1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
5 \origin /systemlyxdir/doc/
8 % DO NOT ALTER THIS PREAMBLE!!!
10 % This preamble is designed to ensure that the file prints
11 % out as advertised. If you mess with this preamble,
12 % parts of this document may not print out as expected. If you
13 % have problems LaTeXing this file, please contact
14 % the documentation team
15 % email: lyx-docs@lists.lyx.org
17 % solves the following problem:
18 % If the dection number consits of too many numerals the section heading
19 % will be printed in the TOC without a space between it and the section number.
20 % As solution more space between the number and the heading is inserted:
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22 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
24 % increase link area for cross-references and autoname them,
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36 % don't load packages twice
37 % see first footnote in sec. 9.3
38 \@ifundefined{textcolor}{\usepackage{color}}{}
40 % the pages of the TOC are numbered roman
41 % and a PDF-bookmark for the TOC is added
43 \let\myTOC\tableofcontents
44 \renewcommand{\tableofcontents}{%
46 \pdfbookmark[1]{\contentsname}{}
49 \pagenumbering{arabic}}
51 % add 0.5 mm vertical space for table rows
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53 \setlength{\extrarowheight}{0.5mm}
55 % insert additional vertical space of 1.5 mm between footnotes,
57 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
59 % makes caption labels bold
60 \setkomafont{captionlabel}{\bfseries}
62 % enables calculation of values
65 % for multiple columns used in sec. 24.7
71 % for the Fourier transformation symbol
74 % define a color, used in sec.9.3
75 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
77 % declare operators (see sec. 10.4 and sec. 15.2)
78 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
79 \DeclareMathOperator{\sgn}{sgn}
81 % example definitions for sec. 20.1
82 \newcommand{\gr}{\Longrightarrow}
83 \newcommand{\us}[1]{\underline{#1}}
84 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
85 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
86 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
88 % example macro from sec. 19.4
89 %\def\tagform@#1{\maketag@@@{|#1|}}
92 % ------------------------------------
93 % used to check for needed LaTeX packages
96 % check for package undertilde
97 % used for the command \utilde
98 \newboolean{undertilde}
99 \IfFileExists{undertilde.sty}
100 {\usepackage{undertilde}
101 \setboolean{undertilde}{true}}
102 {\setboolean{undertilde}{false}}
104 % check for package eurosym
105 % used for the Euro symbol
107 \IfFileExists{eurosym.sty}
108 {\usepackage[gennarrow]{eurosym}
109 \setboolean{eurosym}{true}}
110 {\setboolean{eurosym}{false}}
112 % check for package braket
113 % used for physical vectors
115 \IfFileExists{braket.sty}
117 \setboolean{braket}{true}}
118 {\setboolean{braket}{false}}
120 % check for package cancel
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124 \setboolean{cancel}{true}}
125 {\setboolean{cancel}{false}}
127 % check for package upgreek
129 \IfFileExists{upgreek.sty}
130 {\usepackage{upgreek}
131 \setboolean{upgreek}{true}}
132 {\setboolean{upgreek}{false}}
134 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
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142 \font_sans "lmss" "default"
143 \font_typewriter "lmtt" "default"
144 \font_math "auto" "auto"
145 \font_default_family default
146 \use_non_tex_fonts false
149 \font_sf_scale 100 100
150 \font_tt_scale 100 100
152 \default_output_format pdf2
154 \bibtex_command default
155 \index_command default
159 \pdf_title "LyX's Math Manual"
160 \pdf_author "LyX Team, Uwe Stöhr"
161 \pdf_subject "LyX-documentation about math"
162 \pdf_keywords "LyX, Mathed"
164 \pdf_bookmarksnumbered true
165 \pdf_bookmarksopen true
166 \pdf_bookmarksopenlevel 1
167 \pdf_breaklinks false
171 \pdf_pdfusetitle false
172 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
175 \use_package amsmath 2
176 \use_package amssymb 2
177 \use_package cancel 0
179 \use_package mathdots 1
180 \use_package mathtools 2
181 \use_package mhchem 1
182 \use_package stackrel 0
183 \use_package stmaryrd 0
184 \use_package undertilde 0
186 \cite_engine_type default
190 \paperorientation portrait
194 \notefontcolor #0000ff
201 \paragraph_separation skip
203 \quotes_language english
206 \paperpagestyle plain
210 \tracking_changes true
211 \output_changes false
214 \html_be_strict false
215 \author -1174727462 "Kornel Benko" Kornel.Benko@berlin.de
216 \author 2047637253 "Guillaume Munch"
223 's detailed Math manual
227 by the \SpecialChar LyX
232 \begin_layout Plain Layout
234 If you have comments or error corrections, please send them to the \SpecialChar LyX
239 \begin_inset CommandInset href
241 name "lyx-docs@lists.lyx.org"
242 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
253 \begin_inset Note Note
256 \begin_layout Plain Layout
263 \begin_inset Newline newline
267 \begin_inset Newline newline
275 \begin_layout Standard
276 \begin_inset CommandInset toc
277 LatexCommand tableofcontents
284 \begin_layout Standard
285 \begin_inset Note Note
288 \begin_layout Plain Layout
289 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
292 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
299 If they are not installed the document can be exported anyway but the sections
300 where the packages are required will not appear in the output.
305 ; if it is not installed, this file cannot be exported.
308 \begin_layout Plain Layout
309 The latest PDF-version of this document can be found here:
310 \begin_inset Newline newline
315 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
323 \begin_layout Standard
324 \begin_inset Newpage newpage
330 \begin_layout Section
334 \begin_layout Standard
335 This document explains \SpecialChar LyX
336 's math features and is furthermore a collection
337 of \SpecialChar LaTeX
338 -commands used for mathematical characters and constructs.
339 The explanations are designed for the usage of commands.
340 It is therefore required that you have read the section
351 \begin_layout Standard
352 Most of the characters and many constructs explained in this manual are
353 also accessible via the menu
357 \SpecialChar menuseparator
373 But everybody who has to write lots of formulas will notice that it is
374 much faster to use commands instead of the math toolbar.
375 Therefore this manual is focused on commands but also mentions the correspondin
376 g toolbar buttons when available.
379 \begin_layout Standard
380 If not specially mentioned the commands are only available within formulas.
381 To be able to use all commands explained in this document, the option
385 must be checked in the document settings (menu
387 Document\SpecialChar menuseparator
388 Settings\SpecialChar menuseparator
399 \begin_layout Plain Layout
402 Use AMS math package automatically
408 \begin_layout Plain Layout
417 -math when math constructs are found that are supported by \SpecialChar LyX
426 \begin_layout Standard
427 This document doesn't list all
431 \begin_layout Plain Layout
444 \begin_layout Plain Layout
449 \begin_layout Plain Layout
458 -math commands is in the file
461 \begin_inset CommandInset href
464 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
470 , which is part of every \SpecialChar LaTeX
471 standard installation.
476 for lucidity reasons.
479 \begin_layout Section
483 \begin_layout Standard
484 To create an inline formula
485 \begin_inset Index idx
488 \begin_layout Plain Layout
494 that is embedded into a text line, use one of the shortcuts
500 or the toolbar button
507 \begin_inset Newline newline
510 To create a display style formula
511 \begin_inset Index idx
514 \begin_layout Plain Layout
515 Formula ! display style
520 which will appear bigger, has a different format, and will be in a separate
521 paragraph, use one of these shortcuts:
530 \begin_layout Standard
531 To change a display style formula to an inline formula, set the cursor into
532 the formula and use one of the shortcuts
540 Edit\SpecialChar menuseparator
541 Math\SpecialChar menuseparator
545 The same way is used to change an inline formula to a display style formula.
548 \begin_layout Standard
549 To display parts of an inline formula in the size of a display style formula,
557 \begin_inset Index idx
560 \begin_layout Plain Layout
569 Then a new blue box appears in which the desired formula part is inserted.
572 \begin_layout Standard
573 Only inline formulas are allowed inside tables.
576 \begin_layout Standard
581 can be turned on in the menu
583 View\SpecialChar menuseparator
587 When you click there on
588 \begin_inset Quotes eld
592 \begin_inset Quotes erd
595 the toolbar will be shown permanently at the bottom; this state is visualized
600 menu with a checkmark.
601 When you click in this state again on
602 \begin_inset Quotes eld
606 \begin_inset Quotes erd
617 is only shown when the cursor is within a formula; this state is visualized
618 by the renaming of the menu entry from
619 \begin_inset Quotes eld
623 \begin_inset Quotes erd
627 \begin_inset Quotes eld
635 \begin_inset Quotes erd
641 \begin_layout Standard
644 \begin_inset Index idx
647 \begin_layout Plain Layout
654 is invoked by pressing the toolbar button
662 Insert\SpecialChar menuseparator
674 \begin_layout Standard
675 To change the \SpecialChar LaTeX
677 \begin_inset Index idx
680 \begin_layout Plain Layout
689 Document\SpecialChar menuseparator
690 Settings\SpecialChar menuseparator
700 \begin_layout Standard
701 To edit matrices, case differentiations and multiline formulas subsequently,
704 Edit\SpecialChar menuseparator
709 Edit\SpecialChar menuseparator
711 \begin_inset space \thinspace{}
715 \begin_inset space \thinspace{}
725 When lines and columns are swapped via the menu, the column or line where
726 the cursor is in is exchanged with the column to the right or the line
728 Is the cursor in the last column or row, the exchange is done with the
729 column to the left or the line above.
732 \begin_layout Standard
733 To write text in formulas
737 \begin_layout Plain Layout
738 For multiline formulas the command
745 \begin_inset CommandInset ref
747 reference "subsec:Text-in-multiline"
761 \begin_inset Index idx
764 \begin_layout Plain Layout
771 \begin_inset Index idx
774 \begin_layout Plain Layout
781 This mode is invoked with the shortcut
787 or by the insertion of the command
794 \begin_inset Index idx
797 \begin_layout Plain Layout
806 The text appears black in \SpecialChar LyX
807 and can therefore be distinguished from the
808 other formula parts which appear blue.
809 In the output mathematical text is set upright, in contrary to other formula
813 \begin_layout Subsection*
817 \begin_layout Standard
818 Most of the \SpecialChar LaTeX
819 -commands for math constructs have the following scheme:
822 \begin_layout Standard
838 \begin_layout Standard
839 A command always starts with a backslash
840 \begin_inset Quotes gld
850 \begin_inset Quotes grd
854 To omit optional arguments, also omit the associated brackets.
855 The braces around the required arguments are named in this document as
858 \begin_inset Index idx
861 \begin_layout Plain Layout
869 If you add in a formula a left brace to a command name, \SpecialChar LyX
871 creates a \SpecialChar TeX
873 In all other cases \SpecialChar TeX
874 braces are created in formulas with the command
882 braces appear red in \SpecialChar LyX
883 , in contrary to normal braces which appear blue.
885 mode no command is needed to get \SpecialChar TeX
888 braces don't appear in the output.
891 \begin_layout Standard
892 When commands without arguments, like commands for symbols are entered in
894 mode, a space character must
898 be behind the command to end it.
899 This space doesn't appear in the output.
900 When the space should appear in the output, the space must be followed
901 by a protected space in normal text.
904 \begin_layout Standard
905 A protected space is inserted with
908 arg "command-alternatives space-insert protected ; math-space"
914 \begin_layout Subsection*
915 \begin_inset Newpage newpage
921 \begin_layout Itemize
923 \begin_inset space \textvisiblespace{}
926 denotes a space character to be input.
929 \begin_layout Itemize
931 \begin_inset Formula $\to$
934 denotes the usage of the corresponding arrow key on the keyboard.
939 key can often be used instead of
940 \begin_inset Formula $\to$
944 \begin_inset Formula $\downarrow$
952 \begin_inset Formula $\leftarrow$
956 \begin_inset Formula $\uparrow$
962 \begin_layout Subsection*
966 \begin_layout Standard
968 \begin_inset Float table
974 \begin_layout Plain Layout
976 \begin_inset Caption Standard
978 \begin_layout Plain Layout
979 \begin_inset CommandInset label
981 name "tab:Available-units"
993 \begin_layout Plain Layout
996 <lyxtabular version="3" rows="13" columns="2">
997 <features booktabs="true" tabularvalignment="middle">
998 <column alignment="center" valignment="top">
999 <column alignment="center" valignment="top" width="0pt">
1001 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1004 \begin_layout Plain Layout
1010 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1013 \begin_layout Plain Layout
1021 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1024 \begin_layout Plain Layout
1030 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1033 \begin_layout Plain Layout
1041 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1044 \begin_layout Plain Layout
1050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1053 \begin_layout Plain Layout
1061 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1064 \begin_layout Plain Layout
1070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1073 \begin_layout Plain Layout
1075 \begin_inset space \thinspace{}
1079 \begin_inset space \thinspace{}
1089 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1092 \begin_layout Plain Layout
1098 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1101 \begin_layout Plain Layout
1103 \begin_inset space \thinspace{}
1107 \begin_inset space \thinspace{}
1117 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1120 \begin_layout Plain Layout
1126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1129 \begin_layout Plain Layout
1131 \begin_inset space \thinspace{}
1135 \begin_inset space \thinspace{}
1145 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1148 \begin_layout Plain Layout
1154 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1157 \begin_layout Plain Layout
1159 \begin_inset space \thinspace{}
1163 \begin_inset space \thinspace{}
1173 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1176 \begin_layout Plain Layout
1178 \change_deleted -1174727462 1449863719
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"
1501 \begin_inset Separator parbreak
1507 \begin_layout Standard
1509 \begin_inset Tabular
1510 <lyxtabular version="3" rows="4" columns="2">
1511 <features booktabs="true" tabularvalignment="middle">
1512 <column alignment="center" valignment="top" width="0pt">
1513 <column alignment="center" valignment="top" width="0pt">
1515 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1518 \begin_layout Plain Layout
1524 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1527 \begin_layout Plain Layout
1535 <cell alignment="center" valignment="top" usebox="none">
1538 \begin_layout Plain Layout
1544 <cell alignment="center" valignment="top" usebox="none">
1547 \begin_layout Plain Layout
1548 \begin_inset Formula $B_{V}$
1557 <row topspace="1.5mm">
1558 <cell alignment="center" valignment="top" usebox="none">
1561 \begin_layout Plain Layout
1567 <cell alignment="center" valignment="top" usebox="none">
1570 \begin_layout Plain Layout
1571 \begin_inset Formula $B^{V}$
1580 <row topspace="1.5mm">
1581 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1584 \begin_layout Plain Layout
1586 \begin_inset space \textvisiblespace{}
1594 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1597 \begin_layout Plain Layout
1598 \begin_inset Formula $B^{A}$
1614 \begin_layout Standard
1615 As the caret is in some languages an accent, vowels will be accentuated
1616 in this case and not set as exponents
1620 \begin_layout Plain Layout
1621 Depending on the used keyboard settings this can also happen for characters
1628 To get exponents in this case, press
1632 after the caret as in the last example.
1635 \begin_layout Subsection
1637 \begin_inset CommandInset label
1639 name "subsec:Fractions"
1644 \begin_inset Index idx
1647 \begin_layout Plain Layout
1656 \begin_layout Standard
1657 Fractions are generated with the command
1664 \begin_inset Index idx
1667 \begin_layout Plain Layout
1675 or via the math toolbar button
1678 arg "math-insert \\frac"
1682 The font size is adjusted automatically, depending on whether the fraction
1683 is in an inline or display style formula.
1684 With the math toolbar button
1687 arg "math-insert \\frac-square"
1690 you can select different fraction types.
1693 \begin_layout Standard
1701 \begin_inset Index idx
1704 \begin_layout Plain Layout
1712 a fraction can be created that always has the size of a display style formula.
1720 \begin_inset Index idx
1723 \begin_layout Plain Layout
1731 the fraction appears always with the size of an inline formula.
1735 \begin_layout Standard
1736 A line with the fraction
1737 \begin_inset Formula $\frac{1}{2}$
1740 that was created with the command
1749 \begin_layout Standard
1750 A line with the fraction
1751 \begin_inset Formula $\dfrac{1}{2}$
1754 that was created with the command
1761 \begin_inset Separator parbreak
1767 \begin_layout Standard
1769 \begin_inset Tabular
1770 <lyxtabular version="3" rows="4" columns="2">
1771 <features booktabs="true" tabularvalignment="middle">
1772 <column alignment="center" valignment="top" width="0pt">
1773 <column alignment="center" valignment="top" width="0pt">
1775 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1778 \begin_layout Plain Layout
1784 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1787 \begin_layout Plain Layout
1794 <row topspace="1.5mm">
1795 <cell alignment="center" valignment="top" usebox="none">
1798 \begin_layout Plain Layout
1802 \begin_inset space \textvisiblespace{}
1806 \begin_inset Formula $\downarrow$
1814 <cell alignment="center" valignment="top" usebox="none">
1817 \begin_layout Plain Layout
1818 \begin_inset Formula $\frac{A}{B}$
1827 <row topspace="2mm">
1828 <cell alignment="center" valignment="top" usebox="none">
1831 \begin_layout Plain Layout
1835 \begin_inset space \textvisiblespace{}
1839 \begin_inset Formula $\downarrow$
1847 <cell alignment="center" valignment="top" usebox="none">
1850 \begin_layout Plain Layout
1851 \begin_inset Formula $\dfrac{A}{B}$
1860 <row topspace="2mm" bottomspace="1mm">
1861 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1864 \begin_layout Plain Layout
1868 \begin_inset space \textvisiblespace{}
1874 \begin_inset space \textvisiblespace{}
1878 \begin_inset Formula $\downarrow$
1882 \begin_inset Formula $\downarrow\downarrow$
1890 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1893 \begin_layout Plain Layout
1894 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1910 \begin_layout Standard
1911 \begin_inset VSpace bigskip
1915 \begin_inset Newpage newpage
1918 For nested fractions the command
1925 \begin_inset Index idx
1928 \begin_layout Plain Layout
1938 \begin_inset VSpace -3mm
1944 \begin_layout Standard
1945 \begin_inset Formula
1947 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1948 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1956 \begin_layout Standard
1957 The command for the example above is:
1960 \begin_layout Standard
1966 \begin_inset space \textvisiblespace{}
1970 \begin_inset Formula $\downarrow$
1976 \begin_inset space \textvisiblespace{}
1982 \begin_inset space \textvisiblespace{}
1986 \begin_inset Formula $\downarrow$
1990 \begin_inset Formula $\downarrow$
1996 \begin_layout Standard
1997 \begin_inset VSpace medskip
2003 \begin_layout Standard
2010 sets the fraction always in the size of a displayed formula, also when
2011 it is part of another fraction.
2014 \begin_layout Standard
2015 It is possible to specify the alignment of the numerator.
2022 is used to left align it, the command
2035 centers the numerator.
2036 These fractions demonstrate the different alignments:
2039 \begin_layout Standard
2042 \begin_inset Formula
2044 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2052 \begin_layout Standard
2053 \begin_inset Note Greyedout
2056 \begin_layout Plain Layout
2073 are no real \SpecialChar LaTeX
2074 commands but represent the command
2078 cfrac[alignment]{numerator}{denominator}
2081 Therefore you cannot use them in \SpecialChar TeX
2090 \begin_layout Standard
2091 \begin_inset VSpace medskip
2094 It is often advantageous to combine
2107 \begin_inset Formula
2109 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2117 \begin_layout Standard
2118 For inline fractions with a sloped fraction stroke you can use the command
2126 \begin_inset Index idx
2129 \begin_layout Plain Layout
2138 \begin_inset Formula $\nicefrac{5}{31}$
2148 \begin_inset Index idx
2151 \begin_layout Plain Layout
2160 \begin_inset Formula $\unitfrac{5}{31}$
2163 There is furthermore the command
2169 that offers to write a fraction in combination with a number:
2170 \begin_inset Formula $\unitfrac[2]{1}{3}$
2176 \begin_layout Standard
2177 \begin_inset Note Greyedout
2180 \begin_layout Plain Layout
2191 is not a real \SpecialChar LaTeX
2192 command but the command
2193 \begin_inset Newline newline
2200 unitfrac[number]{numerator}{denominator}
2203 Therefore you cannot use it in \SpecialChar TeX
2212 \begin_layout Standard
2213 How to define own fractions where the fraction stroke can be changed, is
2215 \begin_inset CommandInset ref
2217 reference "subsec:Self-defined-Fractions"
2224 \begin_layout Standard
2225 Multiline fractions are explained in
2226 \begin_inset CommandInset ref
2228 reference "subsec:Multiline-Fractions"
2235 \begin_layout Subsection
2237 \begin_inset Index idx
2240 \begin_layout Plain Layout
2249 \begin_layout Standard
2250 Square roots are created with
2257 \begin_inset Index idx
2260 \begin_layout Plain Layout
2268 or the math toolbar button
2271 arg "math-insert \\sqrt"
2274 , all other roots with the command
2281 \begin_inset Index idx
2284 \begin_layout Plain Layout
2292 or with the math toolbar button
2295 arg "math-insert \\root"
2299 \begin_inset Separator parbreak
2305 \begin_layout Standard
2307 \begin_inset Tabular
2308 <lyxtabular version="3" rows="3" columns="2">
2309 <features booktabs="true" tabularvalignment="middle">
2310 <column alignment="center" valignment="top" width="0pt">
2311 <column alignment="center" valignment="top" width="0pt">
2313 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2316 \begin_layout Plain Layout
2322 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2325 \begin_layout Plain Layout
2332 <row topspace="1mm">
2333 <cell alignment="center" valignment="top" usebox="none">
2336 \begin_layout Plain Layout
2340 \begin_inset space \textvisiblespace{}
2348 <cell alignment="center" valignment="top" usebox="none">
2351 \begin_layout Plain Layout
2352 \begin_inset Formula $\sqrt{A-B}$
2361 <row topspace="1mm">
2362 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2365 \begin_layout Plain Layout
2369 \begin_inset space \textvisiblespace{}
2373 \begin_inset Formula $\downarrow$
2381 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2384 \begin_layout Plain Layout
2385 \begin_inset Formula $\sqrt[3]{A-B}$
2401 \begin_layout Standard
2402 A square root can also be created with
2408 when the root index field is left empty.
2411 \begin_layout Standard
2412 With certain indices the distance to the root is too small, like in this
2414 \begin_inset Formula $\sqrt[\beta]{B}$
2418 \begin_inset Newline newline
2422 \begin_inset Formula $\beta$
2426 To avoid this, the commands
2433 \begin_inset Index idx
2436 \begin_layout Plain Layout
2451 \begin_inset Index idx
2454 \begin_layout Plain Layout
2462 are used with the following scheme:
2465 \begin_layout Standard
2479 \begin_layout Standard
2480 Distance is the number of Big Points (unit bp;
2481 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2484 ), that the index should be moved to the left or top, resp..
2485 The commands are written to the index.
2486 This way the command
2487 \begin_inset Newline newline
2497 \begin_inset Formula $\to$
2503 \begin_inset Formula $\to$
2509 \begin_inset space \textvisiblespace{}
2513 \begin_inset Formula $\to$
2517 \begin_inset Newline newline
2522 produces a correct typeset formula:
2523 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2529 \begin_layout Subsection
2530 Binomial Coefficients
2531 \begin_inset Index idx
2534 \begin_layout Plain Layout
2535 Binomial coefficients
2543 \begin_layout Standard
2544 Binomial coefficients are inserted with the command
2551 \begin_inset Index idx
2554 \begin_layout Plain Layout
2562 or with the submenu of the math toolbar button
2565 arg "math-insert \\frac-square"
2581 there are the commands
2588 \begin_inset Index idx
2591 \begin_layout Plain Layout
2606 \begin_inset Index idx
2609 \begin_layout Plain Layout
2618 For other brackets around binomial coeficients there are the commands
2625 \begin_inset Index idx
2628 \begin_layout Plain Layout
2643 \begin_inset Index idx
2646 \begin_layout Plain Layout
2655 \begin_inset Separator parbreak
2661 \begin_layout Standard
2663 \begin_inset Tabular
2664 <lyxtabular version="3" rows="6" columns="2">
2665 <features booktabs="true" tabularvalignment="middle">
2666 <column alignment="center" valignment="top" width="0pt">
2667 <column alignment="center" valignment="top" width="0pt">
2669 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2672 \begin_layout Plain Layout
2678 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2681 \begin_layout Plain Layout
2688 <row topspace="1mm">
2689 <cell alignment="center" valignment="top" usebox="none">
2692 \begin_layout Plain Layout
2696 \begin_inset space \textvisiblespace{}
2700 \begin_inset Formula $\downarrow$
2708 <cell alignment="center" valignment="top" usebox="none">
2711 \begin_layout Plain Layout
2712 \begin_inset Formula $\binom{A}{B}$
2721 <row topspace="2mm">
2722 <cell alignment="center" valignment="top" usebox="none">
2725 \begin_layout Plain Layout
2729 \begin_inset space \textvisiblespace{}
2733 \begin_inset Formula $\downarrow$
2741 <cell alignment="center" valignment="top" usebox="none">
2744 \begin_layout Plain Layout
2745 \begin_inset Formula $\dbinom{A}{B}$
2754 <row topspace="2mm" bottomspace="0.5mm">
2755 <cell alignment="center" valignment="top" usebox="none">
2758 \begin_layout Plain Layout
2762 \begin_inset space \textvisiblespace{}
2766 \begin_inset Formula $\downarrow$
2774 <cell alignment="center" valignment="top" usebox="none">
2777 \begin_layout Plain Layout
2778 \begin_inset Formula $\tbinom{A}{B}$
2787 <row topspace="1mm">
2788 <cell alignment="center" valignment="top" topline="true" usebox="none">
2791 \begin_layout Plain Layout
2795 \begin_inset space \textvisiblespace{}
2799 \begin_inset Formula $\downarrow$
2807 <cell alignment="center" valignment="top" topline="true" usebox="none">
2810 \begin_layout Plain Layout
2811 \begin_inset Formula ${A \brack B}$
2820 <row topspace="2mm" bottomspace="0.5mm">
2821 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2824 \begin_layout Plain Layout
2828 \begin_inset space \textvisiblespace{}
2832 \begin_inset Formula $\downarrow$
2840 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2843 \begin_layout Plain Layout
2844 \begin_inset Formula ${A \brace B}$
2860 \begin_layout Subsection
2861 Case Differentiations
2862 \begin_inset Index idx
2865 \begin_layout Plain Layout
2866 Case differentiations
2874 \begin_layout Standard
2876 \begin_inset Tabular
2877 <lyxtabular version="3" rows="3" columns="2">
2878 <features booktabs="true" tabularvalignment="middle">
2879 <column alignment="center" valignment="top" width="0pt">
2880 <column alignment="center" valignment="top" width="0pt">
2882 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2885 \begin_layout Plain Layout
2891 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2894 \begin_layout Plain Layout
2902 <cell alignment="center" valignment="top" usebox="none">
2905 \begin_layout Plain Layout
2909 \begin_inset space \textvisiblespace{}
2913 \begin_inset Formula $\to$
2917 \begin_inset Index idx
2920 \begin_layout Plain Layout
2933 <cell alignment="center" valignment="top" usebox="none">
2936 \begin_layout Plain Layout
2937 \begin_inset Formula $\begin{cases}
2947 <row topspace="1.5mm">
2948 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2951 \begin_layout Plain Layout
2955 \begin_inset space \textvisiblespace{}
2961 arg "newline-insert newline"
2969 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2972 \begin_layout Plain Layout
2973 \begin_inset Formula $\begin{cases}
2974 A & \textrm{for }x>0\\
2975 B & \textrm{for }x=0
2992 \begin_layout Standard
2999 or pressing the math toolbar button
3002 arg "math-insert \\cases"
3005 you can create new lines with the shortcut
3008 arg "newline-insert newline"
3011 or the table toolbar button
3014 arg "inset-modify tabular append-row"
3020 \begin_layout Standard
3027 is also available via the menu
3029 Insert\SpecialChar menuseparator
3030 Math\SpecialChar menuseparator
3036 \begin_layout Subsection
3038 \begin_inset Index idx
3041 \begin_layout Plain Layout
3050 \begin_layout Standard
3058 \begin_inset Index idx
3061 \begin_layout Plain Layout
3069 every character can be displayed canceled.
3070 The characters are quasi accentuated by a slash.
3071 \begin_inset Separator parbreak
3077 \begin_layout Standard
3079 \begin_inset Tabular
3080 <lyxtabular version="3" rows="4" columns="2">
3081 <features booktabs="true" tabularvalignment="middle">
3082 <column alignment="center" valignment="top" width="0pt">
3083 <column alignment="center" valignment="top" width="0pt">
3085 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3088 \begin_layout Plain Layout
3094 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3097 \begin_layout Plain Layout
3105 <cell alignment="center" valignment="top" usebox="none">
3108 \begin_layout Plain Layout
3116 <cell alignment="center" valignment="top" usebox="none">
3119 \begin_layout Plain Layout
3120 \begin_inset Formula $\not=$
3130 <cell alignment="center" valignment="top" usebox="none">
3133 \begin_layout Plain Layout
3143 <cell alignment="center" valignment="top" usebox="none">
3146 \begin_layout Plain Layout
3147 \begin_inset Formula $\not\le$
3157 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3160 \begin_layout Plain Layout
3170 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3173 \begin_layout Plain Layout
3174 \begin_inset Formula $\not\parallel$
3190 \begin_layout Standard
3191 The last example shows that not all negations look good.
3192 Therefore there are special commands for some negations (see
3193 \begin_inset CommandInset ref
3195 reference "subsec:Mathematical-Symbols"
3200 \begin_inset CommandInset ref
3202 reference "sec:Relations"
3209 \begin_layout Subsection
3211 \begin_inset CommandInset label
3213 name "subsec:Placeholders"
3218 \begin_inset Index idx
3221 \begin_layout Plain Layout
3228 \begin_inset Index idx
3231 \begin_layout Plain Layout
3232 Chemical characters ! Isotopes
3238 \begin_inset Index idx
3241 \begin_layout Plain Layout
3246 \begin_layout Plain Layout
3257 \begin_layout Plain Layout
3272 \begin_layout Standard
3274 \begin_inset space \thinspace{}
3278 \begin_inset space \space{}
3285 \begin_layout Plain Layout
3286 Typesetting isotopes and chemical symbols is described in
3287 \begin_inset CommandInset ref
3289 reference "subsec:Chemical-Symbols-and"
3298 the following problem occurs:
3299 \begin_inset Separator parbreak
3305 \begin_layout Standard
3307 \begin_inset Tabular
3308 <lyxtabular version="3" rows="2" columns="2">
3309 <features booktabs="true" tabularvalignment="middle">
3310 <column alignment="center" valignment="top" width="0pt">
3311 <column alignment="center" valignment="top" width="0pt">
3313 <cell alignment="center" valignment="top" usebox="none">
3316 \begin_layout Plain Layout
3317 Indices created with sub- and superscripts:
3322 <cell alignment="center" valignment="top" usebox="none">
3325 \begin_layout Plain Layout
3326 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3335 <row topspace="1.5mm">
3336 <cell alignment="center" valignment="top" usebox="none">
3339 \begin_layout Plain Layout
3345 <cell alignment="center" valignment="top" usebox="none">
3348 \begin_layout Plain Layout
3349 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3365 \begin_layout Standard
3366 The shorter index is by default placed below or above the first character
3367 of the longer index.
3368 To avoid this there is the command
3375 \begin_inset Index idx
3378 \begin_layout Plain Layout
3386 or the math toolbar button
3387 \begin_inset space \thinspace{}
3394 \begin_layout Plain Layout
3395 can be found in the submenu of the toolbar button
3398 arg "math-insert \\space"
3412 that creates one or more phantom characters.
3419 a small blue box appears that is superposed with two red arrows.
3420 The arrows indicate that the complete width and height of the box content
3421 will be created as placeholder.
3422 Phantom characters are accordingly placeholders with the size of the characters.
3423 \begin_inset Separator parbreak
3429 \begin_layout Standard
3431 \begin_inset Tabular
3432 <lyxtabular version="3" rows="4" columns="2">
3433 <features booktabs="true" tabularvalignment="middle">
3434 <column alignment="center" valignment="top" width="0pt">
3435 <column alignment="center" valignment="top" width="0pt">
3437 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3440 \begin_layout Plain Layout
3446 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3449 \begin_layout Plain Layout
3456 <row topspace="1.5mm">
3457 <cell alignment="center" valignment="top" usebox="none">
3460 \begin_layout Plain Layout
3462 \begin_inset space \textvisiblespace{}
3468 \begin_inset space \textvisiblespace{}
3472 \begin_inset Formula $\to$
3476 \begin_inset space \textvisiblespace{}
3484 <cell alignment="center" valignment="top" usebox="none">
3487 \begin_layout Plain Layout
3488 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3497 <row topspace="1.5mm" bottomspace="0.5mm">
3498 <cell alignment="center" valignment="top" usebox="none">
3501 \begin_layout Plain Layout
3503 \begin_inset space \textvisiblespace{}
3509 \begin_inset space \textvisiblespace{}
3513 \begin_inset Formula $\to$
3517 \begin_inset space \textvisiblespace{}
3525 <cell alignment="center" valignment="top" usebox="none">
3528 \begin_layout Plain Layout
3529 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3538 <row topspace="1.5mm" bottomspace="0.5mm">
3539 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3542 \begin_layout Plain Layout
3546 \begin_inset space \textvisiblespace{}
3552 \begin_inset space \textvisiblespace{}
3556 \begin_inset Formula $\to$
3560 \begin_inset space \textvisiblespace{}
3568 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3571 \begin_layout Plain Layout
3572 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3588 \begin_layout Standard
3589 Furthermore there are the commands
3596 \begin_inset Index idx
3599 \begin_layout Plain Layout
3620 \begin_inset Index idx
3623 \begin_layout Plain Layout
3644 creates only space for the maximal height of the characters in the box
3645 but not for its width.
3652 creates only space for the width of the box content.
3653 Therefore the boxes of both commands have only one red arrow.
3656 \begin_layout Standard
3657 For example the command
3662 \begin_inset space \textvisiblespace{}
3669 creates space for the height of the integral sign,
3673 \begin_layout Plain Layout
3680 creates an integral sign, see
3681 \begin_inset CommandInset ref
3683 reference "subsec:Big-Operators"
3692 because this is the larger character.
3693 An example application is in
3694 \begin_inset CommandInset ref
3696 reference "subsec:Multiline-Brackets"
3703 \begin_layout Standard
3704 Placeholders can also be used for text when they are inserted via the menu
3707 Insert\SpecialChar menuseparator
3708 Formatting\SpecialChar menuseparator
3714 \begin_layout Standard
3716 \begin_inset Newline newline
3720 \begin_inset Phantom Phantom
3723 \begin_layout Plain Layout
3732 \begin_layout Subsection
3734 \begin_inset Index idx
3737 \begin_layout Plain Layout
3744 \begin_inset Index idx
3747 \begin_layout Plain Layout
3748 Formula ! underlined
3756 \begin_layout Standard
3758 \begin_inset Tabular
3759 <lyxtabular version="3" rows="4" columns="2">
3760 <features booktabs="true" tabularvalignment="middle">
3761 <column alignment="center" valignment="top" width="0pt">
3762 <column alignment="center" valignment="top" width="0pt">
3764 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3767 \begin_layout Plain Layout
3773 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3776 \begin_layout Plain Layout
3783 <row topspace="2mm">
3784 <cell alignment="center" valignment="top" usebox="none">
3787 \begin_layout Plain Layout
3791 \begin_inset space \textvisiblespace{}
3795 \begin_inset Index idx
3798 \begin_layout Plain Layout
3811 <cell alignment="center" valignment="top" usebox="none">
3814 \begin_layout Plain Layout
3815 \begin_inset Formula $\overline{A+B}$
3824 <row bottomspace="1mm">
3825 <cell alignment="center" valignment="top" usebox="none">
3828 \begin_layout Plain Layout
3832 \begin_inset space \textvisiblespace{}
3836 \begin_inset Index idx
3839 \begin_layout Plain Layout
3852 <cell alignment="center" valignment="top" usebox="none">
3855 \begin_layout Plain Layout
3856 \begin_inset Formula $\underline{A+B}$
3865 <row topspace="2mm" bottomspace="1mm">
3866 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3869 \begin_layout Plain Layout
3873 \begin_inset space \textvisiblespace{}
3879 \begin_inset space \textvisiblespace{}
3887 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3890 \begin_layout Plain Layout
3891 \begin_inset Formula $\overline{\underline{A+B}}$
3907 \begin_layout Standard
3908 In the last example it doesn't matter if first
3923 \begin_layout Standard
3924 To double underline use
3933 \begin_layout Standard
3934 It is possible to place up to 6 lines above or below characters.
3937 \begin_layout Standard
3938 \begin_inset VSpace bigskip
3941 Custom lines can be created using the command
3948 \begin_inset Index idx
3951 \begin_layout Plain Layout
3959 which has the following scheme:
3962 \begin_layout Standard
3967 rule[vertical offset]{length}{thickness}
3970 \begin_layout Standard
3971 The optional vertical offset shifts the line upwards (or downwards, when
3972 the value is negative).
3974 \begin_inset CommandInset ref
3976 reference "tab:Available-units"
3980 can be used for the values.
3981 Here are two example lines created with the commands
3982 \begin_inset Newline newline
3989 rule[-2ex]{3cm}{2pt}
4000 \begin_layout Standard
4002 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4008 \begin_layout Standard
4015 can also be used for text when a line is inserted via the menu
4017 Insert\SpecialChar menuseparator
4018 Formatting\SpecialChar menuseparator
4020 \begin_inset space ~
4028 \begin_layout Standard
4030 \begin_inset CommandInset line
4041 \begin_layout Subsection
4043 \begin_inset CommandInset label
4045 name "subsec:Ellipses"
4050 \begin_inset Index idx
4053 \begin_layout Plain Layout
4062 \begin_layout Standard
4063 There are different types of ellipses available.
4067 \begin_layout Plain Layout
4068 In the math toolbar in the submenu of the button
4071 arg "math-insert \\ldots"
4079 For listings dots at the baseline are used (
4086 \begin_inset Index idx
4089 \begin_layout Plain Layout
4097 ), while for operations dots are needed that are on the same height as the
4105 \begin_inset Index idx
4108 \begin_layout Plain Layout
4117 When using the command
4124 \begin_inset Index idx
4127 \begin_layout Plain Layout
4135 , \SpecialChar LaTeX
4136 decides on the basis of the next character what type is used.
4137 \begin_inset Separator parbreak
4143 \begin_layout Standard
4145 \begin_inset Tabular
4146 <lyxtabular version="3" rows="9" columns="2">
4147 <features booktabs="true" tabularvalignment="middle">
4148 <column alignment="center" valignment="top" width="0pt">
4149 <column alignment="center" valignment="top" width="0pt">
4151 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4154 \begin_layout Plain Layout
4160 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4163 \begin_layout Plain Layout
4171 <cell alignment="center" valignment="top" usebox="none">
4174 \begin_layout Plain Layout
4176 \begin_inset space \textvisiblespace{}
4182 \begin_inset space \textvisiblespace{}
4190 <cell alignment="center" valignment="top" usebox="none">
4193 \begin_layout Plain Layout
4194 \begin_inset Formula $A_{1},\dots,A_{n}$
4204 <cell alignment="center" valignment="top" usebox="none">
4207 \begin_layout Plain Layout
4209 \begin_inset space \textvisiblespace{}
4215 \begin_inset space \textvisiblespace{}
4223 <cell alignment="center" valignment="top" usebox="none">
4226 \begin_layout Plain Layout
4227 \begin_inset Formula $A_{1}+\dots+A_{n}$
4237 <cell alignment="center" valignment="top" usebox="none">
4240 \begin_layout Plain Layout
4242 \begin_inset space \textvisiblespace{}
4248 \begin_inset space \textvisiblespace{}
4256 <cell alignment="center" valignment="top" usebox="none">
4259 \begin_layout Plain Layout
4260 \begin_inset Formula $A_{1},\ldots,A_{n}$
4270 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4273 \begin_layout Plain Layout
4275 \begin_inset space \textvisiblespace{}
4281 \begin_inset space \textvisiblespace{}
4289 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4292 \begin_layout Plain Layout
4293 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4303 <cell alignment="center" valignment="top" usebox="none">
4306 \begin_layout Plain Layout
4314 <cell alignment="center" valignment="top" usebox="none">
4317 \begin_layout Plain Layout
4318 \begin_inset Formula $\vdots$
4328 <cell alignment="center" valignment="top" usebox="none">
4331 \begin_layout Plain Layout
4339 <cell alignment="center" valignment="top" usebox="none">
4342 \begin_layout Plain Layout
4343 \begin_inset Formula $\ddots$
4353 <cell alignment="center" valignment="top" usebox="none">
4356 \begin_layout Plain Layout
4364 <cell alignment="center" valignment="top" usebox="none">
4367 \begin_layout Plain Layout
4368 \begin_inset Formula $\iddots$
4378 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4381 \begin_layout Plain Layout
4383 \begin_inset space \thinspace{}
4386 matrix with the different dots
4391 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4394 \begin_layout Plain Layout
4395 \begin_inset Formula $\begin{array}{ccc}
4396 A_{11} & \cdots & A_{1m}\\
4397 \vdots & \ddots & \vdots\\
4398 A_{n1} & \cdots & A_{nm}
4415 \begin_layout Standard
4416 The ellipses available in menu
4418 Insert\SpecialChar menuseparator
4420 \begin_inset space ~
4434 \begin_layout Standard
4435 \begin_inset VSpace medskip
4444 , one of the options
4446 Use mathdots package (automatically)
4448 must be set in the document settings under
4451 \begin_inset space ~
4457 \begin_inset Newline newline
4462 Use mathdots package
4464 will improve the appearance of all dots in the documents if their font
4465 style or size is not the default.
4468 \begin_layout Standard
4469 \begin_inset VSpace medskip
4472 Specially for matrices there are ellipses that span over several columns.
4473 They are created with the command
4480 \begin_inset Index idx
4483 \begin_layout Plain Layout
4491 , that has the following scheme:
4494 \begin_layout Standard
4499 hdotsfor[distance]{number of columns}
4502 \begin_layout Standard
4503 The number of columns specifies how many columns should be spanned.
4504 Distance is a factor for the distance between the dots.
4507 \begin_layout Standard
4508 In the following matrix the command
4514 was inserted in the first box of the second line, to get an ellipsis with
4515 a dot distance twice as long as with the command
4522 \begin_inset Formula
4524 \left(\begin{array}{cccc}
4533 Note that the matrix fields that should be spanned must be empty, otherwise
4534 you get \SpecialChar LaTeX
4538 \begin_layout Standard
4539 \begin_inset VSpace bigskip
4542 Furthermore you can fill with the command
4549 \begin_inset Index idx
4552 \begin_layout Plain Layout
4560 the rest of a line with dots.
4561 The effect of these commands is the same as with
4568 \begin_inset CommandInset ref
4570 reference "subsec:Variable-Space"
4577 \begin_layout Standard
4578 For example the command
4583 \begin_inset space \textvisiblespace{}
4591 \begin_layout Standard
4592 \begin_inset Formula $A\dotfill B$
4598 \begin_layout Standard
4605 there is for a line the command
4612 \begin_inset Index idx
4615 \begin_layout Plain Layout
4626 \begin_layout Standard
4627 \begin_inset Formula $A\hrulefill B$
4633 \begin_layout Standard
4634 To use the commands for text, they have to be inserted in \SpecialChar TeX
4638 \begin_layout Section
4640 \begin_inset CommandInset label
4647 \begin_inset Index idx
4650 \begin_layout Plain Layout
4659 \begin_layout Standard
4660 Matrices can be inserted via the math toolbar button
4663 arg "dialog-show mathmatrix"
4668 Insert\SpecialChar menuseparator
4669 Math\SpecialChar menuseparator
4673 In the matrix dialog you can specify the number of columns and rows, the
4674 alignment and the decoration.
4675 The vertical alignment is only of importance for matrices in inline formulas:
4678 \begin_layout Standard
4679 The first matrix is top
4680 \begin_inset Formula $\begin{array}[t]{cccc}
4688 \begin_inset Formula $\begin{array}{cccc}
4695 and the third bottom
4696 \begin_inset Formula $\begin{array}[b]{cccc}
4706 \begin_layout Standard
4707 The horizontal alignment specifies how the column entries should be aligned.
4708 It is set by entering a letter for every column.
4713 denotes left aligned,
4722 To create for example a 4
4727 \begin_inset space ~
4730 matrix where the first column is left aligned, the second and third are
4731 centered and the last one is right aligned, one enters for the horizontal
4737 Normally in a matrix all columns are centered, therefore the default for
4745 \begin_layout Standard
4746 Horizontal alignment:
4749 \begin_layout Standard
4755 \begin_inset Formula $\begin{array}{lll}
4767 \begin_inset Formula $\begin{array}{ccc}
4779 \begin_inset Formula $\begin{array}{rrr}
4789 \begin_layout Standard
4790 To add or delete rows and columns subsequently, the math toolbar buttons
4794 arg "inset-modify tabular append-row"
4800 arg "inset-modify tabular delete-row"
4804 \begin_inset space \thinspace{}
4809 Edit\SpecialChar menuseparator
4813 New rows can also be created with
4816 arg "newline-insert newline"
4822 \begin_layout Standard
4823 \begin_inset VSpace bigskip
4830 adds parentheses in the selected style around the matrix.
4831 Alternatively, parentheses can can either be created with the commands
4839 \begin_inset Index idx
4842 \begin_layout Plain Layout
4857 \begin_inset Index idx
4860 \begin_layout Plain Layout
4871 \begin_inset space ~
4877 \begin_inset CommandInset ref
4879 reference "subsec:Automatic-Bracket-Size"
4883 , or by using the following commands:
4884 \begin_inset VSpace medskip
4890 \begin_layout Standard
4891 \begin_inset space \hfill{}
4895 \begin_inset Tabular
4896 <lyxtabular version="3" rows="4" columns="2">
4897 <features booktabs="true" tabularvalignment="middle">
4898 <column alignment="center" valignment="top" width="0pt">
4899 <column alignment="center" valignment="top">
4901 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4904 \begin_layout Plain Layout
4910 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4913 \begin_layout Plain Layout
4920 <row topspace="1.5mm">
4921 <cell alignment="center" valignment="top" usebox="none">
4924 \begin_layout Plain Layout
4928 \begin_inset space \textvisiblespace{}
4936 \begin_inset space \thinspace{}
4944 <cell alignment="center" valignment="top" usebox="none">
4947 \begin_layout Plain Layout
4948 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4949 0 & \textrm{-}\mathrm{i}\\
4951 \end{array}\end{bmatrix}$
4960 <row topspace="1.5mm" bottomspace="0.5mm">
4961 <cell alignment="center" valignment="top" usebox="none">
4964 \begin_layout Plain Layout
4968 \begin_inset space \textvisiblespace{}
4976 \begin_inset space \thinspace{}
4984 <cell alignment="center" valignment="top" usebox="none">
4987 \begin_layout Plain Layout
4988 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4989 0 & \textrm{-}\mathrm{i}\\
4991 \end{array}\end{Bmatrix}$
5001 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5004 \begin_layout Plain Layout
5008 \begin_inset space \textvisiblespace{}
5016 \begin_inset space \thinspace{}
5024 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5027 \begin_layout Plain Layout
5028 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5029 0 & \textrm{-}\mathrm{i}\\
5031 \end{array}\end{pmatrix}$
5045 \begin_inset space \hfill{}
5049 \begin_inset Tabular
5050 <lyxtabular version="3" rows="4" columns="2">
5051 <features booktabs="true" tabularvalignment="middle">
5052 <column alignment="center" valignment="top" width="0pt">
5053 <column alignment="center" valignment="top">
5055 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5058 \begin_layout Plain Layout
5064 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5067 \begin_layout Plain Layout
5074 <row topspace="1.5mm">
5075 <cell alignment="center" valignment="top" usebox="none">
5078 \begin_layout Plain Layout
5082 \begin_inset space \textvisiblespace{}
5090 \begin_inset space \thinspace{}
5098 <cell alignment="center" valignment="top" usebox="none">
5101 \begin_layout Plain Layout
5102 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5103 0 & \textrm{-}\mathrm{i}\\
5105 \end{array}\end{vmatrix}$
5114 <row topspace="1.5mm" bottomspace="0.5mm">
5115 <cell alignment="center" valignment="top" usebox="none">
5118 \begin_layout Plain Layout
5122 \begin_inset space \textvisiblespace{}
5130 \begin_inset space \thinspace{}
5138 <cell alignment="center" valignment="top" usebox="none">
5141 \begin_layout Plain Layout
5142 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5143 0 & \textrm{-}\mathrm{i}\\
5145 \end{array}\end{Vmatrix}$
5155 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5158 \begin_layout Plain Layout
5162 \begin_inset space \textvisiblespace{}
5170 \begin_inset space \thinspace{}
5178 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5181 \begin_layout Plain Layout
5182 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5183 0 & \textrm{-}\mathrm{i}\\
5185 \end{array}\end{matrix}$
5199 \begin_inset space \hfill{}
5205 \begin_layout Standard
5206 \begin_inset VSpace medskip
5210 \begin_inset space \thinspace{}
5214 \begin_inset space \space{}
5223 is inserted, a blue box appears between two vertical lines where the matrix
5225 \begin_inset Newline newline
5228 Note that decorated matrices ignore the vertical alignment.
5231 \begin_layout Standard
5232 \begin_inset VSpace bigskip
5235 As all multiline formulas are matrices, the length
5242 \begin_inset Index idx
5245 \begin_layout Plain Layout
5253 that is described in
5254 \begin_inset CommandInset ref
5256 reference "subsec:Column-Separation"
5260 can also be used to change the column separation of matrices.
5263 \begin_layout Standard
5264 To change the row separation, the command
5271 \begin_inset Index idx
5274 \begin_layout Plain Layout
5283 It is used as follows:
5286 \begin_layout Standard
5293 arraystretch}{stretch factor}
5294 \begin_inset Index idx
5297 \begin_layout Plain Layout
5308 \begin_layout Standard
5315 assigns the stretch factor to the predefined command
5323 \begin_inset space \thinspace{}
5327 \begin_inset space \space{}
5330 the row separation, use the factor 2.
5331 This is then used for all following matrices.
5332 To go back to the original separation, assign the factor 1 to
5341 \begin_layout Standard
5342 To set matrices into a text line, the command
5349 \begin_inset Index idx
5352 \begin_layout Plain Layout
5361 When it is inserted a blue box with two dashed lines appears.
5362 In this box the matrix is inserted.
5365 \begin_layout Standard
5367 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5369 \end{smallmatrix}\right)$
5375 \begin_layout Section
5376 Brackets and Delimiters
5377 \begin_inset Index idx
5380 \begin_layout Plain Layout
5387 \begin_inset Index idx
5390 \begin_layout Plain Layout
5399 \begin_layout Subsection
5400 Vertical Brackets and Delimiters
5401 \begin_inset Index idx
5404 \begin_layout Plain Layout
5413 \begin_layout Standard
5414 \begin_inset space \hfill{}
5418 \begin_inset Tabular
5419 <lyxtabular version="3" rows="9" columns="2">
5420 <features booktabs="true" tabularvalignment="middle">
5421 <column alignment="center" valignment="top" width="0pt">
5422 <column alignment="center" valignment="top" width="0pt">
5424 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5427 \begin_layout Plain Layout
5433 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5436 \begin_layout Plain Layout
5444 <cell alignment="center" valignment="top" usebox="none">
5447 \begin_layout Plain Layout
5453 <cell alignment="center" valignment="top" usebox="none">
5456 \begin_layout Plain Layout
5457 \begin_inset Formula $($
5467 <cell alignment="center" valignment="top" usebox="none">
5470 \begin_layout Plain Layout
5476 <cell alignment="center" valignment="top" usebox="none">
5479 \begin_layout Plain Layout
5480 \begin_inset Formula $\{$
5490 <cell alignment="center" valignment="top" usebox="none">
5493 \begin_layout Plain Layout
5499 <cell alignment="center" valignment="top" usebox="none">
5502 \begin_layout Plain Layout
5503 \begin_inset Formula $[$
5513 <cell alignment="center" valignment="top" usebox="none">
5516 \begin_layout Plain Layout
5524 <cell alignment="center" valignment="top" usebox="none">
5527 \begin_layout Plain Layout
5528 \begin_inset Formula $\langle$
5538 <cell alignment="center" valignment="top" usebox="none">
5541 \begin_layout Plain Layout
5549 <cell alignment="center" valignment="top" usebox="none">
5552 \begin_layout Plain Layout
5553 \begin_inset Formula $\lceil$
5563 <cell alignment="center" valignment="top" usebox="none">
5566 \begin_layout Plain Layout
5574 <cell alignment="center" valignment="top" usebox="none">
5577 \begin_layout Plain Layout
5578 \begin_inset Formula $\lfloor$
5588 <cell alignment="center" valignment="top" usebox="none">
5591 \begin_layout Plain Layout
5597 <cell alignment="center" valignment="top" usebox="none">
5600 \begin_layout Plain Layout
5601 \begin_inset Formula $/$
5611 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5614 \begin_layout Plain Layout
5620 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5623 \begin_layout Plain Layout
5624 \begin_inset Formula $|$
5638 \begin_inset space \hfill{}
5642 \begin_inset Tabular
5643 <lyxtabular version="3" rows="9" columns="2">
5644 <features booktabs="true" tabularvalignment="middle">
5645 <column alignment="center" valignment="top" width="0pt">
5646 <column alignment="center" valignment="top" width="0pt">
5648 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5651 \begin_layout Plain Layout
5657 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5660 \begin_layout Plain Layout
5668 <cell alignment="center" valignment="top" usebox="none">
5671 \begin_layout Plain Layout
5677 <cell alignment="center" valignment="top" usebox="none">
5680 \begin_layout Plain Layout
5681 \begin_inset Formula $)$
5691 <cell alignment="center" valignment="top" usebox="none">
5694 \begin_layout Plain Layout
5700 <cell alignment="center" valignment="top" usebox="none">
5703 \begin_layout Plain Layout
5704 \begin_inset Formula $\}$
5714 <cell alignment="center" valignment="top" usebox="none">
5717 \begin_layout Plain Layout
5723 <cell alignment="center" valignment="top" usebox="none">
5726 \begin_layout Plain Layout
5727 \begin_inset Formula $]$
5737 <cell alignment="center" valignment="top" usebox="none">
5740 \begin_layout Plain Layout
5748 <cell alignment="center" valignment="top" usebox="none">
5751 \begin_layout Plain Layout
5752 \begin_inset Formula $\rangle$
5762 <cell alignment="center" valignment="top" usebox="none">
5765 \begin_layout Plain Layout
5773 <cell alignment="center" valignment="top" usebox="none">
5776 \begin_layout Plain Layout
5777 \begin_inset Formula $\rceil$
5787 <cell alignment="center" valignment="top" usebox="none">
5790 \begin_layout Plain Layout
5798 <cell alignment="center" valignment="top" usebox="none">
5801 \begin_layout Plain Layout
5802 \begin_inset Formula $\rfloor$
5812 <cell alignment="center" valignment="top" usebox="none">
5815 \begin_layout Plain Layout
5825 <cell alignment="center" valignment="top" usebox="none">
5828 \begin_layout Plain Layout
5829 \begin_inset Formula $\backslash$
5839 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5842 \begin_layout Plain Layout
5850 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5853 \begin_layout Plain Layout
5854 \begin_inset Formula $\|$
5868 \begin_inset space \hfill{}
5874 \begin_layout Standard
5877 \begin_inset Note Greyedout
5880 \begin_layout Plain Layout
5893 \begin_inset Index idx
5896 \begin_layout Plain Layout
5904 must be used for the backslash, because the command
5912 produces a line break there.
5920 \begin_layout Standard
5921 For all characters listed above the size can be adjusted with the commands
5922 described in the following two subsections.
5923 When using these commands, the characters < and > can directly be used
5924 instead of the commands
5939 \begin_layout Subsubsection
5941 \begin_inset CommandInset label
5943 name "subsec:Manual-Bracket-Size"
5948 \begin_inset Index idx
5951 \begin_layout Plain Layout
5952 Bracket size ! manual
5960 \begin_layout Standard
5961 The bracket size can be specified manually by the \SpecialChar LaTeX
5969 \begin_inset Index idx
5972 \begin_layout Plain Layout
6005 denotes the smallest and
6011 the largest bracket size.
6014 \begin_layout Standard
6015 These commands are used to emphasize levels of brackets:
6016 \begin_inset Separator parbreak
6022 \begin_layout Standard
6024 \begin_inset Tabular
6025 <lyxtabular version="3" rows="2" columns="2">
6026 <features booktabs="true" tabularvalignment="middle">
6027 <column alignment="center" valignment="top" width="0pt">
6028 <column alignment="center" valignment="top" width="0pt">
6030 <cell alignment="center" valignment="top" usebox="none">
6033 \begin_layout Plain Layout
6034 all brackets in the same size:
6039 <cell alignment="center" valignment="top" usebox="none">
6042 \begin_layout Plain Layout
6043 \begin_inset Formula $((A+B)(A-B))^{C}$
6052 <row topspace="2mm">
6053 <cell alignment="center" valignment="top" usebox="none">
6056 \begin_layout Plain Layout
6062 <cell alignment="center" valignment="top" usebox="none">
6065 \begin_layout Plain Layout
6066 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6082 \begin_layout Standard
6083 For the second formula the command
6090 \begin_inset space \textvisiblespace{}
6098 \begin_layout Standard
6099 Here is an overview about all bracket sizes:
6100 \begin_inset Separator parbreak
6106 \begin_layout Standard
6123 \begin_inset space \textvisiblespace{}
6131 \begin_inset space \textvisiblespace{}
6135 \begin_inset space \textvisiblespace{}
6145 \begin_layout Standard
6147 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6153 \begin_layout Standard
6160 -commands there is the variant
6167 \begin_inset Index idx
6170 \begin_layout Plain Layout
6178 that adds a bit more space between the bracket and its content, and the
6192 \begin_inset Index idx
6195 \begin_layout Plain Layout
6205 , that don't add additional space.
6210 at the end of the command
6216 is for a left bracket; for a right bracket this will be replaced by an
6222 A left or right bracket can each be an opening or closing bracket.
6225 \begin_layout Standard
6226 In the following table is a comparison of the variants:
6227 \begin_inset Separator parbreak
6233 \begin_layout Standard
6235 \begin_inset Tabular
6236 <lyxtabular version="3" rows="5" columns="2">
6237 <features booktabs="true" tabularvalignment="middle">
6238 <column alignment="center" valignment="top" width="0pt">
6239 <column alignment="center" valignment="middle">
6241 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6244 \begin_layout Plain Layout
6250 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6253 \begin_layout Plain Layout
6260 <row topspace="2mm">
6261 <cell alignment="center" valignment="top" usebox="none">
6264 \begin_layout Plain Layout
6274 \begin_inset space \textvisiblespace{}
6284 <cell alignment="center" valignment="top" usebox="none">
6287 \begin_layout Plain Layout
6288 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6297 <row topspace="2mm">
6298 <cell alignment="center" valignment="top" usebox="none">
6301 \begin_layout Plain Layout
6311 \begin_inset space \textvisiblespace{}
6321 <cell alignment="center" valignment="top" usebox="none">
6324 \begin_layout Plain Layout
6325 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6334 <row topspace="2mm" bottomspace="0.5mm">
6335 <cell alignment="center" valignment="top" usebox="none">
6338 \begin_layout Plain Layout
6348 \begin_inset space \textvisiblespace{}
6358 <cell alignment="center" valignment="top" usebox="none">
6361 \begin_layout Plain Layout
6362 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6371 <row topspace="1.5mm" bottomspace="0.5mm">
6372 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6375 \begin_layout Plain Layout
6387 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6390 \begin_layout Plain Layout
6391 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6407 \begin_layout Subsubsection
6408 Automatic Bracket Size
6409 \begin_inset CommandInset label
6411 name "subsec:Automatic-Bracket-Size"
6416 \begin_inset Index idx
6419 \begin_layout Plain Layout
6420 Bracket size ! automatic
6428 \begin_layout Standard
6429 Brackets with variable size can be inserted with the commands
6436 \begin_inset Index idx
6439 \begin_layout Plain Layout
6454 \begin_inset Index idx
6457 \begin_layout Plain Layout
6465 or via the math toolbar button
6468 arg "dialog-show mathdelimiter"
6484 the wanted bracket must be inserted.
6485 The bracket size will then automatically be calculated for the output.
6486 \begin_inset Separator parbreak
6492 \begin_layout Standard
6494 normal bracket: The command
6501 \begin_inset space \textvisiblespace{}
6505 \begin_inset Formula $\downarrow$
6509 \begin_inset space \textvisiblespace{}
6515 \begin_inset Formula
6525 \begin_layout Standard
6527 multiline bracket: The command
6536 \begin_inset space \textvisiblespace{}
6540 \begin_inset Formula $\downarrow$
6544 \begin_inset space \textvisiblespace{}
6552 \begin_inset Formula
6554 \ln\left(\frac{A}{C}\right)
6562 \begin_layout Standard
6578 \begin_inset space ~
6584 This has the advantage that you can see in \SpecialChar LyX
6585 immediately the real bracket
6586 size and that the matching right bracket will be created too.
6587 \begin_inset Newline newline
6590 The command for the last example would then be:
6601 \begin_inset space \textvisiblespace{}
6605 \begin_inset Formula $\downarrow$
6611 \begin_layout Standard
6612 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6613 For example the command
6620 \begin_inset space \textvisiblespace{}
6624 \begin_inset Formula $\downarrow$
6628 \begin_inset space \textvisiblespace{}
6638 \begin_inset Formula
6640 \left.\frac{A}{B}\right\}
6659 will be converted by \SpecialChar LyX
6660 to brackets in the right size when the document is
6661 reloaded and an omitted bracket will appear as dashed line.
6664 \begin_layout Standard
6665 \begin_inset VSpace bigskip
6668 Because all popular \SpecialChar LaTeX
6669 distributions use e\SpecialChar TeX
6670 , an extension to \SpecialChar LaTeX
6679 \begin_inset Index idx
6682 \begin_layout Plain Layout
6690 is additionally available for all brackets and limits.
6691 With this command the height of the following character is adapted to the
6692 one of the surrounding brackets, what is e.
6693 \begin_inset space \thinspace{}
6697 \begin_inset space \space{}
6700 needed for physical vectors:
6701 \begin_inset Formula
6703 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6708 For physical vectors there is a special \SpecialChar LaTeX
6709 -package, described in
6710 \begin_inset CommandInset ref
6712 reference "subsec:Physical-Vectors"
6719 \begin_layout Subsection
6721 \begin_inset Index idx
6724 \begin_layout Plain Layout
6725 Brackets ! horizontal
6733 \begin_layout Standard
6735 \begin_inset Tabular
6736 <lyxtabular version="3" rows="4" columns="2">
6737 <features booktabs="true" tabularvalignment="middle">
6738 <column alignment="center" valignment="top" width="0pt">
6739 <column alignment="center" valignment="top" width="0pt">
6741 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6744 \begin_layout Plain Layout
6750 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6753 \begin_layout Plain Layout
6761 <cell alignment="center" valignment="top" usebox="none">
6764 \begin_layout Plain Layout
6768 \begin_inset space \textvisiblespace{}
6772 \begin_inset space \textvisiblespace{}
6776 \begin_inset Index idx
6779 \begin_layout Plain Layout
6792 <cell alignment="center" valignment="top" usebox="none">
6795 \begin_layout Plain Layout
6796 \begin_inset Formula $\overbrace{A+B}^{3}$
6805 <row topspace="2mm">
6806 <cell alignment="center" valignment="top" usebox="none">
6809 \begin_layout Plain Layout
6813 \begin_inset space \textvisiblespace{}
6817 \begin_inset space \textvisiblespace{}
6821 \begin_inset Index idx
6824 \begin_layout Plain Layout
6837 <cell alignment="center" valignment="top" usebox="none">
6840 \begin_layout Plain Layout
6841 \begin_inset Formula $\underbrace{A+B}_{5}$
6851 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6854 \begin_layout Plain Layout
6858 \begin_inset space \textvisiblespace{}
6864 \begin_inset space \textvisiblespace{}
6868 \begin_inset space \textvisiblespace{}
6872 \begin_inset space \textvisiblespace{}
6876 \begin_inset space \textvisiblespace{}
6880 \begin_inset space \textvisiblespace{}
6884 \begin_inset space \textvisiblespace{}
6892 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6895 \begin_layout Plain Layout
6896 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6912 \begin_layout Standard
6913 In the last example it doesn't matter if
6925 is inserted at first.
6928 \begin_layout Standard
6929 \begin_inset VSpace medskip
6935 \begin_layout Standard
6936 If you set in the document settings under
6939 \begin_inset space ~
6949 \begin_inset Index idx
6952 \begin_layout Plain Layout
6953 Packages ! mathtools
6961 \begin_inset space ~
6966 , you have access to square backets:
6967 \begin_inset Separator parbreak
6973 \begin_layout Standard
6975 \begin_inset Tabular
6976 <lyxtabular version="3" rows="4" columns="2">
6977 <features booktabs="true" tabularvalignment="middle">
6978 <column alignment="center" valignment="top" width="0pt">
6979 <column alignment="center" valignment="top" width="0pt">
6981 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6984 \begin_layout Plain Layout
6990 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6993 \begin_layout Plain Layout
7001 <cell alignment="center" valignment="top" usebox="none">
7004 \begin_layout Plain Layout
7032 \begin_inset space \textvisiblespace{}
7036 \begin_inset Index idx
7039 \begin_layout Plain Layout
7052 <cell alignment="center" valignment="top" usebox="none">
7055 \begin_layout Plain Layout
7056 \begin_inset Formula $\overbracket{A+B}^{3}$
7065 <row topspace="2mm">
7066 <cell alignment="center" valignment="top" usebox="none">
7069 \begin_layout Plain Layout
7097 \begin_inset space \textvisiblespace{}
7101 \begin_inset Index idx
7104 \begin_layout Plain Layout
7129 <cell alignment="center" valignment="top" usebox="none">
7132 \begin_layout Plain Layout
7133 \begin_inset Formula $\underbracket{A+B}_{5}$
7143 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7146 \begin_layout Plain Layout
7152 \begin_inset space \textvisiblespace{}
7156 \begin_inset space \textvisiblespace{}
7160 \begin_inset space \textvisiblespace{}
7164 \begin_inset space \textvisiblespace{}
7168 \begin_inset space \textvisiblespace{}
7176 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7179 \begin_layout Plain Layout
7180 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7196 \begin_layout Standard
7209 you can change the thickness of the bracket's stroke by specifying the
7210 desired thickness in square brackets behind the command:
7211 \begin_inset Separator parbreak
7217 \begin_layout Standard
7219 \begin_inset Tabular
7220 <lyxtabular version="3" rows="3" columns="2">
7221 <features booktabs="true" tabularvalignment="middle">
7222 <column alignment="center" valignment="top" width="0pt">
7223 <column alignment="center" valignment="top" width="0pt">
7225 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7228 \begin_layout Plain Layout
7234 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7237 \begin_layout Plain Layout
7245 <cell alignment="center" valignment="top" usebox="none">
7248 \begin_layout Plain Layout
7278 \begin_inset space \textvisiblespace{}
7286 <cell alignment="center" valignment="top" usebox="none">
7289 \begin_layout Plain Layout
7290 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7299 <row topspace="2mm">
7300 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7303 \begin_layout Plain Layout
7333 \begin_inset space \textvisiblespace{}
7341 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7344 \begin_layout Plain Layout
7345 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7361 \begin_layout Standard
7362 \begin_inset VSpace bigskip
7365 When brackets should overlap each other, multiline formulas, as described
7367 \begin_inset CommandInset ref
7369 reference "sec:Multiline-Formulas"
7374 \begin_inset Formula
7376 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7377 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7382 In the first row the formula is inserted together with the first brace.
7383 It is hereby important that the space command
7387 \begin_layout Plain Layout
7388 Space commands are explained in
7389 \begin_inset CommandInset ref
7391 reference "subsec:Predefined-Space"
7406 is inserted before the first
7407 \begin_inset Formula $d$
7410 , because the brace that ends behind the
7411 \begin_inset Formula $q$
7414 prevents that the following
7415 \begin_inset Quotes eld
7419 \begin_inset Quotes erd
7422 is surrounded by space.
7426 \begin_layout Plain Layout
7427 because a bracket is not handled as a character, see
7428 \begin_inset CommandInset ref
7430 reference "subsec:Binary-Operators"
7439 In the second row the second brace is inserted.
7440 As it should begin before the
7441 \begin_inset Formula $b$
7456 \begin_layout Plain Layout
7464 \begin_inset CommandInset ref
7466 reference "subsec:Placeholders"
7475 This space is needed because the
7476 \begin_inset Quotes eld
7480 \begin_inset Quotes erd
7483 is also surrounded by space in the formula.
7484 The brace is placed under the command
7493 \begin_layout Standard
7494 It gets more complicated when brackets overlap each other above and under
7495 the formula, like in the following example:
7499 \begin_layout Plain Layout
7511 \begin_inset Formula
7513 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7514 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7523 \begin_layout Plain Layout
7534 The first formula row is the same as the second row of the previous example,
7535 with the difference that the brace is above.
7536 The second row contains the formula together with the second brace.
7537 To avoid that there is space between the upper brace in the first row and
7538 the formula, the row spacing needs to be reduced.
7539 This is not easily possible due to a bug in \SpecialChar LyX
7544 \begin_layout Plain Layout
7545 \begin_inset CommandInset href
7547 name "LyX-bug #1505"
7548 target "http://www.lyx.org/trac/ticket/1505"
7557 As a solution for the problem, the global formula row separation
7564 \begin_inset Index idx
7567 \begin_layout Plain Layout
7575 must be changed to -6
7576 \begin_inset space \thinspace{}
7579 pt before the formula with the command
7595 is set back after the formula to the standard value of 3
7596 \begin_inset space \thinspace{}
7599 pt using the same command.
7600 More about the row separation in formulas is explained in
7601 \begin_inset CommandInset ref
7603 reference "subsec:Line-Separation"
7610 \begin_layout Section
7612 \begin_inset Index idx
7615 \begin_layout Plain Layout
7624 \begin_layout Standard
7625 Arrows can be inserted via the math toolbar button
7628 arg "math-insert \\leftarrow"
7631 or the commands listed in the following subsections.
7634 \begin_layout Subsection
7636 \begin_inset Index idx
7639 \begin_layout Plain Layout
7648 \begin_layout Standard
7649 \begin_inset space \hfill{}
7653 \begin_inset Tabular
7654 <lyxtabular version="3" rows="8" columns="2">
7655 <features booktabs="true" tabularvalignment="middle">
7656 <column alignment="center" valignment="top" width="0pt">
7657 <column alignment="center" valignment="top" width="0pt">
7659 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7662 \begin_layout Plain Layout
7668 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7671 \begin_layout Plain Layout
7679 <cell alignment="center" valignment="top" usebox="none">
7682 \begin_layout Plain Layout
7690 <cell alignment="center" valignment="top" usebox="none">
7693 \begin_layout Plain Layout
7694 \begin_inset Formula $\gets$
7704 <cell alignment="center" valignment="top" usebox="none">
7707 \begin_layout Plain Layout
7715 <cell alignment="center" valignment="top" usebox="none">
7718 \begin_layout Plain Layout
7719 \begin_inset Formula $\Leftarrow$
7729 <cell alignment="center" valignment="top" usebox="none">
7732 \begin_layout Plain Layout
7740 <cell alignment="center" valignment="top" usebox="none">
7743 \begin_layout Plain Layout
7744 \begin_inset Formula $\longleftarrow$
7754 <cell alignment="center" valignment="top" usebox="none">
7757 \begin_layout Plain Layout
7765 <cell alignment="center" valignment="top" usebox="none">
7768 \begin_layout Plain Layout
7769 \begin_inset Formula $\Longleftarrow$
7779 <cell alignment="center" valignment="top" usebox="none">
7782 \begin_layout Plain Layout
7790 <cell alignment="center" valignment="top" usebox="none">
7793 \begin_layout Plain Layout
7794 \begin_inset Formula $\leftharpoonup$
7804 <cell alignment="center" valignment="top" usebox="none">
7807 \begin_layout Plain Layout
7815 <cell alignment="center" valignment="top" usebox="none">
7818 \begin_layout Plain Layout
7819 \begin_inset Formula $\leftharpoondown$
7829 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7832 \begin_layout Plain Layout
7840 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7843 \begin_layout Plain Layout
7844 \begin_inset Formula $\hookleftarrow$
7858 \begin_inset space \hfill{}
7862 \begin_inset Tabular
7863 <lyxtabular version="3" rows="8" columns="2">
7864 <features booktabs="true" tabularvalignment="middle">
7865 <column alignment="center" valignment="top" width="0pt">
7866 <column alignment="center" valignment="top" width="0pt">
7868 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7871 \begin_layout Plain Layout
7877 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7880 \begin_layout Plain Layout
7888 <cell alignment="center" valignment="top" usebox="none">
7891 \begin_layout Plain Layout
7899 <cell alignment="center" valignment="top" usebox="none">
7902 \begin_layout Plain Layout
7903 \begin_inset Formula $\to$
7913 <cell alignment="center" valignment="top" usebox="none">
7916 \begin_layout Plain Layout
7924 <cell alignment="center" valignment="top" usebox="none">
7927 \begin_layout Plain Layout
7928 \begin_inset Formula $\Rightarrow$
7938 <cell alignment="center" valignment="top" usebox="none">
7941 \begin_layout Plain Layout
7949 <cell alignment="center" valignment="top" usebox="none">
7952 \begin_layout Plain Layout
7953 \begin_inset Formula $\longrightarrow$
7963 <cell alignment="center" valignment="top" usebox="none">
7966 \begin_layout Plain Layout
7974 <cell alignment="center" valignment="top" usebox="none">
7977 \begin_layout Plain Layout
7978 \begin_inset Formula $\Longrightarrow$
7988 <cell alignment="center" valignment="top" usebox="none">
7991 \begin_layout Plain Layout
7999 <cell alignment="center" valignment="top" usebox="none">
8002 \begin_layout Plain Layout
8003 \begin_inset Formula $\rightharpoonup$
8013 <cell alignment="center" valignment="top" usebox="none">
8016 \begin_layout Plain Layout
8024 <cell alignment="center" valignment="top" usebox="none">
8027 \begin_layout Plain Layout
8028 \begin_inset Formula $\rightharpoondown$
8038 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8041 \begin_layout Plain Layout
8049 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8052 \begin_layout Plain Layout
8053 \begin_inset Formula $\hookrightarrow$
8067 \begin_inset space \hfill{}
8073 \begin_layout Standard
8074 \begin_inset space \hfill{}
8078 \begin_inset Tabular
8079 <lyxtabular version="3" rows="6" columns="2">
8080 <features booktabs="true" tabularvalignment="middle">
8081 <column alignment="center" valignment="top" width="0pt">
8082 <column alignment="center" valignment="top" width="0pt">
8084 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8087 \begin_layout Plain Layout
8093 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8096 \begin_layout Plain Layout
8104 <cell alignment="center" valignment="top" usebox="none">
8107 \begin_layout Plain Layout
8115 <cell alignment="center" valignment="top" usebox="none">
8118 \begin_layout Plain Layout
8119 \begin_inset Formula $\leftrightarrow$
8129 <cell alignment="center" valignment="top" usebox="none">
8132 \begin_layout Plain Layout
8140 <cell alignment="center" valignment="top" usebox="none">
8143 \begin_layout Plain Layout
8144 \begin_inset Formula $\Leftrightarrow$
8154 <cell alignment="center" valignment="top" usebox="none">
8157 \begin_layout Plain Layout
8165 <cell alignment="center" valignment="top" usebox="none">
8168 \begin_layout Plain Layout
8169 \begin_inset Formula $\longleftrightarrow$
8179 <cell alignment="center" valignment="top" usebox="none">
8182 \begin_layout Plain Layout
8190 <cell alignment="center" valignment="top" usebox="none">
8193 \begin_layout Plain Layout
8194 \begin_inset Formula $\Longleftrightarrow$
8204 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8207 \begin_layout Plain Layout
8215 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8218 \begin_layout Plain Layout
8219 \begin_inset Formula $\rightleftharpoons$
8233 \begin_inset space \hspace{}
8238 \begin_inset space \hfill{}
8242 \begin_inset Tabular
8243 <lyxtabular version="3" rows="5" columns="2">
8244 <features booktabs="true" tabularvalignment="middle">
8245 <column alignment="center" valignment="top" width="0pt">
8246 <column alignment="center" valignment="top" width="0pt">
8248 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8251 \begin_layout Plain Layout
8257 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8260 \begin_layout Plain Layout
8268 <cell alignment="center" valignment="top" usebox="none">
8271 \begin_layout Plain Layout
8279 <cell alignment="center" valignment="top" usebox="none">
8282 \begin_layout Plain Layout
8283 \begin_inset Formula $\mapsto$
8293 <cell alignment="center" valignment="top" usebox="none">
8296 \begin_layout Plain Layout
8304 <cell alignment="center" valignment="top" usebox="none">
8307 \begin_layout Plain Layout
8308 \begin_inset Formula $\longmapsto$
8318 <cell alignment="center" valignment="top" usebox="none">
8321 \begin_layout Plain Layout
8329 <cell alignment="center" valignment="top" usebox="none">
8332 \begin_layout Plain Layout
8333 \begin_inset Formula $\leadsto$
8343 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8346 \begin_layout Plain Layout
8354 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8357 \begin_layout Plain Layout
8358 \begin_inset Formula $\dasharrow$
8372 \begin_inset space \hfill{}
8378 \begin_layout Standard
8379 \begin_inset VSpace medskip
8382 Arrows used as accents like e.
8383 \begin_inset space \thinspace{}
8387 \begin_inset space \space{}
8390 vector arrows are listed in
8391 \begin_inset CommandInset ref
8393 reference "sec:Accents"
8400 \begin_layout Standard
8401 \begin_inset VSpace bigskip
8404 Furthermore there are the labeled arrows
8405 \begin_inset Index idx
8408 \begin_layout Plain Layout
8421 \begin_inset Index idx
8424 \begin_layout Plain Layout
8439 \begin_inset Index idx
8442 \begin_layout Plain Layout
8449 \begin_layout Plain Layout
8464 When inserting one of these commands in a formula, an arrow with two blue
8465 boxes appear where the label can be inserted.
8466 The length of the arrow adapts to the label width.
8469 \begin_layout Standard
8471 \begin_inset Tabular
8472 <lyxtabular version="3" rows="3" columns="2">
8473 <features booktabs="true" tabularvalignment="middle">
8474 <column alignment="center" valignment="top" width="0pt">
8475 <column alignment="center" valignment="top" width="0pt">
8477 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8480 \begin_layout Plain Layout
8486 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8489 \begin_layout Plain Layout
8497 <cell alignment="center" valignment="top" usebox="none">
8500 \begin_layout Plain Layout
8504 \begin_inset space \textvisiblespace{}
8508 \begin_inset Formula $\downarrow$
8512 \begin_inset Formula $\to$
8520 <cell alignment="center" valignment="top" usebox="none">
8523 \begin_layout Plain Layout
8524 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8533 <row topspace="2mm">
8534 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8537 \begin_layout Plain Layout
8541 \begin_inset space \textvisiblespace{}
8545 \begin_inset Formula $\downarrow$
8549 \begin_inset Formula $\to$
8557 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8560 \begin_layout Plain Layout
8561 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8577 \begin_layout Standard
8578 \begin_inset VSpace medskip
8584 \begin_layout Standard
8585 If you set in the document settings under
8588 \begin_inset space ~
8598 \begin_inset Index idx
8601 \begin_layout Plain Layout
8602 Packages ! mathtools
8610 \begin_inset space ~
8615 , you have access to the following labeled arrows:
8618 \begin_layout Standard
8619 \begin_inset Newpage newpage
8623 \begin_inset Separator parbreak
8629 \begin_layout Standard
8631 \begin_inset space \hspace*{\fill}
8635 \begin_inset Tabular
8636 <lyxtabular version="3" rows="7" columns="2">
8637 <features booktabs="true" tabularvalignment="middle">
8638 <column alignment="center" valignment="top" width="0pt">
8639 <column alignment="center" valignment="top" width="0pt">
8641 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8644 \begin_layout Plain Layout
8650 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8653 \begin_layout Plain Layout
8661 <cell alignment="center" valignment="top" usebox="none">
8664 \begin_layout Plain Layout
8684 <cell alignment="center" valignment="top" usebox="none">
8687 \begin_layout Plain Layout
8688 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8697 <row topspace="2mm">
8698 <cell alignment="center" valignment="top" usebox="none">
8701 \begin_layout Plain Layout
8721 <cell alignment="center" valignment="top" usebox="none">
8724 \begin_layout Plain Layout
8725 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8734 <row topspace="2mm">
8735 <cell alignment="center" valignment="top" usebox="none">
8738 \begin_layout Plain Layout
8758 <cell alignment="center" valignment="top" usebox="none">
8761 \begin_layout Plain Layout
8762 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8771 <row topspace="2mm">
8772 <cell alignment="center" valignment="top" usebox="none">
8775 \begin_layout Plain Layout
8795 <cell alignment="center" valignment="top" usebox="none">
8798 \begin_layout Plain Layout
8799 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8808 <row topspace="2mm">
8809 <cell alignment="center" valignment="top" usebox="none">
8812 \begin_layout Plain Layout
8832 <cell alignment="center" valignment="top" usebox="none">
8835 \begin_layout Plain Layout
8836 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8845 <row topspace="2mm">
8846 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8849 \begin_layout Plain Layout
8869 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8872 \begin_layout Plain Layout
8873 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8887 \begin_inset space \hspace*{\fill}
8891 \begin_inset Tabular
8892 <lyxtabular version="3" rows="7" columns="2">
8893 <features booktabs="true" tabularvalignment="middle">
8894 <column alignment="center" valignment="top" width="0pt">
8895 <column alignment="center" valignment="top" width="0pt">
8897 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8900 \begin_layout Plain Layout
8906 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8909 \begin_layout Plain Layout
8917 <cell alignment="center" valignment="top" usebox="none">
8920 \begin_layout Plain Layout
8940 <cell alignment="center" valignment="top" usebox="none">
8943 \begin_layout Plain Layout
8944 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8953 <row topspace="2mm">
8954 <cell alignment="center" valignment="top" usebox="none">
8957 \begin_layout Plain Layout
8977 <cell alignment="center" valignment="top" usebox="none">
8980 \begin_layout Plain Layout
8981 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8990 <row topspace="2mm">
8991 <cell alignment="center" valignment="top" usebox="none">
8994 \begin_layout Plain Layout
9014 <cell alignment="center" valignment="top" usebox="none">
9017 \begin_layout Plain Layout
9018 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9027 <row topspace="2mm">
9028 <cell alignment="center" valignment="top" usebox="none">
9031 \begin_layout Plain Layout
9051 <cell alignment="center" valignment="top" usebox="none">
9054 \begin_layout Plain Layout
9055 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9064 <row topspace="2mm">
9065 <cell alignment="center" valignment="top" usebox="none">
9068 \begin_layout Plain Layout
9088 <cell alignment="center" valignment="top" usebox="none">
9091 \begin_layout Plain Layout
9092 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9101 <row topspace="2mm">
9102 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9105 \begin_layout Plain Layout
9125 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9128 \begin_layout Plain Layout
9129 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9143 \begin_inset space \hspace*{\fill}
9149 \begin_layout Standard
9150 The command scheme is for all these arrows:
9151 \begin_inset Separator parbreak
9157 \begin_layout Standard
9159 \begin_inset Tabular
9160 <lyxtabular version="3" rows="2" columns="2">
9161 <features booktabs="true" tabularvalignment="middle">
9162 <column alignment="center" valignment="top" width="0pt">
9163 <column alignment="center" valignment="top" width="0pt">
9165 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9168 \begin_layout Plain Layout
9174 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9177 \begin_layout Plain Layout
9184 <row bottomspace="0.5mm">
9185 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9188 \begin_layout Plain Layout
9191 xleftrightarrow[x=a]
9194 \begin_inset Formula $\to$
9202 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9205 \begin_layout Plain Layout
9206 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9222 \begin_layout Subsection
9223 Vertical and diagonal Arrows
9224 \begin_inset Index idx
9227 \begin_layout Plain Layout
9234 \begin_inset Index idx
9237 \begin_layout Plain Layout
9246 \begin_layout Standard
9247 \begin_inset space \hfill{}
9251 \begin_inset Tabular
9252 <lyxtabular version="3" rows="7" columns="2">
9253 <features booktabs="true" tabularvalignment="middle">
9254 <column alignment="center" valignment="top" width="0pt">
9255 <column alignment="center" valignment="top" width="0pt">
9257 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9260 \begin_layout Plain Layout
9266 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9269 \begin_layout Plain Layout
9277 <cell alignment="center" valignment="top" usebox="none">
9280 \begin_layout Plain Layout
9288 <cell alignment="center" valignment="top" usebox="none">
9291 \begin_layout Plain Layout
9292 \begin_inset Formula $\uparrow$
9302 <cell alignment="center" valignment="top" usebox="none">
9305 \begin_layout Plain Layout
9313 <cell alignment="center" valignment="top" usebox="none">
9316 \begin_layout Plain Layout
9317 \begin_inset Formula $\Uparrow$
9327 <cell alignment="center" valignment="top" usebox="none">
9330 \begin_layout Plain Layout
9338 <cell alignment="center" valignment="top" usebox="none">
9341 \begin_layout Plain Layout
9342 \begin_inset Formula $\updownarrow$
9352 <cell alignment="center" valignment="top" usebox="none">
9355 \begin_layout Plain Layout
9363 <cell alignment="center" valignment="top" usebox="none">
9366 \begin_layout Plain Layout
9367 \begin_inset Formula $\Updownarrow$
9377 <cell alignment="center" valignment="top" usebox="none">
9380 \begin_layout Plain Layout
9388 <cell alignment="center" valignment="top" usebox="none">
9391 \begin_layout Plain Layout
9392 \begin_inset Formula $\Downarrow$
9402 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9405 \begin_layout Plain Layout
9413 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9416 \begin_layout Plain Layout
9417 \begin_inset Formula $\downarrow$
9431 \begin_inset space \hfill{}
9435 \begin_inset Tabular
9436 <lyxtabular version="3" rows="5" columns="2">
9437 <features booktabs="true" tabularvalignment="middle">
9438 <column alignment="center" valignment="top" width="0pt">
9439 <column alignment="center" valignment="top" width="0pt">
9441 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9444 \begin_layout Plain Layout
9450 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9453 \begin_layout Plain Layout
9461 <cell alignment="center" valignment="top" usebox="none">
9464 \begin_layout Plain Layout
9472 <cell alignment="center" valignment="top" usebox="none">
9475 \begin_layout Plain Layout
9476 \begin_inset Formula $\nearrow$
9486 <cell alignment="center" valignment="top" usebox="none">
9489 \begin_layout Plain Layout
9497 <cell alignment="center" valignment="top" usebox="none">
9500 \begin_layout Plain Layout
9501 \begin_inset Formula $\searrow$
9511 <cell alignment="center" valignment="top" usebox="none">
9514 \begin_layout Plain Layout
9522 <cell alignment="center" valignment="top" usebox="none">
9525 \begin_layout Plain Layout
9526 \begin_inset Formula $\swarrow$
9536 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9539 \begin_layout Plain Layout
9547 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9550 \begin_layout Plain Layout
9551 \begin_inset Formula $\nwarrow$
9565 \begin_inset space \hfill{}
9571 \begin_layout Standard
9572 \begin_inset VSpace medskip
9575 Vertical arrows can be used also as delimiters together with the commands
9577 \begin_inset CommandInset ref
9579 reference "subsec:Manual-Bracket-Size"
9584 \begin_inset CommandInset ref
9586 reference "subsec:Automatic-Bracket-Size"
9593 \begin_layout Section
9595 \begin_inset CommandInset label
9602 \begin_inset Index idx
9605 \begin_layout Plain Layout
9614 \begin_layout Standard
9615 Accents can be inserted via the math toolbar button
9618 arg "math-insert \\hat"
9621 or the commands listed in the following subsections.
9624 \begin_layout Subsection
9625 Accents for one Character
9629 \begin_layout Plain Layout
9642 \begin_layout Plain Layout
9644 \begin_inset CommandInset ref
9646 reference "subsec:Accents-in-Text"
9659 \begin_layout Plain Layout
9667 \begin_inset Note Note
9670 \begin_layout Plain Layout
9677 is used to avoid that the footnote appears in the PDF-bookmark.
9680 \begin_layout Plain Layout
9688 \begin_inset CommandInset ref
9690 reference "subsec:Formulas-in-Section"
9700 \begin_inset CommandInset label
9702 name "subsec:Accents-for-one"
9707 \begin_inset Index idx
9710 \begin_layout Plain Layout
9711 Accents ! for one character
9719 \begin_layout Standard
9720 \begin_inset space \hfill{}
9724 \begin_inset Tabular
9725 <lyxtabular version="3" rows="8" columns="2">
9726 <features booktabs="true" tabularvalignment="middle">
9727 <column alignment="center" valignment="top" width="0pt">
9728 <column alignment="center" valignment="top" width="0pt">
9730 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9733 \begin_layout Plain Layout
9739 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9742 \begin_layout Plain Layout
9749 <row topspace="1.5mm">
9750 <cell alignment="center" valignment="top" usebox="none">
9753 \begin_layout Plain Layout
9757 \begin_inset space \textvisiblespace{}
9765 <cell alignment="center" valignment="top" usebox="none">
9768 \begin_layout Plain Layout
9769 \begin_inset Formula $\dot{A}$
9778 <row topspace="1.5mm">
9779 <cell alignment="center" valignment="top" usebox="none">
9782 \begin_layout Plain Layout
9786 \begin_inset space \textvisiblespace{}
9794 <cell alignment="center" valignment="top" usebox="none">
9797 \begin_layout Plain Layout
9798 \begin_inset Formula $\ddot{A}$
9807 <row topspace="1.5mm">
9808 <cell alignment="center" valignment="top" usebox="none">
9811 \begin_layout Plain Layout
9815 \begin_inset space \textvisiblespace{}
9823 <cell alignment="center" valignment="top" usebox="none">
9826 \begin_layout Plain Layout
9827 \begin_inset Formula $\dddot{A}$
9836 <row topspace="1.5mm">
9837 <cell alignment="center" valignment="top" usebox="none">
9840 \begin_layout Plain Layout
9844 \begin_inset space \textvisiblespace{}
9852 <cell alignment="center" valignment="top" usebox="none">
9855 \begin_layout Plain Layout
9856 \begin_inset Formula $\ddddot{A}$
9865 <row topspace="1.5mm">
9866 <cell alignment="center" valignment="top" usebox="none">
9869 \begin_layout Plain Layout
9873 \begin_inset space \textvisiblespace{}
9877 \begin_inset Index idx
9880 \begin_layout Plain Layout
9891 <cell alignment="center" valignment="top" usebox="none">
9894 \begin_layout Plain Layout
9895 \begin_inset Formula $\vec{A}$
9904 <row topspace="1.5mm">
9905 <cell alignment="center" valignment="top" usebox="none">
9908 \begin_layout Plain Layout
9912 \begin_inset space \textvisiblespace{}
9920 <cell alignment="center" valignment="top" usebox="none">
9923 \begin_layout Plain Layout
9924 \begin_inset Formula $\bar{A}$
9933 <row topspace="1.5mm">
9934 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9937 \begin_layout Plain Layout
9941 \begin_inset space \textvisiblespace{}
9949 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9952 \begin_layout Plain Layout
9953 \begin_inset Formula $\mathring{A}$
9967 \begin_inset space \hfill{}
9971 \begin_inset Tabular
9972 <lyxtabular version="3" rows="7" columns="2">
9973 <features booktabs="true" tabularvalignment="middle">
9974 <column alignment="center" valignment="top" width="0pt">
9975 <column alignment="center" valignment="top" width="0pt">
9977 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9980 \begin_layout Plain Layout
9986 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9989 \begin_layout Plain Layout
9996 <row topspace="1.5mm">
9997 <cell alignment="center" valignment="top" usebox="none">
10000 \begin_layout Plain Layout
10004 \begin_inset space \textvisiblespace{}
10012 <cell alignment="center" valignment="top" usebox="none">
10015 \begin_layout Plain Layout
10016 \begin_inset Formula $\tilde{A}$
10025 <row topspace="1.5mm">
10026 <cell alignment="center" valignment="top" usebox="none">
10029 \begin_layout Plain Layout
10033 \begin_inset space \textvisiblespace{}
10041 <cell alignment="center" valignment="top" usebox="none">
10044 \begin_layout Plain Layout
10045 \begin_inset Formula $\hat{A}$
10054 <row topspace="1.5mm">
10055 <cell alignment="center" valignment="top" usebox="none">
10058 \begin_layout Plain Layout
10062 \begin_inset space \textvisiblespace{}
10070 <cell alignment="center" valignment="top" usebox="none">
10073 \begin_layout Plain Layout
10074 \begin_inset Formula $\check{A}$
10083 <row topspace="1.5mm">
10084 <cell alignment="center" valignment="top" usebox="none">
10087 \begin_layout Plain Layout
10091 \begin_inset space \textvisiblespace{}
10099 <cell alignment="center" valignment="top" usebox="none">
10102 \begin_layout Plain Layout
10103 \begin_inset Formula $\acute{A}$
10112 <row topspace="1.5mm">
10113 <cell alignment="center" valignment="top" usebox="none">
10116 \begin_layout Plain Layout
10120 \begin_inset space \textvisiblespace{}
10128 <cell alignment="center" valignment="top" usebox="none">
10131 \begin_layout Plain Layout
10132 \begin_inset Formula $\grave{A}$
10141 <row topspace="1.5mm">
10142 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10145 \begin_layout Plain Layout
10149 \begin_inset space \textvisiblespace{}
10157 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10160 \begin_layout Plain Layout
10161 \begin_inset Formula $\breve{A}$
10175 \begin_inset space \hfill{}
10181 \begin_layout Standard
10182 \begin_inset VSpace bigskip
10188 \begin_layout Standard
10189 You can directly insert accents like é to formulas.
10191 will transform them to the corresponding accent command.
10193 \begin_inset Index idx
10196 \begin_layout Plain Layout
10202 it is better to insert a quotation mark before the vowel.
10203 These two characters are then treated by \SpecialChar LaTeX
10208 character when the formula part with the umlaut is marked as German.
10216 \begin_inset Quotes eld
10220 \begin_inset Quotes erd
10223 umlauts are created as demonstrated in the following example:
10226 \begin_layout Standard
10227 \begin_inset VSpace -2mm
10233 \begin_layout Standard
10235 \begin_inset Tabular
10236 <lyxtabular version="3" rows="3" columns="2">
10237 <features booktabs="true" tabularvalignment="middle">
10238 <column alignment="center" valignment="top" width="0pt">
10239 <column alignment="center" valignment="top">
10241 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10244 \begin_layout Plain Layout
10250 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10253 \begin_layout Plain Layout
10261 <cell alignment="center" valignment="top" usebox="none">
10264 \begin_layout Plain Layout
10265 \begin_inset Quotes grd
10273 <cell alignment="center" valignment="top" usebox="none">
10276 \begin_layout Plain Layout
10277 \begin_inset space \hspace{}
10284 \begin_inset Formula $"i$
10293 <row topspace="1.5mm">
10294 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10297 \begin_layout Plain Layout
10301 \begin_inset space \textvisiblespace{}
10309 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10312 \begin_layout Plain Layout
10313 \begin_inset Formula $\ddot{i}$
10329 \begin_layout Standard
10330 Another advantage to
10336 is that umlauts can directly be converted to mathematical text because
10337 the accent commands above are
10343 in mathematical text
10346 To convert an accented character to mathematical text, only the character
10347 under the accent may be converted.
10348 This applies also for all other conversions, e.
10349 \begin_inset space \thinspace{}
10353 \begin_inset space \space{}
10359 \begin_layout Standard
10360 In mathematical text, umlauts and other accented characters can directly
10364 \begin_layout Standard
10365 \begin_inset VSpace bigskip
10371 \begin_layout Standard
10373 also supports a tilde under the character if the \SpecialChar LaTeX
10379 \begin_inset Index idx
10382 \begin_layout Plain Layout
10383 Packages ! undertilde
10388 is installed on your system:
10391 \begin_layout Standard
10395 \begin_layout Plain Layout
10405 \begin_inset Note Note
10408 \begin_layout Plain Layout
10409 The following table will only be displayed when the \SpecialChar LaTeX
10420 \begin_inset Separator parbreak
10426 \begin_layout Standard
10429 \begin_inset Tabular
10430 <lyxtabular version="3" rows="2" columns="2">
10431 <features booktabs="true" tabularvalignment="middle">
10432 <column alignment="center" valignment="top" width="0pt">
10433 <column alignment="center" valignment="top" width="0pt">
10435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10438 \begin_layout Plain Layout
10444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10447 \begin_layout Plain Layout
10455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10458 \begin_layout Plain Layout
10462 \begin_inset space \textvisiblespace{}
10470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10473 \begin_layout Plain Layout
10474 \begin_inset Formula $\utilde{A}$
10490 \begin_layout Standard
10494 \begin_layout Plain Layout
10504 \begin_inset Note Note
10507 \begin_layout Plain Layout
10508 The following will be displayed when the \SpecialChar LaTeX
10521 \begin_layout Standard
10522 You need to install the \SpecialChar LaTeX
10527 to see the rest of this subsection in the output.
10530 \begin_layout Standard
10534 \begin_layout Plain Layout
10546 \begin_layout Standard
10547 \begin_inset Newpage newpage
10553 \begin_layout Subsection
10554 Accents for several Characters
10555 \begin_inset Index idx
10558 \begin_layout Plain Layout
10559 Accents ! for several characters
10567 \begin_layout Standard
10568 \begin_inset space \hfill{}
10572 \begin_inset Tabular
10573 <lyxtabular version="3" rows="5" columns="2">
10574 <features booktabs="true" tabularvalignment="middle">
10575 <column alignment="center" valignment="top" width="0pt">
10576 <column alignment="center" valignment="top" width="0pt">
10578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10581 \begin_layout Plain Layout
10587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10590 \begin_layout Plain Layout
10597 <row topspace="1.5mm">
10598 <cell alignment="center" valignment="top" usebox="none">
10601 \begin_layout Plain Layout
10605 \begin_inset space \textvisiblespace{}
10613 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10616 \begin_layout Plain Layout
10617 \begin_inset Formula $\overleftarrow{A=B}$
10626 <row topspace="1.5mm">
10627 <cell alignment="center" valignment="top" usebox="none">
10630 \begin_layout Plain Layout
10634 \begin_inset space \textvisiblespace{}
10642 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10645 \begin_layout Plain Layout
10646 \begin_inset Formula $\underleftarrow{A=B}$
10655 <row topspace="1.5mm">
10656 <cell alignment="center" valignment="top" usebox="none">
10659 \begin_layout Plain Layout
10663 \begin_inset space \textvisiblespace{}
10671 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10674 \begin_layout Plain Layout
10675 \begin_inset Formula $\overleftrightarrow{A=B}$
10684 <row topspace="1.5mm" bottomspace="1mm">
10685 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10688 \begin_layout Plain Layout
10691 underleftrightarrow
10692 \begin_inset space \textvisiblespace{}
10700 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10703 \begin_layout Plain Layout
10704 \begin_inset Formula $\underleftrightarrow{A=B}$
10718 \begin_inset space \hfill{}
10722 \begin_inset Tabular
10723 <lyxtabular version="3" rows="5" columns="2">
10724 <features booktabs="true" tabularvalignment="middle">
10725 <column alignment="center" valignment="top" width="0pt">
10726 <column alignment="center" valignment="top" width="0pt">
10728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10731 \begin_layout Plain Layout
10737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10740 \begin_layout Plain Layout
10747 <row topspace="1.5mm">
10748 <cell alignment="center" valignment="top" usebox="none">
10751 \begin_layout Plain Layout
10755 \begin_inset space \textvisiblespace{}
10763 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10766 \begin_layout Plain Layout
10767 \begin_inset Formula $\overrightarrow{A=B}$
10776 <row topspace="1.5mm">
10777 <cell alignment="center" valignment="top" usebox="none">
10780 \begin_layout Plain Layout
10784 \begin_inset space \textvisiblespace{}
10792 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10795 \begin_layout Plain Layout
10796 \begin_inset Formula $\underrightarrow{A=B}$
10805 <row topspace="1.5mm">
10806 <cell alignment="center" valignment="top" usebox="none">
10809 \begin_layout Plain Layout
10813 \begin_inset space \textvisiblespace{}
10821 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10824 \begin_layout Plain Layout
10825 \begin_inset Formula $\widetilde{A=B}$
10834 <row topspace="1.5mm" bottomspace="1mm">
10835 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10838 \begin_layout Plain Layout
10842 \begin_inset space \textvisiblespace{}
10850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10853 \begin_layout Plain Layout
10854 \begin_inset Formula $\widehat{A=B}$
10868 \begin_inset space \hfill{}
10874 \begin_layout Standard
10875 \begin_inset VSpace medskip
10878 With these commands as many characters as you like can be accented.
10891 will only be set in the output with a length of three characters, as shown
10892 in the following example:
10893 \begin_inset Formula
10895 \widetilde{A+B=C-D}
10903 \begin_layout Standard
10911 \begin_inset Index idx
10914 \begin_layout Plain Layout
10929 \begin_inset Index idx
10932 \begin_layout Plain Layout
10940 described in the previous subsection it is also possible to accent several
10947 \begin_inset space \textvisiblespace{}
10951 \begin_inset Formula $\downarrow$
10957 \begin_inset Formula
10959 \underset{***}{A=B}
10967 \begin_layout Section
10969 \begin_inset CommandInset label
10971 name "subsec:Space"
10976 \begin_inset Index idx
10979 \begin_layout Plain Layout
10988 \begin_layout Subsection
10990 \begin_inset CommandInset label
10992 name "subsec:Predefined-Space"
10997 \begin_inset Index idx
11000 \begin_layout Plain Layout
11001 Space ! horizontal ! predefined
11009 \begin_layout Standard
11010 Sometimes it is necessary to insert horizontal space into a formula.
11011 This is done by inserting a protected space (shortcut
11014 arg "command-alternatives space-insert protected ; math-space"
11019 \begin_inset Quotes eld
11025 \begin_inset space \textvisiblespace{}
11031 \begin_inset Quotes erd
11034 appears and by pressing
11038 several times one can select one of eight different space sizes.
11039 The spaces can also be inserted using the math toolbar button
11042 arg "math-insert \\space"
11045 or special commands.
11046 Independent from the inserted command, one can select the size again by
11052 \begin_inset Separator parbreak
11058 \begin_layout Standard
11061 \begin_inset Tabular
11062 <lyxtabular version="3" rows="6" columns="3">
11063 <features booktabs="true" tabularvalignment="middle">
11064 <column alignment="center" valignment="top">
11065 <column alignment="center" valignment="top" width="15col%">
11066 <column alignment="center" valignment="top">
11068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11071 \begin_layout Plain Layout
11077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11080 \begin_layout Plain Layout
11090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11093 \begin_layout Plain Layout
11101 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11104 \begin_layout Plain Layout
11112 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11115 \begin_layout Plain Layout
11121 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11124 \begin_layout Plain Layout
11125 \begin_inset Formula $A\,B$
11135 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11138 \begin_layout Plain Layout
11146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11149 \begin_layout Plain Layout
11155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11158 \begin_layout Plain Layout
11159 \begin_inset Formula $A\:B$
11169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11172 \begin_layout Plain Layout
11180 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11183 \begin_layout Plain Layout
11189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11192 \begin_layout Plain Layout
11193 \begin_inset Formula $A\;B$
11203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11206 \begin_layout Plain Layout
11214 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11217 \begin_layout Plain Layout
11223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11226 \begin_layout Plain Layout
11227 \begin_inset Formula $A\quad B$
11237 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11240 \begin_layout Plain Layout
11248 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11251 \begin_layout Plain Layout
11257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11260 \begin_layout Plain Layout
11261 \begin_inset Formula $A\qquad B$
11275 \begin_inset space \hfill{}
11279 \begin_inset Tabular
11280 <lyxtabular version="3" rows="6" columns="3">
11281 <features booktabs="true" tabularvalignment="middle">
11282 <column alignment="center" valignment="top">
11283 <column alignment="center" valignment="top" width="15col%">
11284 <column alignment="center" valignment="top">
11286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11289 \begin_layout Plain Layout
11295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11298 \begin_layout Plain Layout
11308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11311 \begin_layout Plain Layout
11319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11322 \begin_layout Plain Layout
11330 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11333 \begin_layout Plain Layout
11339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11342 \begin_layout Plain Layout
11343 \begin_inset Formula $A\hfill B$
11353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11356 \begin_layout Plain Layout
11364 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11367 \begin_layout Plain Layout
11373 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11376 \begin_layout Plain Layout
11377 \begin_inset Formula $A\hspace*{1em}B$
11387 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11390 \begin_layout Plain Layout
11398 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11401 \begin_layout Plain Layout
11407 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11410 \begin_layout Plain Layout
11411 \begin_inset Formula $A\hspace{1em}B$
11421 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11424 \begin_layout Plain Layout
11428 \begin_inset space \textvisiblespace{}
11436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11439 \begin_layout Plain Layout
11445 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11448 \begin_layout Plain Layout
11449 \begin_inset Formula $A\ B$
11459 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11462 \begin_layout Plain Layout
11470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11473 \begin_layout Plain Layout
11479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11482 \begin_layout Plain Layout
11483 \begin_inset Formula $A\!B$
11499 \begin_layout Standard
11501 \begin_inset space ~
11505 \begin_inset space \thinspace{}
11509 \begin_inset space \thinspace{}
11512 7 are variable spaces which are explained in
11513 \begin_inset CommandInset ref
11515 reference "subsec:Variable-Space"
11521 \begin_inset space ~
11524 9 seems to produce no space.
11525 It is displayed red in \SpecialChar LyX
11526 contrary to the other sizes, because it is a negative
11528 There are two more negative spaces:
11529 \begin_inset Separator parbreak
11535 \begin_layout Standard
11537 \begin_inset Tabular
11538 <lyxtabular version="3" rows="3" columns="3">
11539 <features booktabs="true" tabularvalignment="middle">
11540 <column alignment="center" valignment="middle" width="6.8cm">
11541 <column alignment="center" valignment="top" width="0pt">
11542 <column alignment="center" valignment="top" width="0pt">
11544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11547 \begin_layout Plain Layout
11553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11556 \begin_layout Plain Layout
11564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11567 \begin_layout Plain Layout
11577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11580 \begin_layout Plain Layout
11585 keystrokes after inserting the protected space
11590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11593 \begin_layout Plain Layout
11599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11602 \begin_layout Plain Layout
11610 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11613 \begin_layout Plain Layout
11619 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11622 \begin_layout Plain Layout
11623 \begin_inset Formula $A\negmedspace B$
11631 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11634 \begin_layout Plain Layout
11635 \begin_inset Formula $A\negthickspace B$
11651 \begin_layout Standard
11652 Negative spaces can lead to characters overlapping each other.
11653 Thus they can be used to enforce ligatures, which are e.
11654 \begin_inset space \thinspace{}
11658 \begin_inset space \space{}
11661 useful for summation operators:
11662 \begin_inset Separator parbreak
11668 \begin_layout Standard
11670 \begin_inset Tabular
11671 <lyxtabular version="3" rows="3" columns="2">
11672 <features booktabs="true" tabularvalignment="middle">
11673 <column alignment="center" valignment="top" width="0pt">
11674 <column alignment="center" valignment="top">
11676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11679 \begin_layout Plain Layout
11685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11688 \begin_layout Plain Layout
11696 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11699 \begin_layout Plain Layout
11705 \begin_inset space \textvisiblespace{}
11713 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11716 \begin_layout Plain Layout
11717 \begin_inset Formula $\sum\sum f_{kl}$
11727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11730 \begin_layout Plain Layout
11738 \begin_inset space \textvisiblespace{}
11746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11749 \begin_layout Plain Layout
11750 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11766 \begin_layout Standard
11768 \begin_inset VSpace medskip
11774 \begin_layout Standard
11776 Relations like for example equal signs, are always surrounded by space.
11777 To suppress this, the equal sign is placed into a \SpecialChar TeX
11779 The following example demonstrates this:
11780 \begin_inset Separator parbreak
11786 \begin_layout Standard
11788 \begin_inset Tabular
11789 <lyxtabular version="3" rows="2" columns="2">
11790 <features tabularvalignment="middle">
11791 <column alignment="center" valignment="top" width="0pt">
11792 <column alignment="center" valignment="top" width="0pt">
11794 <cell alignment="center" valignment="top" usebox="none">
11797 \begin_layout Plain Layout
11803 <cell alignment="center" valignment="top" usebox="none">
11806 \begin_layout Plain Layout
11807 \begin_inset Formula $A=B$
11817 <cell alignment="center" valignment="top" usebox="none">
11820 \begin_layout Plain Layout
11821 equation without space
11826 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11829 \begin_layout Plain Layout
11830 \begin_inset Formula $A{=}B$
11846 \begin_layout Standard
11848 The command for the last formula is:
11853 \begin_inset Formula $\to$
11859 \begin_layout Standard
11860 \begin_inset VSpace bigskip
11866 \begin_layout Standard
11867 Spaces are needed for physical units, because the space between the value
11868 and the unit is the smallest one and not a normal space.
11869 For units in text, the smallest space is inserted via the menu
11871 Insert\SpecialChar menuseparator
11872 Formatting\SpecialChar menuseparator
11874 \begin_inset space ~
11882 arg "space-insert thin"
11888 \begin_layout Standard
11889 An example to visualize the difference:
11892 \begin_layout Standard
11893 \begin_inset Tabular
11894 <lyxtabular version="3" rows="2" columns="2">
11895 <features tabularvalignment="middle">
11896 <column alignment="left" valignment="top">
11897 <column alignment="left" valignment="top">
11899 <cell alignment="center" valignment="top" usebox="none">
11902 \begin_layout Plain Layout
11904 \begin_inset Formula $\cdot$
11912 <cell alignment="center" valignment="top" usebox="none">
11915 \begin_layout Plain Layout
11916 space between value and unit
11923 <cell alignment="center" valignment="top" usebox="none">
11926 \begin_layout Plain Layout
11928 \begin_inset space \thinspace{}
11932 \begin_inset Formula $\cdot$
11940 <cell alignment="center" valignment="top" usebox="none">
11943 \begin_layout Plain Layout
11944 smallest space between value and unit
11957 \begin_layout Subsection
11962 \begin_layout Plain Layout
11975 \begin_layout Plain Layout
11976 for vertical space in formulas see
11977 \begin_inset CommandInset ref
11979 reference "subsec:Line-Separation"
11992 \begin_layout Plain Layout
12000 \begin_inset Note Note
12003 \begin_layout Plain Layout
12006 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12009 \begin_layout Plain Layout
12012 texorpdfstring is in section
12013 \begin_inset CommandInset ref
12015 reference "subsec:Formulas-in-Section"
12025 \begin_inset CommandInset label
12027 name "subsec:Variable-Space"
12032 \begin_inset Index idx
12035 \begin_layout Plain Layout
12036 Space ! horizontal ! variable
12044 \begin_layout Standard
12045 Space with a defined length can be inserted with the command
12052 \begin_inset Index idx
12055 \begin_layout Plain Layout
12065 \begin_inset Quotes eld
12071 \begin_inset space \textvisiblespace{}
12077 \begin_inset Quotes erd
12081 The length can be specified by left-clicking on the
12082 \begin_inset Quotes eld
12088 \begin_inset space \textvisiblespace{}
12094 \begin_inset Quotes erd
12098 The length may also be negative.
12099 When a space would be the first character in a line it would be omitted.
12100 To force its output use the command
12112 or left-click on the
12113 \begin_inset Quotes eld
12119 \begin_inset space \textvisiblespace{}
12125 \begin_inset Quotes erd
12128 and check the option
12133 \begin_inset Newline newline
12136 To insert as much space as is available, the command
12143 \begin_inset Index idx
12146 \begin_layout Plain Layout
12157 \begin_layout Standard
12159 \begin_inset Tabular
12160 <lyxtabular version="3" rows="4" columns="2">
12161 <features booktabs="true" tabularvalignment="middle">
12162 <column alignment="center" valignment="top" width="0pt">
12163 <column alignment="center" valignment="top">
12165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12168 \begin_layout Plain Layout
12176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12179 \begin_layout Plain Layout
12187 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12190 \begin_layout Plain Layout
12194 \begin_inset space \textvisiblespace{}
12200 \begin_inset space \thinspace{}
12208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12211 \begin_layout Plain Layout
12212 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12222 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12225 \begin_layout Plain Layout
12229 \begin_inset space \textvisiblespace{}
12235 \begin_inset space \thinspace{}
12243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12246 \begin_layout Plain Layout
12247 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12260 \begin_layout Plain Layout
12264 \begin_inset space \textvisiblespace{}
12272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12275 \begin_layout Plain Layout
12276 \begin_inset Formula $A=A\hfill B=B$
12292 \begin_layout Standard
12293 In the last example the available space is given by the longest column entry
12295 In an inline formula the space depends on the length of the line in which
12303 Thus, when the line uses the full width, no space will be created.
12310 only has an effect on displayed formulas when the formula style
12315 (Formula styles are explained in
12316 \begin_inset CommandInset ref
12318 reference "sec:Formula-Styles"
12325 \begin_layout Standard
12332 , there are the commands
12344 that fill the space with a pattern, see
12345 \begin_inset CommandInset ref
12347 reference "subsec:Ellipses"
12354 \begin_layout Standard
12355 For text, variable space can be inserted via the menu
12357 Insert\SpecialChar menuseparator
12358 Formatting\SpecialChar menuseparator
12360 \begin_inset space ~
12368 \begin_layout Standard
12369 This is a line with
12370 \begin_inset space \hspace{}
12375 \begin_inset space \thinspace{}
12381 \begin_layout Standard
12382 This is a line with
12383 \begin_inset space \hfill{}
12389 \begin_layout Subsection
12390 Space besides inline Formulas
12391 \begin_inset Index idx
12394 \begin_layout Plain Layout
12395 Space ! besides inline formulas
12403 \begin_layout Standard
12404 The space that surrounds inline formulas can be adjusted with the length
12412 \begin_inset Index idx
12415 \begin_layout Plain Layout
12424 The value of a length is set with the command
12431 \begin_inset Index idx
12434 \begin_layout Plain Layout
12442 which has the following scheme:
12445 \begin_layout Standard
12450 setlength{length name}{value}
12453 \begin_layout Standard
12461 \begin_inset space \thinspace{}
12467 \begin_layout Standard
12477 \begin_layout Standard
12478 is inserted in \SpecialChar TeX
12481 \begin_inset space \thinspace{}
12484 mm space will now be set around all inline formulas:
12488 \begin_layout Plain Layout
12502 \begin_layout Standard
12503 This is a line with an inline formula
12504 \begin_inset Formula $A=B$
12508 \begin_inset space \thinspace{}
12511 mm surrounding space.
12515 \begin_layout Plain Layout
12529 \begin_layout Standard
12530 To return to the predefined value,
12536 is set to the value 0
12537 \begin_inset space \thinspace{}
12543 \begin_layout Standard
12544 \begin_inset Newpage newpage
12550 \begin_layout Section
12552 \begin_inset Index idx
12555 \begin_layout Plain Layout
12562 \begin_inset Index idx
12565 \begin_layout Plain Layout
12570 \begin_layout Plain Layout
12581 \begin_layout Plain Layout
12596 \begin_layout Standard
12597 Boxes for text are described in chapter
12604 \begin_inset space ~
12612 \begin_layout Subsection
12614 \begin_inset CommandInset label
12616 name "subsec:Boxes-with-Frame"
12621 \begin_inset Index idx
12624 \begin_layout Plain Layout
12633 \begin_layout Standard
12634 It is possible to frame a formula or part of one with the commands
12641 \begin_inset Index idx
12644 \begin_layout Plain Layout
12659 \begin_inset Index idx
12662 \begin_layout Plain Layout
12673 \begin_layout Standard
12674 When one of these commands is inserted in a formula, a blue box appears
12675 within a frame to enter formula parts.
12682 an additional formula has to be created by
12686 within this box, because the box content will otherwise be treated as mathemati
12694 is used, a new formula is automatically created inside the frame.
12697 \begin_layout Standard
12704 is not suitable to frame displayed formulas because the formula will always
12705 be set in the size of the text.
12712 is in contrary not suitable to frame inline formulas, because the formula
12713 will always be set in the size of a displayed formula.
12716 \begin_layout Standard
12730 \begin_inset Index idx
12733 \begin_layout Plain Layout
12741 where additionally the frame width and the alignment can be specified.
12748 is used in the following scheme:
12751 \begin_layout Standard
12756 framebox[frame width][position]{box content}
12759 \begin_layout Standard
12760 The position can either be
12777 right aligns the formula in the box.
12778 When no position is given, the formula will be centered.
12779 \begin_inset Newline newline
12782 If no width is given, also no position can be given.
12783 In this case the frame width is adjusted to the box content like for
12792 \begin_layout Standard
12799 is inserted, a box appears containing three blue boxes.
12800 The first two boxes are surrounded by brackets and denote the two optional
12802 The third box is for formula parts like for
12809 \begin_inset Separator parbreak
12815 \begin_layout Standard
12817 \begin_inset Tabular
12818 <lyxtabular version="3" rows="5" columns="2">
12819 <features booktabs="true" tabularvalignment="middle">
12820 <column alignment="center" valignment="top" width="0pt">
12821 <column alignment="center" valignment="top">
12823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12826 \begin_layout Plain Layout
12832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12835 \begin_layout Plain Layout
12842 <row topspace="1.5mm">
12843 <cell alignment="center" valignment="top" usebox="none">
12846 \begin_layout Plain Layout
12850 \begin_inset space \textvisiblespace{}
12860 \begin_inset space \textvisiblespace{}
12868 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12871 \begin_layout Plain Layout
12872 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12881 <row topspace="1.5mm">
12882 <cell alignment="center" valignment="top" usebox="none">
12885 \begin_layout Plain Layout
12889 \begin_inset space \textvisiblespace{}
12895 \begin_inset space \textvisiblespace{}
12903 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12906 \begin_layout Plain Layout
12907 \begin_inset Formula $\boxed{\int A=B}$
12916 <row topspace="1.5mm">
12917 <cell alignment="center" valignment="top" usebox="none">
12920 \begin_layout Plain Layout
12924 \begin_inset space \textvisiblespace{}
12932 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12935 \begin_layout Plain Layout
12936 \begin_inset Formula $A+\fbox{B}$
12945 <row topspace="1.5mm" bottomspace="1mm">
12946 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12949 \begin_layout Plain Layout
12953 \begin_inset space \textvisiblespace{}
12957 \begin_inset Formula $\to$
12961 \begin_inset Formula $\to$
12971 \begin_inset space \textvisiblespace{}
12975 \begin_inset Formula $\downarrow$
12983 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12986 \begin_layout Plain Layout
12987 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13003 \begin_layout Standard
13004 The frame thickness can also be adjusted.
13005 To do this the following commands have to be inserted in \SpecialChar TeX
13010 \begin_layout Standard
13020 \begin_inset Quotes eld
13024 \begin_inset Quotes erd
13038 \begin_inset Quotes eld
13042 \begin_inset Quotes erd
13048 \begin_layout Standard
13049 \begin_inset Quotes eld
13053 \begin_inset Quotes erd
13056 specifies the minimal distance between the frame and the first character
13058 An example for this is the following framed formula:
13062 \begin_layout Plain Layout
13074 \begin_inset Formula
13081 Before this formula the commands
13084 \begin_layout Standard
13106 \begin_layout Standard
13107 were inserted in \SpecialChar TeX
13109 The given values are used for all following boxes.
13112 \begin_layout Standard
13113 To return to the standard frame size, the command
13116 \begin_layout Standard
13141 \begin_layout Plain Layout
13155 \begin_layout Standard
13156 is inserted in \SpecialChar TeX
13157 mode before the next formula.
13160 \begin_layout Subsection
13161 Boxes without Frame
13162 \begin_inset CommandInset label
13164 name "subsec:Boxes-without-Frame"
13169 \begin_inset Index idx
13172 \begin_layout Plain Layout
13173 Boxes ! without frame
13181 \begin_layout Standard
13182 For boxes without a frame there are the following box commands:
13189 \begin_inset Index idx
13192 \begin_layout Plain Layout
13207 \begin_inset Index idx
13210 \begin_layout Plain Layout
13225 \begin_inset Index idx
13228 \begin_layout Plain Layout
13239 \begin_layout Standard
13246 a box can be super- or subscripted.
13247 But in contrary to normal super- and subscripting, the characters in the
13248 box keep their font size.
13255 is used in the following scheme:
13258 \begin_layout Standard
13263 raisebox{height}{box content}
13266 \begin_layout Standard
13267 When the box should contain a formula, an extra formula is needed like for
13278 \begin_inset Note Greyedout
13281 \begin_layout Plain Layout
13292 this extra formula is created by pressing
13296 twice instead of once because \SpecialChar LyX
13297 doesn't yet support
13311 \begin_inset Separator parbreak
13317 \begin_layout Standard
13319 \begin_inset Tabular
13320 <lyxtabular version="3" rows="4" columns="2">
13321 <features booktabs="true" tabularvalignment="middle">
13322 <column alignment="center" valignment="top" width="0pt">
13323 <column alignment="center" valignment="top">
13325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13328 \begin_layout Plain Layout
13334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13337 \begin_layout Plain Layout
13345 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13348 \begin_layout Plain Layout
13352 \begin_inset Formula $\to$
13358 \begin_inset Formula $\to$
13366 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13369 \begin_layout Plain Layout
13370 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13380 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13383 \begin_layout Plain Layout
13387 \begin_inset Formula $\to$
13393 \begin_inset Formula $\to$
13401 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13404 \begin_layout Plain Layout
13405 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13418 \begin_layout Plain Layout
13422 \begin_inset Formula $\to$
13438 \begin_inset space \textvisiblespace{}
13446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13449 \begin_layout Plain Layout
13450 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13466 \begin_layout Standard
13491 , with the difference that there is no frame.
13494 \begin_layout Subsection
13496 \begin_inset CommandInset label
13498 name "subsec:Colored-Boxes"
13503 \begin_inset Index idx
13506 \begin_layout Plain Layout
13515 \begin_layout Standard
13516 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13525 \begin_layout Plain Layout
13526 The \SpecialChar LaTeX
13531 is part of every \SpecialChar LaTeX
13532 standard installation.
13538 \begin_inset Index idx
13541 \begin_layout Plain Layout
13547 has to be loaded in the \SpecialChar LaTeX
13548 -preamble with the line
13552 \begin_layout Plain Layout
13553 When text is colored somewhere in the document with a predefined color,
13555 loads the \SpecialChar LaTeX
13561 Thus it is possible that the package is loaded twice, but this does not
13568 \begin_inset Note Note
13571 \begin_layout Plain Layout
13572 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13581 \begin_layout Standard
13589 \begin_layout Standard
13590 \begin_inset VSpace medskip
13593 To color boxes, the command
13600 \begin_inset Index idx
13603 \begin_layout Plain Layout
13611 is used in the following scheme:
13614 \begin_layout Standard
13619 colorbox{color}{box content}
13622 \begin_layout Standard
13623 The box content can also be a box and a
13629 can also be part of another box (see the 2nd and 3rd example).
13630 When the box should contain a formula, an extra formula has to be created,
13631 the same way as for
13641 \begin_layout Plain Layout
13642 This also applies for the command
13656 \begin_layout Standard
13657 One of the following predefined colors can be chosen:
13660 \begin_layout Standard
13694 \begin_inset Separator parbreak
13700 \begin_layout Standard
13702 \begin_inset Tabular
13703 <lyxtabular version="3" rows="4" columns="2">
13704 <features booktabs="true" tabularvalignment="middle">
13705 <column alignment="center" valignment="top" width="0pt">
13706 <column alignment="center" valignment="top">
13708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13711 \begin_layout Plain Layout
13717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13720 \begin_layout Plain Layout
13728 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13731 \begin_layout Plain Layout
13735 \begin_inset Formula $\to$
13745 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13748 \begin_layout Plain Layout
13749 \begin_inset Formula $\colorbox{yellow}{A=B}$
13758 <row topspace="1.5mm">
13759 <cell alignment="center" valignment="top" usebox="none">
13762 \begin_layout Plain Layout
13766 \begin_inset Formula $\to$
13774 \begin_inset space \textvisiblespace{}
13782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13785 \begin_layout Plain Layout
13786 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13795 <row topspace="1.5mm" bottomspace="1mm">
13796 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13799 \begin_layout Plain Layout
13803 \begin_inset space \textvisiblespace{}
13809 \begin_inset Formula $\to$
13825 \begin_inset space \textvisiblespace{}
13833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13836 \begin_layout Plain Layout
13837 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13853 \begin_layout Standard
13860 only colors the box but not the characters in the box.
13861 To color all characters, the whole formula is highlighted and the desired
13862 color is chosen in the
13865 \begin_inset space ~
13871 The dialog can be called with the toolbar button
13874 arg "dialog-show character"
13879 Edit\SpecialChar menuseparator
13881 \begin_inset space ~
13884 Style\SpecialChar menuseparator
13888 The formula number then has the same color as the formula.
13889 When the formula number should get another color than the formula characters,
13890 the color must be changed within the formula.
13893 \begin_layout Standard
13897 \begin_layout Standard
13900 \begin_inset Formula
13902 \int A=B\label{eq:red}
13910 \begin_inset Formula
13912 \textcolor{red}{\int A=B}\label{eq:redgreen}
13920 \begin_layout Standard
13922 \begin_inset CommandInset ref
13928 is completely colored red.
13929 \begin_inset Newline newline
13933 \begin_inset CommandInset ref
13935 reference "eq:redgreen"
13939 was first completely colored green to set the color for the formula number.
13940 Subsequently the formula characters were colored red.
13943 \begin_layout Standard
13944 \begin_inset VSpace bigskip
13947 To color the frame different than the rest of the box, the command
13954 \begin_inset Index idx
13957 \begin_layout Plain Layout
13965 is used in the following scheme:
13968 \begin_layout Standard
13973 fcolorbox{frame color}{color}{box content}
13976 \begin_layout Standard
13983 is an extension of the command
13990 The frame width is set, like for
14013 \begin_layout Plain Layout
14025 \begin_inset Formula
14027 \fcolorbox{cyan}{magenta}{A=B}
14036 \begin_layout Plain Layout
14050 \begin_layout Standard
14051 This formula was created with the command
14052 \begin_inset Newline newline
14060 \begin_inset Formula $\to$
14066 \begin_inset Formula $\to$
14076 \begin_layout Standard
14077 \begin_inset VSpace bigskip
14080 To use other colors than the predefined ones, they have to be defined first.
14083 \begin_layout Standard
14084 One can for example define the color
14085 \begin_inset Quotes eld
14093 \begin_inset Quotes erd
14096 with the \SpecialChar LaTeX
14100 \begin_layout Standard
14105 definecolor{darkgreen}{cmyk}{0.5,
14120 \begin_inset Index idx
14123 \begin_layout Plain Layout
14134 \begin_layout Standard
14139 is the color space that denotes the colors
14156 The four comma separated numbers are the portion factor for the corresponding
14157 colors of the color space.
14158 The factors can be in the range of 0
14159 \begin_inset space \thinspace{}
14163 \begin_inset space \thinspace{}
14171 also the color space
14175 can be used for definitions.
14192 , so that there are in this case three portion factors for the corresponding
14194 Furthermore there is the color space
14198 with one portion factor for the gray value.
14201 \begin_layout Standard
14202 As example a framed box with the new defined color
14206 where the characters have been colored
14211 \begin_inset Formula
14213 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14221 \begin_layout Standard
14222 Self-defined colors can also be used for text with the help of the command
14230 \begin_inset Index idx
14233 \begin_layout Plain Layout
14242 \begin_layout Standard
14246 \begin_layout Plain Layout
14250 textcolor{darkgreen}{
14256 \begin_inset Quotes eld
14260 \begin_inset Quotes erd
14267 \begin_layout Plain Layout
14277 \begin_layout Standard
14285 \begin_inset Index idx
14288 \begin_layout Plain Layout
14296 is used in the scheme
14300 textcolor{color}{characters to color}
14305 \begin_layout Subsection
14307 \begin_inset CommandInset label
14309 name "subsec:Paragraph-Boxes"
14314 \begin_inset Index idx
14317 \begin_layout Plain Layout
14318 Boxes ! as paragraph
14326 \begin_layout Standard
14327 A box that can contain several lines and paragraphs, a so-called paragraph
14328 box (parbox), can be created with the menu
14330 Insert\SpecialChar menuseparator
14333 or the toolbar button
14342 \begin_layout Standard
14343 The following example shows a framed parbox in a line:
14346 \begin_layout Standard
14347 \begin_inset VSpace medskip
14351 \begin_inset Box Boxed
14361 height_special "totalheight"
14366 backgroundcolor "none"
14369 \begin_layout Plain Layout
14370 This is a paragraph box.
14372 \begin_inset space \thinspace{}
14375 cm long and can also contain formulas:
14376 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14387 \begin_layout Standard
14388 \begin_inset VSpace medskip
14394 \begin_layout Standard
14395 Such a box is created by right-clicking on the gray box inset.
14396 A dialog pops up showing the box properties.
14410 \begin_inset space \thinspace{}
14415 Vertical Box Alignment
14420 \begin_layout Standard
14421 \begin_inset VSpace medskip
14424 In \SpecialChar LaTeX
14425 a parbox is created with the command
14432 \begin_inset Index idx
14435 \begin_layout Plain Layout
14443 which has the following scheme:
14446 \begin_layout Standard
14451 parbox[position]{width}{box content}
14454 \begin_layout Standard
14469 \begin_inset Quotes eld
14473 \begin_inset Quotes erd
14476 means that the box is aligned within the surrounding text with its last
14483 \begin_inset Quotes eld
14487 \begin_inset Quotes erd
14490 this is done with the first line.
14491 When no position is given, the box will be vertically centered, see section
14499 \begin_inset space ~
14504 manual for examples.
14507 \begin_layout Standard
14508 \begin_inset VSpace bigskip
14511 To frame formulas completely, including the formula number, the formula
14512 must be set into a parbox.
14513 To do this, the command
14527 is inserted in \SpecialChar TeX
14528 mode before the formula.
14536 \begin_inset Index idx
14539 \begin_layout Plain Layout
14547 is hereby the line width set for the document.
14548 Because the frame is outside the parbox, 2
14549 \begin_inset space \thinspace{}
14552 times the frame separation and the frame thickness must be subtracted from
14554 As this is not automatically done by \SpecialChar LyX
14559 \begin_layout Plain Layout
14560 \begin_inset CommandInset href
14562 name "LyX-bug #4483"
14563 target "http://www.lyx.org/trac/ticket/4483"
14573 mode has to be used.
14574 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14583 \begin_layout Plain Layout
14588 is part of every \SpecialChar LaTeX
14589 standard installation.
14595 \begin_inset Index idx
14598 \begin_layout Plain Layout
14604 must be loaded in the \SpecialChar LaTeX
14605 -preamble with the line
14608 \begin_layout Standard
14616 \begin_layout Standard
14617 Behind the formula both boxes are closed by entering
14621 in \SpecialChar TeX
14623 Here is an example:
14627 \begin_layout Plain Layout
14641 \begin_layout Standard
14645 \begin_layout Plain Layout
14663 \begin_inset Formula
14665 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14674 \begin_layout Plain Layout
14685 \begin_layout Plain Layout
14699 \begin_layout Standard
14700 \begin_inset VSpace medskip
14703 As a parbox is used as the argument of
14709 , there is in this case no difference between
14724 \begin_layout Standard
14725 \begin_inset VSpace bigskip
14728 Paragraph boxes are very useful to comment formulas directly.
14735 is used in combination with the command
14749 \begin_inset CommandInset ref
14751 reference "subsec:User-defined-Numbering"
14758 \begin_layout Standard
14759 An example of a formula commented with
14768 \begin_layout Standard
14772 \begin_layout Plain Layout
14785 This is a description.
14786 It is distinctly separated from the formula and multiline.
14790 \begin_layout Plain Layout
14802 \begin_layout Standard
14803 Such a formula must be inserted completely in \SpecialChar TeX
14804 mode because \SpecialChar LyX
14806 support the command
14813 The formula is created with the following command sequence:
14816 \begin_layout Standard
14829 is inserted in \SpecialChar TeX
14834 \begin_layout Plain Layout
14835 When the formula style
14847 can also be replaced by
14854 (formula styles see
14855 \begin_inset CommandInset ref
14857 reference "sec:Formula-Styles"
14866 Then the description follows as normal text and finally
14872 is inserted in \SpecialChar TeX
14886 hereby create a displayed formula.
14889 \begin_layout Standard
14896 can be seen in this example that was
14897 \begin_inset Quotes eld
14901 \begin_inset Quotes erd
14904 using the mathematical textmode:
14905 \begin_inset Formula
14907 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14915 \begin_layout Section
14917 \begin_inset Index idx
14920 \begin_layout Plain Layout
14929 \begin_layout Subsection
14931 \begin_inset CommandInset label
14933 name "subsec:Big-Operators"
14938 \begin_inset Index idx
14941 \begin_layout Plain Layout
14948 \begin_inset Index idx
14951 \begin_layout Plain Layout
14958 \begin_inset Index idx
14961 \begin_layout Plain Layout
14970 \begin_layout Standard
14971 To be able to use all integral operators listed here, the option
14973 Use esint package automatically
14975 must be set in the document settings under
14978 \begin_inset space ~
14986 \begin_layout Standard
14987 \begin_inset space \hfill{}
14991 \begin_inset Tabular
14992 <lyxtabular version="3" rows="11" columns="2">
14993 <features booktabs="true" tabularvalignment="middle">
14994 <column alignment="center" valignment="top" width="0pt">
14995 <column alignment="center" valignment="top" width="0pt">
14997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15000 \begin_layout Plain Layout
15006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15009 \begin_layout Plain Layout
15017 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15020 \begin_layout Plain Layout
15024 \begin_inset Index idx
15027 \begin_layout Plain Layout
15040 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15043 \begin_layout Plain Layout
15044 \begin_inset Formula $\int$
15054 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15057 \begin_layout Plain Layout
15065 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15068 \begin_layout Plain Layout
15069 \begin_inset Formula $\oint$
15079 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15082 \begin_layout Plain Layout
15090 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15093 \begin_layout Plain Layout
15094 \begin_inset Formula $\ointctrclockwise$
15104 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15107 \begin_layout Plain Layout
15115 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15118 \begin_layout Plain Layout
15119 \begin_inset Formula $\ointclockwise$
15129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15132 \begin_layout Plain Layout
15140 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15143 \begin_layout Plain Layout
15144 \begin_inset Formula $\sqint$
15154 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15157 \begin_layout Plain Layout
15165 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15168 \begin_layout Plain Layout
15170 \begin_inset Formula $\fint$
15180 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15183 \begin_layout Plain Layout
15191 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15194 \begin_layout Plain Layout
15196 \begin_inset Formula $\landupint$
15206 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15209 \begin_layout Plain Layout
15217 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15220 \begin_layout Plain Layout
15222 \begin_inset Formula $\landdownint$
15232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15235 \begin_layout Plain Layout
15243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15246 \begin_layout Plain Layout
15247 \begin_inset Formula $\bigcap$
15257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15260 \begin_layout Plain Layout
15268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15271 \begin_layout Plain Layout
15272 \begin_inset Formula $\bigcup$
15286 \begin_inset space \hfill{}
15290 \begin_inset Tabular
15291 <lyxtabular version="3" rows="11" columns="2">
15292 <features booktabs="true" tabularvalignment="middle">
15293 <column alignment="center" valignment="top" width="0pt">
15294 <column alignment="center" valignment="top" width="0pt">
15296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15299 \begin_layout Plain Layout
15305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15308 \begin_layout Plain Layout
15316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15319 \begin_layout Plain Layout
15323 \begin_inset Index idx
15326 \begin_layout Plain Layout
15339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15342 \begin_layout Plain Layout
15343 \begin_inset Formula $\sum$
15353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15356 \begin_layout Plain Layout
15360 \begin_inset Index idx
15363 \begin_layout Plain Layout
15370 \begin_layout Plain Layout
15389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15392 \begin_layout Plain Layout
15393 \begin_inset Formula $\prod$
15403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15406 \begin_layout Plain Layout
15414 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15417 \begin_layout Plain Layout
15418 \begin_inset Formula $\coprod$
15428 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15431 \begin_layout Plain Layout
15439 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15442 \begin_layout Plain Layout
15443 \begin_inset Formula $\bigodot$
15453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15456 \begin_layout Plain Layout
15464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15467 \begin_layout Plain Layout
15468 \begin_inset Formula $\bigotimes$
15478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15481 \begin_layout Plain Layout
15489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15492 \begin_layout Plain Layout
15493 \begin_inset Formula $\bigoplus$
15503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15506 \begin_layout Plain Layout
15514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15517 \begin_layout Plain Layout
15518 \begin_inset Formula $\bigwedge$
15528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15531 \begin_layout Plain Layout
15539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15542 \begin_layout Plain Layout
15543 \begin_inset Formula $\bigvee$
15553 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15556 \begin_layout Plain Layout
15564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15567 \begin_layout Plain Layout
15568 \begin_inset Formula $\bigsqcup$
15578 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15581 \begin_layout Plain Layout
15589 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15592 \begin_layout Plain Layout
15593 \begin_inset Formula $\biguplus$
15607 \begin_inset space \hfill{}
15613 \begin_layout Standard
15614 All big operators can also be inserted via the math toolbar button
15617 arg "math-insert \\intop"
15623 \begin_layout Standard
15624 The operators are called big because they are bigger than the sometimes
15625 equal looking binary operators.
15626 All big operators can have limits as described in the next subsection.
15629 \begin_layout Standard
15630 For all integral operators there is a second version available, ending in
15648 These operators are different from
15655 \begin_inset space \space{}
15658 in the style the operator limits are displayed, see
15659 \begin_inset CommandInset ref
15661 reference "subsec:Operator-Limits"
15669 \begin_layout Subsubsection*
15670 Advice for Integrals
15673 \begin_layout Standard
15678 in an integral is an operator, that therefore has to be set upright.
15679 This is done by highlighting the
15683 and using the keyboard shortcut
15693 \begin_layout Plain Layout
15699 \begin_inset CommandInset ref
15701 reference "subsec:Font-Styles"
15711 Finally the smallest space is inserted before the
15715 , as this is usual for operators.
15719 \begin_layout Standard
15721 \begin_inset Formula $\int A(x)dx$
15725 \begin_inset Newline newline
15729 \begin_inset Phantom HPhantom
15732 \begin_layout Plain Layout
15739 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15745 \begin_layout Standard
15746 For multiple integrals there are the following commands:
15747 \begin_inset VSpace medskip
15753 \begin_layout Standard
15754 \begin_inset space \hfill{}
15758 \begin_inset Tabular
15759 <lyxtabular version="3" rows="4" columns="2">
15760 <features booktabs="true" tabularvalignment="middle">
15761 <column alignment="center" valignment="top" width="0pt">
15762 <column alignment="center" valignment="top" width="0pt">
15764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15767 \begin_layout Plain Layout
15773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15776 \begin_layout Plain Layout
15783 <row bottomspace="1mm">
15784 <cell alignment="center" valignment="top" usebox="none">
15787 \begin_layout Plain Layout
15795 <cell alignment="center" valignment="top" usebox="none">
15798 \begin_layout Plain Layout
15799 \begin_inset Formula $\iint$
15808 <row bottomspace="1mm">
15809 <cell alignment="center" valignment="top" usebox="none">
15812 \begin_layout Plain Layout
15820 <cell alignment="center" valignment="top" usebox="none">
15823 \begin_layout Plain Layout
15824 \begin_inset Formula $\oiint$
15833 <row bottomspace="1mm">
15834 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15837 \begin_layout Plain Layout
15845 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15848 \begin_layout Plain Layout
15849 \begin_inset Formula $\sqiint$
15863 \begin_inset space \hfill{}
15867 \begin_inset Tabular
15868 <lyxtabular version="3" rows="4" columns="2">
15869 <features booktabs="true" tabularvalignment="middle">
15870 <column alignment="center" valignment="top" width="0pt">
15871 <column alignment="center" valignment="top" width="0pt">
15873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15876 \begin_layout Plain Layout
15882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15885 \begin_layout Plain Layout
15892 <row bottomspace="1mm">
15893 <cell alignment="center" valignment="top" usebox="none">
15896 \begin_layout Plain Layout
15904 <cell alignment="center" valignment="top" usebox="none">
15907 \begin_layout Plain Layout
15908 \begin_inset Formula $\iiint$
15917 <row bottomspace="1mm">
15918 <cell alignment="center" valignment="top" usebox="none">
15921 \begin_layout Plain Layout
15929 <cell alignment="center" valignment="top" usebox="none">
15932 \begin_layout Plain Layout
15933 \begin_inset Formula $\iiiint$
15942 <row bottomspace="1mm">
15943 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15946 \begin_layout Plain Layout
15954 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15957 \begin_layout Plain Layout
15958 \begin_inset Formula $\dotsint$
15972 \begin_inset space \hfill{}
15978 \begin_layout Subsection
15980 \begin_inset CommandInset label
15982 name "subsec:Operator-Limits"
15987 \begin_inset Index idx
15990 \begin_layout Plain Layout
15999 \begin_layout Standard
16000 Limits are created by super- and subscripts:
16001 \begin_inset Separator parbreak
16007 \begin_layout Standard
16009 \begin_inset Tabular
16010 <lyxtabular version="3" rows="2" columns="2">
16011 <features booktabs="true" tabularvalignment="middle">
16012 <column alignment="center" valignment="top" width="0pt">
16013 <column alignment="center" valignment="top" width="0pt">
16015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16018 \begin_layout Plain Layout
16024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16027 \begin_layout Plain Layout
16035 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16038 \begin_layout Plain Layout
16044 \begin_inset space \textvisiblespace{}
16048 \begin_inset Formula $\to$
16052 \begin_inset Formula $\to$
16060 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16063 \begin_layout Plain Layout
16064 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16080 \begin_layout Standard
16081 Limits of inline formulas are set right beside the operator.
16082 Limits in displayed formulas are set above or below the operator, except
16083 for integral limits.
16086 \begin_layout Standard
16087 To force that the limits are set beside the operator, the cursor is set
16088 directly behind the operator and the limits type is changed with the menu
16091 Edit\SpecialChar menuseparator
16092 Math\SpecialChar menuseparator
16111 \begin_layout Standard
16112 The default limits type is this:
16113 \begin_inset Formula
16115 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16120 This is how it looks when the limits type was changed to
16127 \begin_inset Formula
16129 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16134 For integrals, except those ending with
16150 etc., the limits are by default set beside the operator.
16151 But for multiple integrals the limits are often set below the operator.
16152 In the following example the limits type was therefore set to
16156 and so set below the integrals:
16157 \begin_inset Formula
16159 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16167 \begin_layout Standard
16168 \begin_inset VSpace medskip
16171 To specify conditions for limits, the commands
16178 \begin_inset Index idx
16181 \begin_layout Plain Layout
16196 \begin_inset Index idx
16199 \begin_layout Plain Layout
16208 To create for example this expression
16209 \begin_inset Formula
16211 \sum_{\begin{subarray}{c}
16215 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16223 \begin_layout Standard
16224 the following has to be done:
16225 \begin_inset Newline newline
16237 \begin_inset space \textvisiblespace{}
16243 One is now in a blue box under the summation operator and insert there
16249 \begin_inset space \textvisiblespace{}
16255 The blue box is now within a purple box and now several lines can be written
16257 A new line is created by inserting a line break (
16260 arg "newline-insert newline"
16265 \begin_inset Newline newline
16270 0<k<1000 Ctrl+Return
16271 \begin_inset Newline newline
16276 is typed in, a new box appears below for the new line.
16279 \begin_layout Standard
16280 The alignment of the lines can be changed to left aligned with the
16290 Edit\SpecialChar menuseparator
16294 To get right alignment,
16299 \begin_inset space \textvisiblespace{}
16304 is inserted at the beginning of the line.
16307 \begin_layout Standard
16320 with the difference that the lines are always centered.
16323 \begin_layout Standard
16324 \begin_inset VSpace bigskip
16328 \begin_inset CommandInset ref
16330 reference "eq:substack"
16334 there can be too much space beside an operator, because the characters
16335 following the operator are set beside the limits.
16336 To avoid this the command
16343 \begin_inset Index idx
16346 \begin_layout Plain Layout
16355 To activate it, set in the document settings under
16358 \begin_inset space ~
16368 \begin_inset Index idx
16371 \begin_layout Plain Layout
16372 Packages ! mathtools
16380 \begin_inset space ~
16392 sets the space besides the operator to 0
16393 \begin_inset space \thinspace{}
16397 \begin_inset Newline newline
16401 \begin_inset CommandInset ref
16403 reference "eq:substack"
16407 , one uses the command
16410 \begin_layout Standard
16418 \begin_layout Standard
16419 and inserts the operator with its limits into the braces.
16420 Behind the brace one continues the formula:
16421 \begin_inset Formula
16423 \smashoperator{\sum_{\begin{subarray}{c}
16427 \end{subarray}}^{n}}k^{-2}
16435 \begin_layout Standard
16436 It is possible to set the space of only one side of the operator to 0
16437 \begin_inset space \thinspace{}
16441 To do this write either
16460 stands for the left and
16464 for the right side of the operator.
16465 Here is an example of the possible
16474 \begin_layout Standard
16475 \begin_inset Formula
16477 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}
16485 \begin_layout Standard
16486 \begin_inset VSpace bigskip
16492 \begin_layout Standard
16493 When several consecutive operators have limits the typesetting of the limits
16494 looks often imperfect in the output, see this example:
16495 \begin_inset Formula
16497 \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}
16502 To improve the typesetting set in the document settings under
16505 \begin_inset space ~
16515 \begin_inset Index idx
16518 \begin_layout Plain Layout
16519 Packages ! mathtools
16527 \begin_inset space ~
16533 Then insert into your formula the command
16540 \begin_inset Index idx
16543 \begin_layout Plain Layout
16551 directly before the first operator.
16552 The example will then look like this:
16553 \begin_inset Formula
16555 \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}
16563 \begin_layout Standard
16564 \begin_inset VSpace bigskip
16567 How to use one limit for several operators is described in
16568 \begin_inset CommandInset ref
16570 reference "subsec:Self-defined-Operators"
16577 \begin_layout Subsection
16578 Decoration for Operators
16579 \begin_inset Index idx
16582 \begin_layout Plain Layout
16583 Operators ! Decoration
16591 \begin_layout Standard
16599 \begin_inset Index idx
16602 \begin_layout Plain Layout
16617 \begin_inset Index idx
16620 \begin_layout Plain Layout
16628 characters can be placed above or below an operator, respectively.
16636 \begin_inset Index idx
16639 \begin_layout Plain Layout
16647 characters can be set before and behind a big operator.
16650 \begin_layout Standard
16652 \begin_inset space ~
16664 \begin_layout Itemize
16671 is used to set characters at the corners of the operator
16674 \begin_layout Itemize
16681 is used to set characters before and/or behind the operator (this variant
16682 represents \SpecialChar LaTeX
16692 \begin_layout Itemize
16699 is used to set characters at the left corners and/or behind the operator
16702 \begin_layout Itemize
16709 is used to set characters at the right corners and/or before the operator
16712 \begin_layout Standard
16713 For example the command
16718 \begin_inset space \textvisiblespace{}
16724 \begin_inset space \textvisiblespace{}
16728 \begin_inset Formula $\to$
16732 \begin_inset Formula $\to$
16736 \begin_inset space \textvisiblespace{}
16746 \begin_inset Formula
16748 \sideset{}{'}\sum_{k=1}^{n}
16756 \begin_layout Standard
16757 \begin_inset Note Greyedout
16760 \begin_layout Plain Layout
16767 can only be used to decorate big operators, binary operators are not allowed.
16775 \begin_layout Standard
16788 can also be used to decorate symbols and characters.
16789 For example, the command
16794 \begin_inset space \textvisiblespace{}
16800 \begin_inset space \textvisiblespace{}
16806 \begin_inset Formula $\uparrow$
16814 \begin_inset Formula
16816 \overset{a}{\maltese}
16824 \begin_layout Subsection
16826 \begin_inset CommandInset label
16828 name "subsec:Binary-Operators"
16833 \begin_inset Index idx
16836 \begin_layout Plain Layout
16845 \begin_layout Standard
16846 Binary operators are surrounded by space when there is a character before
16848 \begin_inset VSpace medskip
16854 \begin_layout Standard
16855 \begin_inset Tabular
16856 <lyxtabular version="3" rows="13" columns="2">
16857 <features booktabs="true" tabularvalignment="middle">
16858 <column alignment="center" valignment="top" width="0pt">
16859 <column alignment="center" valignment="top" width="0pt">
16861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16864 \begin_layout Plain Layout
16866 \begin_inset Note Note
16869 \begin_layout Plain Layout
16876 is only used as spacer.
16886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16889 \begin_layout Plain Layout
16897 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16900 \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 $+$
16920 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16923 \begin_layout Plain Layout
16929 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16932 \begin_layout Plain Layout
16933 \begin_inset Formula $-$
16943 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16946 \begin_layout Plain Layout
16954 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16957 \begin_layout Plain Layout
16958 \begin_inset Formula $\pm$
16968 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16971 \begin_layout Plain Layout
16979 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16982 \begin_layout Plain Layout
16983 \begin_inset Formula $\mp$
16993 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16996 \begin_layout Plain Layout
17004 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17007 \begin_layout Plain Layout
17008 \begin_inset Formula $\cdot$
17018 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17021 \begin_layout Plain Layout
17029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17032 \begin_layout Plain Layout
17033 \begin_inset Formula $\times$
17043 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17046 \begin_layout Plain Layout
17054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17057 \begin_layout Plain Layout
17058 \begin_inset Formula $\div$
17068 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17071 \begin_layout Plain Layout
17075 \begin_layout Plain Layout
17088 \begin_layout Plain Layout
17100 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17103 \begin_layout Plain Layout
17104 \begin_inset Formula $*$
17114 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17117 \begin_layout Plain Layout
17125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17128 \begin_layout Plain Layout
17129 \begin_inset Formula $\star$
17139 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17142 \begin_layout Plain Layout
17150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17153 \begin_layout Plain Layout
17154 \begin_inset Formula $\circ$
17164 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17167 \begin_layout Plain Layout
17175 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17178 \begin_layout Plain Layout
17179 \begin_inset Formula $\diamond$
17189 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17192 \begin_layout Plain Layout
17200 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17203 \begin_layout Plain Layout
17204 \begin_inset Formula $\bullet$
17218 \begin_inset space \hfill{}
17222 \begin_inset Tabular
17223 <lyxtabular version="3" rows="13" columns="2">
17224 <features booktabs="true" tabularvalignment="middle">
17225 <column alignment="center" valignment="top" width="0pt">
17226 <column alignment="center" valignment="top" width="0pt">
17228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17231 \begin_layout Plain Layout
17237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17240 \begin_layout Plain Layout
17248 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17251 \begin_layout Plain Layout
17259 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17262 \begin_layout Plain Layout
17263 \begin_inset Formula $\nabla$
17273 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17276 \begin_layout Plain Layout
17284 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17287 \begin_layout Plain Layout
17288 \begin_inset Formula $\bigtriangledown$
17298 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17301 \begin_layout Plain Layout
17309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17312 \begin_layout Plain Layout
17313 \begin_inset Formula $\bigtriangleup$
17323 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17326 \begin_layout Plain Layout
17334 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17337 \begin_layout Plain Layout
17338 \begin_inset Formula $\Box$
17348 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17351 \begin_layout Plain Layout
17359 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17362 \begin_layout Plain Layout
17363 \begin_inset Formula $\cap$
17373 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17376 \begin_layout Plain Layout
17384 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17387 \begin_layout Plain Layout
17388 \begin_inset Formula $\cup$
17398 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17401 \begin_layout Plain Layout
17409 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17412 \begin_layout Plain Layout
17413 \begin_inset Formula $\dagger$
17423 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17426 \begin_layout Plain Layout
17434 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17437 \begin_layout Plain Layout
17438 \begin_inset Formula $\ddagger$
17448 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17451 \begin_layout Plain Layout
17459 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17462 \begin_layout Plain Layout
17463 \begin_inset Formula $\wr$
17473 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17476 \begin_layout Plain Layout
17484 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17487 \begin_layout Plain Layout
17488 \begin_inset Formula $\bigcirc$
17498 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17501 \begin_layout Plain Layout
17509 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17512 \begin_layout Plain Layout
17513 \begin_inset Formula $\wedge$
17523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17526 \begin_layout Plain Layout
17534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17537 \begin_layout Plain Layout
17538 \begin_inset Formula $\vee$
17552 \begin_inset space \hfill{}
17556 \begin_inset Tabular
17557 <lyxtabular version="3" rows="13" columns="2">
17558 <features booktabs="true" tabularvalignment="middle">
17559 <column alignment="center" valignment="top" width="0pt">
17560 <column alignment="center" valignment="top" width="0pt">
17562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17565 \begin_layout Plain Layout
17571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17574 \begin_layout Plain Layout
17582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17585 \begin_layout Plain Layout
17593 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17596 \begin_layout Plain Layout
17597 \begin_inset Formula $\oplus$
17607 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17610 \begin_layout Plain Layout
17618 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17621 \begin_layout Plain Layout
17622 \begin_inset Formula $\ominus$
17632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17635 \begin_layout Plain Layout
17643 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17646 \begin_layout Plain Layout
17647 \begin_inset Formula $\otimes$
17657 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17660 \begin_layout Plain Layout
17668 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17671 \begin_layout Plain Layout
17672 \begin_inset Formula $\oslash$
17682 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17685 \begin_layout Plain Layout
17693 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17696 \begin_layout Plain Layout
17697 \begin_inset Formula $\odot$
17707 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17710 \begin_layout Plain Layout
17718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17721 \begin_layout Plain Layout
17722 \begin_inset Formula $\amalg$
17732 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17735 \begin_layout Plain Layout
17743 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17746 \begin_layout Plain Layout
17747 \begin_inset Formula $\uplus$
17757 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17760 \begin_layout Plain Layout
17768 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17771 \begin_layout Plain Layout
17772 \begin_inset Formula $\setminus$
17782 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17785 \begin_layout Plain Layout
17793 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17796 \begin_layout Plain Layout
17797 \begin_inset Formula $\sqcap$
17807 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17810 \begin_layout Plain Layout
17818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17821 \begin_layout Plain Layout
17822 \begin_inset Formula $\sqcup$
17832 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17835 \begin_layout Plain Layout
17843 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17846 \begin_layout Plain Layout
17847 \begin_inset Formula $\triangleleft$
17857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17860 \begin_layout Plain Layout
17868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17871 \begin_layout Plain Layout
17872 \begin_inset Formula $\triangleright$
17888 \begin_layout Standard
17889 All binary operators can also be inserted via the math toolbar button
17892 arg "math-insert \\pm"
17898 \begin_layout Standard
17899 To typeset the Laplace operator also
17916 \begin_inset Formula $\nabla^{2}$
17919 ) can be used instead of
17928 \begin_layout Standard
17935 Insert\SpecialChar menuseparator
17947 \begin_layout Subsection
17948 Self-defined Operators
17949 \begin_inset CommandInset label
17951 name "subsec:Self-defined-Operators"
17956 \begin_inset Index idx
17959 \begin_layout Plain Layout
17960 Operators ! self-defined
17968 \begin_layout Standard
17969 With the help of the command
17973 DeclareMathOperator
17976 \begin_inset Index idx
17979 \begin_layout Plain Layout
17984 DeclareMathOperator
17989 custom operators can be defined in the \SpecialChar LaTeX
17991 Its command scheme is:
17994 \begin_layout Standard
17999 DeclareMathOperator{new command}{display}
18002 \begin_layout Standard
18003 Display can be characters or symbols that define how the operator looks
18005 To define a big operator a * is set behind the command.
18006 All self-defined big operators can have limits as described in
18007 \begin_inset CommandInset ref
18009 reference "subsec:Operator-Limits"
18016 \begin_layout Standard
18017 For example the \SpecialChar LaTeX
18021 \begin_layout Standard
18026 DeclareMathOperator*{
18033 \begin_layout Standard
18034 defines the command
18040 , that inserts a big operator consisting of the lozenge symbol from
18041 \begin_inset CommandInset ref
18043 reference "subsec:Miscellaneous-Symbols"
18048 \begin_inset Formula
18050 \Lozenge_{n=1}^{\infty}
18055 The command for this formula is:
18066 \begin_inset Formula $\to$
18072 \begin_layout Standard
18073 \begin_inset VSpace bigskip
18076 When self-defined operators are not used several times in the document,
18077 they can also be defined with the commands
18084 \begin_inset Index idx
18087 \begin_layout Plain Layout
18102 \begin_inset Index idx
18105 \begin_layout Plain Layout
18113 , which have the following scheme:
18116 \begin_layout Standard
18130 \begin_layout Standard
18137 defines big operators,
18146 \begin_layout Standard
18154 \begin_inset space \thinspace{}
18158 \begin_inset space \space{}
18161 be used to use one limit for several operators:
18164 \begin_layout Standard
18165 \begin_inset Formula
18167 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18175 \begin_layout Standard
18176 The command for the formula above is:
18177 \begin_inset Newline newline
18193 \begin_inset space \textvisiblespace{}
18199 \begin_inset Formula $\to$
18205 \begin_inset space \textvisiblespace{}
18213 \begin_layout Section
18215 \begin_inset Index idx
18218 \begin_layout Plain Layout
18227 \begin_layout Subsection
18229 \begin_inset CommandInset label
18231 name "subsec:Font-Styles"
18236 \begin_inset Index idx
18239 \begin_layout Plain Layout
18248 \begin_layout Standard
18249 Latin letters in formulas can be set in one of the following font styles:
18252 \begin_layout Standard
18254 \begin_inset space \hfill{}
18258 \begin_inset Tabular
18259 <lyxtabular version="3" rows="6" columns="2">
18260 <features booktabs="true" tabularvalignment="middle">
18261 <column alignment="center" valignment="top" width="0pt">
18262 <column alignment="center" valignment="top">
18264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18267 \begin_layout Plain Layout
18273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18276 \begin_layout Plain Layout
18284 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18287 \begin_layout Plain Layout
18293 \begin_inset space \textvisiblespace{}
18303 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18306 \begin_layout Plain Layout
18307 \begin_inset Formula $\mathbb{ABC}$
18317 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18320 \begin_layout Plain Layout
18326 \begin_inset space \textvisiblespace{}
18336 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18339 \begin_layout Plain Layout
18340 \begin_inset Formula $\mathbf{AbC}$
18350 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18353 \begin_layout Plain Layout
18359 \begin_inset space \textvisiblespace{}
18369 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18372 \begin_layout Plain Layout
18373 \begin_inset Formula $\boldsymbol{AbC}$
18383 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18386 \begin_layout Plain Layout
18392 \begin_inset space \textvisiblespace{}
18402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18405 \begin_layout Plain Layout
18406 \begin_inset Formula $\mathcal{ABC}$
18416 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18419 \begin_layout Plain Layout
18425 \begin_inset space \textvisiblespace{}
18435 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18438 \begin_layout Plain Layout
18439 \begin_inset Formula $\mathfrak{AbC}$
18453 \begin_inset space \hfill{}
18457 \begin_inset Tabular
18458 <lyxtabular version="3" rows="6" columns="2">
18459 <features booktabs="true" tabularvalignment="middle">
18460 <column alignment="center" valignment="top" width="0pt">
18461 <column alignment="center" valignment="top">
18463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18466 \begin_layout Plain Layout
18472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18475 \begin_layout Plain Layout
18483 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18486 \begin_layout Plain Layout
18492 \begin_inset space \textvisiblespace{}
18502 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18505 \begin_layout Plain Layout
18506 \begin_inset Formula $\mathit{AbC}$
18516 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18519 \begin_layout Plain Layout
18525 \begin_inset space \textvisiblespace{}
18535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18538 \begin_layout Plain Layout
18539 \begin_inset Formula $\mathrm{AbC}$
18549 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18552 \begin_layout Plain Layout
18558 \begin_inset space \textvisiblespace{}
18568 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18571 \begin_layout Plain Layout
18572 \begin_inset Formula $\mathsf{AbC}$
18582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18585 \begin_layout Plain Layout
18591 \begin_inset space \textvisiblespace{}
18601 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18604 \begin_layout Plain Layout
18605 \begin_inset Formula $\mathtt{AbC}$
18615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18618 \begin_layout Plain Layout
18624 \begin_inset space \textvisiblespace{}
18634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18637 \begin_layout Plain Layout
18638 \begin_inset Formula $\mathscr{ABC}$
18652 \begin_inset space \hfill{}
18658 \begin_layout Standard
18659 \begin_inset Note Greyedout
18662 \begin_layout Plain Layout
18685 can only be used for big letters.
18693 \begin_layout Standard
18694 Predefined is the style
18703 \begin_layout Standard
18704 The style commands work also for letters in mathematical constructs:
18705 \begin_inset Formula
18707 \mathfrak{A=\frac{b}{C}}
18715 \begin_layout Standard
18716 Characters in mathematical text don't appear in a math font style but in
18717 the text font style
18724 That their style can't be set correctly via the text style dialog is a
18725 bug in \SpecialChar LyX
18730 \begin_layout Plain Layout
18731 \begin_inset CommandInset href
18733 name "LyX-bug #4629"
18734 target "http://www.lyx.org/trac/ticket/4629"
18746 \begin_layout Standard
18747 Instead of the style commands the dialog
18749 Edit\SpecialChar menuseparator
18750 Math\SpecialChar menuseparator
18753 or the toolbar button
18756 arg "math-insert \\font"
18762 \begin_layout Subsection
18764 \begin_inset CommandInset label
18766 name "subsec:Bold-Formulas"
18771 \begin_inset Index idx
18774 \begin_layout Plain Layout
18783 \begin_layout Standard
18784 To make a complete formula bold, the command
18790 from the previous subsection cannot be used, because it doesn't work for
18791 small Greek letters.
18792 Furthermore it prints Latin letters always upright, like in the following
18796 \begin_layout Standard
18797 \begin_inset Formula
18799 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18807 \begin_layout Standard
18808 To display the formula correctly, the command
18815 \begin_inset Formula
18817 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18822 It is also possible to set the formula in a
18824 boldmath environment
18827 This environment is created by inserting the command
18834 \begin_inset Index idx
18837 \begin_layout Plain Layout
18845 in \SpecialChar TeX
18847 To end the environment, the command
18854 \begin_inset Index idx
18857 \begin_layout Plain Layout
18865 is inserted in \SpecialChar TeX
18870 \begin_layout Plain Layout
18880 \begin_inset Formula
18882 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18891 \begin_layout Plain Layout
18903 \begin_layout Subsection
18905 \begin_inset Index idx
18908 \begin_layout Plain Layout
18917 \begin_layout Standard
18918 Formulas can be colored like normal text: Highlight a formula or a formula
18924 Here is a formula in magenta:
18925 \begin_inset Formula
18927 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18935 \begin_layout Standard
18936 You can also define your own colors as described in
18937 \begin_inset CommandInset ref
18939 reference "subsec:Colored-Boxes"
18944 They can be used with the \SpecialChar TeX
18952 \begin_inset Index idx
18955 \begin_layout Plain Layout
18966 \begin_layout Standard
18971 textcolor{color}{characters or formula}
18974 \begin_layout Standard
18975 The following example was colored completely dark green and partly red:
18978 \begin_layout Standard
18982 \begin_layout Plain Layout
18986 textcolor{darkgreen}{
18992 \begin_inset Formula
18994 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19003 \begin_layout Plain Layout
19013 \begin_layout Standard
19014 Due to a bug in \SpecialChar LyX
19015 only complete formulas can be colored with self-defined
19020 \begin_layout Plain Layout
19021 \begin_inset CommandInset href
19023 name "LyX-bug #5269"
19024 target "http://www.lyx.org/trac/ticket/5269"
19036 \begin_layout Subsection
19038 \begin_inset CommandInset label
19040 name "subsec:Font-Sizes"
19045 \begin_inset Index idx
19048 \begin_layout Plain Layout
19057 \begin_layout Standard
19058 For characters in formulas there are, analog to characters in text, the
19059 following size commands:
19062 \begin_layout Standard
19106 \begin_inset Newline newline
19128 \begin_layout Standard
19129 The size produced by the commands depends on the document font size, which
19130 corresponds to the command
19137 The other commands produce smaller or larger sizes than
19144 The font size can however not exceed a certain value.
19145 Is for example the document font size 12
19146 \begin_inset space \thinspace{}
19155 switches to the same size as
19165 \begin_layout Standard
19166 A size command is inserted in \SpecialChar TeX
19167 mode before the formula and sets the size
19168 for all following formula and text characters.
19169 To switch back to the initial size, the command
19175 is inserted behind the formula in \SpecialChar TeX
19179 \begin_layout Standard
19180 Within a formula the size can be changed using the following size commands
19181 or the toolbar button
19184 arg "math-insert \\style"
19188 \begin_inset Separator parbreak
19194 \begin_layout Standard
19197 \begin_inset Tabular
19198 <lyxtabular version="3" rows="5" columns="2">
19199 <features booktabs="true" tabularvalignment="middle">
19200 <column alignment="center" valignment="top" width="0pt">
19201 <column alignment="center" valignment="top">
19203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19206 \begin_layout Plain Layout
19212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19215 \begin_layout Plain Layout
19223 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19226 \begin_layout Plain Layout
19230 \begin_inset Index idx
19233 \begin_layout Plain Layout
19246 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19249 \begin_layout Plain Layout
19250 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19259 <row topspace="1mm">
19260 <cell alignment="center" valignment="top" usebox="none">
19263 \begin_layout Plain Layout
19271 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19274 \begin_layout Plain Layout
19275 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19285 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19288 \begin_layout Plain Layout
19296 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19299 \begin_layout Plain Layout
19300 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19313 \begin_layout Plain Layout
19321 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19324 \begin_layout Plain Layout
19325 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19341 \begin_layout Standard
19342 After entering these commands, a blue box appears in which the formula parts
19346 \begin_layout Standard
19347 There is a further method to change the font size, that though only works
19348 for symbols or letters in mathematical text.
19349 To use it, one of the above text size commands is inserted in mathematical
19351 All following characters until the end of the mathematical text or until
19352 another size command will have the selected size.
19354 \begin_inset VSpace -2mm
19360 \begin_layout Standard
19364 \begin_layout Plain Layout
19374 \begin_inset Formula
19376 A=\frac{B}{c}\cdot\maltese
19382 \begin_inset Formula
19384 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19393 \begin_layout Plain Layout
19405 \begin_layout Standard
19406 \begin_inset VSpace medskip
19409 Before both formulas the command
19416 The command for the second formula is:
19417 \begin_inset Newline newline
19425 \begin_inset space \textvisiblespace{}
19431 \begin_inset space \textvisiblespace{}
19437 \begin_inset space \textvisiblespace{}
19443 \begin_inset space \textvisiblespace{}
19447 \begin_inset Formula $\to$
19451 \begin_inset Formula $\to$
19455 \begin_inset Newline newline
19459 \begin_inset space \hspace*{}
19470 \begin_inset space \textvisiblespace{}
19476 \begin_inset space \textvisiblespace{}
19482 \begin_inset space \textvisiblespace{}
19488 \begin_layout Standard
19489 If a symbol cannot be displayed in different sizes, it will always be displayed
19490 in the default size.
19493 \begin_layout Section
19495 \begin_inset Index idx
19498 \begin_layout Plain Layout
19507 \begin_layout Standard
19508 Greek letters can also be inserted via the toolbar button
19511 arg "math-insert \\alpha"
19515 All international typesetting norms purport that Greek letters in math
19516 have to be typeset italic/slanted.
19517 In some languages, like French or Russian, they are nevertheless sometimes
19521 \begin_layout Subsection
19523 \begin_inset Index idx
19526 \begin_layout Plain Layout
19527 Greek letters ! small
19535 \begin_layout Standard
19536 \begin_inset space \hfill{}
19540 \begin_inset Tabular
19541 <lyxtabular version="3" rows="11" columns="2">
19542 <features booktabs="true" tabularvalignment="middle">
19543 <column alignment="center" valignment="top" width="0pt">
19544 <column alignment="center" valignment="top" width="0pt">
19546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19549 \begin_layout Plain Layout
19555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19558 \begin_layout Plain Layout
19566 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19569 \begin_layout Plain Layout
19577 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19580 \begin_layout Plain Layout
19581 \begin_inset Formula $\alpha$
19591 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19594 \begin_layout Plain Layout
19602 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19605 \begin_layout Plain Layout
19606 \begin_inset Formula $\beta$
19616 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19619 \begin_layout Plain Layout
19627 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19630 \begin_layout Plain Layout
19631 \begin_inset Formula $\gamma$
19641 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19644 \begin_layout Plain Layout
19652 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19655 \begin_layout Plain Layout
19656 \begin_inset Formula $\delta$
19666 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19669 \begin_layout Plain Layout
19677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19680 \begin_layout Plain Layout
19681 \begin_inset Formula $\epsilon$
19691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19694 \begin_layout Plain Layout
19702 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19705 \begin_layout Plain Layout
19706 \begin_inset Formula $\varepsilon$
19716 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19719 \begin_layout Plain Layout
19727 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19730 \begin_layout Plain Layout
19731 \begin_inset Formula $\zeta$
19741 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19744 \begin_layout Plain Layout
19752 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19755 \begin_layout Plain Layout
19756 \begin_inset Formula $\eta$
19766 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19769 \begin_layout Plain Layout
19777 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19780 \begin_layout Plain Layout
19781 \begin_inset Formula $\theta$
19791 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19794 \begin_layout Plain Layout
19802 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19805 \begin_layout Plain Layout
19806 \begin_inset Formula $\vartheta$
19820 \begin_inset space \hfill{}
19824 \begin_inset Tabular
19825 <lyxtabular version="3" rows="12" columns="2">
19826 <features booktabs="true" tabularvalignment="middle">
19827 <column alignment="center" valignment="top" width="0pt">
19828 <column alignment="center" valignment="top" width="0pt">
19830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19833 \begin_layout Plain Layout
19839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19842 \begin_layout Plain Layout
19850 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19853 \begin_layout Plain Layout
19861 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19864 \begin_layout Plain Layout
19865 \begin_inset Formula $\iota$
19875 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19878 \begin_layout Plain Layout
19886 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19889 \begin_layout Plain Layout
19890 \begin_inset Formula $\kappa$
19900 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19903 \begin_layout Plain Layout
19911 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19914 \begin_layout Plain Layout
19915 \begin_inset Formula $\varkappa$
19925 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19928 \begin_layout Plain Layout
19936 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19939 \begin_layout Plain Layout
19940 \begin_inset Formula $\lambda$
19950 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19953 \begin_layout Plain Layout
19961 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19964 \begin_layout Plain Layout
19965 \begin_inset Formula $\mu$
19975 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19978 \begin_layout Plain Layout
19986 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19989 \begin_layout Plain Layout
19990 \begin_inset Formula $\nu$
20000 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20003 \begin_layout Plain Layout
20011 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20014 \begin_layout Plain Layout
20015 \begin_inset Formula $\xi$
20025 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20028 \begin_layout Plain Layout
20034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20037 \begin_layout Plain Layout
20038 \begin_inset Formula $o$
20048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20051 \begin_layout Plain Layout
20059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20062 \begin_layout Plain Layout
20063 \begin_inset Formula $\pi$
20073 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20076 \begin_layout Plain Layout
20084 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20087 \begin_layout Plain Layout
20088 \begin_inset Formula $\varpi$
20098 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20101 \begin_layout Plain Layout
20109 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20112 \begin_layout Plain Layout
20113 \begin_inset Formula $\rho$
20127 \begin_inset space \hfill{}
20131 \begin_inset Tabular
20132 <lyxtabular version="3" rows="11" columns="2">
20133 <features booktabs="true" tabularvalignment="middle">
20134 <column alignment="center" valignment="top" width="0pt">
20135 <column alignment="center" valignment="top" width="0pt">
20137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20140 \begin_layout Plain Layout
20146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20149 \begin_layout Plain Layout
20157 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20160 \begin_layout Plain Layout
20168 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20171 \begin_layout Plain Layout
20172 \begin_inset Formula $\varrho$
20182 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20185 \begin_layout Plain Layout
20193 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20196 \begin_layout Plain Layout
20197 \begin_inset Formula $\sigma$
20207 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20210 \begin_layout Plain Layout
20218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20221 \begin_layout Plain Layout
20222 \begin_inset Formula $\varsigma$
20232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20235 \begin_layout Plain Layout
20243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20246 \begin_layout Plain Layout
20247 \begin_inset Formula $\tau$
20257 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20260 \begin_layout Plain Layout
20268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20271 \begin_layout Plain Layout
20272 \begin_inset Formula $\upsilon$
20282 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20285 \begin_layout Plain Layout
20293 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20296 \begin_layout Plain Layout
20297 \begin_inset Formula $\phi$
20307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20310 \begin_layout Plain Layout
20318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20321 \begin_layout Plain Layout
20322 \begin_inset Formula $\varphi$
20332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20335 \begin_layout Plain Layout
20343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20346 \begin_layout Plain Layout
20347 \begin_inset Formula $\chi$
20357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20360 \begin_layout Plain Layout
20368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20371 \begin_layout Plain Layout
20372 \begin_inset Formula $\psi$
20382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20385 \begin_layout Plain Layout
20393 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20396 \begin_layout Plain Layout
20397 \begin_inset Formula $\omega$
20411 \begin_inset space \hfill{}
20417 \begin_layout Standard
20418 \begin_inset VSpace medskip
20424 \begin_layout Standard
20425 How to create special upright Greek letters is explained in
20426 \begin_inset CommandInset ref
20428 reference "subsec:Upright-small-Greek"
20435 \begin_layout Subsection
20437 \begin_inset Index idx
20440 \begin_layout Plain Layout
20441 Greek letters ! big
20449 \begin_layout Standard
20450 \begin_inset space \hfill{}
20454 \begin_inset Tabular
20455 <lyxtabular version="3" rows="7" columns="2">
20456 <features booktabs="true" tabularvalignment="middle">
20457 <column alignment="center" valignment="top" width="0pt">
20458 <column alignment="center" valignment="top" width="0pt">
20460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20463 \begin_layout Plain Layout
20469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20472 \begin_layout Plain Layout
20480 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20483 \begin_layout Plain Layout
20491 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20494 \begin_layout Plain Layout
20495 \begin_inset Formula $\Gamma$
20505 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20508 \begin_layout Plain Layout
20516 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20519 \begin_layout Plain Layout
20520 \begin_inset Formula $\Delta$
20530 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20533 \begin_layout Plain Layout
20541 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20544 \begin_layout Plain Layout
20545 \begin_inset Formula $\Theta$
20555 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20558 \begin_layout Plain Layout
20566 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20569 \begin_layout Plain Layout
20570 \begin_inset Formula $\Lambda$
20580 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20583 \begin_layout Plain Layout
20591 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20594 \begin_layout Plain Layout
20595 \begin_inset Formula $\Xi$
20605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20608 \begin_layout Plain Layout
20616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20619 \begin_layout Plain Layout
20620 \begin_inset Formula $\Pi$
20634 \begin_inset space \hfill{}
20638 \begin_inset Tabular
20639 <lyxtabular version="3" rows="6" columns="2">
20640 <features booktabs="true" tabularvalignment="middle">
20641 <column alignment="center" valignment="top" width="0pt">
20642 <column alignment="center" valignment="top" width="0pt">
20644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20647 \begin_layout Plain Layout
20653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20656 \begin_layout Plain Layout
20664 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20667 \begin_layout Plain Layout
20675 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20678 \begin_layout Plain Layout
20679 \begin_inset Formula $\Sigma$
20689 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20692 \begin_layout Plain Layout
20700 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20703 \begin_layout Plain Layout
20704 \begin_inset Formula $\Upsilon$
20714 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20717 \begin_layout Plain Layout
20725 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20728 \begin_layout Plain Layout
20729 \begin_inset Formula $\Phi$
20739 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20742 \begin_layout Plain Layout
20750 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20753 \begin_layout Plain Layout
20754 \begin_inset Formula $\Psi$
20764 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20767 \begin_layout Plain Layout
20775 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20778 \begin_layout Plain Layout
20779 \begin_inset Formula $\Omega$
20793 \begin_inset space \hfill{}
20799 \begin_layout Standard
20800 \begin_inset VSpace medskip
20803 That the big Greek letters appear upright is caused by a design bug when
20806 To get correct italic big letters, begin every command with
20811 For example the command
20818 \begin_inset Formula $\varGamma$
20822 Another way is to load the package
20830 \begin_layout Plain Layout
20835 is part of the \SpecialChar LaTeX
20841 \begin_inset Index idx
20844 \begin_layout Plain Layout
20849 \begin_layout Plain Layout
20869 \begin_inset Index idx
20872 \begin_layout Plain Layout
20878 with the \SpecialChar LaTeX
20882 \begin_layout Standard
20887 usepackage{fixmath}
20890 \begin_layout Standard
20891 Then all big Greek letters in a document will automatically be typeset italic.
20894 \begin_layout Subsection
20896 \begin_inset Index idx
20899 \begin_layout Plain Layout
20900 Greek letters ! bold
20908 \begin_layout Standard
20909 Greek letters cannot be set with different font styles like Latin letters.
20910 They can only be made bold with the command
20917 \begin_inset Index idx
20920 \begin_layout Plain Layout
20929 \begin_inset Separator parbreak
20935 \begin_layout Standard
20937 \begin_inset Tabular
20938 <lyxtabular version="3" rows="3" columns="2">
20939 <features booktabs="true" tabularvalignment="middle">
20940 <column alignment="center" valignment="top" width="0pt">
20941 <column alignment="center" valignment="top">
20943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20946 \begin_layout Plain Layout
20952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20955 \begin_layout Plain Layout
20963 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20966 \begin_layout Plain Layout
20978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20981 \begin_layout Plain Layout
20982 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20995 \begin_layout Plain Layout
21007 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21010 \begin_layout Plain Layout
21011 \begin_inset Formula $\theta\boldsymbol{\theta}$
21027 \begin_layout Section
21032 \begin_layout Plain Layout
21045 \begin_layout Plain Layout
21046 A list with all symbols of most of the \SpecialChar LaTeX
21047 -packages can be found in
21048 \begin_inset CommandInset citation
21063 \begin_layout Plain Layout
21071 \begin_inset Note Note
21074 \begin_layout Plain Layout
21077 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21080 \begin_layout Plain Layout
21083 texorpdfstring is in section
21084 \begin_inset CommandInset ref
21086 reference "subsec:Formulas-in-Section"
21096 \begin_inset Index idx
21099 \begin_layout Plain Layout
21108 \begin_layout Standard
21109 Many of the symbols listed in this section can also be inserted via the
21113 arg "math-insert \\nabla"
21119 arg "math-insert \\digamma"
21125 \begin_layout Subsection
21126 Mathematical Symbols
21127 \begin_inset CommandInset label
21129 name "subsec:Mathematical-Symbols"
21134 \begin_inset Index idx
21137 \begin_layout Plain Layout
21138 Symbols ! mathematical
21146 \begin_layout Standard
21147 \begin_inset Tabular
21148 <lyxtabular version="3" rows="10" columns="2">
21149 <features booktabs="true" tabularvalignment="middle">
21150 <column alignment="center" valignment="top" width="0pt">
21151 <column alignment="center" valignment="top" width="0pt">
21153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21156 \begin_layout Plain Layout
21162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21165 \begin_layout Plain Layout
21173 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21176 \begin_layout Plain Layout
21184 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21187 \begin_layout Plain Layout
21188 \begin_inset Formula $\neg$
21198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21201 \begin_layout Plain Layout
21209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21212 \begin_layout Plain Layout
21213 \begin_inset Formula $\Im$
21223 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21226 \begin_layout Plain Layout
21234 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21237 \begin_layout Plain Layout
21238 \begin_inset Formula $\Re$
21248 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21251 \begin_layout Plain Layout
21259 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21262 \begin_layout Plain Layout
21263 \begin_inset Formula $\aleph$
21273 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21276 \begin_layout Plain Layout
21284 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21287 \begin_layout Plain Layout
21288 \begin_inset Formula $\partial$
21298 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21301 \begin_layout Plain Layout
21309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21312 \begin_layout Plain Layout
21313 \begin_inset Formula $\infty$
21323 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21326 \begin_layout Plain Layout
21334 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21337 \begin_layout Plain Layout
21338 \begin_inset Formula $\wp$
21348 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21351 \begin_layout Plain Layout
21359 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21362 \begin_layout Plain Layout
21363 \begin_inset Formula $\imath$
21373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21376 \begin_layout Plain Layout
21384 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21387 \begin_layout Plain Layout
21388 \begin_inset Formula $\jmath$
21402 \begin_inset space \hfill{}
21406 \begin_inset Tabular
21407 <lyxtabular version="3" rows="10" columns="2">
21408 <features booktabs="true" tabularvalignment="middle">
21409 <column alignment="center" valignment="top" width="0pt">
21410 <column alignment="center" valignment="top" width="0pt">
21412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21415 \begin_layout Plain Layout
21421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21424 \begin_layout Plain Layout
21426 \begin_inset Note Note
21429 \begin_layout Plain Layout
21436 is only used as spacer.
21448 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21451 \begin_layout Plain Layout
21459 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21462 \begin_layout Plain Layout
21463 \begin_inset Formula $\forall$
21473 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21476 \begin_layout Plain Layout
21484 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21487 \begin_layout Plain Layout
21488 \begin_inset Formula $\exists$
21498 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21501 \begin_layout Plain Layout
21509 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21512 \begin_layout Plain Layout
21513 \begin_inset Formula $\nexists$
21523 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21526 \begin_layout Plain Layout
21534 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21537 \begin_layout Plain Layout
21538 \begin_inset Formula $\emptyset$
21548 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21551 \begin_layout Plain Layout
21559 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21562 \begin_layout Plain Layout
21563 \begin_inset Formula $\varnothing$
21573 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21576 \begin_layout Plain Layout
21584 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21587 \begin_layout Plain Layout
21588 \begin_inset Formula $\dag$
21598 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21601 \begin_layout Plain Layout
21609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21612 \begin_layout Plain Layout
21613 \begin_inset Formula $\ddag$
21623 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21626 \begin_layout Plain Layout
21634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21637 \begin_layout Plain Layout
21641 \begin_layout Plain Layout
21651 \begin_inset Formula $\complement$
21658 \begin_layout Plain Layout
21672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21675 \begin_layout Plain Layout
21683 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21686 \begin_layout Plain Layout
21687 \begin_inset Formula $\Bbbk$
21701 \begin_inset space \hfill{}
21705 \begin_inset Tabular
21706 <lyxtabular version="3" rows="10" columns="2">
21707 <features booktabs="true" tabularvalignment="middle">
21708 <column alignment="center" valignment="top" width="0pt">
21709 <column alignment="center" valignment="top" width="0pt">
21711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21714 \begin_layout Plain Layout
21720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21723 \begin_layout Plain Layout
21731 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21734 \begin_layout Plain Layout
21742 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21745 \begin_layout Plain Layout
21746 \begin_inset Formula $\prime$
21756 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21759 \begin_layout Plain Layout
21767 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21770 \begin_layout Plain Layout
21771 \begin_inset Formula $\backprime$
21781 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21784 \begin_layout Plain Layout
21792 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21795 \begin_layout Plain Layout
21796 \begin_inset Formula $\mho$
21806 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21809 \begin_layout Plain Layout
21817 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21820 \begin_layout Plain Layout
21821 \begin_inset Formula $\triangle$
21831 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21834 \begin_layout Plain Layout
21842 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21845 \begin_layout Plain Layout
21846 \begin_inset Formula $\angle$
21856 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21859 \begin_layout Plain Layout
21867 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21870 \begin_layout Plain Layout
21871 \begin_inset Formula $\measuredangle$
21881 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21884 \begin_layout Plain Layout
21892 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21895 \begin_layout Plain Layout
21896 \begin_inset Formula $\sphericalangle$
21906 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21909 \begin_layout Plain Layout
21917 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21920 \begin_layout Plain Layout
21921 \begin_inset Formula $\top$
21931 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21934 \begin_layout Plain Layout
21942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21945 \begin_layout Plain Layout
21946 \begin_inset Formula $\bot$
21962 \begin_layout Standard
21963 \begin_inset Newpage newpage
21969 \begin_layout Subsection
21970 Miscellaneous Symbols
21971 \begin_inset CommandInset label
21973 name "subsec:Miscellaneous-Symbols"
21978 \begin_inset Index idx
21981 \begin_layout Plain Layout
21982 Symbols ! miscellaneous
21990 \begin_layout Standard
21993 \begin_inset Tabular
21994 <lyxtabular version="3" rows="10" columns="2">
21995 <features booktabs="true" tabularvalignment="middle">
21996 <column alignment="center" valignment="top" width="0pt">
21997 <column alignment="center" valignment="top" width="0pt">
21999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22002 \begin_layout Plain Layout
22008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22011 \begin_layout Plain Layout
22019 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22022 \begin_layout Plain Layout
22030 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22033 \begin_layout Plain Layout
22034 \begin_inset Formula $\flat$
22044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22047 \begin_layout Plain Layout
22055 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22058 \begin_layout Plain Layout
22059 \begin_inset Formula $\natural$
22069 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22072 \begin_layout Plain Layout
22080 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22083 \begin_layout Plain Layout
22084 \begin_inset Formula $\sharp$
22094 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22097 \begin_layout Plain Layout
22105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22108 \begin_layout Plain Layout
22109 \begin_inset Formula $\surd$
22119 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22122 \begin_layout Plain Layout
22130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22133 \begin_layout Plain Layout
22134 \begin_inset Formula $\checkmark$
22144 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22147 \begin_layout Plain Layout
22155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22158 \begin_layout Plain Layout
22159 \begin_inset Formula $\yen$
22169 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22172 \begin_layout Plain Layout
22180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22183 \begin_layout Plain Layout
22184 \begin_inset Formula $\pounds$
22194 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22197 \begin_layout Plain Layout
22203 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22206 \begin_layout Plain Layout
22207 \begin_inset Formula $\$$
22217 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22220 \begin_layout Plain Layout
22226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22229 \begin_layout Plain Layout
22230 \begin_inset Formula $§$
22244 \begin_inset space \hfill{}
22248 \begin_inset Tabular
22249 <lyxtabular version="3" rows="10" columns="2">
22250 <features booktabs="true" tabularvalignment="middle">
22251 <column alignment="center" valignment="top" width="0pt">
22252 <column alignment="center" valignment="top">
22254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22257 \begin_layout Plain Layout
22263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22266 \begin_layout Plain Layout
22274 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22277 \begin_layout Plain Layout
22285 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22288 \begin_layout Plain Layout
22289 \begin_inset Formula $\hbar$
22299 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22302 \begin_layout Plain Layout
22310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22313 \begin_layout Plain Layout
22314 \begin_inset Formula $\hslash$
22324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22327 \begin_layout Plain Layout
22335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22338 \begin_layout Plain Layout
22339 \begin_inset Formula $\clubsuit$
22349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22352 \begin_layout Plain Layout
22360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22363 \begin_layout Plain Layout
22364 \begin_inset Formula $\spadesuit$
22374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22377 \begin_layout Plain Layout
22385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22388 \begin_layout Plain Layout
22389 \begin_inset Formula $\bigstar$
22399 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22402 \begin_layout Plain Layout
22410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22413 \begin_layout Plain Layout
22414 \begin_inset Formula $\blacklozenge$
22424 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22427 \begin_layout Plain Layout
22435 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22438 \begin_layout Plain Layout
22439 \begin_inset Formula $\blacktriangle$
22449 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22452 \begin_layout Plain Layout
22460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22463 \begin_layout Plain Layout
22464 \begin_inset Formula $\blacktriangledown$
22474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22477 \begin_layout Plain Layout
22485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22488 \begin_layout Plain Layout
22489 \begin_inset Formula $\bullet$
22503 \begin_inset space \hfill{}
22507 \begin_inset Tabular
22508 <lyxtabular version="3" rows="10" columns="2">
22509 <features booktabs="true" tabularvalignment="middle">
22510 <column alignment="center" valignment="top" width="0pt">
22511 <column alignment="center" valignment="top" width="0pt">
22513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22516 \begin_layout Plain Layout
22522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22525 \begin_layout Plain Layout
22533 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22536 \begin_layout Plain Layout
22544 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22547 \begin_layout Plain Layout
22548 \begin_inset Formula $\diamondsuit$
22558 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22561 \begin_layout Plain Layout
22569 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22572 \begin_layout Plain Layout
22573 \begin_inset Formula $\Diamond$
22583 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22586 \begin_layout Plain Layout
22594 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22597 \begin_layout Plain Layout
22598 \begin_inset Formula $\heartsuit$
22608 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22611 \begin_layout Plain Layout
22619 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22622 \begin_layout Plain Layout
22623 \begin_inset Formula $\P$
22633 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22636 \begin_layout Plain Layout
22644 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22647 \begin_layout Plain Layout
22648 \begin_inset Formula $\copyright$
22658 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22661 \begin_layout Plain Layout
22669 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22672 \begin_layout Plain Layout
22673 \begin_inset Formula $\circledR$
22683 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22686 \begin_layout Plain Layout
22694 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22697 \begin_layout Plain Layout
22698 \begin_inset Formula $\maltese$
22708 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22711 \begin_layout Plain Layout
22719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22722 \begin_layout Plain Layout
22723 \begin_inset Formula $\diagup$
22733 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22736 \begin_layout Plain Layout
22744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22747 \begin_layout Plain Layout
22748 \begin_inset Formula $\diagdown$
22764 \begin_layout Standard
22765 \begin_inset VSpace medskip
22771 \begin_layout Standard
22772 Some symbols can be displayed in different sizes, see
22773 \begin_inset CommandInset ref
22775 reference "subsec:Font-Sizes"
22782 \begin_layout Subsection
22784 \begin_inset Index idx
22787 \begin_layout Plain Layout
22788 Symbols ! Euro-symbol
22794 \begin_inset Index idx
22797 \begin_layout Plain Layout
22804 \begin_layout Plain Layout
22821 \begin_layout Standard
22822 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22828 \begin_inset Index idx
22831 \begin_layout Plain Layout
22837 must be installed and loaded with the \SpecialChar LaTeX
22841 \begin_layout Standard
22846 usepackage[gennarrow]{eurosym}
22849 \begin_layout Standard
22850 The Euro symbol can now be inserted with the command
22857 \begin_inset Index idx
22860 \begin_layout Plain Layout
22871 \begin_layout Standard
22872 The Euro symbol can directly be inserted with the € key in mathematical
22873 text, without having
22888 can also be inserted in \SpecialChar TeX
22890 The official currency symbol can then be inserted with the command
22897 \begin_inset Index idx
22900 \begin_layout Plain Layout
22908 , that is only available in \SpecialChar TeX
22912 \begin_layout Standard
22916 \begin_layout Plain Layout
22926 \begin_inset Note Note
22929 \begin_layout Plain Layout
22930 The following table will only be displayed when the \SpecialChar LaTeX
22943 \begin_layout Standard
22944 An overview about the different Euro symbols:
22945 \begin_inset Separator parbreak
22951 \begin_layout Standard
22953 \begin_inset Tabular
22954 <lyxtabular version="3" rows="4" columns="3">
22955 <features booktabs="true" tabularvalignment="middle">
22956 <column alignment="center" valignment="top" width="0pt">
22957 <column alignment="center" valignment="top" width="0pt">
22958 <column alignment="center" valignment="top" width="0pt">
22960 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22963 \begin_layout Plain Layout
22967 \begin_layout Plain Layout
22971 cmidrule[0.08em]{2-3}
22981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22984 \begin_layout Plain Layout
22990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22993 \begin_layout Plain Layout
23001 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23004 \begin_layout Plain Layout
23010 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23013 \begin_layout Plain Layout
23021 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23024 \begin_layout Plain Layout
23025 \begin_inset Formula $\euro$
23035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23038 \begin_layout Plain Layout
23044 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23047 \begin_layout Plain Layout
23053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23056 \begin_layout Plain Layout
23057 \begin_inset Formula $\mbox{€}$
23067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23070 \begin_layout Plain Layout
23077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23080 \begin_layout Plain Layout
23088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23091 \begin_layout Plain Layout
23095 \begin_layout Plain Layout
23115 \begin_inset Note Note
23118 \begin_layout Plain Layout
23125 is used here only for table borders.
23135 manual for details.
23143 \begin_layout Standard
23147 \begin_layout Plain Layout
23157 \begin_inset Note Note
23160 \begin_layout Plain Layout
23161 The following will be displayed when the \SpecialChar LaTeX
23174 \begin_layout Standard
23175 You need to install the \SpecialChar LaTeX
23180 to see the rest of this subsection in the output.
23183 \begin_layout Standard
23187 \begin_layout Plain Layout
23199 \begin_layout Standard
23200 \begin_inset Newpage newpage
23206 \begin_layout Section
23208 \begin_inset CommandInset label
23210 name "sec:Relations"
23215 \begin_inset Index idx
23218 \begin_layout Plain Layout
23225 \begin_inset Index idx
23228 \begin_layout Plain Layout
23233 \begin_layout Plain Layout
23244 \begin_layout Plain Layout
23259 \begin_layout Standard
23260 All following relations can also be inserted via the toolbar button
23263 arg "math-insert \\leq"
23269 \begin_layout Standard
23270 \begin_inset Tabular
23271 <lyxtabular version="3" rows="17" columns="2">
23272 <features booktabs="true" tabularvalignment="middle">
23273 <column alignment="center" valignment="top" width="0pt">
23274 <column alignment="center" valignment="top" width="0pt">
23276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23279 \begin_layout Plain Layout
23285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23288 \begin_layout Plain Layout
23296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23299 \begin_layout Plain Layout
23305 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23308 \begin_layout Plain Layout
23309 \begin_inset Formula $<$
23319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23322 \begin_layout Plain Layout
23330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23333 \begin_layout Plain Layout
23334 \begin_inset Formula $\le$
23344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23347 \begin_layout Plain Layout
23355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23358 \begin_layout Plain Layout
23359 \begin_inset Formula $\ll$
23369 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23372 \begin_layout Plain Layout
23380 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23383 \begin_layout Plain Layout
23384 \begin_inset Formula $\prec$
23394 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23397 \begin_layout Plain Layout
23405 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23408 \begin_layout Plain Layout
23409 \begin_inset Formula $\preceq$
23419 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23422 \begin_layout Plain Layout
23430 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23433 \begin_layout Plain Layout
23434 \begin_inset Formula $\subset$
23444 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23447 \begin_layout Plain Layout
23455 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23458 \begin_layout Plain Layout
23459 \begin_inset Formula $\subseteq$
23469 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23472 \begin_layout Plain Layout
23480 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23483 \begin_layout Plain Layout
23484 \begin_inset Formula $\sqsubseteq$
23494 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23497 \begin_layout Plain Layout
23505 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23508 \begin_layout Plain Layout
23509 \begin_inset Formula $\in$
23519 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23522 \begin_layout Plain Layout
23530 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23533 \begin_layout Plain Layout
23534 \begin_inset Formula $\vdash$
23544 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23547 \begin_layout Plain Layout
23555 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23558 \begin_layout Plain Layout
23559 \begin_inset Formula $\smile$
23569 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23572 \begin_layout Plain Layout
23580 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23583 \begin_layout Plain Layout
23584 \begin_inset Formula $\lhd$
23594 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23597 \begin_layout Plain Layout
23605 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23608 \begin_layout Plain Layout
23609 \begin_inset Formula $\unlhd$
23619 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23622 \begin_layout Plain Layout
23630 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23633 \begin_layout Plain Layout
23634 \begin_inset Formula $\gtrless$
23644 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23647 \begin_layout Plain Layout
23655 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23658 \begin_layout Plain Layout
23659 \begin_inset Formula $\mid$
23669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23672 \begin_layout Plain Layout
23680 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23683 \begin_layout Plain Layout
23684 \begin_inset Formula $\nmid$
23698 \begin_inset space \hfill{}
23702 \begin_inset Tabular
23703 <lyxtabular version="3" rows="17" columns="2">
23704 <features booktabs="true" tabularvalignment="middle">
23705 <column alignment="center" valignment="top" width="0pt">
23706 <column alignment="center" valignment="top" width="0pt">
23708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23711 \begin_layout Plain Layout
23717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23720 \begin_layout Plain Layout
23728 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23731 \begin_layout Plain Layout
23737 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23740 \begin_layout Plain Layout
23741 \begin_inset Formula $=$
23751 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23754 \begin_layout Plain Layout
23762 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23765 \begin_layout Plain Layout
23766 \begin_inset Formula $\not=$
23776 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23779 \begin_layout Plain Layout
23787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23790 \begin_layout Plain Layout
23791 \begin_inset Formula $\equiv$
23801 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23804 \begin_layout Plain Layout
23812 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23815 \begin_layout Plain Layout
23816 \begin_inset Formula $\sim$
23826 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23829 \begin_layout Plain Layout
23837 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23840 \begin_layout Plain Layout
23841 \begin_inset Formula $\simeq$
23851 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23854 \begin_layout Plain Layout
23862 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23865 \begin_layout Plain Layout
23866 \begin_inset Formula $\approx$
23876 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23879 \begin_layout Plain Layout
23887 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23890 \begin_layout Plain Layout
23891 \begin_inset Formula $\cong$
23901 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23904 \begin_layout Plain Layout
23912 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23915 \begin_layout Plain Layout
23916 \begin_inset Formula $\bowtie$
23926 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23929 \begin_layout Plain Layout
23937 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23940 \begin_layout Plain Layout
23941 \begin_inset Formula $\notin$
23951 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23954 \begin_layout Plain Layout
23962 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23965 \begin_layout Plain Layout
23966 \begin_inset Formula $\perp$
23976 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23979 \begin_layout Plain Layout
23987 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23990 \begin_layout Plain Layout
23991 \begin_inset Formula $\propto$
24001 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24004 \begin_layout Plain Layout
24012 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24015 \begin_layout Plain Layout
24016 \begin_inset Formula $\asymp$
24026 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24029 \begin_layout Plain Layout
24037 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24040 \begin_layout Plain Layout
24041 \begin_inset Formula $\doteq$
24051 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24054 \begin_layout Plain Layout
24062 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24065 \begin_layout Plain Layout
24066 \begin_inset Formula $\circeq$
24076 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24079 \begin_layout Plain Layout
24087 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24090 \begin_layout Plain Layout
24091 \begin_inset Formula $\models$
24101 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24104 \begin_layout Plain Layout
24112 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24115 \begin_layout Plain Layout
24116 \begin_inset Formula $\widehat{=}$
24130 \begin_inset space \hfill{}
24134 \begin_inset Tabular
24135 <lyxtabular version="3" rows="17" columns="2">
24136 <features booktabs="true" tabularvalignment="middle">
24137 <column alignment="center" valignment="top" width="0pt">
24138 <column alignment="center" valignment="top" width="0pt">
24140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24143 \begin_layout Plain Layout
24149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24152 \begin_layout Plain Layout
24160 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24163 \begin_layout Plain Layout
24169 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24172 \begin_layout Plain Layout
24173 \begin_inset Formula $>$
24183 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24186 \begin_layout Plain Layout
24194 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24197 \begin_layout Plain Layout
24198 \begin_inset Formula $\ge$
24208 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24211 \begin_layout Plain Layout
24219 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24222 \begin_layout Plain Layout
24223 \begin_inset Formula $\gg$
24233 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24236 \begin_layout Plain Layout
24244 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24247 \begin_layout Plain Layout
24248 \begin_inset Formula $\succ$
24258 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24261 \begin_layout Plain Layout
24269 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24272 \begin_layout Plain Layout
24273 \begin_inset Formula $\succeq$
24283 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24286 \begin_layout Plain Layout
24294 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24297 \begin_layout Plain Layout
24298 \begin_inset Formula $\supset$
24308 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24311 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24322 \begin_layout Plain Layout
24323 \begin_inset Formula $\supseteq$
24333 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24336 \begin_layout Plain Layout
24344 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24347 \begin_layout Plain Layout
24348 \begin_inset Formula $\sqsupseteq$
24358 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24361 \begin_layout Plain Layout
24369 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24372 \begin_layout Plain Layout
24373 \begin_inset Formula $\ni$
24383 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24386 \begin_layout Plain Layout
24394 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24397 \begin_layout Plain Layout
24398 \begin_inset Formula $\dashv$
24408 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24411 \begin_layout Plain Layout
24419 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24422 \begin_layout Plain Layout
24423 \begin_inset Formula $\frown$
24433 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24436 \begin_layout Plain Layout
24444 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24447 \begin_layout Plain Layout
24448 \begin_inset Formula $\rhd$
24458 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24461 \begin_layout Plain Layout
24469 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24472 \begin_layout Plain Layout
24473 \begin_inset Formula $\unrhd$
24483 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24486 \begin_layout Plain Layout
24494 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24497 \begin_layout Plain Layout
24498 \begin_inset Formula $\lessgtr$
24508 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24511 \begin_layout Plain Layout
24519 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24522 \begin_layout Plain Layout
24523 \begin_inset Formula $\parallel$
24533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24536 \begin_layout Plain Layout
24544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24547 \begin_layout Plain Layout
24548 \begin_inset Formula $\nparallel$
24564 \begin_layout Standard
24565 \begin_inset VSpace medskip
24580 are bigger than the equal looking operators
24595 \begin_layout Standard
24597 supports also many special relations.
24598 Use the toolbar button
24601 arg "math-insert \\leqq"
24604 to see a list of these relations.
24607 \begin_layout Standard
24608 Relations are, in contrary to symbols, always surrounded by space.
24611 \begin_layout Standard
24612 Relations with labels can be created with the command
24619 \begin_inset Index idx
24622 \begin_layout Plain Layout
24631 \begin_inset Separator parbreak
24637 \begin_layout Standard
24639 \begin_inset Tabular
24640 <lyxtabular version="3" rows="2" columns="2">
24641 <features booktabs="true" tabularvalignment="middle">
24642 <column alignment="center" valignment="top" width="0pt">
24643 <column alignment="center" valignment="top">
24645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24648 \begin_layout Plain Layout
24654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24657 \begin_layout Plain Layout
24664 <row topspace="1.5mm">
24665 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24668 \begin_layout Plain Layout
24672 \begin_inset space \textvisiblespace{}
24680 \begin_inset space \textvisiblespace{}
24684 \begin_inset Formula $\downarrow$
24690 \begin_inset space \textvisiblespace{}
24694 \begin_inset space \textvisiblespace{}
24702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24705 \begin_layout Plain Layout
24706 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24722 \begin_layout Section
24726 \begin_layout Subsection
24727 Predefined Functions
24728 \begin_inset CommandInset label
24730 name "subsec:Predefined-Functions"
24735 \begin_inset Index idx
24738 \begin_layout Plain Layout
24739 Functions ! predefined
24747 \begin_layout Standard
24748 In general, variables are set
24752 in mathematical expressions, but not function names, because
24753 \begin_inset Formula $sin$
24756 could be misunderstood as
24757 \begin_inset Formula $s\cdot i\cdot n$
24761 Therefore there are predefined functionswhich are additionally a bit separated
24763 They are inserted as commands starting with a backslash before their name.
24764 \begin_inset Separator parbreak
24770 \begin_layout Standard
24772 \begin_inset Tabular
24773 <lyxtabular version="3" rows="2" columns="2">
24774 <features booktabs="true" tabularvalignment="middle">
24775 <column alignment="center" valignment="top" width="0pt">
24776 <column alignment="center" valignment="top" width="0pt">
24778 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24781 \begin_layout Plain Layout
24787 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24790 \begin_layout Plain Layout
24798 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24801 \begin_layout Plain Layout
24807 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24810 \begin_layout Plain Layout
24811 \begin_inset Formula $Asin(x)+B$
24825 \begin_inset space \quad{}
24829 \begin_inset Tabular
24830 <lyxtabular version="3" rows="2" columns="2">
24831 <features booktabs="true" tabularvalignment="middle">
24832 <column alignment="center" valignment="top" width="0pt">
24833 <column alignment="center" valignment="top" width="0pt">
24835 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24838 \begin_layout Plain Layout
24844 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24847 \begin_layout Plain Layout
24855 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24858 \begin_layout Plain Layout
24866 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24869 \begin_layout Plain Layout
24870 \begin_inset Formula $A\sin(x)+B$
24886 \begin_layout Standard
24887 The following functions are predefined:
24890 \begin_layout Standard
24891 \begin_inset VSpace -2mm
24897 \begin_layout Standard
24899 \begin_inset Tabular
24900 <lyxtabular version="3" rows="9" columns="4">
24901 <features booktabs="true" tabularvalignment="middle">
24902 <column alignment="center" valignment="top" width="0pt">
24903 <column alignment="center" valignment="top" width="0pt">
24904 <column alignment="center" valignment="top" width="0pt">
24905 <column alignment="center" valignment="top" width="0pt">
24907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24910 \begin_layout Plain Layout
24916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24919 \begin_layout Plain Layout
24925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24928 \begin_layout Plain Layout
24934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24937 \begin_layout Plain Layout
24945 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24948 \begin_layout Plain Layout
24956 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24959 \begin_layout Plain Layout
24967 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24970 \begin_layout Plain Layout
24978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24981 \begin_layout Plain Layout
24991 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24994 \begin_layout Plain Layout
25002 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25005 \begin_layout Plain Layout
25013 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25016 \begin_layout Plain Layout
25024 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25027 \begin_layout Plain Layout
25037 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25040 \begin_layout Plain Layout
25048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25051 \begin_layout Plain Layout
25059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25062 \begin_layout Plain Layout
25070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25073 \begin_layout Plain Layout
25083 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25086 \begin_layout Plain Layout
25094 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25097 \begin_layout Plain Layout
25105 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25108 \begin_layout Plain Layout
25116 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25119 \begin_layout Plain Layout
25129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25132 \begin_layout Plain Layout
25140 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25143 \begin_layout Plain Layout
25151 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25154 \begin_layout Plain Layout
25162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25165 \begin_layout Plain Layout
25175 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25178 \begin_layout Plain Layout
25186 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25189 \begin_layout Plain Layout
25197 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25200 \begin_layout Plain Layout
25208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25211 \begin_layout Plain Layout
25221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25224 \begin_layout Plain Layout
25232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25235 \begin_layout Plain Layout
25243 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25246 \begin_layout Plain Layout
25254 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25257 \begin_layout Plain Layout
25267 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25270 \begin_layout Plain Layout
25278 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25281 \begin_layout Plain Layout
25289 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25292 \begin_layout Plain Layout
25300 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25303 \begin_layout Plain Layout
25319 \begin_layout Standard
25320 They can also be inserted with the math toolbar button
25323 arg "math-insert \\functions"
25329 \begin_layout Subsection
25330 Self-defined Functions
25331 \begin_inset Index idx
25334 \begin_layout Plain Layout
25335 Functions ! self-defined
25343 \begin_layout Standard
25344 To use a function that is not predefined, like for example the sign function
25345 sgn(x), there are two possibilities:
25348 \begin_layout Itemize
25349 Define the function by inserting the following line to the \SpecialChar LaTeX
25354 \begin_layout Plain Layout
25359 DeclareMathOperator
25362 \begin_inset CommandInset ref
25364 reference "subsec:Self-defined-Operators"
25374 \begin_inset Newline newline
25378 \begin_inset VSpace -3mm
25382 \begin_inset Newline newline
25389 DeclareMathOperator{
25394 \begin_inset Index idx
25397 \begin_layout Plain Layout
25402 DeclareMathOperator
25408 \begin_inset Newline newline
25412 \begin_inset VSpace -2mm
25416 \begin_inset Newline newline
25419 Now the new defined function can be called with the command
25428 \begin_layout Itemize
25429 Write the formula as usual, mark the formula name, in our example the letters
25434 , and change it to mathematical text.
25435 Finally, a space is inserted between prefactor and function.
25438 \begin_layout Standard
25439 The result is the same with both methods as with a predefined function
25443 \begin_layout Plain Layout
25444 In \SpecialChar LyX
25445 self-defined functions are displayed red, predefined ones black.
25451 \begin_inset Separator parbreak
25457 \begin_layout Standard
25459 \begin_inset Tabular
25460 <lyxtabular version="3" rows="3" columns="2">
25461 <features booktabs="true" tabularvalignment="middle">
25462 <column alignment="center" valignment="top" width="0pt">
25463 <column alignment="center" valignment="top" width="0pt">
25465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25468 \begin_layout Plain Layout
25474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25477 \begin_layout Plain Layout
25485 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25488 \begin_layout Plain Layout
25496 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25499 \begin_layout Plain Layout
25500 \begin_inset Formula $A\sgn(x)+B$
25510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25513 \begin_layout Plain Layout
25517 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25528 \begin_layout Plain Layout
25529 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25545 \begin_layout Standard
25546 The first method is more suitable when the self-defined function should
25547 be used several times.
25550 \begin_layout Subsection
25552 \begin_inset Index idx
25555 \begin_layout Plain Layout
25564 \begin_layout Standard
25565 For limits, in addition to the commands
25572 \begin_inset Index idx
25575 \begin_layout Plain Layout
25595 the following functions are defined:
25596 \begin_inset Separator parbreak
25602 \begin_layout Standard
25604 \begin_inset Tabular
25605 <lyxtabular version="3" rows="5" columns="2">
25606 <features booktabs="true" tabularvalignment="middle">
25607 <column alignment="center" valignment="top" width="0pt">
25608 <column alignment="center" valignment="top" width="0pt">
25610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25613 \begin_layout Plain Layout
25619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25622 \begin_layout Plain Layout
25630 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25633 \begin_layout Plain Layout
25641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25644 \begin_layout Plain Layout
25645 \begin_inset Formula $\varliminf$
25654 <row topspace="1.5mm">
25655 <cell alignment="center" valignment="top" usebox="none">
25658 \begin_layout Plain Layout
25666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25669 \begin_layout Plain Layout
25670 \begin_inset Formula $\varlimsup$
25679 <row topspace="1.5mm">
25680 <cell alignment="center" valignment="top" usebox="none">
25683 \begin_layout Plain Layout
25691 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25694 \begin_layout Plain Layout
25695 \begin_inset Formula $\varprojlim$
25704 <row topspace="1.5mm" bottomspace="1mm">
25705 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25708 \begin_layout Plain Layout
25716 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25719 \begin_layout Plain Layout
25720 \begin_inset Formula $\varinjlim$
25736 \begin_layout Standard
25737 \begin_inset VSpace medskip
25740 The limit is created by inserting a subscript.
25741 It is set right beside the function in an inline formula:
25744 \begin_layout Standard
25746 \begin_inset Tabular
25747 <lyxtabular version="3" rows="2" columns="2">
25748 <features booktabs="true" tabularvalignment="middle">
25749 <column alignment="center" valignment="top" width="0pt">
25750 <column alignment="center" valignment="top" width="0pt">
25752 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25755 \begin_layout Plain Layout
25761 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25764 \begin_layout Plain Layout
25772 <cell alignment="center" valignment="top" usebox="none">
25775 \begin_layout Plain Layout
25781 \begin_inset space \textvisiblespace{}
25785 \begin_inset space \textvisiblespace{}
25793 <cell alignment="center" valignment="top" usebox="none">
25796 \begin_layout Plain Layout
25797 \begin_inset Formula $\lim_{x\to A}x=B$
25813 \begin_layout Standard
25814 In a displayed formula the limit is set below the formula, as usual:
25815 \begin_inset Formula
25825 \begin_layout Standard
25826 \begin_inset VSpace medskip
25832 \begin_layout Standard
25833 How to adjust the typesetting of the limits see
25834 \begin_inset CommandInset ref
25836 reference "subsec:Operator-Limits"
25843 \begin_layout Subsection
25845 \begin_inset Index idx
25848 \begin_layout Plain Layout
25849 Functions ! modulo-
25857 \begin_layout Standard
25858 The modulo-function is special, because it exists in four variants.
25859 The variants in a displayed formula are:
25860 \begin_inset Formula
25862 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25863 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25864 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25865 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25866 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25874 \begin_layout Standard
25875 In an inline formula less space is set before the function names for all
25877 By default the modulo-functions take only the first following character
25879 To use more than one character, one has to put them into \SpecialChar TeX
25881 \begin_inset Formula
25883 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25884 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25885 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25893 \begin_layout Section
25895 \begin_inset Index idx
25898 \begin_layout Plain Layout
25907 \begin_layout Standard
25908 The characters ^ and _ would normally create a superscript and subscript,
25910 To get these characters you have to insert them with a leading
25913 \begin_inset Separator parbreak
25919 \begin_layout Standard
25922 \begin_inset Tabular
25923 <lyxtabular version="3" rows="3" columns="2">
25924 <features booktabs="true" tabularvalignment="middle">
25925 <column alignment="left" valignment="top" width="0pt">
25926 <column alignment="block" valignment="top">
25928 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25931 \begin_layout Plain Layout
25937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25940 \begin_layout Plain Layout
25948 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25951 \begin_layout Plain Layout
25955 \begin_inset space \textvisiblespace{}
25963 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25966 \begin_layout Plain Layout
25967 \begin_inset Formula $\mathcircumflex$
25977 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25980 \begin_layout Plain Layout
25988 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25991 \begin_layout Plain Layout
25992 \begin_inset Formula $\_$
26008 \begin_layout Subsection
26009 Special Characters in Mathematical Text
26012 \begin_layout Standard
26013 The following commands can only be used in mathematical text or in \SpecialChar TeX
26017 \begin_layout Standard
26018 \begin_inset space \hfill{}
26022 \begin_inset Tabular
26023 <lyxtabular version="3" rows="8" columns="2">
26024 <features booktabs="true" tabularvalignment="middle">
26025 <column alignment="left" valignment="top" width="0pt">
26026 <column alignment="block" valignment="top">
26028 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26031 \begin_layout Plain Layout
26037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26040 \begin_layout Plain Layout
26048 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26051 \begin_layout Plain Layout
26059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26062 \begin_layout Plain Layout
26063 \begin_inset Formula $\textrm{œ}$
26073 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26076 \begin_layout Plain Layout
26084 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26087 \begin_layout Plain Layout
26088 \begin_inset Formula $\textrm{Œ}$
26098 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26101 \begin_layout Plain Layout
26109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26112 \begin_layout Plain Layout
26113 \begin_inset Formula $\textrm{æ}$
26123 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26126 \begin_layout Plain Layout
26134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26137 \begin_layout Plain Layout
26138 \begin_inset Formula $\textrm{Æ}$
26148 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26151 \begin_layout Plain Layout
26159 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26162 \begin_layout Plain Layout
26163 \begin_inset Formula $\textrm{\aa}$
26173 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26176 \begin_layout Plain Layout
26180 \begin_inset Index idx
26183 \begin_layout Plain Layout
26190 \begin_layout Plain Layout
26211 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26214 \begin_layout Plain Layout
26215 \begin_inset Formula $\textrm{Å}$
26225 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26228 \begin_layout Plain Layout
26236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26239 \begin_layout Plain Layout
26240 \begin_inset Formula $\textrm{ı}$
26254 \begin_inset space \hfill{}
26258 \begin_inset Tabular
26259 <lyxtabular version="3" rows="8" columns="2">
26260 <features booktabs="true" tabularvalignment="middle">
26261 <column alignment="left" valignment="top" width="0pt">
26262 <column alignment="center" valignment="top">
26264 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26267 \begin_layout Plain Layout
26269 \begin_inset Note Note
26272 \begin_layout Plain Layout
26274 \begin_inset space \thinspace{}
26277 mm is used for separation, because otherwise the output will be ¡ and ¿
26288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26291 \begin_layout Plain Layout
26299 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26302 \begin_layout Plain Layout
26310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26313 \begin_layout Plain Layout
26314 \begin_inset Formula $\textrm{ø}$
26324 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26327 \begin_layout Plain Layout
26335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26338 \begin_layout Plain Layout
26339 \begin_inset Formula $\textrm{Ø}$
26349 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26352 \begin_layout Plain Layout
26360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26363 \begin_layout Plain Layout
26364 \begin_inset Formula $\textrm{ł}$
26374 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26377 \begin_layout Plain Layout
26385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26388 \begin_layout Plain Layout
26389 \begin_inset Formula $\textrm{Ł}$
26399 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26402 \begin_layout Plain Layout
26404 \begin_inset space \hspace{}
26409 \begin_inset space \textvisiblespace{}
26417 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26420 \begin_layout Plain Layout
26421 \begin_inset Formula $\textrm{!`}$
26431 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26434 \begin_layout Plain Layout
26436 \begin_inset space \hspace{}
26441 \begin_inset space \textvisiblespace{}
26449 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26452 \begin_layout Plain Layout
26453 \begin_inset Formula $\textrm{?`}$
26463 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26466 \begin_layout Plain Layout
26474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26477 \begin_layout Plain Layout
26478 \begin_inset Formula $\textrm{ȷ}$
26492 \begin_inset space \hfill{}
26498 \begin_layout Standard
26500 \begin_inset Formula $\textrm{\textrm{Å}}$
26504 \begin_inset Formula $\textrm{\textrm{Ø}}$
26507 can also be inserted via the math toolbar button
26510 arg "math-insert \\digamma"
26516 \begin_layout Standard
26517 An exception are the commands
26520 \begin_inset space \hspace{}
26529 \begin_inset space \hspace{}
26535 , because they can be inserted in \SpecialChar LyX
26539 \begin_layout Subsection
26541 \begin_inset CommandInset label
26543 name "subsec:Accents-in-Text"
26548 \begin_inset Index idx
26551 \begin_layout Plain Layout
26560 \begin_layout Standard
26561 With the following commands all letters can be accented.
26562 The commands must be inserted in \SpecialChar TeX
26566 \begin_layout Standard
26567 \begin_inset space \hfill{}
26571 \begin_inset Tabular
26572 <lyxtabular version="3" rows="8" columns="2">
26573 <features booktabs="true" tabularvalignment="middle">
26574 <column alignment="left" valignment="top" width="0pt">
26575 <column alignment="block" valignment="top">
26577 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26580 \begin_layout Plain Layout
26586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26589 \begin_layout Plain Layout
26597 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26600 \begin_layout Plain Layout
26604 \begin_inset Quotes grd
26612 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26615 \begin_layout Plain Layout
26619 \begin_layout Plain Layout
26635 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26638 \begin_layout Plain Layout
26646 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26649 \begin_layout Plain Layout
26653 \begin_layout Plain Layout
26669 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26672 \begin_layout Plain Layout
26676 \begin_inset space \textvisiblespace{}
26684 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26687 \begin_layout Plain Layout
26691 \begin_layout Plain Layout
26707 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26710 \begin_layout Plain Layout
26718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26721 \begin_layout Plain Layout
26725 \begin_layout Plain Layout
26741 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26744 \begin_layout Plain Layout
26748 \begin_inset space \textvisiblespace{}
26756 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26759 \begin_layout Plain Layout
26763 \begin_layout Plain Layout
26779 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26782 \begin_layout Plain Layout
26786 \begin_inset space \textvisiblespace{}
26794 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26797 \begin_layout Plain Layout
26801 \begin_layout Plain Layout
26817 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26820 \begin_layout Plain Layout
26824 \begin_inset space \textvisiblespace{}
26832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26835 \begin_layout Plain Layout
26839 \begin_layout Plain Layout
26859 \begin_inset space \hfill{}
26863 \begin_inset Tabular
26864 <lyxtabular version="3" rows="8" columns="2">
26865 <features booktabs="true" tabularvalignment="middle">
26866 <column alignment="left" valignment="top" width="0pt">
26867 <column alignment="center" valignment="top">
26869 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26872 \begin_layout Plain Layout
26878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26881 \begin_layout Plain Layout
26889 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26892 \begin_layout Plain Layout
26896 \begin_inset space \textvisiblespace{}
26904 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26907 \begin_layout Plain Layout
26911 \begin_layout Plain Layout
26927 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26930 \begin_layout Plain Layout
26938 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26941 \begin_layout Plain Layout
26945 \begin_layout Plain Layout
26961 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26964 \begin_layout Plain Layout
26968 \begin_inset Index idx
26971 \begin_layout Plain Layout
26982 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26985 \begin_layout Plain Layout
26989 \begin_layout Plain Layout
27005 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27008 \begin_layout Plain Layout
27016 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27019 \begin_layout Plain Layout
27023 \begin_layout Plain Layout
27039 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27042 \begin_layout Plain Layout
27046 \begin_inset space \textvisiblespace{}
27054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27057 \begin_layout Plain Layout
27061 \begin_layout Plain Layout
27077 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27080 \begin_layout Plain Layout
27084 \begin_inset space \textvisiblespace{}
27092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27095 \begin_layout Plain Layout
27099 \begin_layout Plain Layout
27115 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27118 \begin_layout Plain Layout
27122 \begin_inset space \textvisiblespace{}
27130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27133 \begin_layout Plain Layout
27137 \begin_layout Plain Layout
27157 \begin_inset space \hfill{}
27163 \begin_layout Standard
27164 \begin_inset VSpace medskip
27173 also two different characters can be accented.
27179 \begin_inset space \textvisiblespace{}
27188 \begin_layout Plain Layout
27200 \begin_layout Standard
27213 can in combination with vowels directly be inserted with the keyboard without
27214 using \SpecialChar TeX
27216 The same applies for the tilde
27220 \begin_layout Plain Layout
27221 This only applies for keyboards where the tilde is defined as accent.
27230 in combination with
27245 \begin_layout Standard
27288 and accents that are inserted directly with the keyboard are also available
27289 in mathematical text.
27290 For the other accents there are special math commands to be used in formulas,
27292 \begin_inset CommandInset ref
27294 reference "subsec:Accents-for-one"
27301 \begin_layout Standard
27302 \begin_inset VSpace bigskip
27305 Furthermore, with the command
27312 \begin_inset Index idx
27315 \begin_layout Plain Layout
27323 all numbers and letters can be set into a circle, quasi accented with a
27324 circle, similar to the copyright symbol.
27327 \begin_layout Standard
27329 \begin_inset Tabular
27330 <lyxtabular version="3" rows="3" columns="2">
27331 <features booktabs="true" tabularvalignment="middle">
27332 <column alignment="center" valignment="top" width="0pt">
27333 <column alignment="center" valignment="top">
27335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27338 \begin_layout Plain Layout
27344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27347 \begin_layout Plain Layout
27355 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27358 \begin_layout Plain Layout
27366 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27369 \begin_layout Plain Layout
27373 \begin_layout Plain Layout
27388 <row topspace="1mm">
27389 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27392 \begin_layout Plain Layout
27403 raisebox{-1.5pt}{W}}
27408 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27411 \begin_layout Plain Layout
27415 \begin_layout Plain Layout
27445 \begin_layout Standard
27446 One has to take care that the character fits in the circle.
27457 \begin_layout Plain Layout
27459 \begin_inset CommandInset ref
27461 reference "subsec:Font-Sizes"
27470 specifies thereby the size of the circle.
27481 \begin_layout Plain Layout
27483 \begin_inset CommandInset ref
27485 reference "subsec:Boxes-without-Frame"
27494 the character can be centered.
27497 \begin_layout Subsection
27499 \begin_inset Index idx
27502 \begin_layout Plain Layout
27511 \begin_layout Standard
27512 Old-style figures (also known as old-style numerals) are created with the
27520 \begin_inset Index idx
27523 \begin_layout Plain Layout
27532 The command can be used in formulas and in \SpecialChar TeX
27534 The command scheme is:
27537 \begin_layout Standard
27542 oldstylenums{number}
27545 \begin_layout Standard
27550 oldstylenums{0123456789
27553 \begin_inset Formula $\oldstylenums{0123456789}$
27559 \begin_layout Section
27561 \begin_inset CommandInset label
27563 name "sec:Formula-Styles"
27568 \begin_inset Index idx
27571 \begin_layout Plain Layout
27580 \begin_layout Itemize
27581 There are two different alignment styles:
27582 \begin_inset Separator parbreak
27589 \begin_layout Description
27590 Centered is the predefined standard
27593 \begin_layout Description
27594 Indented for this the option
27598 must be inserted in the menu
27600 Document\SpecialChar menuseparator
27606 \begin_inset space ~
27612 \begin_layout Standard
27617 is used, the indentation can be adjusted with the length
27624 \begin_inset Index idx
27627 \begin_layout Plain Layout
27636 Should the distance be 15
27637 \begin_inset space \thinspace{}
27640 mm, the following command line is inserted in the \SpecialChar LaTeX
27644 \begin_layout Standard
27654 \begin_layout Standard
27655 When no length is specified, the predefined value of 30
27656 \begin_inset space \thinspace{}
27663 \begin_layout Itemize
27664 And two different numbering styles:
27665 \begin_inset Separator parbreak
27672 \begin_layout Description
27673 Right is the predefined standard
27676 \begin_layout Description
27677 Left for this the option
27681 must be inserted in the menu
27683 Document\SpecialChar menuseparator
27689 \begin_inset space ~
27696 \begin_layout Standard
27705 can also be used together.
27706 In this case both options are inserted, separated by a comma.
27709 \begin_layout Standard
27710 The chosen styles are used for all displayed formulas of the document.
27711 When both, centered and indented formulas should be created in a document,
27717 The indented formulas are then set in a flalign environment, see
27718 \begin_inset CommandInset ref
27720 reference "subsec:Flalign-Environment"
27727 \begin_layout Section
27729 \begin_inset CommandInset label
27731 name "sec:Multiline-Formulas"
27736 \begin_inset Index idx
27739 \begin_layout Plain Layout
27740 Formula ! multiline
27748 \begin_layout Subsection
27752 \begin_layout Standard
27753 In \SpecialChar LyX
27754 multiline formulas are created by pressing
27757 arg "newline-insert newline"
27762 \change_deleted 2047637253 1449850740
27763 This creates either an
27765 eqnarray environment
27767 that is described in
27768 \begin_inset CommandInset ref
27770 reference "subsec:Eqnarray-Environment"
27774 or, when the option
27776 Use AMS math package
27778 in the document settings is selected, an
27782 that is described in
27783 \begin_inset CommandInset ref
27785 reference "subsec:Standard-align-Environment"
27791 \change_inserted 2047637253 1449851860
27792 This creates either an
27796 that is described in
27797 \begin_inset CommandInset ref
27799 reference "subsec:Standard-align-Environment"
27803 or, when automatically loading the package
27807 is disabled in the document settings, an
27809 eqnarray environment
27811 that is described in
27812 \begin_inset CommandInset ref
27814 reference "subsec:Eqnarray-Environment"
27821 The align environment is recommended because it provides in any case a typograph
27822 ically correct output.
27825 \begin_layout Standard
27826 There are other multiline formula environments that can be created via the
27829 Insert\SpecialChar menuseparator
27833 These environments are described in the following sections.
27836 \begin_layout Standard
27837 In all multiline formula environments a new line is created by pressing
27841 arg "newline-insert newline"
27845 To add or delete lines, the math toolbar buttons
27848 arg "inset-modify tabular append-row"
27854 arg "inset-modify tabular delete-row"
27857 , respectively, or the menu
27859 Edit\SpecialChar menuseparator
27865 \begin_layout Subsubsection
27867 \begin_inset CommandInset label
27869 name "subsec:Line-Separation"
27874 \begin_inset Index idx
27877 \begin_layout Plain Layout
27878 Formula ! multiline ! Line separation
27886 \begin_layout Standard
27887 There is sometimes not enough space in multiline formulas between the lines:
27888 \begin_inset Formula
27890 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}\\
27891 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
27899 \begin_layout Standard
27900 In \SpecialChar LaTeX
27901 additional line space is specified as optional argument of the new line
27903 This is not yet possible in \SpecialChar LyX
27908 \begin_layout Plain Layout
27910 \begin_inset CommandInset href
27912 name "LyX-bug #1505"
27913 target "http://www.lyx.org/trac/ticket/1505"
27922 , therefore the whole formula must be inserted in \SpecialChar TeX
27924 To add in our example space, the command
27932 is inserted at the end of the first line.
27937 \begin_layout Plain Layout
27944 \begin_layout Plain Layout
27946 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27949 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27956 \begin_layout Plain Layout
27960 left(B^{2}+x_{0}^{2}
27968 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27973 \begin_layout Plain Layout
27985 \begin_layout Standard
27986 \begin_inset VSpace bigskip
27989 To set the line separation for all lines in a formula, the length
27996 \begin_inset Index idx
27999 \begin_layout Plain Layout
28009 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28020 \begin_inset space \thinspace{}
28025 \begin_inset space \thinspace{}
28028 mm additional line separation as in the previous example, the command
28031 \begin_layout Standard
28041 \begin_layout Standard
28042 is inserted in \SpecialChar TeX
28043 mode before the formula.
28044 This requires that the \SpecialChar LaTeX
28053 \begin_layout Plain Layout
28058 is part of every \SpecialChar LaTeX
28059 standard installation.
28065 \begin_inset Index idx
28068 \begin_layout Plain Layout
28074 was loaded in \SpecialChar LaTeX
28075 -preamble with the line
28078 \begin_layout Standard
28086 \begin_layout Standard
28091 \begin_layout Plain Layout
28103 \begin_inset Formula
28105 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}\\
28106 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
28114 \begin_layout Standard
28118 \begin_layout Plain Layout
28129 To get back to the predefined distance,
28135 is set to the value 3
28136 \begin_inset space \thinspace{}
28142 \begin_layout Subsubsection
28144 \begin_inset CommandInset label
28146 name "subsec:Column-Separation"
28151 \begin_inset Index idx
28154 \begin_layout Plain Layout
28155 Formula ! multiline ! Column separation
28163 \begin_layout Standard
28164 Multiline formulas form a matrix.
28165 A formula in the eqnarray environment is for example a matrix with three
28167 By changing the column separation in this environment, the space beside
28168 the relation sign can be changed.
28171 \begin_layout Standard
28172 The column separation is specified with the length
28179 \begin_inset Index idx
28182 \begin_layout Plain Layout
28191 \begin_inset Newline newline
28194 column separation = 2
28195 \begin_inset space \thinspace{}
28205 \begin_inset Newline newline
28211 \begin_layout Standard
28221 \begin_layout Standard
28222 inserted in \SpecialChar TeX
28223 mode, sets for all following formulas a column separation of
28225 \begin_inset space \thinspace{}
28229 To get back to the predefined distance,
28236 \begin_inset space \thinspace{}
28242 \begin_layout Standard
28244 \begin_inset space \thinspace{}
28247 cm column separation:
28251 \begin_layout Plain Layout
28263 \begin_inset Formula
28271 A formula with the predefined column separation for matrices of 10
28272 \begin_inset space \thinspace{}
28279 \begin_layout Plain Layout
28291 \begin_inset Formula
28302 \begin_layout Subsubsection
28304 \begin_inset Index idx
28307 \begin_layout Plain Layout
28316 \begin_layout Standard
28317 Long formulas can be typeset using these methods:
28320 \begin_layout Itemize
28321 When one side of the equation is much shorter than the line width, this
28322 one is chosen for the left side and the right side is typeset over two
28324 \begin_inset Formula
28326 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 \\
28327 & & -\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}
28332 The minus sign at the beginning of the second line does normally not appear
28333 as an operator because it is the first character of the line.
28334 Thus it would not be surrounded by space and could not be distinguished
28335 from the fraction bar.
28337 \begin_inset space \thinspace{}
28340 pt space was inserted behind the minus sign with the command
28350 \begin_layout Plain Layout
28358 \begin_inset CommandInset ref
28360 reference "subsec:Variable-Space"
28370 \begin_inset Index idx
28373 \begin_layout Plain Layout
28384 \begin_layout Itemize
28385 When both sides of the equation are too long, the command
28392 \begin_inset Index idx
28395 \begin_layout Plain Layout
28404 It is inserted in the first column of the first line and causes all further
28405 insertions to overwrite the following columns:
28406 \begin_inset Formula
28408 \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 \\
28409 & & -\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 \\
28410 & & =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}
28415 After the insertion of
28421 , the cursor is in a purple box that is a bit shifted to the left from the
28423 In this the formula is inserted.
28424 \begin_inset Newline newline
28427 The content of the further lines is inserted to the second or another formula
28429 The greater the column number where it was inserted, the larger the indentation.
28430 \begin_inset VSpace medskip
28434 \begin_inset Newline newline
28438 \begin_inset Note Greyedout
28441 \begin_layout Plain Layout
28442 Note the following when using
28451 \begin_layout Itemize
28452 The formula doesn't use the full page width.
28454 \begin_inset space \thinspace{}
28458 \begin_inset space \space{}
28462 \begin_inset Formula $-B^{2}$
28465 is added to the first line in the above example, it would have been outside
28467 To better use the width, negative space can be inserted at the beginning
28471 \begin_layout Itemize
28472 Due to a bug in \SpecialChar LyX
28473 the cursor cannot be set with the mouse into the first
28478 \begin_layout Plain Layout
28479 \begin_inset CommandInset href
28481 name "LyX-bug #1429"
28482 target "http://www.lyx.org/trac/ticket/1429"
28491 One can only set the cursor at the beginning of the line and move it with
28500 \begin_layout Itemize
28501 Other methods to set long formulas are offered by the environments described
28503 \begin_inset CommandInset ref
28505 reference "subsec:Multline-Environment"
28510 \begin_inset CommandInset ref
28512 reference "subsec:Multiline-Formula-Parts"
28519 \begin_layout Subsubsection
28520 Multiline Fractions
28521 \begin_inset CommandInset label
28523 name "subsec:Multiline-Fractions"
28528 \begin_inset Index idx
28531 \begin_layout Plain Layout
28532 Fractions ! multiline
28540 \begin_layout Standard
28541 There are cases where the denominator and/or the numerator of a fraction
28542 is so long that the fraction does not fit into one line.
28543 It is then necessary to add a line break within the fraction.
28544 This can be done using the command
28551 \begin_inset Index idx
28554 \begin_layout Plain Layout
28563 To activate it, set in the document settings under
28566 \begin_inset space ~
28576 \begin_inset Index idx
28579 \begin_layout Plain Layout
28580 Packages ! mathtools
28588 \begin_inset space ~
28603 \begin_layout Standard
28608 splitfrac{first line}{second line}
28611 \begin_layout Standard
28612 and is used as denominator and/or numerator:
28615 \begin_layout Standard
28616 \begin_inset Formula
28618 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}
28623 The command for the first numerator above is:
28626 \begin_layout Standard
28631 splitfrac{xy+xy+xy+xy+xy
28632 \begin_inset space \textvisiblespace{}
28640 \begin_layout Subsubsection
28642 \begin_inset CommandInset label
28644 name "subsec:Multiline-Brackets"
28649 \begin_inset Index idx
28652 \begin_layout Plain Layout
28653 Brackets ! for multiline expressions
28661 \begin_layout Standard
28662 For brackets spanning multiple lines the following problem occurs:
28663 \begin_inset Formula
28665 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28666 & & \left.\cdots+B-D\right]
28674 \begin_layout Standard
28675 The closing bracket is smaller than the opening bracket because brackets
28676 with variable size may not span multiple lines.
28679 \begin_layout Standard
28680 To set the bracket size for the second line correctly, the first line is
28688 \begin_inset Index idx
28691 \begin_layout Plain Layout
28699 and the second line with
28707 \begin_layout Plain Layout
28721 \begin_inset CommandInset ref
28723 reference "subsec:Automatic-Bracket-Size"
28735 \begin_inset Index idx
28738 \begin_layout Plain Layout
28761 \begin_inset space \textvisiblespace{}
28771 \begin_inset space \textvisiblespace{}
28781 \begin_inset space \textvisiblespace{}
28787 \begin_inset Formula $\downarrow$
28793 \begin_inset Index idx
28796 \begin_layout Plain Layout
28804 is inserted, because the multiplication operator with its limits is the
28805 largest symbol in the first line and this should be the size for the bracket
28806 in the second line.
28809 \begin_layout Standard
28810 The result is this:
28811 \begin_inset Formula
28813 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28814 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28822 \begin_layout Subsection
28826 \begin_layout Standard
28827 Align environments can be used for every kind of multiline formulas.
28828 They are especially useful to set several formulas side by side.
28831 \begin_layout Standard
28832 Align environments consist of columns.
28833 The odd columns are right aligned, the even ones left aligned.
28834 Every line in an Align environment can be numbered.
28837 \begin_layout Standard
28838 Align environments are created via the menu
28840 Insert\SpecialChar menuseparator
28846 Edit\SpecialChar menuseparator
28847 Math\SpecialChar menuseparator
28848 Change Formula Type
28850 already existing formulas can be converted to Align environments.
28853 \begin_layout Standard
28854 To add or delete columns, the math toolbar buttons
28857 arg "inset-modify tabular append-column"
28863 arg "inset-modify tabular delete-column"
28866 , respectively, or the menu
28868 Edit\SpecialChar menuseparator
28874 \begin_layout Subsubsection
28875 Standard align Environment
28876 \begin_inset CommandInset label
28878 name "subsec:Standard-align-Environment"
28883 \begin_inset Index idx
28886 \begin_layout Plain Layout
28887 Formula ! multiline ! align environment
28895 \begin_layout Standard
28896 This Align environment is created by pressing
28899 arg "newline-insert newline"
28902 in a formula or by the menu
28904 Insert\SpecialChar menuseparator
28905 Math\SpecialChar menuseparator
28906 AMS align Environment
28911 \begin_layout Standard
28912 An example for two formulas set side by side, that are created with a four
28913 column align environment:
28914 \begin_inset Formula
28916 A & =\sin(B) & C & =D\\
28917 C & \ne A & B & \ne D
28922 As it can be seen, the formulas in this environment are placed so as if
28931 \begin_layout Plain Layout
28939 \begin_inset CommandInset ref
28941 reference "subsec:Variable-Space"
28952 before the first and after every even column.
28953 When the formula style
28959 \begin_layout Plain Layout
28961 \begin_inset CommandInset ref
28963 reference "sec:Formula-Styles"
28974 is used, the formula is set without the
28980 before the first column.
28983 \begin_layout Subsubsection
28984 Alignat Environment
28985 \begin_inset Index idx
28988 \begin_layout Plain Layout
28989 Formula ! multiline ! alignat environment
28997 \begin_layout Standard
28998 The alignat environment has no predefined column separation.
28999 It can be inserted manually with the spaces that are described
29000 \begin_inset CommandInset ref
29002 reference "subsec:Space"
29009 \begin_layout Standard
29010 The above example in the alignat environment where 1
29011 \begin_inset space \thinspace{}
29014 cm space was inserted at the beginning of the second formula:
29015 \begin_inset Formula
29016 \begin{alignat*}{2}
29017 A & =\sin(B) & \hspace{1cm}C & =D\\
29018 C & \ne A & B & \ne D
29023 Because the column separation can be set separately for every column, this
29024 environment is especially suitable to set three and more formulas side
29028 \begin_layout Subsubsection
29029 Flalign Environment
29030 \begin_inset CommandInset label
29032 name "subsec:Flalign-Environment"
29037 \begin_inset Index idx
29040 \begin_layout Plain Layout
29041 Formula ! multiline ! flalign environment
29049 \begin_layout Standard
29050 In this environment the first two columns are always set as much as possible
29051 to the left and the last two ones to the right.
29053 \begin_inset Formula
29055 A & =1 & B & =2 & C & =3\\
29056 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29064 \begin_layout Standard
29065 By creating a flalign environment with an odd number of columns where an
29066 empty \SpecialChar TeX
29067 brace is inserted to the last column, several formulas in a document
29068 can be set to the left, although the formula style
29073 As example the indented formula
29074 \begin_inset CommandInset ref
29076 reference "eq:VolInt"
29081 \begin_inset Formula
29083 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29088 The first two columns contain the formula.
29089 To indent it as with the formula style
29094 \begin_inset space \thinspace{}
29097 pt space was inserted at the beginning of the first column.
29100 \begin_layout Subsection
29101 Eqnarray Environment
29102 \begin_inset CommandInset label
29104 name "subsec:Eqnarray-Environment"
29109 \begin_inset Index idx
29112 \begin_layout Plain Layout
29113 Formula ! multiline ! eqnarray environment
29121 \begin_layout Standard
29122 When this environment has been created, three blue boxes appear.
29123 The content of the first box is right aligned, the content of the last
29125 The content of the middle box appears centered and a bit smaller, because
29126 it is designed to insert there only relation characters.
29127 \begin_inset Formula
29129 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29139 \begin_layout Subsection
29141 \begin_inset Index idx
29144 \begin_layout Plain Layout
29145 Formula ! multiline ! gather environment
29153 \begin_layout Standard
29154 This environment consists of only one centered column.
29155 Every line can be numbered.
29156 \begin_inset Formula
29167 \begin_layout Subsection
29168 Multline Environment
29169 \begin_inset CommandInset label
29171 name "subsec:Multline-Environment"
29176 \begin_inset Index idx
29179 \begin_layout Plain Layout
29180 Formula ! multiline ! multline environment
29188 \begin_layout Standard
29189 The multline environment consists, like the gather environment, of only
29191 But the first line is left aligned, the last one right aligned.
29192 All other lines are centered.
29193 Therefore this environment is suitable for long formulas.
29195 \begin_inset CommandInset ref
29197 reference "eq:lefteqn"
29201 in the multline environment:
29202 \begin_inset Formula
29204 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}\\
29205 -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}\\
29206 =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}}
29214 \begin_layout Standard
29215 In the output only the last (first) line of a multline environment appears
29216 numbered when the document numbering is right (left).
29220 \begin_layout Plain Layout
29221 numbering styles see
29222 \begin_inset CommandInset ref
29224 reference "sec:Formula-Styles"
29236 \begin_layout Standard
29244 \begin_inset Index idx
29247 \begin_layout Plain Layout
29262 \begin_inset Index idx
29265 \begin_layout Plain Layout
29273 a centered line can be right or left aligned, respectively.
29274 The commands are used as follows:
29277 \begin_layout Standard
29282 shoveright{line content}
29288 shoveleft{line content}
29291 \begin_layout Standard
29292 \begin_inset VSpace medskip
29302 \begin_inset Index idx
29305 \begin_layout Plain Layout
29313 specifies the distance of the first line from the left page margin.
29314 Predefined is the length 0
29315 \begin_inset space \thinspace{}
29321 \begin_layout Standard
29322 As example the above formula where the command
29325 \begin_layout Standard
29335 \begin_layout Standard
29336 was inserted in \SpecialChar TeX
29341 \begin_layout Plain Layout
29353 \begin_inset Formula
29355 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}\\
29356 \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}}\\
29357 =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}}
29366 \begin_layout Plain Layout
29377 The second line was left aligned using
29386 \begin_layout Subsection
29387 Multiline Formula Parts
29388 \begin_inset CommandInset label
29390 name "subsec:Multiline-Formula-Parts"
29395 \begin_inset Index idx
29398 \begin_layout Plain Layout
29399 Formula ! multiline ! formula parts
29407 \begin_layout Standard
29408 To display only parts of a formula with multiple lines, one of the following
29409 environments is used:
29426 They can be inserted via the menu
29428 Insert\SpecialChar menuseparator
29431 or by using the commands described in this section.
29434 \begin_layout Standard
29435 The first three have the same properties as the corresponding multiline
29436 formula environments, but it is possible to set further formula parts beside
29439 \begin_inset Formula
29441 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29442 \Delta E\Delta t & \ge\frac{\hbar}{2}
29444 \right\} \textrm{Uncertainty relations}
29452 \begin_layout Standard
29453 To get this formula, a displayed formula is created where the command
29460 \begin_inset Index idx
29463 \begin_layout Plain Layout
29472 A purple box appears around the blue formula box where now columns and
29473 lines can be added.
29474 Outside the multiline environment other formula parts can be set, like
29478 \begin_layout Standard
29479 The aligned environment is also suitable for long formulas whose lines are
29480 horizontally aligned.
29481 Using aligned in a displayed formula has the advantage that the formula
29482 number is vertically centered behind the lines.
29484 \begin_inset CommandInset ref
29486 reference "eq:shortlong"
29490 in the aligned environment:
29491 \begin_inset Formula
29493 \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}|}\\
29494 & -\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}|}
29503 \begin_layout Standard
29504 To use the environments
29523 \begin_inset Index idx
29526 \begin_layout Plain Layout
29541 \begin_inset Index idx
29544 \begin_layout Plain Layout
29559 \begin_inset Index idx
29562 \begin_layout Plain Layout
29570 are inserted, respectively.
29571 The split environment has the same properties as the aligned environment
29572 but it can only have two columns.
29575 \begin_layout Subsection
29576 Text in multiline Formulas
29577 \begin_inset CommandInset label
29579 name "subsec:Text-in-multiline"
29584 \begin_inset Index idx
29587 \begin_layout Plain Layout
29594 \begin_inset Index idx
29597 \begin_layout Plain Layout
29598 Formula ! multiline ! text
29606 \begin_layout Standard
29607 In the Align environments, and the multline and gather environment, text
29608 can be inserted that will appear in a separate line and doesn't affect
29609 the column alignment.
29610 To do this, the command
29617 \begin_inset Index idx
29620 \begin_layout Plain Layout
29628 is used in the following scheme:
29631 \begin_layout Standard
29639 \begin_layout Standard
29640 The text should not be longer than a line because it cannot be hyphenated.
29641 As \SpecialChar LyX
29642 doesn't yet support
29648 directly, the text is written as mathematical text.
29655 must hereby be at the beginning of a line and appears in the output above
29657 An example where the text was inserted at the beginning of the second line:
29658 \begin_inset Formula
29660 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29661 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29669 \begin_layout Standard
29676 always creates some vertical space between the text and the formula lines.
29677 To avoid this space, set in the document settings under
29680 \begin_inset space ~
29690 \begin_inset Index idx
29693 \begin_layout Plain Layout
29694 Packages ! mathtools
29702 \begin_inset space ~
29708 Then you can use the command
29715 \begin_inset Index idx
29718 \begin_layout Plain Layout
29735 \begin_layout Standard
29736 \begin_inset Formula
29738 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29739 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29747 \begin_layout Section
29749 \begin_inset Index idx
29752 \begin_layout Plain Layout
29759 \begin_inset Index idx
29762 \begin_layout Plain Layout
29763 Formula ! numbering|see
29767 \begin_layout Plain Layout
29778 \begin_layout Plain Layout
29793 \begin_layout Subsection
29797 \begin_layout Standard
29798 Numbered formulas can be created with the menu
29800 Insert\SpecialChar menuseparator
29801 Math\SpecialChar menuseparator
29803 \begin_inset space ~
29811 \begin_inset space ~
29817 Existing formulas can be numbered with the menu
29819 Edit\SpecialChar menuseparator
29820 Math\SpecialChar menuseparator
29822 \begin_inset space ~
29830 arg "math-number-toggle"
29834 The formula number is displayed in \SpecialChar LyX
29835 behind the formula as a number sign
29837 The number sign is replaced in the output by the formula number.
29840 \begin_layout Standard
29841 When numbering is turned on in multiline formulas, all lines will be numbered.
29842 But the numbering can be controlled with the menu
29844 Edit\SpecialChar menuseparator
29845 Math\SpecialChar menuseparator
29847 \begin_inset space ~
29851 \begin_inset space ~
29855 \begin_inset space ~
29863 arg "math-number-line-toggle"
29869 \begin_layout Standard
29870 Except for inline formulas, all formulas can be numbered with two different
29872 \begin_inset CommandInset ref
29874 reference "sec:Formula-Styles"
29881 \begin_layout Subsection
29883 \begin_inset Index idx
29886 \begin_layout Plain Layout
29887 Cross-references ! to formulas
29895 \begin_layout Standard
29896 All labeled formulas can be cross-referenced.
29897 A label is added by the menu
29899 Insert\SpecialChar menuseparator
29902 or the toolbar button
29909 The cursor must hereby be inside a displayed formula.
29910 Alternatively you can right-click on the formula and choose
29915 A dialog pops up displaying the prefix
29920 The label is inserted there behind the prefix.
29921 The predefined prefix means
29922 \begin_inset Quotes eld
29926 \begin_inset Quotes erd
29929 and makes it easier to find labels in large documents because it marks
29930 it as formula label to divide it from e.
29931 \begin_inset space \thinspace{}
29935 \begin_inset space \space{}
29939 To change a label, the menu
29941 Insert\SpecialChar menuseparator
29944 is used again or you right-click on a formula and then on
29951 \begin_layout Standard
29952 The name of the label is displayed in \SpecialChar LyX
29953 within two parentheses behind formula.
29954 A formula with a label is always numbered.
29957 \begin_layout Standard
29958 Cross-references are inserted via the menu
29960 Insert\SpecialChar menuseparator
29963 or with the toolbar button
29966 arg "dialog-show-new-inset ref"
29970 A formula cross-reference appears in the output as formula number.
29971 When in the cross-reference dialog window the format
29975 is chosen, the cross-reference appears in the output as formula number
29977 \begin_inset Newline newline
29980 By right-clicking on a cross-reference in \SpecialChar LyX
29981 , one jumps to the formula that
29985 \begin_layout Standard
29986 Here are as examples cross-references to formulas of the following subsections:
29987 \begin_inset Note Note
29990 \begin_layout Plain Layout
29991 Note the different cross-reference types.
29999 \begin_layout Standard
30001 \begin_inset CommandInset ref
30008 \begin_inset CommandInset ref
30016 \begin_inset CommandInset ref
30022 ) big Latin letters are used for the numbering in contrary to (
30023 \begin_inset CommandInset ref
30032 \begin_layout Standard
30033 \begin_inset VSpace medskip
30036 When the argument of
30044 \begin_layout Plain Layout
30052 \begin_inset CommandInset ref
30054 reference "subsec:User-defined-Numbering"
30065 contains a box like in
30066 \begin_inset CommandInset ref
30068 reference "subsec:Paragraph-Boxes"
30072 , the formula cannot be referenced.
30075 \begin_layout Subsection
30077 \begin_inset Index idx
30080 \begin_layout Plain Layout
30081 Formula numbering ! subnumbering
30089 \begin_layout Standard
30090 With the help of the commands
30094 begin{subequations}
30102 formulas can be subnumbered.
30103 Both commands are inserted in \SpecialChar TeX
30107 \begin_layout Standard
30109 \begin_inset Formula
30120 \begin_layout Plain Layout
30124 addtocounter{equation}{-1}
30133 \begin_layout Plain Layout
30137 begin{subequations}
30143 \begin_inset VSpace -5mm
30147 \begin_inset Formula
30155 \begin_inset Formula
30165 \begin_layout Standard
30169 \begin_layout Plain Layout
30181 \begin_layout Standard
30182 To create the example, the following is done:
30185 \begin_layout Enumerate
30186 first formula is inserted
30189 \begin_layout Enumerate
30194 addtocounter{equation}{-1}
30196 begin{subequations}
30197 \begin_inset Index idx
30200 \begin_layout Plain Layout
30209 \begin_inset Newline newline
30214 is inserted after the first formula
30217 \begin_layout Enumerate
30218 second formula is inserted
30221 \begin_layout Enumerate
30222 third formula is inserted
30225 \begin_layout Enumerate
30232 is inserted after the third formula
30235 \begin_layout Standard
30236 Every formula between the commands
30248 is subnumbered as a, b,
30249 \begin_inset Newline linebreak
30252 c, \SpecialChar ldots
30253 For multiline formulas every line will be subnumbered.
30254 All subnumbered formulas are treated as
30259 But as every numbered formula increases the counter
30263 by one, the command
30269 is needed to decrease it.
30270 Otherwise the formulas
30271 \begin_inset CommandInset ref
30278 \begin_inset CommandInset ref
30285 \begin_inset CommandInset ref
30291 would be numbered as
30292 \begin_inset CommandInset ref
30299 \begin_inset CommandInset ref
30306 \begin_inset CommandInset ref
30315 \begin_layout Standard
30316 By inserting the commands in \SpecialChar TeX
30317 mode, a space is created between the first
30320 \begin_inset space \thinspace{}
30323 mm vertical space is inserted after the command
30327 begin{subequations}
30330 When the formula style
30336 \begin_layout Plain Layout
30338 \begin_inset CommandInset ref
30340 reference "sec:Formula-Styles"
30352 \begin_inset space \thinspace{}
30355 mm space is inserted instead.
30358 \begin_layout Standard
30359 Here is an example for a multiline formula where the numbering was turned
30360 off for the second line:
30364 \begin_layout Plain Layout
30368 begin{subequations}
30374 \begin_inset Formula
30376 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30377 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30378 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30387 \begin_layout Plain Layout
30399 \begin_layout Subsection
30400 User-defined Numbering
30401 \begin_inset CommandInset label
30403 name "subsec:User-defined-Numbering"
30408 \begin_inset Index idx
30411 \begin_layout Plain Layout
30412 Formula numbering ! user-defined
30420 \begin_layout Standard
30421 \begin_inset Index idx
30424 \begin_layout Plain Layout
30425 Formula numbering ! self-defined delimiters
30430 With the standard numbering parentheses are set around the formula number.
30431 To replace the parentheses for example by vertical bars, the following
30432 line is added to the \SpecialChar LaTeX
30436 \begin_layout Standard
30448 \begin_inset Note Note
30451 \begin_layout Plain Layout
30452 This macro is already declared in the \SpecialChar LaTeX
30453 -preamble for testing.
30454 To activate it, remove the percent sign at the beginning.
30462 \begin_layout Standard
30463 To use other characters, the vertical bars besides the
30467 are replaced by one ore more characters.
30468 To get only the formula number the vertical bars are omitted.
30471 \begin_layout Standard
30472 \begin_inset VSpace bigskip
30475 When there should be an expression of your choice instead of the consecutive
30476 formula number in parentheses behind the formula, the command
30483 \begin_inset Index idx
30486 \begin_layout Plain Layout
30495 \begin_inset Formula
30497 A+B=C\tag{something}\label{eq:tag}
30502 In this example the command
30507 \begin_inset space \textvisiblespace{}
30512 was inserted in the formula.
30515 \begin_layout Standard
30521 \begin_inset space \textvisiblespace{}
30526 is inserted instead, the star prevents the parentheses around the expression:
30527 \begin_inset Formula
30529 A+B=C\tag*{something}
30537 \begin_layout Standard
30538 \begin_inset VSpace bigskip
30541 To restart the formula numbering with new document parts or sections, the
30542 following command is used:
30545 \begin_layout Standard
30550 @addtoreset{equation}{part}
30553 \begin_inset Index idx
30556 \begin_layout Plain Layout
30561 \begin_layout Plain Layout
30572 \begin_layout Plain Layout
30585 \begin_layout Plain Layout
30596 \begin_layout Plain Layout
30609 \begin_inset Newline newline
30613 \begin_inset Newline newline
30620 @addtoreset{equation}{section}
30623 \begin_layout Standard
30624 To be able to use these commands in \SpecialChar TeX
30626 \begin_inset Quotes eld
30630 \begin_inset Quotes erd
30633 character has to be made
30634 \begin_inset Quotes eld
30638 \begin_inset Quotes erd
30641 for \SpecialChar LaTeX
30656 So the command sequence in \SpecialChar TeX
30660 \begin_layout Standard
30666 \begin_inset Newline newline
30671 @addtoreset{equation}{section}
30672 \begin_inset Newline newline
30680 \begin_layout Standard
30681 In the \SpecialChar LaTeX
30694 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30698 \begin_layout Standard
30713 \begin_layout Plain Layout
30718 is part of the \SpecialChar LaTeX
30724 \begin_inset Index idx
30727 \begin_layout Plain Layout
30728 Packages ! carlisle
30733 that is part of every \SpecialChar LaTeX
30734 standard installation.
30740 \begin_inset Index idx
30743 \begin_layout Plain Layout
30744 Packages ! remreset
30749 has to be loaded in the \SpecialChar LaTeX
30750 -preamble with the line
30753 \begin_layout Standard
30758 usepackage{remreset}
30761 \begin_layout Standard
30769 \begin_inset Index idx
30772 \begin_layout Plain Layout
30777 \begin_layout Plain Layout
30788 \begin_layout Plain Layout
30801 \begin_layout Plain Layout
30812 \begin_layout Plain Layout
30824 can be used with the same scheme as
30833 \begin_layout Standard
30834 \begin_inset VSpace bigskip
30837 Sometimes formulas should be numbered in the following form:
30840 \begin_layout Standard
30843 (section number.formula number)
30846 \begin_layout Standard
30847 The formula number should start with every section with
30848 \begin_inset Quotes eld
30852 \begin_inset Quotes erd
30858 \begin_layout Standard
30859 For this case there is the command
30866 \begin_inset Index idx
30869 \begin_layout Plain Layout
30877 , which is used with the following scheme:
30880 \begin_layout Standard
30885 numberwithin{counter}{sectioning}
30888 \begin_layout Standard
30889 Counter denotes what kind of numbering is affected, sectioning denotes what
30890 number is before the dot.
30893 \begin_layout Standard
30894 Thus in our case the following \SpecialChar LaTeX
30895 preamble or \SpecialChar TeX
30899 \begin_layout Standard
30904 numberwithin{equation}{section}
30907 \begin_layout Standard
30908 This is the result:
30912 \begin_layout Plain Layout
30916 numberwithin{equation}{section}
30922 \begin_inset Formula
30932 \begin_layout Standard
30934 \begin_inset space \thinspace{}
30938 \begin_inset space \space{}
30941 tables so that the number of the part is the sectioning,
30942 \begin_inset Newline newline
30949 numberwithin{table}{part}
30954 \begin_layout Standard
30955 To go back to the standard numbering or to prevent this kind of numbering
30956 when it is defined by the document class, the following command is inserted
30957 as \SpecialChar TeX
30958 code or to the \SpecialChar LaTeX
30962 \begin_layout Standard
30972 \begin_inset Index idx
30975 \begin_layout Plain Layout
30989 \begin_layout Plain Layout
31005 \begin_inset Newline newline
31013 \begin_inset Newline newline
31025 \begin_layout Standard
31032 uses internally the command
31038 , described above, that also needs to be reverted.
31042 \begin_layout Plain Layout
31049 \begin_layout Plain Layout
31053 @removefromreset{equation}{section}
31056 \begin_layout Plain Layout
31068 \begin_layout Subsection
31069 Numbering with Roman Numbers and Letters
31070 \begin_inset Index idx
31073 \begin_layout Plain Layout
31074 Formula numbering ! with letters
31080 \begin_inset Index idx
31083 \begin_layout Plain Layout
31084 Formula numbering ! with Roman numbers
31092 \begin_layout Standard
31093 Formulas can also be numbered with Roman numbers and Latin letters.
31094 To number for example with small Roman numbers, the command
31097 \begin_layout Standard
31109 \begin_layout Standard
31110 is inserted before the formula in \SpecialChar TeX
31119 \begin_inset Index idx
31122 \begin_layout Plain Layout
31130 redefines the predefined command
31146 \begin_layout Plain Layout
31153 has the same scheme like the command
31159 that is described in
31160 \begin_inset CommandInset ref
31162 reference "subsec:The-Command-newcommand"
31175 is the formula counter.
31182 is used as prefix for a counter, the value of the counter is output as
31184 When a formula is numbered, \SpecialChar LaTeX
31185 sets internally the command
31191 behind the formula.
31197 \begin_inset Index idx
31200 \begin_layout Plain Layout
31210 outputs the counter as small Roman number.
31213 \begin_layout Standard
31214 All formulas behind the command
31224 are now numbered Roman.
31225 To switch to numbering with big Roman numbers, the command is inserted
31239 \begin_inset Index idx
31242 \begin_layout Plain Layout
31254 \begin_inset Quotes eld
31258 \begin_inset Quotes erd
31261 with small Latin letters there is the command
31268 \begin_inset Index idx
31271 \begin_layout Plain Layout
31279 , for big ones there is the command
31286 \begin_inset Index idx
31289 \begin_layout Plain Layout
31302 \begin_layout Standard
31303 \begin_inset Note Greyedout
31306 \begin_layout Plain Layout
31313 \begin_inset space ~
31316 formulas can be numbered with Latin letters in one document.
31324 \begin_layout Standard
31328 \begin_layout Plain Layout
31344 \begin_layout Standard
31345 \begin_inset Formula
31347 A=\textrm{small roman}
31356 \begin_layout Plain Layout
31370 \begin_inset Formula
31372 B=\textrm{big Roman}\label{eq:Rom}
31381 \begin_layout Plain Layout
31395 \begin_inset Formula
31397 C=\textrm{small Latin}
31406 \begin_layout Plain Layout
31420 \begin_inset Formula
31422 D=\textrm{big Latin}\label{eq:Lat}
31430 \begin_layout Standard
31431 To switch back to the default numbering, insert the command:
31434 \begin_layout Standard
31444 \begin_inset Index idx
31447 \begin_layout Plain Layout
31458 \begin_layout Standard
31462 \begin_layout Plain Layout
31476 \begin_inset Formula
31486 \begin_layout Standard
31487 \begin_inset VSpace medskip
31490 As you see, formulas are numbered serially independent from the numbering
31492 When then numbering should start with
31493 \begin_inset Quotes eld
31497 \begin_inset Quotes erd
31500 when the style is changed, new equation counters have to be defined.
31501 A description about this can be found in the file
31502 \begin_inset CommandInset href
31504 name "Formula-numbering.lyx"
31505 target "run:Formula-numbering.lyx"
31512 \begin_layout Section
31513 Chemical Symbols and Equations
31514 \begin_inset CommandInset label
31516 name "subsec:Chemical-Symbols-and"
31521 \begin_inset Index idx
31524 \begin_layout Plain Layout
31525 Chemical characters ! Symbols
31531 \begin_inset Index idx
31534 \begin_layout Plain Layout
31541 \begin_inset Index idx
31544 \begin_layout Plain Layout
31553 \begin_layout Standard
31554 An example text from chemistry:
31557 \begin_layout Quote
31559 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31562 -ion reacts with two
31563 \begin_inset Formula $\mathrm{Na^{+}}$
31566 -ions to sodium sulfate
31567 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31571 The chemical equation for this is:
31572 \begin_inset Formula
31574 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31582 \begin_layout Standard
31583 This chemical equation can directly be created as formula.
31584 To avoid that the symbols appear italic, everything is highlighted and
31585 changed by the shortcut
31591 to the upright font style.
31595 \begin_layout Plain Layout
31601 \begin_inset CommandInset ref
31603 reference "subsec:Font-Styles"
31615 \begin_layout Standard
31616 A more convenient way to typeset chemical formulas is to use the command
31624 \begin_inset Index idx
31627 \begin_layout Plain Layout
31635 that is available when the \SpecialChar LaTeX
31641 \begin_inset Index idx
31644 \begin_layout Plain Layout
31657 to a formula a new blue box appears where chemical formulas can be inserted
31658 in an intuitive way.
31659 \begin_inset Separator parbreak
31665 \begin_layout Standard
31667 \begin_inset Tabular
31668 <lyxtabular version="3" rows="10" columns="2">
31669 <features booktabs="true" tabularvalignment="middle">
31670 <column alignment="center" valignment="top" width="0pt">
31671 <column alignment="center" valignment="top">
31673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31676 \begin_layout Plain Layout
31682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31685 \begin_layout Plain Layout
31693 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31696 \begin_layout Plain Layout
31700 \begin_inset space \textvisiblespace{}
31708 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31711 \begin_layout Plain Layout
31712 \begin_inset Formula $\ce{H2CO3}$
31721 <row topspace="1.5mm">
31722 <cell alignment="center" valignment="top" usebox="none">
31725 \begin_layout Plain Layout
31729 \begin_inset space \textvisiblespace{}
31737 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31740 \begin_layout Plain Layout
31741 \begin_inset Formula $\ce{SO4^{2-}}$
31750 <row topspace="1.5mm">
31751 <cell alignment="center" valignment="top" usebox="none">
31754 \begin_layout Plain Layout
31758 \begin_inset space \textvisiblespace{}
31766 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31769 \begin_layout Plain Layout
31770 \begin_inset Formula $\ce{(NH4)2S}$
31779 <row topspace="1.5mm">
31780 <cell alignment="center" valignment="top" usebox="none">
31783 \begin_layout Plain Layout
31787 \begin_inset space \textvisiblespace{}
31795 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31798 \begin_layout Plain Layout
31799 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31808 <row topspace="1.5mm">
31809 <cell alignment="center" valignment="top" usebox="none">
31812 \begin_layout Plain Layout
31816 \begin_inset space \textvisiblespace{}
31822 \begin_inset space \textvisiblespace{}
31828 \begin_inset space \textvisiblespace{}
31836 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31839 \begin_layout Plain Layout
31840 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31849 <row topspace="1.5mm">
31850 <cell alignment="center" valignment="top" usebox="none">
31853 \begin_layout Plain Layout
31857 \begin_inset space \textvisiblespace{}
31861 \begin_inset Formula $\downarrow$
31865 \begin_inset Formula $\to$
31873 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31876 \begin_layout Plain Layout
31877 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31887 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31890 \begin_layout Plain Layout
31894 \begin_inset space \textvisiblespace{}
31900 \begin_inset space \textvisiblespace{}
31906 \begin_inset space \textvisiblespace{}
31914 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31917 \begin_layout Plain Layout
31918 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31931 \begin_layout Plain Layout
31935 \begin_inset space \textvisiblespace{}
31939 \begin_inset space \textvisiblespace{}
31943 \begin_inset space \textvisiblespace{}
31947 \begin_inset space \textvisiblespace{}
31951 \begin_inset space \textvisiblespace{}
31959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31962 \begin_layout Plain Layout
31963 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31972 <row topspace="1.5mm">
31973 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31976 \begin_layout Plain Layout
31980 \begin_inset space \textvisiblespace{}
31984 \begin_inset space \textvisiblespace{}
31988 \begin_inset space \textvisiblespace{}
31992 \begin_inset space \textvisiblespace{}
32000 \begin_inset space \textvisiblespace{}
32008 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
32011 \begin_layout Plain Layout
32012 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
32028 \begin_layout Standard
32029 \begin_inset Note Greyedout
32032 \begin_layout Plain Layout
32038 It is not possible in \SpecialChar LyX
32039 to use the character ^ to get an up-arrow as described
32045 One instead uses a negative thin space followed by the command
32052 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32063 \begin_layout Standard
32070 the command for equation
32071 \begin_inset space ~
32075 \begin_inset CommandInset ref
32077 reference "eq:chem-reaction"
32082 \begin_inset Newline newline
32090 \begin_inset space \textvisiblespace{}
32094 \begin_inset space \textvisiblespace{}
32098 \begin_inset space \textvisiblespace{}
32102 \begin_inset space \textvisiblespace{}
32106 \begin_inset space \textvisiblespace{}
32110 \begin_inset space \textvisiblespace{}
32116 \begin_layout Standard
32117 To create multiline chemical equations first a multiline formula is created
32119 \begin_inset CommandInset ref
32121 reference "sec:Multiline-Formulas"
32126 Afterwards the command
32132 is used in every small blue box of the formula.
32134 \begin_inset CommandInset ref
32136 reference "eq:TEOS-reaction-1"
32141 \begin_inset CommandInset ref
32143 reference "eq:TEOS-reaction-2"
32147 are an example of a multi-stage chemical reaction where every equation
32148 has its own number.
32149 \begin_inset Formula
32151 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32152 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32160 \begin_layout Standard
32171 package provides the command
32178 \begin_inset Index idx
32181 \begin_layout Plain Layout
32189 that has to be used for special cases.
32190 For more information about
32196 and more examples have a look at the documentation of
32201 \begin_inset CommandInset citation
32210 \begin_layout Section
32214 \begin_layout Standard
32216 supports two types of commutative diagrams:
32224 that are explained in the following.
32227 \begin_layout Subsection
32229 \begin_inset Index idx
32232 \begin_layout Plain Layout
32241 \begin_layout Standard
32242 Diagrams of this type visualize relations by vertical and horizontal lines
32244 \begin_inset Formula
32246 \begin{CD}A@>>>B@>>>C\\
32257 \begin_layout Standard
32258 To get them, the command
32263 \begin_inset Index idx
32266 \begin_layout Plain Layout
32276 is inserted to a formula.
32277 A blue box appears with two dashed lines where further commands can be
32282 arg "newline-insert newline"
32285 a new line is created.
32286 Horizontal relations are inserted in odd, vertical in even formula lines.
32289 \begin_layout Standard
32290 To create the relations there are the following commands:
32293 \begin_layout Itemize
32298 creates a left arrow,
32309 \begin_layout Itemize
32314 creates an up arrow,
32322 a vertical equal sign
32325 \begin_layout Itemize
32331 is a placeholder for non-existent relations
32334 \begin_layout Standard
32335 All arrows can be labeled as follows:
32338 \begin_layout Itemize
32339 If text inserted between the first and second < or >, resp., it is placed
32341 When it is inserted between the second and third one, it appears under
32345 \begin_layout Itemize
32346 When text for vertical arrows is inserted between the first and second A
32347 or V, resp., it is placed left beside the arrow.
32348 When it is inserted between the second and third one, it appears right
32350 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32354 \begin_layout Standard
32355 As example a diagram with all possible relations:
32358 \begin_layout Standard
32359 \begin_inset Formula
32361 \begin{CD}A@>j>>B@>>k>C@=F\\
32372 \begin_layout Standard
32373 The command for this is:
32374 \begin_inset Newline newline
32382 \begin_inset space \textvisiblespace{}
32385 A@>j>>B@>>k>C@=F Ctrl+Return
32386 \begin_inset Newline newline
32390 \begin_inset Phantom HPhantom
32393 \begin_layout Plain Layout
32399 \begin_inset space \textvisiblespace{}
32412 \begin_inset Formula $\to$
32418 \begin_inset Newline newline
32422 \begin_inset Phantom HPhantom
32425 \begin_layout Plain Layout
32431 \begin_inset space \textvisiblespace{}
32442 \begin_layout Subsection
32444 \begin_inset Index idx
32447 \begin_layout Plain Layout
32448 Diagrams ! xymatrix
32456 \begin_layout Standard
32457 To be able to use xymatrices, the \SpecialChar LaTeX
32463 A xymatrix is created by inserting the command
32470 Then you are able to add new matrix columns and rows like for normal matrices,
32472 \begin_inset CommandInset ref
32474 reference "sec:Matrices"
32481 \begin_layout Standard
32482 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32484 All possibilities to create commutative diagrams and decorations are explained
32489 that you find in the menu
32491 Help\SpecialChar menuseparator
32493 \begin_inset space ~
32501 \begin_layout Subsection
32507 \begin_inset Index idx
32510 \begin_layout Plain Layout
32519 \begin_layout Standard
32524 -diagrams, the \SpecialChar LaTeX
32534 -diagram is created by inserting the command
32541 Then you are able to add new matrix columns and rows like for normal matrices,
32543 \begin_inset CommandInset ref
32545 reference "sec:Matrices"
32552 \begin_layout Standard
32553 Examples how to create
32557 diagrams in \SpecialChar LyX
32560 Feynman-diagram manual
32562 that you find in the menu
32564 Help\SpecialChar menuseparator
32566 \begin_inset space ~
32574 \begin_layout Standard
32575 \begin_inset Newpage newpage
32581 \begin_layout Section
32582 User-defined Commands
32583 \begin_inset Index idx
32586 \begin_layout Plain Layout
32587 User-defined commands
32595 \begin_layout Standard
32596 \begin_inset Note Greyedout
32599 \begin_layout Plain Layout
32604 The names of user-defined commands and macros may only consist of Latin
32613 \begin_layout Subsection
32617 \begin_inset CommandInset label
32619 name "subsec:The-Command-newcommand"
32624 \begin_inset Index idx
32627 \begin_layout Plain Layout
32628 User-defined commands !
32636 \begin_inset Index idx
32639 \begin_layout Plain Layout
32650 \begin_layout Standard
32651 Many \SpecialChar LaTeX
32652 -commands are too long to be used frequently.
32653 But it is possible to define with the command
32659 new shorter commands.
32662 \begin_layout Standard
32663 The command scheme of
32672 \begin_layout Standard
32677 newcommand{new command name}[number of arguments][optional
32682 \begin_inset Newline newline
32686 \begin_inset Phantom HPhantom
32689 \begin_layout Plain Layout
32699 {command definition}
32702 \begin_layout Standard
32703 \begin_inset Note Greyedout
32706 \begin_layout Plain Layout
32711 Assure that the name of the new command is not already used in your document
32712 or by \SpecialChar LaTeX
32713 -packages that you use.
32714 When you for example define the command
32726 , you get an error message because
32732 is already defined as command for
32733 \begin_inset Quotes eld
32737 \begin_inset Formula $\le$
32741 \begin_inset Quotes erd
32752 \begin_layout Standard
32753 The number of arguments is an integer in the range 0
32754 \begin_inset space \thinspace{}
32758 \begin_inset space \thinspace{}
32761 9 and specifies how many arguments the new command should have.
32762 With the optional value a value for an optional argument can be predefined.
32763 When this is done, the
32771 rgument of the new command is automatically an optional one.
32774 \begin_layout Standard
32775 Here are some examples:
32778 \begin_layout Itemize
32779 To define the command
32791 , the \SpecialChar LaTeX
32793 \begin_inset VSpace medskip
32797 \begin_inset Newline newline
32811 \begin_layout Itemize
32812 To define the command
32824 , the argument (that should be underlined) must be taken into account.
32825 For this the preamble line is:
32826 \begin_inset VSpace medskip
32830 \begin_inset Newline newline
32844 \begin_inset VSpace medskip
32848 \begin_inset Newline newline
32855 acts as argument placeholder, the
32859 behind it denotes that it is the placeholder for the first argument.
32862 \begin_layout Itemize
32870 \begin_inset space \thinspace{}
32874 \begin_inset space \space{}
32884 \begin_inset VSpace medskip
32888 \begin_inset Newline newline
32899 framebox#1#2{$#3$}}
32902 \begin_inset VSpace medskip
32906 \begin_inset Newline newline
32909 The two Dollar signs creates the extra formula needed for
32916 \begin_inset CommandInset ref
32918 reference "subsec:Boxes-with-Frame"
32925 \begin_layout Itemize
32926 To create a new command for
32932 where the color for the box need not be specified, the argument for the
32933 color is defined optional:
32934 \begin_inset VSpace medskip
32938 \begin_inset Newline newline
32949 fcolorbox{#2}{#1}{$#3$}}
32952 \begin_inset VSpace medskip
32956 \begin_inset Newline newline
32959 When the color is not specified when using
32965 , the predefined color
32972 \begin_layout Standard
32973 A test of the new defined commands:
32974 \begin_inset Separator parbreak
32980 \begin_layout Standard
32982 \begin_inset Tabular
32983 <lyxtabular version="3" rows="6" columns="2">
32984 <features booktabs="true" tabularvalignment="middle">
32985 <column alignment="center" valignment="top" width="0pt">
32986 <column alignment="center" valignment="top">
32988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32991 \begin_layout Plain Layout
32997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33000 \begin_layout Plain Layout
33008 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33011 \begin_layout Plain Layout
33015 \begin_inset space \textvisiblespace{}
33023 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33026 \begin_layout Plain Layout
33027 \begin_inset Formula $A\gr B$
33037 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33040 \begin_layout Plain Layout
33048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33051 \begin_layout Plain Layout
33052 \begin_inset Formula $\us{ABcd}$
33061 <row topspace="1mm">
33062 <cell alignment="center" valignment="top" usebox="none">
33065 \begin_layout Plain Layout
33069 \begin_inset Formula $\to$
33075 \begin_inset Formula $\to$
33083 \begin_inset space \textvisiblespace{}
33091 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33094 \begin_layout Plain Layout
33095 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33104 <row topspace="1.5mm">
33105 <cell alignment="center" valignment="top" usebox="none">
33108 \begin_layout Plain Layout
33112 \begin_inset Formula $\to$
33120 \begin_inset space \textvisiblespace{}
33128 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33131 \begin_layout Plain Layout
33132 \begin_inset Formula $\cb{red}{\int A=B}$
33141 <row topspace="1.5mm" bottomspace="1mm">
33142 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33145 \begin_layout Plain Layout
33151 \begin_inset Formula $\to$
33159 \begin_inset space \textvisiblespace{}
33167 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33170 \begin_layout Plain Layout
33171 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33187 \begin_layout Subsection
33189 \begin_inset Index idx
33192 \begin_layout Plain Layout
33193 User-defined commands! Math macros
33199 \begin_inset Index idx
33202 \begin_layout Plain Layout
33211 \begin_layout Standard
33212 User-defined commands are especially convenient for complex expressions.
33213 When you are for example dealing with a document that has quadratic equations,
33214 the same solution type occurs several times.
33215 The general form of a quadratic equation is
33216 \begin_inset Formula
33218 0=\lambda^{2}+p\lambda+q
33223 The general form of the solution is
33224 \begin_inset Formula
33226 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33234 \begin_layout Standard
33235 To define a command for the solution formula where only the three parameters
33237 \begin_inset Formula $\lambda$
33241 \begin_inset Formula $p$
33245 \begin_inset Formula $q$
33248 need to be specified and the index of
33249 \begin_inset Formula $\lambda$
33252 can be given optionally, the \SpecialChar LaTeX
33254 \begin_inset Newline newline
33270 \begin_inset Newline newline
33274 \begin_inset Phantom HPhantom
33277 \begin_layout Plain Layout
33291 frac{#3^{2}}{4}-#4}}
33294 \begin_layout Standard
33295 To create with this the solution formula, the command
33296 \begin_inset Newline newline
33306 \begin_inset Formula $\to$
33312 \begin_inset Formula $\to$
33319 is inserted to a formula
33324 \begin_layout Standard
33325 The definition of the new command is unintuitive because one has to know
33326 the schemes of all used \SpecialChar LaTeX
33328 \begin_inset space \thinspace{}
33332 \begin_inset space \space{}
33335 that a fraction is inserted in \SpecialChar LaTeX
33340 frac{numerator}{denominator}
33343 Furthermore one can easily forget a brace in the definition and cannot
33344 see in \SpecialChar LyX
33345 what the new command is doing.
33346 To avoid these problems \SpecialChar LyX
33347 offers the possibility to use math macros instead
33357 \begin_layout Standard
33358 A math macro is created by using the menu
33360 Insert\SpecialChar menuseparator
33361 Math\SpecialChar menuseparator
33364 or the toolbar button
33367 arg "math-macro newmacroname_newcommand"
33371 The math macro toolbar appears together with the following box where the
33373 \begin_inset Newline newline
33377 \begin_inset space \hspace*{\fill}
33381 \begin_inset Graphics
33382 filename clipart/macrobox.png
33388 \begin_inset space \hspace*{\fill}
33392 \begin_inset Newline newline
33396 \begin_inset FormulaMacro
33397 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33402 newmacroname is the default name of the macro that should be changed to
33403 something sensible.
33404 The wanted formula is inserted in the first blue box.
33405 An argument placeholder is inserted with the command
33412 \begin_inset space \thinspace{}
33416 \begin_inset space \space{}
33425 or by using the macro toolbar button
33428 arg "math-macro-add-param"
33432 Argument placeholders are displayed red.
33434 \begin_inset space ~
33437 arguments are possible.
33438 Optional arguments are created with the toolbar button
33441 arg "math-macro-add-optional-param"
33445 The first non-optional argument can be transformed to an optional one with
33449 arg "math-macro-make-optional"
33453 In the second blue box the appearance of the macro in \SpecialChar LyX
33455 Normally you want to see it as it is defined, so the box is kept empty.
33456 But when you have created a macro that needs lot of space on the screen,
33457 you can insert in the box for example
33458 \begin_inset Newline newline
33488 \begin_inset Newline newline
33493 For the macro only the arguments with the macro name in front of them will
33494 then be displayed in \SpecialChar LyX
33495 , leading to a better overview.
33496 The formula appears in the output as defined in the first box.
33497 \begin_inset Newline newline
33500 The appearance of macros in formulas can furthermore be changed for single
33501 macros by setting the cursor in the macro and using the menu
33503 View\SpecialChar menuseparator
33505 \begin_inset space ~
33509 \begin_inset space ~
33517 \begin_layout Standard
33518 To use a macro, the macro name is inserted as command to a formula, in our
33526 Our macro looks in \SpecialChar LyX
33528 \begin_inset Newline newline
33532 \begin_inset space \hspace*{\fill}
33536 \begin_inset Graphics
33537 filename clipart/macrouse.png
33543 \begin_inset space \hspace*{\fill}
33547 \begin_inset Newline newline
33550 Here is our macro example with the arguments
33551 \begin_inset Formula $x$
33555 \begin_inset Formula $\ln(x)$
33559 \begin_inset Formula $B$
33565 \begin_layout Standard
33566 \begin_inset Formula
33576 \begin_layout Standard
33580 Tools\SpecialChar menuseparator
33581 Preferences\SpecialChar menuseparator
33582 Editing\SpecialChar menuseparator
33585 different styles to edit macros.
33586 To find the style that suits you the most, choose a style and set the cursor
33587 in a macro formula to see the difference.
33590 \begin_layout Standard
33591 A math macro is transformed internally to a
33597 command when exporting the document.
33604 command is not placed in the \SpecialChar LaTeX
33605 -preamble, therefore macros can only be used
33606 in formulas that are in the document below the macro definition box.
33609 \begin_layout Standard
33610 Math macros can also be directly created from a
33617 When writing for example the command
33620 \begin_inset Newline newline
33629 xleftarrow[#2]{#1}}
33630 \begin_inset Newline newline
33635 in \SpecialChar LyX
33636 as normal text, highlighting it completely and using then the shortcut
33641 , the command will be transformed to a math macro.
33642 Using this method you need to be careful that the
33648 command is typed correctly, otherwise you get a faulty macro leading to
33653 \begin_layout Standard
33654 Math macros currently have the problem that further formulas in macro definition
33655 s are handled wrongly.
33656 Therefore the example
33663 \begin_inset CommandInset ref
33665 reference "subsec:The-Command-newcommand"
33669 cannot be created as macro.
33672 \begin_layout Standard
33673 When the cursor is in a macro definition box, you will see the macro toolbar
33674 in \SpecialChar LyX
33678 \begin_layout Standard
33679 \begin_inset VSpace defskip
33685 \begin_layout Standard
33686 \begin_inset Graphics
33687 filename clipart/MacroToolbar.png
33692 \begin_inset Index idx
33695 \begin_layout Plain Layout
33704 \begin_layout Standard
33705 \begin_inset VSpace defskip
33711 \begin_layout Standard
33712 The macro toolbar contains from left to right the following buttons:
33715 \begin_layout Standard
33716 \begin_inset VSpace defskip
33722 \begin_layout Standard
33723 \begin_inset Tabular
33724 <lyxtabular version="3" rows="9" columns="2">
33725 <features islongtable="true" longtabularalignment="center">
33726 <column alignment="left" valignment="top">
33727 <column alignment="left" valignment="top" width="85col%">
33728 <row interlinespace="2.5mm">
33729 <cell alignment="center" valignment="top" usebox="none">
33732 \begin_layout Plain Layout
33735 arg "math-macro-remove-param"
33743 <cell alignment="center" valignment="top" usebox="none">
33746 \begin_layout Plain Layout
33749 Edit\SpecialChar menuseparator
33750 Math\SpecialChar menuseparator
33752 \begin_inset space ~
33755 Definition\SpecialChar menuseparator
33756 Remove Last Argument
33762 <row interlinespace="2.5mm">
33763 <cell alignment="center" valignment="top" usebox="none">
33766 \begin_layout Plain Layout
33769 arg "math-macro-add-param"
33777 <cell alignment="center" valignment="top" usebox="none">
33780 \begin_layout Plain Layout
33783 Edit\SpecialChar menuseparator
33784 Math\SpecialChar menuseparator
33786 \begin_inset space ~
33789 Definition\SpecialChar menuseparator
33796 <row interlinespace="2.5mm">
33797 <cell alignment="center" valignment="top" usebox="none">
33800 \begin_layout Plain Layout
33803 arg "math-macro-make-optional"
33811 <cell alignment="center" valignment="top" usebox="none">
33814 \begin_layout Plain Layout
33817 Edit\SpecialChar menuseparator
33818 Math\SpecialChar menuseparator
33820 \begin_inset space ~
33823 Definition\SpecialChar menuseparator
33824 Transform First Non-Optional to
33825 \begin_inset Newline newline
33829 \begin_inset Phantom HPhantom
33832 \begin_layout Plain Layout
33835 Edit\SpecialChar menuseparator
33836 Math\SpecialChar menuseparator
33838 \begin_inset space ~
33841 Definition\SpecialChar menuseparator
33853 <row interlinespace="2.5mm">
33854 <cell alignment="center" valignment="top" usebox="none">
33857 \begin_layout Plain Layout
33860 arg "math-macro-make-nonoptional"
33868 <cell alignment="center" valignment="top" usebox="none">
33871 \begin_layout Plain Layout
33874 Edit\SpecialChar menuseparator
33875 Math\SpecialChar menuseparator
33877 \begin_inset space ~
33880 Definition\SpecialChar menuseparator
33881 Transform Last Optional to
33882 \begin_inset Newline newline
33886 \begin_inset Phantom HPhantom
33889 \begin_layout Plain Layout
33892 Edit\SpecialChar menuseparator
33893 Math\SpecialChar menuseparator
33895 \begin_inset space ~
33898 Definition\SpecialChar menuseparator
33904 Non-Optional Argument
33910 <row interlinespace="2.5mm">
33911 <cell alignment="center" valignment="top" usebox="none">
33914 \begin_layout Plain Layout
33917 arg "math-macro-remove-optional-param"
33925 <cell alignment="center" valignment="top" usebox="none">
33928 \begin_layout Plain Layout
33931 Edit\SpecialChar menuseparator
33932 Math\SpecialChar menuseparator
33934 \begin_inset space ~
33937 Definition\SpecialChar menuseparator
33938 Remove Optional Argument
33944 <row interlinespace="2.5mm">
33945 <cell alignment="center" valignment="top" usebox="none">
33948 \begin_layout Plain Layout
33951 arg "math-macro-add-optional-param"
33959 <cell alignment="center" valignment="top" usebox="none">
33962 \begin_layout Plain Layout
33965 Edit\SpecialChar menuseparator
33966 Math\SpecialChar menuseparator
33968 \begin_inset space ~
33971 Definition\SpecialChar menuseparator
33972 Insert Optional Argument
33978 <row interlinespace="2.5mm">
33979 <cell alignment="center" valignment="top" usebox="none">
33982 \begin_layout Plain Layout
33985 arg "math-macro-remove-greedy-param"
33993 <cell alignment="center" valignment="top" usebox="none">
33996 \begin_layout Plain Layout
33999 Edit\SpecialChar menuseparator
34000 Math\SpecialChar menuseparator
34002 \begin_inset space ~
34005 Definition\SpecialChar menuseparator
34006 Remove Last Argument
34007 \begin_inset Newline newline
34011 \begin_inset Phantom HPhantom
34014 \begin_layout Plain Layout
34017 Edit\SpecialChar menuseparator
34018 Math\SpecialChar menuseparator
34020 \begin_inset space ~
34023 Definition\SpecialChar menuseparator
34029 Spitting Out To The Right
34035 <row interlinespace="2.5mm">
34036 <cell alignment="center" valignment="top" usebox="none">
34039 \begin_layout Plain Layout
34042 arg "math-macro-append-greedy-param"
34050 <cell alignment="center" valignment="top" usebox="none">
34053 \begin_layout Plain Layout
34056 Edit\SpecialChar menuseparator
34057 Math\SpecialChar menuseparator
34059 \begin_inset space ~
34062 Definition\SpecialChar menuseparator
34064 \begin_inset Newline newline
34068 \begin_inset Phantom HPhantom
34071 \begin_layout Plain Layout
34074 Edit\SpecialChar menuseparator
34075 Math\SpecialChar menuseparator
34077 \begin_inset space ~
34080 Definition\SpecialChar menuseparator
34086 Eating From The Right
34092 <row interlinespace="2.5mm">
34093 <cell alignment="center" valignment="top" usebox="none">
34096 \begin_layout Plain Layout
34099 arg "math-macro-add-greedy-optional-param"
34107 <cell alignment="center" valignment="top" usebox="none">
34110 \begin_layout Plain Layout
34113 Edit\SpecialChar menuseparator
34114 Math\SpecialChar menuseparator
34116 \begin_inset space ~
34119 Definition\SpecialChar menuseparator
34120 Append Optional Argument
34121 \begin_inset Newline newline
34125 \begin_inset Phantom HPhantom
34128 \begin_layout Plain Layout
34131 Edit\SpecialChar menuseparator
34132 Math\SpecialChar menuseparator
34134 \begin_inset space ~
34137 Definition\SpecialChar menuseparator
34143 Eating From The Right
34156 \begin_layout Section
34157 Computer Algebra Systems
34160 \begin_layout Standard
34162 offers the exchange between mathematical expressions written in \SpecialChar LyX
34164 editor and external applications or user defined scripts.
34165 Currently supported applications are
34182 Note that the set of supported mathematical constructs is limited only
34183 to very simple cases.
34186 \begin_layout Subsection
34190 \begin_layout Standard
34191 Write some expression in a formula, go to the
34193 Edit\SpecialChar menuseparator
34194 Math\SpecialChar menuseparator
34195 Use Computer Algebra System
34197 menu and choose the application you have installed on the computer.
34198 After that the result of computation should show on the right side of the
34199 expression together with the
34200 \begin_inset Quotes eld
34204 \begin_inset Quotes erd
34210 \begin_layout Standard
34211 Here are few simple examples (with results from
34215 ) to show what kind of computations can be performed:
34218 \begin_layout Itemize
34219 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34225 \begin_layout Itemize
34226 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34232 \begin_layout Itemize
34233 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34239 \begin_layout Itemize
34240 \begin_inset Formula $\det\left[\begin{array}{ccc}
34244 \end{array}\right]=-56$
34250 \begin_layout Itemize
34251 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34257 \begin_layout Subsection
34261 \begin_layout Standard
34262 Currently there is no keyboard shortcut for calling the algebra applications.
34263 One can easily bind a shortcut to the
34277 \begin_inset space \thinspace{}
34281 \begin_inset space \space{}
34288 key inside the math editor.
34293 one would use this shortcut definition command:
34296 \begin_layout Standard
34299 command-alternatives paragraph-break;math-extern maxima
34302 \begin_layout Section
34304 \begin_inset Index idx
34307 \begin_layout Plain Layout
34316 \begin_layout Subsection
34318 \begin_inset Index idx
34321 \begin_layout Plain Layout
34330 \begin_layout Standard
34331 Negative numbers often look ugly in formulas because the minus sign before
34332 the number is set with the same length as the minus operator sign.
34333 When writing the negative number in normal text, the minus sign appears
34337 \begin_layout Standard
34338 Thus, the problem disappears when converting the minus sign to mathematical
34342 \begin_layout Standard
34343 An example to visualize the problem:
34344 \begin_inset Separator parbreak
34350 \begin_layout Standard
34352 \begin_inset Tabular
34353 <lyxtabular version="3" rows="3" columns="2">
34354 <features booktabs="true" tabularvalignment="middle">
34355 <column alignment="right" valignment="top" width="0pt">
34356 <column alignment="left" valignment="top">
34358 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34361 \begin_layout Plain Layout
34367 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34370 \begin_layout Plain Layout
34378 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34381 \begin_layout Plain Layout
34387 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34390 \begin_layout Plain Layout
34391 \begin_inset Formula $x=-2$
34401 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34404 \begin_layout Plain Layout
34410 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34413 \begin_layout Plain Layout
34414 \begin_inset Formula $x=\textrm{-}2$
34430 \begin_layout Subsection
34431 Comma as decimal Separator
34432 \begin_inset Index idx
34435 \begin_layout Plain Layout
34444 \begin_layout Standard
34445 In \SpecialChar LaTeX
34446 a comma inside a formula is used, according to the English convention,
34447 as number group separator.
34448 So there will be space added behind all commas in formulas.
34451 \begin_layout Standard
34452 To avoid this, the comma is highlighted and changed to mathematical text
34462 \begin_layout Standard
34463 To use all formula commas in the document as decimal separator, the file
34472 \begin_layout Plain Layout
34477 is part of the \SpecialChar LaTeX
34483 \begin_inset Index idx
34486 \begin_layout Plain Layout
34491 \begin_layout Plain Layout
34511 \begin_inset Index idx
34514 \begin_layout Plain Layout
34520 is loaded with the \SpecialChar LaTeX
34524 \begin_layout Standard
34532 \begin_layout Subsection
34534 \begin_inset CommandInset label
34536 name "subsec:Physical-Vectors"
34541 \begin_inset Index idx
34544 \begin_layout Plain Layout
34553 \begin_layout Standard
34554 Predefined vectors are offered by the \SpecialChar LaTeX
34560 \begin_inset Index idx
34563 \begin_layout Plain Layout
34569 that is loaded with the \SpecialChar LaTeX
34573 \begin_layout Standard
34581 \begin_layout Standard
34585 \begin_layout Plain Layout
34595 \begin_inset Note Note
34598 \begin_layout Plain Layout
34599 The following table will only be displayed when the \SpecialChar LaTeX
34612 \begin_layout Standard
34613 The following commands are defined:
34614 \begin_inset Separator parbreak
34620 \begin_layout Standard
34622 \begin_inset Tabular
34623 <lyxtabular version="3" rows="4" columns="2">
34624 <features booktabs="true" tabularvalignment="middle">
34625 <column alignment="center" valignment="top" width="0pt">
34626 <column alignment="center" valignment="top">
34628 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34631 \begin_layout Plain Layout
34637 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34640 \begin_layout Plain Layout
34648 <cell alignment="center" valignment="top" usebox="none">
34651 \begin_layout Plain Layout
34661 <cell alignment="center" valignment="top" usebox="none">
34664 \begin_layout Plain Layout
34665 \begin_inset Formula $\Bra{\psi}$
34675 <cell alignment="center" valignment="top" usebox="none">
34678 \begin_layout Plain Layout
34688 <cell alignment="center" valignment="top" usebox="none">
34691 \begin_layout Plain Layout
34692 \begin_inset Formula $\Ket{\psi}$
34702 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34705 \begin_layout Plain Layout
34717 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34720 \begin_layout Plain Layout
34721 \begin_inset Formula $\Braket{\psi|\phi}$
34737 \begin_layout Standard
34744 assures that all vertical bars are set in the size of the surrounding brackets:
34745 \begin_inset Formula
34747 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34756 \begin_layout Plain Layout
34766 \begin_inset Note Note
34769 \begin_layout Plain Layout
34770 The following will be displayed when the \SpecialChar LaTeX
34783 \begin_layout Standard
34784 You need to install the \SpecialChar LaTeX
34789 to see the rest of this subsection in the output.
34792 \begin_layout Standard
34796 \begin_layout Plain Layout
34808 \begin_layout Standard
34815 can also be achieved using the command
34821 , that is described in
34822 \begin_inset CommandInset ref
34824 reference "subsec:Automatic-Bracket-Size"
34831 \begin_layout Subsection
34832 Self-defined Fractions
34833 \begin_inset CommandInset label
34835 name "subsec:Self-defined-Fractions"
34840 \begin_inset Index idx
34843 \begin_layout Plain Layout
34844 Fractions ! self-defined
34852 \begin_layout Standard
34853 To define custom commands for fractions, the command
34860 \begin_inset Index idx
34863 \begin_layout Plain Layout
34870 \begin_layout Plain Layout
34884 is used in the following scheme:
34887 \begin_layout Standard
34900 bracket}{fraction bar thickness}{style}
34901 \begin_inset Newline newline
34905 \begin_inset Phantom HPhantom
34908 \begin_layout Plain Layout
34918 {numerator}{denominator}
34921 \begin_layout Standard
34922 The style is a number in the range of 0
34923 \begin_inset space \thinspace{}
34927 \begin_inset space \thinspace{}
34931 \begin_inset Separator parbreak
34937 \begin_layout Standard
34939 \begin_inset Tabular
34940 <lyxtabular version="3" rows="5" columns="2">
34941 <features booktabs="true" tabularvalignment="middle">
34942 <column alignment="center" valignment="top" width="0pt">
34943 <column alignment="center" valignment="top">
34945 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34948 \begin_layout Plain Layout
34954 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34957 \begin_layout Plain Layout
34965 <cell alignment="center" valignment="top" usebox="none">
34968 \begin_layout Plain Layout
34974 <cell alignment="center" valignment="top" usebox="none">
34977 \begin_layout Plain Layout
34978 display style formula
34985 <cell alignment="center" valignment="top" usebox="none">
34988 \begin_layout Plain Layout
34994 <cell alignment="center" valignment="top" usebox="none">
34997 \begin_layout Plain Layout
35005 <cell alignment="center" valignment="top" usebox="none">
35008 \begin_layout Plain Layout
35014 <cell alignment="center" valignment="top" usebox="none">
35017 \begin_layout Plain Layout
35025 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35028 \begin_layout Plain Layout
35034 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35037 \begin_layout Plain Layout
35051 \begin_layout Standard
35052 When no style is given, the size is adjusted to the surrounding environment
35053 like for the command
35062 \begin_layout Standard
35063 When no fraction bar thickness is given, the predefined value of 0.4
35064 \begin_inset space \thinspace{}
35070 \begin_layout Standard
35071 \begin_inset VSpace medskip
35074 For example, the commands
35087 \begin_inset CommandInset ref
35089 reference "subsec:Fractions"
35093 are defined with the commands
35096 \begin_layout Standard
35105 genfrac{}{}{}{0}{#1}{#2}}
35108 \begin_layout Standard
35112 \begin_layout Standard
35121 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35124 \begin_layout Standard
35125 \begin_inset VSpace medskip
35128 To define a fraction where the fraction bar thickness can be given as optional
35129 argument, the following line is inserted to the \SpecialChar LaTeX
35133 \begin_layout Standard
35142 genfrac{}{}{#1}{}{#2}{#3}}
35145 \begin_layout Standard
35147 \begin_inset Formula
35149 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35150 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35155 As one can see, the distance of the numerator and the denominator to the
35156 fraction bar is round about three times the bar thickness.
35159 \begin_layout Subsection
35161 \begin_inset Index idx
35164 \begin_layout Plain Layout
35173 \begin_layout Standard
35174 There are four ways to cancel formulas or parts of formulas:
35177 \begin_layout Standard
35181 \begin_layout Plain Layout
35191 \begin_inset Note Note
35194 \begin_layout Plain Layout
35195 The following table will only be displayed when the \SpecialChar LaTeX
35206 \begin_inset Separator parbreak
35212 \begin_layout Standard
35214 \begin_inset Tabular
35215 <lyxtabular version="3" rows="5" columns="2">
35216 <features booktabs="true" tabularvalignment="middle">
35217 <column alignment="center" valignment="top" width="0pt">
35218 <column alignment="center" valignment="top">
35220 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35223 \begin_layout Plain Layout
35229 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35232 \begin_layout Plain Layout
35240 <cell alignment="center" valignment="top" usebox="none">
35243 \begin_layout Plain Layout
35247 \begin_inset space \textvisiblespace{}
35253 \begin_inset space \textvisiblespace{}
35261 <cell alignment="center" valignment="top" usebox="none">
35264 \begin_layout Plain Layout
35265 \begin_inset Formula $\cancel{\int A=B}$
35274 <row topspace="1.5mm">
35275 <cell alignment="center" valignment="top" usebox="none">
35278 \begin_layout Plain Layout
35282 \begin_inset space \textvisiblespace{}
35288 \begin_inset space \textvisiblespace{}
35296 <cell alignment="center" valignment="top" usebox="none">
35299 \begin_layout Plain Layout
35300 \begin_inset Formula $\bcancel{\int A=B}$
35309 <row topspace="1.5mm">
35310 <cell alignment="center" valignment="top" usebox="none">
35313 \begin_layout Plain Layout
35317 \begin_inset space \textvisiblespace{}
35323 \begin_inset space \textvisiblespace{}
35331 <cell alignment="center" valignment="top" usebox="none">
35334 \begin_layout Plain Layout
35335 \begin_inset Formula $\xcancel{\int A=B}$
35345 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35348 \begin_layout Plain Layout
35352 \begin_inset space \textvisiblespace{}
35358 \begin_inset space \textvisiblespace{}
35362 \begin_inset Formula $\to$
35370 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35373 \begin_layout Plain Layout
35374 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35390 \begin_layout Standard
35397 is especially suitable to visualize the reduction of fractions within formulas:
35398 \begin_inset Formula
35400 \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}}}
35408 \begin_layout Standard
35409 To change the size of
35416 \begin_inset Quotes eld
35420 \begin_inset Quotes erd
35423 value one can add the \SpecialChar LaTeX
35427 \begin_layout Standard
35432 PassOptionsToPackage{option}{cancel}
35435 \begin_layout Standard
35444 which leads to the same size as for the canceled value, or
35448 which makes is it a bit smaller than normal.
35451 \begin_layout Standard
35452 To color the cancellation bar one adds this command as \SpecialChar TeX
35456 \begin_layout Standard
35468 \begin_layout Standard
35473 can be replaced by a color of your choice.
35476 \begin_layout Standard
35480 \begin_layout Plain Layout
35496 \begin_layout Standard
35497 \begin_inset Formula
35499 \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}}}
35507 \begin_layout Standard
35511 \begin_layout Plain Layout
35525 \begin_inset Note Note
35528 \begin_layout Plain Layout
35537 \begin_layout Standard
35538 For further customizations, see the documentation of the package
35543 \begin_inset CommandInset citation
35550 \begin_inset Index idx
35553 \begin_layout Plain Layout
35562 \begin_layout Standard
35566 \begin_layout Plain Layout
35576 \begin_inset Note Note
35579 \begin_layout Plain Layout
35580 The following will be displayed when the \SpecialChar LaTeX
35593 \begin_layout Standard
35594 You need to install the \SpecialChar LaTeX
35599 to see the rest of this subsection in the output.
35602 \begin_layout Standard
35606 \begin_layout Plain Layout
35618 \begin_layout Subsection
35619 Formulas in Section Headings
35620 \begin_inset CommandInset label
35622 name "subsec:Formulas-in-Section"
35627 \begin_inset Index idx
35630 \begin_layout Plain Layout
35631 Formula ! in section headings
35639 \begin_layout Standard
35640 When formulas are used in section headings, the following has to be taken
35644 \begin_layout Standard
35645 \begin_inset Note Greyedout
35648 \begin_layout Plain Layout
35654 \begin_inset Index idx
35657 \begin_layout Plain Layout
35658 Packages ! hyperref
35663 support is enabled in the document settings dialog under
35666 \begin_inset space ~
35671 , PDF-bookmarks are created for every section heading in the table of contents.
35672 If a section heading contains formulas, they are incorrectly displayed
35673 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35682 \begin_layout Standard
35683 Both problems can be solved by inserting at the end of the section heading
35684 a short title with the menu
35686 Insert\SpecialChar menuseparator
35688 \begin_inset space ~
35694 Short titles are used as alternative for multiline section headings to
35695 keep the table of contents clearly arranged.
35696 Only the short title appears in the table of contents and therefore also
35697 in the PDF-bookmark.
35700 \begin_layout Standard
35701 When formulas should be used in the table of contents but
35705 is used, one can use the following command in \SpecialChar TeX
35709 \begin_layout Standard
35714 texorpdfstring{part}{alternative}
35715 \begin_inset Index idx
35718 \begin_layout Plain Layout
35729 \begin_layout Standard
35730 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35731 This can be characters, formulas, footnotes, but also cross-references.
35732 The alternative is used instead of the part for the bookmark.
35735 \begin_layout Standard
35736 Here are two example headings:
35737 \begin_inset VSpace -3mm
35744 \begin_layout Plain Layout
35756 \begin_layout Subsubsection
35757 Heading without formula in table of contents
35758 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35762 \begin_inset Argument 1
35765 \begin_layout Plain Layout
35766 Heading without formula in table of contents
35774 \begin_layout Subsubsection
35775 Heading with formula in table of contents
35779 \begin_layout Plain Layout
35789 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35796 \begin_layout Plain Layout
35806 \begin_layout Standard
35810 \begin_layout Plain Layout
35819 In the first heading a short title was used, in the second one
35828 \begin_layout Standard
35829 To get the same formatting as for the other headings, the complete heading
35838 \begin_layout Plain Layout
35840 \begin_inset CommandInset ref
35842 reference "subsec:Bold-Formulas"
35854 \begin_layout Subsection
35855 Formulas in multi-column Text
35856 \begin_inset Index idx
35859 \begin_layout Plain Layout
35860 Formula ! in multi-column text
35868 \begin_layout Standard
35869 Formulas in multi-column text are often too wide to fit into a column and
35870 thus need to be set over the whole page width.
35871 This is done by using the \SpecialChar LaTeX
35880 \begin_layout Plain Layout
35885 is part of every \SpecialChar LaTeX
35886 standard installation.
35892 \begin_inset Index idx
35895 \begin_layout Plain Layout
35896 Packages ! multicol
35901 , that is loaded with the \SpecialChar LaTeX
35905 \begin_layout Standard
35910 usepackage{multicol}
35913 \begin_layout Standard
35914 \begin_inset Note Greyedout
35917 \begin_layout Plain Layout
35918 Note that in this case the setting
35921 \begin_inset space ~
35928 Document\SpecialChar menuseparator
35934 \begin_inset space ~
35954 \begin_layout Standard
35955 Before the multi-column text the command
35958 \begin_layout Standard
35963 begin{multicols}{column number}
35966 \begin_layout Standard
35967 is written in \SpecialChar TeX
35969 The column number is a number in the range of 2
35970 \begin_inset space \thinspace{}
35974 \begin_inset space \thinspace{}
35978 Before the formula the multi-column text is ended by inserting the command
35981 \begin_layout Standard
35989 \begin_layout Standard
35990 in \SpecialChar TeX
35994 \begin_layout Standard
35995 Due to the command some space is automatically added before the formula.
35997 \begin_inset space \thinspace{}
36000 mm vertical space is inserted before the formula.
36001 When the formula style
36007 \begin_layout Plain Layout
36009 \begin_inset CommandInset ref
36011 reference "sec:Formula-Styles"
36023 \begin_inset space \thinspace{}
36026 mm space is inserted instead.
36029 \begin_layout Standard
36030 As example a multi-column text with a displayed formula:
36033 \begin_layout Standard
36039 \begin_layout Plain Layout
36043 begin{multicols}{2}
36048 Das Spektrum wird fouriertransformiert.
36049 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36050 , Lösungsmittel) zu trennen.
36051 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36052 nun das Aussehen des Ausgangssignals.
36053 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36054 über alle Phasen integrieren muss.
36056 \begin_inset Formula $S$
36059 unser normiertes Ausgangssignal und
36060 \begin_inset Formula $P$
36063 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36067 \begin_layout Plain Layout
36077 \begin_inset VSpace -6mm
36081 \begin_inset Formula
36083 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36092 \begin_layout Plain Layout
36096 begin{multicols}{2}
36102 \begin_inset Formula $S_{0}$
36105 das Signal ohne Gradient ist und die Normierungsbedingung
36106 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36110 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36112 \begin_inset Formula $\nicefrac{\pi}{2}$
36116 \begin_inset space \thinspace{}
36119 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36120 das Signal zusätzlich abschwächt.
36121 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36123 \begin_inset Formula $T_{2}$
36129 \begin_layout Standard
36135 \begin_layout Plain Layout
36147 \begin_layout Subsection
36148 Formulas with Description of Variables
36149 \begin_inset Index idx
36152 \begin_layout Plain Layout
36153 Formula ! with description of variables
36161 \begin_layout Standard
36162 To describe variables within a formula, like in formula
36163 \begin_inset CommandInset ref
36165 reference "eq:within"
36174 \begin_inset Formula $n$
36178 \begin_inset space ~
36181 matrix is used with left aligned columns for the
36182 \begin_inset Formula $n$
36189 \begin_layout Plain Layout
36191 \begin_inset CommandInset ref
36193 reference "sec:Matrices"
36202 To set the description in a smaller size, before the matrix e.
36203 \begin_inset space \thinspace{}
36207 \begin_inset space \space{}
36220 \begin_layout Plain Layout
36222 \begin_inset CommandInset ref
36224 reference "subsec:Font-Sizes"
36236 \begin_layout Standard
36237 When the formula style
36243 \begin_layout Plain Layout
36245 \begin_inset CommandInset ref
36247 reference "sec:Formula-Styles"
36268 \begin_layout Plain Layout
36275 only works in formulas with the style
36280 \begin_inset CommandInset ref
36282 reference "subsec:Variable-Space"
36291 is inserted before and after the matrix to have the same separation of
36292 the matrix from the equation and the side margin.
36295 \begin_layout Standard
36296 When the formula style
36300 is used, the method described in
36301 \begin_inset CommandInset ref
36303 reference "subsec:Flalign-Environment"
36307 is used to indent formulas.
36309 \begin_inset CommandInset ref
36311 reference "eq:within"
36315 consists of five columns where in the first two columns contain the equation,
36316 the third the matrix and the last one an empty \SpecialChar TeX
36318 \begin_inset Formula
36320 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36321 \rho & \textrm{density}\\
36322 V & \textrm{volume}\\
36323 g & \textrm{gravitational acceleration}
36324 \end{array} & & {}\label{eq:within}
36332 \begin_layout Subsection
36333 Upright small Greek Letters
36334 \begin_inset CommandInset label
36336 name "subsec:Upright-small-Greek"
36341 \begin_inset Index idx
36344 \begin_layout Plain Layout
36345 Greek letters ! upright
36353 \begin_layout Standard
36354 Most of the math fonts only provide italic small Greek letters.
36355 But for symbols of elementary particles like pions and neutrinos, upright
36356 Greek letters are needed.
36365 \begin_layout Plain Layout
36370 is part of the \SpecialChar LaTeX
36376 \begin_inset Index idx
36379 \begin_layout Plain Layout
36384 \begin_layout Plain Layout
36404 \begin_inset Index idx
36407 \begin_layout Plain Layout
36413 that is loaded with the \SpecialChar LaTeX
36417 \begin_layout Standard
36422 usepackage{upgreek}
36425 \begin_layout Standard
36431 \begin_layout Plain Layout
36441 \begin_inset Note Note
36444 \begin_layout Plain Layout
36445 The following table will only be displayed when the \SpecialChar LaTeX
36455 They are created when the command for a small Greek letter is started with
36461 For example the command
36468 \begin_inset Formula $\uptau$
36474 \begin_layout Standard
36475 With these commands reactions of elementary particles can be typeset:
36476 \begin_inset Formula
36478 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36486 \begin_layout Standard
36487 The upright letters are more bold and wider than the italic ones.
36488 They should therefore not be used for units like
36489 \begin_inset Quotes eld
36493 \begin_inset Quotes erd
36499 \begin_layout Standard
36503 \begin_layout Plain Layout
36513 \begin_inset Note Note
36516 \begin_layout Plain Layout
36517 The following will be displayed when the \SpecialChar LaTeX
36530 \begin_layout Standard
36531 You need to install the \SpecialChar LaTeX
36536 to see the rest of this subsection in the output.
36539 \begin_layout Standard
36543 \begin_layout Plain Layout
36555 \begin_layout Subsection
36556 Text Characters in Formulas
36557 \begin_inset Index idx
36560 \begin_layout Plain Layout
36569 \begin_layout Standard
36570 In some cases you might want to insert text characters directly into formulas.
36571 When for example the centered dot · is often used in formulas like
36572 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36575 , one would have to insert the command
36585 \begin_layout Plain Layout
36587 \begin_inset CommandInset ref
36589 reference "subsec:Binary-Operators"
36598 all the time, because this character is defined in all encodings as text
36600 But the encoding can be changed by this \SpecialChar LaTeX
36604 \begin_layout Standard
36609 Declare Inputtext{183}{
36619 f\SpecialChar ligaturebreak
36623 \begin_layout Standard
36624 The character encoding (menu
36626 Document\SpecialChar menuseparator
36627 Settings\SpecialChar menuseparator
36630 ) specifies what character appears when a keyboard key is pressed.
36631 When the key for the character '·' is pressed, internally the command
36638 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36640 With the changed encoding the right command is chosen automatically, depending
36641 on if the character was inserted into a formula or not.
36644 \begin_layout Standard
36645 The encoding of several characters is saved in definition files.
36646 For example the encoding
36650 is defined in the file
36654 which is in the installation folder of \SpecialChar LaTeX
36656 Encodings should only be changed via the \SpecialChar LaTeX
36657 -preamble and not in the definition
36659 Otherwise documents could not be edited by other \SpecialChar LyX
36660 users working on other
36664 \begin_layout Standard
36665 \begin_inset VSpace medskip
36668 Besides the centered dot, in this document the degree sign ° is defined
36669 with the following \SpecialChar LaTeX
36670 -preamble line so that it can be directly inserted into
36674 \begin_layout Standard
36679 DeclareInputtext{176}{
36689 f\SpecialChar ligaturebreak
36693 \begin_layout Subsection
36695 -comments in formulas
36696 \begin_inset Index idx
36699 \begin_layout Plain Layout
36709 \begin_layout Standard
36710 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36712 code of your file with the menu
36714 Insert\SpecialChar menuseparator
36715 Note\SpecialChar menuseparator
36719 This is not possible in a formula but you can insert \SpecialChar LaTeX
36724 \begin_layout Standard
36732 \begin_layout Standard
36733 This creates a box in which you can write your comment.
36734 Due to a bug in \SpecialChar LyX
36739 \begin_layout Plain Layout
36740 \begin_inset CommandInset href
36742 name "LyX-bug #9002"
36743 target "http://www.lyx.org/trac/ticket/9002"
36752 you cannot write normal text inside the comment, even when you use mathematical
36753 text, you will see its \SpecialChar LaTeX
36754 -commands in the \SpecialChar LaTeX
36756 \begin_inset Newline newline
36759 This a formula with a \SpecialChar LaTeX
36761 \begin_inset Formula
36763 A=B%\text{This is the comment}
36771 \begin_layout Standard
36772 \begin_inset Newpage newpage
36778 \begin_layout Section
36781 \begin_inset Index idx
36784 \begin_layout Plain Layout
36793 \begin_layout Standard
36794 This section is a summary of the most important typographic rules, listed
36799 \begin_layout Plain Layout
36800 This collection was partly taken from the German semi-official dictionary
36802 \begin_inset Quotes eld
36806 \begin_inset Quotes erd
36810 \begin_inset CommandInset citation
36816 that lists some of the ISO rules.
36817 More rules are listed in
36818 \begin_inset CommandInset citation
36832 \begin_layout Itemize
36841 \begin_layout Plain Layout
36842 done with font styles, see
36843 \begin_inset CommandInset ref
36845 reference "subsec:Font-Styles"
36854 , no matter if they appear in italic text: 30
36855 \begin_inset space \thinspace{}
36859 \begin_inset Newline newline
36862 Between the value and the unit is the smallest space, see
36863 \begin_inset CommandInset ref
36865 reference "subsec:Predefined-Space"
36870 \begin_inset Newline newline
36873 This convention is automatically fulfilled when the command
36880 When it is entered to a formula, two boxes appear.
36881 In the first one the value is inserted, in the second one the unit, and
36883 \begin_inset Formula $\unit[30]{km/h}$
36887 \begin_inset space \thinspace{}
36897 is not a real \SpecialChar LaTeX
36898 command but the command
36904 , therefore you cannot use it in \SpecialChar TeX
36908 \begin_layout Itemize
36909 Percent and perthousand signs are set like physical units:
36910 \begin_inset Newline newline
36914 \begin_inset space \thinspace{}
36920 \begin_layout Itemize
36921 The degree sign follows directly on the value: 15°, but not when it is used
36923 \begin_inset space \thinspace{}
36929 \begin_layout Itemize
36930 In numbers with more than four digits the smallest space is inserted before
36931 every third digit to group them:
36941 \begin_inset space \thinspace{}
36945 \begin_inset space \thinspace{}
36951 \begin_layout Itemize
36952 For dimensions like 120×90×40
36953 \begin_inset space \thinspace{}
36956 cm the multiplication sign
36957 \begin_inset Quotes eld
36961 \begin_inset Quotes erd
36965 It is available either via the command
36973 Insert\SpecialChar menuseparator
36974 Special Character\SpecialChar menuseparator
36980 \begin_layout Itemize
36981 Functions with names consisting of several letters are set upright to avoid
36983 \begin_inset CommandInset ref
36985 reference "subsec:Predefined-Functions"
36992 \begin_layout Itemize
36993 Indices consisting of several letters, are set upright:
36994 \begin_inset Formula $E_{\mathrm{kin}}$
36998 \begin_inset Newline newline
37001 Components of matrices are set italic:
37002 \begin_inset Formula $\hat{H}_{kl}$
37008 \begin_layout Itemize
37009 The differentiation/integration operator 'd', the Euler's number 'e' and
37010 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37014 \begin_layout Itemize
37015 The character that denotes a
37019 transformation is inserted either by the command
37024 \begin_inset space \textvisiblespace{}
37031 Insert\SpecialChar menuseparator
37032 Special Character\SpecialChar menuseparator
37033 Symbols\SpecialChar menuseparator
37035 \begin_inset space ~
37041 \begin_inset Formula $\mathscr{F}$
37047 \begin_layout Standard
37048 \begin_inset Newpage newpage
37054 \begin_layout Section
37056 \begin_inset Index idx
37059 \begin_layout Plain Layout
37068 \begin_layout Standard
37069 Some characters and symbols can be created with several commands.
37070 Here is a list of the synonym commands:
37073 \begin_layout Standard
37074 \begin_inset VSpace bigskip
37078 \begin_inset space \hfill{}
37082 \begin_inset Tabular
37083 <lyxtabular version="3" rows="12" columns="2">
37084 <features booktabs="true" tabularvalignment="middle">
37085 <column alignment="center" valignment="top" width="0pt">
37086 <column alignment="center" valignment="top" width="0pt">
37088 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37091 \begin_layout Plain Layout
37097 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37100 \begin_layout Plain Layout
37108 <cell alignment="center" valignment="top" usebox="none">
37111 \begin_layout Plain Layout
37119 <cell alignment="center" valignment="top" usebox="none">
37122 \begin_layout Plain Layout
37130 <cell alignment="center" valignment="top" usebox="none">
37133 \begin_layout Plain Layout
37141 <cell alignment="center" valignment="top" usebox="none">
37144 \begin_layout Plain Layout
37154 <cell alignment="center" valignment="top" usebox="none">
37157 \begin_layout Plain Layout
37165 <cell alignment="center" valignment="top" usebox="none">
37168 \begin_layout Plain Layout
37178 <cell alignment="center" valignment="top" usebox="none">
37181 \begin_layout Plain Layout
37189 <cell alignment="center" valignment="top" usebox="none">
37192 \begin_layout Plain Layout
37200 <cell alignment="center" valignment="top" usebox="none">
37203 \begin_layout Plain Layout
37211 <cell alignment="center" valignment="top" usebox="none">
37214 \begin_layout Plain Layout
37222 <cell alignment="center" valignment="top" usebox="none">
37225 \begin_layout Plain Layout
37233 <cell alignment="center" valignment="top" usebox="none">
37236 \begin_layout Plain Layout
37246 <cell alignment="center" valignment="top" usebox="none">
37249 \begin_layout Plain Layout
37257 <cell alignment="center" valignment="top" usebox="none">
37260 \begin_layout Plain Layout
37270 <cell alignment="center" valignment="top" usebox="none">
37273 \begin_layout Plain Layout
37281 <cell alignment="center" valignment="top" usebox="none">
37284 \begin_layout Plain Layout
37294 <cell alignment="center" valignment="top" usebox="none">
37297 \begin_layout Plain Layout
37305 <cell alignment="center" valignment="top" usebox="none">
37308 \begin_layout Plain Layout
37318 <cell alignment="center" valignment="top" usebox="none">
37321 \begin_layout Plain Layout
37329 <cell alignment="center" valignment="top" usebox="none">
37332 \begin_layout Plain Layout
37340 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37343 \begin_layout Plain Layout
37351 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37354 \begin_layout Plain Layout
37366 \begin_inset space \hfill{}
37370 \begin_inset Tabular
37371 <lyxtabular version="3" rows="12" columns="2">
37372 <features booktabs="true" tabularvalignment="middle">
37373 <column alignment="center" valignment="top" width="0pt">
37374 <column alignment="center" valignment="top" width="0pt">
37376 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37379 \begin_layout Plain Layout
37385 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37388 \begin_layout Plain Layout
37396 <cell alignment="center" valignment="top" usebox="none">
37399 \begin_layout Plain Layout
37407 <cell alignment="center" valignment="top" usebox="none">
37410 \begin_layout Plain Layout
37422 <cell alignment="center" valignment="top" usebox="none">
37425 \begin_layout Plain Layout
37433 <cell alignment="center" valignment="top" usebox="none">
37436 \begin_layout Plain Layout
37446 <cell alignment="center" valignment="top" usebox="none">
37449 \begin_layout Plain Layout
37457 <cell alignment="center" valignment="top" usebox="none">
37460 \begin_layout Plain Layout
37470 <cell alignment="center" valignment="top" usebox="none">
37473 \begin_layout Plain Layout
37481 <cell alignment="center" valignment="top" usebox="none">
37484 \begin_layout Plain Layout
37492 <cell alignment="center" valignment="top" usebox="none">
37495 \begin_layout Plain Layout
37503 <cell alignment="center" valignment="top" usebox="none">
37506 \begin_layout Plain Layout
37514 <cell alignment="center" valignment="top" usebox="none">
37517 \begin_layout Plain Layout
37525 <cell alignment="center" valignment="top" usebox="none">
37528 \begin_layout Plain Layout
37538 <cell alignment="center" valignment="top" usebox="none">
37541 \begin_layout Plain Layout
37549 <cell alignment="center" valignment="top" usebox="none">
37552 \begin_layout Plain Layout
37562 <cell alignment="center" valignment="top" usebox="none">
37565 \begin_layout Plain Layout
37573 <cell alignment="center" valignment="top" usebox="none">
37576 \begin_layout Plain Layout
37586 <cell alignment="center" valignment="top" usebox="none">
37589 \begin_layout Plain Layout
37597 <cell alignment="center" valignment="top" usebox="none">
37600 \begin_layout Plain Layout
37610 <cell alignment="center" valignment="top" usebox="none">
37613 \begin_layout Plain Layout
37621 <cell alignment="center" valignment="top" usebox="none">
37624 \begin_layout Plain Layout
37634 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37637 \begin_layout Plain Layout
37645 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37648 \begin_layout Plain Layout
37662 \begin_inset space \hfill{}
37668 \begin_layout Standard
37669 \begin_inset Newpage newpage
37675 \begin_layout Bibliography
37676 \begin_inset CommandInset bibitem
37677 LatexCommand bibitem
37689 The \SpecialChar LaTeX
37693 Addison Wesley, 2004
37696 \begin_layout Bibliography
37697 \begin_inset CommandInset bibitem
37698 LatexCommand bibitem
37704 \begin_inset CommandInset href
37707 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37711 of \SpecialChar LaTeX
37715 \begin_layout Bibliography
37716 \begin_inset CommandInset bibitem
37717 LatexCommand bibitem
37723 \begin_inset CommandInset href
37726 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37734 \begin_layout Plain Layout
37743 -\SpecialChar LaTeX
37747 \begin_layout Bibliography
37748 \begin_inset CommandInset bibitem
37749 LatexCommand bibitem
37755 \begin_inset CommandInset href
37758 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37762 of all symbols available with \SpecialChar LaTeX
37766 \begin_layout Bibliography
37767 \begin_inset CommandInset bibitem
37768 LatexCommand bibitem
37774 \begin_inset CommandInset href
37776 name "Documentation"
37777 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37781 of the \SpecialChar LaTeX
37787 \begin_inset Index idx
37790 \begin_layout Plain Layout
37799 \begin_layout Bibliography
37800 \begin_inset CommandInset bibitem
37801 LatexCommand bibitem
37807 \begin_inset CommandInset href
37809 name "Documentation"
37810 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37814 of the \SpecialChar LaTeX
37820 \begin_inset Index idx
37823 \begin_layout Plain Layout
37824 Packages ! hyperref
37832 \begin_layout Bibliography
37833 \begin_inset CommandInset bibitem
37834 LatexCommand bibitem
37840 \begin_inset CommandInset href
37842 name "Documentation"
37843 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37847 of the \SpecialChar LaTeX
37853 \begin_inset Index idx
37856 \begin_layout Plain Layout
37865 \begin_layout Bibliography
37866 \begin_inset CommandInset bibitem
37867 LatexCommand bibitem
37878 Auflage, Duden 2001
37881 \begin_layout Bibliography
37882 \begin_inset CommandInset bibitem
37883 LatexCommand bibitem
37889 \begin_inset CommandInset href
37892 target "http://physics.nist.gov/Document/checklist.pdf"
37896 for reviewing manuscripts
37899 \begin_layout Standard
37900 \begin_inset CommandInset index_print
37901 LatexCommand printindex