inset Formula $\begin{array}{ccc}
4747 \begin_inset Formula $\begin{array}{rrr}
4757 \begin_layout Standard
4758 To add or delete rows and columns subsequently, the math toolbar buttons
4762 arg "tabular-feature append-row"
4768 arg "tabular-feature delete-row"
4772 \begin_inset space \thinspace{}
4777 Edit\SpecialChar menuseparator
4781 New rows can also be created with
4784 arg "newline-insert newline"
4790 \begin_layout Standard
4791 \begin_inset VSpace bigskip
4798 adds parentheses in the selected style around the matrix.
4799 Alternatively, parentheses can can either be created with the commands
4807 \begin_inset Index idx
4810 \begin_layout Plain Layout
4825 \begin_inset Index idx
4828 \begin_layout Plain Layout
4839 \begin_inset space ~
4845 \begin_inset CommandInset ref
4847 reference "subsec:Automatic-Bracket-Size"
4851 , or by using the following commands:
4852 \begin_inset VSpace medskip
4858 \begin_layout Standard
4859 \begin_inset space \hfill{}
4863 \begin_inset Tabular
4864 <lyxtabular version="3" rows="4" columns="2">
4865 <features booktabs="true" tabularvalignment="middle">
4866 <column alignment="center" valignment="top" width="0pt">
4867 <column alignment="center" valignment="top">
4869 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4872 \begin_layout Plain Layout
4878 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4881 \begin_layout Plain Layout
4888 <row topspace="1.5mm">
4889 <cell alignment="center" valignment="top" usebox="none">
4892 \begin_layout Plain Layout
4896 \begin_inset space \textvisiblespace{}
4904 \begin_inset space \thinspace{}
4912 <cell alignment="center" valignment="top" usebox="none">
4915 \begin_layout Plain Layout
4916 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4917 0 & \textrm{-}\mathrm{i}\\
4919 \end{array}\end{bmatrix}$
4928 <row topspace="1.5mm" bottomspace="0.5mm">
4929 <cell alignment="center" valignment="top" usebox="none">
4932 \begin_layout Plain Layout
4936 \begin_inset space \textvisiblespace{}
4944 \begin_inset space \thinspace{}
4952 <cell alignment="center" valignment="top" usebox="none">
4955 \begin_layout Plain Layout
4956 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4957 0 & \textrm{-}\mathrm{i}\\
4959 \end{array}\end{Bmatrix}$
4969 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4972 \begin_layout Plain Layout
4976 \begin_inset space \textvisiblespace{}
4984 \begin_inset space \thinspace{}
4992 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4995 \begin_layout Plain Layout
4996 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
4997 0 & \textrm{-}\mathrm{i}\\
4999 \end{array}\end{pmatrix}$
5013 \begin_inset space \hfill{}
5017 \begin_inset Tabular
5018 <lyxtabular version="3" rows="4" columns="2">
5019 <features booktabs="true" tabularvalignment="middle">
5020 <column alignment="center" valignment="top" width="0pt">
5021 <column alignment="center" valignment="top">
5023 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5026 \begin_layout Plain Layout
5032 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5035 \begin_layout Plain Layout
5042 <row topspace="1.5mm">
5043 <cell alignment="center" valignment="top" usebox="none">
5046 \begin_layout Plain Layout
5050 \begin_inset space \textvisiblespace{}
5058 \begin_inset space \thinspace{}
5066 <cell alignment="center" valignment="top" usebox="none">
5069 \begin_layout Plain Layout
5070 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5071 0 & \textrm{-}\mathrm{i}\\
5073 \end{array}\end{vmatrix}$
5082 <row topspace="1.5mm" bottomspace="0.5mm">
5083 <cell alignment="center" valignment="top" usebox="none">
5086 \begin_layout Plain Layout
5090 \begin_inset space \textvisiblespace{}
5098 \begin_inset space \thinspace{}
5106 <cell alignment="center" valignment="top" usebox="none">
5109 \begin_layout Plain Layout
5110 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5111 0 & \textrm{-}\mathrm{i}\\
5113 \end{array}\end{Vmatrix}$
5123 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5126 \begin_layout Plain Layout
5130 \begin_inset space \textvisiblespace{}
5138 \begin_inset space \thinspace{}
5146 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5149 \begin_layout Plain Layout
5150 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5151 0 & \textrm{-}\mathrm{i}\\
5153 \end{array}\end{matrix}$
5167 \begin_inset space \hfill{}
5173 \begin_layout Standard
5174 \begin_inset VSpace medskip
5178 \begin_inset space \thinspace{}
5182 \begin_inset space \space{}
5191 is inserted, a blue box appears between two vertical lines where the matrix
5193 \begin_inset Newline newline
5196 Note that decorated matrices ignore the vertical alignment.
5199 \begin_layout Standard
5200 \begin_inset VSpace bigskip
5203 As all multiline formulas are matrices, the length
5210 \begin_inset Index idx
5213 \begin_layout Plain Layout
5221 that is described in
5222 \begin_inset CommandInset ref
5224 reference "subsec:Column-Separation"
5228 can also be used to change the column separation of matrices.
5231 \begin_layout Standard
5232 To change the row separation, the command
5239 \begin_inset Index idx
5242 \begin_layout Plain Layout
5251 It is used as follows:
5254 \begin_layout Standard
5261 arraystretch}{stretch factor}
5262 \begin_inset Index idx
5265 \begin_layout Plain Layout
5276 \begin_layout Standard
5283 assigns the stretch factor to the predefined command
5291 \begin_inset space \thinspace{}
5295 \begin_inset space \space{}
5298 the row separation, use the factor 2.
5299 This is then used for all following matrices.
5300 To go back to the original separation, assign the factor 1 to
5309 \begin_layout Standard
5310 To set matrices into a text line, the command
5317 \begin_inset Index idx
5320 \begin_layout Plain Layout
5329 When it is inserted a blue box with two dashed lines appears.
5330 In this box the matrix is inserted.
5333 \begin_layout Standard
5335 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5337 \end{smallmatrix}\right)$
5343 \begin_layout Section
5344 Brackets and Delimiters
5345 \begin_inset Index idx
5348 \begin_layout Plain Layout
5355 \begin_inset Index idx
5358 \begin_layout Plain Layout
5367 \begin_layout Subsection
5368 Vertical Brackets and Delimiters
5369 \begin_inset Index idx
5372 \begin_layout Plain Layout
5381 \begin_layout Standard
5382 \begin_inset space \hfill{}
5386 \begin_inset Tabular
5387 <lyxtabular version="3" rows="9" columns="2">
5388 <features booktabs="true" tabularvalignment="middle">
5389 <column alignment="center" valignment="top" width="0pt">
5390 <column alignment="center" valignment="top" width="0pt">
5392 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5395 \begin_layout Plain Layout
5401 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5404 \begin_layout Plain Layout
5412 <cell alignment="center" valignment="top" usebox="none">
5415 \begin_layout Plain Layout
5421 <cell alignment="center" valignment="top" usebox="none">
5424 \begin_layout Plain Layout
5425 \begin_inset Formula $($
5435 <cell alignment="center" valignment="top" usebox="none">
5438 \begin_layout Plain Layout
5444 <cell alignment="center" valignment="top" usebox="none">
5447 \begin_layout Plain Layout
5448 \begin_inset Formula $\{$
5458 <cell alignment="center" valignment="top" usebox="none">
5461 \begin_layout Plain Layout
5467 <cell alignment="center" valignment="top" usebox="none">
5470 \begin_layout Plain Layout
5471 \begin_inset Formula $[$
5481 <cell alignment="center" valignment="top" usebox="none">
5484 \begin_layout Plain Layout
5492 <cell alignment="center" valignment="top" usebox="none">
5495 \begin_layout Plain Layout
5496 \begin_inset Formula $\langle$
5506 <cell alignment="center" valignment="top" usebox="none">
5509 \begin_layout Plain Layout
5517 <cell alignment="center" valignment="top" usebox="none">
5520 \begin_layout Plain Layout
5521 \begin_inset Formula $\lceil$
5531 <cell alignment="center" valignment="top" usebox="none">
5534 \begin_layout Plain Layout
5542 <cell alignment="center" valignment="top" usebox="none">
5545 \begin_layout Plain Layout
5546 \begin_inset Formula $\lfloor$
5556 <cell alignment="center" valignment="top" usebox="none">
5559 \begin_layout Plain Layout
5565 <cell alignment="center" valignment="top" usebox="none">
5568 \begin_layout Plain Layout
5569 \begin_inset Formula $/$
5579 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5582 \begin_layout Plain Layout
5588 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5591 \begin_layout Plain Layout
5592 \begin_inset Formula $|$
5606 \begin_inset space \hfill{}
5610 \begin_inset Tabular
5611 <lyxtabular version="3" rows="9" columns="2">
5612 <features booktabs="true" tabularvalignment="middle">
5613 <column alignment="center" valignment="top" width="0pt">
5614 <column alignment="center" valignment="top" width="0pt">
5616 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5619 \begin_layout Plain Layout
5625 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5628 \begin_layout Plain Layout
5636 <cell alignment="center" valignment="top" usebox="none">
5639 \begin_layout Plain Layout
5645 <cell alignment="center" valignment="top" usebox="none">
5648 \begin_layout Plain Layout
5649 \begin_inset Formula $)$
5659 <cell alignment="center" valignment="top" usebox="none">
5662 \begin_layout Plain Layout
5668 <cell alignment="center" valignment="top" usebox="none">
5671 \begin_layout Plain Layout
5672 \begin_inset Formula $\}$
5682 <cell alignment="center" valignment="top" usebox="none">
5685 \begin_layout Plain Layout
5691 <cell alignment="center" valignment="top" usebox="none">
5694 \begin_layout Plain Layout
5695 \begin_inset Formula $]$
5705 <cell alignment="center" valignment="top" usebox="none">
5708 \begin_layout Plain Layout
5716 <cell alignment="center" valignment="top" usebox="none">
5719 \begin_layout Plain Layout
5720 \begin_inset Formula $\rangle$
5730 <cell alignment="center" valignment="top" usebox="none">
5733 \begin_layout Plain Layout
5741 <cell alignment="center" valignment="top" usebox="none">
5744 \begin_layout Plain Layout
5745 \begin_inset Formula $\rceil$
5755 <cell alignment="center" valignment="top" usebox="none">
5758 \begin_layout Plain Layout
5766 <cell alignment="center" valignment="top" usebox="none">
5769 \begin_layout Plain Layout
5770 \begin_inset Formula $\rfloor$
5780 <cell alignment="center" valignment="top" usebox="none">
5783 \begin_layout Plain Layout
5793 <cell alignment="center" valignment="top" usebox="none">
5796 \begin_layout Plain Layout
5797 \begin_inset Formula $\backslash$
5807 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5810 \begin_layout Plain Layout
5818 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5821 \begin_layout Plain Layout
5822 \begin_inset Formula $\|$
5836 \begin_inset space \hfill{}
5842 \begin_layout Standard
5845 \begin_inset Note Greyedout
5848 \begin_layout Plain Layout
5861 \begin_inset Index idx
5864 \begin_layout Plain Layout
5872 must be used for the backslash, because the command
5880 produces a line break there.
5888 \begin_layout Standard
5889 For all characters listed above the size can be adjusted with the commands
5890 described in the following two subsections.
5891 When using these commands, the characters < and > can directly be used
5892 instead of the commands
5907 \begin_layout Subsubsection
5909 \begin_inset CommandInset label
5911 name "subsec:Manual-Bracket-Size"
5916 \begin_inset Index idx
5919 \begin_layout Plain Layout
5920 Bracket size ! manual
5928 \begin_layout Standard
5929 The bracket size can be specified manually by the \SpecialChar LaTeX
5937 \begin_inset Index idx
5940 \begin_layout Plain Layout
5973 denotes the smallest and
5979 the largest bracket size.
5982 \begin_layout Standard
5983 These commands are used to emphasize levels of brackets:
5986 \begin_layout Standard
5988 \begin_inset Tabular
5989 <lyxtabular version="3" rows="2" columns="2">
5990 <features booktabs="true" tabularvalignment="middle">
5991 <column alignment="center" valignment="top" width="0pt">
5992 <column alignment="center" valignment="top" width="0pt">
5994 <cell alignment="center" valignment="top" usebox="none">
5997 \begin_layout Plain Layout
5998 all brackets in the same size:
6003 <cell alignment="center" valignment="top" usebox="none">
6006 \begin_layout Plain Layout
6007 \begin_inset Formula $((A+B)(A-B))^{C}$
6016 <row topspace="2mm">
6017 <cell alignment="center" valignment="top" usebox="none">
6020 \begin_layout Plain Layout
6026 <cell alignment="center" valignment="top" usebox="none">
6029 \begin_layout Plain Layout
6030 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6046 \begin_layout Standard
6047 For the second formula the command
6054 \begin_inset space \textvisiblespace{}
6062 \begin_layout Standard
6063 Here is an overview about all bracket sizes:
6066 \begin_layout Standard
6083 \begin_inset space \textvisiblespace{}
6091 \begin_inset space \textvisiblespace{}
6095 \begin_inset space \textvisiblespace{}
6105 \begin_layout Standard
6107 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6113 \begin_layout Standard
6120 -commands there is the variant
6127 \begin_inset Index idx
6130 \begin_layout Plain Layout
6138 that adds a bit more space between the bracket and its content, and the
6152 \begin_inset Index idx
6155 \begin_layout Plain Layout
6165 , that don't add additional space.
6170 at the end of the command
6176 is for a left bracket; for a right bracket this will be replaced by an
6182 A left or right bracket can each be an opening or closing bracket.
6185 \begin_layout Standard
6186 In the following table is a comparison of the variants:
6189 \begin_layout Standard
6191 \begin_inset Tabular
6192 <lyxtabular version="3" rows="5" columns="2">
6193 <features booktabs="true" tabularvalignment="middle">
6194 <column alignment="center" valignment="top" width="0pt">
6195 <column alignment="center" valignment="middle">
6197 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6200 \begin_layout Plain Layout
6206 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6209 \begin_layout Plain Layout
6216 <row topspace="2mm">
6217 <cell alignment="center" valignment="top" usebox="none">
6220 \begin_layout Plain Layout
6230 \begin_inset space \textvisiblespace{}
6240 <cell alignment="center" valignment="top" usebox="none">
6243 \begin_layout Plain Layout
6244 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6253 <row topspace="2mm">
6254 <cell alignment="center" valignment="top" usebox="none">
6257 \begin_layout Plain Layout
6267 \begin_inset space \textvisiblespace{}
6277 <cell alignment="center" valignment="top" usebox="none">
6280 \begin_layout Plain Layout
6281 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6290 <row topspace="2mm" bottomspace="0.5mm">
6291 <cell alignment="center" valignment="top" usebox="none">
6294 \begin_layout Plain Layout
6304 \begin_inset space \textvisiblespace{}
6314 <cell alignment="center" valignment="top" usebox="none">
6317 \begin_layout Plain Layout
6318 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6327 <row topspace="1.5mm" bottomspace="0.5mm">
6328 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6331 \begin_layout Plain Layout
6343 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6346 \begin_layout Plain Layout
6347 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6363 \begin_layout Subsubsection
6364 Automatic Bracket Size
6365 \begin_inset CommandInset label
6367 name "subsec:Automatic-Bracket-Size"
6372 \begin_inset Index idx
6375 \begin_layout Plain Layout
6376 Bracket size ! automatic
6384 \begin_layout Standard
6385 Brackets with variable size can be inserted with the commands
6392 \begin_inset Index idx
6395 \begin_layout Plain Layout
6410 \begin_inset Index idx
6413 \begin_layout Plain Layout
6421 or via the math toolbar button
6424 arg "dialog-show mathdelimiter"
6440 the wanted bracket must be inserted.
6441 The bracket size will then automatically be calculated for the output.
6444 \begin_layout Standard
6446 normal bracket: The command
6453 \begin_inset space \textvisiblespace{}
6457 \begin_inset Formula $\downarrow$
6461 \begin_inset space \textvisiblespace{}
6467 \begin_inset Formula
6477 \begin_layout Standard
6479 multiline bracket: The command
6488 \begin_inset space \textvisiblespace{}
6492 \begin_inset Formula $\downarrow$
6496 \begin_inset space \textvisiblespace{}
6504 \begin_inset Formula
6506 \ln\left(\frac{A}{C}\right)
6514 \begin_layout Standard
6530 \begin_inset space ~
6536 This has the advantage that you can see in \SpecialChar LyX
6537 immediately the real bracket
6538 size and that the matching right bracket will be created too.
6539 \begin_inset Newline newline
6542 The command for the last example would then be:
6553 \begin_inset space \textvisiblespace{}
6557 \begin_inset Formula $\downarrow$
6563 \begin_layout Standard
6564 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6565 For example the command
6572 \begin_inset space \textvisiblespace{}
6576 \begin_inset Formula $\downarrow$
6580 \begin_inset space \textvisiblespace{}
6590 \begin_inset Formula
6592 \left.\frac{A}{B}\right\}
6611 will be converted by \SpecialChar LyX
6612 to brackets in the right size when the document is
6613 reloaded and an omitted bracket will appear as dashed line.
6616 \begin_layout Standard
6617 \begin_inset VSpace bigskip
6620 Because all popular \SpecialChar LaTeX
6621 distributions use e\SpecialChar TeX
6622 , an extension to \SpecialChar LaTeX
6631 \begin_inset Index idx
6634 \begin_layout Plain Layout
6642 is additionally available for all brackets and limits.
6643 With this command the height of the following character is adapted to the
6644 one of the surrounding brackets, what is e.
6645 \begin_inset space \thinspace{}
6649 \begin_inset space \space{}
6652 needed for physical vectors:
6653 \begin_inset Formula
6655 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6660 For physical vectors there is a special \SpecialChar LaTeX
6661 -package, described in
6662 \begin_inset CommandInset ref
6664 reference "subsec:Physical-Vectors"
6671 \begin_layout Subsection
6673 \begin_inset Index idx
6676 \begin_layout Plain Layout
6677 Brackets ! horizontal
6685 \begin_layout Standard
6687 \begin_inset Tabular
6688 <lyxtabular version="3" rows="4" columns="2">
6689 <features booktabs="true" tabularvalignment="middle">
6690 <column alignment="center" valignment="top" width="0pt">
6691 <column alignment="center" valignment="top" width="0pt">
6693 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6696 \begin_layout Plain Layout
6702 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6705 \begin_layout Plain Layout
6713 <cell alignment="center" valignment="top" usebox="none">
6716 \begin_layout Plain Layout
6720 \begin_inset space \textvisiblespace{}
6724 \begin_inset space \textvisiblespace{}
6728 \begin_inset Index idx
6731 \begin_layout Plain Layout
6744 <cell alignment="center" valignment="top" usebox="none">
6747 \begin_layout Plain Layout
6748 \begin_inset Formula $\overbrace{A+B}^{3}$
6757 <row topspace="2mm">
6758 <cell alignment="center" valignment="top" usebox="none">
6761 \begin_layout Plain Layout
6765 \begin_inset space \textvisiblespace{}
6769 \begin_inset space \textvisiblespace{}
6773 \begin_inset Index idx
6776 \begin_layout Plain Layout
6789 <cell alignment="center" valignment="top" usebox="none">
6792 \begin_layout Plain Layout
6793 \begin_inset Formula $\underbrace{A+B}_{5}$
6803 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6806 \begin_layout Plain Layout
6810 \begin_inset space \textvisiblespace{}
6816 \begin_inset space \textvisiblespace{}
6820 \begin_inset space \textvisiblespace{}
6824 \begin_inset space \textvisiblespace{}
6828 \begin_inset space \textvisiblespace{}
6832 \begin_inset space \textvisiblespace{}
6836 \begin_inset space \textvisiblespace{}
6844 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6847 \begin_layout Plain Layout
6848 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6864 \begin_layout Standard
6865 In the last example it doesn't matter if
6877 is inserted at first.
6880 \begin_layout Standard
6881 \begin_inset VSpace medskip
6887 \begin_layout Standard
6888 If you set in the document settings under
6891 \begin_inset space ~
6901 \begin_inset Index idx
6904 \begin_layout Plain Layout
6905 Packages ! mathtools
6913 \begin_inset space ~
6918 , you have access to square backets:
6921 \begin_layout Standard
6923 \begin_inset Tabular
6924 <lyxtabular version="3" rows="4" columns="2">
6925 <features booktabs="true" tabularvalignment="middle">
6926 <column alignment="center" valignment="top" width="0pt">
6927 <column alignment="center" valignment="top" width="0pt">
6929 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6932 \begin_layout Plain Layout
6938 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6941 \begin_layout Plain Layout
6949 <cell alignment="center" valignment="top" usebox="none">
6952 \begin_layout Plain Layout
6980 \begin_inset space \textvisiblespace{}
6984 \begin_inset Index idx
6987 \begin_layout Plain Layout
7000 <cell alignment="center" valignment="top" usebox="none">
7003 \begin_layout Plain Layout
7004 \begin_inset Formula $\overbracket{A+B}^{3}$
7013 <row topspace="2mm">
7014 <cell alignment="center" valignment="top" usebox="none">
7017 \begin_layout Plain Layout
7045 \begin_inset space \textvisiblespace{}
7049 \begin_inset Index idx
7052 \begin_layout Plain Layout
7077 <cell alignment="center" valignment="top" usebox="none">
7080 \begin_layout Plain Layout
7081 \begin_inset Formula $\underbracket{A+B}_{5}$
7091 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7094 \begin_layout Plain Layout
7100 \begin_inset space \textvisiblespace{}
7104 \begin_inset space \textvisiblespace{}
7108 \begin_inset space \textvisiblespace{}
7112 \begin_inset space \textvisiblespace{}
7116 \begin_inset space \textvisiblespace{}
7124 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7127 \begin_layout Plain Layout
7128 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7144 \begin_layout Standard
7157 you can change the thickness of the bracket's stroke by specifying the
7158 desired thickness in square brackets behind the command:
7161 \begin_layout Standard
7163 \begin_inset Tabular
7164 <lyxtabular version="3" rows="3" columns="2">
7165 <features booktabs="true" tabularvalignment="middle">
7166 <column alignment="center" valignment="top" width="0pt">
7167 <column alignment="center" valignment="top" width="0pt">
7169 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7172 \begin_layout Plain Layout
7178 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7181 \begin_layout Plain Layout
7189 <cell alignment="center" valignment="top" usebox="none">
7192 \begin_layout Plain Layout
7222 \begin_inset space \textvisiblespace{}
7230 <cell alignment="center" valignment="top" usebox="none">
7233 \begin_layout Plain Layout
7234 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7243 <row topspace="2mm">
7244 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7247 \begin_layout Plain Layout
7277 \begin_inset space \textvisiblespace{}
7285 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7288 \begin_layout Plain Layout
7289 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7305 \begin_layout Standard
7306 \begin_inset VSpace bigskip
7309 When brackets should overlap each other, multiline formulas, as described
7311 \begin_inset CommandInset ref
7313 reference "sec:Multiline-Formulas"
7318 \begin_inset Formula
7320 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7321 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7326 In the first row the formula is inserted together with the first brace.
7327 It is hereby important that the space command
7331 \begin_layout Plain Layout
7332 Space commands are explained in
7333 \begin_inset CommandInset ref
7335 reference "subsec:Predefined-Space"
7350 is inserted before the first
7351 \begin_inset Formula $d$
7354 , because the brace that ends behind the
7355 \begin_inset Formula $q$
7358 prevents that the following
7359 \begin_inset Quotes eld
7363 \begin_inset Quotes erd
7366 is surrounded by space.
7370 \begin_layout Plain Layout
7371 because a bracket is not handled as a character, see
7372 \begin_inset CommandInset ref
7374 reference "subsec:Binary-Operators"
7383 In the second row the second brace is inserted.
7384 As it should begin before the
7385 \begin_inset Formula $b$
7400 \begin_layout Plain Layout
7408 \begin_inset CommandInset ref
7410 reference "subsec:Placeholders"
7419 This space is needed because the
7420 \begin_inset Quotes eld
7424 \begin_inset Quotes erd
7427 is also surrounded by space in the formula.
7428 The brace is placed under the command
7437 \begin_layout Standard
7438 It gets more complicated when brackets overlap each other above and under
7439 the formula, like in the following example:
7443 \begin_layout Plain Layout
7455 \begin_inset Formula
7457 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7458 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7467 \begin_layout Plain Layout
7478 The first formula row is the same as the second row of the previous example,
7479 with the difference that the brace is above.
7480 The second row contains the formula together with the second brace.
7481 To avoid that there is space between the upper brace in the first row and
7482 the formula, the row spacing needs to be reduced.
7483 This is not easily possible due to a bug in \SpecialChar LyX
7488 \begin_layout Plain Layout
7489 \begin_inset CommandInset href
7491 name "LyX-bug #1505"
7492 target "http://www.lyx.org/trac/ticket/1505"
7502 As a solution for the problem, the global formula row separation
7509 \begin_inset Index idx
7512 \begin_layout Plain Layout
7520 must be changed to -6
7521 \begin_inset space \thinspace{}
7524 pt before the formula with the command
7540 is set back after the formula to the standard value of 3
7541 \begin_inset space \thinspace{}
7544 pt using the same command.
7545 More about the row separation in formulas is explained in
7546 \begin_inset CommandInset ref
7548 reference "subsec:Line-Separation"
7555 \begin_layout Section
7557 \begin_inset Index idx
7560 \begin_layout Plain Layout
7569 \begin_layout Standard
7570 Arrows can be inserted via the math toolbar button
7573 arg "math-insert \\leftarrow"
7576 or the commands listed in the following subsections.
7579 \begin_layout Subsection
7581 \begin_inset Index idx
7584 \begin_layout Plain Layout
7593 \begin_layout Standard
7594 \begin_inset space \hfill{}
7598 \begin_inset Tabular
7599 <lyxtabular version="3" rows="8" columns="2">
7600 <features booktabs="true" tabularvalignment="middle">
7601 <column alignment="center" valignment="top" width="0pt">
7602 <column alignment="center" valignment="top" width="0pt">
7604 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7607 \begin_layout Plain Layout
7613 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7616 \begin_layout Plain Layout
7624 <cell alignment="center" valignment="top" usebox="none">
7627 \begin_layout Plain Layout
7635 <cell alignment="center" valignment="top" usebox="none">
7638 \begin_layout Plain Layout
7639 \begin_inset Formula $\gets$
7649 <cell alignment="center" valignment="top" usebox="none">
7652 \begin_layout Plain Layout
7660 <cell alignment="center" valignment="top" usebox="none">
7663 \begin_layout Plain Layout
7664 \begin_inset Formula $\Leftarrow$
7674 <cell alignment="center" valignment="top" usebox="none">
7677 \begin_layout Plain Layout
7685 <cell alignment="center" valignment="top" usebox="none">
7688 \begin_layout Plain Layout
7689 \begin_inset Formula $\longleftarrow$
7699 <cell alignment="center" valignment="top" usebox="none">
7702 \begin_layout Plain Layout
7710 <cell alignment="center" valignment="top" usebox="none">
7713 \begin_layout Plain Layout
7714 \begin_inset Formula $\Longleftarrow$
7724 <cell alignment="center" valignment="top" usebox="none">
7727 \begin_layout Plain Layout
7735 <cell alignment="center" valignment="top" usebox="none">
7738 \begin_layout Plain Layout
7739 \begin_inset Formula $\leftharpoonup$
7749 <cell alignment="center" valignment="top" usebox="none">
7752 \begin_layout Plain Layout
7760 <cell alignment="center" valignment="top" usebox="none">
7763 \begin_layout Plain Layout
7764 \begin_inset Formula $\leftharpoondown$
7774 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7777 \begin_layout Plain Layout
7785 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7788 \begin_layout Plain Layout
7789 \begin_inset Formula $\hookleftarrow$
7803 \begin_inset space \hfill{}
7807 \begin_inset Tabular
7808 <lyxtabular version="3" rows="8" columns="2">
7809 <features booktabs="true" tabularvalignment="middle">
7810 <column alignment="center" valignment="top" width="0pt">
7811 <column alignment="center" valignment="top" width="0pt">
7813 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7816 \begin_layout Plain Layout
7822 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7825 \begin_layout Plain Layout
7833 <cell alignment="center" valignment="top" usebox="none">
7836 \begin_layout Plain Layout
7844 <cell alignment="center" valignment="top" usebox="none">
7847 \begin_layout Plain Layout
7848 \begin_inset Formula $\to$
7858 <cell alignment="center" valignment="top" usebox="none">
7861 \begin_layout Plain Layout
7869 <cell alignment="center" valignment="top" usebox="none">
7872 \begin_layout Plain Layout
7873 \begin_inset Formula $\Rightarrow$
7883 <cell alignment="center" valignment="top" usebox="none">
7886 \begin_layout Plain Layout
7894 <cell alignment="center" valignment="top" usebox="none">
7897 \begin_layout Plain Layout
7898 \begin_inset Formula $\longrightarrow$
7908 <cell alignment="center" valignment="top" usebox="none">
7911 \begin_layout Plain Layout
7919 <cell alignment="center" valignment="top" usebox="none">
7922 \begin_layout Plain Layout
7923 \begin_inset Formula $\Longrightarrow$
7933 <cell alignment="center" valignment="top" usebox="none">
7936 \begin_layout Plain Layout
7944 <cell alignment="center" valignment="top" usebox="none">
7947 \begin_layout Plain Layout
7948 \begin_inset Formula $\rightharpoonup$
7958 <cell alignment="center" valignment="top" usebox="none">
7961 \begin_layout Plain Layout
7969 <cell alignment="center" valignment="top" usebox="none">
7972 \begin_layout Plain Layout
7973 \begin_inset Formula $\rightharpoondown$
7983 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7986 \begin_layout Plain Layout
7994 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7997 \begin_layout Plain Layout
7998 \begin_inset Formula $\hookrightarrow$
8012 \begin_inset space \hfill{}
8018 \begin_layout Standard
8019 \begin_inset space \hfill{}
8023 \begin_inset Tabular
8024 <lyxtabular version="3" rows="6" columns="2">
8025 <features booktabs="true" tabularvalignment="middle">
8026 <column alignment="center" valignment="top" width="0pt">
8027 <column alignment="center" valignment="top" width="0pt">
8029 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8032 \begin_layout Plain Layout
8038 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8041 \begin_layout Plain Layout
8049 <cell alignment="center" valignment="top" usebox="none">
8052 \begin_layout Plain Layout
8060 <cell alignment="center" valignment="top" usebox="none">
8063 \begin_layout Plain Layout
8064 \begin_inset Formula $\leftrightarrow$
8074 <cell alignment="center" valignment="top" usebox="none">
8077 \begin_layout Plain Layout
8085 <cell alignment="center" valignment="top" usebox="none">
8088 \begin_layout Plain Layout
8089 \begin_inset Formula $\Leftrightarrow$
8099 <cell alignment="center" valignment="top" usebox="none">
8102 \begin_layout Plain Layout
8110 <cell alignment="center" valignment="top" usebox="none">
8113 \begin_layout Plain Layout
8114 \begin_inset Formula $\longleftrightarrow$
8124 <cell alignment="center" valignment="top" usebox="none">
8127 \begin_layout Plain Layout
8135 <cell alignment="center" valignment="top" usebox="none">
8138 \begin_layout Plain Layout
8139 \begin_inset Formula $\Longleftrightarrow$
8149 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8152 \begin_layout Plain Layout
8160 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8163 \begin_layout Plain Layout
8164 \begin_inset Formula $\rightleftharpoons$
8178 \begin_inset space \hspace{}
8183 \begin_inset space \hfill{}
8187 \begin_inset Tabular
8188 <lyxtabular version="3" rows="5" columns="2">
8189 <features booktabs="true" tabularvalignment="middle">
8190 <column alignment="center" valignment="top" width="0pt">
8191 <column alignment="center" valignment="top" width="0pt">
8193 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8196 \begin_layout Plain Layout
8202 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8205 \begin_layout Plain Layout
8213 <cell alignment="center" valignment="top" usebox="none">
8216 \begin_layout Plain Layout
8224 <cell alignment="center" valignment="top" usebox="none">
8227 \begin_layout Plain Layout
8228 \begin_inset Formula $\mapsto$
8238 <cell alignment="center" valignment="top" usebox="none">
8241 \begin_layout Plain Layout
8249 <cell alignment="center" valignment="top" usebox="none">
8252 \begin_layout Plain Layout
8253 \begin_inset Formula $\longmapsto$
8263 <cell alignment="center" valignment="top" usebox="none">
8266 \begin_layout Plain Layout
8274 <cell alignment="center" valignment="top" usebox="none">
8277 \begin_layout Plain Layout
8278 \begin_inset Formula $\leadsto$
8288 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8291 \begin_layout Plain Layout
8299 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8302 \begin_layout Plain Layout
8303 \begin_inset Formula $\dasharrow$
8317 \begin_inset space \hfill{}
8323 \begin_layout Standard
8324 \begin_inset VSpace medskip
8327 Arrows used as accents like e.
8328 \begin_inset space \thinspace{}
8332 \begin_inset space \space{}
8335 vector arrows are listed in
8336 \begin_inset CommandInset ref
8338 reference "sec:Accents"
8345 \begin_layout Standard
8346 \begin_inset VSpace bigskip
8349 Furthermore there are the labeled arrows
8350 \begin_inset Index idx
8353 \begin_layout Plain Layout
8366 \begin_inset Index idx
8369 \begin_layout Plain Layout
8384 \begin_inset Index idx
8387 \begin_layout Plain Layout
8394 \begin_layout Plain Layout
8409 When inserting one of these commands in a formula, an arrow with two blue
8410 boxes appear where the label can be inserted.
8411 The length of the arrow adapts to the label width.
8414 \begin_layout Standard
8416 \begin_inset Tabular
8417 <lyxtabular version="3" rows="3" columns="2">
8418 <features booktabs="true" tabularvalignment="middle">
8419 <column alignment="center" valignment="top" width="0pt">
8420 <column alignment="center" valignment="top" width="0pt">
8422 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8425 \begin_layout Plain Layout
8431 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8434 \begin_layout Plain Layout
8442 <cell alignment="center" valignment="top" usebox="none">
8445 \begin_layout Plain Layout
8449 \begin_inset space \textvisiblespace{}
8453 \begin_inset Formula $\downarrow$
8457 \begin_inset Formula $\to$
8465 <cell alignment="center" valignment="top" usebox="none">
8468 \begin_layout Plain Layout
8469 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8478 <row topspace="2mm">
8479 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8482 \begin_layout Plain Layout
8486 \begin_inset space \textvisiblespace{}
8490 \begin_inset Formula $\downarrow$
8494 \begin_inset Formula $\to$
8502 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8505 \begin_layout Plain Layout
8506 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8522 \begin_layout Standard
8523 \begin_inset VSpace medskip
8529 \begin_layout Standard
8530 If you set in the document settings under
8533 \begin_inset space ~
8543 \begin_inset Index idx
8546 \begin_layout Plain Layout
8547 Packages ! mathtools
8555 \begin_inset space ~
8560 , you have access to the following labeled arrows:
8563 \begin_layout Standard
8564 \begin_inset Newpage newpage
8570 \begin_layout Standard
8572 \begin_inset space \hspace*{\fill}
8576 \begin_inset Tabular
8577 <lyxtabular version="3" rows="7" columns="2">
8578 <features booktabs="true" tabularvalignment="middle">
8579 <column alignment="center" valignment="top" width="0pt">
8580 <column alignment="center" valignment="top" width="0pt">
8582 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8585 \begin_layout Plain Layout
8591 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8594 \begin_layout Plain Layout
8602 <cell alignment="center" valignment="top" usebox="none">
8605 \begin_layout Plain Layout
8625 <cell alignment="center" valignment="top" usebox="none">
8628 \begin_layout Plain Layout
8629 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8638 <row topspace="2mm">
8639 <cell alignment="center" valignment="top" usebox="none">
8642 \begin_layout Plain Layout
8662 <cell alignment="center" valignment="top" usebox="none">
8665 \begin_layout Plain Layout
8666 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8675 <row topspace="2mm">
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 $\xRightarrow[x=a]{x>0}$
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 $\xLeftrightarrow[x=a]{x>0}$
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 $\xhookleftarrow[x=a]{x>0}$
8786 <row topspace="2mm">
8787 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8790 \begin_layout Plain Layout
8810 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8813 \begin_layout Plain Layout
8814 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8828 \begin_inset space \hspace*{\fill}
8832 \begin_inset Tabular
8833 <lyxtabular version="3" rows="7" columns="2">
8834 <features booktabs="true" tabularvalignment="middle">
8835 <column alignment="center" valignment="top" width="0pt">
8836 <column alignment="center" valignment="top" width="0pt">
8838 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8841 \begin_layout Plain Layout
8847 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8850 \begin_layout Plain Layout
8858 <cell alignment="center" valignment="top" usebox="none">
8861 \begin_layout Plain Layout
8881 <cell alignment="center" valignment="top" usebox="none">
8884 \begin_layout Plain Layout
8885 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8894 <row topspace="2mm">
8895 <cell alignment="center" valignment="top" usebox="none">
8898 \begin_layout Plain Layout
8918 <cell alignment="center" valignment="top" usebox="none">
8921 \begin_layout Plain Layout
8922 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8931 <row topspace="2mm">
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 $\xrightharpoondown[x=a]{x>0}$
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 $\xrightharpoonup[x=a]{x>0}$
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 $\xleftrightharpoons[x=a]{x>0}$
9042 <row topspace="2mm">
9043 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9046 \begin_layout Plain Layout
9066 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9069 \begin_layout Plain Layout
9070 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9084 \begin_inset space \hspace*{\fill}
9090 \begin_layout Standard
9091 The command scheme is for all these arrows:
9094 \begin_layout Standard
9096 \begin_inset Tabular
9097 <lyxtabular version="3" rows="2" columns="2">
9098 <features booktabs="true" tabularvalignment="middle">
9099 <column alignment="center" valignment="top" width="0pt">
9100 <column alignment="center" valignment="top" width="0pt">
9102 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9105 \begin_layout Plain Layout
9111 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9114 \begin_layout Plain Layout
9121 <row bottomspace="0.5mm">
9122 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9125 \begin_layout Plain Layout
9128 xleftrightarrow[x=a]
9131 \begin_inset Formula $\to$
9139 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9142 \begin_layout Plain Layout
9143 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9159 \begin_layout Subsection
9160 Vertical and diagonal Arrows
9161 \begin_inset Index idx
9164 \begin_layout Plain Layout
9171 \begin_inset Index idx
9174 \begin_layout Plain Layout
9183 \begin_layout Standard
9184 \begin_inset space \hfill{}
9188 \begin_inset Tabular
9189 <lyxtabular version="3" rows="7" columns="2">
9190 <features booktabs="true" tabularvalignment="middle">
9191 <column alignment="center" valignment="top" width="0pt">
9192 <column alignment="center" valignment="top" width="0pt">
9194 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9197 \begin_layout Plain Layout
9203 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9206 \begin_layout Plain Layout
9214 <cell alignment="center" valignment="top" usebox="none">
9217 \begin_layout Plain Layout
9225 <cell alignment="center" valignment="top" usebox="none">
9228 \begin_layout Plain Layout
9229 \begin_inset Formula $\uparrow$
9239 <cell alignment="center" valignment="top" usebox="none">
9242 \begin_layout Plain Layout
9250 <cell alignment="center" valignment="top" usebox="none">
9253 \begin_layout Plain Layout
9254 \begin_inset Formula $\Uparrow$
9264 <cell alignment="center" valignment="top" usebox="none">
9267 \begin_layout Plain Layout
9275 <cell alignment="center" valignment="top" usebox="none">
9278 \begin_layout Plain Layout
9279 \begin_inset Formula $\updownarrow$
9289 <cell alignment="center" valignment="top" usebox="none">
9292 \begin_layout Plain Layout
9300 <cell alignment="center" valignment="top" usebox="none">
9303 \begin_layout Plain Layout
9304 \begin_inset Formula $\Updownarrow$
9314 <cell alignment="center" valignment="top" usebox="none">
9317 \begin_layout Plain Layout
9325 <cell alignment="center" valignment="top" usebox="none">
9328 \begin_layout Plain Layout
9329 \begin_inset Formula $\Downarrow$
9339 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9342 \begin_layout Plain Layout
9350 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9353 \begin_layout Plain Layout
9354 \begin_inset Formula $\downarrow$
9368 \begin_inset space \hfill{}
9372 \begin_inset Tabular
9373 <lyxtabular version="3" rows="5" columns="2">
9374 <features booktabs="true" tabularvalignment="middle">
9375 <column alignment="center" valignment="top" width="0pt">
9376 <column alignment="center" valignment="top" width="0pt">
9378 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9381 \begin_layout Plain Layout
9387 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9390 \begin_layout Plain Layout
9398 <cell alignment="center" valignment="top" usebox="none">
9401 \begin_layout Plain Layout
9409 <cell alignment="center" valignment="top" usebox="none">
9412 \begin_layout Plain Layout
9413 \begin_inset Formula $\nearrow$
9423 <cell alignment="center" valignment="top" usebox="none">
9426 \begin_layout Plain Layout
9434 <cell alignment="center" valignment="top" usebox="none">
9437 \begin_layout Plain Layout
9438 \begin_inset Formula $\searrow$
9448 <cell alignment="center" valignment="top" usebox="none">
9451 \begin_layout Plain Layout
9459 <cell alignment="center" valignment="top" usebox="none">
9462 \begin_layout Plain Layout
9463 \begin_inset Formula $\swarrow$
9473 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9476 \begin_layout Plain Layout
9484 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9487 \begin_layout Plain Layout
9488 \begin_inset Formula $\nwarrow$
9502 \begin_inset space \hfill{}
9508 \begin_layout Standard
9509 \begin_inset VSpace medskip
9512 Vertical arrows can be used also as delimiters together with the commands
9514 \begin_inset CommandInset ref
9516 reference "subsec:Manual-Bracket-Size"
9521 \begin_inset CommandInset ref
9523 reference "subsec:Automatic-Bracket-Size"
9530 \begin_layout Section
9532 \begin_inset CommandInset label
9539 \begin_inset Index idx
9542 \begin_layout Plain Layout
9551 \begin_layout Standard
9552 Accents can be inserted via the math toolbar button
9555 arg "math-insert \\hat"
9558 or the commands listed in the following subsections.
9561 \begin_layout Subsection
9562 Accents for one Character
9566 \begin_layout Plain Layout
9579 \begin_layout Plain Layout
9581 \begin_inset CommandInset ref
9583 reference "subsec:Accents-in-Text"
9596 \begin_layout Plain Layout
9604 \begin_inset Note Note
9607 \begin_layout Plain Layout
9614 is used to avoid that the footnote appears in the PDF-bookmark.
9617 \begin_layout Plain Layout
9625 \begin_inset CommandInset ref
9627 reference "subsec:Formulas-in-Section"
9637 \begin_inset CommandInset label
9639 name "subsec:Accents-for-one"
9644 \begin_inset Index idx
9647 \begin_layout Plain Layout
9648 Accents ! for one character
9656 \begin_layout Standard
9657 \begin_inset space \hfill{}
9661 \begin_inset Tabular
9662 <lyxtabular version="3" rows="8" columns="2">
9663 <features booktabs="true" tabularvalignment="middle">
9664 <column alignment="center" valignment="top" width="0pt">
9665 <column alignment="center" valignment="top" width="0pt">
9667 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9670 \begin_layout Plain Layout
9676 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9679 \begin_layout Plain Layout
9686 <row topspace="1.5mm">
9687 <cell alignment="center" valignment="top" usebox="none">
9690 \begin_layout Plain Layout
9694 \begin_inset space \textvisiblespace{}
9702 <cell alignment="center" valignment="top" usebox="none">
9705 \begin_layout Plain Layout
9706 \begin_inset Formula $\dot{A}$
9715 <row topspace="1.5mm">
9716 <cell alignment="center" valignment="top" usebox="none">
9719 \begin_layout Plain Layout
9723 \begin_inset space \textvisiblespace{}
9731 <cell alignment="center" valignment="top" usebox="none">
9734 \begin_layout Plain Layout
9735 \begin_inset Formula $\ddot{A}$
9744 <row topspace="1.5mm">
9745 <cell alignment="center" valignment="top" usebox="none">
9748 \begin_layout Plain Layout
9752 \begin_inset space \textvisiblespace{}
9760 <cell alignment="center" valignment="top" usebox="none">
9763 \begin_layout Plain Layout
9764 \begin_inset Formula $\dddot{A}$
9773 <row topspace="1.5mm">
9774 <cell alignment="center" valignment="top" usebox="none">
9777 \begin_layout Plain Layout
9781 \begin_inset space \textvisiblespace{}
9789 <cell alignment="center" valignment="top" usebox="none">
9792 \begin_layout Plain Layout
9793 \begin_inset Formula $\ddddot{A}$
9802 <row topspace="1.5mm">
9803 <cell alignment="center" valignment="top" usebox="none">
9806 \begin_layout Plain Layout
9810 \begin_inset space \textvisiblespace{}
9814 \begin_inset Index idx
9817 \begin_layout Plain Layout
9828 <cell alignment="center" valignment="top" usebox="none">
9831 \begin_layout Plain Layout
9832 \begin_inset Formula $\vec{A}$
9841 <row topspace="1.5mm">
9842 <cell alignment="center" valignment="top" usebox="none">
9845 \begin_layout Plain Layout
9849 \begin_inset space \textvisiblespace{}
9857 <cell alignment="center" valignment="top" usebox="none">
9860 \begin_layout Plain Layout
9861 \begin_inset Formula $\bar{A}$
9870 <row topspace="1.5mm">
9871 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9874 \begin_layout Plain Layout
9878 \begin_inset space \textvisiblespace{}
9886 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9889 \begin_layout Plain Layout
9890 \begin_inset Formula $\mathring{A}$
9904 \begin_inset space \hfill{}
9908 \begin_inset Tabular
9909 <lyxtabular version="3" rows="7" columns="2">
9910 <features booktabs="true" tabularvalignment="middle">
9911 <column alignment="center" valignment="top" width="0pt">
9912 <column alignment="center" valignment="top" width="0pt">
9914 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9917 \begin_layout Plain Layout
9923 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9926 \begin_layout Plain Layout
9933 <row topspace="1.5mm">
9934 <cell alignment="center" valignment="top" usebox="none">
9937 \begin_layout Plain Layout
9941 \begin_inset space \textvisiblespace{}
9949 <cell alignment="center" valignment="top" usebox="none">
9952 \begin_layout Plain Layout
9953 \begin_inset Formula $\tilde{A}$
9962 <row topspace="1.5mm">
9963 <cell alignment="center" valignment="top" usebox="none">
9966 \begin_layout Plain Layout
9970 \begin_inset space \textvisiblespace{}
9978 <cell alignment="center" valignment="top" usebox="none">
9981 \begin_layout Plain Layout
9982 \begin_inset Formula $\hat{A}$
9991 <row topspace="1.5mm">
9992 <cell alignment="center" valignment="top" usebox="none">
9995 \begin_layout Plain Layout
9999 \begin_inset space \textvisiblespace{}
10007 <cell alignment="center" valignment="top" usebox="none">
10010 \begin_layout Plain Layout
10011 \begin_inset Formula $\check{A}$
10020 <row topspace="1.5mm">
10021 <cell alignment="center" valignment="top" usebox="none">
10024 \begin_layout Plain Layout
10028 \begin_inset space \textvisiblespace{}
10036 <cell alignment="center" valignment="top" usebox="none">
10039 \begin_layout Plain Layout
10040 \begin_inset Formula $\acute{A}$
10049 <row topspace="1.5mm">
10050 <cell alignment="center" valignment="top" usebox="none">
10053 \begin_layout Plain Layout
10057 \begin_inset space \textvisiblespace{}
10065 <cell alignment="center" valignment="top" usebox="none">
10068 \begin_layout Plain Layout
10069 \begin_inset Formula $\grave{A}$
10078 <row topspace="1.5mm">
10079 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10082 \begin_layout Plain Layout
10086 \begin_inset space \textvisiblespace{}
10094 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10097 \begin_layout Plain Layout
10098 \begin_inset Formula $\breve{A}$
10112 \begin_inset space \hfill{}
10118 \begin_layout Standard
10119 \begin_inset VSpace bigskip
10125 \begin_layout Standard
10126 You can directly insert accents like é to formulas.
10128 will transform them to the corresponding accent command.
10130 \begin_inset Index idx
10133 \begin_layout Plain Layout
10139 it is better to insert a quotation mark before the vowel.
10140 These two characters are then treated by \SpecialChar LaTeX
10145 character when the formula part with the umlaut is marked as German.
10153 \begin_inset Quotes eld
10157 \begin_inset Quotes erd
10160 umlauts are created as demonstrated in the following example:
10163 \begin_layout Standard
10164 \begin_inset VSpace -2mm
10170 \begin_layout Standard
10172 \begin_inset Tabular
10173 <lyxtabular version="3" rows="3" columns="2">
10174 <features booktabs="true" tabularvalignment="middle">
10175 <column alignment="center" valignment="top" width="0pt">
10176 <column alignment="center" valignment="top">
10178 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10181 \begin_layout Plain Layout
10187 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10190 \begin_layout Plain Layout
10198 <cell alignment="center" valignment="top" usebox="none">
10201 \begin_layout Plain Layout
10202 \begin_inset Quotes grd
10210 <cell alignment="center" valignment="top" usebox="none">
10213 \begin_layout Plain Layout
10214 \begin_inset space \hspace{}
10221 \begin_inset Formula $"i$
10230 <row topspace="1.5mm">
10231 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10234 \begin_layout Plain Layout
10238 \begin_inset space \textvisiblespace{}
10246 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10249 \begin_layout Plain Layout
10250 \begin_inset Formula $\ddot{i}$
10266 \begin_layout Standard
10267 Another advantage to
10273 is that umlauts can directly be converted to mathematical text because
10274 the accent commands above are
10280 in mathematical text
10283 To convert an accented character to mathematical text, only the character
10284 under the accent may be converted.
10285 This applies also for all other conversions, e.
10286 \begin_inset space \thinspace{}
10290 \begin_inset space \space{}
10296 \begin_layout Standard
10297 In mathematical text, umlauts and other accented characters can directly
10301 \begin_layout Standard
10302 \begin_inset VSpace bigskip
10308 \begin_layout Standard
10310 also supports a tilde under the character if the \SpecialChar LaTeX
10316 \begin_inset Index idx
10319 \begin_layout Plain Layout
10320 Packages ! undertilde
10325 is installed on your system:
10328 \begin_layout Standard
10332 \begin_layout Plain Layout
10342 \begin_inset Note Note
10345 \begin_layout Plain Layout
10346 The following table will only be displayed when the \SpecialChar LaTeX
10359 \begin_layout Standard
10362 \begin_inset Tabular
10363 <lyxtabular version="3" rows="2" columns="2">
10364 <features booktabs="true" tabularvalignment="middle">
10365 <column alignment="center" valignment="top" width="0pt">
10366 <column alignment="center" valignment="top" width="0pt">
10368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10371 \begin_layout Plain Layout
10377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10380 \begin_layout Plain Layout
10388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10391 \begin_layout Plain Layout
10395 \begin_inset space \textvisiblespace{}
10403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10406 \begin_layout Plain Layout
10407 \begin_inset Formula $\utilde{A}$
10423 \begin_layout Standard
10427 \begin_layout Plain Layout
10437 \begin_inset Note Note
10440 \begin_layout Plain Layout
10441 The following will be displayed when the \SpecialChar LaTeX
10454 \begin_layout Standard
10455 You need to install the \SpecialChar LaTeX
10460 to see the rest of this subsection in the output.
10463 \begin_layout Standard
10467 \begin_layout Plain Layout
10479 \begin_layout Standard
10480 \begin_inset Newpage newpage
10486 \begin_layout Subsection
10487 Accents for several Characters
10488 \begin_inset Index idx
10491 \begin_layout Plain Layout
10492 Accents ! for several characters
10500 \begin_layout Standard
10501 \begin_inset space \hfill{}
10505 \begin_inset Tabular
10506 <lyxtabular version="3" rows="5" columns="2">
10507 <features booktabs="true" tabularvalignment="middle">
10508 <column alignment="center" valignment="top" width="0pt">
10509 <column alignment="center" valignment="top" width="0pt">
10511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10514 \begin_layout Plain Layout
10520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10523 \begin_layout Plain Layout
10530 <row topspace="1.5mm">
10531 <cell alignment="center" valignment="top" usebox="none">
10534 \begin_layout Plain Layout
10538 \begin_inset space \textvisiblespace{}
10546 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10549 \begin_layout Plain Layout
10550 \begin_inset Formula $\overleftarrow{A=B}$
10559 <row topspace="1.5mm">
10560 <cell alignment="center" valignment="top" usebox="none">
10563 \begin_layout Plain Layout
10567 \begin_inset space \textvisiblespace{}
10575 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10578 \begin_layout Plain Layout
10579 \begin_inset Formula $\underleftarrow{A=B}$
10588 <row topspace="1.5mm">
10589 <cell alignment="center" valignment="top" usebox="none">
10592 \begin_layout Plain Layout
10596 \begin_inset space \textvisiblespace{}
10604 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10607 \begin_layout Plain Layout
10608 \begin_inset Formula $\overleftrightarrow{A=B}$
10617 <row topspace="1.5mm" bottomspace="1mm">
10618 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10621 \begin_layout Plain Layout
10624 underleftrightarrow
10625 \begin_inset space \textvisiblespace{}
10633 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10636 \begin_layout Plain Layout
10637 \begin_inset Formula $\underleftrightarrow{A=B}$
10651 \begin_inset space \hfill{}
10655 \begin_inset Tabular
10656 <lyxtabular version="3" rows="5" columns="2">
10657 <features booktabs="true" tabularvalignment="middle">
10658 <column alignment="center" valignment="top" width="0pt">
10659 <column alignment="center" valignment="top" width="0pt">
10661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10664 \begin_layout Plain Layout
10670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10673 \begin_layout Plain Layout
10680 <row topspace="1.5mm">
10681 <cell alignment="center" valignment="top" usebox="none">
10684 \begin_layout Plain Layout
10688 \begin_inset space \textvisiblespace{}
10696 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10699 \begin_layout Plain Layout
10700 \begin_inset Formula $\overrightarrow{A=B}$
10709 <row topspace="1.5mm">
10710 <cell alignment="center" valignment="top" usebox="none">
10713 \begin_layout Plain Layout
10717 \begin_inset space \textvisiblespace{}
10725 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10728 \begin_layout Plain Layout
10729 \begin_inset Formula $\underrightarrow{A=B}$
10738 <row topspace="1.5mm">
10739 <cell alignment="center" valignment="top" usebox="none">
10742 \begin_layout Plain Layout
10746 \begin_inset space \textvisiblespace{}
10754 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10757 \begin_layout Plain Layout
10758 \begin_inset Formula $\widetilde{A=B}$
10767 <row topspace="1.5mm" bottomspace="1mm">
10768 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10771 \begin_layout Plain Layout
10775 \begin_inset space \textvisiblespace{}
10783 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10786 \begin_layout Plain Layout
10787 \begin_inset Formula $\widehat{A=B}$
10801 \begin_inset space \hfill{}
10807 \begin_layout Standard
10808 \begin_inset VSpace medskip
10811 With these commands as many characters as you like can be accented.
10824 will only be set in the output with a length of three characters, as shown
10825 in the following example:
10826 \begin_inset Formula
10828 \widetilde{A+B=C-D}
10836 \begin_layout Standard
10844 \begin_inset Index idx
10847 \begin_layout Plain Layout
10862 \begin_inset Index idx
10865 \begin_layout Plain Layout
10873 described in the previous subsection it is also possible to accent several
10880 \begin_inset space \textvisiblespace{}
10884 \begin_inset Formula $\downarrow$
10890 \begin_inset Formula
10892 \underset{***}{A=B}
10900 \begin_layout Section
10902 \begin_inset CommandInset label
10904 name "subsec:Space"
10909 \begin_inset Index idx
10912 \begin_layout Plain Layout
10921 \begin_layout Subsection
10923 \begin_inset CommandInset label
10925 name "subsec:Predefined-Space"
10930 \begin_inset Index idx
10933 \begin_layout Plain Layout
10934 Space ! horizontal ! predefined
10942 \begin_layout Standard
10943 Sometimes it is necessary to insert horizontal space into a formula.
10944 This is done by inserting a protected space (shortcut
10947 arg "command-alternatives space-insert protected ; math-space"
10952 \begin_inset Quotes eld
10958 \begin_inset space \textvisiblespace{}
10964 \begin_inset Quotes erd
10967 appears and by pressing
10971 several times one can select one of eight different space sizes.
10972 The spaces can also be inserted using the math toolbar button
10975 arg "math-insert \\space"
10978 or special commands.
10979 Independent from the inserted command, one can select the size again by
10987 \begin_layout Standard
10990 \begin_inset Tabular
10991 <lyxtabular version="3" rows="6" columns="3">
10992 <features booktabs="true" tabularvalignment="middle">
10993 <column alignment="center" valignment="top">
10994 <column alignment="center" valignment="top" width="15col%">
10995 <column alignment="center" valignment="top">
10997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11000 \begin_layout Plain Layout
11006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11009 \begin_layout Plain Layout
11019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11022 \begin_layout Plain Layout
11030 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11033 \begin_layout Plain Layout
11041 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11044 \begin_layout Plain Layout
11050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11053 \begin_layout Plain Layout
11054 \begin_inset Formula $A\,B$
11064 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11067 \begin_layout Plain Layout
11075 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11078 \begin_layout Plain Layout
11084 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11087 \begin_layout Plain Layout
11088 \begin_inset Formula $A\:B$
11098 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11101 \begin_layout Plain Layout
11109 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11112 \begin_layout Plain Layout
11118 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11121 \begin_layout Plain Layout
11122 \begin_inset Formula $A\;B$
11132 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11135 \begin_layout Plain Layout
11143 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11146 \begin_layout Plain Layout
11152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11155 \begin_layout Plain Layout
11156 \begin_inset Formula $A\quad B$
11166 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11169 \begin_layout Plain Layout
11177 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11180 \begin_layout Plain Layout
11186 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11189 \begin_layout Plain Layout
11190 \begin_inset Formula $A\qquad B$
11204 \begin_inset space \hfill{}
11208 \begin_inset Tabular
11209 <lyxtabular version="3" rows="6" columns="3">
11210 <features booktabs="true" tabularvalignment="middle">
11211 <column alignment="center" valignment="top">
11212 <column alignment="center" valignment="top" width="15col%">
11213 <column alignment="center" valignment="top">
11215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11218 \begin_layout Plain Layout
11224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11227 \begin_layout Plain Layout
11237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11240 \begin_layout Plain Layout
11248 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11251 \begin_layout Plain Layout
11259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11262 \begin_layout Plain Layout
11268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11271 \begin_layout Plain Layout
11272 \begin_inset Formula $A\hfill B$
11282 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11285 \begin_layout Plain Layout
11293 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11296 \begin_layout Plain Layout
11302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11305 \begin_layout Plain Layout
11306 \begin_inset Formula $A\hspace*{1em}B$
11316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11319 \begin_layout Plain Layout
11327 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11330 \begin_layout Plain Layout
11336 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11339 \begin_layout Plain Layout
11340 \begin_inset Formula $A\hspace{1em}B$
11350 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11353 \begin_layout Plain Layout
11357 \begin_inset space \textvisiblespace{}
11365 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11368 \begin_layout Plain Layout
11374 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11377 \begin_layout Plain Layout
11378 \begin_inset Formula $A\ B$
11388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11391 \begin_layout Plain Layout
11399 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11402 \begin_layout Plain Layout
11408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11411 \begin_layout Plain Layout
11412 \begin_inset Formula $A\!B$
11428 \begin_layout Standard
11430 \begin_inset space ~
11434 \begin_inset space \thinspace{}
11438 \begin_inset space \thinspace{}
11441 7 are variable spaces which are explained in
11442 \begin_inset CommandInset ref
11444 reference "subsec:Variable-Space"
11450 \begin_inset space ~
11453 9 seems to produce no space.
11454 It is displayed red in \SpecialChar LyX
11455 contrary to the other sizes, because it is a negative
11457 There are two more negative spaces:
11460 \begin_layout Standard
11462 \begin_inset Tabular
11463 <lyxtabular version="3" rows="3" columns="3">
11464 <features booktabs="true" tabularvalignment="middle">
11465 <column alignment="center" valignment="middle" width="6.8cm">
11466 <column alignment="center" valignment="top" width="0pt">
11467 <column alignment="center" valignment="top" width="0pt">
11469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11472 \begin_layout Plain Layout
11478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11481 \begin_layout Plain Layout
11489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11492 \begin_layout Plain Layout
11502 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11505 \begin_layout Plain Layout
11510 keystrokes after inserting the protected space
11515 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11518 \begin_layout Plain Layout
11524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11527 \begin_layout Plain Layout
11535 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11538 \begin_layout Plain Layout
11544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11547 \begin_layout Plain Layout
11548 \begin_inset Formula $A\negmedspace B$
11556 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11559 \begin_layout Plain Layout
11560 \begin_inset Formula $A\negthickspace B$
11576 \begin_layout Standard
11577 Negative spaces can lead to characters overlapping each other.
11578 Thus they can be used to enforce ligatures, which are e.
11579 \begin_inset space \thinspace{}
11583 \begin_inset space \space{}
11586 useful for summation operators:
11589 \begin_layout Standard
11591 \begin_inset Tabular
11592 <lyxtabular version="3" rows="3" columns="2">
11593 <features booktabs="true" tabularvalignment="middle">
11594 <column alignment="center" valignment="top" width="0pt">
11595 <column alignment="center" valignment="top">
11597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11600 \begin_layout Plain Layout
11606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11609 \begin_layout Plain Layout
11617 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11620 \begin_layout Plain Layout
11626 \begin_inset space \textvisiblespace{}
11634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11637 \begin_layout Plain Layout
11638 \begin_inset Formula $\sum\sum f_{kl}$
11648 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11651 \begin_layout Plain Layout
11659 \begin_inset space \textvisiblespace{}
11667 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11670 \begin_layout Plain Layout
11671 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11687 \begin_layout Standard
11689 \begin_inset VSpace medskip
11695 \begin_layout Standard
11697 Relations like for example equal signs, are always surrounded by space.
11698 To suppress this, the equal sign is placed into a \SpecialChar TeX
11700 The following example demonstrates this:
11703 \begin_layout Standard
11705 \begin_inset Tabular
11706 <lyxtabular version="3" rows="2" columns="2">
11707 <features tabularvalignment="middle">
11708 <column alignment="center" valignment="top" width="0pt">
11709 <column alignment="center" valignment="top" width="0pt">
11711 <cell alignment="center" valignment="top" usebox="none">
11714 \begin_layout Plain Layout
11720 <cell alignment="center" valignment="top" usebox="none">
11723 \begin_layout Plain Layout
11724 \begin_inset Formula $A=B$
11734 <cell alignment="center" valignment="top" usebox="none">
11737 \begin_layout Plain Layout
11738 equation without space
11743 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11746 \begin_layout Plain Layout
11747 \begin_inset Formula $A{=}B$
11763 \begin_layout Standard
11765 The command for the last formula is:
11770 \begin_inset Formula $\to$
11776 \begin_layout Standard
11777 \begin_inset VSpace bigskip
11783 \begin_layout Standard
11784 Spaces are needed for physical units, because the space between the value
11785 and the unit is the smallest one and not a normal space.
11786 For units in text, the smallest space is inserted via the menu
11788 Insert\SpecialChar menuseparator
11789 Formatting\SpecialChar menuseparator
11791 \begin_inset space ~
11799 arg "space-insert thin"
11805 \begin_layout Standard
11806 An example to visualize the difference:
11809 \begin_layout Standard
11810 \begin_inset Tabular
11811 <lyxtabular version="3" rows="2" columns="2">
11812 <features tabularvalignment="middle">
11813 <column alignment="left" valignment="top">
11814 <column alignment="left" valignment="top">
11816 <cell alignment="center" valignment="top" usebox="none">
11819 \begin_layout Plain Layout
11821 \begin_inset Formula $\cdot$
11829 <cell alignment="center" valignment="top" usebox="none">
11832 \begin_layout Plain Layout
11833 space between value and unit
11840 <cell alignment="center" valignment="top" usebox="none">
11843 \begin_layout Plain Layout
11845 \begin_inset space \thinspace{}
11849 \begin_inset Formula $\cdot$
11857 <cell alignment="center" valignment="top" usebox="none">
11860 \begin_layout Plain Layout
11861 smallest space between value and unit
11874 \begin_layout Subsection
11879 \begin_layout Plain Layout
11892 \begin_layout Plain Layout
11893 for vertical space in formulas see
11894 \begin_inset CommandInset ref
11896 reference "subsec:Line-Separation"
11909 \begin_layout Plain Layout
11917 \begin_inset Note Note
11920 \begin_layout Plain Layout
11923 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11926 \begin_layout Plain Layout
11929 texorpdfstring is in section
11930 \begin_inset CommandInset ref
11932 reference "subsec:Formulas-in-Section"
11942 \begin_inset CommandInset label
11944 name "subsec:Variable-Space"
11949 \begin_inset Index idx
11952 \begin_layout Plain Layout
11953 Space ! horizontal ! variable
11961 \begin_layout Standard
11962 Space with a defined length can be inserted with the command
11969 \begin_inset Index idx
11972 \begin_layout Plain Layout
11982 \begin_inset Quotes eld
11988 \begin_inset space \textvisiblespace{}
11994 \begin_inset Quotes erd
11998 The length can be specified by left-clicking on the
11999 \begin_inset Quotes eld
12005 \begin_inset space \textvisiblespace{}
12011 \begin_inset Quotes erd
12015 The length may also be negative.
12016 When a space would be the first character in a line it would be omitted.
12017 To force its output use the command
12029 or left-click on the
12030 \begin_inset Quotes eld
12036 \begin_inset space \textvisiblespace{}
12042 \begin_inset Quotes erd
12045 and check the option
12050 \begin_inset Newline newline
12053 To insert as much space as is available, the command
12060 \begin_inset Index idx
12063 \begin_layout Plain Layout
12074 \begin_layout Standard
12076 \begin_inset Tabular
12077 <lyxtabular version="3" rows="4" columns="2">
12078 <features booktabs="true" tabularvalignment="middle">
12079 <column alignment="center" valignment="top" width="0pt">
12080 <column alignment="center" valignment="top">
12082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12085 \begin_layout Plain Layout
12093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12096 \begin_layout Plain Layout
12104 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12107 \begin_layout Plain Layout
12111 \begin_inset space \textvisiblespace{}
12117 \begin_inset space \thinspace{}
12125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12128 \begin_layout Plain Layout
12129 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12139 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12142 \begin_layout Plain Layout
12146 \begin_inset space \textvisiblespace{}
12152 \begin_inset space \thinspace{}
12160 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12163 \begin_layout Plain Layout
12164 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12177 \begin_layout Plain Layout
12181 \begin_inset space \textvisiblespace{}
12189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12192 \begin_layout Plain Layout
12193 \begin_inset Formula $A=A\hfill B=B$
12209 \begin_layout Standard
12210 In the last example the available space is given by the longest column entry
12212 In an inline formula the space depends on the length of the line in which
12220 Thus, when the line uses the full width, no space will be created.
12227 only has an effect on displayed formulas when the formula style
12232 (Formula styles are explained in
12233 \begin_inset CommandInset ref
12235 reference "sec:Formula-Styles"
12242 \begin_layout Standard
12249 , there are the commands
12261 that fill the space with a pattern, see
12262 \begin_inset CommandInset ref
12264 reference "subsec:Ellipses"
12271 \begin_layout Standard
12272 For text, variable space can be inserted via the menu
12274 Insert\SpecialChar menuseparator
12275 Formatting\SpecialChar menuseparator
12277 \begin_inset space ~
12285 \begin_layout Standard
12286 This is a line with
12287 \begin_inset space \hspace{}
12292 \begin_inset space \thinspace{}
12298 \begin_layout Standard
12299 This is a line with
12300 \begin_inset space \hfill{}
12306 \begin_layout Subsection
12307 Space besides inline Formulas
12308 \begin_inset Index idx
12311 \begin_layout Plain Layout
12312 Space ! besides inline formulas
12320 \begin_layout Standard
12321 The space that surrounds inline formulas can be adjusted with the length
12329 \begin_inset Index idx
12332 \begin_layout Plain Layout
12341 The value of a length is set with the command
12348 \begin_inset Index idx
12351 \begin_layout Plain Layout
12359 which has the following scheme:
12362 \begin_layout Standard
12367 setlength{length name}{value}
12370 \begin_layout Standard
12378 \begin_inset space \thinspace{}
12384 \begin_layout Standard
12394 \begin_layout Standard
12395 is inserted in \SpecialChar TeX
12398 \begin_inset space \thinspace{}
12401 mm space will now be set around all inline formulas:
12405 \begin_layout Plain Layout
12419 \begin_layout Standard
12420 This is a line with an inline formula
12421 \begin_inset Formula $A=B$
12425 \begin_inset space \thinspace{}
12428 mm surrounding space.
12432 \begin_layout Plain Layout
12446 \begin_layout Standard
12447 To return to the predefined value,
12453 is set to the value 0
12454 \begin_inset space \thinspace{}
12460 \begin_layout Standard
12461 \begin_inset Newpage newpage
12467 \begin_layout Section
12469 \begin_inset Index idx
12472 \begin_layout Plain Layout
12479 \begin_inset Index idx
12482 \begin_layout Plain Layout
12487 \begin_layout Plain Layout
12498 \begin_layout Plain Layout
12513 \begin_layout Standard
12514 Boxes for text are described in chapter
12521 \begin_inset space ~
12529 \begin_layout Subsection
12531 \begin_inset CommandInset label
12533 name "subsec:Boxes-with-Frame"
12538 \begin_inset Index idx
12541 \begin_layout Plain Layout
12550 \begin_layout Standard
12551 It is possible to frame a formula or part of one with the commands
12558 \begin_inset Index idx
12561 \begin_layout Plain Layout
12576 \begin_inset Index idx
12579 \begin_layout Plain Layout
12590 \begin_layout Standard
12591 When one of these commands is inserted in a formula, a blue box appears
12592 within a frame to enter formula parts.
12599 an additional formula has to be created by
12603 within this box, because the box content will otherwise be treated as mathemati
12611 is used, a new formula is automatically created inside the frame.
12614 \begin_layout Standard
12621 is not suitable to frame displayed formulas because the formula will always
12622 be set in the size of the text.
12629 is in contrary not suitable to frame inline formulas, because the formula
12630 will always be set in the size of a displayed formula.
12633 \begin_layout Standard
12647 \begin_inset Index idx
12650 \begin_layout Plain Layout
12658 where additionally the frame width and the alignment can be specified.
12665 is used in the following scheme:
12668 \begin_layout Standard
12673 framebox[frame width][position]{box content}
12676 \begin_layout Standard
12677 The position can either be
12694 right aligns the formula in the box.
12695 When no position is given, the formula will be centered.
12696 \begin_inset Newline newline
12699 If no width is given, also no position can be given.
12700 In this case the frame width is adjusted to the box content like for
12709 \begin_layout Standard
12716 is inserted, a box appears containing three blue boxes.
12717 The first two boxes are surrounded by brackets and denote the two optional
12719 The third box is for formula parts like for
12728 \begin_layout Standard
12730 \begin_inset Tabular
12731 <lyxtabular version="3" rows="5" columns="2">
12732 <features booktabs="true" tabularvalignment="middle">
12733 <column alignment="center" valignment="top" width="0pt">
12734 <column alignment="center" valignment="top">
12736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12739 \begin_layout Plain Layout
12745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12748 \begin_layout Plain Layout
12755 <row topspace="1.5mm">
12756 <cell alignment="center" valignment="top" usebox="none">
12759 \begin_layout Plain Layout
12763 \begin_inset space \textvisiblespace{}
12773 \begin_inset space \textvisiblespace{}
12781 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12784 \begin_layout Plain Layout
12785 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12794 <row topspace="1.5mm">
12795 <cell alignment="center" valignment="top" usebox="none">
12798 \begin_layout Plain Layout
12802 \begin_inset space \textvisiblespace{}
12808 \begin_inset space \textvisiblespace{}
12816 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12819 \begin_layout Plain Layout
12820 \begin_inset Formula $\boxed{\int A=B}$
12829 <row topspace="1.5mm">
12830 <cell alignment="center" valignment="top" usebox="none">
12833 \begin_layout Plain Layout
12837 \begin_inset space \textvisiblespace{}
12845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12848 \begin_layout Plain Layout
12849 \begin_inset Formula $A+\fbox{B}$
12858 <row topspace="1.5mm" bottomspace="1mm">
12859 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12862 \begin_layout Plain Layout
12866 \begin_inset space \textvisiblespace{}
12870 \begin_inset Formula $\to$
12874 \begin_inset Formula $\to$
12884 \begin_inset space \textvisiblespace{}
12888 \begin_inset Formula $\downarrow$
12896 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12899 \begin_layout Plain Layout
12900 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12916 \begin_layout Standard
12917 The frame thickness can also be adjusted.
12918 To do this the following commands have to be inserted in \SpecialChar TeX
12923 \begin_layout Standard
12933 \begin_inset Quotes eld
12937 \begin_inset Quotes erd
12951 \begin_inset Quotes eld
12955 \begin_inset Quotes erd
12961 \begin_layout Standard
12962 \begin_inset Quotes eld
12966 \begin_inset Quotes erd
12969 specifies the minimal distance between the frame and the first character
12971 An example for this is the following framed formula:
12975 \begin_layout Plain Layout
12987 \begin_inset Formula
12994 Before this formula the commands
12997 \begin_layout Standard
13019 \begin_layout Standard
13020 were inserted in \SpecialChar TeX
13022 The given values are used for all following boxes.
13025 \begin_layout Standard
13026 To return to the standard frame size, the command
13029 \begin_layout Standard
13054 \begin_layout Plain Layout
13068 \begin_layout Standard
13069 is inserted in \SpecialChar TeX
13070 mode before the next formula.
13073 \begin_layout Subsection
13074 Boxes without Frame
13075 \begin_inset CommandInset label
13077 name "subsec:Boxes-without-Frame"
13082 \begin_inset Index idx
13085 \begin_layout Plain Layout
13086 Boxes ! without frame
13094 \begin_layout Standard
13095 For boxes without a frame there are the following box commands:
13102 \begin_inset Index idx
13105 \begin_layout Plain Layout
13120 \begin_inset Index idx
13123 \begin_layout Plain Layout
13138 \begin_inset Index idx
13141 \begin_layout Plain Layout
13152 \begin_layout Standard
13159 a box can be super- or subscripted.
13160 But in contrary to normal super- and subscripting, the characters in the
13161 box keep their font size.
13168 is used in the following scheme:
13171 \begin_layout Standard
13176 raisebox{height}{box content}
13179 \begin_layout Standard
13180 When the box should contain a formula, an extra formula is needed like for
13191 \begin_inset Note Greyedout
13194 \begin_layout Plain Layout
13205 this extra formula is created by pressing
13209 twice instead of once because \SpecialChar LyX
13210 doesn't yet support
13224 \begin_layout Standard
13226 \begin_inset Tabular
13227 <lyxtabular version="3" rows="4" columns="2">
13228 <features booktabs="true" tabularvalignment="middle">
13229 <column alignment="center" valignment="top" width="0pt">
13230 <column alignment="center" valignment="top">
13232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13235 \begin_layout Plain Layout
13241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13244 \begin_layout Plain Layout
13252 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13255 \begin_layout Plain Layout
13259 \begin_inset Formula $\to$
13265 \begin_inset Formula $\to$
13273 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13276 \begin_layout Plain Layout
13277 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13290 \begin_layout Plain Layout
13294 \begin_inset Formula $\to$
13300 \begin_inset Formula $\to$
13308 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13311 \begin_layout Plain Layout
13312 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13325 \begin_layout Plain Layout
13329 \begin_inset Formula $\to$
13345 \begin_inset space \textvisiblespace{}
13353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13356 \begin_layout Plain Layout
13357 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13373 \begin_layout Standard
13398 , with the difference that there is no frame.
13401 \begin_layout Subsection
13403 \begin_inset CommandInset label
13405 name "subsec:Colored-Boxes"
13410 \begin_inset Index idx
13413 \begin_layout Plain Layout
13422 \begin_layout Standard
13423 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13432 \begin_layout Plain Layout
13433 The \SpecialChar LaTeX
13438 is part of every \SpecialChar LaTeX
13439 standard installation.
13445 \begin_inset Index idx
13448 \begin_layout Plain Layout
13454 has to be loaded in the \SpecialChar LaTeX
13455 -preamble with the line
13459 \begin_layout Plain Layout
13460 When text is colored somewhere in the document with a predefined color,
13462 loads the \SpecialChar LaTeX
13468 Thus it is possible that the package is loaded twice, but this does not
13475 \begin_inset Note Note
13478 \begin_layout Plain Layout
13479 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13488 \begin_layout Standard
13496 \begin_layout Standard
13497 \begin_inset VSpace medskip
13500 To color boxes, the command
13507 \begin_inset Index idx
13510 \begin_layout Plain Layout
13518 is used in the following scheme:
13521 \begin_layout Standard
13526 colorbox{color}{box content}
13529 \begin_layout Standard
13530 The box content can also be a box and a
13536 can also be part of another box (see the 2nd and 3rd example).
13537 When the box should contain a formula, an extra formula has to be created,
13538 the same way as for
13548 \begin_layout Plain Layout
13549 This also applies for the command
13563 \begin_layout Standard
13564 One of the following predefined colors can be chosen:
13567 \begin_layout Standard
13601 \begin_layout Standard
13603 \begin_inset Tabular
13604 <lyxtabular version="3" rows="4" columns="2">
13605 <features booktabs="true" tabularvalignment="middle">
13606 <column alignment="center" valignment="top" width="0pt">
13607 <column alignment="center" valignment="top">
13609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13612 \begin_layout Plain Layout
13618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13621 \begin_layout Plain Layout
13629 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13632 \begin_layout Plain Layout
13636 \begin_inset Formula $\to$
13646 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13649 \begin_layout Plain Layout
13650 \begin_inset Formula $\colorbox{yellow}{A=B}$
13659 <row topspace="1.5mm">
13660 <cell alignment="center" valignment="top" usebox="none">
13663 \begin_layout Plain Layout
13667 \begin_inset Formula $\to$
13675 \begin_inset space \textvisiblespace{}
13683 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13686 \begin_layout Plain Layout
13687 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13696 <row topspace="1.5mm" bottomspace="1mm">
13697 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13700 \begin_layout Plain Layout
13704 \begin_inset space \textvisiblespace{}
13710 \begin_inset Formula $\to$
13726 \begin_inset space \textvisiblespace{}
13734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13737 \begin_layout Plain Layout
13738 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13754 \begin_layout Standard
13761 only colors the box but not the characters in the box.
13762 To color all characters, the whole formula is highlighted and the desired
13763 color is chosen in the
13766 \begin_inset space ~
13772 The dialog can be called with the toolbar button
13775 arg "dialog-show character"
13780 Edit\SpecialChar menuseparator
13782 \begin_inset space ~
13785 Style\SpecialChar menuseparator
13789 The formula number then has the same color as the formula.
13790 When the formula number should get another color than the formula characters,
13791 the color must be changed within the formula.
13794 \begin_layout Standard
13798 \begin_layout Standard
13801 \begin_inset Formula
13803 \int A=B\label{eq:red}
13811 \begin_inset Formula
13813 \textcolor{red}{\int A=B}\label{eq:redgreen}
13821 \begin_layout Standard
13823 \begin_inset CommandInset ref
13829 is completely colored red.
13830 \begin_inset Newline newline
13834 \begin_inset CommandInset ref
13836 reference "eq:redgreen"
13840 was first completely colored green to set the color for the formula number.
13841 Subsequently the formula characters were colored red.
13844 \begin_layout Standard
13845 \begin_inset VSpace bigskip
13848 To color the frame different than the rest of the box, the command
13855 \begin_inset Index idx
13858 \begin_layout Plain Layout
13866 is used in the following scheme:
13869 \begin_layout Standard
13874 fcolorbox{frame color}{color}{box content}
13877 \begin_layout Standard
13884 is an extension of the command
13891 The frame width is set, like for
13914 \begin_layout Plain Layout
13926 \begin_inset Formula
13928 \fcolorbox{cyan}{magenta}{A=B}
13937 \begin_layout Plain Layout
13951 \begin_layout Standard
13952 This formula was created with the command
13953 \begin_inset Newline newline
13961 \begin_inset Formula $\to$
13967 \begin_inset Formula $\to$
13977 \begin_layout Standard
13978 \begin_inset VSpace bigskip
13981 To use other colors than the predefined ones, they have to be defined first.
13984 \begin_layout Standard
13985 One can for example define the color
13986 \begin_inset Quotes eld
13994 \begin_inset Quotes erd
13997 with the \SpecialChar LaTeX
14001 \begin_layout Standard
14006 definecolor{darkgreen}{cmyk}{0.5,
14021 \begin_inset Index idx
14024 \begin_layout Plain Layout
14035 \begin_layout Standard
14040 is the color space that denotes the colors
14057 The four comma separated numbers are the portion factor for the corresponding
14058 colors of the color space.
14059 The factors can be in the range of 0
14060 \begin_inset space \thinspace{}
14064 \begin_inset space \thinspace{}
14072 also the color space
14076 can be used for definitions.
14093 , so that there are in this case three portion factors for the corresponding
14095 Furthermore there is the color space
14099 with one portion factor for the gray value.
14102 \begin_layout Standard
14103 As example a framed box with the new defined color
14107 where the characters have been colored
14112 \begin_inset Formula
14114 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14122 \begin_layout Standard
14123 Self-defined colors can also be used for text with the help of the command
14131 \begin_inset Index idx
14134 \begin_layout Plain Layout
14143 \begin_layout Standard
14147 \begin_layout Plain Layout
14151 textcolor{darkgreen}{
14157 \begin_inset Quotes eld
14161 \begin_inset Quotes erd
14168 \begin_layout Plain Layout
14178 \begin_layout Standard
14186 \begin_inset Index idx
14189 \begin_layout Plain Layout
14197 is used in the scheme
14201 textcolor{color}{characters to color}
14206 \begin_layout Subsection
14208 \begin_inset CommandInset label
14210 name "subsec:Paragraph-Boxes"
14215 \begin_inset Index idx
14218 \begin_layout Plain Layout
14219 Boxes ! as paragraph
14227 \begin_layout Standard
14228 A box that can contain several lines and paragraphs, a so-called paragraph
14229 box (parbox), can be created with the menu
14231 Insert\SpecialChar menuseparator
14234 or the toolbar button
14243 \begin_layout Standard
14244 The following example shows a framed parbox in a line:
14247 \begin_layout Standard
14248 \begin_inset VSpace medskip
14252 \begin_inset Box Boxed
14262 height_special "totalheight"
14267 backgroundcolor "none"
14270 \begin_layout Plain Layout
14271 This is a paragraph box.
14273 \begin_inset space \thinspace{}
14276 cm long and can also contain formulas:
14277 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14288 \begin_layout Standard
14289 \begin_inset VSpace medskip
14295 \begin_layout Standard
14296 Such a box is created by right-clicking on the gray box inset.
14297 A dialog pops up showing the box properties.
14311 \begin_inset space \thinspace{}
14316 Vertical Box Alignment
14321 \begin_layout Standard
14322 \begin_inset VSpace medskip
14325 In \SpecialChar LaTeX
14326 a parbox is created with the command
14333 \begin_inset Index idx
14336 \begin_layout Plain Layout
14344 which has the following scheme:
14347 \begin_layout Standard
14352 parbox[position]{width}{box content}
14355 \begin_layout Standard
14370 \begin_inset Quotes eld
14374 \begin_inset Quotes erd
14377 means that the box is aligned within the surrounding text with its last
14384 \begin_inset Quotes eld
14388 \begin_inset Quotes erd
14391 this is done with the first line.
14392 When no position is given, the box will be vertically centered, see section
14400 \begin_inset space ~
14405 manual for examples.
14408 \begin_layout Standard
14409 \begin_inset VSpace bigskip
14412 To frame formulas completely, including the formula number, the formula
14413 must be set into a parbox.
14414 To do this, the command
14428 is inserted in \SpecialChar TeX
14429 mode before the formula.
14437 \begin_inset Index idx
14440 \begin_layout Plain Layout
14448 is hereby the line width set for the document.
14449 Because the frame is outside the parbox, 2
14450 \begin_inset space \thinspace{}
14453 times the frame separation and the frame thickness must be subtracted from
14455 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14464 \begin_layout Plain Layout
14469 is part of every \SpecialChar LaTeX
14470 standard installation.
14476 \begin_inset Index idx
14479 \begin_layout Plain Layout
14485 must be loaded in the \SpecialChar LaTeX
14486 -preamble with the line
14489 \begin_layout Standard
14497 \begin_layout Standard
14498 Behind the formula both boxes are closed by entering
14502 in \SpecialChar TeX
14504 Here is an example:
14508 \begin_layout Plain Layout
14522 \begin_layout Standard
14526 \begin_layout Plain Layout
14544 \begin_inset Formula
14546 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14555 \begin_layout Plain Layout
14566 \begin_layout Plain Layout
14580 \begin_layout Standard
14581 \begin_inset VSpace medskip
14584 As a parbox is used as the argument of
14590 , there is in this case no difference between
14605 \begin_layout Standard
14606 \begin_inset VSpace bigskip
14609 Paragraph boxes are very useful to comment formulas directly.
14616 is used in combination with the command
14630 \begin_inset CommandInset ref
14632 reference "subsec:User-defined-Numbering"
14639 \begin_layout Standard
14640 An example of a formula commented with
14649 \begin_layout Standard
14653 \begin_layout Plain Layout
14666 This is a description.
14667 It is distinctly separated from the formula and multiline.
14671 \begin_layout Plain Layout
14683 \begin_layout Standard
14684 Such a formula must be inserted completely in \SpecialChar TeX
14685 mode because \SpecialChar LyX
14687 support the command
14694 The formula is created with the following command sequence:
14697 \begin_layout Standard
14710 is inserted in \SpecialChar TeX
14715 \begin_layout Plain Layout
14716 When the formula style
14728 can also be replaced by
14735 (formula styles see
14736 \begin_inset CommandInset ref
14738 reference "sec:Formula-Styles"
14747 Then the description follows as normal text and finally
14753 is inserted in \SpecialChar TeX
14767 hereby create a displayed formula.
14770 \begin_layout Standard
14777 can be seen in this example that was
14778 \begin_inset Quotes eld
14782 \begin_inset Quotes erd
14785 using the mathematical textmode:
14786 \begin_inset Formula
14788 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14796 \begin_layout Section
14798 \begin_inset Index idx
14801 \begin_layout Plain Layout
14810 \begin_layout Subsection
14812 \begin_inset CommandInset label
14814 name "subsec:Big-Operators"
14819 \begin_inset Index idx
14822 \begin_layout Plain Layout
14829 \begin_inset Index idx
14832 \begin_layout Plain Layout
14839 \begin_inset Index idx
14842 \begin_layout Plain Layout
14851 \begin_layout Standard
14852 To be able to use all integral operators listed here, the option
14854 Use esint package automatically
14856 must be set in the document settings under
14859 \begin_inset space ~
14867 \begin_layout Standard
14868 \begin_inset space \hfill{}
14872 \begin_inset Tabular
14873 <lyxtabular version="3" rows="11" columns="2">
14874 <features booktabs="true" tabularvalignment="middle">
14875 <column alignment="center" valignment="top" width="0pt">
14876 <column alignment="center" valignment="top" width="0pt">
14878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14881 \begin_layout Plain Layout
14887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14890 \begin_layout Plain Layout
14898 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14901 \begin_layout Plain Layout
14905 \begin_inset Index idx
14908 \begin_layout Plain Layout
14921 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14924 \begin_layout Plain Layout
14925 \begin_inset Formula $\int$
14935 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14938 \begin_layout Plain Layout
14946 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14949 \begin_layout Plain Layout
14950 \begin_inset Formula $\oint$
14960 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14963 \begin_layout Plain Layout
14971 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14974 \begin_layout Plain Layout
14975 \begin_inset Formula $\ointctrclockwise$
14985 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14988 \begin_layout Plain Layout
14996 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14999 \begin_layout Plain Layout
15000 \begin_inset Formula $\ointclockwise$
15010 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15013 \begin_layout Plain Layout
15021 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15024 \begin_layout Plain Layout
15025 \begin_inset Formula $\sqint$
15035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15038 \begin_layout Plain Layout
15046 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15049 \begin_layout Plain Layout
15051 \begin_inset Formula $\fint$
15061 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15064 \begin_layout Plain Layout
15072 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15075 \begin_layout Plain Layout
15077 \begin_inset Formula $\landupint$
15087 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15090 \begin_layout Plain Layout
15098 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15101 \begin_layout Plain Layout
15103 \begin_inset Formula $\landdownint$
15113 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15116 \begin_layout Plain Layout
15124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15127 \begin_layout Plain Layout
15128 \begin_inset Formula $\bigcap$
15138 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15141 \begin_layout Plain Layout
15149 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15152 \begin_layout Plain Layout
15153 \begin_inset Formula $\bigcup$
15167 \begin_inset space \hfill{}
15171 \begin_inset Tabular
15172 <lyxtabular version="3" rows="11" columns="2">
15173 <features booktabs="true" tabularvalignment="middle">
15174 <column alignment="center" valignment="top" width="0pt">
15175 <column alignment="center" valignment="top" width="0pt">
15177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15180 \begin_layout Plain Layout
15186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15189 \begin_layout Plain Layout
15197 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15200 \begin_layout Plain Layout
15204 \begin_inset Index idx
15207 \begin_layout Plain Layout
15220 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15223 \begin_layout Plain Layout
15224 \begin_inset Formula $\sum$
15234 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15237 \begin_layout Plain Layout
15241 \begin_inset Index idx
15244 \begin_layout Plain Layout
15251 \begin_layout Plain Layout
15270 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15273 \begin_layout Plain Layout
15274 \begin_inset Formula $\prod$
15284 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15287 \begin_layout Plain Layout
15295 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15298 \begin_layout Plain Layout
15299 \begin_inset Formula $\coprod$
15309 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15312 \begin_layout Plain Layout
15320 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15323 \begin_layout Plain Layout
15324 \begin_inset Formula $\bigodot$
15334 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15337 \begin_layout Plain Layout
15345 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15348 \begin_layout Plain Layout
15349 \begin_inset Formula $\bigotimes$
15359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15362 \begin_layout Plain Layout
15370 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15373 \begin_layout Plain Layout
15374 \begin_inset Formula $\bigoplus$
15384 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15387 \begin_layout Plain Layout
15395 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15398 \begin_layout Plain Layout
15399 \begin_inset Formula $\bigwedge$
15409 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15412 \begin_layout Plain Layout
15420 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15423 \begin_layout Plain Layout
15424 \begin_inset Formula $\bigvee$
15434 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15437 \begin_layout Plain Layout
15445 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15448 \begin_layout Plain Layout
15449 \begin_inset Formula $\bigsqcup$
15459 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15462 \begin_layout Plain Layout
15470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15473 \begin_layout Plain Layout
15474 \begin_inset Formula $\biguplus$
15488 \begin_inset space \hfill{}
15494 \begin_layout Standard
15495 All big operators can also be inserted via the math toolbar button
15498 arg "math-insert \\intop"
15504 \begin_layout Standard
15505 The operators are called big because they are bigger than the sometimes
15506 equal looking binary operators.
15507 All big operators can have limits as described in the next subsection.
15510 \begin_layout Standard
15511 For all integral operators there is a second version available, ending in
15529 These operators are different from
15536 \begin_inset space \space{}
15539 in the style the operator limits are displayed, see
15540 \begin_inset CommandInset ref
15542 reference "subsec:Operator-Limits"
15550 \begin_layout Subsubsection*
15551 Advice for Integrals
15554 \begin_layout Standard
15559 in an integral is an operator, that therefore has to be set upright.
15560 This is done by highlighting the
15564 and using the keyboard shortcut
15574 \begin_layout Plain Layout
15580 \begin_inset CommandInset ref
15582 reference "subsec:Font-Styles"
15592 Finally the smallest space is inserted before the
15596 , as this is usual for operators.
15600 \begin_layout Standard
15602 \begin_inset Formula $\int A(x)dx$
15606 \begin_inset Newline newline
15610 \begin_inset Phantom HPhantom
15613 \begin_layout Plain Layout
15620 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15626 \begin_layout Standard
15627 For multiple integrals there are the following commands:
15628 \begin_inset VSpace medskip
15634 \begin_layout Standard
15635 \begin_inset space \hfill{}
15639 \begin_inset Tabular
15640 <lyxtabular version="3" rows="4" columns="2">
15641 <features booktabs="true" tabularvalignment="middle">
15642 <column alignment="center" valignment="top" width="0pt">
15643 <column alignment="center" valignment="top" width="0pt">
15645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15648 \begin_layout Plain Layout
15654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15657 \begin_layout Plain Layout
15664 <row bottomspace="1mm">
15665 <cell alignment="center" valignment="top" usebox="none">
15668 \begin_layout Plain Layout
15676 <cell alignment="center" valignment="top" usebox="none">
15679 \begin_layout Plain Layout
15680 \begin_inset Formula $\iint$
15689 <row bottomspace="1mm">
15690 <cell alignment="center" valignment="top" usebox="none">
15693 \begin_layout Plain Layout
15701 <cell alignment="center" valignment="top" usebox="none">
15704 \begin_layout Plain Layout
15705 \begin_inset Formula $\oiint$
15714 <row bottomspace="1mm">
15715 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15718 \begin_layout Plain Layout
15726 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15729 \begin_layout Plain Layout
15730 \begin_inset Formula $\sqiint$
15744 \begin_inset space \hfill{}
15748 \begin_inset Tabular
15749 <lyxtabular version="3" rows="4" columns="2">
15750 <features booktabs="true" tabularvalignment="middle">
15751 <column alignment="center" valignment="top" width="0pt">
15752 <column alignment="center" valignment="top" width="0pt">
15754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15757 \begin_layout Plain Layout
15763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15766 \begin_layout Plain Layout
15773 <row bottomspace="1mm">
15774 <cell alignment="center" valignment="top" usebox="none">
15777 \begin_layout Plain Layout
15785 <cell alignment="center" valignment="top" usebox="none">
15788 \begin_layout Plain Layout
15789 \begin_inset Formula $\iiint$
15798 <row bottomspace="1mm">
15799 <cell alignment="center" valignment="top" usebox="none">
15802 \begin_layout Plain Layout
15810 <cell alignment="center" valignment="top" usebox="none">
15813 \begin_layout Plain Layout
15814 \begin_inset Formula $\iiiint$
15823 <row bottomspace="1mm">
15824 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15827 \begin_layout Plain Layout
15835 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15838 \begin_layout Plain Layout
15839 \begin_inset Formula $\dotsint$
15853 \begin_inset space \hfill{}
15859 \begin_layout Subsection
15861 \begin_inset CommandInset label
15863 name "subsec:Operator-Limits"
15868 \begin_inset Index idx
15871 \begin_layout Plain Layout
15880 \begin_layout Standard
15881 Limits are created by super- and subscripts:
15884 \begin_layout Standard
15886 \begin_inset Tabular
15887 <lyxtabular version="3" rows="2" columns="2">
15888 <features booktabs="true" tabularvalignment="middle">
15889 <column alignment="center" valignment="top" width="0pt">
15890 <column alignment="center" valignment="top" width="0pt">
15892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15895 \begin_layout Plain Layout
15901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15904 \begin_layout Plain Layout
15912 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15915 \begin_layout Plain Layout
15921 \begin_inset space \textvisiblespace{}
15925 \begin_inset Formula $\to$
15929 \begin_inset Formula $\to$
15937 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15940 \begin_layout Plain Layout
15941 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
15957 \begin_layout Standard
15958 Limits of inline formulas are set right beside the operator.
15959 Limits in displayed formulas are set above or below the operator, except
15960 for integral limits.
15963 \begin_layout Standard
15964 To force that the limits are set beside the operator, the cursor is set
15965 directly behind the operator and the limits type is changed with the menu
15968 Edit\SpecialChar menuseparator
15969 Math\SpecialChar menuseparator
15988 \begin_layout Standard
15989 The default limits type is this:
15990 \begin_inset Formula
15992 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15997 This is how it looks when the limits type was changed to
16004 \begin_inset Formula
16006 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16011 For integrals, except those ending with
16027 etc., the limits are by default set beside the operator.
16028 But for multiple integrals the limits are often set below the operator.
16029 In the following example the limits type was therefore set to
16033 and so set below the integrals:
16034 \begin_inset Formula
16036 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16044 \begin_layout Standard
16045 \begin_inset VSpace medskip
16048 To specify conditions for limits, the commands
16055 \begin_inset Index idx
16058 \begin_layout Plain Layout
16073 \begin_inset Index idx
16076 \begin_layout Plain Layout
16085 To create for example this expression
16086 \begin_inset Formula
16088 \sum_{\begin{subarray}{c}
16092 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16100 \begin_layout Standard
16101 the following has to be done:
16102 \begin_inset Newline newline
16114 \begin_inset space \textvisiblespace{}
16120 One is now in a blue box under the summation operator and insert there
16126 \begin_inset space \textvisiblespace{}
16132 The blue box is now within a purple box and now several lines can be written
16134 A new line is created by inserting a line break (
16137 arg "newline-insert newline"
16142 \begin_inset Newline newline
16147 0<k<1000 Ctrl+Return
16148 \begin_inset Newline newline
16153 is typed in, a new box appears below for the new line.
16156 \begin_layout Standard
16157 The alignment of the lines can be changed to left aligned with the
16167 Edit\SpecialChar menuseparator
16171 To get right alignment,
16176 \begin_inset space \textvisiblespace{}
16181 is inserted at the beginning of the line.
16184 \begin_layout Standard
16197 with the difference that the lines are always centered.
16200 \begin_layout Standard
16201 \begin_inset VSpace bigskip
16205 \begin_inset CommandInset ref
16207 reference "eq:substack"
16211 there can be too much space beside an operator, because the characters
16212 following the operator are set beside the limits.
16213 To avoid this the command
16220 \begin_inset Index idx
16223 \begin_layout Plain Layout
16232 To activate it, set in the document settings under
16235 \begin_inset space ~
16245 \begin_inset Index idx
16248 \begin_layout Plain Layout
16249 Packages ! mathtools
16257 \begin_inset space ~
16269 sets the space besides the operator to 0
16270 \begin_inset space \thinspace{}
16274 \begin_inset Newline newline
16278 \begin_inset CommandInset ref
16280 reference "eq:substack"
16284 , one uses the command
16287 \begin_layout Standard
16295 \begin_layout Standard
16296 and inserts the operator with its limits into the braces.
16297 Behind the brace one continues the formula:
16298 \begin_inset Formula
16300 \smashoperator{\sum_{\begin{subarray}{c}
16304 \end{subarray}}^{n}}k^{-2}
16312 \begin_layout Standard
16313 It is possible to set the space of only one side of the operator to 0
16314 \begin_inset space \thinspace{}
16318 To do this write either
16337 stands for the left and
16341 for the right side of the operator.
16342 Here is an example of the possible
16351 \begin_layout Standard
16352 \begin_inset Formula
16354 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}
16362 \begin_layout Standard
16363 \begin_inset VSpace bigskip
16369 \begin_layout Standard
16370 When several consecutive operators have limits the typesetting of the limits
16371 looks often imperfect in the output, see this example:
16372 \begin_inset Formula
16374 \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}
16379 To improve the typesetting set in the document settings under
16382 \begin_inset space ~
16392 \begin_inset Index idx
16395 \begin_layout Plain Layout
16396 Packages ! mathtools
16404 \begin_inset space ~
16410 Then insert into your formula the command
16417 \begin_inset Index idx
16420 \begin_layout Plain Layout
16428 directly before the first operator.
16429 The example will then look like this:
16430 \begin_inset Formula
16432 \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}
16440 \begin_layout Standard
16441 \begin_inset VSpace bigskip
16444 How to use one limit for several operators is described in
16445 \begin_inset CommandInset ref
16447 reference "subsec:Self-defined-Operators"
16454 \begin_layout Subsection
16455 Decoration for Operators
16456 \begin_inset Index idx
16459 \begin_layout Plain Layout
16460 Operators ! Decoration
16468 \begin_layout Standard
16476 \begin_inset Index idx
16479 \begin_layout Plain Layout
16494 \begin_inset Index idx
16497 \begin_layout Plain Layout
16505 characters can be placed above or below an operator, respectively.
16513 \begin_inset Index idx
16516 \begin_layout Plain Layout
16524 characters can be set before and behind a big operator.
16527 \begin_layout Standard
16529 \begin_inset space ~
16541 \begin_layout Itemize
16548 is used to set characters at the corners of the operator
16551 \begin_layout Itemize
16558 is used to set characters before and/or behind the operator (this variant
16559 represents \SpecialChar LaTeX
16569 \begin_layout Itemize
16576 is used to set characters at the left corners and/or behind the operator
16579 \begin_layout Itemize
16586 is used to set characters at the right corners and/or before the operator
16589 \begin_layout Standard
16590 For example the command
16595 \begin_inset space \textvisiblespace{}
16601 \begin_inset space \textvisiblespace{}
16605 \begin_inset Formula $\to$
16609 \begin_inset Formula $\to$
16613 \begin_inset space \textvisiblespace{}
16623 \begin_inset Formula
16625 \sideset{}{'}\sum_{k=1}^{n}
16633 \begin_layout Standard
16634 \begin_inset Note Greyedout
16637 \begin_layout Plain Layout
16644 can only be used to decorate big operators, binary operators are not allowed.
16652 \begin_layout Standard
16665 can also be used to decorate symbols and characters.
16666 For example, the command
16671 \begin_inset space \textvisiblespace{}
16677 \begin_inset space \textvisiblespace{}
16683 \begin_inset Formula $\uparrow$
16691 \begin_inset Formula
16693 \overset{a}{\maltese}
16701 \begin_layout Subsection
16703 \begin_inset CommandInset label
16705 name "subsec:Binary-Operators"
16710 \begin_inset Index idx
16713 \begin_layout Plain Layout
16722 \begin_layout Standard
16723 Binary operators are surrounded by space when there is a character before
16725 \begin_inset VSpace medskip
16731 \begin_layout Standard
16732 \begin_inset Tabular
16733 <lyxtabular version="3" rows="13" columns="2">
16734 <features booktabs="true" tabularvalignment="middle">
16735 <column alignment="center" valignment="top" width="0pt">
16736 <column alignment="center" valignment="top" width="0pt">
16738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16741 \begin_layout Plain Layout
16743 \begin_inset Note Note
16746 \begin_layout Plain Layout
16753 is only used as spacer.
16763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16766 \begin_layout Plain Layout
16774 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16777 \begin_layout Plain Layout
16783 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16786 \begin_layout Plain Layout
16787 \begin_inset Formula $+$
16797 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16800 \begin_layout Plain Layout
16806 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16809 \begin_layout Plain Layout
16810 \begin_inset Formula $-$
16820 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16823 \begin_layout Plain Layout
16831 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16834 \begin_layout Plain Layout
16835 \begin_inset Formula $\pm$
16845 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16848 \begin_layout Plain Layout
16856 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16859 \begin_layout Plain Layout
16860 \begin_inset Formula $\mp$
16870 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16873 \begin_layout Plain Layout
16881 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16884 \begin_layout Plain Layout
16885 \begin_inset Formula $\cdot$
16895 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16898 \begin_layout Plain Layout
16906 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16909 \begin_layout Plain Layout
16910 \begin_inset Formula $\times$
16920 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16923 \begin_layout Plain Layout
16931 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16934 \begin_layout Plain Layout
16935 \begin_inset Formula $\div$
16945 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16948 \begin_layout Plain Layout
16952 \begin_layout Plain Layout
16965 \begin_layout Plain Layout
16977 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16980 \begin_layout Plain Layout
16981 \begin_inset Formula $*$
16991 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16994 \begin_layout Plain Layout
17002 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17005 \begin_layout Plain Layout
17006 \begin_inset Formula $\star$
17016 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17019 \begin_layout Plain Layout
17027 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17030 \begin_layout Plain Layout
17031 \begin_inset Formula $\circ$
17041 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17044 \begin_layout Plain Layout
17052 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17055 \begin_layout Plain Layout
17056 \begin_inset Formula $\diamond$
17066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17069 \begin_layout Plain Layout
17077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17080 \begin_layout Plain Layout
17081 \begin_inset Formula $\bullet$
17095 \begin_inset space \hfill{}
17099 \begin_inset Tabular
17100 <lyxtabular version="3" rows="13" columns="2">
17101 <features booktabs="true" tabularvalignment="middle">
17102 <column alignment="center" valignment="top" width="0pt">
17103 <column alignment="center" valignment="top" width="0pt">
17105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17108 \begin_layout Plain Layout
17114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17117 \begin_layout Plain Layout
17125 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17128 \begin_layout Plain Layout
17136 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17139 \begin_layout Plain Layout
17140 \begin_inset Formula $\nabla$
17150 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17153 \begin_layout Plain Layout
17161 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17164 \begin_layout Plain Layout
17165 \begin_inset Formula $\bigtriangledown$
17175 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17178 \begin_layout Plain Layout
17186 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17189 \begin_layout Plain Layout
17190 \begin_inset Formula $\bigtriangleup$
17200 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17203 \begin_layout Plain Layout
17211 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17214 \begin_layout Plain Layout
17215 \begin_inset Formula $\Box$
17225 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17228 \begin_layout Plain Layout
17236 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17239 \begin_layout Plain Layout
17240 \begin_inset Formula $\cap$
17250 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17253 \begin_layout Plain Layout
17261 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17264 \begin_layout Plain Layout
17265 \begin_inset Formula $\cup$
17275 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17278 \begin_layout Plain Layout
17286 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17289 \begin_layout Plain Layout
17290 \begin_inset Formula $\dagger$
17300 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17303 \begin_layout Plain Layout
17311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17314 \begin_layout Plain Layout
17315 \begin_inset Formula $\ddagger$
17325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17328 \begin_layout Plain Layout
17336 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17339 \begin_layout Plain Layout
17340 \begin_inset Formula $\wr$
17350 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17353 \begin_layout Plain Layout
17361 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17364 \begin_layout Plain Layout
17365 \begin_inset Formula $\bigcirc$
17375 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17378 \begin_layout Plain Layout
17386 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17389 \begin_layout Plain Layout
17390 \begin_inset Formula $\wedge$
17400 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17403 \begin_layout Plain Layout
17411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17414 \begin_layout Plain Layout
17415 \begin_inset Formula $\vee$
17429 \begin_inset space \hfill{}
17433 \begin_inset Tabular
17434 <lyxtabular version="3" rows="13" columns="2">
17435 <features booktabs="true" tabularvalignment="middle">
17436 <column alignment="center" valignment="top" width="0pt">
17437 <column alignment="center" valignment="top" width="0pt">
17439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17442 \begin_layout Plain Layout
17448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17451 \begin_layout Plain Layout
17459 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17462 \begin_layout Plain Layout
17470 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17473 \begin_layout Plain Layout
17474 \begin_inset Formula $\oplus$
17484 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17487 \begin_layout Plain Layout
17495 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17498 \begin_layout Plain Layout
17499 \begin_inset Formula $\ominus$
17509 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17512 \begin_layout Plain Layout
17520 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17523 \begin_layout Plain Layout
17524 \begin_inset Formula $\otimes$
17534 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17537 \begin_layout Plain Layout
17545 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17548 \begin_layout Plain Layout
17549 \begin_inset Formula $\oslash$
17559 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17562 \begin_layout Plain Layout
17570 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17573 \begin_layout Plain Layout
17574 \begin_inset Formula $\odot$
17584 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17587 \begin_layout Plain Layout
17595 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17598 \begin_layout Plain Layout
17599 \begin_inset Formula $\amalg$
17609 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17612 \begin_layout Plain Layout
17620 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17623 \begin_layout Plain Layout
17624 \begin_inset Formula $\uplus$
17634 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17637 \begin_layout Plain Layout
17645 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17648 \begin_layout Plain Layout
17649 \begin_inset Formula $\setminus$
17659 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17662 \begin_layout Plain Layout
17670 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17673 \begin_layout Plain Layout
17674 \begin_inset Formula $\sqcap$
17684 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17687 \begin_layout Plain Layout
17695 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17698 \begin_layout Plain Layout
17699 \begin_inset Formula $\sqcup$
17709 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17712 \begin_layout Plain Layout
17720 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17723 \begin_layout Plain Layout
17724 \begin_inset Formula $\triangleleft$
17734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17737 \begin_layout Plain Layout
17745 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17748 \begin_layout Plain Layout
17749 \begin_inset Formula $\triangleright$
17765 \begin_layout Standard
17766 All binary operators can also be inserted via the math toolbar button
17769 arg "math-insert \\pm"
17775 \begin_layout Standard
17776 To typeset the Laplace operator also
17793 \begin_inset Formula $\nabla^{2}$
17796 ) can be used instead of
17805 \begin_layout Standard
17812 Insert\SpecialChar menuseparator
17824 \begin_layout Subsection
17825 Self-defined Operators
17826 \begin_inset CommandInset label
17828 name "subsec:Self-defined-Operators"
17833 \begin_inset Index idx
17836 \begin_layout Plain Layout
17837 Operators ! self-defined
17845 \begin_layout Standard
17846 With the help of the command
17850 DeclareMathOperator
17853 \begin_inset Index idx
17856 \begin_layout Plain Layout
17861 DeclareMathOperator
17866 custom operators can be defined in the \SpecialChar LaTeX
17868 Its command scheme is:
17871 \begin_layout Standard
17876 DeclareMathOperator{new command}{display}
17879 \begin_layout Standard
17880 Display can be characters or symbols that define how the operator looks
17882 To define a big operator a * is set behind the command.
17883 All self-defined big operators can have limits as described in
17884 \begin_inset CommandInset ref
17886 reference "subsec:Operator-Limits"
17893 \begin_layout Standard
17894 For example the \SpecialChar LaTeX
17898 \begin_layout Standard
17903 DeclareMathOperator*{
17910 \begin_layout Standard
17911 defines the command
17917 , that inserts a big operator consisting of the lozenge symbol from
17918 \begin_inset CommandInset ref
17920 reference "subsec:Miscellaneous-Symbols"
17925 \begin_inset Formula
17927 \Lozenge_{n=1}^{\infty}
17932 The command for this formula is:
17943 \begin_inset Formula $\to$
17949 \begin_layout Standard
17950 \begin_inset VSpace bigskip
17953 When self-defined operators are not used several times in the document,
17954 they can also be defined with the commands
17961 \begin_inset Index idx
17964 \begin_layout Plain Layout
17979 \begin_inset Index idx
17982 \begin_layout Plain Layout
17990 , which have the following scheme:
17993 \begin_layout Standard
18007 \begin_layout Standard
18014 defines big operators,
18023 \begin_layout Standard
18031 \begin_inset space \thinspace{}
18035 \begin_inset space \space{}
18038 be used to use one limit for several operators:
18041 \begin_layout Standard
18042 \begin_inset Formula
18044 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18052 \begin_layout Standard
18053 The command for the formula above is:
18054 \begin_inset Newline newline
18070 \begin_inset space \textvisiblespace{}
18076 \begin_inset Formula $\to$
18082 \begin_inset space \textvisiblespace{}
18090 \begin_layout Section
18092 \begin_inset Index idx
18095 \begin_layout Plain Layout
18104 \begin_layout Subsection
18106 \begin_inset CommandInset label
18108 name "subsec:Font-Styles"
18113 \begin_inset Index idx
18116 \begin_layout Plain Layout
18125 \begin_layout Standard
18126 Latin letters in formulas can be set in one of the following font styles:
18129 \begin_layout Standard
18131 \begin_inset Tabular
18132 <lyxtabular version="3" rows="6" columns="3">
18133 <features booktabs="true" tabularvalignment="middle">
18134 <column alignment="center" valignment="top" width="0pt">
18135 <column alignment="center" valignment="top">
18136 <column alignment="center" valignment="top">
18138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18141 \begin_layout Plain Layout
18147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18150 \begin_layout Plain Layout
18156 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18159 \begin_layout Plain Layout
18167 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18170 \begin_layout Plain Layout
18176 \begin_inset space \textvisiblespace{}
18186 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18189 \begin_layout Plain Layout
18190 \begin_inset Formula $\mathbb{ABC}$
18198 <cell alignment="center" valignment="top" usebox="none">
18201 \begin_layout Plain Layout
18209 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18212 \begin_layout Plain Layout
18218 \begin_inset space \textvisiblespace{}
18228 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18231 \begin_layout Plain Layout
18232 \begin_inset Formula $\mathbf{AbC}$
18240 <cell alignment="center" valignment="top" usebox="none">
18243 \begin_layout Plain Layout
18256 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18259 \begin_layout Plain Layout
18265 \begin_inset space \textvisiblespace{}
18275 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18278 \begin_layout Plain Layout
18279 \begin_inset Formula $\boldsymbol{AbC}$
18287 <cell alignment="center" valignment="top" usebox="none">
18290 \begin_layout Plain Layout
18293 arg "font-boldsymbol"
18303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18306 \begin_layout Plain Layout
18312 \begin_inset space \textvisiblespace{}
18322 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18325 \begin_layout Plain Layout
18326 \begin_inset Formula $\mathcal{ABC}$
18334 <cell alignment="center" valignment="top" usebox="none">
18337 \begin_layout Plain Layout
18345 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18348 \begin_layout Plain Layout
18354 \begin_inset space \textvisiblespace{}
18364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18367 \begin_layout Plain Layout
18368 \begin_inset Formula $\mathfrak{AbC}$
18376 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18379 \begin_layout Plain Layout
18393 \begin_layout Standard
18395 \begin_inset Tabular
18396 <lyxtabular version="3" rows="6" columns="3">
18397 <features booktabs="true" tabularvalignment="middle">
18398 <column alignment="center" valignment="top" width="0pt">
18399 <column alignment="center" valignment="top">
18400 <column alignment="center" valignment="top">
18402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18405 \begin_layout Plain Layout
18411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18414 \begin_layout Plain Layout
18420 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18423 \begin_layout Plain Layout
18431 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18434 \begin_layout Plain Layout
18440 \begin_inset space \textvisiblespace{}
18450 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18453 \begin_layout Plain Layout
18454 \begin_inset Formula $\mathit{AbC}$
18462 <cell alignment="center" valignment="top" usebox="none">
18465 \begin_layout Plain Layout
18473 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18476 \begin_layout Plain Layout
18482 \begin_inset space \textvisiblespace{}
18492 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18495 \begin_layout Plain Layout
18496 \begin_inset Formula $\mathrm{AbC}$
18504 <cell alignment="center" valignment="top" usebox="none">
18507 \begin_layout Plain Layout
18520 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18523 \begin_layout Plain Layout
18529 \begin_inset space \textvisiblespace{}
18539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18542 \begin_layout Plain Layout
18543 \begin_inset Formula $\mathsf{AbC}$
18551 <cell alignment="center" valignment="top" usebox="none">
18554 \begin_layout Plain Layout
18567 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18570 \begin_layout Plain Layout
18576 \begin_inset space \textvisiblespace{}
18586 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18589 \begin_layout Plain Layout
18590 \begin_inset Formula $\mathtt{AbC}$
18598 <cell alignment="center" valignment="top" usebox="none">
18601 \begin_layout Plain Layout
18604 arg "font-typewriter"
18614 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18617 \begin_layout Plain Layout
18623 \begin_inset space \textvisiblespace{}
18633 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18636 \begin_layout Plain Layout
18637 \begin_inset Formula $\mathscr{ABC}$
18645 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18648 \begin_layout Plain Layout
18662 \begin_layout Standard
18663 \begin_inset Note Greyedout
18666 \begin_layout Plain Layout
18689 can only be used for big letters.
18697 \begin_layout Standard
18698 Predefined is the style
18707 \begin_layout Standard
18708 The style commands work also for letters in mathematical constructs:
18709 \begin_inset Formula
18711 \mathfrak{A=\frac{b}{C}}
18719 \begin_layout Standard
18720 Characters in mathematical text don't appear in a math font style but in
18721 the text font style
18728 That their style can't be set correctly via the text style dialog is a
18729 bug in \SpecialChar LyX
18734 \begin_layout Plain Layout
18735 \begin_inset CommandInset href
18737 name "LyX-bug #4629"
18738 target "http://www.lyx.org/trac/ticket/4629"
18751 \begin_layout Standard
18752 Instead of the style commands the dialog
18754 Edit\SpecialChar menuseparator
18755 Math\SpecialChar menuseparator
18758 or the toolbar button
18761 arg "math-insert \\font"
18767 \begin_layout Subsection
18769 \begin_inset CommandInset label
18771 name "subsec:Bold-Formulas"
18776 \begin_inset Index idx
18779 \begin_layout Plain Layout
18788 \begin_layout Standard
18789 To make a complete formula bold, the command
18795 from the previous subsection cannot be used, because it doesn't work for
18796 small Greek letters.
18797 Furthermore it prints Latin letters always upright, like in the following
18801 \begin_layout Standard
18802 \begin_inset Formula
18804 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18812 \begin_layout Standard
18813 To display the formula correctly, the command
18820 \begin_inset Formula
18822 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18827 It is also possible to set the formula in a
18829 boldmath environment
18832 This environment is created by inserting the command
18839 \begin_inset Index idx
18842 \begin_layout Plain Layout
18850 in \SpecialChar TeX
18852 To end the environment, the command
18859 \begin_inset Index idx
18862 \begin_layout Plain Layout
18870 is inserted in \SpecialChar TeX
18875 \begin_layout Plain Layout
18885 \begin_inset Formula
18887 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18896 \begin_layout Plain Layout
18908 \begin_layout Subsection
18910 \begin_inset Index idx
18913 \begin_layout Plain Layout
18922 \begin_layout Standard
18923 Formulas can be colored like normal text: Highlight a formula or a formula
18929 Here is a formula in magenta:
18930 \begin_inset Formula
18932 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18940 \begin_layout Standard
18941 You can also define your own colors as described in
18942 \begin_inset CommandInset ref
18944 reference "subsec:Colored-Boxes"
18949 They can be used with the \SpecialChar TeX
18957 \begin_inset Index idx
18960 \begin_layout Plain Layout
18971 \begin_layout Standard
18976 textcolor{color}{characters or formula}
18979 \begin_layout Standard
18980 The following example was colored completely dark green and partly red:
18983 \begin_layout Standard
18987 \begin_layout Plain Layout
18991 textcolor{darkgreen}{
18997 \begin_inset Formula
18999 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19008 \begin_layout Plain Layout
19018 \begin_layout Standard
19019 Due to a bug in \SpecialChar LyX
19020 only complete formulas can be colored with self-defined
19025 \begin_layout Plain Layout
19026 \begin_inset CommandInset href
19028 name "LyX-bug #5269"
19029 target "http://www.lyx.org/trac/ticket/5269"
19042 \begin_layout Subsection
19044 \begin_inset CommandInset label
19046 name "subsec:Font-Sizes"
19051 \begin_inset Index idx
19054 \begin_layout Plain Layout
19063 \begin_layout Standard
19064 For characters in formulas there are, analog to characters in text, the
19065 following size commands:
19068 \begin_layout Standard
19112 \begin_inset Newline newline
19134 \begin_layout Standard
19135 The size produced by the commands depends on the document font size, which
19136 corresponds to the command
19143 The other commands produce smaller or larger sizes than
19150 The font size can however not exceed a certain value.
19151 Is for example the document font size 12
19152 \begin_inset space \thinspace{}
19161 switches to the same size as
19171 \begin_layout Standard
19172 A size command is inserted in \SpecialChar TeX
19173 mode before the formula and sets the size
19174 for all following formula and text characters.
19175 To switch back to the initial size, the command
19181 is inserted behind the formula in \SpecialChar TeX
19185 \begin_layout Standard
19186 Within a formula the size can be changed using the following size commands
19187 or the toolbar button
19190 arg "math-insert \\style"
19196 \begin_layout Standard
19199 \begin_inset Tabular
19200 <lyxtabular version="3" rows="5" columns="2">
19201 <features booktabs="true" tabularvalignment="middle">
19202 <column alignment="center" valignment="top" width="0pt">
19203 <column alignment="center" valignment="top">
19205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19208 \begin_layout Plain Layout
19214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19217 \begin_layout Plain Layout
19225 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19228 \begin_layout Plain Layout
19232 \begin_inset Index idx
19235 \begin_layout Plain Layout
19248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19251 \begin_layout Plain Layout
19252 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19261 <row topspace="1mm">
19262 <cell alignment="center" valignment="top" usebox="none">
19265 \begin_layout Plain Layout
19273 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19276 \begin_layout Plain Layout
19277 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19290 \begin_layout Plain Layout
19298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19301 \begin_layout Plain Layout
19302 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19312 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19315 \begin_layout Plain Layout
19323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19326 \begin_layout Plain Layout
19327 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19343 \begin_layout Standard
19344 After entering these commands, a blue box appears in which the formula parts
19348 \begin_layout Standard
19349 There is a further method to change the font size, that though only works
19350 for symbols or letters in mathematical text.
19351 To use it, one of the above text size commands is inserted in mathematical
19353 All following characters until the end of the mathematical text or until
19354 another size command will have the selected size.
19356 \begin_inset VSpace -2mm
19362 \begin_layout Standard
19366 \begin_layout Plain Layout
19376 \begin_inset Formula
19378 A=\frac{B}{c}\cdot\maltese
19384 \begin_inset Formula
19386 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19395 \begin_layout Plain Layout
19407 \begin_layout Standard
19408 \begin_inset VSpace medskip
19411 Before both formulas the command
19418 The command for the second formula is:
19419 \begin_inset Newline newline
19427 \begin_inset space \textvisiblespace{}
19433 \begin_inset space \textvisiblespace{}
19439 \begin_inset space \textvisiblespace{}
19445 \begin_inset space \textvisiblespace{}
19449 \begin_inset Formula $\to$
19453 \begin_inset Formula $\to$
19457 \begin_inset Newline newline
19461 \begin_inset space \hspace*{}
19472 \begin_inset space \textvisiblespace{}
19478 \begin_inset space \textvisiblespace{}
19484 \begin_inset space \textvisiblespace{}
19490 \begin_layout Standard
19491 If a symbol cannot be displayed in different sizes, it will always be displayed
19492 in the default size.
19495 \begin_layout Section
19497 \begin_inset Index idx
19500 \begin_layout Plain Layout
19509 \begin_layout Standard
19510 Greek letters can also be inserted via the toolbar button
19513 arg "math-insert \\alpha"
19517 All international typesetting norms purport that Greek letters in math
19518 have to be typeset italic/slanted.
19519 In some languages, like French or Russian, they are nevertheless sometimes
19523 \begin_layout Subsection
19525 \begin_inset Index idx
19528 \begin_layout Plain Layout
19529 Greek letters ! small
19537 \begin_layout Standard
19538 \begin_inset space \hfill{}
19542 \begin_inset Tabular
19543 <lyxtabular version="3" rows="11" columns="2">
19544 <features booktabs="true" tabularvalignment="middle">
19545 <column alignment="center" valignment="top" width="0pt">
19546 <column alignment="center" valignment="top" width="0pt">
19548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19551 \begin_layout Plain Layout
19557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19560 \begin_layout Plain Layout
19568 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19571 \begin_layout Plain Layout
19579 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19582 \begin_layout Plain Layout
19583 \begin_inset Formula $\alpha$
19593 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19596 \begin_layout Plain Layout
19604 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19607 \begin_layout Plain Layout
19608 \begin_inset Formula $\beta$
19618 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19621 \begin_layout Plain Layout
19629 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19632 \begin_layout Plain Layout
19633 \begin_inset Formula $\gamma$
19643 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19646 \begin_layout Plain Layout
19654 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19657 \begin_layout Plain Layout
19658 \begin_inset Formula $\delta$
19668 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19671 \begin_layout Plain Layout
19679 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19682 \begin_layout Plain Layout
19683 \begin_inset Formula $\epsilon$
19693 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19696 \begin_layout Plain Layout
19704 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19707 \begin_layout Plain Layout
19708 \begin_inset Formula $\varepsilon$
19718 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19721 \begin_layout Plain Layout
19729 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19732 \begin_layout Plain Layout
19733 \begin_inset Formula $\zeta$
19743 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19746 \begin_layout Plain Layout
19754 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19757 \begin_layout Plain Layout
19758 \begin_inset Formula $\eta$
19768 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19771 \begin_layout Plain Layout
19779 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19782 \begin_layout Plain Layout
19783 \begin_inset Formula $\theta$
19793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19796 \begin_layout Plain Layout
19804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19807 \begin_layout Plain Layout
19808 \begin_inset Formula $\vartheta$
19822 \begin_inset space \hfill{}
19826 \begin_inset Tabular
19827 <lyxtabular version="3" rows="12" columns="2">
19828 <features booktabs="true" tabularvalignment="middle">
19829 <column alignment="center" valignment="top" width="0pt">
19830 <column alignment="center" valignment="top" width="0pt">
19832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19835 \begin_layout Plain Layout
19841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19844 \begin_layout Plain Layout
19852 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19855 \begin_layout Plain Layout
19863 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19866 \begin_layout Plain Layout
19867 \begin_inset Formula $\iota$
19877 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19880 \begin_layout Plain Layout
19888 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19891 \begin_layout Plain Layout
19892 \begin_inset Formula $\kappa$
19902 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19905 \begin_layout Plain Layout
19913 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19916 \begin_layout Plain Layout
19917 \begin_inset Formula $\varkappa$
19927 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19930 \begin_layout Plain Layout
19938 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19941 \begin_layout Plain Layout
19942 \begin_inset Formula $\lambda$
19952 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19955 \begin_layout Plain Layout
19963 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19966 \begin_layout Plain Layout
19967 \begin_inset Formula $\mu$
19977 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19980 \begin_layout Plain Layout
19988 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19991 \begin_layout Plain Layout
19992 \begin_inset Formula $\nu$
20002 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20005 \begin_layout Plain Layout
20013 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20016 \begin_layout Plain Layout
20017 \begin_inset Formula $\xi$
20027 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20030 \begin_layout Plain Layout
20036 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20039 \begin_layout Plain Layout
20040 \begin_inset Formula $o$
20050 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20053 \begin_layout Plain Layout
20061 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20064 \begin_layout Plain Layout
20065 \begin_inset Formula $\pi$
20075 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20078 \begin_layout Plain Layout
20086 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20089 \begin_layout Plain Layout
20090 \begin_inset Formula $\varpi$
20100 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20103 \begin_layout Plain Layout
20111 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20114 \begin_layout Plain Layout
20115 \begin_inset Formula $\rho$
20129 \begin_inset space \hfill{}
20133 \begin_inset Tabular
20134 <lyxtabular version="3" rows="11" columns="2">
20135 <features booktabs="true" tabularvalignment="middle">
20136 <column alignment="center" valignment="top" width="0pt">
20137 <column alignment="center" valignment="top" width="0pt">
20139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20142 \begin_layout Plain Layout
20148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20151 \begin_layout Plain Layout
20159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20162 \begin_layout Plain Layout
20170 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20173 \begin_layout Plain Layout
20174 \begin_inset Formula $\varrho$
20184 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20187 \begin_layout Plain Layout
20195 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20198 \begin_layout Plain Layout
20199 \begin_inset Formula $\sigma$
20209 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20212 \begin_layout Plain Layout
20220 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20223 \begin_layout Plain Layout
20224 \begin_inset Formula $\varsigma$
20234 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20237 \begin_layout Plain Layout
20245 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20248 \begin_layout Plain Layout
20249 \begin_inset Formula $\tau$
20259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20262 \begin_layout Plain Layout
20270 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20273 \begin_layout Plain Layout
20274 \begin_inset Formula $\upsilon$
20284 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20287 \begin_layout Plain Layout
20295 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20298 \begin_layout Plain Layout
20299 \begin_inset Formula $\phi$
20309 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20312 \begin_layout Plain Layout
20320 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20323 \begin_layout Plain Layout
20324 \begin_inset Formula $\varphi$
20334 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20337 \begin_layout Plain Layout
20345 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20348 \begin_layout Plain Layout
20349 \begin_inset Formula $\chi$
20359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20362 \begin_layout Plain Layout
20370 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20373 \begin_layout Plain Layout
20374 \begin_inset Formula $\psi$
20384 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20387 \begin_layout Plain Layout
20395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20398 \begin_layout Plain Layout
20399 \begin_inset Formula $\omega$
20413 \begin_inset space \hfill{}
20419 \begin_layout Standard
20420 \begin_inset VSpace medskip
20426 \begin_layout Standard
20427 How to create special upright Greek letters is explained in
20428 \begin_inset CommandInset ref
20430 reference "subsec:Upright-small-Greek"
20437 \begin_layout Subsection
20439 \begin_inset Index idx
20442 \begin_layout Plain Layout
20443 Greek letters ! big
20451 \begin_layout Standard
20452 \begin_inset space \hfill{}
20456 \begin_inset Tabular
20457 <lyxtabular version="3" rows="7" columns="2">
20458 <features booktabs="true" tabularvalignment="middle">
20459 <column alignment="center" valignment="top" width="0pt">
20460 <column alignment="center" valignment="top" width="0pt">
20462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20465 \begin_layout Plain Layout
20471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20474 \begin_layout Plain Layout
20482 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20485 \begin_layout Plain Layout
20493 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20496 \begin_layout Plain Layout
20497 \begin_inset Formula $\Gamma$
20507 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20510 \begin_layout Plain Layout
20518 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20521 \begin_layout Plain Layout
20522 \begin_inset Formula $\Delta$
20532 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20535 \begin_layout Plain Layout
20543 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20546 \begin_layout Plain Layout
20547 \begin_inset Formula $\Theta$
20557 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20560 \begin_layout Plain Layout
20568 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20571 \begin_layout Plain Layout
20572 \begin_inset Formula $\Lambda$
20582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20585 \begin_layout Plain Layout
20593 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20596 \begin_layout Plain Layout
20597 \begin_inset Formula $\Xi$
20607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20610 \begin_layout Plain Layout
20618 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20621 \begin_layout Plain Layout
20622 \begin_inset Formula $\Pi$
20636 \begin_inset space \hfill{}
20640 \begin_inset Tabular
20641 <lyxtabular version="3" rows="6" columns="2">
20642 <features booktabs="true" tabularvalignment="middle">
20643 <column alignment="center" valignment="top" width="0pt">
20644 <column alignment="center" valignment="top" width="0pt">
20646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20649 \begin_layout Plain Layout
20655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20658 \begin_layout Plain Layout
20666 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20669 \begin_layout Plain Layout
20677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20680 \begin_layout Plain Layout
20681 \begin_inset Formula $\Sigma$
20691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20694 \begin_layout Plain Layout
20702 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20705 \begin_layout Plain Layout
20706 \begin_inset Formula $\Upsilon$
20716 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20719 \begin_layout Plain Layout
20727 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20730 \begin_layout Plain Layout
20731 \begin_inset Formula $\Phi$
20741 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20744 \begin_layout Plain Layout
20752 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20755 \begin_layout Plain Layout
20756 \begin_inset Formula $\Psi$
20766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20769 \begin_layout Plain Layout
20777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20780 \begin_layout Plain Layout
20781 \begin_inset Formula $\Omega$
20795 \begin_inset space \hfill{}
20801 \begin_layout Standard
20802 \begin_inset VSpace medskip
20805 That the big Greek letters appear upright is caused by a design bug when
20808 To get correct italic big letters, begin every command with
20813 For example the command
20820 \begin_inset Formula $\varGamma$
20824 Another way is to load the package
20832 \begin_layout Plain Layout
20837 is part of the \SpecialChar LaTeX
20843 \begin_inset Index idx
20846 \begin_layout Plain Layout
20851 \begin_layout Plain Layout
20871 \begin_inset Index idx
20874 \begin_layout Plain Layout
20880 with the \SpecialChar LaTeX
20884 \begin_layout Standard
20889 usepackage{fixmath}
20892 \begin_layout Standard
20893 Then all big Greek letters in a document will automatically be typeset italic.
20896 \begin_layout Subsection
20898 \begin_inset Index idx
20901 \begin_layout Plain Layout
20902 Greek letters ! bold
20910 \begin_layout Standard
20911 Greek letters cannot be set with different font styles like Latin letters.
20912 They can only be made bold with the command
20919 \begin_inset Index idx
20922 \begin_layout Plain Layout
20933 \begin_layout Standard
20935 \begin_inset Tabular
20936 <lyxtabular version="3" rows="3" columns="2">
20937 <features booktabs="true" tabularvalignment="middle">
20938 <column alignment="center" valignment="top" width="0pt">
20939 <column alignment="center" valignment="top">
20941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20944 \begin_layout Plain Layout
20950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20953 \begin_layout Plain Layout
20961 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20964 \begin_layout Plain Layout
20976 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20979 \begin_layout Plain Layout
20980 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20993 \begin_layout Plain Layout
21005 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21008 \begin_layout Plain Layout
21009 \begin_inset Formula $\theta\boldsymbol{\theta}$
21025 \begin_layout Section
21030 \begin_layout Plain Layout
21043 \begin_layout Plain Layout
21044 A list with all symbols of most of the \SpecialChar LaTeX
21045 -packages can be found in
21046 \begin_inset CommandInset citation
21062 \begin_layout Plain Layout
21070 \begin_inset Note Note
21073 \begin_layout Plain Layout
21076 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21079 \begin_layout Plain Layout
21082 texorpdfstring is in section
21083 \begin_inset CommandInset ref
21085 reference "subsec:Formulas-in-Section"
21095 \begin_inset Index idx
21098 \begin_layout Plain Layout
21107 \begin_layout Standard
21108 Many of the symbols listed in this section can also be inserted via the
21112 arg "math-insert \\nabla"
21118 arg "math-insert \\digamma"
21124 \begin_layout Subsection
21125 Mathematical Symbols
21126 \begin_inset CommandInset label
21128 name "subsec:Mathematical-Symbols"
21133 \begin_inset Index idx
21136 \begin_layout Plain Layout
21137 Symbols ! mathematical
21145 \begin_layout Standard
21146 \begin_inset Tabular
21147 <lyxtabular version="3" rows="10" columns="2">
21148 <features booktabs="true" tabularvalignment="middle">
21149 <column alignment="center" valignment="top" width="0pt">
21150 <column alignment="center" valignment="top" width="0pt">
21152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21155 \begin_layout Plain Layout
21161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21164 \begin_layout Plain Layout
21172 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21175 \begin_layout Plain Layout
21183 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21186 \begin_layout Plain Layout
21187 \begin_inset Formula $\neg$
21197 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21200 \begin_layout Plain Layout
21208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21211 \begin_layout Plain Layout
21212 \begin_inset Formula $\Im$
21222 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21225 \begin_layout Plain Layout
21233 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21236 \begin_layout Plain Layout
21237 \begin_inset Formula $\Re$
21247 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21250 \begin_layout Plain Layout
21258 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21261 \begin_layout Plain Layout
21262 \begin_inset Formula $\aleph$
21272 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21275 \begin_layout Plain Layout
21283 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21286 \begin_layout Plain Layout
21287 \begin_inset Formula $\partial$
21297 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21300 \begin_layout Plain Layout
21308 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21311 \begin_layout Plain Layout
21312 \begin_inset Formula $\infty$
21322 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21325 \begin_layout Plain Layout
21333 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21336 \begin_layout Plain Layout
21337 \begin_inset Formula $\wp$
21347 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21350 \begin_layout Plain Layout
21358 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21361 \begin_layout Plain Layout
21362 \begin_inset Formula $\imath$
21372 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21375 \begin_layout Plain Layout
21383 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21386 \begin_layout Plain Layout
21387 \begin_inset Formula $\jmath$
21401 \begin_inset space \hfill{}
21405 \begin_inset Tabular
21406 <lyxtabular version="3" rows="10" columns="2">
21407 <features booktabs="true" tabularvalignment="middle">
21408 <column alignment="center" valignment="top" width="0pt">
21409 <column alignment="center" valignment="top" width="0pt">
21411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21414 \begin_layout Plain Layout
21420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21423 \begin_layout Plain Layout
21425 \begin_inset Note Note
21428 \begin_layout Plain Layout
21435 is only used as spacer.
21447 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21450 \begin_layout Plain Layout
21458 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21461 \begin_layout Plain Layout
21462 \begin_inset Formula $\forall$
21472 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21475 \begin_layout Plain Layout
21483 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21486 \begin_layout Plain Layout
21487 \begin_inset Formula $\exists$
21497 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21500 \begin_layout Plain Layout
21508 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21511 \begin_layout Plain Layout
21512 \begin_inset Formula $\nexists$
21522 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21525 \begin_layout Plain Layout
21533 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21536 \begin_layout Plain Layout
21537 \begin_inset Formula $\emptyset$
21547 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21550 \begin_layout Plain Layout
21558 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21561 \begin_layout Plain Layout
21562 \begin_inset Formula $\varnothing$
21572 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21575 \begin_layout Plain Layout
21583 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21586 \begin_layout Plain Layout
21587 \begin_inset Formula $\dag$
21597 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21600 \begin_layout Plain Layout
21608 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21611 \begin_layout Plain Layout
21612 \begin_inset Formula $\ddag$
21622 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21625 \begin_layout Plain Layout
21633 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21636 \begin_layout Plain Layout
21640 \begin_layout Plain Layout
21650 \begin_inset Formula $\complement$
21657 \begin_layout Plain Layout
21671 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21674 \begin_layout Plain Layout
21682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21685 \begin_layout Plain Layout
21686 \begin_inset Formula $\Bbbk$
21700 \begin_inset space \hfill{}
21704 \begin_inset Tabular
21705 <lyxtabular version="3" rows="10" columns="2">
21706 <features booktabs="true" tabularvalignment="middle">
21707 <column alignment="center" valignment="top" width="0pt">
21708 <column alignment="center" valignment="top" width="0pt">
21710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21713 \begin_layout Plain Layout
21719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21722 \begin_layout Plain Layout
21730 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21733 \begin_layout Plain Layout
21741 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21744 \begin_layout Plain Layout
21745 \begin_inset Formula $\prime$
21755 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21758 \begin_layout Plain Layout
21766 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21769 \begin_layout Plain Layout
21770 \begin_inset Formula $\backprime$
21780 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21783 \begin_layout Plain Layout
21791 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21794 \begin_layout Plain Layout
21795 \begin_inset Formula $\mho$
21805 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21808 \begin_layout Plain Layout
21816 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21819 \begin_layout Plain Layout
21820 \begin_inset Formula $\triangle$
21830 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21833 \begin_layout Plain Layout
21841 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21844 \begin_layout Plain Layout
21845 \begin_inset Formula $\angle$
21855 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21858 \begin_layout Plain Layout
21866 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21869 \begin_layout Plain Layout
21870 \begin_inset Formula $\measuredangle$
21880 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21883 \begin_layout Plain Layout
21891 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21894 \begin_layout Plain Layout
21895 \begin_inset Formula $\sphericalangle$
21905 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21908 \begin_layout Plain Layout
21916 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21919 \begin_layout Plain Layout
21920 \begin_inset Formula $\top$
21930 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21933 \begin_layout Plain Layout
21941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21944 \begin_layout Plain Layout
21945 \begin_inset Formula $\bot$
21961 \begin_layout Subsection
21962 Miscellaneous Symbols
21963 \begin_inset CommandInset label
21965 name "subsec:Miscellaneous-Symbols"
21970 \begin_inset Index idx
21973 \begin_layout Plain Layout
21974 Symbols ! miscellaneous
21982 \begin_layout Standard
21985 \begin_inset Tabular
21986 <lyxtabular version="3" rows="10" columns="2">
21987 <features booktabs="true" tabularvalignment="middle">
21988 <column alignment="center" valignment="top" width="0pt">
21989 <column alignment="center" valignment="top" width="0pt">
21991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21994 \begin_layout Plain Layout
22000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22003 \begin_layout Plain Layout
22011 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22014 \begin_layout Plain Layout
22022 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22025 \begin_layout Plain Layout
22026 \begin_inset Formula $\flat$
22036 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22039 \begin_layout Plain Layout
22047 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22050 \begin_layout Plain Layout
22051 \begin_inset Formula $\natural$
22061 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22064 \begin_layout Plain Layout
22072 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22075 \begin_layout Plain Layout
22076 \begin_inset Formula $\sharp$
22086 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22089 \begin_layout Plain Layout
22097 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22100 \begin_layout Plain Layout
22101 \begin_inset Formula $\surd$
22111 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22114 \begin_layout Plain Layout
22122 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22125 \begin_layout Plain Layout
22126 \begin_inset Formula $\checkmark$
22136 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22139 \begin_layout Plain Layout
22147 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22150 \begin_layout Plain Layout
22151 \begin_inset Formula $\yen$
22161 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22164 \begin_layout Plain Layout
22172 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22175 \begin_layout Plain Layout
22176 \begin_inset Formula $\pounds$
22186 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22189 \begin_layout Plain Layout
22195 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22198 \begin_layout Plain Layout
22199 \begin_inset Formula $\$$
22209 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22212 \begin_layout Plain Layout
22218 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22221 \begin_layout Plain Layout
22222 \begin_inset Formula $§$
22236 \begin_inset space \hfill{}
22240 \begin_inset Tabular
22241 <lyxtabular version="3" rows="10" columns="2">
22242 <features booktabs="true" tabularvalignment="middle">
22243 <column alignment="center" valignment="top" width="0pt">
22244 <column alignment="center" valignment="top">
22246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22249 \begin_layout Plain Layout
22255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22258 \begin_layout Plain Layout
22266 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22269 \begin_layout Plain Layout
22277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22280 \begin_layout Plain Layout
22281 \begin_inset Formula $\hbar$
22291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22294 \begin_layout Plain Layout
22302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22305 \begin_layout Plain Layout
22306 \begin_inset Formula $\hslash$
22316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22319 \begin_layout Plain Layout
22327 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22330 \begin_layout Plain Layout
22331 \begin_inset Formula $\clubsuit$
22341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22344 \begin_layout Plain Layout
22352 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22355 \begin_layout Plain Layout
22356 \begin_inset Formula $\spadesuit$
22366 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22369 \begin_layout Plain Layout
22377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22380 \begin_layout Plain Layout
22381 \begin_inset Formula $\bigstar$
22391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22394 \begin_layout Plain Layout
22402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22405 \begin_layout Plain Layout
22406 \begin_inset Formula $\blacklozenge$
22416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22419 \begin_layout Plain Layout
22427 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22430 \begin_layout Plain Layout
22431 \begin_inset Formula $\blacktriangle$
22441 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22444 \begin_layout Plain Layout
22452 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22455 \begin_layout Plain Layout
22456 \begin_inset Formula $\blacktriangledown$
22466 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22469 \begin_layout Plain Layout
22477 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22480 \begin_layout Plain Layout
22481 \begin_inset Formula $\bullet$
22495 \begin_inset space \hfill{}
22499 \begin_inset Tabular
22500 <lyxtabular version="3" rows="10" columns="2">
22501 <features booktabs="true" tabularvalignment="middle">
22502 <column alignment="center" valignment="top" width="0pt">
22503 <column alignment="center" valignment="top" width="0pt">
22505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22508 \begin_layout Plain Layout
22514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22517 \begin_layout Plain Layout
22525 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22528 \begin_layout Plain Layout
22536 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22539 \begin_layout Plain Layout
22540 \begin_inset Formula $\diamondsuit$
22550 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22553 \begin_layout Plain Layout
22561 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22564 \begin_layout Plain Layout
22565 \begin_inset Formula $\Diamond$
22575 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22578 \begin_layout Plain Layout
22586 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22589 \begin_layout Plain Layout
22590 \begin_inset Formula $\heartsuit$
22600 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22603 \begin_layout Plain Layout
22611 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22614 \begin_layout Plain Layout
22615 \begin_inset Formula $\P$
22625 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22628 \begin_layout Plain Layout
22636 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22639 \begin_layout Plain Layout
22640 \begin_inset Formula $\copyright$
22650 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22653 \begin_layout Plain Layout
22661 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22664 \begin_layout Plain Layout
22665 \begin_inset Formula $\circledR$
22675 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22678 \begin_layout Plain Layout
22686 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22689 \begin_layout Plain Layout
22690 \begin_inset Formula $\maltese$
22700 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22703 \begin_layout Plain Layout
22711 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22714 \begin_layout Plain Layout
22715 \begin_inset Formula $\diagup$
22725 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22728 \begin_layout Plain Layout
22736 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22739 \begin_layout Plain Layout
22740 \begin_inset Formula $\diagdown$
22756 \begin_layout Standard
22757 \begin_inset VSpace medskip
22763 \begin_layout Standard
22764 Some symbols can be displayed in different sizes, see
22765 \begin_inset CommandInset ref
22767 reference "subsec:Font-Sizes"
22774 \begin_layout Subsection
22776 \begin_inset Index idx
22779 \begin_layout Plain Layout
22780 Symbols ! Euro-symbol
22786 \begin_inset Index idx
22789 \begin_layout Plain Layout
22796 \begin_layout Plain Layout
22813 \begin_layout Standard
22814 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22820 \begin_inset Index idx
22823 \begin_layout Plain Layout
22829 must be installed and loaded with the \SpecialChar LaTeX
22833 \begin_layout Standard
22838 usepackage[gennarrow]{eurosym}
22841 \begin_layout Standard
22842 The Euro symbol can now be inserted with the command
22849 \begin_inset Index idx
22852 \begin_layout Plain Layout
22863 \begin_layout Standard
22864 The Euro symbol can directly be inserted with the € key in mathematical
22865 text, without having
22880 can also be inserted in \SpecialChar TeX
22882 The official currency symbol can then be inserted with the command
22889 \begin_inset Index idx
22892 \begin_layout Plain Layout
22900 , that is only available in \SpecialChar TeX
22904 \begin_layout Standard
22908 \begin_layout Plain Layout
22918 \begin_inset Note Note
22921 \begin_layout Plain Layout
22922 The following table will only be displayed when the \SpecialChar LaTeX
22935 \begin_layout Standard
22936 An overview about the different Euro symbols:
22939 \begin_layout Standard
22941 \begin_inset Tabular
22942 <lyxtabular version="3" rows="4" columns="3">
22943 <features booktabs="true" tabularvalignment="middle">
22944 <column alignment="center" valignment="top" width="0pt">
22945 <column alignment="center" valignment="top" width="0pt">
22946 <column alignment="center" valignment="top" width="0pt">
22948 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22951 \begin_layout Plain Layout
22955 \begin_layout Plain Layout
22959 cmidrule[0.08em]{2-3}
22969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22972 \begin_layout Plain Layout
22978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22981 \begin_layout Plain Layout
22989 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22992 \begin_layout Plain Layout
22998 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23001 \begin_layout Plain Layout
23009 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23012 \begin_layout Plain Layout
23013 \begin_inset Formula $\euro$
23023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23026 \begin_layout Plain Layout
23032 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23035 \begin_layout Plain Layout
23041 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23044 \begin_layout Plain Layout
23045 \begin_inset Formula $\mbox{€}$
23055 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23058 \begin_layout Plain Layout
23065 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23068 \begin_layout Plain Layout
23076 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23079 \begin_layout Plain Layout
23083 \begin_layout Plain Layout
23103 \begin_inset Note Note
23106 \begin_layout Plain Layout
23113 is used here only for table borders.
23123 manual for details.
23131 \begin_layout Standard
23135 \begin_layout Plain Layout
23145 \begin_inset Note Note
23148 \begin_layout Plain Layout
23149 The following will be displayed when the \SpecialChar LaTeX
23162 \begin_layout Standard
23163 You need to install the \SpecialChar LaTeX
23168 to see the rest of this subsection in the output.
23171 \begin_layout Standard
23175 \begin_layout Plain Layout
23187 \begin_layout Section
23189 \begin_inset CommandInset label
23191 name "sec:Relations"
23196 \begin_inset Index idx
23199 \begin_layout Plain Layout
23206 \begin_inset Index idx
23209 \begin_layout Plain Layout
23214 \begin_layout Plain Layout
23225 \begin_layout Plain Layout
23240 \begin_layout Standard
23241 All following relations can also be inserted via the toolbar button
23244 arg "math-insert \\leq"
23250 \begin_layout Standard
23251 \begin_inset Tabular
23252 <lyxtabular version="3" rows="17" columns="2">
23253 <features booktabs="true" tabularvalignment="middle">
23254 <column alignment="center" valignment="top" width="0pt">
23255 <column alignment="center" valignment="top" width="0pt">
23257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23260 \begin_layout Plain Layout
23266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23269 \begin_layout Plain Layout
23277 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23280 \begin_layout Plain Layout
23286 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23289 \begin_layout Plain Layout
23290 \begin_inset Formula $<$
23300 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23303 \begin_layout Plain Layout
23311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23314 \begin_layout Plain Layout
23315 \begin_inset Formula $\le$
23325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23328 \begin_layout Plain Layout
23336 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23339 \begin_layout Plain Layout
23340 \begin_inset Formula $\ll$
23350 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23353 \begin_layout Plain Layout
23361 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23364 \begin_layout Plain Layout
23365 \begin_inset Formula $\prec$
23375 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23378 \begin_layout Plain Layout
23386 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23389 \begin_layout Plain Layout
23390 \begin_inset Formula $\preceq$
23400 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23403 \begin_layout Plain Layout
23411 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23414 \begin_layout Plain Layout
23415 \begin_inset Formula $\subset$
23425 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23428 \begin_layout Plain Layout
23436 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23439 \begin_layout Plain Layout
23440 \begin_inset Formula $\subseteq$
23450 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23453 \begin_layout Plain Layout
23461 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23464 \begin_layout Plain Layout
23465 \begin_inset Formula $\sqsubseteq$
23475 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23478 \begin_layout Plain Layout
23486 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23489 \begin_layout Plain Layout
23490 \begin_inset Formula $\in$
23500 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23503 \begin_layout Plain Layout
23511 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23514 \begin_layout Plain Layout
23515 \begin_inset Formula $\vdash$
23525 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23528 \begin_layout Plain Layout
23536 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23539 \begin_layout Plain Layout
23540 \begin_inset Formula $\smile$
23550 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23553 \begin_layout Plain Layout
23561 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23564 \begin_layout Plain Layout
23565 \begin_inset Formula $\lhd$
23575 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23578 \begin_layout Plain Layout
23586 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23589 \begin_layout Plain Layout
23590 \begin_inset Formula $\unlhd$
23600 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23603 \begin_layout Plain Layout
23611 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23614 \begin_layout Plain Layout
23615 \begin_inset Formula $\gtrless$
23625 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23628 \begin_layout Plain Layout
23636 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23639 \begin_layout Plain Layout
23640 \begin_inset Formula $\mid$
23650 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23653 \begin_layout Plain Layout
23661 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23664 \begin_layout Plain Layout
23665 \begin_inset Formula $\nmid$
23679 \begin_inset space \hfill{}
23683 \begin_inset Tabular
23684 <lyxtabular version="3" rows="17" columns="2">
23685 <features booktabs="true" tabularvalignment="middle">
23686 <column alignment="center" valignment="top" width="0pt">
23687 <column alignment="center" valignment="top" width="0pt">
23689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23692 \begin_layout Plain Layout
23698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23701 \begin_layout Plain Layout
23709 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23712 \begin_layout Plain Layout
23718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23721 \begin_layout Plain Layout
23722 \begin_inset Formula $=$
23732 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23735 \begin_layout Plain Layout
23743 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23746 \begin_layout Plain Layout
23747 \begin_inset Formula $\not=$
23757 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23760 \begin_layout Plain Layout
23768 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23771 \begin_layout Plain Layout
23772 \begin_inset Formula $\equiv$
23782 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23785 \begin_layout Plain Layout
23793 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23796 \begin_layout Plain Layout
23797 \begin_inset Formula $\sim$
23807 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23810 \begin_layout Plain Layout
23818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23821 \begin_layout Plain Layout
23822 \begin_inset Formula $\simeq$
23832 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23835 \begin_layout Plain Layout
23843 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23846 \begin_layout Plain Layout
23847 \begin_inset Formula $\approx$
23857 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23860 \begin_layout Plain Layout
23868 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23871 \begin_layout Plain Layout
23872 \begin_inset Formula $\cong$
23882 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23885 \begin_layout Plain Layout
23893 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23896 \begin_layout Plain Layout
23897 \begin_inset Formula $\bowtie$
23907 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23910 \begin_layout Plain Layout
23918 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23921 \begin_layout Plain Layout
23922 \begin_inset Formula $\notin$
23932 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23935 \begin_layout Plain Layout
23943 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23946 \begin_layout Plain Layout
23947 \begin_inset Formula $\perp$
23957 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23960 \begin_layout Plain Layout
23968 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23971 \begin_layout Plain Layout
23972 \begin_inset Formula $\propto$
23982 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23985 \begin_layout Plain Layout
23993 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23996 \begin_layout Plain Layout
23997 \begin_inset Formula $\asymp$
24007 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24010 \begin_layout Plain Layout
24018 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24021 \begin_layout Plain Layout
24022 \begin_inset Formula $\doteq$
24032 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24035 \begin_layout Plain Layout
24043 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24046 \begin_layout Plain Layout
24047 \begin_inset Formula $\circeq$
24057 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24060 \begin_layout Plain Layout
24068 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24071 \begin_layout Plain Layout
24072 \begin_inset Formula $\models$
24082 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24085 \begin_layout Plain Layout
24093 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24096 \begin_layout Plain Layout
24097 \begin_inset Formula $\widehat{=}$
24111 \begin_inset space \hfill{}
24115 \begin_inset Tabular
24116 <lyxtabular version="3" rows="17" columns="2">
24117 <features booktabs="true" tabularvalignment="middle">
24118 <column alignment="center" valignment="top" width="0pt">
24119 <column alignment="center" valignment="top" width="0pt">
24121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24124 \begin_layout Plain Layout
24130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24133 \begin_layout Plain Layout
24141 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24144 \begin_layout Plain Layout
24150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24153 \begin_layout Plain Layout
24154 \begin_inset Formula $>$
24164 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24167 \begin_layout Plain Layout
24175 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24178 \begin_layout Plain Layout
24179 \begin_inset Formula $\ge$
24189 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24192 \begin_layout Plain Layout
24200 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24203 \begin_layout Plain Layout
24204 \begin_inset Formula $\gg$
24214 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24217 \begin_layout Plain Layout
24225 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24228 \begin_layout Plain Layout
24229 \begin_inset Formula $\succ$
24239 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24242 \begin_layout Plain Layout
24250 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24253 \begin_layout Plain Layout
24254 \begin_inset Formula $\succeq$
24264 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24267 \begin_layout Plain Layout
24275 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24278 \begin_layout Plain Layout
24279 \begin_inset Formula $\supset$
24289 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24292 \begin_layout Plain Layout
24300 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24303 \begin_layout Plain Layout
24304 \begin_inset Formula $\supseteq$
24314 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24317 \begin_layout Plain Layout
24325 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24328 \begin_layout Plain Layout
24329 \begin_inset Formula $\sqsupseteq$
24339 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24342 \begin_layout Plain Layout
24350 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24353 \begin_layout Plain Layout
24354 \begin_inset Formula $\ni$
24364 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24367 \begin_layout Plain Layout
24375 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24378 \begin_layout Plain Layout
24379 \begin_inset Formula $\dashv$
24389 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24392 \begin_layout Plain Layout
24400 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24403 \begin_layout Plain Layout
24404 \begin_inset Formula $\frown$
24414 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24417 \begin_layout Plain Layout
24425 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24428 \begin_layout Plain Layout
24429 \begin_inset Formula $\rhd$
24439 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24442 \begin_layout Plain Layout
24450 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24453 \begin_layout Plain Layout
24454 \begin_inset Formula $\unrhd$
24464 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24467 \begin_layout Plain Layout
24475 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24478 \begin_layout Plain Layout
24479 \begin_inset Formula $\lessgtr$
24489 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24492 \begin_layout Plain Layout
24500 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24503 \begin_layout Plain Layout
24504 \begin_inset Formula $\parallel$
24514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24517 \begin_layout Plain Layout
24525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24528 \begin_layout Plain Layout
24529 \begin_inset Formula $\nparallel$
24545 \begin_layout Standard
24546 \begin_inset VSpace medskip
24561 are bigger than the equal looking operators
24576 \begin_layout Standard
24578 supports also many special relations.
24579 Use the toolbar button
24582 arg "math-insert \\leqq"
24585 to see a list of these relations.
24588 \begin_layout Standard
24589 Relations are, in contrary to symbols, always surrounded by space.
24592 \begin_layout Standard
24593 Relations with labels can be created with the command
24600 \begin_inset Index idx
24603 \begin_layout Plain Layout
24614 \begin_layout Standard
24616 \begin_inset Tabular
24617 <lyxtabular version="3" rows="2" columns="2">
24618 <features booktabs="true" tabularvalignment="middle">
24619 <column alignment="center" valignment="top" width="0pt">
24620 <column alignment="center" valignment="top">
24622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24625 \begin_layout Plain Layout
24631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24634 \begin_layout Plain Layout
24641 <row topspace="1.5mm">
24642 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24645 \begin_layout Plain Layout
24649 \begin_inset space \textvisiblespace{}
24657 \begin_inset space \textvisiblespace{}
24661 \begin_inset Formula $\downarrow$
24667 \begin_inset space \textvisiblespace{}
24671 \begin_inset space \textvisiblespace{}
24679 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24682 \begin_layout Plain Layout
24683 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24699 \begin_layout Section
24703 \begin_layout Subsection
24704 Predefined Functions
24705 \begin_inset CommandInset label
24707 name "subsec:Predefined-Functions"
24712 \begin_inset Index idx
24715 \begin_layout Plain Layout
24716 Functions ! predefined
24724 \begin_layout Standard
24725 In general, variables are set
24729 in mathematical expressions, but not function names, because
24730 \begin_inset Formula $sin$
24733 could be misunderstood as
24734 \begin_inset Formula $s\cdot i\cdot n$
24738 Therefore there are predefined functions which are additionally a bit separated
24740 They are inserted as commands starting with a backslash before their name.
24743 \begin_layout Standard
24745 \begin_inset Tabular
24746 <lyxtabular version="3" rows="2" columns="2">
24747 <features booktabs="true" tabularvalignment="middle">
24748 <column alignment="center" valignment="top" width="0pt">
24749 <column alignment="center" valignment="top" width="0pt">
24751 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24754 \begin_layout Plain Layout
24760 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24763 \begin_layout Plain Layout
24771 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24774 \begin_layout Plain Layout
24780 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24783 \begin_layout Plain Layout
24784 \begin_inset Formula $Asin(x)+B$
24798 \begin_inset space \quad{}
24802 \begin_inset Tabular
24803 <lyxtabular version="3" rows="2" columns="2">
24804 <features booktabs="true" tabularvalignment="middle">
24805 <column alignment="center" valignment="top" width="0pt">
24806 <column alignment="center" valignment="top" width="0pt">
24808 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24811 \begin_layout Plain Layout
24817 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24820 \begin_layout Plain Layout
24828 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24831 \begin_layout Plain Layout
24839 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24842 \begin_layout Plain Layout
24843 \begin_inset Formula $A\sin(x)+B$
24859 \begin_layout Standard
24860 The following functions are predefined:
24863 \begin_layout Standard
24864 \begin_inset VSpace -2mm
24870 \begin_layout Standard
24872 \begin_inset Tabular
24873 <lyxtabular version="3" rows="9" columns="4">
24874 <features booktabs="true" tabularvalignment="middle">
24875 <column alignment="center" valignment="top" width="0pt">
24876 <column alignment="center" valignment="top" width="0pt">
24877 <column alignment="center" valignment="top" width="0pt">
24878 <column alignment="center" valignment="top" width="0pt">
24880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24883 \begin_layout Plain Layout
24889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24892 \begin_layout Plain Layout
24898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24901 \begin_layout Plain Layout
24907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24910 \begin_layout Plain Layout
24918 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24921 \begin_layout Plain Layout
24929 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24932 \begin_layout Plain Layout
24940 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24943 \begin_layout Plain Layout
24951 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24954 \begin_layout Plain Layout
24964 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24967 \begin_layout Plain Layout
24975 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24978 \begin_layout Plain Layout
24986 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24989 \begin_layout Plain Layout
24997 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25000 \begin_layout Plain Layout
25010 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25013 \begin_layout Plain Layout
25021 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25024 \begin_layout Plain Layout
25032 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25035 \begin_layout Plain Layout
25043 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25046 \begin_layout Plain Layout
25056 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25059 \begin_layout Plain Layout
25067 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25070 \begin_layout Plain Layout
25078 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25081 \begin_layout Plain Layout
25089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25092 \begin_layout Plain Layout
25102 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25105 \begin_layout Plain Layout
25113 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25116 \begin_layout Plain Layout
25124 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25127 \begin_layout Plain Layout
25135 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25138 \begin_layout Plain Layout
25148 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25151 \begin_layout Plain Layout
25159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25162 \begin_layout Plain Layout
25170 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25173 \begin_layout Plain Layout
25181 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25184 \begin_layout Plain Layout
25194 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25197 \begin_layout Plain Layout
25205 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25208 \begin_layout Plain Layout
25216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25219 \begin_layout Plain Layout
25227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25230 \begin_layout Plain Layout
25240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25243 \begin_layout Plain Layout
25251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25254 \begin_layout Plain Layout
25262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25265 \begin_layout Plain Layout
25273 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25276 \begin_layout Plain Layout
25292 \begin_layout Standard
25293 They can also be inserted with the math toolbar button
25296 arg "math-insert \\functions"
25302 \begin_layout Subsection
25303 Self-defined Functions
25304 \begin_inset Index idx
25307 \begin_layout Plain Layout
25308 Functions ! self-defined
25316 \begin_layout Standard
25317 To use a function that is not predefined, like for example the sign function
25318 sgn(x), there are two possibilities:
25321 \begin_layout Itemize
25322 Define the function by inserting the following line to the \SpecialChar LaTeX
25327 \begin_layout Plain Layout
25332 DeclareMathOperator
25335 \begin_inset CommandInset ref
25337 reference "subsec:Self-defined-Operators"
25347 \begin_inset Newline newline
25351 \begin_inset VSpace -3mm
25355 \begin_inset Newline newline
25362 DeclareMathOperator{
25367 \begin_inset Index idx
25370 \begin_layout Plain Layout
25375 DeclareMathOperator
25381 \begin_inset Newline newline
25385 \begin_inset VSpace -2mm
25389 \begin_inset Newline newline
25392 Now the new defined function can be called with the command
25401 \begin_layout Itemize
25402 Write the formula as usual, mark the formula name, in our example the letters
25407 , and change it to mathematical text.
25408 Finally, a space is inserted between prefactor and function.
25411 \begin_layout Standard
25412 The result is the same with both methods as with a predefined function
25416 \begin_layout Plain Layout
25417 In \SpecialChar LyX
25418 self-defined functions are displayed red, predefined ones black.
25426 \begin_layout Standard
25428 \begin_inset Tabular
25429 <lyxtabular version="3" rows="3" columns="2">
25430 <features booktabs="true" tabularvalignment="middle">
25431 <column alignment="center" valignment="top" width="0pt">
25432 <column alignment="center" valignment="top" width="0pt">
25434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25437 \begin_layout Plain Layout
25443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25446 \begin_layout Plain Layout
25454 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25457 \begin_layout Plain Layout
25465 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25468 \begin_layout Plain Layout
25469 \begin_inset Formula $A\sgn(x)+B$
25479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25482 \begin_layout Plain Layout
25486 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25497 \begin_layout Plain Layout
25498 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25514 \begin_layout Standard
25515 The first method is more suitable when the self-defined function should
25516 be used several times.
25519 \begin_layout Subsection
25521 \begin_inset Index idx
25524 \begin_layout Plain Layout
25533 \begin_layout Standard
25534 For limits, in addition to the commands
25541 \begin_inset Index idx
25544 \begin_layout Plain Layout
25564 the following functions are defined:
25567 \begin_layout Standard
25569 \begin_inset Tabular
25570 <lyxtabular version="3" rows="5" columns="2">
25571 <features booktabs="true" tabularvalignment="middle">
25572 <column alignment="center" valignment="top" width="0pt">
25573 <column alignment="center" valignment="top" width="0pt">
25575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25578 \begin_layout Plain Layout
25584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25587 \begin_layout Plain Layout
25595 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25598 \begin_layout Plain Layout
25606 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25609 \begin_layout Plain Layout
25610 \begin_inset Formula $\varliminf$
25619 <row topspace="1.5mm">
25620 <cell alignment="center" valignment="top" usebox="none">
25623 \begin_layout Plain Layout
25631 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25634 \begin_layout Plain Layout
25635 \begin_inset Formula $\varlimsup$
25644 <row topspace="1.5mm">
25645 <cell alignment="center" valignment="top" usebox="none">
25648 \begin_layout Plain Layout
25656 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25659 \begin_layout Plain Layout
25660 \begin_inset Formula $\varprojlim$
25669 <row topspace="1.5mm" bottomspace="1mm">
25670 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25673 \begin_layout Plain Layout
25681 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25684 \begin_layout Plain Layout
25685 \begin_inset Formula $\varinjlim$
25701 \begin_layout Standard
25702 \begin_inset VSpace medskip
25705 The limit is created by inserting a subscript.
25706 It is set right beside the function in an inline formula:
25709 \begin_layout Standard
25711 \begin_inset Tabular
25712 <lyxtabular version="3" rows="2" columns="2">
25713 <features booktabs="true" tabularvalignment="middle">
25714 <column alignment="center" valignment="top" width="0pt">
25715 <column alignment="center" valignment="top" width="0pt">
25717 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25720 \begin_layout Plain Layout
25726 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25729 \begin_layout Plain Layout
25737 <cell alignment="center" valignment="top" usebox="none">
25740 \begin_layout Plain Layout
25746 \begin_inset space \textvisiblespace{}
25750 \begin_inset space \textvisiblespace{}
25758 <cell alignment="center" valignment="top" usebox="none">
25761 \begin_layout Plain Layout
25762 \begin_inset Formula $\lim_{x\to A}x=B$
25778 \begin_layout Standard
25779 In a displayed formula the limit is set below the formula, as usual:
25780 \begin_inset Formula
25790 \begin_layout Standard
25791 \begin_inset VSpace medskip
25797 \begin_layout Standard
25798 How to adjust the typesetting of the limits see
25799 \begin_inset CommandInset ref
25801 reference "subsec:Operator-Limits"
25808 \begin_layout Subsection
25810 \begin_inset Index idx
25813 \begin_layout Plain Layout
25814 Functions ! modulo-
25822 \begin_layout Standard
25823 The modulo-function is special, because it exists in four variants.
25824 The variants in a displayed formula are:
25825 \begin_inset Formula
25827 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25828 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25829 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25830 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25831 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25839 \begin_layout Standard
25840 In an inline formula less space is set before the function names for all
25842 By default the modulo-functions take only the first following character
25844 To use more than one character, one has to put them into \SpecialChar TeX
25846 \begin_inset Formula
25848 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25849 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25850 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25858 \begin_layout Section
25860 \begin_inset Index idx
25863 \begin_layout Plain Layout
25872 \begin_layout Standard
25873 The characters ^ and _ would normally create a superscript and subscript,
25875 To get these characters you have to insert them with a leading
25880 \begin_layout Standard
25883 \begin_inset Tabular
25884 <lyxtabular version="3" rows="3" columns="2">
25885 <features booktabs="true" tabularvalignment="middle">
25886 <column alignment="left" valignment="top" width="0pt">
25887 <column alignment="block" valignment="top">
25889 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25892 \begin_layout Plain Layout
25898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25901 \begin_layout Plain Layout
25909 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25912 \begin_layout Plain Layout
25916 \begin_inset space \textvisiblespace{}
25924 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25927 \begin_layout Plain Layout
25928 \begin_inset Formula $\mathcircumflex$
25938 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25941 \begin_layout Plain Layout
25949 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25952 \begin_layout Plain Layout
25953 \begin_inset Formula $\_$
25969 \begin_layout Subsection
25970 Special Characters in Mathematical Text
25973 \begin_layout Standard
25974 The following commands can only be used in mathematical text or in \SpecialChar TeX
25978 \begin_layout Standard
25979 \begin_inset space \hfill{}
25983 \begin_inset Tabular
25984 <lyxtabular version="3" rows="8" columns="2">
25985 <features booktabs="true" tabularvalignment="middle">
25986 <column alignment="left" valignment="top" width="0pt">
25987 <column alignment="block" valignment="top">
25989 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25992 \begin_layout Plain Layout
25998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26001 \begin_layout Plain Layout
26009 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26012 \begin_layout Plain Layout
26020 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26023 \begin_layout Plain Layout
26024 \begin_inset Formula $\textrm{œ}$
26034 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26037 \begin_layout Plain Layout
26045 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26048 \begin_layout Plain Layout
26049 \begin_inset Formula $\textrm{Œ}$
26059 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26062 \begin_layout Plain Layout
26070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26073 \begin_layout Plain Layout
26074 \begin_inset Formula $\textrm{æ}$
26084 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26087 \begin_layout Plain Layout
26095 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26098 \begin_layout Plain Layout
26099 \begin_inset Formula $\textrm{Æ}$
26109 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26112 \begin_layout Plain Layout
26120 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26123 \begin_layout Plain Layout
26124 \begin_inset Formula $\textrm{å}$
26134 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26137 \begin_layout Plain Layout
26141 \begin_inset Index idx
26144 \begin_layout Plain Layout
26151 \begin_layout Plain Layout
26172 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26175 \begin_layout Plain Layout
26176 \begin_inset Formula $\textrm{Å}$
26186 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26189 \begin_layout Plain Layout
26197 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26200 \begin_layout Plain Layout
26201 \begin_inset Formula $\textrm{ı}$
26215 \begin_inset space \hfill{}
26219 \begin_inset Tabular
26220 <lyxtabular version="3" rows="8" columns="2">
26221 <features booktabs="true" tabularvalignment="middle">
26222 <column alignment="left" valignment="top" width="0pt">
26223 <column alignment="center" valignment="top">
26225 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26228 \begin_layout Plain Layout
26230 \begin_inset Note Note
26233 \begin_layout Plain Layout
26235 \begin_inset space \thinspace{}
26238 mm is used for separation, because otherwise the output will be ¡ and ¿
26249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26252 \begin_layout Plain Layout
26260 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26263 \begin_layout Plain Layout
26271 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26274 \begin_layout Plain Layout
26275 \begin_inset Formula $\textrm{ø}$
26285 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26288 \begin_layout Plain Layout
26296 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26299 \begin_layout Plain Layout
26300 \begin_inset Formula $\textrm{Ø}$
26310 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26313 \begin_layout Plain Layout
26321 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26324 \begin_layout Plain Layout
26325 \begin_inset Formula $\textrm{ł}$
26335 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26338 \begin_layout Plain Layout
26346 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26349 \begin_layout Plain Layout
26350 \begin_inset Formula $\textrm{Ł}$
26360 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26363 \begin_layout Plain Layout
26365 \begin_inset space \hspace{}
26370 \begin_inset space \textvisiblespace{}
26378 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26381 \begin_layout Plain Layout
26382 \begin_inset Formula $\textrm{!`}$
26392 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26395 \begin_layout Plain Layout
26397 \begin_inset space \hspace{}
26402 \begin_inset space \textvisiblespace{}
26410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26413 \begin_layout Plain Layout
26414 \begin_inset Formula $\textrm{?`}$
26424 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26427 \begin_layout Plain Layout
26435 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26438 \begin_layout Plain Layout
26439 \begin_inset Formula $\textrm{ȷ}$
26453 \begin_inset space \hfill{}
26459 \begin_layout Standard
26461 \begin_inset Formula $\textrm{\textrm{Å}}$
26465 \begin_inset Formula $\textrm{\textrm{Ø}}$
26468 can also be inserted via the math toolbar button
26471 arg "math-insert \\digamma"
26477 \begin_layout Standard
26478 An exception are the commands
26481 \begin_inset space \hspace{}
26490 \begin_inset space \hspace{}
26496 , because they can be inserted in \SpecialChar LyX
26500 \begin_layout Subsection
26502 \begin_inset CommandInset label
26504 name "subsec:Accents-in-Text"
26509 \begin_inset Index idx
26512 \begin_layout Plain Layout
26521 \begin_layout Standard
26522 With the following commands all letters can be accented.
26523 The commands must be inserted in \SpecialChar TeX
26527 \begin_layout Standard
26528 \begin_inset space \hfill{}
26532 \begin_inset Tabular
26533 <lyxtabular version="3" rows="8" columns="2">
26534 <features booktabs="true" tabularvalignment="middle">
26535 <column alignment="left" valignment="top" width="0pt">
26536 <column alignment="block" valignment="top">
26538 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26541 \begin_layout Plain Layout
26547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26550 \begin_layout Plain Layout
26558 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26561 \begin_layout Plain Layout
26565 \begin_inset Quotes grd
26573 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26576 \begin_layout Plain Layout
26580 \begin_layout Plain Layout
26596 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26599 \begin_layout Plain Layout
26607 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26610 \begin_layout Plain Layout
26614 \begin_layout Plain Layout
26630 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26633 \begin_layout Plain Layout
26637 \begin_inset space \textvisiblespace{}
26645 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26648 \begin_layout Plain Layout
26652 \begin_layout Plain Layout
26668 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26671 \begin_layout Plain Layout
26679 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26682 \begin_layout Plain Layout
26686 \begin_layout Plain Layout
26702 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26705 \begin_layout Plain Layout
26709 \begin_inset space \textvisiblespace{}
26717 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26720 \begin_layout Plain Layout
26724 \begin_layout Plain Layout
26740 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26743 \begin_layout Plain Layout
26747 \begin_inset space \textvisiblespace{}
26755 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26758 \begin_layout Plain Layout
26762 \begin_layout Plain Layout
26778 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26781 \begin_layout Plain Layout
26785 \begin_inset space \textvisiblespace{}
26793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26796 \begin_layout Plain Layout
26800 \begin_layout Plain Layout
26820 \begin_inset space \hfill{}
26824 \begin_inset Tabular
26825 <lyxtabular version="3" rows="8" columns="2">
26826 <features booktabs="true" tabularvalignment="middle">
26827 <column alignment="left" valignment="top" width="0pt">
26828 <column alignment="center" valignment="top">
26830 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26833 \begin_layout Plain Layout
26839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26842 \begin_layout Plain Layout
26850 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26853 \begin_layout Plain Layout
26857 \begin_inset space \textvisiblespace{}
26865 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26868 \begin_layout Plain Layout
26872 \begin_layout Plain Layout
26888 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26891 \begin_layout Plain Layout
26899 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26902 \begin_layout Plain Layout
26906 \begin_layout Plain Layout
26922 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26925 \begin_layout Plain Layout
26929 \begin_inset Index idx
26932 \begin_layout Plain Layout
26943 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26946 \begin_layout Plain Layout
26950 \begin_layout Plain Layout
26966 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26969 \begin_layout Plain Layout
26977 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26980 \begin_layout Plain Layout
26984 \begin_layout Plain Layout
27000 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27003 \begin_layout Plain Layout
27007 \begin_inset space \textvisiblespace{}
27015 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27018 \begin_layout Plain Layout
27022 \begin_layout Plain Layout
27038 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27041 \begin_layout Plain Layout
27045 \begin_inset space \textvisiblespace{}
27053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27056 \begin_layout Plain Layout
27060 \begin_layout Plain Layout
27076 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27079 \begin_layout Plain Layout
27083 \begin_inset space \textvisiblespace{}
27091 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27094 \begin_layout Plain Layout
27098 \begin_layout Plain Layout
27118 \begin_inset space \hfill{}
27124 \begin_layout Standard
27125 \begin_inset VSpace medskip
27134 also two different characters can be accented.
27140 \begin_inset space \textvisiblespace{}
27149 \begin_layout Plain Layout
27161 \begin_layout Standard
27174 can in combination with vowels directly be inserted with the keyboard without
27175 using \SpecialChar TeX
27177 The same applies for the tilde
27181 \begin_layout Plain Layout
27182 This only applies for keyboards where the tilde is defined as accent.
27191 in combination with
27206 \begin_layout Standard
27249 and accents that are inserted directly with the keyboard are also available
27250 in mathematical text.
27251 For the other accents there are special math commands to be used in formulas,
27253 \begin_inset CommandInset ref
27255 reference "subsec:Accents-for-one"
27262 \begin_layout Standard
27263 \begin_inset VSpace bigskip
27266 Furthermore, with the command
27273 \begin_inset Index idx
27276 \begin_layout Plain Layout
27284 all numbers and letters can be set into a circle, quasi accented with a
27285 circle, similar to the copyright symbol.
27288 \begin_layout Standard
27290 \begin_inset Tabular
27291 <lyxtabular version="3" rows="3" columns="2">
27292 <features booktabs="true" tabularvalignment="middle">
27293 <column alignment="center" valignment="top" width="0pt">
27294 <column alignment="center" valignment="top">
27296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27299 \begin_layout Plain Layout
27305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27308 \begin_layout Plain Layout
27316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27319 \begin_layout Plain Layout
27327 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27330 \begin_layout Plain Layout
27334 \begin_layout Plain Layout
27349 <row topspace="1mm">
27350 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27353 \begin_layout Plain Layout
27364 raisebox{-1.5pt}{W}}
27369 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27372 \begin_layout Plain Layout
27376 \begin_layout Plain Layout
27406 \begin_layout Standard
27407 One has to take care that the character fits in the circle.
27418 \begin_layout Plain Layout
27420 \begin_inset CommandInset ref
27422 reference "subsec:Font-Sizes"
27431 specifies thereby the size of the circle.
27442 \begin_layout Plain Layout
27444 \begin_inset CommandInset ref
27446 reference "subsec:Boxes-without-Frame"
27455 the character can be centered.
27458 \begin_layout Subsection
27460 \begin_inset Index idx
27463 \begin_layout Plain Layout
27472 \begin_layout Standard
27473 Old-style figures (also known as old-style numerals) are created with the
27481 \begin_inset Index idx
27484 \begin_layout Plain Layout
27493 The command can be used in formulas and in \SpecialChar TeX
27495 The command scheme is:
27498 \begin_layout Standard
27503 oldstylenums{number}
27506 \begin_layout Standard
27511 oldstylenums{0123456789
27514 \begin_inset Formula $\oldstylenums{0123456789}$
27520 \begin_layout Section
27522 \begin_inset CommandInset label
27524 name "sec:Formula-Styles"
27529 \begin_inset Index idx
27532 \begin_layout Plain Layout
27541 \begin_layout Itemize
27542 There are two different alignment styles:
27546 \begin_layout Description
27547 Centered is the predefined standard
27550 \begin_layout Description
27551 Indented for this the option
27555 must be inserted in the menu
27557 Document\SpecialChar menuseparator
27563 \begin_inset space ~
27569 \begin_layout Standard
27574 is used, the indentation can be adjusted with the length
27581 \begin_inset Index idx
27584 \begin_layout Plain Layout
27593 Should the distance be 15
27594 \begin_inset space \thinspace{}
27597 mm, the following command line is inserted in the \SpecialChar LaTeX
27601 \begin_layout Standard
27611 \begin_layout Standard
27612 When no length is specified, a predefined value will be used.
27613 The value depends on the used document class.
27617 \begin_layout Itemize
27618 And two different numbering styles:
27622 \begin_layout Description
27623 Right is the predefined standard
27626 \begin_layout Description
27627 Left for this the option
27631 must be inserted in the menu
27633 Document\SpecialChar menuseparator
27639 \begin_inset space ~
27646 \begin_layout Standard
27655 can also be used together.
27656 In this case both options are inserted, separated by a comma.
27659 \begin_layout Standard
27660 The chosen styles are used for all displayed formulas of the document.
27661 When both, centered and indented formulas should be created in a document,
27667 The indented formulas are then set in a flalign environment, see
27668 \begin_inset CommandInset ref
27670 reference "subsec:Flalign-Environment"
27677 \begin_layout Section
27679 \begin_inset CommandInset label
27681 name "sec:Multiline-Formulas"
27686 \begin_inset Index idx
27689 \begin_layout Plain Layout
27690 Formula ! multiline
27698 \begin_layout Subsection
27702 \begin_layout Standard
27703 In \SpecialChar LyX
27704 multiline formulas are created by pressing
27707 arg "newline-insert newline"
27711 This creates either an
27715 that is described in
27716 \begin_inset CommandInset ref
27718 reference "subsec:Standard-align-Environment"
27722 or, when automatically loading the package
27726 is disabled in the document settings, an
27728 eqnarray environment
27730 that is described in
27731 \begin_inset CommandInset ref
27733 reference "subsec:Eqnarray-Environment"
27738 The align environment is recommended because it provides in any case a
27739 typographically correct output.
27742 \begin_layout Standard
27743 There are other multiline formula environments that can be created via the
27746 Insert\SpecialChar menuseparator
27750 These environments are described in the following sections.
27753 \begin_layout Standard
27754 In all multiline formula environments a new line is created by pressing
27758 arg "newline-insert newline"
27762 To add or delete lines, the math toolbar buttons
27765 arg "tabular-feature append-row"
27771 arg "tabular-feature delete-row"
27774 , respectively, or the menu
27776 Edit\SpecialChar menuseparator
27782 \begin_layout Subsubsection
27784 \begin_inset CommandInset label
27786 name "subsec:Line-Separation"
27791 \begin_inset Index idx
27794 \begin_layout Plain Layout
27795 Formula ! multiline ! Line separation
27803 \begin_layout Standard
27804 There is sometimes not enough space in multiline formulas between the lines:
27805 \begin_inset Formula
27807 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}\\
27808 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
27816 \begin_layout Standard
27817 In \SpecialChar LaTeX
27818 additional line space is specified as optional argument of the new line
27820 This is not yet possible in \SpecialChar LyX
27825 \begin_layout Plain Layout
27827 \begin_inset CommandInset href
27829 name "LyX-bug #1505"
27830 target "http://www.lyx.org/trac/ticket/1505"
27840 , therefore the whole formula must be inserted in \SpecialChar TeX
27842 To add in our example space, the command
27850 is inserted at the end of the first line.
27855 \begin_layout Plain Layout
27862 \begin_layout Plain Layout
27864 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27867 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27874 \begin_layout Plain Layout
27878 left(B^{2}+x_{0}^{2}
27886 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27891 \begin_layout Plain Layout
27903 \begin_layout Standard
27904 \begin_inset VSpace bigskip
27907 To set the line separation for all lines in a formula, the length
27914 \begin_inset Index idx
27917 \begin_layout Plain Layout
27927 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27938 \begin_inset space \thinspace{}
27943 \begin_inset space \thinspace{}
27946 mm additional line separation as in the previous example, the command
27949 \begin_layout Standard
27959 \begin_layout Standard
27960 is inserted in \SpecialChar TeX
27961 mode before the formula.
27962 This requires that the \SpecialChar LaTeX
27971 \begin_layout Plain Layout
27976 is part of every \SpecialChar LaTeX
27977 standard installation.
27983 \begin_inset Index idx
27986 \begin_layout Plain Layout
27992 was loaded in \SpecialChar LaTeX
27993 -preamble with the line
27996 \begin_layout Standard
28004 \begin_layout Standard
28009 \begin_layout Plain Layout
28021 \begin_inset Formula
28023 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}\\
28024 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
28032 \begin_layout Standard
28036 \begin_layout Plain Layout
28047 To get back to the predefined distance,
28053 is set to the value 3
28054 \begin_inset space \thinspace{}
28060 \begin_layout Subsubsection
28062 \begin_inset CommandInset label
28064 name "subsec:Column-Separation"
28069 \begin_inset Index idx
28072 \begin_layout Plain Layout
28073 Formula ! multiline ! Column separation
28081 \begin_layout Standard
28082 Multiline formulas form a matrix.
28083 A formula in the eqnarray environment is for example a matrix with three
28085 By changing the column separation in this environment, the space beside
28086 the relation sign can be changed.
28089 \begin_layout Standard
28090 The column separation is specified with the length
28097 \begin_inset Index idx
28100 \begin_layout Plain Layout
28109 \begin_inset Newline newline
28112 column separation = 2
28113 \begin_inset space \thinspace{}
28123 \begin_inset Newline newline
28129 \begin_layout Standard
28139 \begin_layout Standard
28140 inserted in \SpecialChar TeX
28141 mode, sets for all following formulas a column separation of
28143 \begin_inset space \thinspace{}
28147 To get back to the predefined distance,
28154 \begin_inset space \thinspace{}
28160 \begin_layout Standard
28162 \begin_inset space \thinspace{}
28165 cm column separation:
28169 \begin_layout Plain Layout
28181 \begin_inset Formula
28189 A formula with the predefined column separation for matrices of 10
28190 \begin_inset space \thinspace{}
28197 \begin_layout Plain Layout
28209 \begin_inset Formula
28220 \begin_layout Standard
28221 \begin_inset Newpage newpage
28227 \begin_layout Subsubsection
28229 \begin_inset Index idx
28232 \begin_layout Plain Layout
28241 \begin_layout Standard
28242 Long formulas can be typeset using these methods:
28245 \begin_layout Itemize
28246 When one side of the equation is much shorter than the line width, this
28247 one is chosen for the left side and the right side is typeset over two
28249 \begin_inset Formula
28251 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 \\
28252 & & -\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}
28257 The minus sign at the beginning of the second line does normally not appear
28258 as an operator because it is the first character of the line.
28259 Thus it would not be surrounded by space and could not be distinguished
28260 from the fraction bar.
28262 \begin_inset space \thinspace{}
28265 pt space was inserted behind the minus sign with the command
28275 \begin_layout Plain Layout
28283 \begin_inset CommandInset ref
28285 reference "subsec:Variable-Space"
28295 \begin_inset Index idx
28298 \begin_layout Plain Layout
28309 \begin_layout Itemize
28310 When both sides of the equation are too long, the command
28317 \begin_inset Index idx
28320 \begin_layout Plain Layout
28329 It is inserted in the first column of the first line and causes all further
28330 insertions to overwrite the following columns:
28331 \begin_inset Formula
28333 \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 \\
28334 & & -\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 \\
28335 & & =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}
28340 After the insertion of
28346 , the cursor is in a purple box that is a bit shifted to the left from the
28348 In this the formula is inserted.
28349 \begin_inset Newline newline
28352 The content of the further lines is inserted to the second or another formula
28354 The greater the column number where it was inserted, the larger the indentation.
28355 \begin_inset VSpace medskip
28359 \begin_inset Newline newline
28363 \begin_inset Note Greyedout
28366 \begin_layout Plain Layout
28367 Note the following when using
28376 \begin_layout Itemize
28377 The formula doesn't use the full page width.
28379 \begin_inset space \thinspace{}
28383 \begin_inset space \space{}
28387 \begin_inset Formula $-B^{2}$
28390 is added to the first line in the above example, it would have been outside
28392 To better use the width, negative space can be inserted at the beginning
28396 \begin_layout Itemize
28397 Due to a bug in \SpecialChar LyX
28398 the cursor cannot be set with the mouse into the first
28403 \begin_layout Plain Layout
28404 \begin_inset CommandInset href
28406 name "LyX-bug #1429"
28407 target "http://www.lyx.org/trac/ticket/1429"
28417 One can only set the cursor at the beginning of the line and move it with
28426 \begin_layout Itemize
28427 Other methods to set long formulas are offered by the environments described
28429 \begin_inset CommandInset ref
28431 reference "subsec:Multline-Environment"
28436 \begin_inset CommandInset ref
28438 reference "subsec:Multiline-Formula-Parts"
28445 \begin_layout Subsubsection
28446 Multiline Fractions
28447 \begin_inset CommandInset label
28449 name "subsec:Multiline-Fractions"
28454 \begin_inset Index idx
28457 \begin_layout Plain Layout
28458 Fractions ! multiline
28466 \begin_layout Standard
28467 There are cases where the denominator and/or the numerator of a fraction
28468 is so long that the fraction does not fit into one line.
28469 It is then necessary to add a line break within the fraction.
28470 This can be done using the command
28477 \begin_inset Index idx
28480 \begin_layout Plain Layout
28489 To activate it, set in the document settings under
28492 \begin_inset space ~
28502 \begin_inset Index idx
28505 \begin_layout Plain Layout
28506 Packages ! mathtools
28514 \begin_inset space ~
28529 \begin_layout Standard
28534 splitfrac{first line}{second line}
28537 \begin_layout Standard
28538 and is used as denominator and/or numerator:
28541 \begin_layout Standard
28542 \begin_inset Formula
28544 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}
28549 The command for the first numerator above is:
28552 \begin_layout Standard
28557 splitfrac{xy+xy+xy+xy+xy
28558 \begin_inset space \textvisiblespace{}
28566 \begin_layout Subsubsection
28568 \begin_inset CommandInset label
28570 name "subsec:Multiline-Brackets"
28575 \begin_inset Index idx
28578 \begin_layout Plain Layout
28579 Brackets ! for multiline expressions
28587 \begin_layout Standard
28588 For brackets spanning multiple lines the following problem occurs:
28589 \begin_inset Formula
28591 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28592 & & \left.\cdots+B-D\right]
28600 \begin_layout Standard
28601 The closing bracket is smaller than the opening bracket because brackets
28602 with variable size may not span multiple lines.
28605 \begin_layout Standard
28606 To set the bracket size for the second line correctly, the first line is
28614 \begin_inset Index idx
28617 \begin_layout Plain Layout
28625 and the second line with
28633 \begin_layout Plain Layout
28647 \begin_inset CommandInset ref
28649 reference "subsec:Automatic-Bracket-Size"
28661 \begin_inset Index idx
28664 \begin_layout Plain Layout
28687 \begin_inset space \textvisiblespace{}
28697 \begin_inset space \textvisiblespace{}
28707 \begin_inset space \textvisiblespace{}
28713 \begin_inset Formula $\downarrow$
28719 \begin_inset Index idx
28722 \begin_layout Plain Layout
28730 is inserted, because the multiplication operator with its limits is the
28731 largest symbol in the first line and this should be the size for the bracket
28732 in the second line.
28735 \begin_layout Standard
28736 The result is this:
28737 \begin_inset Formula
28739 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28740 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28748 \begin_layout Subsection
28752 \begin_layout Standard
28753 Align environments can be used for every kind of multiline formulas.
28754 They are especially useful to set several formulas side by side.
28757 \begin_layout Standard
28758 Align environments consist of columns.
28759 The odd columns are right aligned, the even ones left aligned.
28760 Every line in an Align environment can be numbered.
28763 \begin_layout Standard
28764 Align environments are created via the menu
28766 Insert\SpecialChar menuseparator
28772 Edit\SpecialChar menuseparator
28773 Math\SpecialChar menuseparator
28774 Change Formula Type
28776 already existing formulas can be converted to Align environments.
28779 \begin_layout Standard
28780 To add or delete columns, the math toolbar buttons
28783 arg "tabular-feature append-column"
28789 arg "tabular-feature delete-column"
28792 , respectively, or the menu
28794 Edit\SpecialChar menuseparator
28800 \begin_layout Subsubsection
28801 Standard align Environment
28802 \begin_inset CommandInset label
28804 name "subsec:Standard-align-Environment"
28809 \begin_inset Index idx
28812 \begin_layout Plain Layout
28813 Formula ! multiline ! align environment
28821 \begin_layout Standard
28822 This Align environment is created by pressing
28825 arg "newline-insert newline"
28828 in a formula or by the menu
28830 Insert\SpecialChar menuseparator
28831 Math\SpecialChar menuseparator
28832 AMS align Environment
28837 \begin_layout Standard
28838 An example for two formulas set side by side, that are created with a four
28839 column align environment:
28840 \begin_inset Formula
28842 A & =\sin(B) & C & =D\\
28843 C & \ne A & B & \ne D
28848 As it can be seen, the formulas in this environment are placed so as if
28857 \begin_layout Plain Layout
28865 \begin_inset CommandInset ref
28867 reference "subsec:Variable-Space"
28878 before the first and after every even column.
28879 When the formula style
28885 \begin_layout Plain Layout
28887 \begin_inset CommandInset ref
28889 reference "sec:Formula-Styles"
28900 is used, the formula is set without the
28906 before the first column.
28909 \begin_layout Subsubsection
28910 Alignat Environment
28911 \begin_inset Index idx
28914 \begin_layout Plain Layout
28915 Formula ! multiline ! alignat environment
28923 \begin_layout Standard
28924 The alignat environment has no predefined column separation.
28925 It can be inserted manually with the spaces that are described
28926 \begin_inset CommandInset ref
28928 reference "subsec:Space"
28935 \begin_layout Standard
28936 The above example in the alignat environment where 1
28937 \begin_inset space \thinspace{}
28940 cm space was inserted at the beginning of the second formula:
28941 \begin_inset Formula
28942 \begin{alignat*}{2}
28943 A & =\sin(B) & \hspace{1cm}C & =D\\
28944 C & \ne A & B & \ne D
28949 Because the column separation can be set separately for every column, this
28950 environment is especially suitable to set three and more formulas side
28954 \begin_layout Subsubsection
28955 Flalign Environment
28956 \begin_inset CommandInset label
28958 name "subsec:Flalign-Environment"
28963 \begin_inset Index idx
28966 \begin_layout Plain Layout
28967 Formula ! multiline ! flalign environment
28975 \begin_layout Standard
28976 In this environment the first two columns are always set as much as possible
28977 to the left and the last two ones to the right.
28979 \begin_inset Formula
28981 A & =1 & B & =2 & C & =3\\
28982 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28990 \begin_layout Standard
28991 By creating a flalign environment with an odd number of columns where an
28992 empty \SpecialChar TeX
28993 brace is inserted to the last column, several formulas in a document
28994 can be set to the left, although the formula style
28999 As example the indented formula
29000 \begin_inset CommandInset ref
29002 reference "eq:VolInt"
29007 \begin_inset Formula
29009 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29014 The first two columns contain the formula.
29015 To indent it as with the formula style
29020 \begin_inset space \thinspace{}
29023 pt space was inserted at the beginning of the first column.
29026 \begin_layout Subsection
29027 Eqnarray Environment
29028 \begin_inset CommandInset label
29030 name "subsec:Eqnarray-Environment"
29035 \begin_inset Index idx
29038 \begin_layout Plain Layout
29039 Formula ! multiline ! eqnarray environment
29047 \begin_layout Standard
29048 When this environment has been created, three blue boxes appear.
29049 The content of the first box is right aligned, the content of the last
29051 The content of the middle box appears centered and a bit smaller, because
29052 it is designed to insert there only relation characters.
29053 \begin_inset Formula
29055 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29065 \begin_layout Subsection
29067 \begin_inset Index idx
29070 \begin_layout Plain Layout
29071 Formula ! multiline ! gather environment
29079 \begin_layout Standard
29080 This environment consists of only one centered column.
29081 Every line can be numbered.
29082 \begin_inset Formula
29093 \begin_layout Subsection
29094 Multline Environment
29095 \begin_inset CommandInset label
29097 name "subsec:Multline-Environment"
29102 \begin_inset Index idx
29105 \begin_layout Plain Layout
29106 Formula ! multiline ! multline environment
29114 \begin_layout Standard
29115 The multline environment consists, like the gather environment, of only
29117 But the first line is left aligned, the last one right aligned.
29118 All other lines are centered.
29119 Therefore this environment is suitable for long formulas.
29121 \begin_inset CommandInset ref
29123 reference "eq:lefteqn"
29127 in the multline environment:
29128 \begin_inset Formula
29130 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}\\
29131 -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}\\
29132 =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}}
29140 \begin_layout Standard
29141 In the output only the last (first) line of a multline environment appears
29142 numbered when the document numbering is right (left).
29146 \begin_layout Plain Layout
29147 numbering styles see
29148 \begin_inset CommandInset ref
29150 reference "sec:Formula-Styles"
29162 \begin_layout Standard
29170 \begin_inset Index idx
29173 \begin_layout Plain Layout
29188 \begin_inset Index idx
29191 \begin_layout Plain Layout
29199 a centered line can be right or left aligned, respectively.
29200 The commands are used as follows:
29203 \begin_layout Standard
29208 shoveright{line content}
29214 shoveleft{line content}
29217 \begin_layout Standard
29218 \begin_inset VSpace medskip
29228 \begin_inset Index idx
29231 \begin_layout Plain Layout
29239 specifies the distance of the first line from the left page margin.
29240 Predefined is the length 0
29241 \begin_inset space \thinspace{}
29247 \begin_layout Standard
29248 As example the above formula where the command
29251 \begin_layout Standard
29261 \begin_layout Standard
29262 was inserted in \SpecialChar TeX
29267 \begin_layout Plain Layout
29279 \begin_inset Formula
29281 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}\\
29282 \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}}\\
29283 =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}}
29292 \begin_layout Plain Layout
29303 The second line was left aligned using
29312 \begin_layout Subsection
29313 Multiline Formula Parts
29314 \begin_inset CommandInset label
29316 name "subsec:Multiline-Formula-Parts"
29321 \begin_inset Index idx
29324 \begin_layout Plain Layout
29325 Formula ! multiline ! formula parts
29333 \begin_layout Standard
29334 To display only parts of a formula with multiple lines, one of the following
29335 environments is used:
29352 They can be inserted via the menu
29354 Insert\SpecialChar menuseparator
29357 or by using the commands described in this section.
29360 \begin_layout Standard
29361 The first three have the same properties as the corresponding multiline
29362 formula environments, but it is possible to set further formula parts beside
29365 \begin_inset Formula
29367 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29368 \Delta E\Delta t & \ge\frac{\hbar}{2}
29370 \right\} \textrm{Uncertainty relations}
29378 \begin_layout Standard
29379 To get this formula, a displayed formula is created where the command
29386 \begin_inset Index idx
29389 \begin_layout Plain Layout
29398 A purple box appears around the blue formula box where now columns and
29399 lines can be added.
29400 Outside the multiline environment other formula parts can be set, like
29404 \begin_layout Standard
29405 The aligned environment is also suitable for long formulas whose lines are
29406 horizontally aligned.
29407 Using aligned in a displayed formula has the advantage that the formula
29408 number is vertically centered behind the lines.
29410 \begin_inset CommandInset ref
29412 reference "eq:shortlong"
29416 in the aligned environment:
29417 \begin_inset Formula
29419 \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}|}\\
29420 & -\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}|}
29429 \begin_layout Standard
29430 To use the environments
29449 \begin_inset Index idx
29452 \begin_layout Plain Layout
29467 \begin_inset Index idx
29470 \begin_layout Plain Layout
29485 \begin_inset Index idx
29488 \begin_layout Plain Layout
29496 are inserted, respectively.
29497 The split environment has the same properties as the aligned environment
29498 but it can only have two columns.
29501 \begin_layout Subsection
29502 Text in multiline Formulas
29503 \begin_inset CommandInset label
29505 name "subsec:Text-in-multiline"
29510 \begin_inset Index idx
29513 \begin_layout Plain Layout
29520 \begin_inset Index idx
29523 \begin_layout Plain Layout
29524 Formula ! multiline ! text
29532 \begin_layout Standard
29533 In the Align environments, and the multline and gather environment, text
29534 can be inserted that will appear in a separate line and doesn't affect
29535 the column alignment.
29536 To do this, the command
29543 \begin_inset Index idx
29546 \begin_layout Plain Layout
29554 is used in the following scheme:
29557 \begin_layout Standard
29565 \begin_layout Standard
29566 The text should not be longer than a line because it cannot be hyphenated.
29567 As \SpecialChar LyX
29568 doesn't yet support
29574 directly, the text is written as mathematical text.
29581 must hereby be at the beginning of a line and appears in the output above
29583 An example where the text was inserted at the beginning of the second line:
29584 \begin_inset Formula
29586 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29587 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29595 \begin_layout Standard
29602 always creates some vertical space between the text and the formula lines.
29603 To avoid this space, set in the document settings under
29606 \begin_inset space ~
29616 \begin_inset Index idx
29619 \begin_layout Plain Layout
29620 Packages ! mathtools
29628 \begin_inset space ~
29634 Then you can use the command
29641 \begin_inset Index idx
29644 \begin_layout Plain Layout
29661 \begin_layout Standard
29662 \begin_inset Formula
29664 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29665 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29673 \begin_layout Section
29675 \begin_inset Index idx
29678 \begin_layout Plain Layout
29685 \begin_inset Index idx
29688 \begin_layout Plain Layout
29689 Formula ! numbering|see
29693 \begin_layout Plain Layout
29704 \begin_layout Plain Layout
29719 \begin_layout Subsection
29723 \begin_layout Standard
29724 Numbered formulas can be created with the menu
29726 Insert\SpecialChar menuseparator
29727 Math\SpecialChar menuseparator
29729 \begin_inset space ~
29737 \begin_inset space ~
29743 Existing formulas can be numbered with the menu
29745 Edit\SpecialChar menuseparator
29746 Math\SpecialChar menuseparator
29748 \begin_inset space ~
29756 arg "math-number-toggle"
29760 The formula number is displayed in \SpecialChar LyX
29761 behind the formula as a number sign
29763 The number sign is replaced in the output by the formula number.
29766 \begin_layout Standard
29767 When numbering is turned on in multiline formulas, all lines will be numbered.
29768 But the numbering can be controlled with the menu
29770 Edit\SpecialChar menuseparator
29771 Math\SpecialChar menuseparator
29773 \begin_inset space ~
29777 \begin_inset space ~
29781 \begin_inset space ~
29789 arg "math-number-line-toggle"
29795 \begin_layout Standard
29796 Except for inline formulas, all formulas can be numbered with two different
29798 \begin_inset CommandInset ref
29800 reference "sec:Formula-Styles"
29807 \begin_layout Subsection
29809 \begin_inset Index idx
29812 \begin_layout Plain Layout
29813 Cross-references ! to formulas
29821 \begin_layout Standard
29822 All labeled formulas can be cross-referenced.
29823 A label is added by the menu
29825 Insert\SpecialChar menuseparator
29828 or the toolbar button
29835 The cursor must hereby be inside a displayed formula.
29836 Alternatively you can right-click on the formula and choose
29841 A dialog pops up displaying the prefix
29846 The label is inserted there behind the prefix.
29847 The predefined prefix means
29848 \begin_inset Quotes eld
29852 \begin_inset Quotes erd
29855 and makes it easier to find labels in large documents because it marks
29856 it as formula label to divide it from e.
29857 \begin_inset space \thinspace{}
29861 \begin_inset space \space{}
29865 To change a label, the menu
29867 Insert\SpecialChar menuseparator
29870 is used again or you right-click on a formula and then on
29877 \begin_layout Standard
29878 The name of the label is displayed in \SpecialChar LyX
29879 within two parentheses behind formula.
29880 A formula with a label is always numbered.
29883 \begin_layout Standard
29884 Cross-references are inserted via the menu
29886 Insert\SpecialChar menuseparator
29889 or with the toolbar button
29892 arg "dialog-show-new-inset ref"
29896 A formula cross-reference appears in the output as formula number.
29897 When in the cross-reference dialog window the format
29901 is chosen, the cross-reference appears in the output as formula number
29903 \begin_inset Newline newline
29906 By right-clicking on a cross-reference in \SpecialChar LyX
29907 , one jumps to the formula that
29911 \begin_layout Standard
29912 Here are as examples cross-references to formulas of the following subsections:
29913 \begin_inset Note Note
29916 \begin_layout Plain Layout
29917 Note the different cross-reference types.
29925 \begin_layout Standard
29927 \begin_inset CommandInset ref
29934 \begin_inset CommandInset ref
29942 \begin_inset CommandInset ref
29948 ) big Latin letters are used for the numbering in contrary to (
29949 \begin_inset CommandInset ref
29958 \begin_layout Standard
29959 \begin_inset VSpace medskip
29962 When the argument of
29970 \begin_layout Plain Layout
29978 \begin_inset CommandInset ref
29980 reference "subsec:User-defined-Numbering"
29991 contains a box like in
29992 \begin_inset CommandInset ref
29994 reference "subsec:Paragraph-Boxes"
29998 , the formula cannot be referenced.
30001 \begin_layout Subsection
30003 \begin_inset Index idx
30006 \begin_layout Plain Layout
30007 Formula numbering ! subnumbering
30015 \begin_layout Standard
30016 With the help of the commands
30020 begin{subequations}
30028 formulas can be subnumbered.
30029 Both commands are inserted in \SpecialChar TeX
30033 \begin_layout Standard
30035 \begin_inset Formula
30046 \begin_layout Plain Layout
30050 begin{subequations}
30056 \begin_inset VSpace -5mm
30060 \begin_inset Formula
30068 \begin_inset Formula
30078 \begin_layout Standard
30082 \begin_layout Plain Layout
30094 \begin_layout Standard
30095 To create the example, the following is done:
30098 \begin_layout Enumerate
30099 first formula is inserted
30102 \begin_layout Enumerate
30107 begin{subequations}
30108 \begin_inset Newline newline
30113 is inserted after the first formula
30116 \begin_layout Enumerate
30117 second formula is inserted
30120 \begin_layout Enumerate
30121 third formula is inserted
30124 \begin_layout Enumerate
30131 is inserted after the third formula
30134 \begin_layout Standard
30135 Every formula between the commands
30147 will be subnumbered with a, b, c, \SpecialChar ldots
30149 For multiline formulas every line will be subnumbered.
30152 \begin_layout Standard
30153 Referencing subequations work like for normal equations:
30154 \begin_inset CommandInset ref
30161 \begin_inset CommandInset ref
30168 If you want to reference the subequations collectively, insert a label
30173 begin{subequations}
30177 \begin_inset CommandInset ref
30179 reference "eq:Here-is-an"
30186 \begin_layout Standard
30187 By inserting commands in \SpecialChar TeX
30188 mode, a space is created between the first two
30191 \begin_inset space \thinspace{}
30194 mm vertical space is inserted after the command
30198 begin{subequations}
30201 When the formula style
30207 \begin_layout Plain Layout
30209 \begin_inset CommandInset ref
30211 reference "sec:Formula-Styles"
30223 \begin_inset space \thinspace{}
30226 mm space is inserted instead.
30229 \begin_layout Standard
30230 To get another subnumber instead of small Latin letters, insert this command
30235 begin{subequations}
30240 \begin_layout Standard
30249 theparentequation -
30254 \begin_layout Standard
30261 creates hereby the parent number and
30267 adds a small Roman number as subnumber.
30268 For more information about the customization of the numbering, see
30269 \begin_inset CommandInset ref
30271 reference "subsec:Numbering-with-Roman"
30278 \begin_layout Standard
30279 Here is an example for a multiline formula where the numbering is customized
30280 and turned off for the second line:
30284 \begin_layout Plain Layout
30288 begin{subequations}
30294 \begin_inset CommandInset label
30296 name "eq:Here-is-an"
30304 \begin_layout Plain Layout
30312 theparentequation -
30320 \begin_inset Formula
30322 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30323 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30324 & = & B^{2}-2BZ+Z^{2}
30333 \begin_layout Plain Layout
30345 \begin_layout Subsection
30346 User-defined Numbering
30347 \begin_inset CommandInset label
30349 name "subsec:User-defined-Numbering"
30354 \begin_inset Index idx
30357 \begin_layout Plain Layout
30358 Formula numbering ! user-defined
30366 \begin_layout Standard
30367 \begin_inset Index idx
30370 \begin_layout Plain Layout
30371 Formula numbering ! self-defined delimiters
30376 With the standard numbering parentheses are set around the formula number.
30377 To replace the parentheses for example by vertical bars, the following
30378 line is added to the \SpecialChar LaTeX
30382 \begin_layout Standard
30394 \begin_inset Note Note
30397 \begin_layout Plain Layout
30398 This macro is already declared in the \SpecialChar LaTeX
30399 -preamble for testing.
30400 To activate it, remove the percent sign at the beginning.
30408 \begin_layout Standard
30409 To use other characters, the vertical bars besides the
30413 are replaced by one ore more characters.
30414 To get only the formula number the vertical bars are omitted.
30417 \begin_layout Standard
30418 \begin_inset VSpace bigskip
30421 When there should be an expression of your choice instead of the consecutive
30422 formula number in parentheses behind the formula, the command
30429 \begin_inset Index idx
30432 \begin_layout Plain Layout
30441 \begin_inset Formula
30443 A+B=C\tag{something}\label{eq:tag}
30448 In this example the command
30453 \begin_inset space \textvisiblespace{}
30458 was inserted in the formula.
30461 \begin_layout Standard
30467 \begin_inset space \textvisiblespace{}
30472 is inserted instead, the star prevents the parentheses around the expression:
30473 \begin_inset Formula
30475 A+B=C\tag*{something}
30483 \begin_layout Standard
30484 \begin_inset VSpace bigskip
30487 To restart the formula numbering with new document parts or sections, the
30488 following command is used:
30491 \begin_layout Standard
30496 @addtoreset{equation}{part}
30499 \begin_inset Index idx
30502 \begin_layout Plain Layout
30507 \begin_layout Plain Layout
30518 \begin_layout Plain Layout
30531 \begin_layout Plain Layout
30542 \begin_layout Plain Layout
30555 \begin_inset Newline newline
30559 \begin_inset Newline newline
30566 @addtoreset{equation}{section}
30569 \begin_layout Standard
30570 To be able to use these commands in \SpecialChar TeX
30572 \begin_inset Quotes eld
30576 \begin_inset Quotes erd
30579 character has to be made
30580 \begin_inset Quotes eld
30584 \begin_inset Quotes erd
30587 for \SpecialChar LaTeX
30602 So the command sequence in \SpecialChar TeX
30606 \begin_layout Standard
30612 \begin_inset Newline newline
30617 @addtoreset{equation}{section}
30618 \begin_inset Newline newline
30626 \begin_layout Standard
30627 In the \SpecialChar LaTeX
30640 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30644 \begin_layout Standard
30659 \begin_layout Plain Layout
30664 is part of the \SpecialChar LaTeX
30670 \begin_inset Index idx
30673 \begin_layout Plain Layout
30674 Packages ! carlisle
30679 that is part of every \SpecialChar LaTeX
30680 standard installation.
30686 \begin_inset Index idx
30689 \begin_layout Plain Layout
30690 Packages ! remreset
30695 has to be loaded in the \SpecialChar LaTeX
30696 -preamble with the line
30699 \begin_layout Standard
30704 usepackage{remreset}
30707 \begin_layout Standard
30715 \begin_inset Index idx
30718 \begin_layout Plain Layout
30723 \begin_layout Plain Layout
30734 \begin_layout Plain Layout
30747 \begin_layout Plain Layout
30758 \begin_layout Plain Layout
30770 can be used with the same scheme as
30779 \begin_layout Standard
30780 \begin_inset VSpace bigskip
30783 Sometimes formulas should be numbered in the following form:
30786 \begin_layout Standard
30789 (section number.formula number)
30792 \begin_layout Standard
30793 The formula number should start with every section with
30794 \begin_inset Quotes eld
30798 \begin_inset Quotes erd
30804 \begin_layout Standard
30805 For this case there is the command
30812 \begin_inset Index idx
30815 \begin_layout Plain Layout
30823 , which is used with the following scheme:
30826 \begin_layout Standard
30831 numberwithin{counter}{sectioning}
30834 \begin_layout Standard
30835 Counter denotes what kind of numbering is affected, sectioning denotes what
30836 number is before the dot.
30839 \begin_layout Standard
30840 Thus in our case the following \SpecialChar LaTeX
30841 preamble or \SpecialChar TeX
30845 \begin_layout Standard
30850 numberwithin{equation}{section}
30853 \begin_layout Standard
30854 This is the result:
30858 \begin_layout Plain Layout
30862 numberwithin{equation}{section}
30868 \begin_inset Formula
30878 \begin_layout Standard
30880 \begin_inset space \thinspace{}
30884 \begin_inset space \space{}
30887 tables so that the number of the part is the sectioning,
30888 \begin_inset Newline newline
30895 numberwithin{table}{part}
30900 \begin_layout Standard
30901 To go back to the standard numbering or to prevent this kind of numbering
30902 when it is defined by the document class, the following command is inserted
30903 as \SpecialChar TeX
30904 code or to the \SpecialChar LaTeX
30908 \begin_layout Standard
30918 \begin_inset Index idx
30921 \begin_layout Plain Layout
30935 \begin_layout Plain Layout
30951 \begin_inset Newline newline
30959 \begin_inset Newline newline
30971 \begin_layout Standard
30978 uses internally the command
30984 , described above, that also needs to be reverted.
30988 \begin_layout Plain Layout
30995 \begin_layout Plain Layout
30999 @removefromreset{equation}{section}
31002 \begin_layout Plain Layout
31014 \begin_layout Standard
31015 \begin_inset Newpage newpage
31021 \begin_layout Subsection
31022 Numbering with Roman Numbers and Letters
31023 \begin_inset CommandInset label
31025 name "subsec:Numbering-with-Roman"
31030 \begin_inset Index idx
31033 \begin_layout Plain Layout
31034 Formula numbering ! with letters
31040 \begin_inset Index idx
31043 \begin_layout Plain Layout
31044 Formula numbering ! with Roman numbers
31052 \begin_layout Standard
31053 Formulas can also be numbered with Roman numbers and Latin letters.
31054 To number for example with small Roman numbers, the command
31057 \begin_layout Standard
31069 \begin_layout Standard
31070 is inserted before the formula in \SpecialChar TeX
31079 \begin_inset Index idx
31082 \begin_layout Plain Layout
31090 redefines the predefined command
31106 \begin_layout Plain Layout
31113 has the same scheme like the command
31119 that is described in
31120 \begin_inset CommandInset ref
31122 reference "subsec:The-Command-newcommand"
31135 is the formula counter.
31142 is used as prefix for a counter, the value of the counter is output as
31144 When a formula is numbered, \SpecialChar LaTeX
31145 sets internally the command
31151 behind the formula.
31157 \begin_inset Index idx
31160 \begin_layout Plain Layout
31170 outputs the counter as small Roman number.
31173 \begin_layout Standard
31174 All formulas behind the command
31184 are now numbered Roman.
31185 To switch to numbering with big Roman numbers, the command is inserted
31199 \begin_inset Index idx
31202 \begin_layout Plain Layout
31214 \begin_inset Quotes eld
31218 \begin_inset Quotes erd
31221 with small Latin letters there is the command
31228 \begin_inset Index idx
31231 \begin_layout Plain Layout
31239 , for big ones there is the command
31246 \begin_inset Index idx
31249 \begin_layout Plain Layout
31262 \begin_layout Standard
31263 \begin_inset Note Greyedout
31266 \begin_layout Plain Layout
31273 \begin_inset space ~
31276 formulas can be numbered with Latin letters in one document.
31284 \begin_layout Standard
31288 \begin_layout Plain Layout
31304 \begin_layout Standard
31305 \begin_inset Formula
31307 A=\textrm{small roman}
31316 \begin_layout Plain Layout
31330 \begin_inset Formula
31332 B=\textrm{big Roman}\label{eq:Rom}
31341 \begin_layout Plain Layout
31355 \begin_inset Formula
31357 C=\textrm{small Latin}
31366 \begin_layout Plain Layout
31380 \begin_inset Formula
31382 D=\textrm{big Latin}\label{eq:Lat}
31390 \begin_layout Standard
31391 To switch back to the default numbering, insert the command:
31394 \begin_layout Standard
31404 \begin_inset Index idx
31407 \begin_layout Plain Layout
31418 \begin_layout Standard
31422 \begin_layout Plain Layout
31436 \begin_inset Formula
31446 \begin_layout Standard
31447 \begin_inset VSpace medskip
31450 As you see, formulas are numbered serially independent from the numbering
31452 When then numbering should start with
31453 \begin_inset Quotes eld
31457 \begin_inset Quotes erd
31460 when the style is changed, new equation counters have to be defined.
31461 A description about this can be found in the file
31462 \begin_inset CommandInset href
31464 name "Formula-numbering.lyx"
31465 target "run:Formula-numbering.lyx"
31473 \begin_layout Section
31474 Chemical Symbols and Equations
31475 \begin_inset CommandInset label
31477 name "subsec:Chemical-Symbols-and"
31482 \begin_inset Index idx
31485 \begin_layout Plain Layout
31486 Chemical characters ! Symbols
31492 \begin_inset Index idx
31495 \begin_layout Plain Layout
31502 \begin_inset Index idx
31505 \begin_layout Plain Layout
31514 \begin_layout Standard
31515 An example text from chemistry:
31518 \begin_layout Quote
31520 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31523 -ion reacts with two
31524 \begin_inset Formula $\mathrm{Na^{+}}$
31527 -ions to sodium sulfate
31528 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31532 The chemical equation for this is:
31533 \begin_inset Formula
31535 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31543 \begin_layout Standard
31544 This chemical equation can directly be created as formula.
31545 To avoid that the symbols appear italic, everything is highlighted and
31546 changed by the shortcut
31552 to the upright font style.
31556 \begin_layout Plain Layout
31562 \begin_inset CommandInset ref
31564 reference "subsec:Font-Styles"
31576 \begin_layout Standard
31577 A more convenient way to typeset chemical formulas is to use the command
31585 \begin_inset Index idx
31588 \begin_layout Plain Layout
31596 that is available when the \SpecialChar LaTeX
31602 \begin_inset Index idx
31605 \begin_layout Plain Layout
31618 to a formula a new blue box appears where chemical formulas can be inserted
31619 in an intuitive way.
31622 \begin_layout Standard
31624 \begin_inset Tabular
31625 <lyxtabular version="3" rows="10" columns="2">
31626 <features booktabs="true" tabularvalignment="middle">
31627 <column alignment="center" valignment="top" width="0pt">
31628 <column alignment="center" valignment="top">
31630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31633 \begin_layout Plain Layout
31639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31642 \begin_layout Plain Layout
31650 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31653 \begin_layout Plain Layout
31657 \begin_inset space \textvisiblespace{}
31665 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31668 \begin_layout Plain Layout
31669 \begin_inset Formula $\ce{H2CO3}$
31678 <row topspace="1.5mm">
31679 <cell alignment="center" valignment="top" usebox="none">
31682 \begin_layout Plain Layout
31686 \begin_inset space \textvisiblespace{}
31694 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31697 \begin_layout Plain Layout
31698 \begin_inset Formula $\ce{SO4^{2-}}$
31707 <row topspace="1.5mm">
31708 <cell alignment="center" valignment="top" usebox="none">
31711 \begin_layout Plain Layout
31715 \begin_inset space \textvisiblespace{}
31723 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31726 \begin_layout Plain Layout
31727 \begin_inset Formula $\ce{(NH4)2S}$
31736 <row topspace="1.5mm">
31737 <cell alignment="center" valignment="top" usebox="none">
31740 \begin_layout Plain Layout
31744 \begin_inset space \textvisiblespace{}
31752 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31755 \begin_layout Plain Layout
31756 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31765 <row topspace="1.5mm">
31766 <cell alignment="center" valignment="top" usebox="none">
31769 \begin_layout Plain Layout
31773 \begin_inset space \textvisiblespace{}
31779 \begin_inset space \textvisiblespace{}
31785 \begin_inset space \textvisiblespace{}
31793 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31796 \begin_layout Plain Layout
31797 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31806 <row topspace="1.5mm">
31807 <cell alignment="center" valignment="top" usebox="none">
31810 \begin_layout Plain Layout
31814 \begin_inset space \textvisiblespace{}
31818 \begin_inset Formula $\downarrow$
31822 \begin_inset Formula $\to$
31830 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31833 \begin_layout Plain Layout
31834 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31844 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31847 \begin_layout Plain Layout
31851 \begin_inset space \textvisiblespace{}
31857 \begin_inset space \textvisiblespace{}
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 $\ce{\ensuremath{\mu\hyphen}Cl}$
31885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31888 \begin_layout Plain Layout
31892 \begin_inset space \textvisiblespace{}
31896 \begin_inset space \textvisiblespace{}
31900 \begin_inset space \textvisiblespace{}
31904 \begin_inset space \textvisiblespace{}
31908 \begin_inset space \textvisiblespace{}
31916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31919 \begin_layout Plain Layout
31920 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31929 <row topspace="1.5mm">
31930 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31933 \begin_layout Plain Layout
31937 \begin_inset space \textvisiblespace{}
31941 \begin_inset space \textvisiblespace{}
31945 \begin_inset space \textvisiblespace{}
31949 \begin_inset space \textvisiblespace{}
31957 \begin_inset space \textvisiblespace{}
31965 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31968 \begin_layout Plain Layout
31969 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31985 \begin_layout Standard
31986 \begin_inset Note Greyedout
31989 \begin_layout Plain Layout
31995 It is not possible in \SpecialChar LyX
31996 to use the character ^ to get an up-arrow as described
32002 One instead uses a negative thin space followed by the command
32009 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32020 \begin_layout Standard
32027 the command for equation
32028 \begin_inset space ~
32032 \begin_inset CommandInset ref
32034 reference "eq:chem-reaction"
32039 \begin_inset Newline newline
32047 \begin_inset space \textvisiblespace{}
32051 \begin_inset space \textvisiblespace{}
32055 \begin_inset space \textvisiblespace{}
32059 \begin_inset space \textvisiblespace{}
32063 \begin_inset space \textvisiblespace{}
32067 \begin_inset space \textvisiblespace{}
32073 \begin_layout Standard
32074 To create multiline chemical equations first a multiline formula is created
32076 \begin_inset CommandInset ref
32078 reference "sec:Multiline-Formulas"
32083 Afterwards the command
32089 is used in every small blue box of the formula.
32091 \begin_inset CommandInset ref
32093 reference "eq:TEOS-reaction-1"
32098 \begin_inset CommandInset ref
32100 reference "eq:TEOS-reaction-2"
32104 are an example of a multi-stage chemical reaction where every equation
32105 has its own number.
32106 \begin_inset Formula
32108 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32109 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32117 \begin_layout Standard
32128 package provides the command
32135 \begin_inset Index idx
32138 \begin_layout Plain Layout
32146 that has to be used for special cases.
32147 For more information about
32153 and more examples have a look at the documentation of
32158 \begin_inset CommandInset citation
32168 \begin_layout Section
32172 \begin_layout Standard
32174 supports two types of commutative diagrams:
32182 that are explained in the following.
32185 \begin_layout Subsection
32187 \begin_inset Index idx
32190 \begin_layout Plain Layout
32199 \begin_layout Standard
32200 Diagrams of this type visualize relations by vertical and horizontal lines
32202 \begin_inset Formula
32204 \begin{CD}A@>>>B@>>>C\\
32215 \begin_layout Standard
32216 To get them, the command
32221 \begin_inset Index idx
32224 \begin_layout Plain Layout
32234 is inserted to a formula.
32235 A blue box appears with two dashed lines where further commands can be
32240 arg "newline-insert newline"
32243 a new line is created.
32244 Horizontal relations are inserted in odd, vertical in even formula lines.
32247 \begin_layout Standard
32248 To create the relations there are the following commands:
32251 \begin_layout Itemize
32256 creates a left arrow,
32267 \begin_layout Itemize
32272 creates an up arrow,
32280 a vertical equal sign
32283 \begin_layout Itemize
32289 is a placeholder for non-existent relations
32292 \begin_layout Standard
32293 All arrows can be labeled as follows:
32296 \begin_layout Itemize
32297 If text inserted between the first and second < or >, resp., it is placed
32299 When it is inserted between the second and third one, it appears under
32303 \begin_layout Itemize
32304 When text for vertical arrows is inserted between the first and second A
32305 or V, resp., it is placed left beside the arrow.
32306 When it is inserted between the second and third one, it appears right
32308 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32312 \begin_layout Standard
32313 As example a diagram with all possible relations:
32316 \begin_layout Standard
32317 \begin_inset Formula
32319 \begin{CD}A@>j>>B@>>k>C@=F\\
32330 \begin_layout Standard
32331 The command for this is:
32332 \begin_inset Newline newline
32340 \begin_inset space \textvisiblespace{}
32343 A@>j>>B@>>k>C@=F Ctrl+Return
32344 \begin_inset Newline newline
32348 \begin_inset Phantom HPhantom
32351 \begin_layout Plain Layout
32357 \begin_inset space \textvisiblespace{}
32370 \begin_inset Formula $\to$
32376 \begin_inset Newline newline
32380 \begin_inset Phantom HPhantom
32383 \begin_layout Plain Layout
32389 \begin_inset space \textvisiblespace{}
32400 \begin_layout Subsection
32402 \begin_inset Index idx
32405 \begin_layout Plain Layout
32406 Diagrams ! xymatrix
32414 \begin_layout Standard
32415 To be able to use xymatrices, the \SpecialChar LaTeX
32421 A xymatrix is created by inserting the command
32428 Then you are able to add new matrix columns and rows like for normal matrices,
32430 \begin_inset CommandInset ref
32432 reference "sec:Matrices"
32439 \begin_layout Standard
32440 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32442 All possibilities to create commutative diagrams and decorations are explained
32447 that you find in the menu
32449 Help\SpecialChar menuseparator
32451 \begin_inset space ~
32459 \begin_layout Subsection
32465 \begin_inset Index idx
32468 \begin_layout Plain Layout
32477 \begin_layout Standard
32482 -diagrams, the \SpecialChar LaTeX
32492 -diagram is created by inserting the command
32499 Then you are able to add new matrix columns and rows like for normal matrices,
32501 \begin_inset CommandInset ref
32503 reference "sec:Matrices"
32510 \begin_layout Standard
32511 Examples how to create
32515 diagrams in \SpecialChar LyX
32518 Feynman-diagram manual
32520 that you find in the menu
32522 Help\SpecialChar menuseparator
32524 \begin_inset space ~
32532 \begin_layout Standard
32533 \begin_inset Newpage newpage
32539 \begin_layout Section
32540 User-defined Commands
32541 \begin_inset Index idx
32544 \begin_layout Plain Layout
32545 User-defined commands
32553 \begin_layout Standard
32554 \begin_inset Note Greyedout
32557 \begin_layout Plain Layout
32562 The names of user-defined commands and macros may only consist of Latin
32571 \begin_layout Subsection
32575 \begin_inset CommandInset label
32577 name "subsec:The-Command-newcommand"
32582 \begin_inset Index idx
32585 \begin_layout Plain Layout
32586 User-defined commands !
32594 \begin_inset Index idx
32597 \begin_layout Plain Layout
32608 \begin_layout Standard
32609 Many \SpecialChar LaTeX
32610 -commands are too long to be used frequently.
32611 But it is possible to define with the command
32617 new shorter commands.
32620 \begin_layout Standard
32621 The command scheme of
32630 \begin_layout Standard
32635 newcommand{new command name}[number of arguments][optional
32640 \begin_inset Newline newline
32644 \begin_inset Phantom HPhantom
32647 \begin_layout Plain Layout
32657 {command definition}
32660 \begin_layout Standard
32661 \begin_inset Note Greyedout
32664 \begin_layout Plain Layout
32669 Assure that the name of the new command is not already used in your document
32670 or by \SpecialChar LaTeX
32671 -packages that you use.
32672 When you for example define the command
32684 , you get an error message because
32690 is already defined as command for
32691 \begin_inset Quotes eld
32695 \begin_inset Formula $\le$
32699 \begin_inset Quotes erd
32710 \begin_layout Standard
32711 The number of arguments is an integer in the range 0
32712 \begin_inset space \thinspace{}
32716 \begin_inset space \thinspace{}
32719 9 and specifies how many arguments the new command should have.
32720 With the optional value a value for an optional argument can be predefined.
32721 When this is done, the
32729 rgument of the new command is automatically an optional one.
32732 \begin_layout Standard
32733 Here are some examples:
32736 \begin_layout Itemize
32737 To define the command
32749 , the \SpecialChar LaTeX
32751 \begin_inset VSpace medskip
32755 \begin_inset Newline newline
32769 \begin_layout Itemize
32770 To define the command
32782 , the argument (that should be underlined) must be taken into account.
32783 For this the preamble line is:
32784 \begin_inset VSpace medskip
32788 \begin_inset Newline newline
32802 \begin_inset VSpace medskip
32806 \begin_inset Newline newline
32813 acts as argument placeholder, the
32817 behind it denotes that it is the placeholder for the first argument.
32820 \begin_layout Itemize
32828 \begin_inset space \thinspace{}
32832 \begin_inset space \space{}
32842 \begin_inset VSpace medskip
32846 \begin_inset Newline newline
32857 framebox#1#2{$#3$}}
32860 \begin_inset VSpace medskip
32864 \begin_inset Newline newline
32867 The two Dollar signs creates the extra formula needed for
32874 \begin_inset CommandInset ref
32876 reference "subsec:Boxes-with-Frame"
32883 \begin_layout Itemize
32884 To create a new command for
32890 where the color for the box need not be specified, the argument for the
32891 color is defined optional:
32892 \begin_inset VSpace medskip
32896 \begin_inset Newline newline
32907 fcolorbox{#2}{#1}{$#3$}}
32910 \begin_inset VSpace medskip
32914 \begin_inset Newline newline
32917 When the color is not specified when using
32923 , the predefined color
32930 \begin_layout Standard
32931 A test of the new defined commands:
32934 \begin_layout Standard
32936 \begin_inset Tabular
32937 <lyxtabular version="3" rows="6" columns="2">
32938 <features booktabs="true" tabularvalignment="middle">
32939 <column alignment="center" valignment="top" width="0pt">
32940 <column alignment="center" valignment="top">
32942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32945 \begin_layout Plain Layout
32951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32954 \begin_layout Plain Layout
32962 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32965 \begin_layout Plain Layout
32969 \begin_inset space \textvisiblespace{}
32977 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32980 \begin_layout Plain Layout
32981 \begin_inset Formula $A\gr B$
32991 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32994 \begin_layout Plain Layout
33002 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33005 \begin_layout Plain Layout
33006 \begin_inset Formula $\us{ABcd}$
33015 <row topspace="1mm">
33016 <cell alignment="center" valignment="top" usebox="none">
33019 \begin_layout Plain Layout
33023 \begin_inset Formula $\to$
33029 \begin_inset Formula $\to$
33037 \begin_inset space \textvisiblespace{}
33045 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33048 \begin_layout Plain Layout
33049 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33058 <row topspace="1.5mm">
33059 <cell alignment="center" valignment="top" usebox="none">
33062 \begin_layout Plain Layout
33066 \begin_inset Formula $\to$
33074 \begin_inset space \textvisiblespace{}
33082 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33085 \begin_layout Plain Layout
33086 \begin_inset Formula $\cb{red}{\int A=B}$
33095 <row topspace="1.5mm" bottomspace="1mm">
33096 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33099 \begin_layout Plain Layout
33105 \begin_inset Formula $\to$
33113 \begin_inset space \textvisiblespace{}
33121 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33124 \begin_layout Plain Layout
33125 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33141 \begin_layout Subsection
33143 \begin_inset Index idx
33146 \begin_layout Plain Layout
33147 User-defined commands! Math macros
33153 \begin_inset Index idx
33156 \begin_layout Plain Layout
33165 \begin_layout Standard
33166 User-defined commands are especially convenient for complex expressions.
33167 When you are for example dealing with a document that has quadratic equations,
33168 the same solution type occurs several times.
33169 The general form of a quadratic equation is
33170 \begin_inset Formula
33172 0=\lambda^{2}+p\lambda+q
33177 The general form of the solution is
33178 \begin_inset Formula
33180 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33188 \begin_layout Standard
33189 To define a command for the solution formula where only the three parameters
33191 \begin_inset Formula $\lambda$
33195 \begin_inset Formula $p$
33199 \begin_inset Formula $q$
33202 need to be specified and the index of
33203 \begin_inset Formula $\lambda$
33206 can be given optionally, the \SpecialChar LaTeX
33208 \begin_inset Newline newline
33224 \begin_inset Newline newline
33228 \begin_inset Phantom HPhantom
33231 \begin_layout Plain Layout
33245 frac{#3^{2}}{4}-#4}}
33248 \begin_layout Standard
33249 To create with this the solution formula, the command
33250 \begin_inset Newline newline
33260 \begin_inset Formula $\to$
33266 \begin_inset Formula $\to$
33273 is inserted to a formula
33278 \begin_layout Standard
33279 The definition of the new command is unintuitive because one has to know
33280 the schemes of all used \SpecialChar LaTeX
33282 \begin_inset space \thinspace{}
33286 \begin_inset space \space{}
33289 that a fraction is inserted in \SpecialChar LaTeX
33294 frac{numerator}{denominator}
33297 Furthermore one can easily forget a brace in the definition and cannot
33298 see in \SpecialChar LyX
33299 what the new command is doing.
33300 To avoid these problems \SpecialChar LyX
33301 offers the possibility to use math macros instead
33311 \begin_layout Standard
33312 A math macro is created by using the menu
33314 Insert\SpecialChar menuseparator
33315 Math\SpecialChar menuseparator
33318 or the toolbar button
33321 arg "math-macro newmacroname_newcommand"
33325 The math macro toolbar appears together with the following box where the
33327 \begin_inset Newline newline
33331 \begin_inset space \hspace*{\fill}
33335 \begin_inset Graphics
33336 filename clipart/macrobox.png
33342 \begin_inset space \hspace*{\fill}
33346 \begin_inset Newline newline
33350 \begin_inset FormulaMacro
33351 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33356 newmacroname is the default name of the macro that should be changed to
33357 something sensible.
33358 The wanted formula is inserted in the first blue box.
33359 An argument placeholder is inserted with the command
33366 \begin_inset space \thinspace{}
33370 \begin_inset space \space{}
33379 or by using the macro toolbar button
33382 arg "math-macro-add-param"
33386 Argument placeholders are displayed red.
33388 \begin_inset space ~
33391 arguments are possible.
33392 Optional arguments are created with the toolbar button
33395 arg "math-macro-add-optional-param"
33399 The first non-optional argument can be transformed to an optional one with
33403 arg "math-macro-make-optional"
33407 In the second blue box the appearance of the macro in \SpecialChar LyX
33409 Normally you want to see it as it is defined, so the box is kept empty.
33410 But when you have created a macro that needs lot of space on the screen,
33411 you can insert in the box for example
33412 \begin_inset Newline newline
33442 \begin_inset Newline newline
33447 For the macro only the arguments with the macro name in front of them will
33448 then be displayed in \SpecialChar LyX
33449 , leading to a better overview.
33450 The formula appears in the output as defined in the first box.
33451 \begin_inset Newline newline
33454 The appearance of macros in formulas can furthermore be changed for single
33455 macros by setting the cursor in the macro and using the menu
33457 View\SpecialChar menuseparator
33459 \begin_inset space ~
33463 \begin_inset space ~
33471 \begin_layout Standard
33472 To use a macro, the macro name is inserted as command to a formula, in our
33480 Our macro looks in \SpecialChar LyX
33482 \begin_inset Newline newline
33486 \begin_inset space \hspace*{\fill}
33490 \begin_inset Graphics
33491 filename clipart/macrouse.png
33497 \begin_inset space \hspace*{\fill}
33501 \begin_inset Newline newline
33504 Here is our macro example with the arguments
33505 \begin_inset Formula $x$
33509 \begin_inset Formula $\ln(x)$
33513 \begin_inset Formula $B$
33519 \begin_layout Standard
33520 \begin_inset Formula
33530 \begin_layout Standard
33534 Tools\SpecialChar menuseparator
33535 Preferences\SpecialChar menuseparator
33536 Editing\SpecialChar menuseparator
33539 different styles to edit macros.
33540 To find the style that suits you the most, choose a style and set the cursor
33541 in a macro formula to see the difference.
33544 \begin_layout Standard
33545 A math macro is transformed internally to a
33551 command when exporting the document.
33558 command is not placed in the \SpecialChar LaTeX
33559 -preamble, therefore macros can only be used
33560 in formulas that are in the document below the macro definition box.
33563 \begin_layout Standard
33564 Math macros can also be directly created from a
33571 When writing for example the command
33574 \begin_inset Newline newline
33583 xleftarrow[#2]{#1}}
33584 \begin_inset Newline newline
33589 in \SpecialChar LyX
33590 as normal text, highlighting it completely and using then the shortcut
33595 , the command will be transformed to a math macro.
33596 Using this method you need to be careful that the
33602 command is typed correctly, otherwise you get a faulty macro leading to
33607 \begin_layout Standard
33608 Math macros currently have the problem that further formulas in macro definition
33609 s are handled wrongly.
33610 Therefore the example
33617 \begin_inset CommandInset ref
33619 reference "subsec:The-Command-newcommand"
33623 cannot be created as macro.
33626 \begin_layout Standard
33627 When the cursor is in a macro definition box, you will see the macro toolbar
33628 in \SpecialChar LyX
33632 \begin_layout Standard
33633 \begin_inset VSpace defskip
33639 \begin_layout Standard
33640 \begin_inset Graphics
33641 filename clipart/MacroToolbar.png
33646 \begin_inset Index idx
33649 \begin_layout Plain Layout
33658 \begin_layout Standard
33659 \begin_inset VSpace defskip
33665 \begin_layout Standard
33666 The macro toolbar contains from left to right the following buttons:
33669 \begin_layout Standard
33670 \begin_inset VSpace defskip
33676 \begin_layout Standard
33677 \begin_inset Tabular
33678 <lyxtabular version="3" rows="9" columns="2">
33679 <features islongtable="true" longtabularalignment="center">
33680 <column alignment="left" valignment="top">
33681 <column alignment="left" valignment="top" width="85col%">
33682 <row interlinespace="2.5mm">
33683 <cell alignment="center" valignment="top" usebox="none">
33686 \begin_layout Plain Layout
33689 arg "math-macro-remove-param"
33697 <cell alignment="center" valignment="top" usebox="none">
33700 \begin_layout Plain Layout
33703 Edit\SpecialChar menuseparator
33704 Math\SpecialChar menuseparator
33706 \begin_inset space ~
33709 Definition\SpecialChar menuseparator
33710 Remove Last Argument
33716 <row interlinespace="2.5mm">
33717 <cell alignment="center" valignment="top" usebox="none">
33720 \begin_layout Plain Layout
33723 arg "math-macro-add-param"
33731 <cell alignment="center" valignment="top" usebox="none">
33734 \begin_layout Plain Layout
33737 Edit\SpecialChar menuseparator
33738 Math\SpecialChar menuseparator
33740 \begin_inset space ~
33743 Definition\SpecialChar menuseparator
33750 <row interlinespace="2.5mm">
33751 <cell alignment="center" valignment="top" usebox="none">
33754 \begin_layout Plain Layout
33757 arg "math-macro-make-optional"
33765 <cell alignment="center" valignment="top" usebox="none">
33768 \begin_layout Plain Layout
33771 Edit\SpecialChar menuseparator
33772 Math\SpecialChar menuseparator
33774 \begin_inset space ~
33777 Definition\SpecialChar menuseparator
33778 Transform First Non-Optional to
33779 \begin_inset Newline newline
33783 \begin_inset Phantom HPhantom
33786 \begin_layout Plain Layout
33789 Edit\SpecialChar menuseparator
33790 Math\SpecialChar menuseparator
33792 \begin_inset space ~
33795 Definition\SpecialChar menuseparator
33807 <row interlinespace="2.5mm">
33808 <cell alignment="center" valignment="top" usebox="none">
33811 \begin_layout Plain Layout
33814 arg "math-macro-make-nonoptional"
33822 <cell alignment="center" valignment="top" usebox="none">
33825 \begin_layout Plain Layout
33828 Edit\SpecialChar menuseparator
33829 Math\SpecialChar menuseparator
33831 \begin_inset space ~
33834 Definition\SpecialChar menuseparator
33835 Transform Last Optional to
33836 \begin_inset Newline newline
33840 \begin_inset Phantom HPhantom
33843 \begin_layout Plain Layout
33846 Edit\SpecialChar menuseparator
33847 Math\SpecialChar menuseparator
33849 \begin_inset space ~
33852 Definition\SpecialChar menuseparator
33858 Non-Optional Argument
33864 <row interlinespace="2.5mm">
33865 <cell alignment="center" valignment="top" usebox="none">
33868 \begin_layout Plain Layout
33871 arg "math-macro-remove-optional-param"
33879 <cell alignment="center" valignment="top" usebox="none">
33882 \begin_layout Plain Layout
33885 Edit\SpecialChar menuseparator
33886 Math\SpecialChar menuseparator
33888 \begin_inset space ~
33891 Definition\SpecialChar menuseparator
33892 Remove Optional Argument
33898 <row interlinespace="2.5mm">
33899 <cell alignment="center" valignment="top" usebox="none">
33902 \begin_layout Plain Layout
33905 arg "math-macro-add-optional-param"
33913 <cell alignment="center" valignment="top" usebox="none">
33916 \begin_layout Plain Layout
33919 Edit\SpecialChar menuseparator
33920 Math\SpecialChar menuseparator
33922 \begin_inset space ~
33925 Definition\SpecialChar menuseparator
33926 Insert Optional Argument
33932 <row interlinespace="2.5mm">
33933 <cell alignment="center" valignment="top" usebox="none">
33936 \begin_layout Plain Layout
33939 arg "math-macro-remove-greedy-param"
33947 <cell alignment="center" valignment="top" usebox="none">
33950 \begin_layout Plain Layout
33953 Edit\SpecialChar menuseparator
33954 Math\SpecialChar menuseparator
33956 \begin_inset space ~
33959 Definition\SpecialChar menuseparator
33960 Remove Last Argument
33961 \begin_inset Newline newline
33965 \begin_inset Phantom HPhantom
33968 \begin_layout Plain Layout
33971 Edit\SpecialChar menuseparator
33972 Math\SpecialChar menuseparator
33974 \begin_inset space ~
33977 Definition\SpecialChar menuseparator
33983 Spitting Out To The Right
33989 <row interlinespace="2.5mm">
33990 <cell alignment="center" valignment="top" usebox="none">
33993 \begin_layout Plain Layout
33996 arg "math-macro-append-greedy-param"
34004 <cell alignment="center" valignment="top" usebox="none">
34007 \begin_layout Plain Layout
34010 Edit\SpecialChar menuseparator
34011 Math\SpecialChar menuseparator
34013 \begin_inset space ~
34016 Definition\SpecialChar menuseparator
34018 \begin_inset Newline newline
34022 \begin_inset Phantom HPhantom
34025 \begin_layout Plain Layout
34028 Edit\SpecialChar menuseparator
34029 Math\SpecialChar menuseparator
34031 \begin_inset space ~
34034 Definition\SpecialChar menuseparator
34040 Eating From The Right
34046 <row interlinespace="2.5mm">
34047 <cell alignment="center" valignment="top" usebox="none">
34050 \begin_layout Plain Layout
34053 arg "math-macro-add-greedy-optional-param"
34061 <cell alignment="center" valignment="top" usebox="none">
34064 \begin_layout Plain Layout
34067 Edit\SpecialChar menuseparator
34068 Math\SpecialChar menuseparator
34070 \begin_inset space ~
34073 Definition\SpecialChar menuseparator
34074 Append Optional Argument
34075 \begin_inset Newline newline
34079 \begin_inset Phantom HPhantom
34082 \begin_layout Plain Layout
34085 Edit\SpecialChar menuseparator
34086 Math\SpecialChar menuseparator
34088 \begin_inset space ~
34091 Definition\SpecialChar menuseparator
34097 Eating From The Right
34110 \begin_layout Section
34111 Computer Algebra Systems
34114 \begin_layout Standard
34116 offers the exchange between mathematical expressions written in \SpecialChar LyX
34118 editor and external applications or user defined scripts.
34119 Currently supported applications are
34136 Note that the set of supported mathematical constructs is limited only
34137 to very simple cases.
34140 \begin_layout Subsection
34144 \begin_layout Standard
34145 Write some expression in a formula, go to the
34147 Edit\SpecialChar menuseparator
34148 Math\SpecialChar menuseparator
34149 Use Computer Algebra System
34151 menu and choose the application you have installed on the computer.
34152 After that the result of computation should show on the right side of the
34153 expression together with the
34154 \begin_inset Quotes eld
34158 \begin_inset Quotes erd
34164 \begin_layout Standard
34165 Here are few simple examples (with results from
34169 ) to show what kind of computations can be performed:
34172 \begin_layout Itemize
34173 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34179 \begin_layout Itemize
34180 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34186 \begin_layout Itemize
34187 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34193 \begin_layout Itemize
34194 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34198 \begin_inset Newline newline
34202 \begin_inset Note Greyedout
34205 \begin_layout Plain Layout
34210 One needs to use proper delimiter insets
34211 \begin_inset Formula $\left(\right)$
34214 instead of simple '(' ')' characters.
34222 \begin_layout Itemize
34223 \begin_inset Formula $\det\left[\begin{array}{ccc}
34227 \end{array}\right]=-56$
34233 \begin_layout Itemize
34234 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34240 \begin_layout Itemize
34241 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34247 \begin_layout Itemize
34248 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34254 \begin_layout Subsection
34258 \begin_layout Standard
34259 Currently there is no keyboard shortcut for calling the algebra applications.
34260 One can easily bind a shortcut to the
34274 \begin_inset space \thinspace{}
34278 \begin_inset space \space{}
34285 key inside the math editor.
34290 one would use this shortcut definition command:
34293 \begin_layout Standard
34296 command-alternatives paragraph-break;math-extern maxima
34299 \begin_layout Section
34301 \begin_inset Index idx
34304 \begin_layout Plain Layout
34313 \begin_layout Subsection
34315 \begin_inset Index idx
34318 \begin_layout Plain Layout
34327 \begin_layout Standard
34328 Negative numbers often look ugly in formulas because the minus sign before
34329 the number is set with the same length as the minus operator sign.
34330 When writing the negative number in normal text, the minus sign appears
34334 \begin_layout Standard
34335 Thus, the problem disappears when converting the minus sign to mathematical
34339 \begin_layout Standard
34340 An example to visualize the problem:
34343 \begin_layout Standard
34345 \begin_inset Tabular
34346 <lyxtabular version="3" rows="3" columns="2">
34347 <features booktabs="true" tabularvalignment="middle">
34348 <column alignment="right" valignment="top" width="0pt">
34349 <column alignment="left" valignment="top">
34351 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34354 \begin_layout Plain Layout
34360 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34363 \begin_layout Plain Layout
34371 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34374 \begin_layout Plain Layout
34380 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34383 \begin_layout Plain Layout
34384 \begin_inset Formula $x=-2$
34394 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34397 \begin_layout Plain Layout
34403 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34406 \begin_layout Plain Layout
34407 \begin_inset Formula $x=\textrm{-}2$
34423 \begin_layout Subsection
34424 Comma as decimal Separator
34425 \begin_inset Index idx
34428 \begin_layout Plain Layout
34437 \begin_layout Standard
34438 In \SpecialChar LaTeX
34439 a comma inside a formula is used, according to the English convention,
34440 as number group separator.
34441 So there will be space added behind all commas in formulas.
34444 \begin_layout Standard
34445 To avoid this, the comma is highlighted and changed to mathematical text
34455 \begin_layout Standard
34456 To use all formula commas in the document as decimal separator, the file
34465 \begin_layout Plain Layout
34470 is part of the \SpecialChar LaTeX
34476 \begin_inset Index idx
34479 \begin_layout Plain Layout
34484 \begin_layout Plain Layout
34504 \begin_inset Index idx
34507 \begin_layout Plain Layout
34513 is loaded with the \SpecialChar LaTeX
34517 \begin_layout Standard
34525 \begin_layout Subsection
34527 \begin_inset CommandInset label
34529 name "subsec:Physical-Vectors"
34534 \begin_inset Index idx
34537 \begin_layout Plain Layout
34546 \begin_layout Standard
34547 Predefined vectors are offered by the \SpecialChar LaTeX
34553 \begin_inset Index idx
34556 \begin_layout Plain Layout
34562 that is loaded with the \SpecialChar LaTeX
34566 \begin_layout Standard
34574 \begin_layout Standard
34578 \begin_layout Plain Layout
34588 \begin_inset Note Note
34591 \begin_layout Plain Layout
34592 The following table will only be displayed when the \SpecialChar LaTeX
34605 \begin_layout Standard
34606 The following commands are defined:
34609 \begin_layout Standard
34611 \begin_inset Tabular
34612 <lyxtabular version="3" rows="4" columns="2">
34613 <features booktabs="true" tabularvalignment="middle">
34614 <column alignment="center" valignment="top" width="0pt">
34615 <column alignment="center" valignment="top">
34617 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34620 \begin_layout Plain Layout
34626 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34629 \begin_layout Plain Layout
34637 <cell alignment="center" valignment="top" usebox="none">
34640 \begin_layout Plain Layout
34650 <cell alignment="center" valignment="top" usebox="none">
34653 \begin_layout Plain Layout
34654 \begin_inset Formula $\Bra{\psi}$
34664 <cell alignment="center" valignment="top" usebox="none">
34667 \begin_layout Plain Layout
34677 <cell alignment="center" valignment="top" usebox="none">
34680 \begin_layout Plain Layout
34681 \begin_inset Formula $\Ket{\psi}$
34691 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34694 \begin_layout Plain Layout
34706 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34709 \begin_layout Plain Layout
34710 \begin_inset Formula $\Braket{\psi|\phi}$
34726 \begin_layout Standard
34733 assures that all vertical bars are set in the size of the surrounding brackets:
34734 \begin_inset Formula
34736 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34745 \begin_layout Plain Layout
34755 \begin_inset Note Note
34758 \begin_layout Plain Layout
34759 The following will be displayed when the \SpecialChar LaTeX
34772 \begin_layout Standard
34773 You need to install the \SpecialChar LaTeX
34778 to see the rest of this subsection in the output.
34781 \begin_layout Standard
34785 \begin_layout Plain Layout
34797 \begin_layout Standard
34804 can also be achieved using the command
34810 , that is described in
34811 \begin_inset CommandInset ref
34813 reference "subsec:Automatic-Bracket-Size"
34820 \begin_layout Subsection
34821 Self-defined Fractions
34822 \begin_inset CommandInset label
34824 name "subsec:Self-defined-Fractions"
34829 \begin_inset Index idx
34832 \begin_layout Plain Layout
34833 Fractions ! self-defined
34841 \begin_layout Standard
34842 To define custom commands for fractions, the command
34849 \begin_inset Index idx
34852 \begin_layout Plain Layout
34859 \begin_layout Plain Layout
34873 is used in the following scheme:
34876 \begin_layout Standard
34889 bracket}{fraction bar thickness}{style}
34890 \begin_inset Newline newline
34894 \begin_inset Phantom HPhantom
34897 \begin_layout Plain Layout
34907 {numerator}{denominator}
34910 \begin_layout Standard
34911 The style is a number in the range of 0
34912 \begin_inset space \thinspace{}
34916 \begin_inset space \thinspace{}
34922 \begin_layout Standard
34924 \begin_inset Tabular
34925 <lyxtabular version="3" rows="5" columns="2">
34926 <features booktabs="true" tabularvalignment="middle">
34927 <column alignment="center" valignment="top" width="0pt">
34928 <column alignment="center" valignment="top">
34930 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34933 \begin_layout Plain Layout
34939 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34942 \begin_layout Plain Layout
34950 <cell alignment="center" valignment="top" usebox="none">
34953 \begin_layout Plain Layout
34959 <cell alignment="center" valignment="top" usebox="none">
34962 \begin_layout Plain Layout
34963 display style formula
34970 <cell alignment="center" valignment="top" usebox="none">
34973 \begin_layout Plain Layout
34979 <cell alignment="center" valignment="top" usebox="none">
34982 \begin_layout Plain Layout
34990 <cell alignment="center" valignment="top" usebox="none">
34993 \begin_layout Plain Layout
34999 <cell alignment="center" valignment="top" usebox="none">
35002 \begin_layout Plain Layout
35010 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35013 \begin_layout Plain Layout
35019 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35022 \begin_layout Plain Layout
35036 \begin_layout Standard
35037 When no style is given, the size is adjusted to the surrounding environment
35038 like for the command
35047 \begin_layout Standard
35048 When no fraction bar thickness is given, the predefined value of 0.4
35049 \begin_inset space \thinspace{}
35055 \begin_layout Standard
35056 \begin_inset VSpace medskip
35059 For example, the commands
35072 \begin_inset CommandInset ref
35074 reference "subsec:Fractions"
35078 are defined with the commands
35081 \begin_layout Standard
35090 genfrac{}{}{}{0}{#1}{#2}}
35093 \begin_layout Standard
35097 \begin_layout Standard
35106 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35109 \begin_layout Standard
35110 \begin_inset VSpace medskip
35113 To define a fraction where the fraction bar thickness can be given as optional
35114 argument, the following line is inserted to the \SpecialChar LaTeX
35118 \begin_layout Standard
35127 genfrac{}{}{#1}{}{#2}{#3}}
35130 \begin_layout Standard
35132 \begin_inset Formula
35134 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35135 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35140 As one can see, the distance of the numerator and the denominator to the
35141 fraction bar is round about three times the bar thickness.
35144 \begin_layout Standard
35145 \begin_inset Newpage newpage
35151 \begin_layout Subsection
35153 \begin_inset Index idx
35156 \begin_layout Plain Layout
35165 \begin_layout Standard
35166 There are four ways to cancel formulas or parts of formulas:
35169 \begin_layout Standard
35173 \begin_layout Plain Layout
35183 \begin_inset Note Note
35186 \begin_layout Plain Layout
35187 The following table will only be displayed when the \SpecialChar LaTeX
35200 \begin_layout Standard
35202 \begin_inset Tabular
35203 <lyxtabular version="3" rows="5" columns="2">
35204 <features booktabs="true" tabularvalignment="middle">
35205 <column alignment="center" valignment="top" width="0pt">
35206 <column alignment="center" valignment="top">
35208 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35211 \begin_layout Plain Layout
35217 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35220 \begin_layout Plain Layout
35228 <cell alignment="center" valignment="top" usebox="none">
35231 \begin_layout Plain Layout
35235 \begin_inset space \textvisiblespace{}
35241 \begin_inset space \textvisiblespace{}
35249 <cell alignment="center" valignment="top" usebox="none">
35252 \begin_layout Plain Layout
35253 \begin_inset Formula $\cancel{\int A=B}$
35262 <row topspace="1.5mm">
35263 <cell alignment="center" valignment="top" usebox="none">
35266 \begin_layout Plain Layout
35270 \begin_inset space \textvisiblespace{}
35276 \begin_inset space \textvisiblespace{}
35284 <cell alignment="center" valignment="top" usebox="none">
35287 \begin_layout Plain Layout
35288 \begin_inset Formula $\bcancel{\int A=B}$
35297 <row topspace="1.5mm">
35298 <cell alignment="center" valignment="top" usebox="none">
35301 \begin_layout Plain Layout
35305 \begin_inset space \textvisiblespace{}
35311 \begin_inset space \textvisiblespace{}
35319 <cell alignment="center" valignment="top" usebox="none">
35322 \begin_layout Plain Layout
35323 \begin_inset Formula $\xcancel{\int A=B}$
35333 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35336 \begin_layout Plain Layout
35340 \begin_inset space \textvisiblespace{}
35346 \begin_inset space \textvisiblespace{}
35350 \begin_inset Formula $\to$
35358 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35361 \begin_layout Plain Layout
35362 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35378 \begin_layout Standard
35385 is especially suitable to visualize the reduction of fractions within formulas:
35386 \begin_inset Formula
35388 \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}}}
35396 \begin_layout Standard
35397 To change the size of
35404 \begin_inset Quotes eld
35408 \begin_inset Quotes erd
35411 value one can add the \SpecialChar LaTeX
35415 \begin_layout Standard
35420 PassOptionsToPackage{option}{cancel}
35423 \begin_layout Standard
35432 which leads to the same size as for the canceled value, or
35436 which makes is it a bit smaller than normal.
35439 \begin_layout Standard
35440 To color the cancellation bar one adds this command as \SpecialChar TeX
35444 \begin_layout Standard
35456 \begin_layout Standard
35461 can be replaced by a color of your choice.
35464 \begin_layout Standard
35468 \begin_layout Plain Layout
35484 \begin_layout Standard
35485 \begin_inset Formula
35487 \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}}}
35495 \begin_layout Standard
35499 \begin_layout Plain Layout
35513 \begin_inset Note Note
35516 \begin_layout Plain Layout
35525 \begin_layout Standard
35526 For further customizations, see the documentation of the package
35531 \begin_inset CommandInset citation
35539 \begin_inset Index idx
35542 \begin_layout Plain Layout
35551 \begin_layout Standard
35555 \begin_layout Plain Layout
35565 \begin_inset Note Note
35568 \begin_layout Plain Layout
35569 The following will be displayed when the \SpecialChar LaTeX
35582 \begin_layout Standard
35583 You need to install the \SpecialChar LaTeX
35588 to see the rest of this subsection in the output.
35591 \begin_layout Standard
35595 \begin_layout Plain Layout
35607 \begin_layout Subsection
35608 Formulas in Section Headings
35609 \begin_inset CommandInset label
35611 name "subsec:Formulas-in-Section"
35616 \begin_inset Index idx
35619 \begin_layout Plain Layout
35620 Formula ! in section headings
35628 \begin_layout Standard
35629 When formulas are used in section headings, the following has to be taken
35633 \begin_layout Standard
35634 \begin_inset Note Greyedout
35637 \begin_layout Plain Layout
35643 \begin_inset Index idx
35646 \begin_layout Plain Layout
35647 Packages ! hyperref
35652 support is enabled in the document settings dialog under
35655 \begin_inset space ~
35660 , PDF-bookmarks are created for every section heading in the table of contents.
35661 If a section heading contains formulas, they are incorrectly displayed
35662 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35671 \begin_layout Standard
35672 Both problems can be solved by inserting at the end of the section heading
35673 a short title with the menu
35675 Insert\SpecialChar menuseparator
35677 \begin_inset space ~
35683 Short titles are used as alternative for multiline section headings to
35684 keep the table of contents clearly arranged.
35685 Only the short title appears in the table of contents and therefore also
35686 in the PDF-bookmark.
35689 \begin_layout Standard
35690 When formulas should be used in the table of contents but
35694 is used, one can use the following command in \SpecialChar TeX
35698 \begin_layout Standard
35703 texorpdfstring{part}{alternative}
35704 \begin_inset Index idx
35707 \begin_layout Plain Layout
35718 \begin_layout Standard
35719 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35720 This can be characters, formulas, footnotes, but also cross-references.
35721 The alternative is used instead of the part for the bookmark.
35724 \begin_layout Standard
35725 Here are two example headings:
35726 \begin_inset VSpace -3mm
35733 \begin_layout Plain Layout
35745 \begin_layout Subsubsection
35746 Heading without formula in table of contents
35747 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35751 \begin_inset Argument 1
35754 \begin_layout Plain Layout
35755 Heading without formula in table of contents
35763 \begin_layout Subsubsection
35764 Heading with formula in table of contents
35768 \begin_layout Plain Layout
35778 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35785 \begin_layout Plain Layout
35795 \begin_layout Standard
35799 \begin_layout Plain Layout
35808 In the first heading a short title was used, in the second one
35817 \begin_layout Standard
35818 To get the same formatting as for the other headings, the complete heading
35827 \begin_layout Plain Layout
35829 \begin_inset CommandInset ref
35831 reference "subsec:Bold-Formulas"
35843 \begin_layout Subsection
35844 Formulas in multi-column Text
35845 \begin_inset Index idx
35848 \begin_layout Plain Layout
35849 Formula ! in multi-column text
35857 \begin_layout Standard
35858 Formulas in multi-column text are often too wide to fit into a column and
35859 thus need to be set over the whole page width.
35860 This is done by using the \SpecialChar LaTeX
35869 \begin_layout Plain Layout
35874 is part of every \SpecialChar LaTeX
35875 standard installation.
35881 \begin_inset Index idx
35884 \begin_layout Plain Layout
35885 Packages ! multicol
35890 , that is loaded with the \SpecialChar LaTeX
35894 \begin_layout Standard
35899 usepackage{multicol}
35902 \begin_layout Standard
35903 \begin_inset Note Greyedout
35906 \begin_layout Plain Layout
35907 Note that in this case the setting
35910 \begin_inset space ~
35917 Document\SpecialChar menuseparator
35923 \begin_inset space ~
35943 \begin_layout Standard
35944 Before the multi-column text the command
35947 \begin_layout Standard
35952 begin{multicols}{column number}
35955 \begin_layout Standard
35956 is written in \SpecialChar TeX
35958 The column number is a number in the range of 2
35959 \begin_inset space \thinspace{}
35963 \begin_inset space \thinspace{}
35967 Before the formula the multi-column text is ended by inserting the command
35970 \begin_layout Standard
35978 \begin_layout Standard
35979 in \SpecialChar TeX
35983 \begin_layout Standard
35984 Due to the command some space is automatically added before the formula.
35986 \begin_inset space \thinspace{}
35989 mm vertical space is inserted before the formula.
35990 When the formula style
35996 \begin_layout Plain Layout
35998 \begin_inset CommandInset ref
36000 reference "sec:Formula-Styles"
36012 \begin_inset space \thinspace{}
36015 mm space is inserted instead.
36018 \begin_layout Standard
36019 As example a multi-column text with a displayed formula:
36022 \begin_layout Standard
36028 \begin_layout Plain Layout
36032 begin{multicols}{2}
36037 Das Spektrum wird fouriertransformiert.
36038 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36039 , Lösungsmittel) zu trennen.
36040 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36041 nun das Aussehen des Ausgangssignals.
36042 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36043 über alle Phasen integrieren muss.
36045 \begin_inset Formula $S$
36048 unser normiertes Ausgangssignal und
36049 \begin_inset Formula $P$
36052 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36056 \begin_layout Plain Layout
36066 \begin_inset VSpace -6mm
36070 \begin_inset Formula
36072 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36081 \begin_layout Plain Layout
36085 begin{multicols}{2}
36091 \begin_inset Formula $S_{0}$
36094 das Signal ohne Gradient ist und die Normierungsbedingung
36095 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36099 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36101 \begin_inset Formula $\nicefrac{\pi}{2}$
36105 \begin_inset space \thinspace{}
36108 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36109 das Signal zusätzlich abschwächt.
36110 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36112 \begin_inset Formula $T_{2}$
36118 \begin_layout Standard
36124 \begin_layout Plain Layout
36136 \begin_layout Subsection
36137 Formulas with Description of Variables
36138 \begin_inset Index idx
36141 \begin_layout Plain Layout
36142 Formula ! with description of variables
36150 \begin_layout Standard
36151 To describe variables within a formula, like in formula
36152 \begin_inset CommandInset ref
36154 reference "eq:within"
36163 \begin_inset Formula $n$
36167 \begin_inset space ~
36170 matrix is used with left aligned columns for the
36171 \begin_inset Formula $n$
36178 \begin_layout Plain Layout
36180 \begin_inset CommandInset ref
36182 reference "sec:Matrices"
36191 To set the description in a smaller size, before the matrix e.
36192 \begin_inset space \thinspace{}
36196 \begin_inset space \space{}
36209 \begin_layout Plain Layout
36211 \begin_inset CommandInset ref
36213 reference "subsec:Font-Sizes"
36225 \begin_layout Standard
36226 When the formula style
36232 \begin_layout Plain Layout
36234 \begin_inset CommandInset ref
36236 reference "sec:Formula-Styles"
36257 \begin_layout Plain Layout
36264 only works in formulas with the style
36269 \begin_inset CommandInset ref
36271 reference "subsec:Variable-Space"
36280 is inserted before and after the matrix to have the same separation of
36281 the matrix from the equation and the side margin.
36284 \begin_layout Standard
36285 When the formula style
36289 is used, the method described in
36290 \begin_inset CommandInset ref
36292 reference "subsec:Flalign-Environment"
36296 is used to indent formulas.
36298 \begin_inset CommandInset ref
36300 reference "eq:within"
36304 consists of five columns where in the first two columns contain the equation,
36305 the third the matrix and the last one an empty \SpecialChar TeX
36307 \begin_inset Formula
36309 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36310 \rho & \textrm{density}\\
36311 V & \textrm{volume}\\
36312 g & \textrm{gravitational acceleration}
36313 \end{array} & & {}\label{eq:within}
36321 \begin_layout Subsection
36322 Upright small Greek Letters
36323 \begin_inset CommandInset label
36325 name "subsec:Upright-small-Greek"
36330 \begin_inset Index idx
36333 \begin_layout Plain Layout
36334 Greek letters ! upright
36342 \begin_layout Standard
36343 Most of the math fonts only provide italic small Greek letters.
36344 But for symbols of elementary particles like pions and neutrinos, upright
36345 Greek letters are needed.
36354 \begin_layout Plain Layout
36359 is part of the \SpecialChar LaTeX
36365 \begin_inset Index idx
36368 \begin_layout Plain Layout
36373 \begin_layout Plain Layout
36393 \begin_inset Index idx
36396 \begin_layout Plain Layout
36402 that is loaded with the \SpecialChar LaTeX
36406 \begin_layout Standard
36411 usepackage{upgreek}
36414 \begin_layout Standard
36420 \begin_layout Plain Layout
36430 \begin_inset Note Note
36433 \begin_layout Plain Layout
36434 The following table will only be displayed when the \SpecialChar LaTeX
36444 They are created when the command for a small Greek letter is started with
36450 For example the command
36457 \begin_inset Formula $\uptau$
36463 \begin_layout Standard
36464 With these commands reactions of elementary particles can be typeset:
36465 \begin_inset Formula
36467 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36475 \begin_layout Standard
36476 The upright letters are more bold and wider than the italic ones.
36477 They should therefore not be used for units like
36478 \begin_inset Quotes eld
36482 \begin_inset Quotes erd
36488 \begin_layout Standard
36492 \begin_layout Plain Layout
36502 \begin_inset Note Note
36505 \begin_layout Plain Layout
36506 The following will be displayed when the \SpecialChar LaTeX
36519 \begin_layout Standard
36520 You need to install the \SpecialChar LaTeX
36525 to see the rest of this subsection in the output.
36528 \begin_layout Standard
36532 \begin_layout Plain Layout
36544 \begin_layout Subsection
36545 Text Characters in Formulas
36546 \begin_inset Index idx
36549 \begin_layout Plain Layout
36558 \begin_layout Standard
36559 In some cases you might want to insert text characters directly into formulas.
36560 When for example the centered dot · is often used in formulas like
36561 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36564 , one would have to insert the command
36574 \begin_layout Plain Layout
36576 \begin_inset CommandInset ref
36578 reference "subsec:Binary-Operators"
36587 all the time, because this character is defined in all encodings as text
36589 But the encoding can be changed by this \SpecialChar LaTeX
36593 \begin_layout Standard
36598 Declare Inputtext{183}{
36608 f\SpecialChar ligaturebreak
36612 \begin_layout Standard
36613 The character encoding (menu
36615 Document\SpecialChar menuseparator
36616 Settings\SpecialChar menuseparator
36619 ) specifies what character appears when a keyboard key is pressed.
36620 When the key for the character '·' is pressed, internally the command
36627 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36629 With the changed encoding the right command is chosen automatically, depending
36630 on if the character was inserted into a formula or not.
36633 \begin_layout Standard
36634 The encoding of several characters is saved in definition files.
36635 For example the encoding
36639 is defined in the file
36643 which is in the installation folder of \SpecialChar LaTeX
36645 Encodings should only be changed via the \SpecialChar LaTeX
36646 -preamble and not in the definition
36648 Otherwise documents could not be edited by other \SpecialChar LyX
36649 users working on other
36653 \begin_layout Standard
36654 \begin_inset VSpace medskip
36657 Besides the centered dot, in this document the degree sign ° is defined
36658 with the following \SpecialChar LaTeX
36659 -preamble line so that it can be directly inserted into
36663 \begin_layout Standard
36668 DeclareInputtext{176}{
36678 f\SpecialChar ligaturebreak
36682 \begin_layout Subsection
36684 -comments in formulas
36685 \begin_inset Index idx
36688 \begin_layout Plain Layout
36698 \begin_layout Standard
36699 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36701 code of your file with the menu
36703 Insert\SpecialChar menuseparator
36704 Note\SpecialChar menuseparator
36708 This is not possible in a formula but you can insert \SpecialChar LaTeX
36713 \begin_layout Standard
36721 \begin_layout Standard
36722 This creates a box in which you can write your comment.
36723 Due to a bug in \SpecialChar LyX
36728 \begin_layout Plain Layout
36729 \begin_inset CommandInset href
36731 name "LyX-bug #9002"
36732 target "http://www.lyx.org/trac/ticket/9002"
36742 you cannot write normal text inside the comment, even when you use mathematical
36743 text, you will see its \SpecialChar LaTeX
36744 -commands in the \SpecialChar LaTeX
36746 \begin_inset Newline newline
36749 This a formula with a \SpecialChar LaTeX
36751 \begin_inset Formula
36753 A=B%\text{This is the comment}
36761 \begin_layout Standard
36762 \begin_inset Newpage newpage
36768 \begin_layout Section
36771 \begin_inset Index idx
36774 \begin_layout Plain Layout
36783 \begin_layout Standard
36784 This section is a summary of the most important typographic rules, listed
36789 \begin_layout Plain Layout
36790 This collection was partly taken from the German semi-official dictionary
36792 \begin_inset Quotes eld
36796 \begin_inset Quotes erd
36800 \begin_inset CommandInset citation
36807 that lists some of the ISO rules.
36808 More rules are listed in
36809 \begin_inset CommandInset citation
36824 \begin_layout Itemize
36833 \begin_layout Plain Layout
36834 done with font styles, see
36835 \begin_inset CommandInset ref
36837 reference "subsec:Font-Styles"
36846 , no matter if they appear in italic text: 30
36847 \begin_inset space \thinspace{}
36851 \begin_inset Newline newline
36854 Between the value and the unit is the smallest space, see
36855 \begin_inset CommandInset ref
36857 reference "subsec:Predefined-Space"
36862 \begin_inset Newline newline
36865 This convention is automatically fulfilled when the command
36872 When it is entered to a formula, two boxes appear.
36873 In the first one the value is inserted, in the second one the unit, and
36875 \begin_inset Formula $\unit[30]{km/h}$
36879 \begin_inset space \thinspace{}
36889 is not a real \SpecialChar LaTeX
36890 command but the command
36896 , therefore you cannot use it in \SpecialChar TeX
36900 \begin_layout Itemize
36901 Percent and perthousand signs are set like physical units:
36902 \begin_inset Newline newline
36906 \begin_inset space \thinspace{}
36912 \begin_layout Itemize
36913 The degree sign follows directly on the value: 15°, but not when it is used
36915 \begin_inset space \thinspace{}
36921 \begin_layout Itemize
36922 In numbers with more than four digits the smallest space is inserted before
36923 every third digit to group them:
36933 \begin_inset space \thinspace{}
36937 \begin_inset space \thinspace{}
36943 \begin_layout Itemize
36944 For dimensions like 120×90×40
36945 \begin_inset space \thinspace{}
36948 cm the multiplication sign
36949 \begin_inset Quotes eld
36953 \begin_inset Quotes erd
36957 It is available either via the command
36965 Insert\SpecialChar menuseparator
36966 Special Character\SpecialChar menuseparator
36972 \begin_layout Itemize
36973 Functions with names consisting of several letters are set upright to avoid
36975 \begin_inset CommandInset ref
36977 reference "subsec:Predefined-Functions"
36984 \begin_layout Itemize
36985 Indices consisting of several letters, are set upright:
36986 \begin_inset Formula $E_{\mathrm{kin}}$
36990 \begin_inset Newline newline
36993 Components of matrices are set italic:
36994 \begin_inset Formula $\hat{H}_{kl}$
37000 \begin_layout Itemize
37001 The differentiation/integration operator 'd', the Euler's number 'e' and
37002 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37006 \begin_layout Itemize
37007 The character that denotes a
37011 transformation is inserted either by the command
37016 \begin_inset space \textvisiblespace{}
37023 Insert\SpecialChar menuseparator
37024 Special Character\SpecialChar menuseparator
37025 Symbols\SpecialChar menuseparator
37027 \begin_inset space ~
37033 \begin_inset Formula $\mathscr{F}$
37039 \begin_layout Standard
37040 \begin_inset Newpage newpage
37046 \begin_layout Section
37048 \begin_inset Index idx
37051 \begin_layout Plain Layout
37060 \begin_layout Standard
37061 Some characters and symbols can be created with several commands.
37062 Here is a list of the synonym commands:
37065 \begin_layout Standard
37066 \begin_inset VSpace bigskip
37070 \begin_inset space \hfill{}
37074 \begin_inset Tabular
37075 <lyxtabular version="3" rows="12" columns="2">
37076 <features booktabs="true" tabularvalignment="middle">
37077 <column alignment="center" valignment="top" width="0pt">
37078 <column alignment="center" valignment="top" width="0pt">
37080 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37083 \begin_layout Plain Layout
37089 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37092 \begin_layout Plain Layout
37100 <cell alignment="center" valignment="top" usebox="none">
37103 \begin_layout Plain Layout
37111 <cell alignment="center" valignment="top" usebox="none">
37114 \begin_layout Plain Layout
37122 <cell alignment="center" valignment="top" usebox="none">
37125 \begin_layout Plain Layout
37133 <cell alignment="center" valignment="top" usebox="none">
37136 \begin_layout Plain Layout
37146 <cell alignment="center" valignment="top" usebox="none">
37149 \begin_layout Plain Layout
37157 <cell alignment="center" valignment="top" usebox="none">
37160 \begin_layout Plain Layout
37170 <cell alignment="center" valignment="top" usebox="none">
37173 \begin_layout Plain Layout
37181 <cell alignment="center" valignment="top" usebox="none">
37184 \begin_layout Plain Layout
37192 <cell alignment="center" valignment="top" usebox="none">
37195 \begin_layout Plain Layout
37203 <cell alignment="center" valignment="top" usebox="none">
37206 \begin_layout Plain Layout
37214 <cell alignment="center" valignment="top" usebox="none">
37217 \begin_layout Plain Layout
37225 <cell alignment="center" valignment="top" usebox="none">
37228 \begin_layout Plain Layout
37238 <cell alignment="center" valignment="top" usebox="none">
37241 \begin_layout Plain Layout
37249 <cell alignment="center" valignment="top" usebox="none">
37252 \begin_layout Plain Layout
37262 <cell alignment="center" valignment="top" usebox="none">
37265 \begin_layout Plain Layout
37273 <cell alignment="center" valignment="top" usebox="none">
37276 \begin_layout Plain Layout
37286 <cell alignment="center" valignment="top" usebox="none">
37289 \begin_layout Plain Layout
37297 <cell alignment="center" valignment="top" usebox="none">
37300 \begin_layout Plain Layout
37310 <cell alignment="center" valignment="top" usebox="none">
37313 \begin_layout Plain Layout
37321 <cell alignment="center" valignment="top" usebox="none">
37324 \begin_layout Plain Layout
37332 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37335 \begin_layout Plain Layout
37343 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37346 \begin_layout Plain Layout
37358 \begin_inset space \hfill{}
37362 \begin_inset Tabular
37363 <lyxtabular version="3" rows="12" columns="2">
37364 <features booktabs="true" tabularvalignment="middle">
37365 <column alignment="center" valignment="top" width="0pt">
37366 <column alignment="center" valignment="top" width="0pt">
37368 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37371 \begin_layout Plain Layout
37377 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37380 \begin_layout Plain Layout
37388 <cell alignment="center" valignment="top" usebox="none">
37391 \begin_layout Plain Layout
37399 <cell alignment="center" valignment="top" usebox="none">
37402 \begin_layout Plain Layout
37414 <cell alignment="center" valignment="top" usebox="none">
37417 \begin_layout Plain Layout
37425 <cell alignment="center" valignment="top" usebox="none">
37428 \begin_layout Plain Layout
37438 <cell alignment="center" valignment="top" usebox="none">
37441 \begin_layout Plain Layout
37449 <cell alignment="center" valignment="top" usebox="none">
37452 \begin_layout Plain Layout
37462 <cell alignment="center" valignment="top" usebox="none">
37465 \begin_layout Plain Layout
37473 <cell alignment="center" valignment="top" usebox="none">
37476 \begin_layout Plain Layout
37484 <cell alignment="center" valignment="top" usebox="none">
37487 \begin_layout Plain Layout
37495 <cell alignment="center" valignment="top" usebox="none">
37498 \begin_layout Plain Layout
37506 <cell alignment="center" valignment="top" usebox="none">
37509 \begin_layout Plain Layout
37517 <cell alignment="center" valignment="top" usebox="none">
37520 \begin_layout Plain Layout
37530 <cell alignment="center" valignment="top" usebox="none">
37533 \begin_layout Plain Layout
37541 <cell alignment="center" valignment="top" usebox="none">
37544 \begin_layout Plain Layout
37554 <cell alignment="center" valignment="top" usebox="none">
37557 \begin_layout Plain Layout
37565 <cell alignment="center" valignment="top" usebox="none">
37568 \begin_layout Plain Layout
37578 <cell alignment="center" valignment="top" usebox="none">
37581 \begin_layout Plain Layout
37589 <cell alignment="center" valignment="top" usebox="none">
37592 \begin_layout Plain Layout
37602 <cell alignment="center" valignment="top" usebox="none">
37605 \begin_layout Plain Layout
37613 <cell alignment="center" valignment="top" usebox="none">
37616 \begin_layout Plain Layout
37626 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37629 \begin_layout Plain Layout
37637 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37640 \begin_layout Plain Layout
37654 \begin_inset space \hfill{}
37660 \begin_layout Standard
37661 \begin_inset Newpage newpage
37667 \begin_layout Bibliography
37668 \begin_inset CommandInset bibitem
37669 LatexCommand bibitem
37682 The \SpecialChar LaTeX
37686 Addison Wesley, 2004
37689 \begin_layout Bibliography
37690 \begin_inset CommandInset bibitem
37691 LatexCommand bibitem
37698 \begin_inset CommandInset href
37701 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37706 of \SpecialChar LaTeX
37710 \begin_layout Bibliography
37711 \begin_inset CommandInset bibitem
37712 LatexCommand bibitem
37719 \begin_inset CommandInset href
37722 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37731 \begin_layout Plain Layout
37740 -\SpecialChar LaTeX
37744 \begin_layout Bibliography
37745 \begin_inset CommandInset bibitem
37746 LatexCommand bibitem
37753 \begin_inset CommandInset href
37756 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37761 of all symbols available with \SpecialChar LaTeX
37765 \begin_layout Bibliography
37766 \begin_inset CommandInset bibitem
37767 LatexCommand bibitem
37774 \begin_inset CommandInset href
37776 name "Documentation"
37777 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37782 of the \SpecialChar LaTeX
37788 \begin_inset Index idx
37791 \begin_layout Plain Layout
37800 \begin_layout Bibliography
37801 \begin_inset CommandInset bibitem
37802 LatexCommand bibitem
37809 \begin_inset CommandInset href
37811 name "Documentation"
37812 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37817 of the \SpecialChar LaTeX
37823 \begin_inset Index idx
37826 \begin_layout Plain Layout
37827 Packages ! hyperref
37835 \begin_layout Bibliography
37836 \begin_inset CommandInset bibitem
37837 LatexCommand bibitem
37844 \begin_inset CommandInset href
37846 name "Documentation"
37847 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37852 of the \SpecialChar LaTeX
37858 \begin_inset Index idx
37861 \begin_layout Plain Layout
37870 \begin_layout Bibliography
37871 \begin_inset CommandInset bibitem
37872 LatexCommand bibitem
37884 Auflage, Duden 2001
37887 \begin_layout Bibliography
37888 \begin_inset CommandInset bibitem
37889 LatexCommand bibitem
37896 \begin_inset CommandInset href
37899 target "http://physics.nist.gov/Pubs/SP811/sec11.html"
37904 for reviewing manuscripts
37907 \begin_layout Standard
37908 \begin_inset CommandInset index_print
37909 LatexCommand printindex